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3 years ago

What is the surface area of the regular pyramid

Mathematics

1 answer:

Gemiola [76]3 years ago

7 0

The total area is the sum of the area of the base (65 m^2) and six times the area of one of the triangular sides. This area (of one side) is (1/2)(base)(height), or (1/2)(5)(12), so the total area of the sides is 6(1/2)(5)(12) = 180 m^2. Thus, the total area is 65 m^2 + 180 m^2 = 245 m^2.

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Follow the Order of Operations to simplify each expression below. 2(9-6)2/18

kenny6666 [7]

Answer:

Step-by-step explanation:

8 0

3 years ago

A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N. A new batch of yarn was made, usin

AlexFokin [52]

Answer:

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction of normal variables.

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

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

Subtraction of normal variables:

When we subtract two normal variables, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

A sample of 125 pieces of yarn had mean breaking strength 6.1 N and standard deviation 0.7 N.

This means that $\mu_1 = 6.1, s_1 = \frac{0.7}{\sqrt{125}} = 0.0626$

In a sample of 75 pieces of yarn from the new batch, the mean breaking strength was 5.8 N and the standard deviation was 1.0 N.

This means that $\mu_2 = 5.8, s_2 = \frac{1}{\sqrt{75}} = 0.1155$

Distribution of the difference:

$\mu = \mu_1 - \mu_2 = 6.1 - 5.8 = 0.3$

$s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0626^2+0.1155^2} = 0.1314$

Confidence interval:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = zs$

$M = 1.645*0.1314 = 0.22$

The lower end of the interval is the sample mean subtracted by M. So it is 0.3 - 0.22 = 0.08N

The upper end of the interval is the sample mean added to M. So it is 0.3 + 0.22 = 0.52N

The 90% confidence interval for the difference in mean breaking strength between the two types of yarn is (0.08N, 0.52N).

3 0

3 years ago

A carpenter sawed a board into 5 equal pieces each 3 1/8 inches long. How long was the board?

zavuch27 [327]

Hi there! To solve this question, we can just simply multiply 3 1/8 and 5, because we're looking for the total length of the board, before it was cut into 5 equal pieces. To multiply fractions, just do it straight across. Numerator * numerator / denominator * denominator. 3 1/8 as a mixed number is 25/8 and 25/8 * 5/1 is 125/8 or 15 5/8 in mixed number form. There. The board was 15 5/8 inches long. The answer is D.

4 0

4 years ago

A credit card contains 16 digits between 0 and 9. However, only 100 million numbers are valid. If a number is entered randomly,

marusya05 [52]

Answer:

$P(valid) = 1 * 10^{-8}$