MATHEMATICS COLLEGE

Question 3 of 5A basketball has a radius of 4.5 inches. If the
ball is filled with 350 cubic inches of air, how
much more air is needed to fill it completely?
Round to the nearest whole number.

Answers

Answer 1

Answer:

Answer:

32 cubic inches of air are needed to fill it completely.

Step-by-step explanation:

A basketball has the format of a sphere.

The volume of a sphere with radius r is given by the following equation:

$V = (4\pi r^(3))/(3)$

In this question:

Radius of 4.5 inches. So the volume, in cubic inches, is:

$V = (4\pi*(4.5)^(3))/(3) = 382$

The volume of the ball is 382 cubic inches.

350 cubic inches have already been filled.

So 382-350 = 32 cubic inches of air are needed to fill it completely.

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What is the first step in using the square root property?

Answers

Answer: Isolate the term that contains the squared variable. Then, take the square root of both sides and solve.

Step-by-step explanation:

To solve an equation by using the square root property, you will first isolate the term that contains the squared variable. You can then take the square root of both sides and solve for the variable. Make sure to write the final answer in simplified form.

15 points PLEASE HELPKirk earns $27.50 an hour and he worked 80 hours this pay period. His deductions are $396 for taxes. $264 for insurance, and $175 for retirement What is
his net pay for this pay period?

Answers

Answer:

27.50(80) is 2,200

2,200-396-175-264= 1,365

I think this is how u do it correct me if I'm wrong

Solve the equation. -3x + 1 + 10x = x + 4

Answers

Answer:

$x=[tex](1)/(2)$ [/tex]

Step-by-step explanation:

Solving the equation mean finding the value of x

Equation given is:

$-3x+1+10x=x+4$

Now what we need to do is take the values with x in it to the left side of the equation and the other numbers to the right side of the equation.

$-3x+10x-x=4-1$

Now simplify values with x and the numbers.

$6x=3$

$x=[tex](1)/(2)$ [/tex]

Therefore $x=[tex](1)/(2)$ [/tex]

x = $(1)/(2)$

simplify the left side by collecting like terms

7x + 1 = x + 4 ( subtract x from both sides )

6x + 1 = 4 ( subtract 1 from both sides )

6x = 3 ( divide both sides by 6 )

x = $(3)/(6)$ = $(1)/(2)$

Population the populations P (in thousands) of Las Vegas Nevada from 1960 through 2009 can be modeled by p = 70.751e 0.0451t, where t is the time in years,with t = 0 corresponding to 1960.(a) Find the populations in 1960,1970,1980,1990,2000,and 2009.
(b) Explain why the change in population from 1960to 1970 is not the same as the change in population from 1980 to 1990.
(c) Use the model to estimate the population in 2020.

Answers

Answer:

the answer is below

Step-by-step explanation:

The model is:

$p=70751e^(0.0451t)$ where t is the time in years.

when t=0 (year 1960) $p=70751e^(0.0451*0)=70751$

when t=10 (year 1970) $p=70751e^(0.0451*10)=111071$

when t=20 (year 1980) $p=70751e^(0.0451*20)=174368$

when t=30 (year 1990) $p=70751e^(0.0451*30)=273737$

when t=40 (year 2000) $p=70751e^(0.0451*40)=429734$

when t=49 (year 2009) $p=70751e^(0.0451*49)=644882$

The change in population from 1960to 1970 is 111071-70751 =40320

The change in population from 1980 to 1990 is 273737-174368=99369

The change from 1960to 1970 is not the same as the change from 1980 to 1990 because the model function is not linear, it is exponential. Therefore, the rate of the change is not constant.

The population in 2020 using the model can be estimated as

when t=60 (year 2020) $p=70751e^(0.0451*60)=1059091$