What is the volume of a ball with a diameter of 7 centimeters?

Andreas93 [3]

Answer:

Step-by-step explanation:

$4 {x}^{2} + 8x - 7 - (3 {x}^{2} - x + 9)$

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression:

$4 {x}^{2} + 8x - 7 - 3 {x}^{2} + x - 9$

Collect like terms

$4 {x}^{2} - 3 {x}^{2} + 8x + x - 7 - 9$

${x}^{2} + 9x - 7 - 9$

Calculate

${x}^{2} + 9x - 16$

Hope this helps...

Good luck on your assignment...

5 0

3 years ago

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Kareem cuts 12 identical circles of pastry form a 30cm by 40cm sheet. Find the area of pastry {which remains}

ch4aika [34]

<h3>Exact Area = 1200 - 300pi square cm</h3><h3>Approximate Area = 257.522203923062 square cm</h3>

Work Shown:

The area of the rectangle is 40*30 = 1200 square cm

Note how we have 4 circles along the horizontal dimension which is 40 cm, so each diameter is 40/4 = 10 cm, and the radius is 10/2 = 5 cm

Each circle has an area of pi*r^2 = pi*5^2 = 25pi

There are 4*3 = 12 circles, so the circle areas combine to 12*25pi = 300pi

Using a calculator, we find that 1200 - 300pi = 257.522203923062 approximately. Round this however you need to.

6 0

3 years ago

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explain how I determined the answer to number 3 on the assignment today and give the answer as well. ( give the steps you did to

Sonbull [250]

Huh? what’s the question for #3?

7 0

2 years ago

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Consider the probability that exactly 90 out of 148 students will pass their college placement exams. Assume the probability tha

Pepsi [2]

Answer:

0.0491 = 4.91% probability that exactly 90 out of 148 students will pass their college placement exams.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

$E(X) = np$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that $\mu = E(X)$ , $\sigma = \sqrt{V(X)}$ .

Assume the probability that a given student will pass their college placement exam is 64%.

This means that $p = 0.64$

Sample of 148 students:

This means that $n = 148$

Mean and standard deviation:

$\mu = E(X) = np = 148(0.64) = 94.72$

$\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{148*0.64*0.36} = 5.84$

Consider the probability that exactly 90 out of 148 students will pass their college placement exams.

Due to continuity correction, 90 corresponds to values between 90 - 0.5 = 89.5 and 90 + 0.5 = 90.5, which means that this probability is the p-value of Z when X = 90.5 subtracted by the p-value of Z when X = 89.5.

X = 90.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{90.5 - 94.72}{5.84}$

$Z = -0.72$

$Z = -0.72$ has a p-value of 0.2358.

X = 89.5

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{89.5 - 94.72}{5.84}$

$Z = -0.89$

$Z = -0.89$ has a p-value of 0.1867.

0.2358 - 0.1867 = 0.0491.

0.0491 = 4.91% probability that exactly 90 out of 148 students will pass their college placement exams.

5 0

3 years ago

A store sells cooking oil of two different brands in bottles of the same size. The table below and the equation each show the pr

djyliett [7]

Answer:

Brand A

Number of Bottles, x Price (dollars), y

2

22

3

33

4

44

5

55

Brand B

y = 17x

How many dollars more is the price of 8 bottles of brand B oil than the price of 8 bottles of brand A oil?

$5

$6

$28

$48

Step-by-step explanation:

5 0

3 years ago