A Realtor claims that no more than half of the homes he sells are sold for less than the asking price. When reviewing a random sample of 14 sales over the past year, he found that actually 10 were sold below the asking price.

Required:
a. The assumption of normality is justified.
b. Calculate a p-value for the observed sample outcome, using the normal distribution.
c. At the 0.05 level of significance in a right-tailed test, is the proportion of homes sold for less than the asking price greater than 50%?

Answer:

Step-by-step explanation:

This is  the method I am familiar with.

I Hope It helps :)

[tex]METHOD- 1 : Elimination\\6x - 2y=10------(1)\\2x+3y =51------(2)\\Multiply -eq-(1)- by -the-coefficient-of-x-in-equation (2)\\Multiply-eq-(2) -by -the-coefficient-of-x-in-equation (1)\\6x - 2y=10------(1) *2\\2x+3y =51------(2)*6\\\\12x-4y=20 ------(3)\\12x+18y=306 ------(4)\\Subtract -eq- (4)- from- eq -(3)\\-22y =-286\\\frac{-22y}{-22} =\frac{-286}{-22} \\y =13\\[/tex]

[tex]Substitute- 13- for y -in-equation -(1)-or-(2)\\6x - 2y=10------(1)\\6x -2(13)=10\\6x -26=10\\6x =10+26\\6x =36\\\frac{6x}{6} =\frac{36}{6} \\x =6[/tex]

Answer:

Correct answers is

Step-by-step explanation:

1. 3

2. B

3. 6

4. (6,13)

Answer:

The sum of the two remaining numbers, x and y = 60

Question:

The question isn't clear enough as some information have been omitted. Let's consider the following:

Model with Math. The average of six numbers is 18. If the average of four numbers is 12. What must be the sum of the two remaining numbers, x and y?

Write an equation to show how to find this sum.

Step-by-step explanation:

Mathematical models are applied to represent things in the real world in order to solve problems.

The formula we would use to solve this problem is an example of a mathematical model.

Types of mathematical model we can use include equations and graphs.

Using equations:

Average of six numbers = 18

Average of four of the numbers = 12

Total sum of the four numbers = 4×12 = 48

the two unknown numbers are x and y

Average of six numbers = (Sum of all 6 numbers)/6

=(Total sum of four numbers + x + y)/6

(48 + x + y)/6 = 18

The equation that shows how to find the sum:

(1/6)(48 + x + y) = 18

48 + x + y = 18×6

48 + x + y = 108

x + y = 108-48

x+y = 60

The sum of the two remaining numbers, x and y = 60

Step-by-step explanation:

-8x + 4 > 5 - 3x

-8x + 3x > 5 - 4

-5x > 1

x > 1 / - 5

Answer:

B. You shouldnt take a random sample of more than 5% of the population size.

Step-by-step explanation:

B. You shouldnt take a random sample of more than 5% of the population size. This is True, so as to avoid the research analysis to be more complex to interpret and analyzed

However, the following are not true statements:

A. Random samples only generate unbiased estimates of long-run proportions, not long-run means. This is False, as there may be sampling error, when picking the sample, which will lead to bias estimates in the long run proportions

C. There is no way that a random sample of 100 people can be representative of all adults living in the United States. This is False, as using the right factors such as gender, age, income, etc, in selecting the sample, 100 people is enough to use as sample of adults living in the United States

D. If this question is voted out, the alternate option is "larger samples are always better than smaller samples, regardless of how the sample was collected." This is False, larger samples are not always better than smaller samples. In fact, they are often difficult to analyze and interpret.

E. Nonrandom samples are always poor representations of the population: This is False, depending on the expected outcome of the research study. Some research studies required the research to use Nonrandom samples to reach verifiable conclusion.

Answer:

A = 19.6 ft²

Step-by-step explanation:

A = πr²            Use this equation to find the area of the circle

A = π(2.5)²      Multiply

A = π(6.25)     Multiply

A = 19.6 ft²

Answer:

so we have an inequality for y -

7.995<y<8.005

Then now we need in inequality for x

(y-4)/5 = x

so that means that so if we have (7.995-4)/5 we get 3.995/5 = 7.99

so we have our first 7.99<x<b

Now we solve for b

So that means that 5.005/5 = 1.001

since we are changing it we switch our signs

from 7.99<x<1.001

we do 7.99>x>1.001

therefore

1.001<x<7.99

Answer:

0.795 [tex]\leq[/tex] y [tex]\leq[/tex] 0.805

Step-by-step explanation:

