How are the lengths of the four sides of the parallelogram related ?

Answer:

The x-intercept is -6.

Step-by-step explanation:

You could use a graphing calculator, which would make it so much easier to find, but under the circumstances you aren't allowed to do so, you should:

1) Start from the y-intercept. In your case, it is -2. Since the y-intercept is negative, you want to apply the slope in a certain way.

The line will remain the same if your slope is -1/3 or if it is 1/-3. In your case, since your y-intercept is -2, you want to apply the slope 1/-3.

2) Move the point (0,-2) up 1, then left 3. This will get you the point (-3,-1). Your final answer should be in the format (x,0).

3) Now, move the point (-3,-1) up 1, then left 3. This will result in your point being (-6,0). Notice how the y-value is 0, so this is your final answer.

Keep in mind that this technique will not always be so easy to use. This particular problem is fine, though.

Answer:

Step-by-step explanation:

+ You click on -15 for a point.

+ Then you move the mouse to the left.

+ Because x<-15, that means you do not take -15, you click on the -15 one more.

That is all.

Hope you understand.

Answer:

1.) You click on -15 for a point.

2.) Then you move the mouse to the left.

3.) Because x<-15, that means you do not take -15, you click on the -15 one more.

Answer:

Use order of operation

Step-by-step explanation:

Answer:

2(x+8)(x-7)

Step-by-step explanation:

If the question is asking 2x^2+2x-112, then the answer is 2(x+8)(x-7).

First, you factor out the two: 2(x^2+x-56)

Next, you find something that adds to x and multiplies to -56: 8 and -7

After, you get 2(x+8)(x-7)

Answer:

The answer is A. True

Step-by-step explanation:

The range of Fx) = 7*4^x is all positive real numbers.

hope this helps : )

Answer:

It's D.

Step-by-step explanation:

Answer:

3(x - 2)(x - 5)

Step-by-step explanation:

Factor 3 from all terms within the trinomial:

(3x² - 21x + 30)/3 = x² - 7x + 10

3(x² - 7x + 10)

Simplify.

(x² - 7x + 10)

x               -5

x               -2

3(x - 2)(x - 5)* is your answer.

* remember to bring the 3 that you factored out in the beginning and stick it to the front.

~

Answer:

99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].

Step-by-step explanation:

We are given that a survey that asked whether people agree or disagree with the statement ‘‘There is only one true love for each person." has been conducted. The result is that 735 of the 2625 respondents agreed, 1812 disagreed, and 78 answered ‘‘don’t know."

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

                                 P.Q. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of people who disagree with the statement = [tex]\frac{1812}{2625}[/tex] = 0.69

           n = sample of respondents = 2625

           p = population proportion of people who disagree with statement

Here for constructing 99% confidence interval we have used One-sample z proportion statistics.

So, 99% confidence interval for the population proportion, p is ;

P(-2.58 < N(0,1) < 2.58) = 0.99  {As the critical value of z at 0.5% level

                                                   of significance are -2.58 & 2.58}  

P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99

P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99

99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]

= [ [tex]0.69-2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }[/tex] , [tex]0.69+2.58 \times {\sqrt{\frac{0.69(1-0.69)}{2625} } }[/tex] ]

 = [0.667 , 0.713]

Therefore, 99% confidence interval for the proportion of people who disagree with the statement is [0.667 , 0.713].

Answer:

The difference between mistrust and distrust comes down to nuances in meaning. Distrust is a withholding of trust based on evidence or informed opinion. Many people distrust salespeople working on commission, for instance, knowing that these salespeople personally benefit from their purchases.

Step-by-step explanation:

Answer:

The alternative hypothesis H0, should be rejected, if sample mean, X' < 25.051

Step-by-step explanation:

Given:

Sample size, n = 40

Mean, μ = 27

Significance level = 0.02

Standard deviation = 6

For null hypothesis :

H0 : μ ≥ 27

For alternative hypothesis :

H1 : μ < 27

At significance level, α = 0.02, from Z table, Zα = 2.054

This is a left tailed test

Solving for X' we have:

[tex] X' = u - Za \frac{\sigma}{\sqrt{n}}[/tex]

[tex] X' = 27 - 2.054 \frac{6}{\sqrt{40}}= 25.051[/tex]

The alternative hypothesis H0, should be rejected, if sample mean, X' < 25.051

The rejection rule is based on the value of for the test to determine whether the manufacturer's claim should be rejected is [tex]\mu<27[/tex].

