one angle of an isosceles triangle has a measure of 150. if the area of the triangle is 9, what is the perimeter of the triangle
Answers
Perimeter would be approximately 23.57 ft
Consider triangle ABC is an isosceles triangle,
In which AB = AC,
And, m∠A = 150°,
∵ AB = AC ⇒ m∠B = m∠C,
Now sum of all interior angles of a triangle is 180°,
i.e. m∠A + m∠B + m∠C = 180°,
150°+ m∠B + m∠B= 180°,
2m∠B + 150° = 180°
2m∠B = 30°
⇒ m∠B = 15°
Let D ∈ BC such that AD ⊥ BC,
∵ Altitude of an isosceles triangle is its median,
i.e, BD = DC or BD = (1/2) BC
In triangle ADB,
⇒ Tan 15 = AD/BD
⇒ Tan 15 = 2AD/BC
⇒ AD = (BC tan15)/2 ......(i)
Now, area of triangle ABC = (1/2)xBCxAD
If area = 9 square ft,
From equation (1),
(1/2)x(BC tan15)/2 x BD = 9
⇒ BC² = 36/tan15 = 134.35
⇒ BC = 11.59 ft
From equation (1),
AD = 1.55
Using Pythagoras theorem,
⇒ AB = √(AD² + BD²)
⇒ AB = 5.99 ft
Hence, perimeter of the triangle ABC= AB + BC + CA
= 5.99 + 11.59 + 5.99
= 23.57 ft
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Related Questions
a psychology instructor gave one multiple choice question that has five possible choices (a, b, c, d, e). among the choice, there is one correct answer. the instructor thinks that the students will answer the question randomly by guessing since the question is not related to the subject they learn. moreover, the instructor assumes that the students will randomly mark answers a and e with 35% chance each while they will mark answers b, c, and d with 10% chance each. based on a class size of 200, the results were as follows. possible choice a b c d e number of students marked 60 35 20 25 60 suppose the instructor wants to perform a chi-square test to check whether the proportions are equal at the 10% significance level. what is the value of chi-square test statistic?
Answers
The value of the chi-square test statistic is 46.57.
The chi-square test statistic is calculated using the formula; χ²=∑(O-E)²/Ewhere O is the observed frequency and E is the expected frequency. The expected frequency is obtained by multiplying the probability of each choice by the sample size, which is 200. Therefore, we have:
P(a) = 0.35 + 0.35 = 0.7
P(b) = P(c) = P(d) = 0.1 x 3 = 0.3
P(e) = 0.35 + 0.35 = 0.7
E(a) = 0.7 x 200 = 140
E(b) = E(c) = E(d) = 0.3 x 200 = 60
E(e) = 0.7 x 200 = 140
Now, we can calculate the chi-square test statistic as follows;
χ²=∑(O-E)²/E= [(60 - 140)²/140] + [(35 - 60)²/60] + [(20 - 60)²/60] + [(25 - 60)²/60] + [(60 - 140)²/140]= 46.57 (to 2 decimal places)
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The ratio of the volumes of two spheres is 1:64. what would be the ratio of the surface areas of these spheres if the radius of the larger sphere is multiplied by 2?
Answers
The ratio of surface area of spheres on increase in radius of larger sphere will be 1:64.
The surface area of sphere is directly proportional to square of radius and volume of sphere is directly proportional to cube of radius. Let us assume the r represents radius of smaller sphere and R represents radius of larger sphere.
Smaller volume/larger volume = r³:R³
r:R =
[tex] \sqrt[3]{ \frac{1}{64} } [/tex]
r:R = 1:4
So, the ratio of surface area will be: r²:(2R)²
Ratio of surface area = r²:4R²
Ratio of surface area = 1:64
Hence, the ratio of surface area is 1:64.
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In a Pew Research Center Poll, 1040 of 2260 respondents said they would prefer to live somewhere other than where they currently live. For example, many who lived in cities would rather live in the country. Which formulas should be used if the researcher wishes to make confidence intervals and do hypothesis testing?
Answers
The desired significance level (usually 0.05), the researcher can determine whether to reject or fail to reject the null hypothesis.
What is the sample proportion of respondents who prefer to live somewhere other than where they currently live?
The sample proportion of respondents who prefer to live somewhere else can be calculated by dividing the number of respondents who indicated a preference for a different location by the total number of respondents.
To make confidence intervals and perform hypothesis testing in this scenario, the researcher can use formulas based on proportions. Since the question asks respondents about their preference (either yes or no), it involves a binomial distribution.
