In the diagram to the​ right, GKNM ~ VRPT.
Find the value of x. Give the scale factor of the left polygon to the right polygon.

In The Diagram To The Right, GKNM ~ VRPT.Find The Value Of X. Give The Scale Factor Of The Left Polygon

Answers

Answer 1

The value of x is 2.8 The scale factor of left polygon to the right polygon, GKNM to RPTV is 1.4.

Since the two polygons GKNM and RPTV are similar, their corresponding sides are proportional. Thus, we can set up the following proportion

(GK + KN + NM)/GK = (RP + PT + TV + VR)/RP

Plugging in the given values and simplifying, we get

(8.4 + 3x - 2 + 4)/8.4 = (x + 5 + 3 + 3 + 6.3)/(x + 5)

15.4/(3x + 2.4) = (x + 17.3)/(x + 5)

Cross-multiplying and solving for x, we get

x = 2.8

To find the scale factor of GKNM to RPTV, we can divide the corresponding side lengths

(GK + KN + NM)/(RP + PT + TV + VR) = (8.4 + 3(2.8) - 2 + 4)/(2.8 + 5 + 3 + 3 + 6.3) = 1.4

Therefore, the scale factor of GKNM to RPTV is 1.4.

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Related Questions

How many hours is 1,000,00 minutes

Answers

Answer:

16.6666 hours.

Step-by-step explanation:

This conversion of 1,000 minutes to hours has been calculated by multiplying 1,000 minutes by 0.0166 and the result is 16.6666 hours.

Answer:

16,666.67 hours

Step-by-step explanation:

A minute is a unit of time equal to 60 seconds.

Resume the totat revenue from the sale of them is given by R(x) * 25 1n (6x + 1), while the total cost to produce x items is C(x)=ſ. Find the approximate number of items that should be manufactured so that profit, RIX-C) is maximum G A 143 Rems OB. 84 items C. 47 items OD 114 items

Answers

The approximate number of items that should be manufactured so that the profit, P(x) = R(x) - C(x), is maximum is 47 items (option C).

To find the approximate number of items that should be manufactured to maximize profit, we need to first find the profit function P(x) by subtracting the total cost, C(x), from the total revenue, R(x). Then, we need to find the critical points of P(x) and determine which one corresponds to the maximum profit.

process of finding profit:

Step 1: Find the profit function P(x) = R(x) - C(x)
Given R(x) = 25 ln(6x + 1) and C(x) = ∫x, let's find P(x):
P(x) = R(x) - C(x)
P(x) = 25 ln(6x + 1) - ∫x
Step 2: Find the critical points of P(x)
To find the critical points, we need to take the derivative of P(x) and set it equal to 0:
P'(x) = d/dx [25 ln(6x + 1) - ∫x]
Since the derivative of ln(6x + 1) is (6/(6x + 1)), and the derivative of ∫x is x:
P'(x) = 25 [tex]\times[/tex] (6/(6x + 1)) - x
Now, set P'(x) = 0 and solve for x:
25 [tex]\times[/tex] (6/(6x + 1)) - x = 0
Step 3: Determine which critical point corresponds to the maximum profit
The approximate number of items that should be manufactured so that the profit, P(x) = R(x) - C(x), is maximum is 47 items (option C).

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Find the error & explain why it is wrong:
megan solved the following problem. what did she do wrong?
what is (f - g)(2)?
f(x) = 3x2 – 2x + 4
g(x) = x2 – 5x + 2

Answers

The value of (f-g)(2) is 16, provided that Megan has made no mistakes in the calculation.

Find the error in the given problem solved by Megan?

The problem asks us to compute the value of (f - g)(2) where f(x) = 3x^2 - 2x + 4 and g(x) = x^2 - 5x + 2.

The notation (f - g)(2) means that we need to subtract g(x) from f(x) and then evaluate the result at x = 2. We can do this as follows:

(f - g)(x) = f(x) - g(x) = (3x^2 - 2x + 4) - (x^2 - 5x + 2) = 2x^2 + 3x + 2

Substituting x = 2, we get:

(f - g)(2) = 2(2)^2 + 3(2) + 2 = 16

Therefore, the value of (f - g)(2) is 16.

