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Using the theories of Application of derivative,we got that  59.11221inches³/sec  is rate of volume changing when the radius is 2.3 inches.

We are given rate of change of radius (dr/dt)=0.6inches

We know very well that volume of sphere is given by (4/3)πr³

where r is the radius of the sphere.

Now, differentiating the volume with respect to radius, we get

=>dV/dr=4πr²

=>dV/dt=(dv/dr)·(dr/dt)

=>dV/dt=4πr².(dr/dt)

We are given that dr/dt=0.6inches/sec

So, dV/dt=4πr²·(0.6)

Now, putting values of r=2.3

 dV/dt=4π(2.3)²×(0.6)

=>dV/dt=4×3.14×2.3×2.3×0.6

=>dV/dt=59.11221inches³/sec

Hence, if we suppose suppose that the radius is expanding at a rate of 0.6 inches per second, the volume is changing at the rate of 59.11221inches³/sec when the radius is 2.3 inches.

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Answer:

y = 4x - 6

Step-by-step explanation:

linear equation:

y = mx + b

1. find the slope m

first select two point

im gonna take point 1 (-1,-7) and point 2 (3,9)

m = (y2-y1)/(x2-x1)

m = (9-(-7))/(3-(-1)) = 16/4 = 4

2. find b

first select a point

im gonna reuse point 2 (3,9)

y = mx + b

9 = 5(3) + b

9 = 15 + b

b = 9 - 15 = -6

3. keep x y, substitute m,b to linear equation

y = 4x - 6

Answer:

x = 3

Step-by-step explanation:

Collect like terms

0.5x = 4.5 - 3

0.5x = 1.5

Divide both sides by 0.5

0.5x/0.5 = 1.5/0.5

x = 3

Using fractions,

1/2x = 9/2 - 3

1/2x = 3/2

Divide both sides by 1/2

x = 3/2÷1/2

Reciprocate

x = 3/2 × 2/1

x = 6/2

x = 3

The equation of the line into slope-intercept form is y = x/3 - 6

Linear equations are equations that have constant average rates of change.

Note that the constant average rates of change can also be regarded as the slope or the gradient

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

9y−3x= −54

Rewrite properly

This gives

9y - 3x = -54

Divide through the equation by 3

So, we have the following representation

9y/3 - 3x/3 = -54/3

Evaluate

3y - x = -18

To rewrite as slope-intercept form is to make y the subject

So, we have

3y = x - 18

Divide through the equation by 3

So, we have the following representation

y = x/3 - 6

Hence, the equation is y = x/3 - 6

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The mean is 76 and the standard deviation is 7.

What is mean and standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

In mathematics, particularly in statistics, there are various types of means. Each mean summarizes a particular set of data, frequently to help determine the overall significance of a particular data set.

Let, 95% of students in statistics scored between 62 and 90 points.

Here,

Mean = [tex]\frac{62+90}{2} = \frac{152}{2} = 76[/tex]

And the standard deviation is,

SD = [tex]\frac{90-76}{2}= \frac{14}{2} = 7[/tex]

Hence, the mean is 76 and the standard deviation is 7.

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Answer:

4

Step-by-step explanation:

Let x be the unknown number.

[tex]\begin{aligned}&\textsf{A number is raised to the third power}: & x^3&\\&\textsf{Subtracted from 15}: & 15-x^3&\\&\textsf{To get 7}: & 15-x^3&=7\end{aligned}[/tex]

Solve the found equation for x:

[tex]\begin{aligned}&\textsf{Given}: & 15-x^3&=7\\&\textsf{Subtract $15$ from both sides}: & -x^3&=-8\\&\textsf{Divide both sides by $-1$}: & x^3&=8\\&\textsf{Rewrite $8$ as $2^3$}: &x^3&=2^3\\&\textsf{Cube root both sides}: & x&=2\end{aligned}[/tex]

Therefore, the number squared is:

[tex]\implies x^2=2^2=4[/tex]

Answer:

739

Step-by-step explanation:

2217 (weight) / 3 ( # of blocks)

After solving the value of x is 2.

From the figure:

Let ABCDE be the figure such that:

AB = 6x , BC = 6 , CD = 4,and DE = CE - CD  = 12 - 4 = 8.

BD and AE are parallel lines such that:

AB/BC = ED/CD

6x/6 = 8/4

x = 8/4

x = 2.

Therefore After solving the value of x is 2.

