A statistics student examined whether a relationship exists between city miles per gallon (mpg) and highway miles per gallon (mpg) for cars. The miles per gallon of a car describe the typical number of miles the car can drive on one gallon of gas. Using a random sample of 50 cars, the student obtained the least-squares regression equation:
predicted highway mpg = 1.14.(city mpg) +5.8
Which statement below accurately describes the meaning of the number 1.14 in the regression equation?
a. If a vehicle's city mpg increases by 1 mile per gallon, its predicted highway mpg will decrease by 1.14 miles per gallon.
b. If a vehicle's city mpg increases by 1.14 mile per gallon, its predicted highway mpg will increase by 5.8 miles per gallon.
c. If a vehicle's city mpg increases by 1 mile per gallon, its predicted highway miles per gallon will increase by 1.14 miles per gallon.
d. If a vehicle's city mpg increases by 1.14 mile per gallon, its predicted highway mpg will increase by 1 mile per gallon.

Answer:

the answer is 5

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

5x-10=15

5x=25

x=5

Answer:

Step-by-step explanation:

A. x² = –100

This equation has no solution because x² is always positive.

B. 5x² = 1

then x² = 1/5

then x = 1/(√5) or x = -1/(√5)

C. 6x² + 17 = 11

then 6x² = 11 - 17 = -6

then x² = -6/6 = -1  

This equation has no solution because x² is always positive.

D. 7(x + 6) = 42

then x + 6 = 42/7 = 6

then x = 6 - 6 = 0

_____________________

:)

Answer:

[tex]\frac{28}{3}[/tex]

Step-by-step explanation:

[tex]2\frac{1}{3}=\frac{7}{3}[/tex]

[tex]\frac{7}{3}*4=\frac{28}{3}[/tex]

Answer:

9 1/3

Step-by-step explanation:

2 1/3=7/3

7/3 divide 1/4=7/3 x 4/1=28/3=9 1/3

Answer:

Step-by-step explanation:

These are mostly calculator problems. The only trick is the last one. Your calculator will have either a y^x button or ^ button. They both do the same thing.

So for the last one, you must do it as

64 y/x (1÷6)= and you will get 2. Perhaps all of them should be done that way.

If your calculator uses ^ then you would do it

64^(1÷6)= which is the same thing.

Answers

a 4

b 10

c 5

d 2

Answer:

The answer would be 50%

Step-by-step explanation:

You Would get this by dviding 36/72 which would give you .5 and then you convert that to a percentage

Answer:

50%

Step-by-step explanation:

Answer:

  x = 4.1 cm

Step-by-step explanation:

The long leg of the right triangle is half the chord length, so is ...

  15.6 cm/2 = 7.8 cm

Then the leg marked x can be found from the Pythagorean theorem.

  x^2 +7.8^2 = 8.8^2

  x = √(77.44 -60.84) = √16.6 ≈ 4.1

x is about 4.1 cm.

Answer:

(9x - 1)²

Step-by-step explanation:

If you can tell, the square root of 81 is 9. This should be a clue that the polynomial could be one binomial squared. If you tried factoring starting out with 9x in both parenthesis, you could see that you would get (9x - 1)² as your answer.

Answer:

(9x-1)²

Step-by-step explanation:

81x² - 18x + 1= (9x)²- 2*9x+1²= (9x-1)²

Answer:

80

Step-by-step explanation:

46+15+19 which should give you a total answer of 80

Answer:

Step-by-step explanation:

Hello!

The objective is to test the claim that less than 41% of the publisher's readers own a laptop.

To do so, a sample of 320 readers was taken and the proportion of readers that own a laptop resulted in 36%

Be X: number of readers that own a laptop.

X~Bi(n;p)

n=320

Sample proportion p'= 0.36

The hypotheses are:

H₀: p ≥ 0.41

H₁: p < 0.41

α: 0.05

[tex]Z=\frac{p'-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex]≈N(0;1)

[tex]Z_{H_0}=\frac{0.36-0.41}{\sqrt{\frac{0.41(1-0.41)}{320} } }= -1.82[/tex]

This test is one-tailed to the left, meaning, that you'll reject the null hypothesis to small values of Z, there is only one critical value that defined the rejection region:

[tex]Z_{\alpha }= Z_{0.05}= -1.645[/tex]

The decision rule is:

If [tex]Z_{H_0}[/tex] ≤ -1.645, reject the null hypothesis.

If [tex]Z_{H_0}[/tex] > -1.645, do not reject the null hypothesis.

The calculated value is less than the critical value, then the decision is to reject the null hypothesis.

So at a 5% significance level, the test is significant. You can conclude that the population proportion of the publisher's readers that own a laptop is less than 41%.

I hope this helps!

