The manufacturer of hardness testing equipment uses​ steel-ball indenters to penetrate metal that is being tested.​ However, the manufacturer thinks it would be better to use a diamond indenter so that all types of metal can be tested. Because of differences between the two types of​ indenters, it is suspected that the two methods will produce different hardness readings. The metal specimens to be tested are large enough so that two indentions can be made.​ Therefore, the manufacturer uses both indenters on each specimen and compares the hardness readings. Construct a​ 95% confidence interval to judge whether the two indenters result in different measurements.

Answer:

$6.74

Step-by-step explanation:

Subtract 15.49 and 8.75

Answer: 6.74.

Step-by-step explanation: I took the quiz before!

Hope this helps! (✪ ω ✪)

Answer:

His salary after 20 years is $48892

Step-by-step explanation:

Kevin started his new job with a salary of $26,550.

We are also given that every year, he receives a 3.1% increase in his salary

So, rate of increase = 3.1%

Formula : [tex]y(t)=y_0(1+r)^t[/tex]

Where y(t)= Amount after t years

[tex]y_0[/tex] = initial amount = 26550

r = rate of increase in decimals = [tex]\frac{3.1}{100}[/tex]

t = time =20

we are supposed to find his salary after 20 years

Substitute the values in the formula :

Salary after 20 years = [tex]26500(1+\frac{3.1}{100})^{20}=48892.00[/tex]

Hence His salary after 20 years is $48892

Answer:it’s strong the person under me is slow

Step-by-step explanation: cause I said so

Answer:

     3x^2 + 18x + 27 = 0

<=> 3(x^2 + 6x + 9) = 0

<=> 3(x + 3)^2 = 0

<=> x = -3

Hope this helps!

:)

Answer:

C -9a - 15

Step-by-step explanation:

bionomial means two terms

Answer:

10

Step-by-step explanation:

3+2=5+26=31+9=40/4=10

Step-by-step explanation:

When finding mean, you have to add up all of the number and divide that answer by the number of numbers used.

3 + 2 + 26 + 9 = 40

Now, we will divide 40 by 4 because there are 4 numbers.

40 / 4 = 10

So, the mean of the set is 10.

Answer:

0.8 or 80%

Step-by-step explanation:

To easily find percents, divide the numerator with the denominator. Or, first you can simplify the fraction first.

20/25 can be divided by 5. Which is 4/5.

4/5=0.8

So, the answer is 80%

Answer:

80%

Step-by-step explanation:

[tex]\frac{20}{25} = \frac{4}{5}[/tex]

To find the percentage, multiply by 100:

[tex]\frac{4}{5} * 100 = 80[/tex]

Answer:

Probability of even = 0.5

Step-by-step explanation:

Probability of even = total number of even numbers/ total number

Total number of Eve number = [ 2,4,6] = 3

Total numbers = [ 1,2,3,4,5,6] = 6

Probability of even = 3/6

Probability of even = 1/2

Probability of even = 0.5

Answer: is their any picture? or an example?

Answer:

Jo : μ ≤ 64.

Jo : μ > 64.

Step-by-step explanation:

From the question, the Important information to solve this question is that; ''the speed limit on this portion of Interstate 95 is 64 mph''.

The question wants us to find the fact that the average speed is greater or more than the speed limit.

Therefore, In order to solve this question, the formula to use is the ''null and alternative" hypothesis. It states that;

Jo : μ ≤ 64.

Jo : μ > 64.

The above expression is the competing hypotheses in order to determine if the average speed is greater than the speed limit.

The solid figure that is shown by the net would be a Rectangular prism.

The number of vertices would be 8 vertices.

A rectangular prism is a 3D shape with six faces, eight vertices, and twelve edges. It is a type of polyhedron, which is a solid figure with flat faces and straight edges.

The net given is a rectangular prism because the dashed lines show that the sides would fold up along with the triangles to form a rectangular prism.  