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Answer:

-11, -2, 3, 6

-16, -5, 19, 21

Step-by-step explanation:

The train will catch up with the dog in 1.996 seconds

The problem is solved using the formula for speed which is

distance / time

speed of the train = length of track / time

= 1900 / 40

= 475 m/s

speed of the dog is given to be 6 m/s

The relative velocity = 475 - 6 = 469 m/s

The time to catch up is calculated using relative velocity

469 * time = 936 meters

time = 936 / 469

= 1.996 seconds

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The factor of 36 in order from smallest to largest is 2 × 2× 3× 3.

Prime factor:

Factors are the numbers you multiply together to get another number. In simple words, a prime factor is finding which prime numbers multiply together to make the original number.

Here we have to find the prime factor 36.

That is we have to find the smallest multiplication of digits to get the value.

36 = 2 × 2 × 3 × 3

Therefore the prime factor is 2 × 2×3×3.

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Total earning = Salary + 10% of sales

According to question, we have

14000 = 9500 + 10% of sales

4500 = 0.1 sales

sales = 4500*10 = 45000

So, her total sales was Rs 45000

Answer:

evaluation or perhaps difference

Step-by-step explanation:

ex: 6b 2a 2b+1

diff: 6(2b+1)b 2 a 2b

The price per cup for a 2-pint bucket of paint costs $11.08 is $2.77.

It should be noted that 1 pint = 2 cup

In this case, 2-pint bucket will be:

= (2 × 2)

= 4 cups.

Therefore, 4 cups cost $11.08.

The price per cup will be:

= Total cost / Number of cups

= $11.08 / 4

= $2.77

The price is $2.77.

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The depth of snowdrift changed from Thursdays to Friday by -4 inches

The change of depth of snowdrift from Monday to Thursday = -8  inches

From Thursday to Friday, the depth changed by half as much

The equation is the mathematical statement that shows the relationship between two expression with and equal sign. The equation may consist of variables, numbers and arithmetic operators

Then the equation will be

The change of depth of snowdrift from Thursday to Friday = -8 /2

Here we have to use the division

Divide the terms

The change of depth of snowdrift from Thursday to Friday = -4 inches

Hence, depth of snowdrift changed from Thursdays to Friday by -4 inches

The complete question is :

From Monday to Thursday, the depth of a snowdrift changed by -8 inches. From Thursday to Friday, the depth changed by half as much. What is the change in the depth of the snowdrift from Thursday to Friday?

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The boys in the class that wear glae are 6 people.

The boys in the class that wear glae can be calculated as follows:

First we should calculate how many boys there are in the class. We can calculate it by multiplying the percent of the boys to the total students.

Boys in the class = [tex]\frac{20}{100} X 50[/tex] = 10 people.

Thus, we can calculate the boys who wear the glae by multiplying the percent of the boys wearing glae of the boys in the class.

Boys wear glae = [tex]\frac{60}{100} X 10[/tex] = 6 people.

Hence, The boys in the class that wear glae are 6 people.

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Answer:

8.8 L

Step-by-step explanation:

volume/time

176/22

=8.8

Answer:

x=9

y=-5

Or

(9,-5)

Step-by-step explanation:

-x+y=-14

+x.    +x

y=x-14

2x-3(x-14)=33

2x-3x+42=33

-x+42=33

   -42. -42

-x=-9

/-1. /-1

x=9

-(9)+y=-14

+9.      +9

y=-5

Hopes this helps please mark brainliest

Answer: 150 square inches

Step-by-step explanation:

Set up the proportional ratios (convert feet to inches first):

30 ft = 360 inches (there are 12 inches in 1 foot)

20 ft = 240 inches (I'm assuming there is an error in the question and the width is 20 ft, NOT 20 inches!)

360/15 = 240/x

x is the width of the scaled down rectangle

solve for x:

360x = 3600

x = 10 in

Now calculate Area = length x width

A = 15 x 10 = 150 square inches

For minima,

C'(x) = 0

6x-30 = 0

x = 5

If C"(x) >0, then minima

So, C"(x) = 6 > 0

So, for x = 5 , thr value of C(x) will be minimum.

Option C is correct

Answer: 144 dresses in 1440 minutes.

Step-by-step explanation:

Divide 144 and 12 you get 12. So you multiply 12 and 120 and you get 1440.

The rate is 120min/12dresses. Let's simplify it.

12/120 = 10min/1dress (or just 10)

Lets use this rate for 144 dresses

10 x 144 = 1140

It will take 1440 minutes to sell 144 dresses.

Answer:

Step-by-step explanation:

Let the number of 2 liter cans be x and 5 liter cans be y.

