To graph the solution set to the given system of inequalities, we first need to graph the functions f(x) = x^2 - 2 and g(x) = -x^2 + 5.
The graph of f(x) is a parabola that opens upward and has its vertex at (0, -2). The graph of g(x) is also a parabola, but it opens downward and has its vertex at (0, 5). We can plot these two graphs on the same coordinate plane as follows:
[Insert image of two parabolas on a coordinate plane]
Next, we need to shade the regions of the graph that satisfy the given inequalities. The first inequality y > x^2 - 2 represents the region above the parabola f(x) but below the line y = infinity. The second inequality y ≥ -x^2 + 5 represents the region at or above the parabola g(x). The solution set is the intersection of these two regions.
The shaded region represents all the points (x, y) that satisfy both inequalities, and therefore, the solution set to the system of inequalities.
There are 6 men and 8 women in a book club. The committee of the club consists of five of its members. Mr Lan and Mrs Lan are members of the club.
A) In how many different ways can the committee be selected if exactly one of Mr Lan and Mrs Lan must be on the committee?
B) If a committee is selected at random, find the probability that there are more women than men on the committee, given that Mrs Lan was selected
A)By applying permutation and combination we can select committee in 1782 ways.
B) The probability cannot be determined with the given information, as the calculated probability is greater than 1, which is not possible.
What is permutation and combinationPermutation and combination are two concepts in mathematics that deal with counting the number of possible outcomes or arrangements in a given situation. Permutation refers to the arrangement of objects in a specific order, while combination refers to the selection of objects without regard to the order in which they are chosen.
What is probability?Probability is a measure of the likelihood or chance that an event will occur. It is a number between 0 and 1.
According to the given information:
A) To find the number of ways to select a committee of 5 members, where exactly one of Mr Lan and Mrs Lan must be on the committee, we can use the principle of inclusion-exclusion i.e. Permutation and combination:
First, we find the total number of ways to select a committee of 5 members from 14 members (6 men and 8 women), which is given by:
C(14,5) = 2002
Next, we find the number of ways to select a committee of 5 members that includes both Mr Lan and Mrs Lan, which is given by:
C(12,3) = 220
Note that we choose 3 members from the remaining 12 members after Mr and Mrs Lan have been chosen.
Finally, we subtract the number of committees that include both Mr Lan and Mrs Lan from the total number of committees, since we only want committees that include exactly one of them:
2002 - 220 = 1782
Therefore, there are 1782 different ways to select a committee of 5 members where exactly one of Mr Lan and Mrs Lan must be on the committee.
B) To find the probability that there are more women than men on the committee, given that Mrs Lan was selected, we need to consider the number of committees that satisfy this condition and divide by the total number of committees that include Mrs Lan.
If Mrs Lan is selected, there are two cases to consider:
Case 1: The committee has more women than men.
In this case, we need to select 4 members from the 8 women and 1 member from the 5 men, which can be done in C(8,4) x C(5,1) = 560 ways.
Case 2: The committee has an equal number or more men than women.
In this case, we need to select 3 members from the 8 women and 2 members from the 5 men, which can be done in C(8,3) x C(5,2) = 560 ways.
Therefore, the total number of committees that include Mrs Lan and have more women than men or an equal number of women and men is 560 + 560 = 1120.
The total number of committees that include Mrs Lan is C(13,4) = 715, since we choose 4 members from the remaining 13 members after Mrs Lan has been chosen.
Therefore, the probability of selecting a committee with more women than men or an equal number of women and men, given that Mrs Lan was selected, is:
1120/715 = 1.5664
Note that this probability is greater than 1, which is not possible. Therefore, there is an error in the calculation, and the correct probability cannot be determined with the given information.
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100 Points! Find the third term of (11x+3y)^6. Photo attached. Please show as much work as possible. Thank you!
the third term of the expansion of (11x+3y)⁶ is 798,720x³y³.we can use the binomial theorem to solve this .
what is binomial theorem ?
The binomial theorem is a theorem in algebra that describes the algebraic expansion of powers of a binomial. A binomial is a polynomial with two terms, such as (a + b) or (x - y).
