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3 years ago

Julio cubes a number then takes the cube root of the result. He ends up with 20. What number did Julio start with

Mathematics

1 answer:

Vesnalui [34]3 years ago

6 0

Let us say that the number is x.

So the first step that Julio do is to cube the number so that:

x^3

Then the next he did was take cube root of the number, so that:

(x^3)^(1/3)

Solving this would result in:

x^(3/3) = x^1 = x

Since he ends up with 20, therefore:

x = 20

<span>Julio started and ended with the same number which is 20.</span>

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Amelia needs 3 2/3 cups of sugar to make cupcakes. Which improper fraction names this amount?

Dmitrij [34]

C because you multiply the big number with the lower number then you add the number on top. 3 times 3 equals 9 plus 2 = 11. you keep the bottom number under your new number

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3 years ago

The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 104 inches, and a standard

dsp73

Answer:

91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 104, \sigma = 14, n = 49, s = \frac{14}{\sqrt{49}} = 2$

What is the probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

This is the pvalue of Z when X = 106.8. So

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

By the Central Limit Theorem

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

$Z = \frac{106.8 - 104}{2}$

$Z = 1.4$

$Z = 1.4$ has a pvalue of 0.9192

0.9192 = 91.92% probability that the mean annual precipitation during 49 randomly picked years will be less than 106.8 inches

8 0

3 years ago

STatiana [176]

Answer:

(e^3 / e^2n)

Step-by-step explanation:

isn't this the same question

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3 years ago

An umbrella has 12 evenly spaced ribs. If viewed as a flat circle of radius 11 units,

erica [24]

Answer:

Area = 121pi/12

~= 31.66 sq units

Step-by-step explanation:

They are talking about looking at an umbrella like its a circle. The radius is 11 units. That is from the center to the edge.

Consecutive means "in a row" or "next to each other" The 12 "ribs" are the like skeleton structure in the umbrella. But they cut the umbrella into 12 areas. They are asking for the area of one "slice". It is 1/12 of the area of the whole circle.

Area of a circle is

A = pi × r^2

Area of one slice is 1/12 of the whole.

A(1 slice)

= 1/12× pi × r^2

See image.

4 0

2 years ago