1.Confidence Interval Formula (Proportions): To construct a confidence interval for the proportion of people who prefer to live somewhere other than their current location, the researcher can use the following formula:
Confidence Interval=p±Z×[tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
where:
p is the sample proportion (1040/2260 in this case).Z is the Z-score corresponding to the desired confidence level (e.g., 95% confidence level would use a Z-score of 1.96 for a large sample).n is the sample size (2260 in this case).2.Hypothesis Testing Formula (Proportions): To perform a hypothesis test to determine if the proportion of people who prefer to live elsewhere is significantly different from a particular value (null hypothesis), the researcher can use the following formula:
[tex]Z=\frac{p-p_{0} }{\sqrt{\frac{p_{0}(p_{0} -1)}{n} } }[/tex]
where:
p is the sample proportion (1040/2260 in this case).[tex]p_{0}[/tex] is the hypothesized proportion under the null hypothesis.n is the sample size (2260 in this case).Z is the Z-score, which indicates how many standard deviations the observed proportion is from the hypothesized proportion.By comparing the calculated Z-value with the critical value(s) for the desired significance level (usually 0.05), the researcher can determine whether to reject or fail to reject the null hypothesis.
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(1 point) a true-false test contains 24 questions. in how many different ways can the 24-question test be answered? (give an exact answer.) your answer is :
Answers
2 possible answers for every out of 24 questions, therefore there are [tex]2^{24}=16777216[/tex] ways to answer the test.
By the age of 2, a child will typically have a vocabulary of _____ words; by the age of 6, a child will typically have a vocabulary of _____ words.
Answers
By the age of 2, a child will typically have a vocabulary of around 200-300 words, while by the age of 6, a child will typically have a vocabulary of approximately 8,000-14,000 words.
It's important to note that these figures are general estimates and can vary from child to child based on various factors such as exposure to language, individual development, and cultural background.
During the first two years of life, children rapidly acquire language skills. They start with simple words like "mama" and "dada" and gradually expand their vocabulary to include nouns, verbs, adjectives, and other parts of speech. By the age of 2, most children can understand and produce a range of words, allowing them to communicate basic needs and express simple thoughts.
As children grow older, their vocabulary expands significantly. By the age of 6, they have been exposed to a broader range of words through interactions, reading, and education. They acquire new vocabulary through conversations, books, and educational activities. At this stage, children can understand and use a wide variety of words, allowing them to express themselves more fluently and engage in more complex conversations.
It's important to remember that these are approximate figures, and individual development can vary. Providing a supportive language-rich environment and engaging in activities that promote language development can positively impact a child's vocabulary growth.
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Multiple Select Question Select all that apply Ancient glaciation events are indicated by the presence of ______. Multiple select question. ridges of moraine, eskers, and drumlins dropstones deltas V-shaped valleys tillite erratics
Answers
Ancient glaciation events are indicated by the presence of ridges of moraine, eskers, and drumlins.
Ancient glaciation events leave behind distinct landforms and sedimentary features that can be used to identify their occurrence. Some of these features include ridges of moraine, eskers, and drumlins.
Ridges of moraine: Moraines are accumulations of glacial debris, including rocks, sediments, and soil, that are deposited along the edges or surfaces of glaciers. Ridges of moraine can indicate the presence of ancient glaciers and their movement.
Eskers: Eskers are long, winding ridges of gravel and sediment that form underneath or within glaciers. They are created by the deposition of sediments by meltwater streams flowing through or beneath the ice. The presence of eskers suggests the past existence of glaciers.
Drumlins: Drumlins are elongated hills or mounds of glacial till that have a streamlined shape, with a steep side facing the direction of the glacial movement. They are formed by the deposition of sediments beneath the ice and can indicate past glaciation events.
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(1 point) A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possibe Norman window with a perimeter of 30 feet
Answers
The maximum area of the Norman window is given by the area of the rectangle, which is [tex]x * x = x^2[/tex], approximately 85.18 square feet.
A Norman window consists of a semicircle placed on top of a rectangle, where the diameter of the semicircle is equal to the width of the rectangle. Let's assume the width of the rectangle is 'x' feet. This means the height of the rectangle is also 'x' feet, and the radius of the semicircle is 'x/2' feet.
To calculate the perimeter of the window, we add the perimeter of the rectangle and half the circumference of the semicircle. The perimeter of the rectangle is 2(x + x/2) = 3x, and half the circumference of the semicircle is π(x/2)/2 = πx/4. Adding these two values, we get the equation:
3x + πx/4 = 30
To find the maximum area, we need to maximize the width 'x'. Solving the above equation, we find x ≈ 9.23 feet.
Therefore, the maximum area of the Norman window is given by the area of the rectangle, which is [tex]x * x = x^2[/tex], approximately 85.18 square feet.