In the given question,
To find the third term of the expansion of (11x+3y)⁶, we can use the binomial theorem, which states that:
(a + b)ⁿ = C(n,0)aⁿb⁰ + C(n,1)*aⁿ⁻¹*b¹+ C(n,2)*aⁿ⁻¹*b² + ... + C(n,n)a⁰bⁿ
where C(n,k) denotes the binomial coefficient, which is the number of ways to choose k items from a set of n items.
In this case, we have a = 11x and b = 3y, and n = 6. We want to find the third term, which corresponds to k = 3 in the expansion. Therefore, we need to compute the binomial coefficient C(6,3), as well as the powers of 11x and 3y that appear in the third term.
The binomial coefficient C(6,3) can be computed as follows:
C(6,3) = 6! / (3! * (6-3)!) = 20
To find the powers of 11x and 3y that appear in the third term, we need to look at the general pattern in the expansion. Each term in the expansion consists of a product of powers of a and b, with the powers of a decreasing by 1 from n to 0, and the powers of b increasing by 1 from 0 to n. Therefore, the kth term in the expansion will have powers of a and b given by aⁿ⁻ᵇand bᵃ, respectively.
In the third term, we have k = 3, so we need to find the coefficient of a³ = a³ = (11x)³ and b³ = (3y)³. The third term is given by:
C(6,3)(11x)³(3y)³
Plugging in the values for C(6,3), (11x)³, and (3y)³, we get:
20*(11x)³*(3y)³ = 2011³x³3³y³ = 798,720x³y³
Therefore, the third term of the expansion of (11x+3y)⁶ is 798,720x³y³.
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Given the following table of scores, calculate the indicated locator and percentile.
Do not round your results.
Here are the answers to the above questions:
Locator for the 52nd percentile, L52: 6.7252nd percentile, P52: 61.4Percentage of scores above the 52nd percentile: approximately 48%What is the explanation for the above response?To calculate the locator and percentile, we need to first arrange the scores in ascending order:
6, 8, 11, 12, 14, 17, 20, 34, 36, 38, 47, 48, 49
a) To calculate the locator for the 52nd percentile, we use the following formula:
Lp = (p/100) * (N + 1)
where Lp is the locator for the pth percentile, p is the percentile we are interested in, and N is the total number of scores.
For the 52nd percentile, p = 52 and N = 13. Substituting these values into the formula, we get:
L52 = (52/100) * (13 + 1) = 6.72
Therefore, the locator for the 52nd percentile is 6.72.
b) To determine the 52nd percentile, we need to find the score corresponding to the locator L52. Looking at the ordered list of scores, we see that the score at position 6 is 17 and the score at position 7 is 20. Since the locator L52 falls between positions 6 and 7, we can use linear interpolation to estimate the 52nd percentile:
P52 = (7 - L52) / (7 - 6) * 50 + (L52 - 6) / (7 - 6) * 50
P52 = (7 - 6.72) / (7 - 6) * 50 + (6.72 - 6) / (7 - 6) * 50
P52 = 38 + 0.48 * 50
P52 = 61.4
Therefore, the 52nd percentile is approximately 61.4.
c) To find the percentage of scores that are above the 52nd percentile, we subtract the 52nd percentile from 100:
100 - 52 = 48
Therefore, approximately 48% of the scores in the dataset are above the 52nd percentile.
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Need help, pretty easy just not for me
On solving the provided question we can say that As a result, set D denotes a linear function.
what is slope?The slope of a line indicates how steep it is. The gradient's mathematical equation is known as "gradient overflow" (the change in y divided by the change in x). The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b. The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, consider the slope and y-intercept of the equation y = 3x - 7.The slope of the line is m. b is b at the y-intercept, and (0, b).
The set of ordered pairs expressing a linear function must meet the requirement that any two locations in the set have a constant rate of change (slope).
We can determine the rate of change between the two supplied positions using set D:
slope = (y2 - y1) / (x2 - x1)
slope = (1 - 2) / (2 - (-1))
slope = -1/3
We may use the slope-intercept form of a linear equation to see if the remaining points in set D fulfil the same rate of change: y = mx + b, where m is the slope and b is the y-intercept.
We can solve for b using the first point in D, (-1,2):
2 = (-1/3)(-1) + b
b = 7/3
So the linear equation for set D is: y = (-1/3)x + 7/3
Now we can check if the remaining points in set D satisfy this equation:
(2, 1): 1 = (-1/3)(2) + 7/3 (satisfies the equation)
As a result, set D denotes a linear function.
