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Vesnalui [34]
3 years ago
7

A sphere has a volume of 1 cubic foot. What is the approximate diameter of the sphere?

Mathematics
2 answers:
erma4kov [3.2K]3 years ago
8 0

Answer:

1.24 ft

Step-by-step explanation:

the volume of sphere = 4/3π.r³ = 1

=> r³ = 3/(4π)= 3/(12.56) = 0.239

r = ³√0.239

r = 0.62

d = 2×0.62 = 1.24 ft

Lana71 [14]3 years ago
3 0

Answer:

volume \ of \ sphere = \frac{4}{3} \pi  r^3 \\\\1 =\frac{4}{3} \pi r^3\\\\r^ 3 = \frac{3}{4\pi} \\\\r = (\frac{3}{4\pi })^{\frac{1}{3} } \\\\r = 0.62ft\\\\diameter = 2 * 0.62 = 1.24ft

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Jenny bought a desk on sale for 119.60 the price was 75% less than the original price was the original price
olasank [31]

Answer:

100 - 75 = 25%

25%=119.60

need to find 1%

25/25=1%

119.60/25=1%

1%=4.784

now multiply by 100 to find original price

100% = 478.40

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5 0
3 years ago
If f (x) = 8(5x-2) find f -1 (x).
saw5 [17]

Step-by-step explanation:

f(x)=8(5x-2)

interchanging the role of x&y

x=8(5y-2)

  • x=40y-16
  • x+16=401y
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f-1(x)=(x+16)/10

<h3>stay safe healthy and happy.</h3>
6 0
3 years ago
AB and BC form a right angle at point B. If A = (-3,-1) and B = (4,4), what is the equation of BC
m_a_m_a [10]

Answer:

y=-1.4x+9.6

Step-by-step explanation:

If A = (-3,-1) and B = (4,4),  the slope of AB is

\text{Slope}_{AB}=\dfrac{-1-4}{-3-4}=\dfrac{-5}{-7}=\dfrac{5}{7}

Two perpendicular lines have slopes that have product of -1:

\text{Slopee}_{AB}\cdot \text{Slope}_{BC}=-1\\ \\\dfrac{5}{7}\cdot \text{Slope}_{BC}=-1\\ \\\text{Slope}_{BC}=-\dfrac{7}{5}=-1.4

The equation of the line BC with slope -1.4 and passing through the point B(4,4) is

y-4=-1.4(x-4)\\ \\y-4=-1.4x+5.6\\ \\y=-1.4x+9.6

7 0
3 years ago
An article written for a magazine claims that 78% of the magazine's subscribers report eating healthily the previous day. Suppos
Schach [20]

Answer:

89.44% probability that less than 80% of the sample would report eating healthily the previous day

Step-by-step explanation:

We use the binomial approximation to the normal to solve this question.

Binomial probability distribution

Probability of exactly x sucesses 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 samples 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)}.

In this problem, we have that:

p = 0.78, n = 675

So

\mu = E(X) = np = 675*0.78 = 526.5

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{675*0.78*0.22} = 10.76

What is the approximate probability that less than 80% of the sample would report eating healthily the previous day?

This is the pvalue of Z when X = 0.8*675 = 540. So

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

Z = \frac{540 - 526.5}{10.76}

Z = 1.25

Z = 1.25 has a pvalue of 0.8944

89.44% probability that less than 80% of the sample would report eating healthily the previous day

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