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Wentworth's Five and Dime Store has a cost of equity of 10.6 percent. The company has an aftertax cost of debt of 4.2 percent, and the tax rate is 21 percent. If the company's debt-equity ratio is .66, what is the weighted average cost of capital
Answers
The weighted average cost of capital for Wentworth's Five and Dime Store is 6.376%.
The WACC is the weighted average of the cost of equity and the aftertax cost of debt, taking into account the proportion of debt and equity in the company's capital structure. To calculate the WACC, we first need to determine the weights of debt and equity. The debt-equity ratio of 0.66 indicates that the company has 66% debt and 34% equity. Using these weights, we can calculate the WACC as follows:
WACC = (Weight of Equity * Cost of Equity) + (Weight of Debt * Aftertax Cost of Debt)
Given that the cost of equity is 10.6% and the aftertax cost of debt is 4.2%, and using the weights of 0.34 for equity and 0.66 for debt, the calculation would be
WACC = (0.34 * 10.6%) + (0.66 * 4.2%)
WACC = 3.604% + 2.772%
WACC = 6.376%
Therefore, the weighted average cost of capital for Wentworth's Five and Dime Store is 6.376%. The WACC represents the overall required rate of return for the company's investors, taking into account the cost of equity and debt financing and the respective proportions of each in the capital structure.
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of the last 20 trains to arrive at danville station, 15 were on time. what is the experimental probability that the next train to arrive will be on time?
Answers
Answer:
the experimental probability that the next train to arrive at Danville Station will be on time is 0.75 or 75%.
Step-by-step explanation:
Alex has 10 different kinds of lunch meat and 9 different kinds of cheese. If he wants to make a sandwich with one kind of meat and two kinds of cheese, how many different sandwiches could he make
Answers
Alex can make a total of 180 different sandwiches by choosing one kind of meat from 10 options and two kinds of cheese from 9 options.
To determine the number of different sandwiches Alex can make, we need to consider the combinations of meat and cheese. Since Alex can choose one kind of meat from 10 options, there are 10 choices for the meat component of the sandwich. For the cheese component, Alex can choose two kinds of cheese from 9 options.
To calculate the total number of combinations, we can use the formula for combinations without repetition. The formula is nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of choices. In this case, n is 9 (number of cheese options) and r is 2 (number of cheese choices). Thus, the number of combinations of two kinds of cheese is [tex]9C2[/tex]= 9! / (2!(9-2)!) = 36.
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Jane Ramirez owns shares in the Touchstone Small Cap fund that have a current value of $18,700. The fund charges an annual 12b-1 fee of 0.50 percent. What is the amount of the 12b-1 fee Ms. Ramirez must pay
Answers
The amount of the 12b-1 fee that Ms. Ramirez must pay is $93.50. This fee is based on a percentage of the current value of her shares in the Touchstone Small Cap fund, with a fee rate of 0.50 percent.
To calculate the amount of the 12b-1 fee that Ms. Ramirez must pay, we can use the formula:
12b-1 fee = (12b-1 fee rate) * (current value of shares)
The 12b-1 fee rate is given as 0.50 percent, which needs to be converted to a decimal by dividing it by 100:
12b-1 fee rate = 0.50% = 0.50/100 = 0.005
Now we can substitute the values into the formula:
12b-1 fee = 0.005 * $18,700
Calculating the multiplication:
12b-1 fee = $93.50
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In the regression model Yi = β0 + β1Xi + β2Di + β3(Xi × Di) + ui, where X is a continuous variable and D is a binary variable, β2
A. is usually positive.
B. indicates the difference in the intercept for D=1 versus D=0.
C. is the difference in means in Y between the two categories.
Answers
C. β2 is the difference in means in Y between the two categories.
In the given regression model, β2 represents the effect of the binary variable D on the outcome variable Y, while holding the continuous variable X constant. Since D is a binary variable, it can take on only two values (0 or 1). Therefore, β2 represents the difference in the mean of Y between the two categories represented by D=1 and D=0.
Option A is incorrect because β2 can be either positive or negative, depending on the direction and magnitude of the effect of D on Y.
Option B is incorrect because the difference in the intercept for D=1 versus D=0 is represented by β0, not β2.
Therefore, option C is the correct statement.
The emerging role of the ________ in competition policy suggests the EU is increasingly willing and able to intervene and impose conditions on companies proposing mergers and acquisitions.
Answers
The emerging role of the European Commission in competition policy suggests that the EU is becoming more inclined and capable of intervening and imposing conditions on companies involved in mergers and acquisitions.
The European Commission, as the executive body of the European Union, plays a crucial role in enforcing competition policy and ensuring fair market competition within the EU. In recent years, the European Commission has been increasingly active in scrutinizing mergers and acquisitions to prevent anti-competitive practices and protect consumer welfare.
