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2 years ago

A basketball has a diameter of 9.5

Mathematics

1 answer:

zubka84 [21]2 years ago

4 0

Answer:

C. $\dfrac{4}{3}\pi\cdot(4.75)^3\ cm^3$

Step-by-step explanation:

The volume of the ball with radius R can be calculated using formula

$V=\dfrac{4}{3}\pi R^3$

A basketball has a diameter of 9.5 cm, so its radius is

$R=\dfrac{D}{2}=\dfrac{9.5}{2}=4.75\ cm$

Hence, the volume of air the basketball can hold is

$V=\dfrac{4}{3}\pi\cdot(4.75)^3\ cm^3$

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Answer:

I) 32.5

ii) 100.1

Step-by-step explanation:

I) 1056.25 = √1056.25

= 32.5

ii) 10020.01= √10020.01

=100.1

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Babe Ruth's 1931 salary was $80,000, Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015. Ruth's

Lady_Fox [76]

Answer:

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

Step-by-step explanation:

This question can be solved by a rule of three.

Government statistics show a consumer price index of 15.2 for 1931 and 237 for 2015.

This means that $15.2 in 1931 is equivalent to $237 in 2015. So

$15.2 in 1931 - $237 in 2015

$80,000 in 1931 - $x in 2015

$15.2x = 237*80,000$

$x = \frac{237*80,000}{15.2}$

$x = 1,247,368$

Ruth's 1931 salary was equivalent to a 2015 salary of $1,247,368.

8 0

2 years ago

Pedro cut a sheet of poster board into 10 equal parts. His brother used some of the poster board and now 8/10 is left. Pedro wan

yawa3891 [41]

Answer: 8

Step-by-step explanation:

Given: Pedro cut a sheet of poster board into 10 equal parts.

let x be the total sheet.

then, one part of sheet= $\frac{1}{10}$ of the sheet

Now, His brother used some of the poster board and now 8/10 is left.

Therefore, if Pedro wants to make a sign from each remaining part of the poster board.

then, The number of signs he can make= $\frac{8}{10}\div \frac{1}{10}=\frac{8}{10}\times\frac{10}{1}=8$

Hence, Pedro can make 8 signs.

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2 years ago

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The Wall Street Journal reports that 33% of taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deduction

Len [333]

Answer:

(a) n : 20 50 100 500

P (-200 < X - μ < 200) : 0.2886 0.4444 0.5954 0.9376

(b) The correct option is (b).

Step-by-step explanation:

Let the random variable X represent the amount of deductions for taxpayers with adjusted gross incomes between $30,000 and $60,000 itemized deductions on their federal income tax return.

The mean amount of deductions is, μ = $16,642 and standard deviation is, σ = $2,400.

Assuming that the random variable X follows a normal distribution.

(a)

Compute the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $200 of the population mean as follows:

For a sample size of n = 20

$P(\mu-200$

$=P(-0.37$

For a sample size of n = 50

$P(\mu-200$

$=P(-0.59$

For a sample size of n = 100

$P(\mu-200$

$=P(-0.83$

For a sample size of n = 500

$P(\mu-200$

$=P(-1.86$

n : 20 50 100 500

P (-200 < X - μ < 200) : 0.2886 0.4444 0.5954 0.9376

(b)

The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample ( $\bar x$ ) approaches the whole population mean ( $\mu_{x}$ ).

Consider the probabilities computed in part (a).

As the sample size increases from 20 to 500 the probability that the sample mean is within $200 of the population mean gets closer to 1.

So, a larger sample increases the probability that the sample mean will be within a specified distance of the population mean.

Thus, the correct option is (b).

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2 years ago