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Answer:

2.5 or 5/2

Step-by-step explanation:

The formula for the area of a triangle is \dfrac{bh}{2}, where b represents the length of the base and h represents the length of the height. With this in mind, you can set up the following equation:

[tex]\dfrac{15}{8}=\dfrac{1.5b}{2}[/tex]

[tex]\dfrac{15}{4}=1.5b[/tex]

b=2.5 or [tex]\frac{5}{2}[/tex]

Hope this helps!

The number at the end of the equation shifts the graph up or down.

Changing the 1/2 to a -2 would shift the graph down which would change the y-intercept.

The answer is D.

g(x) = ⅞x - ½

g(7) = ⅞(7) - ½

= 49/8 - ½

= 49/8 - 4/8

= 45/8

= 5 ⅝

So, the value of g(7) for that function is 5 ⅝

Hope it helpful and useful :)

The value of the given function for g(7) is 45/8.

The given function is [tex]g(x)=\frac{7}{8}x-\frac{1}{2}[/tex].

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

We need to find the value of g(7)

Substitute x=7 in the given function and simplify, we get

[tex]g(7)=\frac{7}{8}(7)-\frac{1}{2}[/tex]

= 49/8 - 1/2

= 49/8 - 4/8

= 45/8

Hence, the value of the given function for g(7) is 45/8.

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Answer: 1/2

Step-by-step explanation:

Complete Question

The line plot shows the amount of green ooze (in cup) carried by ten contestants. Find the amount each contestant would carry if the total amount carried (5 cups) was redistributed equally among all the contestants.

Answer:

1/2 Cup

Step-by-step explanation:

This is a Line Plot in which:

Total

[tex]=(\frac{1}{4}X2) +(\frac{3}{8}X2) +(\frac{1}{2}X2) +(\frac{5}{8}X3) +(\frac{7}{8}X1) \\\\=\frac{2}{4} +\frac{6}{8} +1 +\frac{15}{8} +\frac{7}{8}\\\\$=5 Cups[/tex]

If this amount was redistributed equally among the ten contestants:

Each contestant would carry (5/10) cups =1/2 cup.

Answer:

$159075.84

Step-by-step explanation:

100-7.6=92.4

1721.60*92.4=$159075.84

Answer:

 0 days 3 hours 40 minutes 0 seconds

- 0 days 1 hours 55 minutes 0 seconds

= 0 days 1 hours 45 minutes 0 seconds

= 0.0729167 days

= 1.75 hours

= 105 minutes

= 6,300 seconds

Step-by-step explanation:

Final answer:

To calculate the difference between given times, convert them into minutes and subtract. The result will be the time difference in minutes.

Explanation:

Compute: 3:40 - 1:55

To compute the difference between 3:40 and 1:55, you need to subtract the two times. First, convert both times into minutes: 3:40 = 3 x 60 + 40 = 180 + 40 = 220 minutes, and 1:55 = 1 x 60 + 55 = 60 + 55 = 115 minutes. Then, subtract 115 from 220 to get the result.

The difference between 3:40 and 1:55 is 105 minutes.

Answer:585 cubic inch

Step-by-step explanation:

volume=15 x 10 x 3 + 9 x 3 x 5

Volume=450 + 135

Volume=585

Answer:

The committee can be formed in 31,752 ways.

Step-by-step explanation:

Every committee position has the same duties and voting rights. This means that the order in which the members are chosen is not important to solve this question. So the combinations formula is used.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In how many ways can the committee be formed

4 faculty members from a set of 9

5 students from a set of 10.

Then

[tex]T = C_{9,4} \times C_{10,5} = \frac{9!}{4!(9-4)!} \times \frac{10!}{5!(10-5)!} = 31752[/tex]

The committee can be formed in 31,752 ways.