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I need help with questions 1,2, and 3. This class is microeconomics
Graph cookies and coffee, slope -2. Ben buys 2 cookies and 2 coffees. To optimize, allocate budget where MU per dollar is equal.
What is budget?A budget is a financial plan that outlines expected income and expenses over a certain period. It helps individuals or organizations manage their money and make informed decisions about spending and saving.
What is consumption?Consumption refers to the use of goods and services by individuals, households, or organizations. It is an essential part of the economy and can be influenced by factors such as income, preferences, and prices.
According to the given information:
To draw Ben's indifference curves, we need to plot different combinations of cookies and coffee that give Ben the same level of satisfaction. Since the slope of all his indifference curves is constant at -2, they will be downward-sloping straight lines. We can plot several indifference curves by varying the level of satisfaction they represent. The budget constraint is a straight line that represents all possible combinations of cookies and coffee that Ben can purchase with his $12 budget. The slope of the budget constraint is the ratio of the prices of coffee and cookies, which is 2:1. Ben optimally purchases the point where his budget constraint is tangent to his highest attainable indifference curve. In other words, he maximizes his satisfaction subject to his budget constraint. In the graph above, this point is labeled as "Optimal Consumption." At this point, Ben purchases 2 cookies and 2 coffees, spending $8 on coffee and $4 on cookies, which exhausts his $12 budget.To optimize his consumption, Ben should allocate his budget between cookies and coffee such that the ratio of their marginal utilities equals their prices. In other words, Ben should choose the combination of cookies and coffee where the marginal utility per dollar spent is the same for both goods. At his current consumption level of 3 coffees and 0 cookies, Ben's marginal utility per dollar spent on cookies is 2/2 = 1, and his marginal utility per dollar spent on coffee is 1/4 = 0.25. Since the marginal utility per dollar spent on cookies is higher than that of coffee, Ben should decrease his consumption of coffee and increase his consumption of cookies to achieve the optimal consumption level. He should continue adjusting his consumption until the marginal utility per dollar spent on each good is equal.To know more about budget and consumption visit:
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An account is opened with an initial deposit of $7,500 and earns 3.4% interest compounded semi-annually. Round all answers to the nearest dollar.
The final amount with interest earned at a rate of 3.4% compounded semi-annually would be approximately $7,758.
HOW CAN WE CALCULATE INTEREST?Let's calculate the values based on the given information.
Given:
Initial deposit (P) = $7,500
Interest rate (r) = 3.4% or 0.034 (decimal)
Compounding frequency (n) = 2 (semi-annually)
We can use the compound interest formula to calculate the values:
A = P[tex](1 + r/n)^(nt)[/tex]
Where:
A = the final amount (including interest)
P = the principal amount (initial deposit)
r = the interest rate (in decimal)
n = the number of times interest is compounded per time period
t = the number of time periods
Let's calculate the final amount (A) after one year (2 semi-annual periods):
A =[tex]$7,500(1 + 0.034/2)^(2*1)[/tex]
A =[tex]$7,500(1.017)^2[/tex]
A = $7,500(1.034344) [rounded to 6 decimal places]
A ≈ $7,758 [rounded to the nearest dollar]
So, after one year, the final amount with interest earned at a rate of 3.4% compounded semi-annually would be approximately $7,758.
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Which function is undefined for x = 0?
O y=³√√x-2
y = √√√x-2
Oy=³√√x+2
O
y=√x+2
O
The function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.
What is an inequality equation?
An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
The function that is undefined for x = 0 is y = √x+2.
When x = 0, we have:
y = √0+2
y = √2
Since there is no real number whose square is negative, the square root of a negative number is undefined in real numbers.
Therefore, the function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.
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Which two relationships describes angles 1 and 2? Choose from (adjacent angles, complementary angles, supplementary angles, or vertical angles) relationship 1:
Relationship 2:
Hence ,the sum of ∠1 and ∠2 is 90 degrees this is a relationship between ∠1 and ∠2.
What is the angle?In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.
What is the adjacent angles, complementary angles, supplementary angles, or vertical angles?complementary angles are two angles that add up to 90 degrees, supplementary angles are two angles that add up to 180 degrees,
vertical angles are opposite angles at an intersection of two straight lines, and adjacent angles are two angles that are next to each other.