Number of cans:

Amount of paint:

Solve the system by elimination, double the first equation and subtract from the second one:

Find x:

Step-by-step explanation:

let's use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

so,

5.4/sin(K/2) = 12.3/sin(M1)

8.2/sin(K/2) = x/sin(M2)

M1 + M2 = 180 (as complementary angles or linear pair)

M2 = 180 - M1

sin(K/2) = 5.4×sin(M1)/12.3

sin(K/2) = 8.2×sin(M2)/x

therefore

5.4×sin(M1)/12.3 = 8.2×sin(180 - M1)/x

since sin(a) = sin(180 - a)

5.4×sin(M1)/12.3 = 8.2×sin(M1)/x

and then

5.4/12.3 = 8.2/x

x×5.4 = 8.2×12.3

x = 8.2×12.3/5.4 = 18.67777777... ≈ 18.7

Step-by-step explanation:Step-by-step explanation:

let's use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

so,

5.4/sin(K/2) = 12.3/sin(M1)

8.2/sin(K/2) = x/sin(M2)

M1 + M2 = 180 (as complementary angles or linear pair)

M2 = 180 - M1

Answer:

19%

Step-by-step explanation:

Of the female students, there are:

Out of 16 total students, 3 are juniors, so the probability is [tex]\frac{3}{16} \approx 19\%[/tex]

if we just randomly guess on each of the 4 questions, Then the probability that you get exactly 1 question correct is 1/4.

Probability formula: P(E) = favourable outcomes/Total outcomes

The number of questions is 10

The options for each question are 4.

Possible answers are 1.

Then,

favourable events = 1 × 10= 10

Total events = 4× 10= 40

Now, find the probability by putting the values as follows:

P(E) = favourable outcomes/Total outcomes

P(E) = 10/40

P(E) = 1/4

Therefore, the probability of doing all questions correct is 1/4

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Answer:

8 hours

Step-by-step explanation:

We can use an algebraic equation to solve this problem.

7.5x + 10 = 70

7.5x + 10 (-10) = 70 (-10)

7.5x (/7.5)= 60 (/7.5)

x = 8

The Slope of the first function is greater than the slope of the second function.  We can say that the function f(x) =x is steeper than the second function

What is a Slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, m = y/x, where m is the slope, can be used to express the change in the y coordinate with regard to the change in the x coordinate.

Take notice that tan = y/x.

In the given question, we have: two functions:

So, finding the slope of each of the functions;

The slope of the first function;  f(x) =x is 1;

The slope of the second function: m(x) =[tex]\frac{3}{5} f(x)[/tex];
Since the Slope of the first function is greater than the slope of the second function.  We can say that the function f(x) =x is steeper than the second function because the graph depends on the slope.

Hence,

the Slope of the first function is greater than the slope of the second function.  We can say that the function f(x) =x is steeper than the second function.

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Answer:

9 dimes, 4 nickels, 12 quarters

90 cents + 20 cents + 300 cents = 410 cents = $6.83

Step-by-step explanation:

q=5+d

n=d-7

q+n+d=25

5 + d + d - 7 + d = 25

3d-2=25

3d=27

d=9

25 - 9 = 16 nickels and quarters

q + n = 16 ---> q=16-n

n=d-7 ---> d=n+7

q=5 + n + 7

q=n+12

n+12 = 16-n

2n=4

n=4

25-(9+4)= 12 quarters

He has 2 nickels, 9 dimes, and 14 quarters, with a total value of $4.50

I am going to assume that the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than" because otherwise, there is no context in this question. If my answer is incorrect, please tell me how to correctly interpret this question.

In this scenario, the "and" in "five more quarters and dimes" and the "and" in "seven fewer nickels and dimes" is actually "than."

Amount of nickels - x

If there are seven fewer nickels than dimes, the amount of dimes is x + 7. There are five more quarters than dimes, so the amount of quarters is x + 7 + 5, which equals x + 12.

Therefore, there are 2 nickels. Now we must figure out the number of quarters and dimes.

x + 7 = 9

x + 12 = 14

There are 9 dimes and 14 quarters.

Nickels are each worth 5 cents. 2 times 5 is 10 cents.

Dimes are each worth 10 cents. 9 times 10 is 90 cents.

Quarters are each worth 25 cents. 14 times 25 is 350 cents.

Now, we add. 10 + 90 + 350 = 100 + 350 = 450.

REMEMBER, THIS IS IN CENTS. WE MUST STILL CONVERT IT INTO DOLLARS.

450 divided by 100 is $4.50