What is the mean of the data set? 108, 305, 252, 113, 191 Enter your answer in the box.

Answer:

0.2389 = 23.89% probability that Yuki's time is faster than Zana's.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Subtraction of normal variables:

When normal variables are subtracted, the mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.

Yuki's times in this race are normally distributed with a mean 80 seconds and standard deviation of 4.2 seconds. Zana's times are also normally distributed with a mean of 85 seconds and a standard deviation of 5.6 seconds.

Yuki's is faster than Zana if the subtraction of Yuki by Zana is larger than 0.

The mean is:

[tex]\mu = 80 - 85 = -5[/tex]

The standard deviation is:

[tex]\sigma = \sqrt{4.2^2 + 5.6^2} = 7[/tex]

Find the probability that Yuki's time is faster than Zana's.

This is P(X > 0), which is 1 subtracted by the pvalue of Z when X = 0.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{0 - (-5)}{7}[/tex]

[tex]Z = 0.71[/tex]

[tex]Z = 0.71[/tex] has a pvalue of 0.7611

1 - 0.7611 = 0.2389

0.2389 = 23.89% probability that Yuki's time is faster than Zana's.

Answer:

A. H0:μ≥29;HA:μ<29

Pvalue < 0.01

D. Reject H0; the hourly wage is less than $29

Step-by-step explanation:

The null hypothesis will negate the claim which will be the hypothesis to be tested. Therefore, since the claim is to test if hourly wage is less Than 29 ; then the null will be that hourly wage is equal to or greater than 29

H0:μ≥29;HA:μ<29

The Pvalue measure the probability that the extremity of our finding against a certain α level. The Pvalue obtained using the Excel function should be 0.00058

When Pvalue is < α ; We reject the null hypothesis

Hence, Reject H0; the hourly wage is less than $29 and conclude that hourly wage is less Than $29

Answer:

A.) ŷ = 0.73986X + 18.98921

B.) 80

C.) r = 0.9205

Step-by-step explanation:

Given :

1st test grade (X) :

98

77

88

80

96

61

66

95

69

final average (Y) :

93

78

84

73

84

64

64

95

76

Using a linear regression calculator :

The model obtained is :

ŷ = 0.73986X + 18.98921

Student with x = 83

ŷ = 0.73986(83) + 18.98921

ŷ = 80.39759

ŷ = 80 (nearest whole number)

The R value is : 0.9205 which shows that there is a strong linear correlation between the first test grade and the final average a student Obtian in an exam because the r value is very close to 1.

R² = √0.9205 = 0.8473 ; this means about 84.73% of variation in final average can be explained by the regression line.

Answer:

638 in.²

Step-by-step explanation:

Assuming you need to cover just the surface area of the box with no overlaps, and the shape is a rectangular prism, then you need to find the surface area of a rectangular prism.

SA = PH + 2LW

where

P = perimeter of base = 2(L + W),

H = height of prism

L = length of base

W = width of base

SA = 2(16 + 7)(9) + 2(16)(7)

SA = 638

Answer:

Step-by-step explanation:

¡Hola! Lo siento, pero no hablo español. ¡qué tengas un lindo día! También necesito puntos porque soy nuevo.

Answer:

False

Step-by-step explanation:

The definition described is Perimeter

Area is found by multiplying the base by the height or the length by the width

Answer:

There are many answers

Step-by-step explanation:

So, since we are finding the equivalent fraction there can be many answers

Here are 5 answers that can help you

• -8/14

• -12/21

• -16/28

• -40/70

• -24/42

Answer:

The sampling distribution of the sample average score for this random sample of 64 students is approximately normal, with mean 19.6 and standard deviation 0.625.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

Mean of 19.6 and a standard deviation of 5.0.

This means that [tex]\mu = 19.6, \sigma = 5[/tex]

What is the sampling distribution of the sample average score for this random sample of 64 students?

By the Central Limit Thoerem, the sampling distribution of the sample average score for this random sample of 64 students is approximately normal, with mean 19.6 and standard deviation [tex]s = \frac{5}{\sqrt{64}} = \frac{5}{8} = 0.625[/tex]

Answer:

Step-by-step explanation:

Answer:

That did not make sense

Answer:

x = 3

Step-by-step explanation:

Verified correct with test results.