8 = 5x + 4

5x = 4

x = 4/5 or 0.800

therefore 0.800 + .005 and 0.800 - .005 =

0.795 [tex]\leq[/tex] y [tex]\leq[/tex] 0.805

Answer:  0.0003

Step-by-step explanation:  Solution for fraction 3/10000 to decimal conversion

In the given, we want to convert 3 / 10000 to decimal form, we can compute this by dividing numerator 3 by denominator 10000

3/10000 = 0.0003

Answer:

20 total

Shelves 3 shelves /20 total=0.15=15%

Signs 2/20=0.10=10%

Benches 6/20=0.30=30%

Tablet Holders 9/20=0.45=45%

Step-by-step explanation:

Answer:

Shelves: 15%

Signs: 10%

Benches: 30%

Tablet Holders: 45%

Step-by-step explanation:

Shelves: [tex]\frac{3}{3+2+6+9} =\frac{3}{20} =\frac{15}{100} =[/tex] 15%

Signs: [tex]\frac{2}{3+2+6+9} =\frac{2}{20} =\frac{10}{100} =[/tex] 10%

Benches: [tex]\frac{6}{3+2+6+9} =\frac{6}{20} =\frac{30}{100}=[/tex] 30%

Tablet Holders: [tex]\frac{9}{3+2+6+9} =\frac{9}{20} =\frac{45}{100} =[/tex] 45%

Answer:

.30

Step-by-step explanation:

the answer is .30333 (with the 3 repeating) and since 3 is less than 5 you leave the second number as is.

Answer:

2

Step-by-step explanation:

1. Divide by four

2. two of the fours will cancel out leaving you to divide 4 by - 2 which is 2

Answer:

5 / (x+4)      x ≠2 x≠-4

Step-by-step explanation:

5(x-2)/(x-2)(x+4)

The denominator cannot be zero so x ≠2 x≠-4

Cancel like terms in the numerator and denominator

5 / (x+4)      x ≠2 x≠-4

Answer:

The 80% confidence interval for the average net change is (8.596, 12.904).

Critical value t=1.638.

Step-by-step explanation:

First, we calculate the mean and standard deviation of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{4}(12+7+13+11)\\\\\\M=\dfrac{43}{4}\\\\\\M=10.75\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{3}((12-10.75)^2+(7-10.75)^2+(13-10.75)^2+(11-10.75)^2)\\\\\\s=\dfrac{20.75}{3}\\\\\\s=6.92\\\\\\[/tex]

We have to calculate a 80% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=10.75.

The sample size is N=4.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.63}{\sqrt{4}}=\dfrac{2.63}{2}=1.315[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=4-1=3[/tex]

The t-value for a 80% confidence interval and 3 degrees of freedom is t=1.638.

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

[tex]MOE=t\cdot s_M=1.638 \cdot 1.315=2.154[/tex]

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

[tex]LL=M-t \cdot s_M = 10.75-2.154=8.596\\\\UL=M+t \cdot s_M = 10.75+2.154=12.904[/tex]

The 80% confidence interval for the average net change is (8.596, 12.904).

Answer:

A. x-1 and x-5

Step-by-step explanation:

zeros are 1 and 5

so the factors are:

x-1 and x-5

Option A is correct

Answer:

sale prices = $252

Step-by-step explanation: 280 - (280 x 10%) = 280 - 28 = $252

Answer:

$189

Step-by-step explanation:

10% of 210 = 21

210 - 21  = 189

Answer:

Mean of the binomial distribution  μ = 82.68

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 106 diamonds

The probability that the diamonds fail to qualify as "gemstone grade

p = 78% =0.78

We will use binomial distribution

Mean of the binomial distribution

                                       μ = n p

                                       μ = 106 × 0.78

                                       μ = 82.68

conclusion:-

Mean of the binomial distribution  μ = 82.68

Answer:

37 years difference.

Step-by-step explanation:

K = Kissi

k = Age of Kissi

E = Esinam

e = Age of Esinam

L = Lariba

l = Age of Lariba

k + e + l = 147

K : E

3 : 5 → (×3) → 12 : 15

E : L

3 : 5 → (×5) → 15 : 25

K : E : L

12 : 15 : 25

12 + 15 + 25 = 52

147/52 = 2.8269...