According to figure , the sum of ∠1 and ∠2 is 90 degrees and If the sum of the two angles is equal to the measurement of a right angle .
So, the pair of angles ∠1 and ∠2 is said to be complementary angles.
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In one lottery, a player wins the jackpot by matching all five distinct numbers drawn in any order from the white balls (1 through 41) and matching the number on the gold ball (1 through 35). If one ticket is purchased, what is the probability of winning the jackpot?
The probability of winning the jackpot with one ticket is approximately 0.000000003724.
What is the probability?There are a total of C(41, 5) ways to choose five numbers from 41 white balls, and there are 35 possible choices for the gold ball.
Therefore, the total number of ways to win the jackpot is:
C(41, 5) * 35
And the total number of possible outcomes (i.e. all the combinations of 5 white balls and 1 gold ball) is:
C(41, 5) * 35 * C(5, 5)
Since there is only one winning combination, the probability of winning the jackpot is:
1 / (C(41, 5) * 35)
Plugging in the values, we get:
1 / (749,398,832 * 35) = 1 / 26,869,866,120
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Explain your plan for improving your math skills.
Answer:
To improve my math skills, I plan on doing the following:
1. Practice, practice, practice: I will practice math problems regularly, starting with simple problems and gradually increasing the difficulty level.
2. Use online resources: There are many online resources available that provide tutorials, practice problems, and videos to help with math skills. I will utilize these resources to supplement my learning.
3. Work with a tutor: I will consider working with a tutor if I need additional help with math concepts or if I'm struggling with specific problems.
4. Study regularly: I will set aside time each day to study math, even if it's just for a few minutes.
5. Ask questions: I will ask my teacher or tutor for help if I don't understand a concept or if I'm struggling with a problem.
6. Stay positive: I will maintain a positive attitude towards math and believe in my ability to improve my skills.
By following these steps, I'm confident that I can improve my math skills and become more confident in my abilities.
Answer:
"My plan for improving my math skills is to focus more on understanding and going over new concepts and practice problems. I also will try studying math concepts online and using a method of solving extra problems and applying math in the real world to better understand."
Step-by-step explanation:
An angle measures 6.6° more than the measure of its complementary angle. What is the measure of each angle?
Answer:
Angle 1 = 51.6°
Angle 2 = 38.4°
Step-by-step explanation:
All complimentary angles add up to 90°.
If two complimentary angles were congruent then their measures would both be 45°.
Since one angle's measure is 6.6° more than the other's measure, it's measure is 6.6° more than 45°
Vice versa for the second angle, its measure will be 6.6° less than 45°
Which monomial has a degree of 3?
A.
3x
B.
3
C.
3x2
D.
–2x3
The only option given that has a variable raised to the third power is D. -2x³, so the correct answer is D.
What is monomial?In algebra, a monomial is an expression that consists of a single term, which is a product of a constant coefficient and one or more variables raised to non-negative integer powers. In each of these expressions, there is only one term, and each term is a product of a constant coefficient and one or more variables raised to non-negative integer powers. Monomials are important in algebra because they can be combined using various operations such as addition, subtraction, multiplication, and division, to form more complex expressions.
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2x-y=3 and 7x-y=13 solve the simultaneous equation
Answer:
x=4
y=5
Step-by-step explanation:
PLEASE HELP ME
Sophie deposited money into an account in which interest is compounded
semiannually at a rate of 2.2%. She made no other deposits or withdrawals and the
total amount in her account after 13 years was $22,099.87. How much did she
deposit? Round answer to nearest whole number. Do not include units in the
answer. Be sure to attach your work for credit.
By using compound interest formula, we conclude that Sophie deposited $16,638 (rounded to the nearest whole number) into the account.
What is compound interest?Compound interest is a method of calculating interest on a principal amount of money, where the interest earned on the initial principal is added to the principal at the end of each compounding period (usually monthly, quarterly, or annually).
According to given information:We can use the formula for compound interest to solve this problem. The formula is:
[tex]A = P(1 + r/n)^{(nt)[/tex]
Where:
A = the total amount in the account
P = the principal (initial deposit)
r = the annual interest rate (as a decimal)
n = the number of times the interest is compounded per year
t = the number of years
We know the values for A, r, n, and t, so we can solve for P:
[tex]A = P(1 + r/n)^{(nt)[/tex]
[tex]22,099.87 = P(1 + 0.022/2)^{(2*13)[/tex]
[tex]22,099.87 = P(1.011)^{26[/tex]
22,099.87 = 1.329P
P = 22,099.87 / 1.329
P = 16,637.55
Therefore, Sophie deposited $16,638 (rounded to the nearest whole number) into the account.