It's worth noting that the problem statement mentions "what did she do wrong?" without providing any context or information about what Megan did or didn't do. So, it's not possible to identify any error in Megan's solution based on the given information. However, based on the correct computation above, we can be sure that (f - g)(2) is indeed equal to 16.

In other words, it can be described as,

The error in Megan's solution is not clear from the given statement. However, it seems that she may have made an error while computing (f-g)(2).

To compute (f-g)(2), we need to subtract g(2) from f(2) as follows:

f(2) = 3(2)^2 - 2(2) + 4 = 12

g(2) = (2)^2 - 5(2) + 2 = -4

Therefore, (f-g)(2) = f(2) - g(2) = 12 - (-4) = 16. is the final conclusion.

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Find f'(4) for f(x) 8/In(3x^2) Round to 3 decimal places, if necessary.

Answers

To find f'(4), we need to take the derivative of f(x) with respect to x and then evaluate it at x=4. Using the chain rule, we get:
f'(x) = -16x/(ln(3x^2))^2

So, f'(4) = -16(4)/(ln(3(4)^2))^2 = -64/(ln(48))^2

Rounding to 3 decimal places, we get f'(4) = -0.019.
To find f'(4) for f(x) = 8/ln(3x^2), we first need to differentiate f(x) with respect to x. We will use the quotient rule and the chain rule for this purpose.

The quotient rule states: (u/v)' = (u'v - uv')/v^2, where u = 8 and v = ln(3x^2).

Now, differentiate u and v with respect to x:
u' = 0 (since 8 is a constant)
v' = d(ln(3x^2))/dx = (1/(3x^2)) * d(3x^2)/dx (using chain rule)

Now, differentiate 3x^2 with respect to x:
d(3x^2)/dx = 6x

So, v' = (1/(3x^2)) * (6x) = 2/x

Now, apply the quotient rule for f'(x):
f'(x) = (0 - 8 * (2/x))/(ln(3x^2))^2 = -16/(x * (ln(3x^2))^2)

Now, plug in x = 4 to find f'(4):
f'(4) = -16/(4 * (ln(3*(4^2)))^2) = -16/(4 * (ln(48))^2)

Rounded to 3 decimal places, f'(4) ≈ -0.171.

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3. The scale of a room in a blueprint is 2 inches : 1 foot. A window in the same blueprint is 12 inches. Complete the table. Blueprint Length (in.) Actual Length (ft) a. How long is the actual window? 2 1 4 3 4 10 12 5 6 b. A mantel in the room has an actual width of 8 feet. What is the width of the mantel in the blueprint?​

Answers

Therefor, the length of mantel in blueprint is > 30 ft

width of the mantel in the blueprint 8ft×2inc/1ft=16inch

what is width?

The term "width" refers to the length from side to side of anything. For instance, the shorter side of a rectangle would be the width.

we know that

[scale]=[blueprint]/[actual]-------> [actual]=[blueprint]/[scale]

[scale]=3/5 in/ft

for [wall blueprint]=18 in

[wall actual]=[wall blueprint]/[scale]-------> 18/(3/5)----> 30 ft

Part A)