By closely examining proposed mergers and acquisitions, the European Commission can assess their potential impact on competition and market dynamics. If it determines that a merger or acquisition could lead to anti-competitive behavior or harm consumers, the Commission has the authority to intervene and impose conditions or remedies on the company involved.
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A powderman set a fuse for a blast to take place in 3030 seconds. He ran away at a rate of 88 yards per second. Sound travels at the rate of 10801080 feet per second. When the powderman heard the blast, he had run approximately:
Answers
When the powderman heard the blast, he had run approximately 975,840 yards.
The time it took for the blast sound to reach the powderman can be calculated by dividing the distance traveled by the speed of sound. In this case, the distance traveled is not given directly, but we can calculate it using the powderman's running speed and the time it took for the blast to occur. The powderman ran away at a rate of 88 yards per second, and the blast was set to occur in 3030 seconds.
Multiply the powderman's running speed (88 yards per second) by the time it took for the blast (3030 seconds) gives us the distance covered by the powderman, which is approximately 267,840 yards. However, it's important to note that the question asks for the distance in yards, while the given information provides the speed of sound in feet per second.
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Quel est la la solution de 3x-4=2x+1
Answers
Answer:
x = 5
Step-by-step explanation:
3x - 4 = 2x + 1 ( subtract 2x from both sides )
x - 4 = 1 ( add 4 to both sides )
x = 5
the great pyramid in egypt is a square pyramid. exact measurements of the pyramids were taken in the late 1800's. at that time, each side of the base was 252 yards long and the height of the pyramid was 160 yards. what was the volume of the great pyramid when it was measured in the late 1800's
Answers
The volume of the Great Pyramid in Egypt, when measured in the late 1800s, can be calculated using the formula for the volume of a square pyramid. The pyramid is described as having each side of the base measuring 252 yards long and a height of 160 yards.
To calculate the volume, we can use the formula: V = (1/3) × base area × height. Since the base of the pyramid is square, we can find the base area by squaring the length of one side. In this case, the base area would be (252 yards) × (252 yards) = 63,504 square yards.
Plugging the values into the volume formula, we get: V = (1/3) × 63,504 square yards × 160 yards. Multiplying these values together, we find that the volume of the Great Pyramid in the late 1800s was approximately 3,216,960 cubic yards.
It's important to note that this volume measurement corresponds to the dimensions recorded in the late 1800s and may differ slightly from current estimates due to factors such as erosion or the use of different measurement techniques. However, these measurements provide valuable insights into the scale and grandeur of the Great Pyramid of Egypt.
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Plot the points on the coordinate plane and answer the questions. Plot the points: A(4, 5), B(3, 3), C(6, 9), D(8, 13), and E(10, 15). All but one of the points are on the same line. Which one is not?
Answers
The correct point which are not lie on line is,
⇒ Point (10, 15)
We have to given that;
All the coordinates are,
A(4, 5),
B(3, 3),
C(6, 9),
D(8, 13),
and E(10, 15)
Since, A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.
Now, We can plot all the point on graph and then draw a line.
Hence, From graph we can see that,
Point (10, 15) is not lie on the line and rest all are lies on line.
Therefore, The correct point which are not lie on line is,
⇒ Point (10, 15)
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how many independent variables can you test in a single experiment?
Answers
The number of independent variables that can be tested in a single experiment depends on various factors, including the research design, resources, and the complexity of the study. In general, it is best to limit the number of independent variables to maintain control over the experiment and facilitate clear interpretation of results.
In simpler experiments, researchers often focus on a single independent variable to study its effect on the dependent variable while controlling for other factors. This allows for a clear cause-and-effect relationship to be established.
However, in more complex experiments, researchers may introduce multiple independent variables to examine their combined effects or interactions. This can provide insights into how different factors influence the outcome simultaneously.
The exact number of independent variables that can be tested in a single experiment varies, but it is generally recommended to keep the number manageable and avoid excessive complexity. This ensures that the experiment remains feasible, interpretable, and effectively addresses the research question or hypothesis.
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The marketing platform used to measure, predict, and optimize for traditional and digital media is a A. Inbound marketing platform B. Data management platform C. Comprehensive marketing measurement and optimization platform D. None of these
Answers
The marketing platform used to measure, predict, and optimize for traditional and digital media is a Comprehensive marketing measurement and optimization platform.
The marketing landscape has evolved to encompass both traditional and digital media, necessitating the need for comprehensive tools to measure, predict, and optimize marketing efforts. A comprehensive marketing measurement and optimization platform fulfills this role by providing a unified solution to track, analyze, and improve marketing performance across various channels.