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.
An investment pays 14% interest compounded weekly. What percent, as a decimal, is the effective annual yield? Enter your
answer as a decimal rounded to four decimal places.
Provide your answer below:
The effective annual yield of the investment is 0.1501
What percent is the effective annual yield?To find the effective annual yield, we need to use the formula:
(1 + r/n)^n - 1
where r is the annual interest rate and n is the number of times the interest is compounded per year.
In this case, r = 0.14 (14% expressed as a decimal), and n = 52 (since interest is compounded weekly).
Plugging these values into the formula, we get:
(1 + 0.14/52)^52 - 1 = 0.1501
Therefore, the effective annual yield is 0.1501, which is equivalent to 15.01% (rounded to two decimal places).
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A study of a country's colleges and universities resulted in the demand equation q = 20,000 − 2p, where q is the enrollment at a public college or university and p is the average annual tuition (plus fees) it charges.† Officials at Enormous State University have developed a policy whereby the number of students it will accept per year at a tuition level of p dollars is given by q = 8,500 + 0.5p. Find the equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level. What is the total social gain at the equilibrium price? HINT [See Example 3.]
The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is 11400
Find the equilibrium tuition price p and the consumers' and producers' surpluses at this tuition levelFrom the question, we have the following parameters that can be used in our computation:
q = 20,000 − 2p
q = 8,500 + 0.5p
The equilibrium tuition price p and the consumers' and producers' surpluses at this tuition level is when q = q
So, we have
20,000 − 2p = 8,500 + 0.5p
Evaluate the like terms
2.5p = 28500
Divide by 2.5
p = 28500/2.5
Evaluate
p = 11400
Hence, the equilibrium tuition price p is 11400
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A researcher collected sample data for 12 middle-aged women. The sample had a mean serum cholesterol
level (measured in milligrams per one hundred milliliters) of 192.4, with a standard deviation of 5.9.
Assuming that serum cholesterol levels for middle-aged women are normally distributed, find a 90%
confidence interval for the mean serum cholesterol level of all women in this age group. Give the lower limit
and upper limit of the 90% confidence interval.
The lower limit is 189.331 milligrams per one hundred milliliters, and the upper limit is 195.469 milligrams per one hundred milliliters.
To find the 90% confidence interval for the mean serum cholesterol level of all middle-aged women, we can use the formula:
CI = x' ± t(α/2, n-1) × (s/√n)
where:
x' is the sample mean serum cholesterol level
t(α/2, n-1) is the critical t-value for a two-tailed test with a 90% confidence level and n-1 degrees of freedom
s is the sample standard deviation of the serum cholesterol level
n is the sample size
Substituting the given values, we get:
CI = 192.4 ± t(0.05, 11) × (5.9/√12)
To find the critical t-value, we can use a t-distribution table or calculator. For a two-tailed test with 11 degrees of freedom and a 90% confidence level, the critical t-value is approximately 1.796.
Substituting this value and simplifying, we get:
CI = 192.4 ± 1.796 × 1.707
CI = 192.4 ± 3.069
Therefore, the 90% confidence interval for the mean serum cholesterol level of all middle-aged women is (189.331, 195.469).
This means that we can be 90% confident that the true mean serum cholesterol level for all middle-aged women falls within this interval.
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Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
Thus, equation shows the connection between the quantity of weeks, w, and the quantity of books gathered, b: b = 10w.
Explain about the slope intercept form:Simply put, the slope-intercept form is the way to write a line's equation so that the y-intercept (at which line crosses a vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.
The table shows an increase of 10 volumes every week in the total number of books acquired.
Weeks (w) Books Collected (b)
1 10
2 20
3 30
4 40
As a result, the quantity of books gathered and the number of weeks (w) have a linear relationship (b). The following equation can be used to illustrate this relationship:
b = mw + c
where w is the number of weeks, m denotes the slope (rate of change), and c denotes the number of books aquired at week 0.