the actual wall is 30 ft  long

Part B) window has actual width of 2.5 ft

[ window blueprint]=[scale]*[actual window]-----> (3/5)*2.5----> 1.5 in

the width of the window in the blueprint is 1.5 in

Part C) Complete the table

For [blueprint length]=4 in

[actual length]=[blueprint length]/[scale]-------> 4/(3/5)----> 20/3 ft

For [blueprint length]=5 in

[actual length]=[blueprint length]/[scale]-------> 5/(3/5)----> 25/3 ft

For [blueprint length]=6 in

[actual length]=[blueprint length]/[scale]-------> 6/(3/5)----> 30/3=10 ft

For [blueprint length]=7 in

[actual length]=[blueprint length]/[scale]-------> 7/(3/5)----> 35/3 ft

For [actual length]=6 ft

[blueprint length]=[actual length]*[scale]-------> 6*(3/5)----> 18/5 in

For [actual length]=7 ft

[blueprint length]=[actual length]*[scale]-------> 7*(3/5)----> 21/5 in

For [actual length]=8 ft

[blueprint length]=[actual length]*[scale]-------> 8*(3/5)----> 24/5 in

For [actual length]=9 ft

[blueprint length]=[actual length]*[scale]-------> 9*(3/5)----> 27/5 in

B) width of the mantel in the blueprint 8ft×2inc/1ft=16inch

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Compound Interest:
In March 2003, Natalie invested $800 in an account that earns 4. 8% interest compounded monthly. After 5 years, she withdrew all the money and reinvested it in a new account that earns 6% interest compounded semiannually. Assuming there were no other deposits or withdrawals, how much total interest will she have earned by March 2025?

I NEED HELP, CAN SOMEONE HELP ME, PLEASE?

Answers

Natalie will have earned a total of $488.97 in interest by March 2025.

"What is compound interest formula?

To solve this problem, we can use the formula for compound interest:

A = [tex]P(1 + r/n)^(nt)[/tex]

where A is the total amount, P is the principal amount, r is the annual interest rate as a decimal, n is the number of times the interest is compounded per year, and t is the time in years.

First, let's find out how much money Natalie will have in her first account after 5 years:

P = $800

r = 4.8% per year = 0.048

n = 12 (compounded monthly)

t = 5 years

A = [tex]800(1 + 0.048/12)^(12*5)[/tex]

A = $995.08

So after 5 years, Natalie will have $995.08 in her first account.

Next, let's find out how much money Natalie will have in her second account:

P = $995.08

r = 6% per year = 0.06

n = 2 (compounded semiannually)

t = 5 years

A = [tex]995.08(1 + 0.06/2)^(2*5)[/tex]

A = $1,288.97

So after reinvesting her money in the second account, Natalie will have $1,288.97 after 5 years.

Finally, let's calculate the total interest earned:

Total interest = A - P

Total interest = $1,288.97 - $800

Total interest = $488.97

Therefore, Natalie will have earned a total of $488.97 in interest by March 2025.

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Tell whether the angles are adjacent or vertical. Then find the value of x. Please help with this question

Answers

Answers - adjacent angles, x = 63 degrees

Explanation

Adjacent angles share a side, vertical angles are across from each other so this is adjacent

This is a straight angle that includes these adjacent angles, a straight angle sum is 180 degrees.

180 - 117 = 63

X = 63 degrees
Answers - adjacent angles, × = 63 degrees

In the diagram shown, segments AE and CF are both perpendicular to DB.
DE=FB, AE=CF. Prove that ABCD is a parallelogram.

Answers

Answer:

Step-by-step explanation:

Given:- ABCD is a parallelogram, and AE and CF bisect ∠A and ∠C respectively. To prove:- AE∥CF Proof:- Since in a parallelogram, opposite angles are equal.

find the critical numbers of f(x)=4−5x/4 + x and classify any local extrema.

Answers

The function has a global maximum at the vertex (2/5, 41/25), and there are no local maxima or minima.

To find the critical numbers of the function f(x) = 4 - 5x/4 + x, we first need to find its derivative:

f'(x) = -5/4 + 1

f'(x) = -1/4

To find the critical numbers, we set f'(x) equal to zero and solve for x:

-1/4 = 0

This is never true, so there are no critical numbers for f(x).

Since there are no critical numbers, there are no local maxima or minima for the function. Instead, we can analyze the behavior of the function to determine if it has any extrema.

One way to do this is to examine the end behavior of the function. As x approaches positive or negative infinity, the leading term of the function is -5x/4, which dominates the constant term. Therefore, as x becomes large in either direction, the function approaches negative infinity. This suggests that the function has a global maximum at its vertex.