These platforms offer advanced analytics capabilities that enable marketers to measure the effectiveness of their campaigns, understand consumer behavior, and make data-driven decisions. They integrate data from multiple sources, including traditional media channels like television, radio, and print, as well as digital media platforms such as social media, search engines, and online advertising networks.
By leveraging sophisticated algorithms and predictive modeling techniques, these platforms provide insights into campaign performance, audience targeting, and media allocation. Marketers can identify which marketing channels and tactics are driving the best results and optimize their strategies accordingly. This helps maximize return on investment (ROI) by allocating resources effectively and delivering targeted messages to the right audience.
In conclusion, a comprehensive marketing measurement and optimization platform is the marketing platform of choice for measuring, predicting, and optimizing traditional and digital media. It offers integrated analytics, predictive modeling, and optimization capabilities to empower marketers with data-driven insights and enable them to make informed decisions for their marketing campaigns.
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for the quadrant in which the following point is located determine which of the functions are positive (8,-15) cot, tan, cos, csc, sec, sin
Answers
Based on the point (8, -15) in the fourth quadrant, the positive trigonometric functions are cos (θ) and sec (θ).
We must take into account the signs of the functions depending on the provided point (8, -15) in order to identify which trigonometric functions are positive in the fourth quadrant.
Located in the fourth quadrant:
The x-coordinate is 8 and positive.
(-15) represents the negative y-coordinate.
Based on these coordinates, we can determine the signs of the trigonometric functions as follows:
cot (θ): cot(θ) = x/y. Since x is positive and y is negative, cot(θ) is negative in the fourth quadrant.
tan (θ): tan(θ) = y/x. Since both x and y have different signs (one positive and the other negative), tan(θ) is negative in the fourth quadrant.
cos (θ): cos(θ) = x/r, where r is the hypotenuse or radius. Since x is positive and r is always positive, cos(θ) is positive in the fourth quadrant.
csc (θ): csc(θ) = r/y. Since y is negative and r is always positive, csc(θ) is negative in the fourth quadrant.
sec (θ): sec(θ) = r/x. Since x is positive and r is always positive, sec(θ) is positive in the fourth quadrant.
sin (θ): sin(θ) = y/r. Since y is negative and r is always positive, sin(θ) is negative in the fourth quadrant.
So, based on the point (8, -15) in the fourth quadrant, the positive trigonometric functions are cos (θ) and sec (θ), while the negative trigonometric functions are cot (θ), tan (θ), csc (θ), and sin (θ).
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what are the portfolio weights for a portfolio that has 135 shares of stock a that sell for $84 per share and 110 shares of stock b that sell for $82 per share? (do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.1616.) portfolio weight stock a % stock b %
Answers
The portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.
To calculate the portfolio weights for stock A and stock B, we need to determine the total value of the portfolio and the proportion of each stock's value within that total.
The total value of the portfolio can be calculated as follows:
Total value = (Number of shares of stock A × Price per share of stock A) + (Number of shares of stock B × Price per share of stock B)
Total value = (135 × $84) + (110 × $82)
Total value = $11,340 + $9,020
Total value = $20,360
Now, we can calculate the portfolio weights for each stock:
Weight of stock A = (Value of stock A ÷ Total value) × 100%
Weight of stock A = (($84 × 135) ÷ $20,360) × 100%
Weight of stock A = $11,340 ÷ $20,360
Weight of stock A ≈ 0.5569 or 55.69%
Weight of stock B = (Value of stock B ÷ Total value) × 100%
Weight of stock B = (($82 × 110) ÷ $20,360) × 100%
Weight of stock B = $9,020 ÷ $20,360
Weight of stock B ≈ 0.4431 or 44.31%
Therefore, the portfolio weights for stock A and stock B are approximately 55.69% and 44.31%, respectively.
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A gardener made a scale drawing of a lawn with a scale factor of 18. The dimensions of his drawing are 9 inches long by 5 inches wide His partner plans to make another scale drawing of the lawn, but with a scale factor of 1 16 What are the dimensions of this scale drawing O A The length is 25 inches and the wo 45 inches OB. The length is 10 inches and the chia 18 inches OC. The length is 18 inches and the D. The length is 45 inches and the 25th
Answers
The main answer is that the dimensions of the partner's scale drawing with a scale factor of 1:16 are approximately 1.125 inches long and 0.625 inches wide. Option A is the correct answer.
To find the dimensions of the partner's scale drawing with a scale factor of 1:16, we need to scale down the dimensions of the original drawing (1:8 scale).
If the original drawing is 9 inches long, dividing it by the scale factor of 8 gives us the length of the partner's drawing: 9 inches / 8 = 1.125 inches.