Answer:

it is 6,358.2. hope this helps

The 95% confidence interval for the number of hours students at the college study weekly, given a sample size of 49, mean of 12.2 hours, and standard deviation of 1.6, is from 11.62 hours to 12.78 hours.

In statistics, the 95% confidence interval for the mean number of hours students study in a week can be calculated using the collected data and the t-distribution. Given that the sample size is 49 (n=49), the sample mean(x) is 12.2 hours, and the standard deviation(s) is 1.6 hours, we need to apply the formula for the confidence interval which is x ± t∗(s/√n). The t-value for 95% confidence with 48 degrees of freedom (49-1) can be found using the t-distribution Inverse Calculator applet, which is about 2.01 (it varies slightly depending on the calculator used).

Now, plug in the given values into the formula: 12.2 ± 2.01 * (1.6 / √49), it simplifies to 12.2 ± 0.58. So, the 95% confidence interval for the number of hours students in the college study each week is from 11.62 hours to 12.78 hours.

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Answer:

V = (10*6*12)/3

V = 720/3

V = 240 cm^3

Step-by-step explanation:

V = LWH/3

L = base length

W = base width

H = pyramid height

Answer:

Step-by-step explanation:

Hello!

The variable of interest is

X: Systolic blood pressure of a U.S. adult. (mmHg)

X~N(μ;σ²)

μ= 122 mmHg

σ= 20 mmHg

For all calculations you have to work under the standard normal distribution, because it is tabulated. It is easier and faster to standardize or "translate" all values of X into values of Z and look for the corresponding probabilities in the table than to manually calculate them using the density function of the normal distribution.

The standard normal distribution is derived from the normal distribution. Considering a random variable X with normal distribution, mean μ and variance δ², the variable Z =(X-μ)/δ ~N(0;1) is determined.

Any value of any random variable X with normal distribution can be "converted" by subtracting the variable from its mean and dividing it by its standard deviation.

Since the distribution is centered in zero, there are two entries for its table, the left entry shows the cumulated probabilities corresponding to negative values of Z: P(Z≤z)=α and the right entry show the cumulated probabilities corresponding to positive values of Z: P(Z≤z)= 1 - α

a)

You need to calculate the percentage/ proportion of U.S. adults that have a systolic pressure greater than 142 mmHg, symbolically:

P(X>142) = 1 - P(X≤142)

To standardize this value od the variable you have to do the following calculation:

Z =(X-μ)/δ= (142-122)/20= 1

Now you look in the right entry for the cumulative probability until z= 1.00

(Remember, the first column of the table shows you the integer and first digit, the first row of the table shows you the second integer of the z value)

P(Z≤1)= 0.84134

Now you calculate the asked value:

P(X>142) = 1 - P(X≤142)= 1 - P(Z≤1)= 1 - 0.84134= 0.15866

b)

The sample mean is derived from a random variable with a normal distribution it shares that distribution with the exception that its variance is directly affected by the sample size:

X[bar]~N(μ;σ²/n)

μ= 122 mmHg

σ/√n= 20/√29= 3.71 mmHg

c)

The claim is that the mean systolic pressure of the employees is higher than the national average, symbolically μ> 122

The statistical hypotheses are:

H₀: μ≤ 122

H₁: μ> 122

d)

t= 5.495 p-value: 0.000003591

In this example the test statistic depends on the mean and the p-value is 3.591*10⁻⁶. This value indicates that 0.0003591% of the samples with size n=29 taken from a population with mean 122 mmHg, will produce a mean that provides evidence as (or stronger) than the current sample that μ is not at most 122 mmHg.

e)

The type II error is the scenario when you fail to reject the null hypothesis when the hypothesis is false. In this case, it is to fail to reject that the average systolic pressure of the company's employees is at most as the national average.

f)

The variable "X: Age of an employee" was recorded and linear regression of the systolic blood pressure as a function of the employee's ages estimated.

