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The fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.

Given that, r= -0.774.

To solve such problems we must know about the fraction of the variability in data values or R-squared.

The fraction by which the variance of the dependent variable is greater than the variance of the errors is known as R-squared.

It is called so because it is the square of the correlation between the dependent and independent variables, which is commonly denoted by “r”  in a simple regression model.

Fraction of the variability in data values = (coefficient of correlation)²= r²

Now, the variability in fuel economy = r²= (-0.774)²

= 0.599076%= 59.91%

Hence, the fraction of the variability in fuel economy accounted for by the engine size is 59.91%.

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Answer:

D

Step-by-step explanation:

To find angle B, you should subtract 62 from 90 since because a right angle is 90 degrees.

The length of PR = 18 .

A chord is a line segment whose both points lie on the circle.

When a chord is extended it is called secant .

When two chords meet outside the circle , the product of length of the secant and its external segment is equal to the product of length of other secant and its external segment.

According to the given data

FR and FP are the secants of the circle

To determine the measure of PR

From the secant theorem

(7+9) * 9 = (5x+8) * 8

16 * 9 = (5x+8) *8

2 *9 = 5x+8

18 = 5x+8

5x = 10

x = 2

Therefore the length of PR = 5x+8 = 10+8 = 18

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Answer: When a coin is tossed and a die is rolled the probability of getting a head or an even number is = 3/4

Step-by-step explanation:

probability : The ratio of the favorable outcome to the total outcomes is gives the probability.

        (1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)

        (1,H),(2,H),(3,H),(4,H),(5,H),(6,H)

       (2,T),(4,T),(6,T)

        6+3 = 9

Therefore the probability is given by 9/12 = 3/4

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Answer: The probability of getting a head or an even number is = 3/4

  (1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)

      So, no. of possible outcomes 12

           (1,H),(2,H),(3,H),(4,H),(5,H),(6,H)

            (2,T),(4,T),(6,T)

       6+3 = 9

Total outcomes = 12

Probability = [tex]\frac{No. of favorable outcomes}{total outcomes}[/tex]

Probability for this case is =  [tex]\frac{9}{12} =\frac{3}{4}[/tex]

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The solution to the inequality d / 7 + 4 ≤ 0 will be (–∞, –28]. Then the correct option is B.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The inequality equation is given below.

d / 7 + 4 ≤ 0

By simplifying the equation, we have

d / 7 ≤ – 4

    d ≤ – 28

Then the value of d must be less than or equal to the negative 28.

Then the correct option is B.

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Answer: linear polynomial

Step-by-step explanation:

The number of student tickets is 175 and the number of adult tickets is 425.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

Suppose the number of the student ticket is St and adult are At.

St + At = 600

St = 600 - At

Another expression for the total amount will be given as:-

13.5St + 17At = 9587.50

Put the value of St in the equation to find the value of At.

13.5( 600 - At) + 17At = 9587.50

8100 - 13.5At +17At = 9587.5

17At - 13.5 At = 9587. 5 - 8100

3.5 At = 1487.5

At = 425

St + At = 600

St = 600 - At = 600 - 425 = 175

Therefore the number of student tickets is 175 and the number of adult tickets is 425.

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Answer: By 8 hours, there will be 65536 bacteria in the culture.

Step-by-step explanation:

The numerical expression used for this problem is [tex]4^{8}[/tex].

You can find the value of this on a calculator. I hope this helps!! :)

If that is not the answer, then try 32 because 4*8=32.

Answer:

[tex]\textsf {p(-4) = -134}[/tex]

Step-by-step explanation:

[tex]\textsf {Given :}\\[/tex]

[tex]\mathsf {p(x) = x^{3} - 3x^{2} + 7x + 6}[/tex]

[tex]\textsf {Substitute x = -4 to find p(-4) :}[/tex]

[tex]\mathsf {p(-4) = (-4)^{3} - 3(-4)^{2} + 7(-4) + 6}[/tex]

[tex]\mathsf {p(-4) = -64 - 48 - 28 + 6}[/tex]

[tex]\textsf {p(-4) = 6 - 140}[/tex]

[tex]\textsf {p(-4) = -134}[/tex]

Using the t-distribution, the correct option regarding the test statistic and the p-value is given as follows:

t = –1.85; the P-value is between 0.025 and 0.05.

The null hypothesis is:

[tex]H_0: \mu = 25[/tex]

The alternative hypothesis is:

[tex]H_1: \mu < 25[/tex]

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

In this problem, the values of the parameters are given as follows:

[tex]\overline{x} = 23.5, \mu = 25, s = 4.8, n = 35[/tex]

Hence the value of the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{23.5 - 25}{\frac{4.8}{\sqrt{35}}}[/tex]

t = -1.85.

