Josh does a weekly exercise program consisting of cardiovascular work and weight training. Each week, he exercises for at least 10 hours. He spends at most 8
hours doing cardiovascular work. He spends at most 6 hours on weight training. Let x denote the time (in hours) that Josh spends doing cardiovascular work.
Let y denote the time (in hours) that he spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.
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The probability that a point falls in the red-shaded square is given as follows:

p = 9/16.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The probability that a point falls in the red shared square is then given by the division of the area of the red shaded square by the division of the area of the larger square.

The area of the red-shaded square is given as follows:

3² = 9.

The area of the larger square is given as follows:

4² = 16.

Hence the probability is given as follows:

p = 9/16.

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The point estimate of the population mean is 10.5.

The point estimate of the population standard deviation is 3.240, rounded to 3 decimals.

The margin of error for the estimation of the population mean with 95% confidence is 3.1

The 95% confidence interval for the population mean is [7.4, 13.6]

a. The point estimate of the population mean is the sample mean.

We can calculate it by adding up all the sample values and dividing by the sample size:

(10 + 8 + 12 + 15 + 13 + 11 + 6 + 5) / 8 = 10.5

Therefore, the point estimate of the population mean is 10.5.

b. The point estimate of the population standard deviation is the sample standard deviation. We can calculate it using the following formula:

s = √Σ(xi - x)² / (n - 1) ]

Plugging in the sample values, we get:

x = 10.5

s = √((10-10.5)² + (8-10.5)² + (12-10.5)² + (15-10.5)²+ (13-10.5)² + (11-10.5)²+ (6-10.5)² + (5-10.5)²) / (8 - 1) ]

s = 3.240

c.

margin of error = t-value × (sample standard deviation /  √(sample size))

Plugging in the values we found, we get:

margin of error = 2.365 × (3.240 /  √(8))

margin of error=3.067

d. Finally, we can use the following formula to find the 95% confidence interval for the population mean:

confidence interval = sample mean ± margin of error

confidence interval = 10.5 ± 3.067

confidence interval = [7.4, 13.6]

Therefore, the 95% confidence interval for the population mean is [7.4, 13.6]

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The required graph has been attached below that represents the inverse equation f(x) = 4x-1.

To graph the inverse equation f(x) = 4x - 1, we can follow these steps:

Replace f(x) with y:

y = 4x - 1

Switch the x and y variables: x = 4y - 1

Solve for y:

y = (x + 1) / 4

The graph of the original function f(x) = 4x - 1 is a line with a slope of 4 and a y-intercept of -1.

The graph of the inverse function is the reflection of this line over the line y = x, which means that the x and y coordinates of each point are swapped.

To plot points for the inverse function, we can choose some values of x and find the corresponding values of y using the equation y = (x + 1) / 4. For example:

x y

-3 -1/4

-2 0

-1 1/4

0 1/4

1 1/2

2 3/4

3 1

Therefore, the graph of the inverse equation f(x) = 4x - 1 is a line that passes through the points (-3, -1/4), (-2, 0), (-1, 1/4), (0, 1/4), (1, 1/2), (2, 3/4), and (3, 1).

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Answer:

Step-by-step explanation:

The area of the square is given as 1134 m². Let's assume that the side length of the square is "s". Then, we can write the area of the square as s² = 1134. Solving for "s", we get s = √1134. The perimeter of the square is given by P = 4s. Substituting the value of "s", we get P = 4√1134. To simplify this expression, we can factor out the perfect square factor of 36 from 1134, which gives us 1134 = 36 x 31. Therefore, P = 4√(36 x 31) = 4 x 6√31 = 24√31. Hence, the perimeter of the square is 24√31 m.

Answer:

The zeroes of this function are 2 and -1.

A and C are the correct choices.

The standard deviation of the given data is approximately 3.08.

To find the standard deviation of the given data (5, 6, 8, 13), we first need to find the mean (X) of the data.