To find the vertex, we can complete the square:

f(x) = 4 - 5x/4 + x

[tex]f(x) = -(5/4)x^2 + x + 4[/tex]

[tex]f(x) = -(5/4)(x^2 - (4/5)x) + 4[/tex]

[tex]f(x) = -(5/4)(x - 2/5)^2 + 4 + (5/4)(2/5)^2\\f(x) = -(5/4)(x - 2/5)^2 + 41/25[/tex]

Therefore, the function has a global maximum at the vertex (2/5, 41/25), and there are no local maxima or minima.

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In an effort to eat healthier, Bridget is tracking her food intake by using an application on her phone. She records what she eats, and then the


application indicates how many calories she has consumed. One Monday, Bridget eats 10 medium strawberries and 8 vanilla wafer cookies as an


after-school snack. The caloric intake from these items is 192 calories. The next day, she eats 20 medium strawberries and 1 vanilla wafer cookie as an after-school snack. The caloric intake from these items is 99 calories.



a. Write a system of equations for this problem situation. Let S represent the number of calories in one strawberry and let W represent the number of calories in one vanilla wafer cookie.



The equation _____ represents the calories Bridget ate on Monday and the equation _____ represents the calories she ate the next day.



b. Solve the system of equations using the substitution method. Check your work.



The number of calories in each strawberry is ____


And the number of calories in each vanilla wafer cookie is ____. The solution is ____.



PLEASE HELP ME

Answers

The equation 10S + 8W = 192 represents the calories Bridget ate on Monday and the equation 20S + 1W = 99 represents the calories she ate the next day.

The number of calories in each strawberry is 4, and the number of calories in each vanilla wafer cookie is 19.

a. We have two equations for the two days, using S for the number of calories in a strawberry and W for the number of calories in a vanilla wafer cookie:

On Monday:
10S + 8W = 192

On Tuesday:
20S + 1W = 99

b. To solve the system of equations using the substitution method, first solve one of the equations for one of the variables. We'll choose the second equation and solve for W:

W = 99 - 20S

Now substitute this expression for W in the first equation:

10S + 8(99 - 20S) = 192

Expand and simplify:

10S + 792 - 160S = 192

Combine like terms:

-150S = -600

Now divide by -150:

S = 4

Now that we have the value for S, substitute it back into the expression for W:

W = 99 - 20(4)

W = 99 - 80

W = 19

So the number of calories in each strawberry is 4, and the number of calories in each vanilla wafer cookie is 19. The solution is (S, W) = (4, 19).

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Emily brought some homemade cookies for the school bake sale. The ingredients cost her $1.50 per cookie, but she sells them for a higher price at $3.00 per cookie. What is the percent markup per cookie?

Answers

The value of the calculated percent markup of the cookie is 100%

Finding the the percent markup per cookie

From the question, we have the following parameters that can be used in our computation:

The ingredients cost her $1.50 per cookieShe sells them for a higher price at $3.00 per cookie

The percent markup of the cookie is then calculated as

Percentage = (Selling price - cost price)/cost price

substitute the known values in the above equation, so, we have the following representation

Percentage = (3 - 1.5)/1.5

Evaluate

Percentage = 100%

Hence, the percent markup of the cookie is 100%

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What is -2(x + 12y - 5 - 17x - 16y + 4) simplified?

-40x + 8y + 2

28x + 8y +2

28x + 6y + 2

-28x - 8y + 2

Answers

Answer:

Step-by-step explanation:

First, we can simplify the expression inside the parentheses by combining like terms:

-2(x + 12y - 5 - 17x - 16y + 4) = -2(-16x - 4y - 1)

Next, we can distribute the -2 to each term inside the parentheses:

-2(-16x - 4y - 1) = 32x + 8y + 2

Therefore, -2(x + 12y - 5 - 17x - 16y + 4) simplified is 32x + 8y + 2.

The simplified expression is 32x + 8y + 2.

Simplification of an algebrai expression can be defined as the process of writing an expression in the most efficient and compact form without affecting the value of the original expression.

The process entails collecting like terms, which implies adding or subtracting terms in an expression.

Simplify the expression -2(x + 12y - 5 - 17x - 16y + 4).

