Factor Completely;;;;;​

Answer:

Hello your question is incomplete below is the missing part of the  question

Metropolitan Research, Inc., a consumer research organization, conducts surveys designed to evaluate a wide variety of products and services available to consumers. In one particular study, Metropolitan looked at consumer satisfaction with the performance of automobiles produced by a major Detroit manufacturer. A questionnaire sent to owners of one of the manufacturer's full-sized cars reviewed several complaints about early transmission problems. To learn more about the transmission failures, Metropolitan used a sample of actual transmission repairs provided by a transmission repair firm in the Detroit area. The following data show the actual number of miles driven for 50 vehicles at the time of transmission failure:

Miles

85092

39323

64342

74276

74425

37831

77539

32609

89641

61978

66998

67202

89341

88798

59465

94219

67998

40001

118444

73341

77437

116803

59817

72069

53500

85288

32534

92857

101769

25066

79294

138114

64090

63436

95774

77098

64544

53402

32464

65605

121352

69922

86813

85586

59902

85861

69568

35662

116269

82256

 4.) How many repair records should be sampled if the research firm wants the population mean number of miles driven until transmission failure to be estimated with a margin of error of 5000 miles? Use 95% confidence.

answer : 1) Min value = 25070  1st quarter = 60420,Median = 72700,Mean = 73340,3rd quarter = 86580,Max value = 138100

2)  ( 66438.73, 80241.87 )

3) The statistical results shows that some owners of the automobiles experienced early transmission failures

4) 95

Step-by-step explanation:

1) The transmission failure ( using descriptive statistics )

Min = 25070

1st quarter = 60420

Median = 72700

Mean = 73340

3rd quarter = 86580

Max = 138100

2) managerial interpretation of interval estimate

given 95% confidence interval

a = 0.05

z(0.025) = 1.96

Hence the 95% confidence interval for the mean number of miles driven until transmission failure

= xbar +/- Z*s/vn

⇒ 73340.3 +/- 1.96*24898.72 * \(\sqrt{50}\)

= ( 66438.73, 80241.87 )

3) The findings shows that some owners of the automobiles experienced early transmission failures

4 ) number of repair records

n = ( Z * S/E) ^2   ------- 1

Where : Z = 1.96, S = 24898.72, E = 5000

 = 1.96 * 24898.72 / 5000 ) ^2

 = 95

The value of x is 0.918 for the equation 3.2x - 1.7x + 5.5 = 10.

To determine this equation 3.2x - 1.7x + 5.5 = 10,

3.2x - 1.7x + 5.5 = 10

Subtract 10 on both side,

3.2x - 1.7x + 5.5 - 10 = 10 - 10

3.2x - 1.7x + 4.5 = 0

Subtract 4.5 on both side,

3.2x - 1.7x = -4.5.

4.9x = -4.5

x = 0.918.

Therefore, the value of x is 0.918.

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Answer:

y<5/3 I believe. sorry if I am wrong!

Subtracting decimals, just like adding decimals, is similar to subtracting whole numbers. Just like adding decimals, the only difference is that we line up according to the decimal point instead of the last digit

One type of number that has a whole number and a fractional component separated by a decimal point is a decimal. The decimal point is the dot that appears between the parts of a whole number and a fraction. An example of a decimal number is 34.5.

Comparable to subtracting whole numbers is the operation of adding and subtracting decimals. The only difference between adding decimals and doing so is that we line up according to the decimal point rather than the last digit.

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The value of fraction 0.5 7  is equal to 1/2.

We are given that;

Number = 0.57

Now,

There are different ways to express a fraction as a decimal, but one common method is to divide the numerator by the denominator.

For example, 1/2 as a decimal is 1 ÷ 2 = 0.512.

Another method is to use a fraction to decimal conversion chart or calculator345. According to these sources, 0.5 as a fraction is equal to 5/10 or 1/2.

These fractions are equivalent because they have the same value when simplified or reduced.

To simplify a fraction, we can divide both the numerator and the denominator by their greatest common factor (GCF).

Therefore, by algebra the answer will be 1/2.

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Answer:

a

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

I might be wrong but i'm pretty sure it's right

Answer:

The product of 10 and 6v 96 in simplest radical form is 64

Step-by-step explanation:

hope this helpsss :)

Answer:

No

She needs 3/80 cup more

Step-by-step explanation:

She needs 3/8 cup plus 3/5 cup.

3/8 + 3/5 = 15/40 + 24/40 = 39/40

She has 15/16 cup

15/16

39/40 = 78/80

15/16 = 75/80

She has 75/80 cup and needs 78/80 cup.

She does not have enough sugar.

78/80 - 75/80 = 3/80

She needs 3/80 cup more.

Answer:

4(10+9) - 40 + 36

9(5+2) - 45 + 18

3(12+7) - 36 + 21

Answer:

C.    AA

Step-by-step explanation:

Since m<Y = 27°, then m<W = 27°.

We have two angles of one triangle (A and B) congruent to two angles of the other triangle (W and X).

Answer: C.   AA

Answer:

Q=7.18

Step-by-step explanation:

9.2-2.02=7.18

Answer:

7.18

Step-by-step explanation:

subtract 2.02 from 9.2

Hello!

