Answer:
The correct line of reflection that maps the polygon ABCDE to its image polygon A' B' C' D' E' is:
C. Reflection across the x-axis
Explanation:
The given vertices of the original polygon ABCDE are:
A(-3, 3)
B(-3, 6)
C(1, 6)
D(1, 3)
E(-1, 1)
The given vertices of the image polygon A' B' C' D' E' are:
A'(-5, 3)
B'(-5, 6)
C'(-9, 6)
D'(-9, 3)
E'(-7, 1)
Comparing the coordinates of the original polygon ABCDE and its image polygon A' B' C' D' E', we can see that the y-coordinates are negated, while the x-coordinates remain the same. This indicates that the reflection is happening along the x-axis, as it is the line that reverses the y-coordinates while keeping the x-coordinates unchanged.
Therefore, the correct line of reflection is the x-axis, as shown by option C. Reflection across the x-axis.
Double-check this answer i wrote.
Destiny's mother started a college fund when Destiny was born. She deposited $9,300 into a CD (certicate of deposit) that yields an interest rate of 0.46%
compounded annually. How much money will the CD be worth when Destiny turns 16 years old?
Answer:
Step-by-step explanation:
$10,008.61
What is the power of the hypothesis test, using the decision rule given above, if the population mean amount of mercury is 11.5 micrograms per ounce? Give your answer to 4 decimal places.
The true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.
In hypothesis testing, the power of a test refers to the probability of correctly rejecting a false null hypothesis.
To calculate the power of a test, we need to know the significance level of the test, the sample size, the effect size, and the variance of the population.
Additionally, we need to know the specific hypothesis being tested, as the decision rule and power calculation depend on the null and alternative hypotheses.
A hypothesis test for the population mean amount of mercury in a certain type of fish.
Test whether the mean amount of mercury is different from 11.5 micrograms per ounce, using a two-tailed test at a significance level of 0.05.
If the sample size is 100, the effect size is 0.5, and the population variance is 4, then the power of the test is approximately 0.7629.
This means that if the true population mean amount of mercury is actually 12 micrograms per ounce (which is a difference of 0.5 from the null hypothesis value of 11.5), then the test has a 76.29% chance of correctly rejecting the null hypothesis and concluding that the mean amount of mercury is different from 11.5 micrograms per ounce.
The hypothesis test, it is impossible to calculate the power.
It is essential to know the specific hypothesis being tested, as well as the details of the test, such as the sample size, effect size, and variance.
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will give brainliest to first answer
space 1 options:
-maximum
-minimum
space 2 options:
0
-2
6
1
space 3 options:
0
-2
6
1
Thus, the function has a minimum value of -2 at x = -1.
Explain about the maxima and minima of function:There are "hills and valleys" in functions, or points where their value reaches a minimum or maximum.
Locally, it may not be the lowest or maximum for the entire function.
An "Absolute" meaning "Global" maximum as well as minimum is the value at which the function has reached its maximum or minimum.There can be more than a local maximum or minimum, but there is only single global maximum (one and global minimum).Stated function:
g(x) = 2x² + 4x
Differentiate the function to find the critical points with respect to x.
g'(x) = 4x + 4 ...eq 1
Put g'(x) = 0
4x + 4 = 0
4(x + 1) = 0
x = - 1 (critical point)
Again Differentiate the function to check for maxima or minima:
g'(x) = 4x + 4
g''(x) = 4
g''(x) > 0 (minimum function)
At x = -1 , the function will be minimum.
Minimum value : Put x = -1 in function.
g(x) = 2(-1)² + 4(-1)
g(x) = 2 - 4
g(x) = -2
Thus, the function has a minimum value of -2 at x = -1.
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At a recent football game of 8,450 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Relish Chili
54 36 60
Based on the data in this sample, how many of the people in attendance would prefer chili on a hot dog?
5,070
3,380
2,986
2,084
Answer:3,380
Step-by-step explanation:
we need to apply cross-multiplication to the ratio of chili preferences in the sample (60) against the total attendance (8450). This gives us:
(60/150) = (x/8450)
where x is the number of people in attendance who would prefer chili on a hot dog.
Simplifying this equation, we get:
x = (60/150) * 8450x = 3,380
Given f(x) =-3x^2 - 2r
Find f(8)
Answer: f(8) = -208
Step-by-step explanation:
To solve, we will substitute 8 into the equation for x.