Answer:87

Step-by-step explanation:

866

Answer:

y= 3/2x -2

Step-by-step explanation:

make y be on one side by itself ( -2y = -3x + 4 )

divide by negative 2 in order to get y by itself ( -2y/-2 = -3/-2 + 4/-2 )

two negatives make a positive ( y = 3/2 + -2 )

Answer:

(C)72.4 in

Step-by-step explanation:

Given an acute triangle in which the longest side measures 30 inches; and the other two sides are congruent.

Consider the attached diagram

AB=BC=x

However to be able to solve for x, we form a right triangle with endpoints A and C.

Since the hypotenuse is always the longest side in a right triangle

Hypotenuse, AC=30 Inches

Using Pythagoras Theorem

[tex]30^2=x^2+x^2\\900=2x^2\\x^2=450\\x=\sqrt{450}\\x=21.21$ inches[/tex]

Therefore, the smallest possible perimeter of the triangle

Perimeter=2x+30

=2(21.21)+30

=42.42+30

=72.4 Inches (rounded to the nearest tenth)

Answer:

(1/2, 1)

2

Step-by-step explanation:

x² + y² − x − 2y − 11/4 = 0

x² − x + y² − 2y = 11/4

Complete the squares.

x² − x + 1/4 + y² − 2y + 1 = 11/4 + 1/4 + 1

(x − 1/2)² + (y − 1)² = 4

The center of the circle is (1/2, 1) and the radius of the circle is 2.

Answer:

Option  A

Step-by-step explanation:

[tex](\frac{1}2} ,1)[/tex], 2 units

Answer:

The differential equation is  [tex]\frac{dx(t)}{dt} = k x(t) [7000 - x(t)][/tex]

Step-by-step explanation:

From the question we are told that

     The number of students are [tex]n = 7000[/tex]

      The number of student that have contracted the flu is  x(t)

The number of student that don't have the flu is mathematically represented as

      [tex]z = 7000 - x(t)[/tex]

The rate at which the disease spread is proportional to the number of interactions between students with the flu and students who have not yet contracted it, which can be mathematically represented as

         [tex]\frac{dx(t)}{dt} \ \ \ \alpha\ \ \ x(t) [7000 - x(t)][/tex]

=>     [tex]\frac{dx(t)}{dt} = k x(t) [7000 - x(t)][/tex]

Answer:

286 degrees and 143 degrees

Step-by-step explanation:

When line intersect the two vertical angle adds up to 180 degrees

To find the other vertical angle:

180 -37=143 degrees

So for two vertical angles

we take (180*2)-(37*2)=286 degrees

Answer:

work is shown and pictured

Answer:

The approximate percentage of cars that remain in service between 73 and 84 months

P( 73 < x < 84 ) = 0.02145 = 2.1 %

Step-by-step explanation:

Explanation:-

Given mean of the Population 'μ ' = 51 months

Standard deviation of the Population 'σ' = 11 months

Let 'X' be the random variable of Normal distribution

Let    'X'  = 73

[tex]Z = \frac{x-mean}{S.D} = \frac{73-51}{11} = 2[/tex]

Let  'X' = 84

[tex]Z = \frac{84-51}{11} = 3[/tex]

The approximate percentage of cars that remain in service between 73 and 84 months

P( 73 < x < 84 )      = P( 2 < Z < 3)

                              = P( Z<3) - P( Z <2)

                             =  0.5 + A(3) - ( 0.5 + A(2))

                            = A(3) - A( 2)

                            = 0.49865 - 0.4772     ( From Normal table)

                            = 0.02145

 P( 73 < x < 84 ) = 0.02145

The approximate percentage of cars that remain in service between 73 and 84 months

P( 73 < x < 84 ) = 0.02145 = 2.1 %

Answer:

The Supreme Court.

Step-by-step explanation:

After the end of the Civil War and the enactment of the Thirteenth Amendment in 1865, slavery was officially abolished in the United States. Thus, the millions of African American slaves that inhabited the southern states of the country won their freedom and equality before the law against whites.

Now this situation began to dismember in 1877, when federal troops left the southern states and Reconstruction officially came to an end. From then on, Democratic governors and legislators began to sanction the Black Codes and Jim Crow Laws, aimed at curtailing the civil and political rights of African-Americans.

This situation was tested before the Supreme Court in 1896 in the case Plessy v. Ferguson. But in the ruling of said case, the Supreme Court established that racial segregation was constitutional and therefore neglected African Americans and their rights.

Answer:

Step-by-step explanation:

Confidence interval for the difference between two population means is written in the form,

difference in sample means ± margin of error

The difference in sample means is the point estimate for the difference in population means. In the given scenario, the point estimate is the difference in mean amount spent by the sampled customers on a trip to Target or​ Walmart.

Since the interval was (- $15.05​,$2.95), it means that the lower limit is - $15.05 and the upper limit us $2.95.

Therefore, the 95% confidence interval is providing a range that we are 95% confident that the true difference in mean amount spent by Target customers and Walmart customers falls between - $15.05​ and $2.95

[tex]the \: answer \: is \: 22.4 \: cm \\ please \: see \: the \: attached \: picture \\ for \: full \: solution \\ hope \: it \: helps[/tex]

The length of AE is 22.4cm rounded to one decimal place.

