If (x + 8) is a factor of f(x), which of the following must be true?
GOF
Both x = 8 and x = 8 are roots of f(x).
Neither x = -8 nor x = 8 is a root of f(x).
F-8) = 0
f(8) = 0

Answer:

a. [tex]f^-^1(x)=\frac{x}{4} +3[/tex]

b. [tex]f(-9)=-48[/tex]

c. [tex]f^-^1(-9)=\frac{3}{4}[/tex]

Step-by-step explanation:

In a, the -1 means inverse of f(x). To find the inverse, you rewrite the equation in terms of x and y. You replace the x with y and y with x. Then you solve for y.

[tex]f^-^1(x)=4x-12[/tex]

[tex]y=4x-12[/tex]

[tex]x=4y-12[/tex]

[tex]x+12=4y[/tex]

[tex]\frac{x}{4} +3=y[/tex]

[tex]f^-^1(x)=\frac{x}{4} +3[/tex]

In b, all you have to do is plug in -9 into f(x).

[tex]f(9)=4(9)-12[/tex]

[tex]f(9)=-48[/tex]

In c, you plug in -9 into inverse function f.

[tex]f^-^1(-9)=\frac{3}{4}[/tex]

Answer:

[tex] (17-14) -1.64 \sqrt{\frac{4.2^2}{30} +\frac{4.2^2}{30}}=1.222[/tex]

[tex] (17-14) +1.64 \sqrt{\frac{4.2^2}{30} +\frac{4.2^2}{30}}=4.778[/tex]

So then we can conclude at 90% of confidence that the difference in the two means is between 1.222 and 4.778 beats per minute

Step-by-step explanation:

For this case we have the following info given:

[tex] \bar X_1 = 17[/tex] sample mean for the first sample

[tex] \bar X_2 = 14[/tex] sample mean for the second sample

[tex]\sigma =4.2[/tex] represent the population deviation

[tex] n_1= n_2 =30[/tex] represent the sample size ofr each case

We can construct the confidence interval for the difference of means with the following formula:

[tex] (\bar X_1 -\bar X_2) \pm z_{\alpha/2} \sqrt{\frac{\sigma^2_1}{n_1} +\frac{\sigma^2_2}{n_2}}[/tex]

And the confidence for this case is 90% or 0.9 so then the significance level is [tex]\alpha=1-0.9=0.1[/tex] and [tex]\alpha/2 =0.05[/tex] the critical value for this case is:

[tex] z_{\alpha/2}=1.64[/tex]

And replacing we got:

[tex] (17-14) -1.64 \sqrt{\frac{4.2^2}{30} +\frac{4.2^2}{30}}=1.222[/tex]

[tex] (17-14) +1.64 \sqrt{\frac{4.2^2}{30} +\frac{4.2^2}{30}}=4.778[/tex]

So then we can conclude at 90% of confidence that the difference in the two means is between 1.222 and 4.778 beats per minute

Answer:

Explained below.

Step-by-step explanation:

In this case we need to select a sample of 6 students from the entire statistics class.

(a)

A simple random sample is a part of a statistical population in which every individual of the population has an equal probability of being selected.

Assigning each individual of the population a unique number and using a computer or random number generator for selection is a procedure to select a simple random sample.

So, we can assign unique numbers to each student in the class and use a random number generator to select any six.

(b)

Systematic sampling is a kind of probability sampling method in which individuals from a larger population are nominated according to a random initial point and a static, periodic interval.  

For instance, consider a study where the researcher first selects a name randomly from the alphabetized order and then follow a fixed pattern of selecting every 10th person from the population.

Suppose there are n students in the class.

And the first student selected is the kth student. Then the remaining five can be selected in a equal interval of k students.

That is, the second student selected will be the 2kth student, the 3rd will be the 3kth, the 4th will be the 4kth, the 5th will be the 5kth and the 6th will be the 6kth.

The sample selected will be a systematic random sample.

(c)

Stratified sampling is a kind of sampling in which whole population is distributed into homogeneous subgroups before one takes a sample. These subgroups are called strata which is mutually exclusive or related.

In this process the population members cannot be excluded.