Given:
f(x) = -3x² - 2x
Substitute 8 for x:
f(8) = -3(8)² - 2(8)
Square:
f(8) = -3(64) - 2(8)
Multiply:
f(8) = -192 - 16
Subtract:
f(8) = -208
Laura and Rich have been approved for a $325,000, 15-year mortgage with an APR of 5.3%. Using the mortgage and interest formulas, complete the two-month amortization table.
First, let's calculate the monthly interest rate (i), which is the APR divided by 12 months:
i = APR / 12 months
i = 5.3% / 12
i = 0.00442 or 0.442%
Next, let's calculate the number of months (n) for the mortgage, which is 15 years multiplied by 12 months:
n = 15 years x 12 months/year
n = 180 months
Now, let's calculate the monthly payment (PMT) using the following formula:
PMT = P * i / [tex](1 - (1 + i)^(-n)[/tex])
where P is the principal amount, i is the monthly interest rate, and n is the number of months.
PMT = $325,000 * 0.00442 / (1 - [tex](1 + 0.00442)^(-180)[/tex]
PMT = $2,613.67 (rounded to the nearest cent)
Now, let's create the amortization table for the first two months:
Month | Payment | Interest | Principal | Remaining Balance
1 | $2,613.67 | $1,431.25 | $1,182.42 | $323,817.58
2 | $2,613.67 | $1,428.60 | $1,185.07 | $322,632.51
For each month, the Payment column shows the fixed monthly payment, the Interest column shows the calculated interest based on the remaining balance multiplied by the monthly interest rate, the Principal column shows the portion of the payment that goes towards reducing the principal, and the Remaining Balance column shows the remaining balance after subtracting the principal payment from the previous remaining balance.
The amortization table will continue in this manner for the remaining months until the mortgage is paid off.
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The interest and principal amounts for the first payment are:
Interest = $325,000 * 0.0044167 = $1,426.25
Principal = $2,549.67 - $1,426.25 = $1,123.42
Balance = $325,000 - $1,123.42 = $323,876.58
For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:
Interest = $323,876.58 * 0.0044167 = $1,420.47
Principal = $2,549.67 - $1,420.47 = $1,129.20
Balance = $323,876.58 - $1,129.20 = $322,747.38
To complete the two-month amortization table, we need to calculate the monthly payment, as well as the principal and interest amounts for each payment.
The formula for calculating a fixed-rate mortgage payment is:
[tex]Payment = P * r * (1 + r)^n / [(1 + r)^n - 1][/tex]
Where:
P = Principal amount borrowed
r = Monthly interest rate
n = Total number of payments
First, let's calculate the monthly interest rate.
Since the APR is an annual rate, we need to divide it by 12 to get the monthly rate:
Monthly interest rate = 5.3% / 12 = 0.0044167
Next, we need to calculate the total number of payments.
Since this is a 15-year mortgage, and we're completing a two-month amortization table, the total number of payments is:
Total number of payments = 15 years * 12 months per year = 180
Number of payments for two months = 2
Now we can plug these values into the formula to calculate the monthly payment:
Payment = [tex]$325,000 * 0.0044167 * (1 + 0.0044167)^180 / [(1 + 0.0044167)^180 - 1][/tex]
= $2,549.67
So the monthly payment is $2,549.67
Now we can use this value to complete the two-month amortization table:
Payment Interest Principal Balance
Month 1 $1,426.25 $1,123.42 $323,876.58
Month 2 $1,420.47 $1,129.20 $322,747.38
To calculate the interest and principal amounts for each payment, we use the following formulas:
Interest = Balance * Monthly interest rate
Principal = Payment - Interest
Balance = Balance - Principal
We start with the initial balance of $325,000 and apply the formulas for each payment.
The interest and principal amounts for the first payment are:
Interest = $325,000 * 0.0044167 = $1,426.25
Principal = $2,549.67 - $1,426.25 = $1,123.42
Balance = $325,000 - $1,123.42 = $323,876.58
For the second payment, we start with the new balance of $323,876.58 and apply the formulas again:
Interest = $323,876.58 * 0.0044167 = $1,420.47
Principal = $2,549.67 - $1,420.47 = $1,129.20
Balance = $323,876.58 - $1,129.20 = $322,747.38
And so on, for each subsequent payment.
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x2 − 12x + 49 = 22.
Which equation has the same solution(s) as the given equation?