Mean (X) = (5 + 6 + 8 + 13) / 4 = 32 / 4 = 8

Next, we calculate the deviations from the mean for each data point:

Deviation from the mean = Data point - Mean

For 5: 5 - 8 = -3

For 6: 6 - 8 = -2

For 8: 8 - 8 = 0

For 13: 13 - 8 = 5

Then, we square each deviation:

(-3)^2 = 9

(-2)^2 = 4

0^2 = 0

5^2 = 25

Next, we calculate the sum of the squared deviations:

Sum of squared deviations = 9 + 4 + 0 + 25 = 38

To find the variance, we divide the sum of squared deviations by the number of data points:

Variance = Sum of squared deviations / Number of data points = 38 / 4 = 9.5

Finally, we take the square root of the variance to find the standard deviation:

Standard deviation = √Variance = √9.5 ≈ 3.08

Therefore, the standard deviation of the given data is approximately 3.08.

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The surface area of the prism is A = 227.953 cm²

Given data ,

Let the prism be represented as T

Now , the surface area of the prism is A

where the side lengths of the prism are

a = 6 cm

b = 7 cm

c = 4 cm

And , the height of the prism is h = 12 cm

Now , total surface area of prism is A = A ( top ) + A ( bot ) + A ( lat )

where A ( top ) = ( 1/4 ) √ ( a + b + c ) ( b + c - a ) ( c + a - b ) ( a + b - c )

And , A ( top ) = 11.9765 cm²

where A ( bot ) = A ( top ) = 11.9765 cm²

And , A ( lat ) = h ( a + b + c )

A ( lat ) = 12 ( 6 + 7 + 4 )

A ( lat ) = 204 cm²

So , the total surface area A = 227.953 cm²

Hence , the surface area of prism is A = 227.953 cm²

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The  greater rate of change is 12.5, which is the rate of change of the first function.

The rate of change of a linear function is the slope of the line, which is represented by the coefficient of x in the equation y = mx + b. Therefore, the rate of change of the first function y = 12.5x + 2 is 12.5.

To find the rate of change of the second function, we can use any two points on the table and use the formula:

rate of change = (change in y) / (change in x)

Let's use the points (-3, -28.5) and (3, 37.5):

rate of change = (37.5 - (-28.5)) / (3 - (-3))

rate of change = 66 / 6

rate of change = 11

Therefore, the greater rate of change is 12.5, which is the rate of change of the first function.

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Answer: x = 15

Step-by-step explanation:

Answer:

the answer for 2/3(x-6) = 6. what's x? is 15

The value of the variable x = 21/32

Algebraic expressions are simply described as expressions that are composed of variables, coefficients, terms, constants and factors.

These expressions are also made up of certain arithmetic or mathematical operations.

These operations includes;

From the information given, we have that;

3/8=4/7x

cross multiply the values, we have;

7x(3) = 8(4)

multiply the values and expand the brackets, we get the values;

21x = 32

Divide both sides by the coefficient of the variable x, we get;

x = 32/21

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Answer: -4, -2 and 5, 7

Step-by-step explanation:

The equation of the line having slope 0 and passing through (-3,-2) is f(x) = -2.

Any horizontal line has the same y-value for every point on the line. We are given that the line passes through the point (-3,-2). This means that f(-3) = -2, since the y-value of the point (-3,-2) corresponds to the value of the function at x = -3.

This is because no matter what x-value we plug into the function, the output (y-value) will always be -2. Therefore, the equation of the line in function notation is f(x) = -2.

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Answer:

Step-by-step explanation:

The problem specifies that you may use a calculator. The formula, as reference, is:

You can use a regular calculator or an online spreadsheet to solve. In sheets, arrange your data and use the =PERCENTILE( ) function. In the parentheses, write the range of your data and the requested percentile as a decimal. So if I type the data (the ages of the signers for this example) in cells A:4 through A:23, I'd write =percentile(A7:A23,0.25).

So the answers:

25th percentile is 34.

80th percentile is 48.4.

The figure is not a rectangular pyramid but it is a triangular prism.

The base is a triangle not a rectangle.