First, let's distribute the -2 to each term inside the parentheses:

-2(x) + (-2)(12y) - (-2)(5) - (-2)(17x) - (-2)(16y) + (-2)(4)

Now we'll multiply: -2x - 24y + 10 + 34x + 32y - 8

Next, we'll combine like terms:

(-2x + 34x) + (-24y + 32y) + (10 - 8)

The result is 32x + 8y + 2

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Pedro is walking down the longest staircase ever, which contains 4000 steps. She


starts from the top and is walking down the staircase at 150 steps a minute. Hal is


walking up the staircase, starting at the bottom, at 80 steps a minute. After how


many minutes will they meet?

Answers

Pedro and Hal will walk 1800 steps staircase and meet after 25 minutes.

Pedro is walking down the longest staircase ever, which contains 4000 steps. She starts from the top and is walking down the staircase at 150 steps a minute. Hal is walking up the staircase, starting at the bottom, at 80 steps a minute. After how many minutes will they meet?

Let's assume that they will meet at point X, which is y steps away from the top and z steps away from the bottom. As Pedro is walking down the staircase, she will cover a distance of y steps, while Hal is walking up the staircase, he will cover a distance of (4000-z) steps.

The time taken by Pedro to cover a distance of y steps is y/150 minutes, while the time taken by Hal to cover a distance of (4000-z) steps is (4000-z)/80 minutes. Since they will meet at the same point X, we can set these two times equal to each other and solve for y and z.

y/150 = (4000-z)/80

Solving this equation, we get y = 1800 and z = 2200. This means that Pedro will have covered 1800 steps in y/150 = 12 minutes and Hal will have covered (4000-2200) = 1800 steps in (4000-2200)/80 = 25 minutes.

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Solve for the missing length and the other two angles in the triangle below.

Answers

By law of cosine, the triangle has a side of 1.348 units and two angles of 129.852° and 35.148°, respectively.

How to find missing lengths and angles in a triangle

In this problem we find the representation of a triangle, in which we must determine the value of a missing side and two missing angles. This can be done by law of cosine. First, find the missing side:

x = √(3² + 4² - 2 · 3 · 4 · cos 15°)

x = 1.348

Second, find the missing angles:

4² = 3² + 1.348² - 2 · 3 · 1.348 · cos α

cos α = - 0.641

α = 129.852°

β = 180° - 15° - 129.852°

β = 35.148°

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A line includes the points (0,-7) and (n, -8) has a slope of -1/6. What is the value of n?

Answers

Answer:

n = 6.

Step-by-step explanation:

The slope of the line = (y2 - y1) / (x2 - x1) where the 2 points are (x1, y1) and (x2, y2).

So, (-8 - (-7)) / (n - 0) = -1/6

-1/n = -1/6

n = 6.

expand and simplify(2w-3)3

Answers

Answer:

6w-9

Step-by-step explanation:

2w×3=6w

-3×3=-9

=6w-9

The box plot displays the number of push-ups completed by 9 students in a PE class.

A box plot uses a number line from 12 to 58 with tick marks every 2 units. The box extends from 27.5 to 42.5 on the number line. A line in the box is at 37. The lines outside the box end at 15 and 55. The graph is titled Push-Ups In PE and the line is labeled Number of Push-Ups.

Which of the following represents the value of the lower quartile of the data?

27.5
37
42.5
55

Answers

Given that 27.5 is the bottom end of the box, the lower quartile's value equation (Q1) must fall between 27.5 and 30. Hence, the appropriate response is 37.

Since, A mathematical equation links two statements and utilizes the equals sign (=) to indicate equality.

In algebra, an equation is a mathematical assertion that proves the equality of two mathematical expressions.

For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The logo and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.

Here, 25% of the data fall inside the lower quartile (Q1), which is represented by that number. Q1 is situated near the bottom of the box in the box plot.

According to the description, the box's boundary is at 30, and its size ranges from 27.5 to 42.5 on the number line. As a result, the median value of the middle 50% of the data is 37, with a range of 27.5 to 42.5.

There are some data points outside the middle 50% since the lines outside the box finish at 15 and 55.

Hence; 27.5 is the bottom end of the box, the lower quartile's value (Q1) must fall between 27.5 and 42.5.