M. (x − 6)2 = 9
P. (x − 7)2 = 22
R. (x + 7)2 = 4.7
S. (x − 12)2 = −27
By quadratic formula the equation that has the same solution(s) as X² − 12x + 49 = 22 is M. (x − 6)² = 9 since it has solutions x=3 and x=9 which are also solutions to X² − 12x + 49 = 22
quadratic formula defined?The quadratic equation ax² + bx + c = 0 can be resolved using the quadratic formula.
that uses the constants (a, b, c) and the numerical coefficients.
When factoring cannot be utilized to solve the quadratic expressions, this approach of solving a quadratic equation is typically used.
x = √(b² - 4ac) / (-b √(b²) / (2a)
We must solve each of the preceding equations to determine which one has the same solution(s) as X²- 12x + 49 = 22 in order to determine which equation has the same solution(s) as X²- 12x + 49 = 22.
Let's start by figuring out X²- 12x + 49 = 22:
X² − 12x + 49 = 22
X² − 12x + 27 = 0
The quadratic formula can then be used to find the value of x:
x = √(b² - 4ac) / (-b√(b²) / (2a)
where a=1; b=-12; and c=27.
x = (-(-12) ±√((-12)² - 4(1)(27))) / (2(1))
x = (12 ±√(144 - 108)) / 2
x = (12 √(36))/ 2
x = (12 6) / 2
x = 6,3
So x = 6,3 is the answer to the equation X²- 12x + 49 = 22.
Let's now resolve each of the provided equations:
M. (x − 6)² = 9 (x -6)² -9=0
(x-6+3)(x-6-3)=0
(x-3)(x-9)=0, where x=3 or x=9
P. (x − 7)² = 22 (x-7)²-22=0
(x-7+√(22))=0
(x=7+√(22))
or (x=7-√(22))
R. (x + 7)² = 4.7 (x+7)²-4.7=0
(x+7+√(4.7))(x+7-√(4.7))=0
No effective remedies
S. (x − 12)²= −27 (x-12)²+27=0
No effective remedies
Therefore, the equation that has the same solution(s) as X² − 12x + 49 = 22 is M. (x − 6)² = 9
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The point p has a value of 2 and is represented on the top number line with a point. All that is known about point q is that |q| = 5. Using the top number line, locate p + q and p + (-q)
Using the top number line, p + q and p + (-q) can be located as shown in the attached image.
How to locate points on a number line?A number line is a line on which numbers are marked at intervals, used to illustrate simple numerical operations. It is also a pictorial representation of the real numbers.
Since point p has a value of 2 and point q has |q| = 5. We can say:
p + q = 2 + 5 = 7
p + (-q) = 2 + (-5) = -3
Therefore, using the top number line, we can then locate p + q and p + (-q) with their calculated values (Check the green dot in the attached image).
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Complete Question
Check the attached image
calculate a lower confidence bound using a confidence level of 99% for the percentage of all such homes that have electrical/environmental problems.
With a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.
To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have electrical/environmental problems, we need to have a sample of data on this issue. Let's assume that we have a random sample of 100 homes, and 20 of them were found to have electrical/environmental problems.
To calculate the lower confidence bound, we can use the formula:
Lower bound = p - zα/2 * sqrt(p * (1-p) / n)
where:
p = proportion of homes in the sample that have electrical/environmental problems = 20/100 = 0.2
zα/2 = z-score for the given confidence level of 99% = 2.576 (obtained from a standard normal distribution table or calculator)
n = sample size = 100
Plugging in these values, we get:
Lower bound = 0.2 - 2.576 * sqrt(0.2 * 0.8 / 100) = 0.083
Therefore, with a 99% confidence level, we can say that the true proportion of all homes that have electrical/environmental problems is at least 8.3%.
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This means we can be 99% confident that the true percentage of all homes with electrical/environmental problems is
at least 17.5%.
To calculate a lower confidence bound using a confidence level of 99% for the percentage of all homes that have
electrical/environmental problems, you would need a sample of homes and the number of homes in the sample that
have such problems. Using this information, you could calculate the sample proportion (p-hat) of homes with
electrical/environmental problems.
Then, using a formula or calculator, you could find the lower confidence bound by subtracting the margin of error (ME)
from the sample proportion.
The margin of error can be calculated using the sample proportion, sample size, and the chosen confidence level (in
this case, 99%).