Similarly, if the original drawing is 5 inches wide, dividing it by the scale factor of 8 gives us the width of the partner's drawing: 5 inches / 8 = 0.625 inches.
Therefore, the dimensions of the partner's scale drawing are approximately 1.125 inches long and 0.625 inches wide, which corresponds to option A: The length is 4.5 inches and the width is 2.5 inches.
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The question is -
A gardener made a scale drawing of a lawn with a scale factor of 1:8. The dimensions of his drawing are 9 inches long by 5 inches wide. His partner plans to make another scale drawing of the lawn, but with a scale factor of 1:16. What are the dimensions of his scale drawing?
A. The length is 4.5 inches and the width is 2.5 inches.
B. The length is 10 inches and the width is 18 inches.
C. The length is 2.5 inches and the width is 4.5 inches.
D. The length is 18 inches and the width is 10 inches.
Given circle E with diameter CD and radius EA. AB is tangent to E at A. If
EA = 8 and EB = 17, solve for AB. Round your answer to the nearest tenth if
necessary. If the answer cannot be determined, click "Cannot be determined."
Answers
The length of AB is 15 units in the circle E with diameter CD and radius EA.
Given circle E with diameter CD and radius EA.
We have to find the length of AB, which is the tangent line from point A to circle E.
Since AB is tangent to circle E, we can draw a right triangle by connecting points A, B, and the center of the circle (O).
The radius EA is perpendicular to AB at point A.
We are given that EA = 8 and EB = 17.
Using the Pythagorean theorem, we can find the length of AB:
AB² = EB² - EA²
AB² = 17² - 8²
AB² = 289 - 64
AB² = 225
Taking the square root of both sides to find AB:
AB = √225
AB = 15
Therefore, the length of AB is 15 units.
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a math 110 student decides to make monthly payments of $1,000 into a retirement account paying 8% interest per year compounded continuously. if the student continues to make these payments for 40 years, compute each of the following values. account balance after 40 years (exact value)
Answers
The account balance after 40 years, with continuous compounding and monthly payments of $1,000, is approximately $23,845.825.
To compute the account balance after 40 years, we can use the formula for the future value of a continuous compounding account:
A = P * e^(r * t)
Where:
A is the account balance after time t,
P is the monthly payment (also known as the principal),
e is the base of the natural logarithm (approximately 2.71828),
r is the interest rate per year (expressed as a decimal),
t is the time period in years.
In this case, the monthly payment is $1,000, the interest rate is 8% per year (or 0.08 as a decimal), and the time period is 40 years.
Let's calculate the account balance:
P = $1,000
r = 0.08
t = 40
A = 1000 * e^(0.08 * 40)
Using a calculator or software that supports exponentials, we can compute:
A ≈ 1000 * e^(3.2)
A ≈ 1000 * 23.845825
A ≈ $23,845.825
Therefore, the account balance after 40 years, with continuous compounding and monthly payments of $1,000, is approximately $23,845.825.
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On 7/1/Year 1, the Ish-U-Bonds Company issued bonds with a face amount of $1,000,000 due in 20 years. Coupons are paid semi-annually on December 31 and July 1, beginning 12/31/ Year 1. The annual coupon rate is 8%, and the annual market yield on the issuance day is 6%. What are the bonds issuance proceeds
Answers
The issuance proceeds of the bonds are approximately $854,872.48
To calculate the issuance proceeds of the bonds, we need to determine the present value of the future cash flows associated with the bond.
The bond has a face amount of $1,000,000 and a coupon rate of 8%, which is paid semi-annually. Since coupons are paid semi-annually, the bond will make a total of 40 coupon payments over its 20-year life (2 payments per year for 20 years).
The coupon payments can be calculated as follows:
Coupon Payment = Face Amount × Coupon Rate / Number of Coupon Payments per Year
Coupon Payment = $1,000,000 × 8% / 2
Coupon Payment = $40,000
To calculate the present value of the coupon payments, we need to discount each semi-annual payment at the market yield rate of 6% per year. Since there are 40 semi-annual payments, we can use a financial calculator or a spreadsheet to calculate the present value of an ordinary annuity.
Using a financial calculator, the present value of the coupon payments can be calculated as follows:
Present Value of Coupon Payments = Coupon Payment × [1 - (1 + Yield Rate) ^ (-Number of Coupon Payments)] / Yield Rate
Present Value of Coupon Payments = $40,000 × [1 - (1 + 6%) ^ (-40)] / 6%
Present Value of Coupon Payments ≈ $40,000 × 13.5909 ≈ $543,636.36
The present value of the coupon payments is approximately $543,636.36.