Hence, the appropriate response is,

= 37

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what are the coefficients in the expression (2x+15)(9x-3) need it asap

Answers

Answer:

2x and 9x are the coefficients.

Step-by-step explanation:

In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series, or any expression; it is usually a number, but may be any expression (including variables such as a, b and c ).

FILL IN THE BLANK. Find the maximum and minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9. maximum value =_____ minimum value =_____

Answers

Maximum and Minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9.

The maximum value is 3

The minimum value is -3

To find the maximum and minimum values of f(x, y) = xy on the ellipse 3x² + y² = 9, follow these steps:

how to find maximum and minimum value:

1. Use the constraint equation (ellipse equation) to solve for one of the variables, either x or y.

Here, let's solve for y:
y² = 9 - 3x²
y = ±√(9 - 3x²)

2. Substitute y in the function f(x, y) with the expressions found in step 1:
f(x, y) = x(±√(9 - 3x²))

3. Differentiate f(x, y) with respect to x to find critical points (maximum or minimum):
f'(x, y) = ±(√(9 - 3x²) - (3x² / √(9 - 3x²)))

4. Set f'(x, y) = 0 and solve for x:
√(9 - 3x²) - (3x² / √(9 - 3x²)) = 0

5. Find the corresponding y values for the x values found in step 4 by substituting x back into the expressions found in step 1.

6. Evaluate f(x, y) at each critical point (x, y) found in steps 4 and 5 to determine the maximum and minimum values.

The maximum value of f(x, y) = xy on the ellipse 3x² + y² = 9 is 3, and the minimum value is -3.

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How many 4-digit numbers have the second digit even and the fourth digit at least twice the second digit?

Answers

There are 1350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.

To form a 4-digit number, we have 10 choices for each digit, except the first digit, which can't be 0. Hence, there are 9 choices for the first digit.

For the second digit, there are 5 even digits (0, 2, 4, 6, 8) to choose from.

For the third digit, there are 10 choices.

For the fourth digit, we can choose any of the even digits we picked for the second digit, or any of the larger odd digits 4, 6, 8.

Hence, the number of 4-digit numbers that meet the given criteria is

9 × 5 × 10 × 3 = 1350.

Therefore, there are 1,350 4-digit numbers that have the second digit even and the fourth digit at least twice the second digit.

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Volume question 5 of 5 the rectangle represents the base of a right rectangular prism. the height of the prism is 6 inches. what is the volume of the prism? 13 o a. 87.9 in o b. 105.8 in 3 3 in o c. 12.6 in 2 o d. 75.6 in 3 submit​

Answers

The volume of prism is 75.6 [tex]in^3[/tex]. The correct answer is option d,

We are given that the rectangle represents the base of a right rectangular prism and the height of the prism is 6 inches. To find the volume of the prism, we need to multiply the area of the rectangle by the height.

The area of the rectangle can be found by multiplying its length and width. However, we are not given any specific values for the length and width of the rectangle. Therefore, we cannot directly calculate its area.

Since we are given answer choices, we can use them to check which option gives the correct volume of the prism. We can start by assuming that the length, width, and height of the prism are integers, and then calculate the volume for each option until we find the one that matches.

Option a: 87.9 in^3 - This is not an integer, so we can eliminate this option.

Option b: 105.8 in^3 - This is not an integer, so we can eliminate this option.

Option c: 12.6 in^3 - This is too small, so we can eliminate this option.

Option d: 75.6 in^3 - To check if this is the correct answer, we can calculate the area of the rectangle by dividing the volume by the height.

Volume of the prism = area of rectangle x height

75.6 in^3 = (length x width) x 6 in

Length x width = 12.6 in^2

Now, we need to find two integers whose product is 12.6 in^2 and whose sum is 16 in (since the rectangle represents the base of a right rectangular prism). After some trial and error, we find that 3.15 in and 4 in satisfy these conditions.

Therefore, the length of the rectangle is 4 inches and the width is 3.15 inches.