For example, if the sample proportion is 0.25 and the sample size is 100, the margin of error would be 0.075 and the
lower confidence bound would be 0.175 (0.25 - 0.075).
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A candle is in the shape of a cylinder. The candle has a diameter of 3. 5 inches and a height of h inches. Which equation can be used to find V, the volume of this candle in cubic inches?
The volume of the candle is,⇒ V = 31.4 in³.What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.Given that;A candle in the shape of a cylinder has the dimensions shown, in inches.And, Diameter of candle = 5 in.Height of candle = 8 in.We know that;Volume of cylinder = πr²hHence, We get;The volume of the candle is,⇒ V = 3.14 × (5/2)² × 8⇒ V = 3.14 × 10⇒ V = 31.4 in³.Thus, The volume of the candle is,⇒ V = 31.4 in³.
What type of triangle 38, 38, and 104
Answer:
A triangle with side lengths of 38, 38, and 104 is an isosceles triangle. This is because it has two sides of equal length (the two sides that are both 38 units long).
Step-by-step explanation:
a hose fills hot tub at 4.6 gallons per minute. how many hours will it take to fill a 440-gallon hot tub?
It will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute
Assuming that the filling rate of the hose is constant, we can use the formula:
time = volume / rate
where time is the time taken to fill the hot tub, volume is the volume of the hot tub (440 gallons), and rate is the filling rate of the hose (4.6 gallons per minute).
Substituting the values, we get:
time = 440 / 4.6
which simplifies to:
time = 95.65 minutes
To convert minutes to hours, we divide by 60 (since there are 60 minutes in an hour):
time = 95.65 / 60
which simplifies to:
time = 1.59 hours
Therefore, it will take approximately 1.59 hours to fill the hot tub with a hose that has a filling rate of 4.6 gallons per minute.
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It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.
To determine how many hours follow these steps:
First, we need to find out how many minutes it takes to fill the hot tub.
Divide the total volume of the hot tub (440 gallons) by the rate at which the hose fills (4.6 gallons per minute):
440 gallons ÷ 4.6 gallons/minute = 95.65 minutes
Now, we need to convert the minutes into hours.
Since there are 60 minutes in an hour, divide the minutes by 60:
95.65 minutes ÷ 60 minutes/hour = 1.594 hours
It will take approximately 1.594 hours to fill a 440-gallon hot tub with a hose that fills at a rate of 4.6 gallons per minute.
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which of the following statement is not true of unnormalized data?a. unnormalized data is raw data.b. unnormalized data is related data.c. unnormalized data might contain redundant data.d. unnormalized data is multivalued data.
The statement that is not true of unnormalized data is option (d) unnormalized data is multivalued data.
Unnormalized data refers to raw data that has not been organized or processed in any way. It may contain redundancies, inconsistencies, and other issues that make it difficult to work with. However, it does not necessarily involve multivalued data.
Multivalued data refers to data that has multiple values for a single attribute. For example, if a customer can have multiple phone numbers, that data would be considered multivalued. Unnormalized data may or may not have multivalued data, depending on the nature of the data itself.
Therefore, the correct option is (d) unnormalized data is multivalued data
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A study has a 2 Ã 2 Ã 3 within-groups factorial design. This example has a total of ___ cell(s). Researchers would need to investigate ___ main effect(s), ___ two-way interaction(s), and ___ three-way interaction(s) in this study.
A study has a 2 Ã 2 Ã 3 within-groups factorial design. This example has a total of _12_ cell(s). Researchers would need to investigate _three__ main effect(s), _Three two-way interactions __ two-way interaction(s), and _ One three-way interaction__ three-way interaction(s) in this study.
a 2 x 2 x 3 within-groups factorial design, you have:
A total of 2 x 2 x 3 = 12 cells
Three main effects to investigate (one for each factor)
Three two-way interactions to investigate (AxB, AxC, and BxC)
4. One three-way interaction to investigate (AxBxC)
So, in this study, there are 12 cells, researchers would need to investigate 3 main effects, 3 two-way interactions, and 1 three-way interaction.
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Write a division expresion that has the same value as 51. 2 divided by 6. 4 but is easier to use to find the value. Then, find the value using long division
The value of 51. 2 divided by 6. 4 using long division is 8.0
To find the value of 512 divided by 64, we can use long division. We start by dividing 5 (the first digit of 512) by 6 (the first digit of 64). Since 5 is less than 6, we bring down the next digit (1) to form the new dividend, 51. We then add a decimal point to the quotient and bring down the next digit (2) to form 512.
