A die is rolled if the number rolled is less than 5 what is the probability that it is the bumber 2?

The volumes of two similar solids are 729 inches3 and 125 inches3. If the surface area of the smaller solid is 74. 32 inches2, w

Lelu [443]

The surface area of the larger solid, rounded to the nearest hundredth is given by: Option B: $240.80\: \rm inch^2$

<h3>How can we interpret volume of a solid?</h3>

Volume of a solid is usually expressed in cubic units, or units cube.

Suppose that the volume was expressed in x cubic units. Then you can say that the considered solid takes same space as the volume occupied by x cubes of 1 unit as their side lengths.

<h3>What are similar objects?</h3>

They're like zoomed version of each other(might be non-zoomed, zoomed in, or zoomed out). Their sides can be obtained by multiplying one object's sides by a single constant(by single constant, we mean constant which will be same for obtaining any corresponding side).

For the given case, we're given that:

Volume of first solid = 729 cubic inches.
Volume of second solid = 125 cubic inches.

Both solids are similar.

Thus, let the scale factor by which their sides change be 'f'.

Then, we get:

Side of first solid = f × side of second solid

Surface area of first solid(a square piece chosen on its surface) = f × f × surface area of second solid

(as two times sides multiplied, so two times f got multiplied).

Similarly,

volume of first solid = f × f × f × volume of second solid.

Or

$729 = f^3 \times 125\\f = \: ^3\sqrt{\dfrac{729}{125}} = \dfrac{9}{5} = 1.8$

As surface area of smaller solid(second solid is smaller as its volume is less) is 74.32 sq. inches, and f = 1.8, thus, we get:

$S_{\text{larger solid}} = f^2 \times S_{\text{smaller solid}} = (1.8)^2 \times 74.32\\S_{\text{larger solid}} = 240.7968 \approx 240.80 \: \rm inch^3$

Thus, the surface area of the larger solid, rounded to the nearest hundredth is given by: Option B: $240.80\: \rm inch^2$

Learn more about volume and surface area here:

brainly.com/question/2952465

8 0

2 years ago

What is the value 6^-8/6^-5?

Kisachek [45]

Answer:

0.00462962962

Step-by-step explanation:

8 0

3 years ago

Suppose that the distribution for total amounts spent by students vacationing for a week in Florida is normally distributed with

Charra [1.4K]

Answer:

96.24% probability that a SRS of 25 students will spend an average of between 600 and 700 dollars

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are 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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 650, \sigma = 120, n = 25, s = \frac{120}{\sqrt{25}} = 24$

What is the probability that a SRS of 25 students will spend an average of between 600 and 700 dollars

This is the pvalue of Z when X = 700 subtracted by the pvalue of Z when X = 600. So

X = 700

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

By the Central Limit Theorem

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

$Z = \frac{700 - 650}{24}$

$Z = 2.08$

$Z = 2.08$ has a pvalue of 0.9812

X = 600

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

$Z = \frac{600 - 650}{24}$

$Z = -2.08$

$Z = -2.08$ has a pvalue of 0.0188

0.9812 - 0.0188 = 0.9624

96.24% probability that a SRS of 25 students will spend an average of between 600 and 700 dollars

6 0

3 years ago

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A random sample of 10 college students was drawn from a large university. Their ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and

inessss [21]

Answer:

The test statistic t = 1.219 < 2.262 at 5% level of significance

we accept significance of level that the population mean is less than 20.

Step-by-step explanation:

Given ages are 22, 17, 27, 20, 23, 19, 24, 18, 19, and 24

The random sample (n) = 10

Null hypothesis (H0): μ = 20

Alternative hypothesis(H1) : μ < 20 (left tailed test)

we will use statistic 't' distribution with small sample 10 < 30

$t = \frac{χ-μ}{\frac{S.D}{\sqrt{n-1} } }$

mean (χ) = sum of observations divided by no of observations

mean(x) = ∑x / n = $\frac{22+17+27+20+23+19+24+18+19+24}{10} = 21.3$

x x - mean (x-mean)^2

22 22-21.3 = 0.7 0.49

17 17-21.3 = -4.3 18.49

27 27-21.3 = 5.7 32.49

20 20-21.3 =-1.3 1.69

23 23-21.3 = 1.7 2.89

19 19-21.3 = -2.3 5.29

24 24-21.3 = 2.7 7.29

18 18-21.3 = -3.3 10.89

19 19-21.3 = -2.3 5.29

24 24-21.3 = -=2.7 7.29

$S^{2} = \frac{∑(x-mean)^2}{n-1}= \frac{92.1}{10-1}$

$S^{2} = \frac{92.1}{9} = 10.2$

S = 3.198

The test statistic (t) = $t = \frac{21.3-20}{\frac{3.198}{\sqrt{10-1} } }$

t = 1.219

The degrees of freedom = n-1 = 10-1 =9

Tabulated value of t for 9 degrees of freedom at 5% level of significance

= 2.262

since calculated t < tabulated t we accept the null hypothesis

we accept significance of level that the population mean is less than 20.

5 0

3 years ago

What is the volume for the sphere?

SVETLANKA909090 [29]

Answer:

268 cm^4

Step-by-step explanation:

hope this helps :)

8 0

3 years ago

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