The given figure is a triangular prism not a rectangular pyramid

A triangular prism is a prism composed of two triangular bases and three rectangular sides.

Rectangular pyramid is a solid with a rectangle-shaped base and triangular lateral faces

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Answer:

The answer is 43°

Step-by-step explanation:

137+137+x+43=360°

x+317=360

x=360-317

x=43°

7 groups of 2/7 is equivalent to the whole, which is represented by the number 2.

When we have 7 groups of 2/7, we are essentially multiplying the fraction 2/7 by the whole number 7. To perform this operation, we can use the following formula:

a/b × c/d = ac/bd

where a, b, c, and d are any numbers, and a/b and c/d are two fractions.

In our case, a is 2, b is 7, c is 7, and d is 1. This is because we want to multiply 2/7 by 7 to get 7 groups of 2/7. Therefore, we can substitute these values into the formula:

2/7 × 7/1 = (2 × 7) / (7 × 1) = 14/7

The result is a fraction 14/7, which can be simplified to 2. This means that 7 groups of 2/7 is equal to 2. To simplify this further, we can say that if we divide a whole into 7 equal parts, each part is 2/7. If we have 7 of these parts, we have the whole.

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After considering all the given data we conclude that the probability of randomly choosing a specified point within the circle that comes in the red-shaded square is 0.06.

Now we can clearly evaluate the possible probability of selecting a point randomly inside the circle under the section of red shaded square and derive a formula
[tex]P = (d - 4r)^2 / d^2[/tex]
Here,
d = diameter of the circle
r = square side length
For the given case,
d = 4 and r = 3.
Then,
P = (4 - 4×3)² / 4²
P = (4 - 12)²/ 4²
P = 0.06
Rounding to the nearest hundredth, P = 0.06.

Hence, the evaluated probability of selecting a point randomly inside a circle which falls in the red-shaded square is approximately 0.06.
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The probability that that arrow will land on the part labelled C after the first spin would be = 1/5.

To calculate the probability of the chosen event, the formula for probability should be used which is given as follows:

Probability = possible outcome/ sample space

Where possible outcome = 2

sample space = A,B,B,B,C,C,D,D,D,E = 10

Therefore the probability that the arrow will land on the part labelled C after the first spin = 2/10 = 1/5.

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Answer:

Option 2 and Option 3 are equivalent to 5-3 × [10x (6-2)]

Step-by-step explanation:

Option 2:

5-3 × [10x (6-2)] = 5-3 × [10x4] = 5-3 × 40 = 5-120 = -115

Option 3:

5-3 × [10x (6-2)] = 5-3 × 40 = 5-120 = -115

The value of secβ = (-21√10)/60.

Given that

Cosecβ = 7/3

Cotβ = -(2[tex]\sqrt{10}[/tex])/3

Since,

Cosecβ  =  1/sinβ = 7/3

⇒ sinβ = 3/7

And Cotβ = -(2[tex]\sqrt{10}[/tex])/3

⇒ cosβ/sinβ =  -(2[tex]\sqrt{10}[/tex])/3

⇒ 1/cosβ = -3/[(2[tex]\sqrt{10}[/tex])sinβ]

⇒ secβ = -21/(6√10)

Hence,

⇒ secβ = (-21√10)/60

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Answer: it's 300cm, hope this helps

The surface area of the two hemispheres combined is 100π square meters, and the volume of the two hemispheres combined is (500/3)π cubic meters.

The circumference of a great circle on a sphere is given by the formula C = 2πr, where r is the radius of the sphere.

In this case, we are given that the circumference of the great circle is 10π meters, so we can set up an equation:

10π = 2πr

Dividing both sides by 2π, we get:

r = 5

So the radius of the sphere is 5 meters.

When the sphere is cut in half, we get two equal hemispheres. The surface area of a closed hemisphere is given by the formula A = 2πr^2, where r is the radius of the hemisphere.