Using a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value and 35 - 1 = 34 df, the p-value is of 0.0365.

Hence the correct statement is:

t = –1.85; the P-value is between 0.025 and 0.05.

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Answer:

150 x - 80 y + 50 - 50 x - 25 y + 20

Arranging like terms

150 x - 50 x -25 y - 80y + 50 + 20

100x - 105 y + 70

Answer:

20x - 21y + 14

Explanation:

[tex]\rightarrow \sf \dfrac{1}{5} (150x - 80y + 50 - 50x - 25y + 20)[/tex]

collect like terms

[tex]\rightarrow \sf \dfrac{1}{5} (150x-50x - 80y -25y + 50 + 20)[/tex]

add/subtract like terms

[tex]\rightarrow \sf \dfrac{1}{5} (100x - 105y+70)[/tex]

distribute inside parenthesis

[tex]\rightarrow \sf \dfrac{1}{5} (100x) + \dfrac{1}{5}( - 105y) + \dfrac{1}{5}(70)[/tex]

simplify the following

[tex]\rightarrow \sf 20x -21y + 14[/tex]

Answer:

  5/6 mile

Step-by-step explanation:

The formula for the area of a rectangle can be used with the given values to write an equation for the length of the farmland.

__

Here is the equation for the area of a rectangle.

  A = LW . . . . . area is the product of length and width

When we fill in the area and width, we have ...

  5/9 mi² = L(2/3 mi) . . . . . equation for the length of the farmland

Solving this equation gives ...

  L = (5/9)/(2/3) mi . . . . . . . . divide by the coefficient of L

  L = (5/9)/(6/9) mi = 5/6 mi . . . . . perform the division

The length of Sandra's farmland is 5/6 mile.

Answer :

10.5 miles

Given :

7 miles in 50 mins

Step-by-step explanation :

Calculate how many miles in 1 minute :

Divide both by 50 :

7/50 miles in 1 minute

To work out 75 minutes we multiply both by 75 :

75 × 7/50 =

10.5

Therefore our final answer is 10.5 miles

Hope this helped and have a good day

Answer:

In standard form thats 4.4024

In standard form, 4+0.4+0.0024 can be written as 4.4024

Concept: Any number we can write as a decimal number, between 1.0 and 10.0, multiplied by 10, is said to be in the normal range. 1.23 × 108;

If you look closely, 1.23 is a decimal number between 1.0 and 10.0 so we have a standard form 123,000,000 as 1.23 × 108.

Given: 4+0.4+0.0024

In this case,4 is the integral value and 0.4 is at the first decimal place followed by 0.0024 at the third and 4th decimal place so combining them all together and writing them in standard form we get,4.4024

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The number of ways to choose the colors is 36

The given parameters are:

Colors = 9

Colors to choose = 7

Since order does not matter, then it is combination

This is calculated using:

[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]

This gives

[tex]^nC_r = \frac{9!}{7!2!}[/tex]

Evaluate

[tex]^nC_r = 36[/tex]

Hence, the number of ways is 36

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Bikash borrowed Rs150,000 from Anish at the rare 21% per year at the end of 9 month. How compound interest should he pay compound half yearly.

Answer: ZT = ZS

Step-by-step explanation: ZT = ZS must be true under all circumstances. This is because a perpendicular bisector of a line cuts the line into two equal pieces. It is the midpoint of the entire line. Thus, ZT is the same as ZS since the line is equally cut in half and thus are the same.

Answer:

4 kg

Step-by-step explanation:

so 1.6 * 4 is 6.4 so you just double check if you want

4 + 1.6 which is 1/4 of 6.4 will be 5.6 (matches with the question)

4 + (1.6*4) (indicates it's full) = 10.4( also Matches with the question)

there is another way by setting up an equation. let me know in comments if you want to see it that way

If  tank weighs 5.6kg when it 1/4 filled with water. If it weighs 10.4kg when it is full , then weight when it is empty is 0.93kg

Two or more expressions with an Equal sign is called as Equation.

Given,

A tank weighs 5.6kg when it 1/4 filled with water

Tank weighs 10.4kg when it is full

We need to find the weight when it is empty.​

Let weight of the tank “x” and the weight of the water in the full tank “y”.

From the problem statements, we deduce the following equations:

x + y/4 = 5.6kg => x = 5.6kg - y/4

x + y = 10.4kg => y = 10.5kg - x

y = 10.5kg - (5.6kg - y/4)

3y/4 = 4.9

Thus y = 6.53kg; x = 0.93kg

Hence, weight of the tank when it is empty is 0.93kg.