Just had to delete the jibberish to find the actual question for this problem:

The figure shows 2 right triangles, triangle A B C with right angle B and triangle B D C with right angle D. The measure of angle B A C is 45 degrees. The measure of angle D B C is 60 degrees. The length of side C A is 6 square root 2. The length of side B D is x. What is the value of x?

Answer:

Step-by-step explanation:

30

Answer:

x ≈ − 1.25593754, 1.70270637

Step-by-step explanation:

Graph each side of the equation. The solution is the x-value of the point of intersection.

Answer:

See Below.

Step-by-step explanation:

We want to prove the trigonometric identity:

[tex]\displaystyle \frac{\sec^2(\theta)-1}{\sin(\theta)}=\frac{\sin(\theta)}{1-\sin^2(\theta)}[/tex]

To start, let's simplify the right side. Recall the Pythagorean Identity:

[tex]\sin^2(\theta)+\cos^2(\theta)=1[/tex]

Therefore:

[tex]\cos^2(\theta)=1-\sin^2(\theta)[/tex]

Substitute:

[tex]\displaystyle \frac{\sin(\theta)}{1-\sin^2(\theta)}=\frac{\sin(\theta)}{\cos^2(\theta)}[/tex]

Split:

[tex]\displaystyle =\frac{\sin(\theta)}{\cos(\theta)}\left(\frac{1}{\cos(\theta)}\right)=\tan(\theta)\sec(\theta)[/tex]

Therefore, our equation becomes:

[tex]\displaystyle \frac{\sec^2(\theta)-1}{\sin(\theta)}=\tan(\theta)\sec(\theta)[/tex]

From the Pythagorean Identity, we can divide both sides by cos²(θ). This yields:

[tex]\displaystyle \tan^2(\theta)+1=\sec^2(\theta)[/tex]

So:

[tex]\tan^2(\theta)=\sec^2(\theta)-1[/tex]

Substitute:

[tex]\displaystyle \frac{\tan^2(\theta)}{\sin(\theta)}=\tan(\theta)\sec(\theta)[/tex]

Rewrite:

[tex]\displaystyle (\tan(\theta))^2\left(\frac{1}{\sin(\theta)}\right)=\tan(\theta)\sec(\theta)[/tex]

Recall that tan(θ) = sin(θ)/cos(θ). So:

[tex]\displaystyle \frac{\sin^2(\theta)}{\cos^2(\theta)}\left(\frac{1}{\sin(\theta)}\right)=\tan(\theta)\sec(\theta)[/tex]

Simplify:

[tex]\displaystyle \frac{\sin(\theta)}{\cos^2(\theta)}=\tan(\theta)\sec(\theta)[/tex]

Simplify:

[tex]\tan(\theta)\sec(\theta)=\tan(\theta)\sec(\theta)}[/tex]

Hence proven.  

Answer:

A D 1 Vertical

Step-by-step explanation:

x always represents 1

Answer:

1738.28

Step-by-step explanation:

Given that

The number is 1738.279

We need to round off to 2 decimal places

Now as we know that

If the rounded number would be followed by 0, 1, 2, 3 or 4, so the number would be down

Let us suppose the number is 32 so it would be 30

If the rounded number would be followed by 5,6,7,8 or 9 so the number would be up

Let us suppose the number be 37 so it would be 40

Now as per the given case, the number is 1738.279

So after rounding to 2 decimal places, the number is 1738.28

Answer:

Step-by-step explanation:

i don't know  sorry

Answer:

36/21 (simplified)

Step-by-step explanation:

To use KCF, multiply by the reciprocal. 16/21 x 9/4

Just flip the denominator with the numerator

Answer:

[tex]y=\frac{3}{2} x+0[/tex]

Step-by-step explanation:

points on the line are:-

[tex](0,0) and(2,3)[/tex]

[tex]m=\frac{3-0}{2-0} =\frac{3}{2}[/tex]

[tex]y=mx+b[/tex]

[tex]y=\frac{3}{2} x+b[/tex]

[tex]0=\frac{3}{2}(0)+b[/tex]

[tex]0=b[/tex]

so...

[tex]y=\frac{3}{2} x+0[/tex]

[tex]---------[/tex]

hope it helps...

have a great day!!