We repeat the process of dividing 51 by 6, which gives us 8 with a remainder of 3. We write the quotient (8) above the next digit of the dividend (2) and bring down the next digit (0) to form the new dividend, 30. We continue this process until we have brought down all the digits of the dividend.
At the end of the process, we get a quotient of 8.0, which is the value of our original expression, 51.2 divided by 6.4.
Therefore, 512 divided by 64 is equal to 8.0.
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A use case description documents (among other things) ____.
A. a description of alternative courses of action
B. post conditions
C. preconditions
D. assumptions
A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C. preconditions. These elements help provide a clear understanding of how a system should interact with its users and the expected outcomes.
A document can be defined as a form of information that might be useful to a user or set of users1. It can be either digital or nondigital1. Different methods are used to store digital and non-digital documents
There are different types of documents such as job descriptions2, and project descriptions. and technical descriptions5.
A use case description documents (among other things) A. a description of alternative courses of action, B. postconditions, and C.
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What is the sum and the product of x^2-9x+8
The sum of the roots of x² - 9x + 8 is 9. The product of the roots of x² - 9x + 8 is 8.
What is quadratic equation?A quadratic equation is a second-degree polynomial equation in one variable, typically written in the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.
According to question:The expression x² - 9x + 8 can be factored as follows:
x² - 9x + 8 = (x - 1)(x - 8)
To check that this factorization is correct, you can expand the expression using the distributive property:
(x - 1)(x - 8) = x² - 8x - x + 8 = x² - 9x + 8
So the factorization is indeed correct.
The sum of the roots of the quadratic equation ax² + bx + c = 0 is given by -b/a, where a, b, and c are the coefficients of the equation. In this case, a = 1, b = -9, and c = 8, so the sum of the roots is:
-sum of roots = -b/a = -(-9)/1 = 9
Therefore, the sum of the roots of x² - 9x + 8 is 9.
The product of the roots of the quadratic equation ax² + bx + c = 0 is given by c/a. In this case, c = 8 and a = 1, so the product of the roots is:
product of roots = c/a = 8/1 = 8
Therefore, the product of the roots of x² - 9x + 8 is 8.
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number 1 i need help with please
The volume of the cube is 1.82 in³
How to find the volume of the cube?We know that the formula for the area of the cube, as a function of the volume, is:
A = 326*V^(2/3)
Solving that equation for V, we will get.
V = (A/326)^(3/2)
Then the volume of a cube whose surface area is A = 486 square inches is:
V = (486 in²/326)^(3/2)
V = 1.82 in³
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an engineer has designed a valve that will regulate water pressure on an automobile engine. the valve was tested on 130 engines and the mean pressure was 5.9 lbs/square inch. assume the standard deviation is known to be 1 . if the valve was designed to produce a mean pressure of 5.8 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve performs above the specifications? state the null and alternative hypotheses for the above scenario.
Here the p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.
We have to evaluate null and alternative hypotheses for the scenario .
In this scenario, the null hypothesis is
H0: μ = 5.8
here
μ = true mean pressure produced by the valve.
Now for the alternative hypothesis is
HA: μ > 5.8
here
μ = true mean pressure produced by the valve.
Therefore to determine if there is sufficient observation at the 0.05 level that the valve performs above specifications,
Here we can utilize a one-tailed z-test with
α = 0.05
Then, test statistic can be evaluated as
z = (X' - μ) / (σ / √n)
where:
X' = sample mean
μ = hypothesized value concerning the population mean
σ = population standard deviation
n = sample size
Substituting in our values, we get:
z = (5.9 - 5.8) / (1 / √130) = 1.8856
Now utilizing a z-table we can evaluate that the p-value associated with this test statistic is approximately 0.0292.
Since this p-value is less than the significance level of 0.05, we can reject the null hypothesis and conclude that there is sufficient evidence at the 0.05 level that the valve performs above specifications.
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if the median of 127 numbers is 35, which of the following must be true? i) at least 64 of the numbers are greater than or equal to 35 ii) at least 64 of the numbers are smaller than 35 iii) at most 64 numbers are greater than or equal to 35
Answer:
Option i) At least 64 of the numbers are greater than or equal to 35 must be true
Since the median is 35, we know that there are 63 numbers greater than 35 and 63 numbers smaller than 35. However, since there is an odd number of total numbers (127), the median itself must be included in one of these groups. Therefore, there are at least 64 numbers that are greater than or equal to 35.
