Your assigned 32 math exercises for homework you complete 87.5of these before dinner how many do you hav to do after dinner.

When the radius of a cylinder is increased by a factor of 5, the volume of the cylinder increases by a factor of 25.

The volume of a cylinder can be calculated using the formula V = πr2h, where V is the volume, r is the radius, and h is the height. In this case, the radius of the cylinder is increased by a factor of 5, but the height remains the same. Let's consider the original radius as r and the increased radius as 5r. The volume of the original cylinder is πr2h, and the volume of the new cylinder is π(5r)2h.

Simplifying the expression for the volume of the new cylinder, we get V' = 25πr2h. Comparing the volume of the new cylinder to the volume of the original cylinder, we can see that the volume has increased by a factor of 25. Therefore, statement B is correct: The volume of the cylinder increases by a factor of 25.

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The correct answer is B) The volume of the cylinder increases by a factor of [tex]25.[/tex]

Let's analyze the relationship between the volume of a cylinder and its dimensions.

The volume [tex]\( V \)[/tex] of a cylinder is given by the formula:

[tex]\[ V = \pi r^2 h \][/tex]

where:

[tex]\( r \)[/tex] is the radius of the cylinder,

[tex]\( h \)[/tex] is the height of the cylinder.

Given that the height [tex]\( h \)[/tex] remains unchanged, if the radius [tex]\( r \)[/tex] is increased by a factor of [tex]5[/tex], the new radius [tex]\( r' \)[/tex] becomes[tex]\( 5r \).[/tex]

Now, let's compare the volumes before and after the increase in radius:

1. Original Volume [tex](\( V_{\text{original}} \))[/tex]

[tex]\[ V_{\text{original}} = \pi r^2 h \][/tex]

2. New Volume [tex](\( V_{\text{new}} \))[/tex]

After increasing the radius by a factor of [tex]5[/tex], the new radius [tex]\( r' = 5r \)[/tex].

[tex]\[ V_{\text{new}} = \pi (5r)^2 h = \pi (25r^2) h \][/tex]

Now, compare [tex]\( V_{\text{new}} \)[/tex] with [tex]\( V_{\text{original}} \)[/tex]

[tex]\[ \frac{V_{\text{new}}}{V_{\text{original}}} = \frac{\pi (25r^2) h}{\pi r^2 h} = \frac{25r^2 h}{r^2 h} = 25 \][/tex]

Answer:

Option c. Population: 10 shipments of 1000 cartons of eggs

sample: every 50th carton in each shipment.

Step-by-step explanation:

First we find out population :

For ten shipments of 1000 cartons of eggs. In other words in each 10 shipments there are 1000 cartons of eggs.

Therefore, 1000 × 10 = 10,000  cartons of eggs.

Population : 10,000 cartons of eggs

Now it is given that she examines every 50th carton to see how many cartons contain cracked eggs.

Hence, Sample would be every 50th carton in each shipment.

In option a and b given cartons of eggs are 1,000,000, so they would be eliminated and in option d it is given that sample is only 50th carton of eggs

Therefore, option c would be correct.

The value of 'y' in the isosceles trapezoid ABCD is 14 and this can be determined by using the properties of isosceles trapezoid.

Given :

The two legs are of equal length In any isosceles trapezoid that means:

7y - 4 = 8y - 18

Add 18 on both sides in the above equation.

7y - 4 + 18 = 8y - 18 + 18

7y + 14 = 8y

Now, subtract 7y on both sides in the above equation.

7y + 14 - 7y = 8y - 7y

Simplify the above expression in order to get the value of 'y'.

y = 14

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Answer:

The grasshopper needs to eat 10 blades of grass each day.

Step-by-step explanation:

The grasshopper in the food pyramid above must eat half its body weight in grass each day.

The average weight of the grasshopper is 2 grams.

The weight of one blade of grass is 0.1 grams.

Now,

The weight of grass eating by the grasshopper per day is 1 gram.

Let us assume that the grasshopper eats the "n" number of blades of the grass.

