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3 years ago

Which of the following best corresponds to the x-value where the function f(x)=cos x is a minimum in the interval x=|25,30|

1 answer:

3 0

Answer: On the interval [25, 30] the function y = cos x is at it's minimum at x = 9pi or about 28.26.

The graph of y = cos x starts at 1 and moves in the shape of a wave from -1 to 1. It reaches it's first minimum value when x = pi. The period of the wave is 2 pi.

Therefore, it is at its lowest value at the following values, 1pi, 3pi, 5pi, 7pi, 9pi... The value in our given interval is 9pi.

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According to an article in Newsweek, the rate of water pollution in China is more than twice that measured in the US and more th

jeyben [28]

Answer:

(a) 0.119

(b) 0.1699

Solution:

As per the question:

Mean of the emission, $\mu = 11.7$ million ponds/day

Standard deviation, $\sigma = 2.8$ million ponds/day

Now,

(a) The probability for the water pollution to be at least 15 million pounds/day:

$P(X\geq 15) = P(\frac{X - /mu}{\sigma} \geq \frac{15 - 11.7}{2.8})$

$P(X\geq 15) = P(Z \geq 1.178)$

$P(X\geq 15)$ = 1 - P(Z < 1.178)

Using the Z score table:

$P(X\geq 15)$ = 1 - 0.881 = 0.119

The required probability is 0.119

(b) The probability when the water pollution is in between 6.2 and 9.3 million pounds/day:

$P(6.2 < X < 9.3) = P(\frac{6.2 - 11.7}{2.8} < \frac{X - \mu}{\sigma} < \frac{9.3 - 11.7}{2.8})$

$P(6.2 < X < 9.3) = P(- 1.96 < Z < - 0.86)$

P(Z < - 0.86) - P(Z < - 1.96)

Now, using teh Z score table:

0.1949 - 0.025 = 0.1699

4 0

3 years ago

Plz help I will make you brainliest!Thanks

STatiana [176]

Use the formula V=AbH and 48=16h will be the second step and then divide by 16 and then you get the answer

7 0

3 years ago

Read 2 more answers

Suppose that the national average for the math portion of the College Board's SAT is 515. The College Board periodically rescale

nasty-shy [4]

Answer:

a) 16% of students have an SAT math score greater than 615.

b) 2.5% of students have an SAT math score greater than 715.

c) 34% of students have an SAT math score between 415 and 515.

d) $Z = 1.05$

e) $Z = -1.10$

Step-by-step explanation:

To solve this question, we have to understand the normal probability distribution and the empirical rule.

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.

Empirical rule

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

$\mu = 515, \sigma = 100$

(a) What percentage of students have an SAT math score greater than 615?

615 is one standard deviation above the mean.

68% of the measures are within 1 standard deviation of the mean. The other 32% are more than 1 standard deviation from the mean. The normal probability distribution is symmetric. So of those 32%, 16% are more than 1 standard deviation above the mean and 16% more then 1 standard deviation below the mean.

So, 16% of students have an SAT math score greater than 615.

(b) What percentage of students have an SAT math score greater than 715?

715 is two standard deviations above the mean.

95% of the measures are within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. The normal probability distribution is symmetric. So of those 5%, 2.5% are more than 2 standard deviations above the mean and 2.5% more then 2 standard deviations below the mean.

So, 2.5% of students have an SAT math score greater than 715.

(c) What percentage of students have an SAT math score between 415 and 515?

415 is one standard deviation below the mean.

515 is the mean

68% of the measures are within 1 standard deviation of the mean. The normal probability distribution is symmetric, which means that of these 68%, 34% are within 1 standard deviation below the mean and the mean, and 34% are within the mean and 1 standard deviation above the mean.

So, 34% of students have an SAT math score between 415 and 515.

(d) What is the z-score for student with an SAT math score of 620?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 620. So

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

$Z = \frac{620 - 515}{100}$

$Z = 1.05$

(e) What is the z-score for a student with an SAT math score of 405?

We have that:

$\mu = 515, \sigma = 100$

This is Z when X = 405. So

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

$Z = \frac{405 - 515}{100}$

$Z = -1.10$

3 0

4 years ago

The equation of line fis - 3y + 4x = 9 write the equation of a line that is parallel to line and passes through the point (- 12,

ollegr [7]

Answer:

$y = - 4x - 42$

Step-by-step explanation:

The equation of the line that is parallel to the line we are trying to find is

$- 3y + 4x = 9 \\ or \\ - 3y = - 4x + 9 \:(standard form) \\ \\therefore \: the \: slope \: of \: the \: line \\ \: is \: - 4$

We can recall that when two lines are parallel it means that they have the same slope. Therefore the slope of the line we are trying to find is also -4. We now know that:

$y = 6 \: \: \: x = - 12 \: \: \: slope = - 4$