C an someone show me step by step how to do this and correctly please
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
I need the answer now
please help
The volume of the solid is 761.97 in².
The mistake the student made is that the student did not subtract the square of the radius of the inner hollow cylinder from the square of the radius of the main cylinder.
How to find the volume of the solid?
The volume of the solid can be found by adding the volume of hollow cylinder and the volume of the cone. That is:
Volume of solid = volume of hollow cylinder + volume of the cone
Volume of solid = π(R²-r²)H + 1/3πR²h
where R = 8/2 = 4 in, r = 2 in, H = 18 in and h = 5 in
Volume of solid = [3.14 * (4²-2²) * 18] + [1/3 * 3.14 * 4² * 5]
Volume of solid = 678.24 + 83.73
Volume of solid = 761.97 in²
The mistake the student made is that the student did not subtract the square of the radius of the inner hollow cylinder from the square of the radius of the main cylinder.
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My apologies about the poor camera quality
The quadratic equation in the given graph is:
y = -3(x - 1)^2 + 4
How to write the quadratic.
Look at the vertex, is it at (1, 4), then we can write the general quadratic equation in the vertex form (with a leading coefficient a) as follows:
y = a(x - 1)^2 + 4
Now the function passes through (0, 1) then we can replace these values in the equation above to get.
1 = a(0 - 1)^2 + 4
1 = a + 4
1 - 4 = a
-3 =a
The quadratic equation is:
y = -3(x - 1)^2 + 4
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jim tosses a fair coin to decide whether his next vacation will be in hawaii or alaska. if it is a head, jim visits hawaii, or else he decides to visit alaska. if in hawaii, jim surfs during the vacation with a probability of 0.9. if in alaska, jim is going to surf in the ocean with probability 0.1 only. given that we know that jim went on surf- ing during the vacation, what is the conditional probability that his vacation was in alaska?
the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation is 0.1, or 10%.
Let A be the event that Jim's vacation was in Alaska, and let S be the event that Jim went surfing during the vacation. We want to find P(A|S), the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation.
By Bayes' theorem, we have:
P(A|S) = P(S|A) * P(A) / P(S)
We can calculate each term as follows:
P(S|A) = 0.1: the probability that Jim went surfing during the vacation given that he was in Alaska.
P(A) = 0.5: the probability that Jim's vacation was in Alaska, since he tosses a fair coin to decide between Hawaii and Alaska.
P(S) = P(S|A) * P(A) + P(S|H) * P(H) = 0.1 * 0.5 + 0.9 * 0.5 = 0.5: the total probability of Jim going surfing during the vacation, since he either went surfing in Alaska with probability 0.1 or went surfing in Hawaii with probability 0.9.
Therefore, we have:
P(A|S) = P(S|A) * P(A) / P(S) = 0.1 * 0.5 / 0.5 = 0.1
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A couple gets financing for 80% of the $150,000 purchase price of a house at the rate of 6% on the monthly unpaid balance. Use the table provided to find the total amount paid to the finance company if the loan is repaid in 40 years. A 5-column table with 4 rows titled Monthly Payments per 1000 dollars of mortgage. Column 1 is labeled Interest Rate (percent) with entries 5, 5.5, 6, 6.5. Column 2 is labeled 10 Years with entries 10.61, 10.86, 11.11, 11.36. Column 3 is labeled 20 years with entries 6.60, 6.88, 7.17, 7.46. Column 4 is labeled 30 years with entries 5.37, 5.68, 6.00, 6.33. Column 5 is labeled 40 years with entries 4.83, 5.16, 5.51, 5.86. a. $231,948.00 c. $317,376.00 b. $289,005.00 d. $141,509.00
The total amount paid to the finance company if the loan is repaid in 40 years is $317,376.00 (option c).
First, we need to find out how much money the couple borrowed. Since they got financing for 80% of the $150,000 purchase price, they borrowed $120,000 ($150,000 x 0.8 = $120,000).
Next, we need to find the monthly interest rate. Since the interest rate is 6% per year, the monthly interest rate is 0.06/12 = 0.005.