Therefore,

[tex]\begin{aligned}n \times 0.1\;\rm{gm}&=1\;\rm{gm}\\n&=\dfrac{1}{0.1}\\n&=10\end{aligned}[/tex]

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Answer:

C. Yes, the number is written in scientific notation.

Step-by-step explanation:

We have been given a number [tex]5.6\times 10^{12}[/tex]. We are asked to determine whether our given number is written in scientific notation or not.

We know that when a number greater than 1 and less than 10 is multiplied by a power of 10, then the number is written in scientific notation.

Upon looking at our given number we can see the number 5.6 is between 1 and 10. In addition, 5.6 is being multiplied by 10 to the power 12.

Therefore, our given number is written in scientific notation and option C is the correct choice..

Answer:

52 Days

Step-by-step explanation:

Answer:

The correct answer is:

Michigan.

Michigan is the state that had a flat state income tax in 2009.

Step-by-step explanation:

A flat tax (short for flat-rate tax) is a tax system with a constant marginal rate, usually applied to individual or corporate income.

Flat tax benefits higher income brackets progressively due to decline in marginal value.

The state that had a flat state income tax in 2009 is:

Michigan.

Michigan is a flat-tax state that levies a state income tax of 4.25%

Answer:

$3.50 per hour

Step-by-step explanation:

Given : For working 13 hours you earned $45.50 and $94.50 for 27 hours

To Find :What is your rate of pay in dollars per hour?

Solution :

Pay for 13 hours =  $45.50

So, Pay for 1 hour =  [tex]\frac{45.50}{13}[/tex]

Pay for 1 hour =  [tex]3.50[/tex]

So, rate is $3.50 per hour

So, Option B is true

Hence rate of pay in dollars per hour is $3.50 per hour

Answer:

45% of 40 is 18% of 100

Step-by-step explanation:

45% of 40 is 18% of what number

First we find out what is 45% of number 40

45% times 40

[tex]\frac{45}{100} * 40= 18[/tex]

Now we find

18 = 18% of what number

Let the unknown number be x

18 = 18% * x

[tex]18= \frac{18}{100} * x[/tex]

18 = 0.18 * x

Divide by 0.18 on both sides

100= x

So 45% of 40 is 18% of 100

The complete statement is 45% of 40 is 18% of 100

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

45% of 40 is 18% of what number

Represent the number with x

So, we have

45% of 40 is 18% of x

Express as an equation

45% of 40 = 18% of x

Next, we have

18 = 0.18x

Divide through by 0.18

x = 100

Hence, 45% of 40 is 18% of 100

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The function rule is  y = -5x - 1 , obtained by observing the linear relationship where  y  decreases by 5 as  x increases by 1.

To find the function rule that relates the values of  x  to  y , let's first observe the pattern in the given data:

[tex]x & y \\-2 & 9 \\-1 & 4 \\0 & -1 \\1 & -6 \\2 & -11 \\[/tex]

Notice that as  x  increases by 1,  y  decreases by 5. This suggests a linear relationship between  x and  y , where the slope of the line is -5.

The general form of a linear function is ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.

To find the y-intercept, let's pick any point from the table, for example, when ( x = 0 ), ( y = -1 ).

So, we can plug the values of ( x ) and ( y ) into the linear function formula:

[tex]\[-1 = (-5)(0) + b\][/tex]

[tex]\[-1 = 0 + b\][/tex]

[tex]\[b = -1\][/tex]

Now we have the slope (( m = -5 )) and the y-intercept (( b = -1 )), so the function rule is:

[tex]\[ y = -5x - 1 \][/tex]

Now, let's verify this function rule with another point from the table, for example, when ( x = 2 ):

[tex]\[ y = -5(2) - 1 \][/tex]

[tex]\[ y = -10 - 1 \][/tex]

[tex]\[ y = -11 \][/tex]

This matches the value of ( y ) in the table, confirming that our function rule is correct.

Answer: -7/5

Substitute the value of the variable into the expression and simplify.

Exact Form:  −7/6

Answer:

D. The manager should check both relative frequencies by row and by column to look for an association.

Step-by-step explanation:

the correct answer would be D