^Y= 97.0771 + 0.9493Xi

0.9493mmHg/years is the modification of the estimated average systolic blood pressure of the company's employees when their age increases one year.

g)

To determine the type of linear regression between the two variables, you have to analyze the slope of the equation:

As you can see in the graphic, the slope of the regression is positive, which means there is a positive regression between the systolic pressure and the age of the employees. I.e. each time the age of the employee increases, his systolic pressure also increases.

To determine the strength of the regression between these two variables you have to analyze the coefficient of determination R²:

The coefficient of determination gives you an idea of how much of the variability of the dependent variable (Y) is due to the explanatory variables under the estimated regression. It takes values between 0 to 1 or 0 to 100% if expressed in percentage. The closer the coefficient is to zero, the weaker the relationship between these two variables.

The closer the coefficient is to 100%, the stronger the relationship between these two variables.

R²= 0.712

71.2% of the variability of the systolic pressure is explained by the age fo the employees under this estimated model ^Y= 97.0771 + 0.9493Xi

The relationship between these variables is strong enough to consider the regression.

I hope this helps!

Answer: D

H0: μ=522

H1: μ>522

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

So, for this case;

The null hypothesis is that the mean score equals to 522

H0: μ=522

The alternative hypothesis is that the mean score is greater than 522.

H1: μ>522

The correct answer is D. [tex]Upper H_0: = 522, Upper H_1 > 522[/tex].

In this scenario, the math teacher is claiming that her review course increases the scores of students on the math portion of a college entrance exam. Therefore, the null hypothesis [tex](H_0)[/tex]  should represent the claim that there is no increase in the mean score, which would be that the mean score is equal to the population mean of 522. The alternative hypothesis [tex](H_1)[/tex]   should represent the teacher's claim that the mean score has increased, which would be that the mean score is greater than 522.The null hypothesis is a statement of no effect or no difference and serves as the baseline for testing. The alternative hypothesis is what we aim to support; it is a statement that there is an effect or a difference. In this case, we are testing whether the mean score of students after taking the review course is greater than the population mean.Therefore, the correct hypotheses are:- Null Hypothesis [tex](H_0): = 522[/tex] , indicating no increase in the mean score.- Alternative Hypothesis [tex](H_1): > 522[/tex] , indicating an increase in the mean score.This is a one-tailed test because we are only interested in whether the mean score has increased, not whether it has changed at all (which would require a two-tailed test).

Answer:

D. This scenario should be analysed using paired data because the groups are dependent and have a natural pairing.

Step-by-step explanation:

Paired Data can be defined as data set, when sample units of one data set are related to sample units in other data set.

Research Study about spouses number of hours of sleep each night is paired data. As, each man in the male sample group is related to a corresponding woman (his wife) in the female sample group. So, they have a natural paring & they, their sleep schedules are dependent on each other.

Based on the information given, this scenario should be analyzed using paired data because the groups are dependent and have a natural pairing.

In conclusion, the correct option is D.

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Answer:

The test statistic value is 1.474.

Step-by-step explanation:

In this case we need to determine whether the plant is making a higher than expected number of irregular t-shirts.

If more than 8% of the t-shirts manufactured at a plant are classified as irregular, the manager has to do an investigation to try to find the source of the increased mistakes in the manufacturing process..

The hypothesis for this test can be defined as follows:

H₀: The proportion of irregular t-shirts is 8%, i.e. p = 0.08.

Hₐ: The proportion of irregular t-shirts is more than 8%, i.e. p > 0.08.

The information provided is:

n = 100

X = number of irregular t-shirts = 12

Compute the sample proportion as follows:

[tex]\hat p=\frac{X}{n}=\frac{12}{100}=0.12[/tex]

Compute the test statistic as follows:

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

  [tex]=\frac{0.12-0.08}{\sqrt{\frac{0.08(1-0.08)}{100}}}\\\\=1.47441\\\\\approx 1.474[/tex]

Thus, the test statistic value is 1.474.