Given :

The following steps can be used in order to determine the rejection rule based on the value of the test:

Step 1 - The Hypothesis test can be used in order to determine the rejection rule based on the value of the test.

The null hypothesis is given below:

[tex]H_0 : \mu\geq 27[/tex]

The alternate hypothesis is given below:

[tex]H_a : \mu<27[/tex]

Step 2 - Now, the formula of X' is given below:

[tex]X' = \mu-Z_\alpha \dfrac{\sigma}{\sqrt{n} }[/tex]

Step 3 - Now, substitute the values of the known terms in the above formula.

[tex]X' = 27-2.054 \dfrac{6}{\sqrt{40} }[/tex]

Step 4 - SImplify the above expression.

[tex]X' = 25.051[/tex]

From the above steps, it can be concluded that the null hypothesis is rejected.

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Answer:x-2y

Step-by-step explanation:

-1/2(-2x+4y)

Open the brackets

2x/2 - 4y/2

x - 2y

Answer:

a. Gwen expect to make 3.75 sets

b. The variance for the number of sets Gwen will make is 0.9375

c. Gwen expect to make 2 shots

Step-by-step explanation:

a. According to the given data we have the following:

Here this follows negative binomial distribution with parameter r =3 and p=0.8

To calculate how many sets does Gwen expect to make we have to calculate the following formula:

expected number of sets =r/p

expected number of sets =3/0.8=3.75

Gwen expect to make 3.75 sets.

b. In order to calculate the variance for the number of sets Gwen will make we have to use the following formula:

variance for the number of sets=σ∧2=r(1-p)/p∧2

variance for the number of sets=3*(1-0.8)/0.8^2

variance for the number of sets=0.9375

The variance for the number of sets Gwen will make is 0.9375

c. To calculate how many shots does Gwen expect to make, we have to calculate first the probability she shoots all the three in the set as follows:

probability she shoots all the three in the set=0.8∧3=0.512

if E(X)=1/p, therefore, 1/p=1/0.512=1.95

Gwen expect to make 2 shots

Answer:

C

Step-by-step explanation:

Answer:

[tex]P(x\geq 17)=0.00128[/tex]

Step-by-step explanation:

The probability that the man gets x out of 20 correct follows a Binomial distribution, so the probability is calculated as:

[tex]P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}[/tex]

Where n is the number of identical experiments and p is the probability of success. In this case n is 20.

Additionally, if he has no ESP the probability that he predict correctly is 0.5, because he is only guessing.

Then, the probability that he gets x out of 20 correct is equal to:

[tex]P(x)=\frac{20!}{x!(20-x)!}*0.5^{x}*(1-0.5)^{20-x}[/tex]

Therefore the probability that he would have done at least 17 out of 20 well if he had no ESP is:

[tex]P(x\geq 17)=P(17)+P(18)+P(19)+P(20)\\[/tex]

Where:

[tex]P(17)=\frac{20!}{17!(20-17)!}*0.5^{17}*(1-0.5)^{20-17}=0.00108719\\P(18)=\frac{20!}{18!(20-18)!}*0.5^{18}*(1-0.5)^{20-18}=0.00018119\\P(19)=\frac{20!}{19!(20-19)!}*0.5^{19}*(1-0.5)^{20-19}=0.00001907\\P(20)=\frac{20!}{20!(20-20)!}*0.5^{20}*(1-0.5)^{20-20}=0.00000095[/tex]

So, [tex]P(x\geq 17)[/tex] is equal to:

[tex]P(x\geq 17)=0.00108719+0.00018119+0.00001907+0.00000095\\P(x\geq 17)=0.00128[/tex]

The probability that he would have done at least 17 out of 20 if he had no ESP is 0.00128 and this can be determined by using the binomial distribution formula.

Given :

A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped 20 times, and the man is asked to predict the outcome in advance. He gets 17 out of 20 correct.

The formula of the binomial distribution is given by:

[tex]\rm P(x)=\dfrac{n!}{x!(n-x)!}\times p^x \times (1-p)^{n-x}[/tex]

Now, put all the known terms in the above formula.