To select six students we first divide the entire class into 6 subgroups or 6 strata.

Then select one student from each group.

The sample selected will be a stratified random sample.

(d)

Cluster Sampling is a method to randomly select samples from a population that is too enormous for simple random sampling.  

Using cluster sampling, the experimenter distributes the entire population into distinct groups, called clusters.  

Then, a simple random sample of clusters is chosen from the population. Then the experimenter performs the analysis on data from the sampled clusters.

To select a cluster sample, first divided the entire class into various small groups consisting of 2 or 3 students each.

Then select a simple random sample of these groups to select 6 students.

The sample selected will be a cluster sample.

Answer:

(A) Probability that the port handles less than 5 million tons of cargo per week is 0.7291.

(B) Probability that the port handles 3 or more million tons of cargo per week is 0.9664.

(C) Probability that the port handles between 3 million and 4 million tons of cargo per week is 0.2373.

(D) The number of tons of cargo per week that will require the port to extend its operating hours is 3.65 million tons.

Step-by-step explanation:

We are given that the port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge.

The U.S. Army Corps of Engineers reports that the port handles a mean of 4.5 million tons of cargo per week with a standard deviation of 0.82 million tons.

Let X = Number of tons of cargo handled per week

SO, X ~ Normal([tex]\mu=4.5,\sigma^{2}=0.82^{2}[/tex])

The z score probability distribution for normal distribution is given by;

                               Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 4.5 million tons

            [tex]\sigma[/tex] = standard deviation = 0.82 million tons

(A) Probability that the port handles less than 5 million tons of cargo per week is given by = P(X < 5 million tons)

        P(X < 5) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{5-4.5}{0.82}[/tex] ) = P(Z < 0.61) = 0.7291

The above probability is calculated by looking at the value of x = 0.61 in the z table which has an area of 0.7291.

(B) Probability that the port handles 3 or more million tons of cargo per week is given by = P(X [tex]\geq[/tex] 3 million tons)

        P(X [tex]\geq[/tex] 3) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\geq[/tex] [tex]\frac{3-4.5}{0.82}[/tex] ) = P(Z [tex]\geq[/tex] -1.83) = P(Z [tex]\leq[/tex] 1.83)

                                                                          = 0.9664

The above probability is calculated by looking at the value of x = 1.83 in the z table which has an area of 0.9664.

(C) Probability that the port handles between 3 million and 4 million tons of cargo per week is given by = P(3 million tons < X < 4 million tons)

     P(3 million tons < X < 4 million tons) = P(X < 4) - P(X [tex]\leq[/tex] 3)

      P(X < 4) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{4-4.5}{0.82}[/tex] ) = P(Z < -0.61) = 1 - P(Z [tex]\leq[/tex] 0.61)

                                                = 1 - 0.7291 = 0.2709

      P(X [tex]\leq[/tex] 3) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{3-4.5}{0.82}[/tex] ) = P(Z [tex]\leq[/tex] -1.83) = 1 - P(Z < 1.83)

                                                 = 1 - 0.9664 = 0.0336

The above probability is calculated by looking at the value of x = 0.61 and x = 1.83 in the z table which has an area of 0.7291 and 0.9664 respectively.

Therefore, P(3 < X < 4) = 0.2709 - 0.0336 = 0.2373

(D) Now, it is given that 85% of the time the port can handle the weekly cargo volume without extending operating hours, that means;

           P(X > x) = 0.85     {where x is the required no. of tons of cargo}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-4.5}{0.82}[/tex] ) = 0.85

           P(Z > [tex]\frac{x-4.5}{0.82}[/tex] ) = 0.85

In the z table, the critical value of x which represents top 85% area is given as -1.036, that is;

                      [tex]\frac{x-4.5}{0.82} = -1.036[/tex]  

                    [tex]{x-4.5} = -1.036\times 0.82[/tex]

                     x  =  4.5 - 0.85 = 3.65 million tons

Hence, the number of tons of cargo per week that will require the port to extend its operating hours is 3.65 million tons.