Answer:

Step-by-step explanation:

5x - c = k

Add c  to each side

5x - c+c = k+c

5x = (k+c)

Divide each side by 5

5x/5 = (k+c)/5

x = (k+c)/5

Answer:

x=(k+c)/5

Step-by-step explanation:

5x-c=k (Original Equation)

5x-c+c=k+c (Addition Property of Equality)

5x=k+c (Simplify)

x=(k+c)/5 (Division Property of Equality)

Answer:

Due to the higher Z-score, Norma should be offered the job

Step-by-step explanation:

Z-score:

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Whoever has the higher z-score should be offered the job.

Alissa:

[tex]X = 68.5, \mu = 60.4, \sigma = 9[/tex]

So

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

[tex]Z = \frac{68.5 - 60.4}{9}[/tex]

[tex]Z = 0.9[/tex]

Morgan:

[tex]X = 252.5, \mu = 227, \sigma = 17[/tex]

So

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

[tex]Z = \frac{252.5 - 227}{17}[/tex]

[tex]Z = 1.5[/tex]

Norma:

[tex]X = 7.96, \mu = 6.7, \sigma = 0.7[tex]

So

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

[tex]Z = \frac{7.96 - 6.7}{0.7}[/tex]

[tex]Z = 1.8[/tex]

Due to the higher Z-score, Norma should be offered the job

Answer:

72.1

Step-by-step explanation:

G(x) =19.60 + 1.75x

Let x = 30

G(30) =19.60 + 1.75*30

          =19.60 +52.5

            72.1

Answer:

89

Step-by-step explanation:

Answer:

m∠3 = 115°

Step-by-step explanation:

Since measure of angle 6 = (2x - 5)°

And measure of angle 8 = (x + 5)°

Since ∠6 and ∠8 are the supplementary angles,

m∠6 + m∠8 = 180°

(2x - 5)° + (x + 5)° = 180°

3x = 180°

x = 60°

Therefore, m∠6 = (2x - 5) = (120 - 5) = 115°

and m∠8 = (x + 5) = 65°

Since angle 6 and angle 3 are interior alternate angles,

Therefore, m∠6 = m∠3 = 115° will be the answer.

Answer:

Answer 1.

Step-by-step explanation:

The complete question is:

The line whose equation is 3x - 5y = 4 is dilated by a scale factor of 3 centered at the origin. Which statement is correct?

1. The image of the line has the same slope as the pre-image but a different y-intercept.

2. The image of the line has the same y-intercept as the pre-image but a different slope.

3. The image of the line has the same slope and the same y-intercept as the pre-image.

4. The image of the line has a different slope and a different y-intercept from the pre-image.

Recall that a dilation by a scale factor r centered at the origin takes a point (x,y) and maps it to the point (r*x,r*y).

Consider also a line of equation [tex]ax+by=c[/tex]. From this equation, the slope of the line is given by the number [tex]\frac{-a}{b}[/tex] and the y-intercept is given by [tex]\frac{c}{b}[/tex].

Consider the given equation 3x-5y =4. If we replace (x,y) with (3x,3y), we get

[tex]3(3x)-5(3y) = 4 = 3 (3x-5y) = 4 [/tex]

which is equivalent to

[tex] 3x-5y = \frac{4}{3}[/tex]

Note that comparing the equations 3x-5y=4 and [tex]3x-5y=\frac{4}{3}[/tex] the values of a and b are equal but the value of c is different. This means that they have the same slope but a different y-intercept.

Answer:

1-5: Make it 1 unit tall

6-10: Make it 4 units tall

11-15: Make it 1 unit tall

16-20: Make it 0 units tall (Change nothing)

21-25: Make it 5 units tall

Step-by-step explanation:

1-5: 1 (1 number)

6-10: 7, 9, 9, 10 (4 numbers)

11-15: 13 (1 number)

16-20: (0 numbers)

21-25: 21, 23, 23, 25, 25 (5 numbers)

Answer:

  A'(4, 3)

Step-by-step explanation:

When a point is reflected across the line y = x, the transformation is ...

  (x, y) ⇒ (y, x)

  A(3, 4) ⇒ A'(4, 3)

The reflected point is (4, 3).

Answer:

a) $12,440.43

b) $8,000.00

c) $4,440.43

Step-by-step explanation:

the question is a bit ambiguous, I calculated from zero initial Deposit to $100 per quarter. If they deposited $100 initially and then $100 quarterly for 20 years then the numbers are as follows.

a) $12,671.05

b) $8,100

c) $4,571.05

a) $12,440.43

b) $8,000.00

c) $4,440.43

Step-by-step explanation:

the question is a bit ambiguous, I calculated from zero initial Deposit to $100 per quarter. If they deposited $100 initially and then $100 quarterly for 20 years then the numbers are as follows.

a) $12,671.05

b) $8,100

c) $4,571.05