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Answer:

1.6

Step-by-step explanation:

4,4-2.8 = 1.6

6-4.4 = 1.6

7.6-6 = 1.6

Then common difference is 1.6

Answer: [tex]AB=4.7, BC=8.8, \angle C=28^{\circ}[/tex]

Step-by-step explanation:

As angles in a triangle add to 180 degrees,

[tex]\angle C=180^{\circ}-90^{\circ}-62^{\circ}=\boxed{28^{\circ}}[/tex]

We know that:

[tex]\sin 62^{\circ}=\frac{BC}{10}\\\\BC=10\sin 62^{\circ} \approx \boxed{8.8}[/tex]

Similarly,

[tex]\cos 62^{\circ}=\frac{AB}{10}\\\\AB=10\cos 62^{\circ} \approx \boxed{4.7}[/tex]

The median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.

A box and whisker plot is a method of abstracting a set of data that is approximated using an interval scale. It's also known as a box plot. These are primarily used to interpret data.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have a box and whisker plot shown in the picture.

From the box plot, the line between the box ends represents the median of the data.

The median = 40

The least number of smartphones distributed = 33

Q3 = 48

Thus, the median is 40, the least number of smartphones distributed is 33, and the third quartile is 48.

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Answer: Y

Step-by-step explanation:

Since f(x) passes through (0,3), its inverse should pass through (3,0).

Also, since f(x) has a negative slope, so its inverse should also have a negative slope.

The graph of the inverse of function is shown in figure.

We have to given that,

Function is defined as,

f (x) = - 3x + 3

Hence, The inverse of function f (x) is,

f (x) = - 3x + 3

y = - 3x + 3

Solve for x,

3x = y + 3

Divide by 3;

x = (y + 3) / 3

Hence,

f⁻¹ (x) = (x + 3) / 3

f⁻¹ (x) = x/3 + 1

Therefore, The graph of the inverse of function is shown in figure.

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Answer:

48 cm²

Explanation:

The figure can be cut into 1 rectangle and 1 triangle.

Area of the figure:

⇒ area of rectangle + area of triangle

⇒ Length × Width  +  1/2 × Base × Height

⇒ 6 × 4  +  1/2 × 6 × 8

⇒ 24  +  24

⇒ 48

Therefore, area of figure is 48 cm².

Answer:

48 cm squared

Step-by-step explanation:

The given figure is composed of a rectangle (L=6 cm and W = 4 cm) and a right angled triangle { Base = (12- 4) = 8 cm, height = 6 cm. }

Area of the two figures is to be calculated separately and then added to get the required result.

Area of the rectangle = l × w

= 6 × 4

= 24 cm²

Area of the right triangle = ½ × base × height

= ½ × 8 × 6

= 24 cm²

Hence, area of the given figure = 24 + 24

= 48 cm squared.

Answer:

1

Step-by-step explanation:

49 is divisible by 7, 1, 49. 25 is divisible by 5, 1, 25. they are exclusively prime so the highest factor is 1 and the only

Answer:

Step-by-step explanation:

[tex]25x^4-49y^2=(5x^2)^2-(7y)^2\\=(5x^2+7y)(5x^2-7y)\\=(5x^2+7y)[(\sqrt{5} x)^2-(\sqrt{7y} )^2]\\=(5x^2+7y)(\sqrt{5} x+\sqrt{7y} )(\sqrt{5} x-\sqrt{7y} )[/tex]

Answer:

16 or -2

Step-by-step explanation:

Let the number be x.

Difference between the number and 7

= x -7 or 7-x

The square of the difference between x and 7

= (x -7)²

(x -7)²= 81

Square root both sides:

[tex]x - 7= \pm \sqrt{81} [/tex]

[tex]x - 7 = \pm9[/tex]

Add 7 to both sides:

[tex]x = 7\pm9[/tex]

x= 16 or x= -2

Thus, the number could either be 16 or -2.

Answer:

wrong question please place correctly thanks

Answer:

[tex]\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}[/tex]

Step-by-step explanation:

                      [tex]y \ = \ x^{3} \ - \ \displaystyle\frac{1}{\sqrt{x}} \ + \ \displaystyle\frac{3}{x^{4}} \\ \\ y \ = \ x^{3} \ - \ x^{-\frac{1}{2}} \ + \ 3x^{-4} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{3 \ - \ 1} \ - \ \left(-\displaystyle\frac{1}{2}\right)x^{-\frac{1}{2} \ - \ 1} \ + \ \left(-4 \ \times \ 3\right)x^{-4-1}[/tex]

                       [tex]\displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2}x^{-\frac{3}{2}} \ - \ 12x^{-5} \\ \\ \displaystyle\frac{dy}{dx} \ = \ 3x^{2} \ + \ \displaystyle\frac{1}{2\sqrt{x^{3}}} \ - \ \displaystyle\frac{12}{x^{5}}[/tex]