K is the young since out of the three part ratio, 12 is the smallest and likewise, L is the oldest.

k = 12 × 2.8269... = 33.923... → 34 y/o

e = 15 × 2.8269... = 42.40... → 42 y/o

l = 25 × 2.8269... = 70.673... → 71 y/o

∴ The difference between the youngest and oldest is:

71 - 34 = 37

Answer:

2 times some thing and plus 3 equals -7

Step-by-step explanation:

x = -5

Answer:

Step-by-step explanation:

If a sequence c1,c2,c3,...has limit K then the sequence ec1,ec2,ec3,...has limit e^K. Use this fact together with l'Hopital's rule to compute the limit of the sequence given by

bn=(n)^(5.6/n).

a)

[tex]L = \lim_{n \to \infty} b_n \\\\\\L= \lim_{n \to \infty} n^{\frac{5.6}{n} }[/tex]

Log on both sides

[tex]In (L) = \lim_{n \to \infty} In (n)^{\frac{5.6}{n} }\\\\= \lim_{n \to \infty} \frac{5.6}{n} In(n)[/tex]

[tex]=5.6 \lim_{n \to \infty} \frac{d}{dn} In(n)/\frac{d}{dn} (n)\\\\=5.6 \lim_{n \to \infty} \frac{1}{n} /1 \\\\=5.6 \lim_{n \to \infty} \frac{1}{n} \\\\=5.6 \times 0\\\\In(L) =0\\\\L=e^0\\\\L=1[/tex]

[tex]\therefore \lim_{n \to \infty} (n)^{\frac{5.6}{n} =1[/tex]

The limit value of given sequece is 1.

To understand more, check below explanation.

The given sequence is,

                   [tex]b_{n}=n^{5.6/n}[/tex]

We have to find limit of above sequence.

           [tex]L=\lim_{n \to \infty} b_n \\\\L=\lim_{n \to \infty}n^{5.6/n} \\\\ln(L)=\lim_{n \to \infty}\frac{5.6}{n}ln(n) \\\\ln(L)=5.6\lim_{n \to \infty}\frac{ln(n)}{n} \\\\ln(L)=5.6\lim_{n \to \infty}\frac{1/n}{1} \\\\ln(L)=5.6*0=0\\\\L=e^{0}=1[/tex]

Therefore, the limit value of given sequece is 1.

Learn more about the limit of function here:

https://brainly.com/question/2166212

Answer:

[tex]F=\frac{s^2_1}{s^2_2}=\frac{0.2^2}{0.126^2}=2.520[/tex]

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_1 -1 =10-1=9[/tex] and for the denominator we have [tex]n_2 -1 =20-1=19[/tex] and the F statistic have 9 degrees of freedom for the numerator and 19 for the denominator. And the P value is given by:

Now we can calculate the p value with this probability:

[tex]p_v =P(F_{9,19}>2.520)=0.043[/tex]

Using a significance level of 5% we see that the p value is lower than this value and we have enough evidence to reject the null hypothesis and we can conclude that the variation for the new process is lower than the new one.

Step-by-step explanation:

Information given

[tex]n_1 = 10 [/tex] represent the sampe size old

[tex]n_2 =20[/tex] represent the sample size new

[tex]s_1 = 0.2[/tex] represent the sample deviation for old

[tex]s_2 = 0.126[/tex] represent the sample deviation for new

The statistic is given by:

[tex]F=\frac{s^2_1}{s^2_2}[/tex]

Hypothesis to test

We want to test if the new process is less variable than the old, so the system of hypothesis are:

H0: [tex] \sigma^2_1 \leq \sigma^2_2[/tex]

H1: [tex] \sigma^2_1 >\sigma^2_2[/tex]

The statistic is given by:

[tex]F=\frac{s^2_1}{s^2_2}=\frac{0.2^2}{0.126^2}=2.520[/tex]

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_1 -1 =10-1=9[/tex] and for the denominator we have [tex]n_2 -1 =20-1=19[/tex] and the F statistic have 9 degrees of freedom for the numerator and 19 for the denominator. And the P value is given by:

Now we can calculate the p value with this probability:

[tex]p_v =P(F_{9,19}>2.520)=0.043[/tex]

Using a significance level of 5% we see that the p value is lower than this value and we have enough evidence to reject the null hypothesis and we can conclude that the variation for the new process is lower than the new one.

Answer:

five dollars and forty cents

5.40$

Step-by-step explanation:

90+6%= 95.40

Answer:

me marca como melhor resposta ☺️❤️

Step-by-step explanation:

.....

Answer:

400

brigadaaaaaaaaaaaaaa

Answer:

16:0

Step-by-step explanation:

Answer:

The number of days the cat food will last is 8 days.

Step-by-step explanation:

In this case, it it provided that Grandmother bought enough cat food for her four cats to last for 12 days.

Assume that each cat consumes x portions of food each day.

Then the four cats will consume, 4x portions of food each day.