To calculate the present value of the face amount (the final payment), we can use the formula for the present value of a single payment:
Present Value of Face Amount = Face Amount / (1 + Yield Rate) ^ Number of Coupon Payments
Present Value of Face Amount = $1,000,000 / (1 + 6%) ^ 40 ≈ $311,236.12
The present value of the face amount is approximately $311,236.12.
Finally, to calculate the issuance proceeds, we add the present value of the coupon payments and the present value of the face amount:
Issuance Proceeds = Present Value of Coupon Payments + Present Value of Face Amount
Issuance Proceeds ≈ $543,636.36 + $311,236.12 ≈ $854,872.48
Therefore, the issuance proceeds of the bonds are approximately $854,872.48.
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A student weighs out a 4.05 g sample of Na2SO4, transfers it to a 125 mL volumetric flask, adds enough water to dissolve it and then adds water to the 125 mL tick mark. What is the molarity of sodium sulfate in the resulting solution
Answers
The molarity of sodium sulfate in the resulting solution is 0.259 M. To determine the molarity (M) of the sodium sulfate solution, we need to calculate the number of moles of Na2SO4 present in the 4.05 g sample and then divide it by the volume of the solution in liters.
First, we calculate the number of moles of Na2SO4 using its molar mass. The molar mass of Na2SO4 is calculated as follows: 2(Na) + 1(S) + 4(O) = 2(22.99 g/mol) + 32.07 g/mol + 4(16.00 g/mol) = 142.04 g/mol.
Next, we convert the mass of the sample to moles by dividing it by the molar mass:
moles of Na2SO4 = 4.05 g / 142.04 g/mol = 0.0285 mol.
The volume of the solution is given as 125 mL, which is equivalent to 0.125 L.
Finally, we divide the number of moles of Na2SO4 by the volume in liters to obtain the molarity:
Molarity (M) = moles of Na2SO4 / volume of solution (in liters) = 0.0285 mol / 0.125 L = 0.228 M.
Therefore, the molarity of sodium sulfate in the resulting solution is 0.259 M.
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Simplify. Your answer should only contain exponents. Please explain how to do this.
Answers
Answer:
[tex]1. \: \frac{8v {}^{5} }{u} [/tex]
[tex]2. \: 32 {}^{6} y {}^{8} [/tex]
Step-by-step explanation:
[tex]2vu {}^{ - 4} .4u {}^{3} v {}^{4} = 8.(v {}^{1} \times v {}^{4} ).(u {}^{ - 4} \times u {}^{3} ) = 8.v {}^{5} .u {}^{ - 1} = 8.v {}^{5} . \frac{1}{u} = \frac{8v {}^{5} }{u} [/tex]
[tex]4x {}^{3} y {}^{2} .2y {}^{4} .4x {}^{3} = (4 \times 2 \times 4).(x {}^{3} \times x {}^{3} ).(y {}^{2} \times y {}^{4} ) = 32.x {}^{3 + 3}.y {}^{2 + 6} = 32x {}^{6} y {}^{8} [/tex]
An example of an optimistic explanatory style would be viewing a bad grade on a test as Group of answer choices a. something that doesn't often happen, will probably not effect your final grade and is probably because you did not get enough sleep the night before the test. b. something that always happens to you, but is really not that bad, and may simply be because the test is hard c. something that only happened this time, but could ruin the semester, and is always the teachers fault a. something which only happened this time, is not likely to effect your grade, but something that is your fault because of your study habits.
Answers
An example of an optimistic explanatory style would be viewing a bad grade on a test as something that doesn't often happen, will probably not affect your final grade, and is probably because you did not get enough sleep the night before the test.
An optimistic explanatory style involves interpreting negative events or outcomes in a positive and constructive manner. It involves attributing the causes of negative events to external, temporary, or specific factors rather than internal, permanent, or global factors.
In the given example, option (a) demonstrates an optimistic explanatory style. It suggests that the bad grade on the test is not a common occurrence ("something that doesn't often happen"), indicating that it is viewed as an isolated incident. Furthermore, it minimizes the impact of the bad grade by stating that it will probably not affect the final grade. Instead of attributing the cause to personal incompetence or intelligence.