Answer:

2 isnt the domain

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Yes, because the product of their slopes are -1. Rest explanation in the attached file. Hope it helps :)

Answer:

AB(y = ax + b) contains A(2, 1) and B(3, 4)

=> 2a + b = 1

    3a + b =4

=> a = 3, b= -5 => Slope AB = a = 3

CD (y = cx + d) contains C(-2, -1) and D(1, -2)

=> -2c + d = -1

       c  + d = -2

=> c = -1/3, d = -5/3 => Slope CD = c =-1/3

If AB is perpendicular to CD, then Slope's AB x Slope's CD = -1

Check:

a x c = 3 x (-1/3) = -1

=> AB is perpendicular to CD

=> Option B is correct.

Hope this helps!

:)

Answer:

not sure

Step-by-step explanation:

can someone explain?  

Answer:

Yes

Step-by-step explanation:

For a triangle to be rights angled.

It should follow Pythagoras theorem.

Pythagoras theorem states that if sides containing right angle is  a and b

then  is given by

hypotenuse =  [tex]\sqrt{a^2+b^2}[/tex]

As hypotenuse is always the greatest side

Out of the given sides 144m,165m,219m

219 can only be hypotenuse

Thus side containing right angle will be 144m and 165m .

Lets plug these value in formula of Pythagoras theorem

[tex]hypotenuse = \sqrt{144^2 + 165^2} \\hypotenuse = \sqrt{20,736 + 27,225} \\hypotenuse = \sqrt{47961} \\hypotenuse = 219\\[/tex]

As we can see that hypotenuse calculated by us is same as given in problem.

Thus the given triangle is right angled.

Answer:

(5/4), (1.3), (1 8/25)

Step-by-step explanation:

5/4 as a decimal is 1.25

1.3 comes next

1 and 8/25 as a decimal is 1.32

1.25 < 1.3 < 1.32

Answer:

5/4 (1.25) , 1.3, 1 8/25 (0.32)

Step-by-step explanation:

Answer:

5 yards.

Step-by-step explanation:

5 yards = 180 inches

Answer:

$20 after the applied coupon

Step-by-step explanation:

The required sale price of the shirt after getting  1/3 off is $20.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

Here,
A $30 shirt is marked, "Get 1/3 off.
The sale price of the shirt,
= 30 - 1 / 3×30
= 30 - 10
= $ 20

Thus, the required sale price of the shirt after getting  1/3 off is $20.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ1

Answer:

Limit does not exist.

Step-by-step explanation:

From the graph, notice that the limit does not exist, when you move to the right the limit tend to -3 and when you approach from the left your limit approaches 4, therefore since the right and left limit are not equal the limit does not exist.

Answer:

166 quarters,  40 dimes

Step-by-step explanation:

x - quarters

y - dimes

      x  +        y =  206

0.25x + 0.10y = 45.50

y = 206 - x

0.25x + 0.10(206 - x) = 45.50

0.25x + 20.6 - 0.10x = 45.50

0.15x = 45.50 - 20.6

0.15 x = 24.9

x = 24.9/ 0.15 = 166 quarters

y =206 - 166 = 40 dimes

Check:

0.25*166+ 0.10*40 = 45.50

45.50 = 45.50

Answer:

  see below

Step-by-step explanation:

A percentage change is computed as follows:

  percent change = ((new value) -(original value))/(original value) × 100%

For your first one, this looks like ...

  percent change = ($25 -$75)/$75 × 100% = (-50/75) × 100% = -0.667×100%

  percent change = -66.7%

__

When there are a lot of similar calculations to do, I like to use a spreadsheet. See below for the other percentage changes (rightmost column).

Answer:

Option (3)

Step-by-step explanation:

From the given figure,

Two triangles ΔABC and ΔDEF are similar.

ΔABC ~ ΔDEF

By the definition of similarity of two triangles, corresponding sides of the similar triangles are in the same ratio.

[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]

Now from this relation,

[tex]\frac{BC}{EF}=\frac{AC}{DF}[/tex]

[tex]\frac{DF}{EF}=\frac{AC}{BC}[/tex]

Therefore, Option (3) will be the correct proportionality statement.

Answer:

The other endpoint of the​ segment is [tex](-18,-7)[/tex].

Step-by-step explanation:

The midpoint of the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by the following formula:

                                          [tex](x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )[/tex]

where [tex](x_m,y_m)[/tex] = coordinates of the midpoint.

