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3 years ago

I just need someone to check my answer.

1 answer:

6 0

Well actually it would be a and be because the difference is only 453 where the difference of a and d would be 505

to the second question
the difference between the two stars is 453 kilometers

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Find the area between the graph of the function and the x-axis over the given interval, if possible.

vodomira [7]

Answer:

$A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5$

So then the integral converges and the area below the curve and the x axis would be 5.

Step-by-step explanation:

In order to calculate the area between the function and the x axis we need to solve the following integral:

$A = \int_{-\infty}^1 \frac{5}{(x-2)^2}$

For this case we can use the following substitution $u = x-2$ and we have $dx = du$

$A = \int_{a}^b \frac{5}{u^2} du = 5\int_{a}^b u^{-2}du$

And if we solve the integral we got:

$A= -\frac{5}{u} \Big|_a^b$

And we can rewrite the expression again in terms of x and we got:

$A = -\frac{5}{x-2} \Big|_{-\infty}^1$

And we can solve this using the fundamental theorem of calculus like this:

$A= -\frac{5}{-1} - \lim_{x\to\infty} \frac{5}{x-2} = 5-0 = 5$

So then the integral converges and the area below the curve and the x axis would be 5.

7 0

3 years ago

The inside diameter of a randomly selected piston ring is a random variable with mean value 8 cm and standard deviation 0.03 cm.

S_A_V [24]

Answer:

a) P(7.99 ≤ X ≤ 8.01) = 0.8164

b) P(X ≥ 8.01) = 0.0475.

Step-by-step explanation:

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

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.

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 can be approximated to a normal distribution with mean

In this problem, we have that:

$\mu = 8, \sigma = 0.03$

(a) Calculate P(7.99 ≤ X ≤ 8.01) when n = 16.

n = 16, so $s = \frac{0.03}{4} = 0.0075$

This probability is the pvalue of Z when X = 8.01 subtracted by the pvalue of Z when X = 7.99. So

X = 8.01

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

Applying the Central Limit Theorem

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

$Z = \frac{8.01 - 8}{0.0075}$

$Z = 1.33$

$Z = 1.33$ has a pvalue of 0.9082

X = 7.99

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

$Z = \frac{7.99 - 8}{0.0075}$

$Z = -1.33$

$Z = -1.33$ has a pvalue of 0.0918

0.9082 - 0.0918 = 0.8164

P(7.99 ≤ X ≤ 8.01) = 0.8164

(b) How likely is it that the sample mean diameter exceeds 8.01 when n = 25? P(X ≥ 8.01) =

n = 25, so $s = \frac{0.03}{5} = 0.006$

This is 1 subtracted by the pvalue of Z when X = 8.01. So

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

$Z = \frac{8.01 - 8}{0.006}$

$Z = 1.67$

$Z = 1.67$ has a pvalue of 0.9525

1 - 0.9525 = 0.0475

P(X ≥ 8.01) = 0.0475.

4 0

3 years ago

Rectangle ABCD with coordinates A(1, 1), B(4, 1), C(4, 2), and D(1, 2) dilates with respect to the origin to give rectangle A'B'

Virty [35]

Scale factor is a ratio. The correct option is C.

<h3>How are scale drawings formed?</h3>

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

$\rm 1\: ft : \dfrac{s}{k}\: in.$

All feet measurements will then be multiplied by s/k to get the drawing's corresponding lengths.

The length of AB can be written as,

AB = √[(1-4)²+ (1-1)²]

AB = 3

Since the length A'B' is 6 units, therefore, the scale factor will be,

Scale factor = (Length after transformation)/(Length before transformation)

Scale factor = 6 /3 = 2

Hence, the correct option is C.

Learn more about Scale factors:

brainly.com/question/8765466

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8 0

2 years ago

2 if x = 137,2° and sin(x-y) Determine the numerical value of: cos y.tanx y = 114,99

Amanda [17]

Answer:

....................

3 0

3 years ago

In the fraction below, which number is the numerator?<br> 3<br> 4<br> ।

vesna_86 [32]

Answer: The 3 is the numerator.

The top number is always the numerator.

6 0

3 years ago

Read 2 more answers