[tex]\rm P(x)=\dfrac{20!}{x!(20-x)!}\times 0.5^x \times (1-05)^{20-x}[/tex]

Now, the probability that he would have done at least 17 out of 20 if he had no ESP:

[tex]\rm P(x\geq 17) = P(17)+P(18)+P(19)+P(20)[/tex]

where:

[tex]\rm P(17)=\dfrac{20!}{(20-17!)}\times 0.5^{17}\times 0.5^{20-17}=0.00108719[/tex]

[tex]\rm P(18)=\dfrac{20!}{(20-18!)}\times 0.5^{18}\times 0.5^{20-18}=0.00018119[/tex]

[tex]\rm P(19)=\dfrac{20!}{(20-19!)}\times 0.5^{19}\times 0.5^{20-19}=0.00001907[/tex]

[tex]\rm P(20)=\dfrac{20!}{(20-20!)}\times 0.5^{20}\times 0.5^{20-20}=0.00000095[/tex]

So, the value of P(x [tex]\geq[/tex] 17) is:

[tex]\rm P(x\geq 17)= 0.00108719+0.00018119+0.00001907+0.00000095[/tex]

[tex]\rm P(x\geq 17)= 0.00128[/tex]

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Answer:

  see the bullet list below

Step-by-step explanation:

Given the expression: p² -3 +3p -8 +p +p³

The following statements are true:

_____

Terms are generally separated by + or - signs. (The sign is considered to be part of the term.) In the context of a polynomial, terms may be constants, or may be a product with factors that are constants or variables.

_____

Further comments on "term"

In other contexts, the word "term" is used for various purposes. It can designate a member of a sequence, the left or right side of an equation, the numerator or denominator of a rational expression, or just about any identifiable expression that can be considered as a unit. Whereas "coefficient" or "factor" may apply to just about any subset of the (prime) factors of a product, the word "term" is generally restricted to consideration of the product as a whole.

In the given expression, -3 and -8 are like terms, while 3p and p are also like terms. The expression contains six terms and like terms have the same variables raised to the same powers. However, not all terms with variables are like terms in this instance.

The expression given is p squared minus 3 + 3p minus 8 + p + p cubed. When we look into it, we can see a couple of true statements.

However, the terms p squared, 3p, p, and p cubed are not like terms since the powers of p in each term are different. Similarly, the terms p squared and p cubed are not like terms since the powers of p are 2 and 3, which are not the same.

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Answer:

y = 41/6

Step-by-step explanation:

This means that  y = kx.    k is a constant.

6 = k*72

and.

y = k*82 ...

k = 6/72 = 1/12

y = 82/12

y = 41/6

Answer: B. You may use the t procedure, provided your sample size is large, say, at least 30.

Step-by-step explanation: To use a T test hypothesis, the following steps is considered;

1. Add the test hypothesis when using a T test module in the experiment

2. Add the date set that contains the columns that is to be analyzed

3. Decide which kind of T test is appropriated for the data

4. If single sample is been used, the adequate parameters should be used.

The correct statement in this case is "You may use the t procedure, provided your sample size is large, say, at least 30."

We have been given that Layana’s house is located at [tex](2\frac{2}{3}, 7\frac{1}{3})[/tex] on a map. The store where she works is located at [tex](-1\frac{1}{3}, 7\frac{1}{3})[/tex].

We are asked to find the distance from Layana’s home to the store

We will use distance formula to solve our given problem.

Let us convert our given coordinates in improper fractions.

[tex]2\frac{2}{3}\Rightarrow \frac{8}{3}[/tex]

[tex]7\frac{1}{3}\Rightarrow \frac{22}{3}[/tex]

[tex]-1\frac{1}{3}\Rightarrow -\frac{4}{3}[/tex]

Now we will use distance formula to solve our given problem.

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Upon substituting coordinates of our given point in above formula, we will get:

[tex]D=\sqrt{(\frac{22}{3}-\frac{22}{3})^2+(\frac{8}{3}-(-\frac{4}{3}))^2}[/tex]

[tex]D=\sqrt{(0)^2+(\frac{8}{3}+\frac{4}{3})^2}[/tex]

[tex]D=\sqrt{0+(\frac{8+4}{3})^2}[/tex]

[tex]D=\sqrt{(\frac{12}{3})^2}[/tex]

[tex]D=\sqrt{(4)^2}[/tex]

[tex]D=4[/tex]

Therefore, the distance from Layana's home to the store is 4 units and option A is the correct choice.

Answer:

its A ^3^

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

We notice this is an arithmetic sequence.

14, 9,  4.

common difference = d = 14 - 9 = 5

first term a_1 = 14

Find 6th term a_6

a_n = (n -1)*d + a_1

a_6 = (6 -1)*5 + 14

a_6 = 5*5 + 14 = 25 + 14 = 39

Answer:

452.16

Step-by-step explanation:

Area of a circle = pi*radius squared

A= 3.14(12)^2

=3.14*144

=452.16

Final answer:

The area of a circle with a radius of 12 cm can be calculated using the formula A = \u03C0r^2. By applying the radius to this formula with pi approximated to 3.14, we obtain an area of 452.16 cm^2, which corresponds to option D.