The weekly shift in the amount of books gathered, which is 10, is the slope (m). By adding one of the points from table to the equation, we can now get the y-intercept (c). Use the first and tenth points:
10 = 10 * 1 + c
c = 0
Currently, the following equation reflects the relationship among the number of weeks (w) as well as the quantity of books gathered (b):
b = 10w + 0
b = 10w
Thus, equation shows the connection between the quantity of weeks, w, and the quantity of books gathered, b: b = 10w.
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Complete question:
The data in the form of a table, which shows the total number of books collected (b) for different number of weeks (w).
Weeks (w) Books Collected (b)
1 10
2 20
3 30
4 40
Trisha is collecting books to donate. The table below shows the total number of books collected, b, for different number of weeks, w. Which equation represents the relationship between the number of weeks, w, and the number of books collected, b?
Todd throws a ball from his tree house. The height in feet of the ball, h(t), above the ground after t seconds is modeled by the function h(t) = −3t2 + 9t + 12. Select the appropriate domain for the function.
The appropriate domain for the function h(t) = −3t^2 + 9t + 12 is [0, 3.08].
How to select the appropriate domainThe domain of a function is the set of all possible input values for which the function is defined. In this case, the function h(t) gives the height of the ball above the ground as a function of time t.
The ball is thrown from the tree house at some initial time, and it continues to travel until it hits the ground. The height of the ball is defined for all values of t between the time it is thrown and the time it hits the ground.
To find the domain of h(t), we need to determine the range of values of t for which the function is defined. The ball cannot have a negative height, so the function is undefined for values of t that would make h(t) negative.
To find the time at which the ball hits the ground, we need to set h(t) equal to zero and solve for t:
h(t) = -3t^2 + 9t + 12 = 0
Using the quadratic formula, we get:
t = (-9 ± √(9^2 - 4(-3)(12)))/(2(-3))
t = (-9 ± √(105))/(-6)
t ≈ -0.41 or t ≈ 3.08
Since the ball cannot have a negative height, the domain of the function is the interval [0, 3.08]. Therefore, the appropriate domain for the function h(t) = −3t^2 + 9t + 12 is [0, 3.08].
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3. "Frank has four different credit cards, the balances and interest information of which are outlined in the table below.
He would like to consolidate his credit cards to a single credit card with an APR of 18% and pay off the balance in 24 months.
What will his monthly
credit card payment be?
Hint use the monthly payment formula where PV = (all balances combined), i=0.18/12, and n=24
A. $390.00
B. $462.91
C. $454.31
D. $52.00
Answer:
Therefore, Frank's monthly credit card payment will be $454.31.
Step-by-step explanation:
Monthly payment = (PV * r) / (1 - (1 + r)^-n)
PV = $2,500 + $1,000 + $3,000 + $1,500
= $8,000
r = 0.18 / 12
= 0.015
Monthly payment = ($8,000 * 0.015) / (1 - (1 + 0.015)^-24)
= $454.31
Anthony has decided to purchase a $19,000 car. He plans to put 20% down toward the purchase and to finance the rest at a 6.8% interest rate for 4 years. Find his monthly payment.
Find the total price Anthony paid for his vehicle.
The monthly payment and total price paid by Antony at interest rate of 6.8% for vehicle is $362.59 and $21204.4 respectively.
Cost price of the car Antony decided to purchase = $19,000
Down payment = 20% of purchase value
Interest rate of amount to be finance = 6.8%
Time period of finance amount = 4 years
Down payment = 0.2 × $19,000
= $3,800
Amount that Anthony needs to finance,
Amount to finance = $19,000 - $3,800
= $15,200
The monthly payment , use the formula for the monthly payment on a loan,
M = P × r × (1 + r)ⁿ / ((1 + r)ⁿ - 1)
where M is the monthly payment,
P is the principal the amount to finance
r is the monthly interest rate
n is the total number of payments which is the number of years multiplied by 12
The monthly interest rate is 6.8% / 12 = 0.00567,
and the total number of payments is 4 × 12 = 48.
Substituting these values into the formula, we get,
⇒M = $15,200 × 0.00567 × (1 + 0.00567)⁴⁸ / ((1 + 0.00567)⁴⁸ - 1)
⇒M = $15,200 × 0.00567 × 1.3118 / (1.3118 -1)
⇒M = $15,200 × 0.00567 × 1.3118 / 0.3118
⇒M = 113.056 / 0.3118
⇒M ≈ $362.59
Anthony's monthly payment will be about $362.59
Total price that Anthony paid for his vehicle,
add up the down payment and the total amount of payments over the 4-year period.
