I need help on this

(4.3 x 10^-3)(2 x 10^-2) in standard form

notka56 [123]

Answer:

8.6•10^-5 or 0.000086

6 0

3 years ago

Student records suggest that the population of students spends an average of 6.30 hours per week playing organized sports. The p

Ymorist [56]

Answer:

a) 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.

b) 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.

Step-by-step explanation:

To solve this question, it is important to know 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 $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .

In this problem, we have that:

$\mu = 6.3, \sigma = 2.1, n = 49, s = \frac{2.1}{\sqrt{49}} = 0.3$

A) What is the chance HLI will find a sample mean between 5.5 and 7.1 hours?

This is the pvalue of Z when X = 7.1 subtracted by the pvalue of Z when X = 5.5.

By the Central Limit Theorem, the formula for Z is:

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

X = 7.1

$Z = \frac{7.1 - 6.3}{0.3}$

$Z = 2.67$

$Z = 2.67$ has a pvalue of 0.9962

X = 5.5

$Z = \frac{5.5 - 6.3}{0.3}$

$Z = -2.67$

$Z = -2.67$ has a pvalue of 0.0038

So there is a 0.9962 - 0.0038 = 0.9924 = 99.24% chance HLI will find a sample mean between 5.5 and 7.1 hours.

B) Calculate the probability that the sample mean will be between 5.9 and 6.7 hours.

This is the pvalue of Z when X = 6.7 subtracted by the pvalue of Z when X = 5.9

X = 6.7

$Z = \frac{6.7 - 6.3}{0.3}$

$Z = 1.33$

$Z = 1.33$ has a pvalue of 0.9082

X = 5.9

$Z = \frac{5.9 - 6.3}{0.3}$

$Z = -1.33$

$Z = -1.33$ has a pvalue of 0.0918.

So there is a 0.9082 - 0.0918 = 0.8164 = 81.64% probability that the sample mean will be between 5.9 and 6.7 hours.

5 0

3 years ago

Line segment XY is tangent to circle Z at point U. If the measure of is 84°, what is the measure of ? 42° 84° 96° 168°

Andreas93 [3]

Answer:

The measure of angle YUV is equal to $m$

Step-by-step explanation:

see the attached figure to better understand the problem

we have that

$arc\ UV=84\°$ -----> given problem

so

$m$ ------> by central angle

we know that

The triangle UZV is an isosceles triangle

because

$ZU=ZV=radius$

so

$m$ -----> bases angle of the isosceles triangle

Remember that

The sum of the internal angles of a triangle is equal to $180\°$

so

$m$

$2m$

substitute and solve for m<ZUV

$2m$

$m$

$m$ ------> by complementary angles

solve for m<YUZ

$48\°+m$

$m$

7 0

3 years ago

Read 2 more answers

Given that 32✓2=2^a , find the value of a

NNADVOKAT [17]

Answer:

Step-by-step explanation:

All you need is something that when you divide the right side (the way I've written it) by 2, you get 32 sqrt(2). So a must also have sqrt(2) in it. In addition, it must also have 16 as well so that when you multiply by 2, you get 32.

2a = 32*sqrt(2) Divide by 2

a = 16*sqrt(2)

5 0

3 years ago

Read 2 more answers

A class of 49 students took a test. 17 students had an average score of 74. the other students had

Ann [662]

Answer: 83

Step-by-step explanation:

2816+1258/49

4074/49

582/7

83

6 0

2 years ago