P
E
MD
AS
Simplify using
order of operations.
14 + 6 x 2-16+8

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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The height should you drop an object in order for it to have a velocity of 60 ft/sec is 55.9 feet

The equation given in the problem is written below

v = √2ha

velocity, v =  60 ft/sec

height, h = ?

acceleration due to gravity, a = 32.2ft/sec^2

The problem asks for height hence we make h the subject of the formula

v = √2ha

v^2 = 2ha

h = v^2 / 2a

substituting the values in to the equation

h = 60^2 / (2 * 32.2)

h = 3600 / 64.4

h = 55.9 feet

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Assuming no deposits or withdrawals are made,  the amount in the  account after 19 years is: 11,454. 133.

Using this formula

A = P(1+r/100)ⁿ

Where:

A = Amount =?

P = Principal = $4700

r = Interest rate =4.8%

n = the number of periods =19 years

Let plug in the formula

A = 4,700 (1 + 4.8/100)¹⁹

A = 4,700 (1 + 0.048)¹⁹

A = 4,700 (1.048)¹⁹

A = $11,454. 133

Therefore the amount is $11,454. 133.

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Answer:

739

Step-by-step explanation:

2217 (weight) / 3 ( # of blocks)

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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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.

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:

Circle, hexagon, and oval

Step-by-step explanation:

They are all 2d.  

The linear function that models the data-set is given as follows:

v = 4 + 0.4x.

The slope-intercept representation of a linear function is presented as follows:

y = mx + b

The coefficients of the function and their meaning are obtained as follows:

For this problem, the values of these parameters are given as follows:

Hence the equation is given as follows:

v = 4 + 0.4x.

The table is given by:

Money Spent (x) $0 $20 $40 $60

Pounds of Food (v) 4 12 20 28

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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

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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Answer:

evaluation or perhaps difference

Step-by-step explanation:

ex: 6b 2a 2b+1

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

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:

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:

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]

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

Out of 3000 students at the school , 200 student plays foot ball .

In the question ,

it is given that ,

fraction of students that are involved in sports at Greenville High School = 1/3 of total students ,

percent of students that plays football = 20% of sports students .

given that the total number of students present at the school = 3000

So , the number of students involved in sports = (1/3) × 3000

= 1000

number of students who plays football = 20% of 1000

= 0.20 × 1000            ....because 20% = 0.20

= 200

Therefore , Out of 3000 students at the school , 200 student plays foot ball .

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The sum of consecutive odd cubes of 8128 is 1³+3³+5³+7³+9³+11³+13³+15³

Therefore, 1+27+125+343+729+1331+2197+3375=8128

Consecutive numbers are those that come after each other in descending order from the smallest to the largest. The difference between consecutive numbers is always fixed and follows a predictable pattern. For example, the first three consecutive natural numbers are 1, 2, 3. The simplest way to find consecutive numbers is to look at the number set and find the number that is either before or after the term of interest.

We know that consecutive odd numbers are 1,3,5,7,9,11,13,15,17..

Here 8128 is a perfect square

And it can be written as the sum of consecutive odd cubes as follows:

1³=1

3³=27

5³=125

7³=343

9³=729

11³=1331

13³=2197

15³=3375

The sum of consecutive odd cubes of 8128 is

=1³+3³+5³+7³+9³+11³+13³+15³

=1+27+125+343+729+1331+2197+3375

=8128

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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:

21. A basket holds n apples. You pick (2n - 3) apples, and your friend picks

(n+4) apples. How many apples do you and your friend pick together?

How many baskets do you need to carry all the apples? Justify your answer.

Step-by-step explanation:

(2n - 3)(n + 4) binomial times a binomial equals

2n^2 + 5n - 12

Answer:

-11, -2, 3, 6

-16, -5, 19, 21

Step-by-step explanation:

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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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:

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]

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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The correct statement regarding the solution of the inequality 8x - 6 < 3x + 19 is given as follows:

D. She knows that the solution must be either all the values less than 5 or all the values greater than 5.

The inequality is presented as follows:

8x - 6 < 3x + 19.

Lin finds the value of x = 5 for which the two sides of the inequality are equal. Then, there are only two cases for the solution, which are listed as follows:

Thus option D gives the correct option regarding how to find the solution.

The justifications for the other options being wrong are given as follows:

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Answer:

I think its D.... id/k I think it is.

Step-by-step explanation:

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:

8.8 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