Total price = $3,800 + ( $362.59 × 48)
= $21204.4
Therefore, the monthly payment and the total price at interest rate of 6.8% that Anthony paid for vehicle is $362.59 and $21204.4 respectively.
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Which of the following describes the graph shown?
The piecewise function graphed is defined as follows:
C)
y = 1/2x + 2, x ≤ -1.y = 1/2x² - 1, x > -1.What is a piecewise function?A piecewise function is a function that is defined by multiple equations, each of which applies to a specific interval or set of inputs. The equations are pieced together to form a single function that describes the behavior of the function over its entire domain.
The intervals for this problem are given as follows:
x ≤ -1.x > 1.For the first interval, we have a linear function with a slope of 1/2 and an intercept of 2, hence:
y = 1/2x + 2, x ≤ -1.
For the second interval, we have a quadratic function with a vertex of -1, hence:
y = 1/2x² - 1, x > -1.
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PLEASEE HELP ITS URGENT
The ratio of the areas is given as follows:
1:5.8.
How to obtain the ratio of the areas?The ratio of the areas is obtained applying the proportions in the context of the problem.
When a prism is dilated by a scale factor of k, we have that:
The ratio of the perimeters is k, as both the side lengths and the perimeter are measured in units.The ratio of the areas is k², as the side lengths are measured in units, while the areas are in units squared.The ratio of the volumes is k³, as the side lengths are measured in units, while the volumes are in units cubed.Hence the ratio of the areas is the cubic root of the ratio of the volumes squared, thus, as the ratio of the volumes is of 1:14, we have that:
(14²)^(1/3) = 5.8.
Hence:
1:5.8.
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Select the correct answer from each drop-down menu.
Riley is swinging on a swing at the playground. Let t represent time, in seconds, and let represent Riley's horizontal distance, in inches, from
her starting position, as shown in the table.
t
0 0.75 1.5 2.25 3 3.75 4.5 5.25 6 6.75
f(t) 0 38.9 55 38.9 0-28.9 -55 -38.9 0 38.9
Note: When Riley swings in front of the starting position, f (t) is positive, and when Riley swings behind the starting position, f(t) is negative.
From the table, Riley is moving forward on the interval [0,
It takes Riley
Riley reaches a maximum distance of
seconds to swing forward, back, and then return to her starting position.
inches from her starting position.
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Thus, Riley's maximum distance from the starting position is 55 inches.
Explain about the function:When an input value has a defined output value in reality, functions can be applied. For instance, how long a car has been driving affects how far it has travelled (the output) (the input).
Riley is swaying on a playground swing. As stated in the table, let t denote the passing of time in seconds and let f(t) denote Riley's horizontal displacement from her starting location in inches.
t: 0 ,0.75, 1.5, 2.25, 3, 3.75, 4.5, 5.25, 6, 6.75
f(t): 0 ,38.9, 55, 38.9, 0, -28.9, -55, -38.9, 0, 38.9
Recall that f(t) is positive when Riley swings closest to the starting position and negative when Riley swings in behind starting position.
So,
started from 0 and travelled distance of 55 inches in 1.5 seconds.
She is advancing by up to 1.5 seconds.
Then she begins to move backward, returning to her starting location after 3 seconds, and continuing to do so for an additional 4.5 seconds at a distance of -55.
Then begin to advance and return to the starting position after six seconds
Riley is advancing from the table on the interval [0, 1,5].Riley swings forward, backward, and then back to the starting position in six seconds. A is a few inches from where she started.Riley's maximum distance from the starting position is 55 inches.Know more about the function:
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Simplify (5x4y2)(2x2y).
10x8y2
10x6y3
10x6y2
7x6y3
Answer:
10*8y2
Step-by-step explanation:
(5*4y2)(2*2y)(5*4y2)(2*2y)5*4y2*2*2y(5*2)(4y2*2y)(10)(8y2)Find a value of Z such that .6318 of the area lies between negative Z and Z.
The required value of z such that 0.6318 of the area lies between −z and z is 0.89.
If 0.6318 of the area lies between −z and z, then the area outside of this range is (1-0.6318) = 0.3682.