Explanation:

To calculate the area of the circle with a radius of 12 cm, we use the formula: A = \\u03C0r^2\

Where (pi) is approximately 3.14 and r is the radius of the circle.

Plugging the radius into the formula:

A = 3.14 * (12 cm)^2

A = 3.14 * 144 cm^2

A = 452.16 cm^2

Thus, the correct answer is D. 452.16 cm^2.

Answer:

38 bananas

Step-by-step explanation:

6(7)=42 bananas 42-4=38 bananas

Answer:

A.

I say this is the answer because if she has gotten into a habait of buying and breaking glasses,shes just very careless

Answer:

hope she won

t

Step-by-step explanation:

Answer:

the answer is 262 days

Step-by-step explanation:

To find the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius, you need to solve the equation T(t) = 20. This involves finding the inverse cosine of a specific value, setting up an equation, and adding one year to the solution. After performing these steps, you can find the value of t that corresponds to the second time.

To find the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius, we need to solve the equation T(t) = 20. We can rewrite this equation as 7.5cos(2π/365t) + 21.5 = 20. Subtracting 21.5 from both sides gives us 7.5cos(2π/365t) = -1.5. Dividing both sides by 7.5 and simplifying further, we have cos(2π/365t) = -0.2. To find the second time, we need to find the value of t that satisfies this equation.

To find the value of t, we need to use the inverse cosine function (also known as arccosine). The inverse cosine function (cos^(-1)) gives us the angle whose cosine is a specific value. In this case, we want to find t such that cos(2π/365t) = -0.2. We can use a calculator or math software to find the inverse cosine of -0.2. Let's assume the inverse cosine of -0.2 is x.

Now we can set up an equation: 2π/365t = x. Solving for t, we get t = (365x)/(2π). However, we need to find the second time after the hottest day, so we need to find the value of t that satisfies the equation after adding one year (365 days) to the original value. Therefore, the second time after the hottest day of the year that the daily high temperature is 20 degrees Celsius is t = (365x)/(2π) + 365.

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

[tex]H_0:\mu_x=\mu_y=\mu_z[/tex]

Alternative hypothesis: the means are not equal

[tex]H_a: \mu_x\neq\mu_y\neq\mu_z[/tex]

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

[tex]s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33[/tex]

Then, we calculate the mean standard error (MSE):

[tex]MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78[/tex]

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

[tex]M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91[/tex]

The MSB is then:

[tex]s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172[/tex]

Now we calculate the F statistic as:

[tex]F=MSB/MSE=172/23.78=7.23[/tex]

The degrees of freedom of the numerator are:

[tex]dfn=a-1=3-1=2[/tex]

The degrees of freedom of the denominator are:

[tex]dfd=N-a=3*4-3=12-3=9[/tex]

The P-value of F=7.23, dfn=2 and dfd=9 is:

[tex]P-value=P(F>7.23)=0.01342[/tex]

As the P-value (0.013) is smaller than the significance level (0.05), the null hypothesis is rejected.

There is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Answer:

P(1) = 0.2857

P(2) = 0.1428

P(3) = 0.1428

P(4) = 0.1428

P(5) = 0.1428

P(6) = 0.1428

Step-by-step explanation:

From the question, we know that Rolling a 1 with the red die is twice as likely as rolling each of the other five numbers, so we can write the following equation:

P(1) = 2X        

Where X is the probability of rolling each of the other five numbers or:

P(2) = P(3) = P(4) = P(5) = P(6) = X  

Additionally, the sum of all the probabilities is 1, so:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

Now, we can replace P(1) by 2X and P(2), P(3), P(4), P(5) and P(6) by X, as:

P(1) + P(2) + P(3) + P(4) + P(5) + P(6) = 1

2X  +   X   +    X   +   X  +   X   +   X  = 1

Finally, solving for X, we get:

7X = 1

X = 1/7

X = 0.1428

So, the probability of rolling a 1 is equal to:

P(1) = 2X  = 2*(0.1428) = 0.2857

And the probability of rolling each of the other five numbers is:

P(2) = P(3) = P(4) = P(5) = P(6) = X  

P(2) = P(3) = P(4) = P(5) = P(6) = 0.1428

Answer:

95​% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Step-by-step explanation:

