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Alenkasestr [34]
2 years ago
13

65. If the diameter of the sphere is halved, what will be the difference in volume?

Mathematics
1 answer:
Murrr4er [49]2 years ago
7 0

Answer:

Hi there !

  • A. 1/8 of the original volume
  • 24 is the mode

<h2>Step-by-step explanation:</h2>

<h3>Question 1 :-</h3>

LET RADIUS OF SPHERE= R

VOLUME OF SPHERE= ( \frac{4}{3})\pi \:  {r}^{3}

WHEN RADIUS IS HALVED RADIUS IF SPHERE=R/2

VOLUME= ( \frac{4}{3} )\pi( \frac{r}{2})^{3} = {(4/3)πR^3}/8

THE VOLUME WILL BECOME 1/8 TH OF THE ORIGINAL VOLUME.

<h2>Question 2 :-</h2>

Wehave,

Mode+2×Mean=3×Median

⇒Mode=3×Median−2×Mean

Given : Mean=21 and Median=22

Putting the given values, we get

Mode=3×22−2×21=66−42=24.

Hope it helps u....

Stay safe, stay healthy and blessed

Have a great day !

Thank you

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The distance from the satellite to the Earth's horizon is 6398 km

<h3>Pythagoras theorem</h3>

Pythagoras theorem is used to show the relationship between the sides of a right angled triangle. It is given by:

Hypotenuse side² = Adjacent side² + Opposite side²

Let x represent the distance from the satellite to the Earth's horizon

Hence:

  • x² = 6370² + 600²
  • x² = 40936900
  • x = 6398 km

The distance from the satellite to the Earth's horizon is 6398 km

Find out more on Pythagoras theorem at: brainly.com/question/343682

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Step-by-step explanation:

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Of the total population of the United States, 20% live in the northeast. If 200 residents of the United States are selected at r
Snezhnost [94]

Answer:

0.0465 = 4.65% probability that at least 50 live in the northeast.

Step-by-step explanation:

I am going to use the normal approximation to the binomial 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:

n = 200, p = 0.2

So

\mu = E(X) = np = 200*0.2 = 40

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.2*0.8} = 5.65685

Approximate the probability that at least 50 live in the northeast.

Using continuity correction, this is P(X \geq 50 - 0.5) = P(X \geq 49.5, which is 1 subtracted by the pvalue of Z when X = 49.5. So

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

Z = \frac{49.5 - 40}{5.65685}

Z = 1.68

Z = 1.68 has a pvalue of 0.9535

1 - 0.9535 = 0.0465

0.0465 = 4.65% probability that at least 50 live in the northeast.

3 0
3 years ago
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