Now we can use the table to find the monthly payment per $1000 of mortgage for a 40-year loan with a 6% interest rate. Looking at the fifth column of the table, we find the entry that corresponds to a 6% interest rate and a 40-year loan, which is 5.86. This means that for each $1000 borrowed, the monthly payment is $5.86.
To find the monthly payment for the couple's $120,000 loan, we multiply the monthly payment per $1000 by 120 (since they borrowed $120,000). So the monthly payment is 5.86 x 120 = $703.20.
Finally, we need to calculate the total amount paid to the finance company over the 40-year period. Since the couple will make 12 payments per year for 40 years, the total number of payments will be 12 x 40 = 480. So the total amount paid will be the monthly payment ($703.20) multiplied by the total number of payments (480). This gives us a total of $317,376.
Therefore, the correct option is (c).
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A water sprinkler sends water out in a circular pattern. What is the area formed by the water pattern if it can spray out 21 feet in any direction? Use 3.14 for r.
If "water-sprinkler" sends out water 21 feet in any direction in circular pattern, then the area formed by water pattern is 1384.74 feet².
If the sprinkler can spray water out 21 feet in any direction, then the radius of the circular pattern formed by the water is 21 feet.
The formula for area of circular pattern is : A = πr², where 'r" is = radius of the circle.
Substituting the radius of circular pattern as 21 feet,
We get,
⇒A = πr² = 3.14 × 21 × 21 = 1384.74 ft².
Therefore, the area formed by the water pattern is 1384.74 square feet.
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A car has 12,500 miles on its odometer. Say the car is driven an average of 40 miles per day. Choose the model that expresses the number of miles N that will be on its odometer after x days Choose the correct answer below ( A. N(x)=12.500x + 40 OB. N(x)--40x + 12,500 OC. Nx)-40-12,500 O D. N(x)-40x+12,500
The correct answer is B.
N(x) = 40x + 12,500.
This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.
Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.
Based on the given information, the correct answer is B.
N(x) = 40x + 12,500
This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.
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The correct answer is B.N(x) = 40x + 12,500.
This is because we know that the car is driven an average of 40 miles per day, so after x days, it will have traveled a total of 40x miles.
Adding this to the initial 12,500 miles on the odometer gives us the expression N(x) = 40x + 12,500 for the total number of miles on the car's odometer after x days.
Based on the given information, the correct answer is B.
N(x) = 40x + 12,500
This model represents the total number of miles (N) on the odometer after x days, taking into account the initial 12,500 miles and the average daily increase of 40 miles.
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annie sold her camers for $250 making a loss of 12% what price was the camera when annie bought it? round your answer to the nearest cent
Let's assume that the original price of the camera is x.
Since Annie sold the camera at a loss of 12%, the selling price is 88% of the original price.
So we can set up the equation:
0.88x = $250
To solve for x, we can divide both sides by 0.88:
x = $250 ÷ 0.88
x = $284.09
Therefore, the original price of the camera was $284.09.
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The values of the positive intergers a and b is 2 and 3 respectively and the value of 2a+3b is 13.
What is algebraic expression?An algebraic expression are the expression which consist the variables, coefficients of variables and constants. In the given problem, a and b are positive integers. The given expression in the problem is: ^2b^3=108.
Let us the hit and trial method to make both the equation equal. For a=1 and b= 1 the expression will be equal to 1. For a =2 and b=3,
(2)^2(3)^3 = 108
(4)(27) = 108
108 = 108
Here, left hand side of the expression is equal to the right hand side of the expression for a =2 and b=3. Thus the value of a and b are,
a = 2
b = 3
The value of the expression we have to find is, 2a+3b. Put the values of a and b in the above expression, we get,
2a+3b = 2^(2)+3^(3)
2a+3b = 4+9
2a+3b = 13
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You deposit $200 in an account that earns simple interest at an annual rate of 5.2%. How much money is in the account after 5 years?
The money in the account will be $252.
For simple interest, use the formula:
I = Prt
where I stands for interest earned, P for principle (amount paid in the beginning), r for yearly interest rate (in decimal form), and t for the time in years.
P equals $200, r equals 0.052, and t equals 5. With these values entered into the formula, we obtain:
I = Prt = ($200)(0.052)(5) = $52
The account will thus have $52 in interest after 5 years. After five years, we add the interest to the principal to determine the account's total balance:
Total = $200 + $52 = $252
Therefore, after five years, the account will have $252.
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