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4 years ago

Find the radius round your answer to the nearest tenth

Mathematics

1 answer:

Thepotemich [5.8K]4 years ago

4 0

Answer:

r = 3m

Step-by-step explanation:

Formula for the volume of a sphere: V = $\frac{4}{3}$ $\pi$ $r^{3}$

We want to find the radius so we use algebra to rearrange the equation to make the radius (r) the subject of the equation

Divide both sides by $\frac{4}{3}$

$\frac{3V}{4}$ = $\pi$ $r^{3}$

Divide both sides by $\pi$

$\frac{3V}{4\pi }$ = $r^{3}$

Take the cube root of both sides

$\sqrt[3]{\frac{3V}{4\pi } }$ = r

Substitute V = 36 $\pi$ into the equation

r = $\sqrt[3]{\frac{3(36\pi) }{4\pi } }$

Expand the bracket

r = $\sqrt[3]{\frac{108\pi }{4\pi } }$

Divide 108 $\pi$ by 4 $\pi$ (For this, the two $\pi$ in the numerator and denominator cancel each other out, and you only need to divide 108/4)

r = $\sqrt[3]{27}$

The cube root of 27 is 3, because $3^{3}$ = 3 x 3 x 3 = 27

r = 3

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Suppose that several insurance companies conduct a survey. They randomly surveyed 350 drivers and found that 280 claimed to alwa

KATRIN_1 [288]

Answer:

Lower limit = 0.76

Upper limit = 0.84

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 350

Number of drivers that buckle = 280

Formula:

$p' = \dfrac{x}{n} = \dfrac{280}{350} = 0.8$

$q' = 1-p' = 1 - 0.8 = 0.2$

The standard deviation for sp =

$=\sqrt{\displaystyle\frac{p'q'}{n}}\\\\=\sqrt{\dfrac{0.8\times 0.2}{350}} = 0.02138$

95% Confidence Interval:

$p' \pm z_{critical}(s_p)$

$z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.96$

Putting the values, we get,

$0.8 \pm 1.96(0.02138)\\= 0.8 \pm 0.0419048\\=(0.7580952, 0.8419048)\\\approx (0.76,0.84)$

Lower limit = 0.76

Upper limit = 0.84

3 0

3 years ago

g The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control

Rudiy27

Answer:

0.1426 = 14.26% probability that at least one of the births results in a defect.

Step-by-step explanation:

For each birth, there are only two possible outcomes. Either it results in a defect, or it does not. The probability that a birth results in a defect is independent of any other birth. This means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

The proportion of U.S. births that result in a birth defect is approximately 1/33 according to the Centers for Disease Control and Prevention (CDC).

This means that $p = \frac{1}{33}$