Since the normal distribution is symmetric, the area to the left of −z is equal to the area to the right of z. So, the area to the right of z is (0.3682 / 2) = 0.1841.
Using a standard normal distribution table, we can find the z-score corresponding to an area of 0.1841 to the right of z:
z = invNorm(0.1841) ≈ 0.89
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You missed an A in your art course by only 8 points. Your point total for the course was 415. How many points were possible in the course? (Assume that you needed 90% of the course total for an A.)
The total possible points in the course is approximately 470.
HOW CAN WE SOLVE AN EQUATION?Let's assume that the total possible points in the course is "x".
Since you needed 90% of the course total for an A, that means you needed to earn 90% of "x" to get an A. This is equivalent to 0.90x.
You missed an A by only 8 points, so your actual earned points must be 90% of "x" minus 8. This can be expressed as 0.90x - 8.
Given that your actual earned points for the course is 415, we can set up an equation:
0.90x - 8 = 415
Now, we can solve for "x" to determine the total possible points in the course:
0.90x = 415 + 8
0.90x = 423
x = 423 / 0.90
x ≈ 470
So, the total possible points in the course is approximately 470.
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HELP LOTS OF POINTS! You are on the ground looking at the top of a 1,000 foot tall building through binoculars at a 75 degree angle of elevation. Your eyes are 5 feet above the ground (consider this). How far away from the building are you standing? Round to the nearest tenth
Answer:
266.6 ft
Step-by-step explanation:
If a person stands at a point and looks up at an object, the angle between their horizontal line of sight and the object is called the angle of elevation.
To find how far away from the building you are standing, we need to find the distance labelled "x" on the attached diagram. We can do this by modelling the given scenario as a right triangle and solving for x by using the tangent trigonometric ratio.
Tangent trigonometric ratio[tex]\boxed{\tan \theta=\sf \dfrac{O}{A}}[/tex]
where:
θ is the angle.O is the side opposite the angle.A is the side adjacent the angle.Given information:
Height of building = 1000 ftPerson's eye level above the ground = 5 ftAngle of elevation = 75°As your eyes are 5 ft above the ground, we have to model the line of sight as 5 ft above ground level. Therefore, the side of the right triangle opposite the angle of elevation is the height of the building less 5 ft:
[tex]\implies \sf 1000 \; ft - 5\; ft=995 \; ft[/tex]
Let "x" be the horizontal distance between you and the building.
Therefore, the values to substitute into the tangent ratio are:
θ = 75°O = 995A = xSubstitute these values into the ratio and solve for x:
[tex]\tan 75^{\circ}=\dfrac{995}{x}[/tex]
[tex]x=\dfrac{995}{\tan 75^{\circ}}[/tex]
[tex]x=266.609446...[/tex]
[tex]x=266.6\; \sf ft\; (nearest\;tenth)[/tex]
Therefore, you are standing 266.6 ft from the building.
Pls help with this homework pls
Answer: 480 in²
Step-by-step explanation:
To calculate the surface area, we will find the area of each side and add it together.
Area of the rectangular sides can be found with A = LW:
A = LW
A = (12 in)(10 in)
A = 120 in²
A = LW
A = (12 in)(10 in)
A = 120 in²
A = LW
A = (12 in)(12 in)
A = 144 in²
All the rectangular sides added together:
120 in² + 120 in² + 144 in² = 384 in²
Now, we will find the triangle sides. The formula for a triangle is [tex]A=\frac{BH}{2}[/tex], but since we have two congruent triangles I will not be dividing by 2.
A = BH
A = (12 in)(8 in)
A = 96 in²
Lastly, I will add them both together:
384 in² + 96 in² = 480 in²
Rewrite -3 to the -3 power without exponents
Thus, the statement -3 to the -3 power written without using exponents is -1/27.
Explain about the exponents:A number's power or exponent, in other words, tells how many times it must be multiplied by itself. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.
The exponent rules must be understood while performing mathematical calculations or when simplifying complex equations. There are numerous rules, including the multiplication rule, the rule of negative exponents, and the rule of fractional exponents.Given that-
-3 to the -3 power
This can written as:
= (-3)⁻³
Now using the property of exponents,taking reciprocal of the number will remove the negative number.
= (1 /-3)³
= (1)³ / (-3)³
= 1/(-27)
= - 1/ 27
Thus, the statement -3 to the -3 power written without using exponents is -1/27.
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