Now, we can calculate the area of the rectangle by multiplying its length and width:

Area of rectangle = length x width = 4 in x 3.15 in = 12.6 in^2

Finally, we can calculate the volume of the prism:

Volume of prism = area of rectangle x height = 12.6 in^2 x 6 in = 75.6 in^3

Therefore, the correct answer is option d, 75.6 [tex]in^3[/tex].

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A company responsible for making gumballs found that their gumballs had an average diameter of 2. 21 cm and a standard deviation of 0. 01 cm. What is the percentage of gumballs that are within standard deviations of the mean?

Answers

Percentage of gumballs that are within standard deviations of the mean is 68% and have a diameter between 2.20 cm and 2.22 cm.

To find the percentage of gumballs that are within one standard deviation of the mean, we need to use the empirical rule, also known as the 68-95-99.7 rule. According to this rule, for a normal distribution:

Approximately 68% of the data falls within one standard deviation of the mean.Approximately 95% of the data falls within two standard deviations of the mean.Approximately 99.7% of the data falls within three standard deviations of the mean.

Here we want to find the percentage of gumballs that are within one standard deviation of the mean. So we can use the first part of the empirical rule and say that approximately 68% of the gumballs have a diameter between:

Mean - Standard deviation = 2.21 - 0.01 = 2.20 cm and Mean + Standard deviation = 2.21 + 0.01 = 2.22 cm

Therefore, approximately 68% of the gumballs have a diameter between 2.20 cm and 2.22 cm.

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Hannah has an offer from a credit card issuer for 0% APR for the first 30 days


and 12. 22% APR afterwards, compounded daily. What effective interest rate


is Hannah being offered?

Answers

To find the effective interest rate that Hannah is being offered, we need to take into account the compounding period, which is daily in this case. The effective annual interest rate (EAR) can be calculated using the formula:

EAR = (1 + APR/n)^n - 1

where APR is the annual percentage rate, and n is the number of compounding periods per year.

For the first 30 days, Hannah is offered a 0% APR, so the EAR for this period is simply 0.

After 30 days, Hannah is offered a 12.22% APR compounded daily, which means that there are 365 compounding periods per year. Therefore, the EAR for this period can be calculated as follows:

EAR = (1 + 0.1222/365)^365 - 1

   ≈ 0.1267

So the effective interest rate that Hannah is being offered is approximately 12.67%.

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If a point is randomly located on an interval (a, b) and if y denotes the location of the point, then y is assumed to have a uniform distribution over (a, b). a plant efficiency expert randomly selects a location along a 500-foot assembly line from which to observe the work habits of the workers on the line. what is the probability that the point she selects is:closer to the beginning of the line than to the end of the line

Answers

The probability that the point she selects is closer to the beginning of the line than to the end of the line is 0.5 or 50%.



If a point is randomly located on an interval (a, b), and y denotes the location of the point, then y is assumed to have a uniform distribution over (a, b). In this case, the interval is the assembly line of length 500 feet, where a is the beginning and b is the end of the line.

The question asks for the probability that the point she selects is closer to the beginning of the line than to the end of the line. For the point to be closer to the beginning, it must be located in the first half of the line, which is an interval of length 250 feet (500/2).

Since the point has a uniform distribution, the probability of the point being within any sub-interval is equal to the length of the sub-interval divided by the total length of the interval (500 feet).

So, the probability that the point she selects is closer to the beginning of the line than to the end of the line is the length of the first half (250 feet) divided by the total length (500 feet).

Probability = (Length of the first half) / (Total length)
Probability = (250 feet) / (500 feet)
Probability = 0.5 or 50%

There is a 50% chance that the place she chooses will be closer to the line's beginning than its finish.

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Recent studies show that the number of​ three-legged frogs in a particular area is increasing due to exposure to chemical pollutants. The first set of data reported in 2000 estimates a population of 5000​ three-legged frogs. Statistics show an annual increase of​ 15%. Let denote the number of​ three-legged frogs projected to inhabit this area in the year 2000N. How many​ three-legged frogs are projected to inhabit this area by​ 2009? Round to the nearest whole number

Answers

By 2009, it is projected that approximately 13,956 three-legged frogs will inhabit the area.