Since we are dealing with a radius of 5 meters, the surface area of one hemisphere is:

A = 2π(5^2) = 50π

Therefore, the surface area of the two hemispheres combined is:

2A = 2(50π) = 100π

The volume of a closed hemisphere is given by the formula V = (2/3)πr^3. Again, since we are dealing with a radius of 5 meters, the volume of one hemisphere is:

V = (2/3)π(5^3) = (2/3)π125 = (250/3)π

Therefore, the volume of the two hemispheres combined is:

2V = 2(250/3)π = (500/3)π

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Solution:

1. t/5 + 3/4

+4      

___   + 5-3= 20

20

2. Combine fractions w/ common denominator.

3. multiply the #'s.

4. last but not least is: Solution:

4t+15

_____

20

The apothem and the lateral surface area are 5/2√3 and 210 square units while the surface areas are 210 + 75√3 square units and 339.90 square units

Given that

Side length, s = 5

The apothem is calculated as

a = 1/2√3 * s

Where

Side length, s = 5

So, we have

a = 1/2√3 * 5

Evaluate

a = 5/2√3

The lateral area of the prism is calculated as

LA = 6sh

So, we have

LA = 6 * 5 * 7

LA = 210

This is calculated as

SA = LA + 3√3 s²

So, we have

SA = 210 + 3√3 * 5²

Evaluate

SA = 210 + 75√3

In decimal form, we have

SA = 339.90

Hence, the decimal form of the surface area is 339.90 square units

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Answer:

(4,0) & (9,5)

Step-by-step explanation:

Where the equations cross are the solutions!

Hope this Helps! :)
Happy Studies

A) rectangle

C) parallelogram

D) rhombus

E) rectangle

Answer:

The x-intercepts are -3,1

Step-by-step explanation:

The x-intercepts are where it crosses the x-axis.

It crosses the x-axis at -3 and 1

The x-intercepts are -3,1

Answer:

D. 1,0 & -3,0

Step-by-step explanation:

have a nice day.

Answer:

Fairview and Union are 9 cm apart on the map, and the scale is 1 cm: 10 km. So, to figure out the actual distance between the two cities, we need to use some math.

If 1 cm on the map represents 10 km in real life, then 9 cm on the map represents 90 km in real life. Therefore, Fairview and Union are actually 90 km apart.

Hope that helps!

Step-by-step explanation:

Answer:

90 km

Step-by-step explanation:

The scale of the map is

1 cm : 10 km

The scale of a map is a ratio. We can use a proportion to solve this problem.

1 cm is to 10 km as 9 cm is to x km

1/10 = 9/x

1 × x = 10 × 9

x = 90

Answer: 90 km

By using the synthetic division we have find that the quotient of x³-4x²+7 divided by x-3 is x² - x - 3, with a remainder of 4.

To use synthetic division, we first need to set up the equation in the correct format. We write the coefficients of the polynomial equation in descending order, and then we include any missing coefficients as 0. In this case, the equation x^3-4x²+7 can be written as:

1x^3 - 4x² + 0x + 7

Next, we write the linear equation in the format (x-a), where "a" is the value being divided out of the polynomial equation. In this case, a = 3, so we write the linear equation as:

(x-3)

We start by copying the first coefficient (1) from the top row to the bottom row.

We then multiply this coefficient by the value of "a" (3) and write the result (3) under the next coefficient (which is -4).

We add these two values together to get -1, which we write under the 0 coefficient.

We then repeat this process by multiplying -1 by 3 to get -3, which we write under the last coefficient (which is 7). We add these two values together to get 4.

Our synthetic division table should look like this:

3 | 1 -4 0 7 | 3 -1 -3

-----------------------------

   | 1 -1 -3 4

The bottom row of the table shows the coefficients of the quotient, which are 1, -1, and -3. These coefficients form the quotient of the division, which can be written as:

x² - x - 3

The last number in the bottom row of the table (4) is the remainder of the division. This means that our original equation x³-4x²+7, when divided by x-3, has a remainder of 4.

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Answer:

Step-by-step explanation:

the answer is 22

hoped this helped !