We know that the midpoint is (-15, 2) and an endpoint is (-12, 11). Substituting the information we have gives:

                                         [tex](-15,2)=(\frac{x_1-12}{2}, \frac{y_1+11}{2} )[/tex]

To find [tex]x_1[/tex] we need to solve this equation:

[tex]-15=\frac{x_1-12}{2} \\\\\frac{x_1-12}{2}=-15\\\\\frac{2\left(x_1-12\right)}{2}=2\left(-15\right)\\\\x_1-12=-30\\\\x_1-12+12=-30+12\\\\x_1=-18[/tex]

and to find [tex]y_1[/tex] we need to solve this equation:

[tex]2= \frac{y_1+11}{2} \\\\\frac{y_1+11}{2}=2\\\\\frac{2\left(y_1+11\right)}{2}=2\cdot \:2\\\\y_1+11=4\\\\y_1=-7[/tex]

The other endpoint of the​ segment is [tex](x_1,y_1)=(-18,-7)[/tex].

Answer:

26

Step-by-step explanation:

The quotient of 16 and 8 = 16/8 = 2

24 + 2 = 26

Answer:

  16/8 +24

Step-by-step explanation:

The quotient of 16 and 8 is written as ...

  16/8

If we start with this as the first element of the sum then the sum that represents 24 added to this is ...

  16/8 +24

Answer:

The large pizza has the lower cost per square inch, so it is the better buy.

Step-by-step explanation:

A pizza has the format of a circle.

The area of a circle with radius r is given by the following equation:

[tex]A = \pi r^{2}[/tex]

A large pizza with an 18 inch diameter for $20

The radius is half the diameter, so [tex]r = 9[/tex].

In square inches, the area is:

[tex]A = \pi*9^{2} = 81\pi = 254.47[/tex]

254.47 square inches cost $20. So the price per square inch is 20/254.47 = 0.0786.

Medium pizza with a 14 inch diameter for $14:

Radius is 7. So

[tex]A = \pi*7^{2} = 49\pi = 153.938[/tex]

153.938 square inches cost $14. So the price per square inch is 14/153.938 = 0.0909.

The large pizza has the lower cost per square inch, so it is the better buy.

Answer:

  4/5π

Step-by-step explanation:

30 minutes corresponds to π radians, so 24 minutes is ...

  (24/30)π = 4/5π radians

Answer:

4 ft

Step-by-step explanation:

The area of a triangle is

A = 1/2 bh

9 = 1/2 (4.5)h

9 =2.25 h

Divide each side by 2.25

9/2.25 = 2.25h/2.25

4 =h

Answer:

Hieght=4

hope it helps u...

Step-by-step explanation:

Answer:

64.40$

Step-by-step explanation:

Answer:

3kg = $34.20

34kg= ?

x= (34 x $34.20)/3

x= 1162,80/3

x= $387,60

Answer:

C -- It is the difference between limited resources and wants and needs.

Step-by-step explanation:

I've done a lesson on scarcity before.

Plz click the Thanks button!

<Jayla>

It is the difference between limited resources and wants and needs. Reset N.

A government is the system or group of people governing an organized community, generally a state.

Scarcity "refers to the basic fact of life that there exists only a finite amount of human and nonhuman resources which the best technical knowledge is capable of using to produce only limited maximum amounts of each economic good.

In the given  statements.

A. It is a situation in which people cannot pay for goods and services.

B. It is an economic situation where the government has to import items. C. It is the difference between limited resources and wants and needs. Reset N

C describes scarcity.

Hence, It is the difference between limited resources and wants and needs. Reset N.

To learn more on Government click:

https://brainly.com/question/16940043

#SPJ2

Answer:

9

Step-by-step explanation:

For one throw the probability of a miss is 1/2 since there are just two outcomes

Similarly for one throw the probability of a score is 1/2 since there are two outcomes.