Recent studies have indicated a growing concern for the population of three-legged frogs in a specific area, as they have been exposed to chemical pollutants. In the year 2000, data estimated that there were about 5,000 three-legged frogs (N) in this area. With an annual increase of 15%, we can project the number of frogs in future years using the formula:

Future population = N * (1 + growth rate) ^ number of years

In this case, we want to determine the number of three-legged frogs in the area by 2009. To calculate this, we will use the given values:

Future population = 5,000 * (1 + 0.15) ^ (2009 - 2000)

Future population = 5,000 * (1.15)⁹

Future population ≈ 13,956

Therefore, by 2009, it is projected that approximately 13,956 three-legged frogs will inhabit the area, rounding to the nearest whole number. This increase in population highlights the potential ecological consequences of chemical pollutants on the environment and the need for further investigation and mitigation measures.

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Make a number line and mark all the points that represent the following values of x. X < -1 and x > 1​

Answers

To make a number line for the values of x that are less than -1 and greater than 1, we can start by drawing a horizontal line and marking a point at 0. Then, we can label the left side of the line with negative numbers and the right side with positive numbers.

Next, we need to mark all the points that represent the values of x that satisfy the condition X < -1 and x > 1. This means we are looking for all the numbers that are less than -1 and greater than 1 at the same time. However, there are no numbers that satisfy this condition since a number cannot be both less than -1 and greater than 1 simultaneously.

Therefore, there are no points to mark on the number line for this condition.

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help i need this done pls 50 points

Answers

The length of the diagonal is 12. 7in

How to determine the length

To determine the length of the diagonal, we need to know the Pythagorean theorem.

The Pythagorean theorem states that the square of the hypotenuse side is equal to the sum of the squares of the other two sides of a triangle.

The other two sides are the opposite and the adjacent sides.

From the information given in the diagram, we have that;

The opposite side = 12in

The adjacent side = 4in

Substitute the values

x² = 12² + 4²

find the squares

x² = 160

find the square root

x = 12. 7 in

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HELP!!!

Find the Area of a Rectengle with the base of 3x+1 in and a height of 2x-3 in.

A.5x^2-2 in^2

B.6x^2+7x-2 in^2

C.10x-4 in

D.6x^2-7x-3 in^2

Answers

The area of a rectangle with base of 3x+1 in and a height of 2x-3 in is given as follows:

D. A = 6x² - 7x - 3 in².

How to obtain the area of a rectangle?

The area of a rectangle of length l and width w is given by the multiplication of dimensions, as follows:

A = lw.

The dimensions for this problem are given as follows:

w = 3x + 1.l = 2x - 3.

Hence the expression for the area of the rectangle is given as follows:

A = (3x + 1)(2x - 3)

A = 6x² - 9x + 2x - 3

A = 6x² - 7x - 3 in².

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A dth tv connection provides channels in english and other languages in the ratio 7:13. what percentage of the channels are in english

Answers

A DTH TV connection provides channels in English and other languages in the ratio 7:13. To find out what percentage of the channels are in English, you need to divide the number of English channels by the total number of channels and then multiply the result by 100.

Let's assume that there are a total of 100 channels available on this DTH TV connection. According to the given ratio, 7 out of every 20 channels will be in English. So, the percentage of channels in English will be:

(7/20) x 100 = 35%

Therefore, 35% of the channels on this DTH TV connection are in English.

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James says the fraction 3 4 has the same value as the expression 4 ÷ 3. Use the drop-down menus to state whether you agree or not, and why. James is Choose. . A fraction can be interpreted as division of the Choose. By the Choose.

Answers

James says the fraction 3/4 has the same value as the expression 4 ÷ 3. I disagree with James' statement.

The fraction 3/4 is not the same as the expression 4 ÷ 3. A fraction can be interpreted as division of the numerator (top number) by the denominator (bottom number). In this case, 3/4 represents the division of 3 by 4, whereas 4 ÷ 3 represents the division of 4 by 3. These two expressions have different values and are not equal.

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

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