Then in 12 days the amount of food consumed by the 4 cats will be:

Total amount of cat food = 12 × 4x

                                          = 48x.

Now, it is provided that she on her way home she brought back two stray cats.

Then the six cats will consume, 6x portions of food each day.

Compute the number of days the cat food will last as follows:

[tex]\text{Number of days the cat food will last}=\frac{\text{Total amount of cat food}}{\text{Amount of food consumed each day}}[/tex]

                                                           [tex]=\frac{48x}{6x}\\\\=\frac{48}{6}\\\\=8[/tex]

Thus, the number of days the cat food will last is 8 days.

Answer:

If there is no decimal just put number and if the number is higher than 5 you round up example 1.46 you would put 1.5

Step-by-step explanation:

HOPE IT HELPS

Answer:

Janas rate is of 4 miles per day.

Step-by-step explanation:

Her rate is the number of miles she ran per day.

We can solve this using a rule of three.

In 7 days, she ran 28 miles. How many miles she ran a day, that is, in one day?

1 day - x miles

7 days - 28 miles

[tex]7x = 28[/tex]

[tex]x = \frac{28}{7}[/tex]

[tex]x = 4[/tex]

Janas rate is of 4 miles per day.

Answer:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Step-by-step explanation:

Information given

[tex]\bar X= 28.1[/tex] represent the sample mean

[tex]\mu[/tex] population mean

[tex]\sigma =4.7[/tex] represent the population standard deviation

n=40 represent the sample size  

Confidence interval

The confidence interval for the mean is given by the following formula:

[tex]\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]   (1)

The Confidence level is is 0.95 or 95%, the significance would be [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and we can calculate the critical value using the normal standard distribution and we got [tex]z_{\alpha/2}=1.96[/tex]

And replacing we got:

[tex]28.1-1.96\frac{4.7}{\sqrt{40}}=26.64[/tex]    

[tex]28.1+ 1.96\frac{4.7}{\sqrt{40}}=29.56[/tex]    

We are confident at 95% of confidence that the true mean for the mpg is between 26.64 and 29.56. And since the lower limit from the confidence interval is highert than 25.8 then we can conclude that we have a significant increase from 1975

Answer:

[tex]x=\frac{5}{7}[/tex]

Step-by-step explanation:

[tex]3x - 2 = 3 - 4x[/tex]

Add [tex]2[/tex] and [tex]4x[/tex] on both sides of the equation.

[tex]3x - 2 +2+4x= 3 - 4x+2+4x[/tex]

[tex]3x+4x=-4x+5+4x[/tex]

[tex]7x=5[/tex]

Divide [tex]7[/tex] on both sides of the equation.

[tex]\frac{7x}{7}=\frac{5}{7}[/tex]

[tex]x=\frac{5}{7}[/tex]

55°

The sum or measures of interior angle in a triangle is 180°.

Angle A, 35° + Angle C, 90° =125°

Angle B= 180°-125°=55°[angle B]

Answer: B

Step-by-step explanation:

For this problem, to solve for x, you want to move all like terms to one side.

[tex]\frac{1}{4}x-\frac{1}{2}x=\frac{7}{8} +\frac{1}{8}[/tex]

Now that you have moved like terms to one side, you can directly add and subtract to combine like terms.

[tex]-\frac{1}{4} x=1[/tex]

x=-4

Answer:

[tex]x = - 4[/tex]

Second answer is correct

Step-by-step explanation:

[tex] \frac{1}{4} x - \frac{1}{8} = \frac{7}{8} + \frac{1}{2} x \\ \frac{1}{4} x - \frac{1}{2} x = \frac{1}{8} + \frac{7}{8} \\ \frac{1x - 2x}{4} = \frac{8}{8} \\ - \frac{1}{4} x = 1 \\ - 1x = 1 \times 4 \\ - 1x = 4 \\ x = - 4[/tex]

hope this helps you

Answer:

0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Given to a woman.

Event B: Masters degree.

21% were master’s degrees

This means that [tex]P(B) = 0.21[/tex]

Women earned 40% of masters

This means that [tex]P(A|B) = 0.4[/tex]

Probability of the degree being given to a women:

52% of 76%, 40% of 21% and 22% of 3%. So

[tex]P(A) = 0.52*0.76 + 0.4*0.21 + 0.22*0.03 = 0.4858[/tex]

What is the probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman?

[tex]P(B|A) = \frac{0.21*0.4}{0.4858} = 0.1729[/tex]

0.1729 = 17.29% probability that a randomly chosen mathematics degree was a master's degree given that it was awarded to a woman