Therefore for 8 trials we expect at least for different trials starting from 1

8 miss 0 score

7 miss 1 score

6 miss 2 score

5 miss 3 score

4 miss 4 score

3 miss 5 score

2 miss 6 score

1 miss 7 score

0 miss 8 score

So the number of possible outcomes is 9

And this define by what we call the binomial probability and is defined as

Answer:

72 in³

Step-by-step explanation:

THe volume = area of the base × height

area of the base (trapezoid) = [(8×(12+6)]÷2 = 72

height = 1

then

the volume = ((8×(12+6))÷2)×1 = 72

Answer:

82.76

Step-by-step explanation:

77 x 7.5%=5.775

5.775 +77

Answer:

c) A matched-pairs t-interval for a population mean difference

Step-by-step explanation:

Matched-Pairs t-Test. A matched-pairs t-test is used to test whether there is a significant mean difference between two sets of paired data.

A matched pair t test is used for comparison between means of two sets of paired data.

Thus, Option C: A matched-pairs t-interval for a population mean difference. is correct choice.

The selected sample of people will have to give pretest and then training and then post-test and the difference in the scores is recorded.

The researches want to identify the resultant difference so as to identify the effectiveness of the program.

For such type of cases, we use matched pair t test.

A matched pair t test is used to see if there is significant difference between means of two sets of paired data.

By paired data, we mean the data in both set which is paired.

Since the person is same who gives pre and post  test after training, thus the data is paired.

Also since the difference is to be analyzed to check the significance of the reading program, thus matched pair t test is perfect fit here.

Thus, option C: A matched pairs t-interval for a population mean difference is correct option.

Learn more about t-tests here:

https://brainly.com/question/1189751

Answer:D

Step-by-step explanation:

It’s a permutation

Answer:

1) As the P-value (0.097) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the women's claim that female employees were passed over for management training in favor of their male colleagues.

2) The 95% confidence interval for the population proportion is (0.173, 0.427).

The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.

Step-by-step explanation:

This is a hypothesis test for a proportion.

The claim is that female employees were passed over for management training in favor of their male colleagues.

We use the women's part for sample and population proportions.

Then, the null and alternative hypothesis are:

[tex]H_0: \pi=0.4\\\\H_a:\pi<0.4[/tex]

The significance level is 0.05.

The sample has a size n=50 persons.

The sample proportion is p=0.3.

[tex]p=X/n=15/50=0.3[/tex]

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.4*0.6}{50}}\\\\\\ \sigma_p=\sqrt{0.0048}=0.069[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.3-0.4+0.5/50}{0.069}=\dfrac{-0.09}{0.069}=-1.299[/tex]

This test is a left-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=P(z<-1.299)=0.097[/tex]

As the P-value (0.097) is greater than the significance level (0.05), the effect is  not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that female employees were passed over for management training in favor of their male colleagues.

b) We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.3.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.3*0.7}{50}}\\\\\\ \sigma_p=\sqrt{0.0042}=0.0648[/tex]

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.0648=0.127[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sigma_p = 0.3-0.127=0.173\\\\UL=p+z \cdot \sigma_p = 0.3+0.127=0.427[/tex]

The 95% confidence interval for the population proportion is (0.173, 0.427).

The populations proportion (π=0.4) is included in this confidence interval, so the claim has no enough evidence to be supported.

Answer:

Step-by-step explanation:

Given data;

n = 17

[tex]\sum x =7692[/tex]

[tex]\sum x^2=3685124[/tex]

[tex]\sum y =7656\\\\ \sum xy=3662682[/tex]

Slope:

[tex]\hat B_1=\frac{n \sum xy - \sum x \sum y}{n \sum x^2 - ( \sum x)^2} \\\\=0.96994[/tex]

≅ 0.970

y - intercept :

[tex]\hat B_0 = \frac{\sum y}{n} - \hat B\frac{\sum x}{n} \\\\=11.48178[/tex]

≅ 11.482

a)

Equation :

[tex]\hat y = 11.482+0.970x[/tex]

b)

Predicted wright meter reading

[tex]\hat y = 11.48178+0.96994(563)\\\\=557.558[/tex]

c)Predicted wright meter reading

[tex]\hat y = 11.48178+0.96994(342)\\\\= 343.201[/tex]

Answer:

96 feet

Step-by-step explanation:

12 feet × 8 feet = 97 feet