We are given that the National Center for Education Statistics surveyed a random sample of 4400 college graduates about the lengths of time required to earn their bachelor’s degrees. The mean was 5.15 years and the standard deviation was 1.68 years respectively.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                              P.Q. =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = sample mean time = 5.15 years

            [tex]\sigma[/tex] = sample standard deviation = 1.68 years

            n = sample of college graduates = 4400

            [tex]\mu[/tex] = population mean time

Here for constructing 95% confidence interval we have used One-sample z test statistics although we are given sample standard deviation because the sample size is very large so at large sample values t distribution also follows normal.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

                                               level of significance are -1.96 & 1.96}  

P(-1.96 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 1.96) = 0.95

P( [tex]-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]

                                              = [ [tex]5.15-1.96 \times {\frac{1.68}{\sqrt{4400} } }[/tex] , [tex]5.15+1.96 \times {\frac{1.68}{\sqrt{4400} } }[/tex] ]

                                             = [5.10 , 5.20]

Therefore, 95​% confidence interval for the mean time required to earn a bachelor’s degree by all college students is [5.10 years , 5.20 years].

Answer:

D.

Step-by-step explanation:

Answer:

D.He divided the exponents in the parentheses instead of subtracting.

Step-by-step explanation:

Edge 2022

Answer:

The fraction that represents the proportion of students that go make their homework is 1/6

Step-by-step explanation:

The sum of the percentage of students is 100% = 1.

In this problem, we have that:

1/3 said they watch television

1/2 said they go to sports practice

x said they do homework.

This is a sum of fractions, and the lesser common multiple of 3 and 2 is 6.

So

[tex]\frac{1}{3} + \frac{1}{2} + x = 1[/tex]

[tex]\frac{2 + 3 + 6x}{6} = 1[/tex]

[tex]5 + 6x = 6[/tex]

[tex]6x = 1[/tex]

[tex]x = \frac{1}{6}[/tex]

The fraction that represents the proportion of students that go make their homework is 1/6

Answer:

a) A 95% confidence interval for μ is 25.5 ±2.2284 3.01

The 95% of confidence intervals for mean μ is determined by

(23.478 , 27.522)

Step-by-step explanation:

Step( i ) :-

Given sample size 'n' =11

The mean of the sample x⁻ = 25.5

The standard deviation of the sample 'S' = 3.01

95% of confidence intervals:

The 95% of confidence intervals for mean μ is determined by

[tex]( x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} + t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )[/tex]

Step(ii):-

The critical value ∝ =0.05

[tex]t_{\frac{\alpha }{2} } = 2.228[/tex]

The degrees of freedom ν=n-1 = 11-1 =10

[tex]( 25.5 - 2.228 \frac{3.01}{\sqrt{11} } , 25.5 + 2.228 \frac{3.01}{\sqrt{11} } )[/tex]

(25.5-2.0220, 25.5 + 2.0220)

(23.478 , 27.522)

Final answer:-

The 95% of confidence intervals for mean μ is determined by

(23.478 , 27.522)

Final answer:

The correct statement is: a. A 95% confidence interval for μ is 25.5 ±2.2284 3.01. To calculate the confidence interval for the population mean, we use the formula: sample mean ± (critical value) × (standard deviation / square root of sample size).

Explanation:

The correct statement is:

a. A 95% confidence interval for μ is 25.5 ±2.2284 3.01

To calculate the confidence interval for the population mean, we use the formula: sample mean ± (critical value) × (standard deviation / square root of sample size).

In this case, with a sample mean of 25.5, standard deviation of 3.01, and a sample size of 11, the critical value for a 95% confidence level is 2.2284. Therefore, the correct confidence interval is 25.5 ± 2.2284 × 3.01.

Answer:

Step-by-step explanation:

The volume of a cube is the cube of the edge dimension. Here, that dimension is 5/8 in, so the volume is ...

  V = s³ = (5/8 in)³ = 125/512 in³ . . . volume of the cube

The volume of a cube 1/8 inch on a side is ...

  V = (1/8 in)³ = 1/512 in³

Clearly, a volume that is 125/512 in³ will require 125 of the cubes of size 1/512 in³ to fill it.

  125 of the smaller cubes will fit inside.

_____

Alternate solution

You can also determine the number of smaller cubes by considering it takes 5 of them in each direction to make 5/8 inch. Then the volume is 5³ = 125 of the smaller cubes.

Answer:

5

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Answer: as the x values increase the y values decrease

Step-by-step explanation:

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