Answer:

D. 2/5

Step-by-step explanation:

First, find the total number of sock pairs in his drawer:

5 + 1 + 4

= 10

Since there are 4 pairs of blue socks, the probability that he will choose a blue pair of socks is 4/10.

This can be simplified by dividing each number by 2.

Simplified, the probability is 2/5.

So, the correct answer is D. 2/5

Answer:

.4

Step-by-step explanation:

Sample proportion of 90% confidence interval for a proportion (0.37, 0.43) is 0.40 .

Thus option C is correct.

Given, A 90% confidence interval for a proportion is found to be (0.37, 0.43) .

Sample proportion - margin of error = 0.37

Sample proportion + margin of error = 0.43

Therefore, the sample proportion will.be the average of the values given above and this will be:

= (0.37 + 0.43)/2

= 0.80/2

= 0.40

Therefore option C is correct.

Know more about sample proportions,

https://brainly.com/question/32835750

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Answer:

The answer is B 100 in^2

Step-by-step explanation:

add 15+11+24 = 50 X 2 = 100

so yeah

good luck :D

Answer:

B) Vertex (1,2), maximum

Step-by-step explanation:

First, determine if the graph has a maximum or a minimum value. Since the graph opens downwards, it has a maximum value.

The maximum is the point that has the greatest y value. We can see that the greatest y value is at [tex]y=2[/tex]. Going down two units from that spot, we can see that the x value is at [tex]x=1[/tex]. We can plug those into the vertex form, [tex](x,y)[/tex]. By plugging in we get the point [tex](1,2)[/tex].

Incomplete question. However, I answered from a general research perspective.

Explanation:

Note, the term sample used in statistical research refers to subjects or persons carefully selected (using a particular sampling method/type ) to represent the target population.

A randomly selected sample could be done as either:

Using any of the above sampling methods could result in 70% of the population being from low-income families as this is a matter of chance. Hence, we can agree with the research results.

Using the z-distribution, it is found that since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the children were not randomly selected.

At the null hypothesis, we test if they were really randomly selected, that is, the proportion is of 80%:

[tex]H_0: p = 0.8[/tex]

At the alternative hypothesis, we test if they were not randomly selected, that is, the proportion is of less than 80%.

[tex]H_1: p < 0.8[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]p = 0.8, n = 150, \overline{p} = 0.7[/tex]

Then, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.7 - 0.8}{\sqrt{\frac{0.8(0.2)}{150}}}[/tex]

[tex]z = -3.06[/tex]

The critical value for a left-tailed test, as we are testing if the proportion is less than a value, with a significance level of 0.05, is of [tex]z^{\ast} = -1.645[/tex].

Since the test statistic is less than the critical value for the left-tailed test, there is enough evidence to conclude that the children were not randomly selected.

A similar problem is given at https://brainly.com/question/24166849

Answer:

A (g(x) = }(x-2)5.1).

Step-by-step explanation:

The function which results after the sequence of transformations given is B. g(x) = 1/2 (x + 2)⁵ - 1.

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given function is,

f(x) = x⁵

When a function is compressed vertically, then new function formed will be of the form, k f(x), where k is the factor that is compressed.

After compress vertically by 1/2,

f(x) changes to 1/2 f(x) = 1/2 x⁵

After the horizontal translation of 2 units to the left,

1/2 f(x) changes to 1/2 f(x + 2) = 1/2 (x + 2)⁵.

After vertical translation of 1 unit to the down,

1/2 f(x + 2) changes to 1/2 f(x + 2) - 1 = 1/2 (x + 2)⁵ - 1

Hence the correct option is B . g(x) = 1/2 (x + 2)⁵ - 1.

Learn more about Transformations of Functions here :

https://brainly.com/question/13810353

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Your answer would be C (8,15,17) and E (15,20,15) or is it 25?

Step-by-step explanation:

:)

Answer:

7.57

Step-by-step explanation:

Answer:

20°

Step-by-step explanation:

Congruent Triangles:

If two triangles are congruent, their angles have the same measure.

Angle P corresponds to Angle J

Angle J measures 20º, so angle P will also measure 20º

Para calcular el volumen  de un prisma rectangular, multiplica sus 3 dimensiones: longitud x ancho x altura.