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Alguien me puede ayudar
Answers
Step-by-step explanation:
a. 1
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8
b. 1
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7
c. 10
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21
espero que isso te ajude
Vamos a resolver las operaciones utilizando la regla de multiplicación de fracciones y luego simplificaremos los resultados.
a) [tex]\sf\:\frac{1}{6} \times \frac{3}{4}\\[/tex]
Para multiplicar estas fracciones, multiplicamos los numeradores entre sí y los denominadores entre sí:
Numerador: [tex]\sf\:1 \times 3 = 3\\[/tex]
Denominador: [tex]\sf\:6 \times 4 = 24\\[/tex]
Entonces, [tex]\sf\:\frac{1}{6}\:\times\:\frac{3}{4} = \frac{3}{24}\\[/tex]
Podemos simplificar esta fracción dividiendo tanto el numerador como el denominador por el máximo común divisor, que en este caso es 3:
[tex]\sf\:\frac{3}{24} = \frac{3 \div 3}{24 \div 3} = \frac{1}{8}\\[/tex]
Por lo tanto, el resultado simplificado es [tex]\sf\:\frac{1}{8}\\[/tex].
b) [tex]\sf\:\frac{1}{2} \times \frac{2}{7}\\[/tex]
Aplicando la regla de multiplicación de fracciones:
Numerador: [tex]\sf\:1 \times 2 = 2\\[/tex]
Denominador: [tex]\sf\:2 \times 7 = 14\\[/tex]
Entonces, [tex]\sf\:\frac{1}{2} \times \frac{2}{7} = \frac{2}{14}\\[/tex]
Podemos simplificar esta fracción dividiendo tanto el numerador como el denominador por el máximo común divisor, que en este caso es 2:
[tex]\sf\:\frac{2}{14} = \frac{2 \div 2}{14 \div 2} = \frac{1}{7}\\[/tex]
Por lo tanto, el resultado simplificado es [tex]\sf\:\frac{1}{7}\\[/tex].
c) [tex]\sf\:\frac{4}{7} \times \frac{5}{6}\\[/tex]
Siguiendo la regla de multiplicación de fracciones:
Numerador: [tex]\sf\:4 \times 5 = 20\\[/tex]
Denominador: [tex]\sf\:7 \times 6 = 42\\[/tex]
Entonces, [tex]\sf\:\frac{4}{7} \times \frac{5}{6} = \frac{20}{42}\\[/tex]
Podemos simplificar esta fracción dividiendo tanto el numerador como el denominador por el máximo común divisor, que en este caso es 2:
[tex]\sf\:\frac{20}{42} = \frac{20 \div 2}{42 \div 2} = \frac{10}{21}\\[/tex]
No podemos simplificar aún más esta fracción, por lo que el resultado simplificado es [tex]\sf\:\frac{10}{21}\\[/tex].
Resumiendo las respuestas:
a) [tex]\sf\:\frac{1}{6} \times \frac{3}{4} = \frac{1}{8}\\[/tex]
b) [tex]\sf\:\frac{1}{2} \times \frac{2}{7} = \frac{1}{7}\\[/tex]
c) [tex]\sf\:\frac{4}{7} \times \frac{5}{6} = \frac{10}{21}\\[/tex]
Stock Repurchase [LO4] Awake Corporation is evaluating an extra dividend ver- sus a share repurchase. In either case, $17,500 would be spent. Current earnings are $1.89 per share, and the stock currently sells for $64 per share. There are 2.000 shares outstanding. Ignore taxes and other imperfections in answering the first two questions. Evaluate the two alternatives in terms of the effect on the price per share of the stock and shareholder wealth. What will be the effect on the company's EPS and PE ratio under the two different scenarios
Answers
The effect under the scenarios are:
Choosing the extra dividend option would result in a decrease in the stock price per share and a decrease in the PE ratio.Choosing the share repurchase option would result in a lower stock price per share,The extra dividendTotal Dividend = $17,500
Dividend per Share = Total Dividend / Number of Shares
= $17,500 / 2,000
= $8.75 per share
Effect on Share Price:
Typically, when a dividend is paid, the stock price tends to decrease by the amount of the dividend. Therefore, the stock price per share would decrease by the dividend per share:
New Stock Price per Share = Current Stock Price - Dividend per Share
= $64 - $8.75
= $55.25
New Shares Outstanding = Current Shares Outstanding - Number of Shares Repurchased
= 2,000 - 273.44
= 1,726.56 shares
New Stock Price per Share = Total Amount Spent / New Shares Outstanding
= $17,500 / 1,726.56
= $10.14
EPS = Earnings / Number of Shares
= $1.89 / 2,000
= $0.000945
The PE (Price-to-Earnings) ratio is calculated by dividing the stock price per share by the EPS. Let's calculate the PE ratio under each scenario:
PE Ratio before the decision = Stock Price / EPS
= $64 / $0.000945
= 67772.49
PE Ratio with Extra Dividend = New Stock Price per Share / EPS
= $55.25 / $0.000945
≈ 58413.92
PE Ratio with Share Repurchase = New Stock Price per Share / EPS
= $10.14 / $0.000945 ≈ 10727.51
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