3x² + 6x + 4 = -3x² + 4

6x² + 6x = 0

6x(x + 1) = 0

6x = 0                 x + 1 = 0

x = 0                   x = -1

Answer:

936

7 2

×  1 3

2  

2 1 6

7 2 0

9 3 6

Brainleist?

so the idea being, we have a system of equations of two variables and 4 equations, each one rendering a line, for this case these aren't equations per se, they're INEquations, so pretty much the function will be the same for an equation but we'll use > or < instead of =, but fairly the function is basically the same, the behaviour differs a bit.

we have a line passing through (-6,0) and (0,8), side one

we have a line passing through the x-axis and -6, namely (-6,0) and the y-axis and -4, namely (0,-4), side two

we have a line passing through (0,-4) and (6,4), side three

now, side four is simply the line connecting one and three.

the intersection of all four lines looks like the one in the picture below, so what are those lines with their shading producing that quadrilateral?

well, we have two points for all four, and that's all we need to get the equation of a line, once we get the equation, with its shading like that in the picture, we'll make it an inequality.

\((\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{8 -0}{0 +6} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = \cfrac{4}{3} ( x +6) \\\\\\ y=\cfrac{4}{3}x+8\hspace{5em}\stackrel{\textit{side one} }{\boxed{y < \cfrac{4}{3}x+8}}\)

\(\rule{34em}{0.25pt}\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 -0}{0 +6} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = - \cfrac{2}{3} ( x +6) \\\\\\ y=-\cfrac{2}{3}x-4\hspace{5em}\stackrel{\textit{side two} }{\boxed{y > -\cfrac{2}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{4 +4}{6 -0} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{0}) \implies y +4 = \cfrac{4}{3} ( x -0) \\\\\\ y=\cfrac{4}{3}x-4\hspace{5em}\stackrel{ \textit{side three} }{\boxed{y > \cfrac{4}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}\)

\((\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{6}}} \implies \cfrac{ 4 }{ -6 } \implies - \cfrac{2}{3}\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{6}) \\\\\\ y=-\cfrac{2}{3}x+8\hspace{5em}\stackrel{ \textit{side four} }{\boxed{y < -\cfrac{2}{3}x+8}}\)

now, we can make that quadrilateral a trapezoid by simply moving one point for "side four", say we change the point (0 , 8) and in essence slide it down over the line to  (-3 , 4).  Notice, all we did was slide it down the line of side one, that means the equation for side one never changed and thus its inequality is the same function.

now, with the new points for side for of (-3,4) and (6,4), let's rewrite its inequality

\((\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{4 -4}{6 +3} \implies \cfrac{ 0 }{ 9 } \implies 0\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 0}(x-\stackrel{x_1}{(-3)}) \implies y -4 = 0 ( x +3) \\\\\\ y=4\hspace{5em}\stackrel{ \textit{side four changed} }{\boxed{y < 4}}\)

Answer:

1. 45

2.40

Step-by-step explanation:

The solution set of f(x) > 0 is x ∈ (-2, 8).

To find the solution set of f(x) > 0, we need to first determine the critical values of x where f(x) changes sign.

Let's start by finding the domain of the function:

x² - 6x - 16 ≠ 0

We can solve for x by using the quadratic formula:

x = [6 ± √(6² + 4(16))]/2 = [6 ± √52]/2 = 3 ± √13

So the domain of f(x) is (-∞, 3 - √13) U (3 + √13, ∞).

Now let's factor the numerator and denominator of f(x):

f(x) = (x + 10)/[(x - 8)(x + 2)]

The critical points occur where the numerator or denominator of f(x) changes sign.

The numerator changes sign at x = -10, and the denominator changes sign at x = -2 and x = 8.

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Answer:

x=8

Step-by-step explanation

Vertical angles are always congruent which means they are equal

Since we know this we can simply set the two angle equal to each other so...

5x-5=2x+19

Now what we do is add five to 19 and subtract 2x from 5x to get

3x=24

simply divide 24 by 3 to isolate x and now we have

x=8

Hope this was helpful!

Answer:

8.25

Step-by-step explanation:

interest= principal x time x rate

1089=1100 x 12 x r/100

108900=13200r

r=8.25

The total cost C of construction as a function of h is:

\(C = \frac{10 + 5\sqrt{2}~ h^2}{h}\)

As the pen is in the shape of an isosceles right angle, one of the

angle must be 90 degrees.

Also, the two sides of the triangle are equal and the base angles

are equal.

Here, x represents the length of legs of isosceles right triangle

and h be the length of hypotenuse of isosceles right triangle

Using Pythagoras theorem,

x² + x² = h²

2x² = h²

x² = h² / 2

x = \(\sqrt{\frac{h^2}{2} }\)

So, x = \(\frac{h}{\sqrt{2} }\)

The fencing costs $5 per feet for the legs and $10 per feet for the hypotenuse.

So, the fencing cost for the legs would be,

= 5 × (2x)

= 10x

= \(10\times \frac{h}{\sqrt{2} }\)

= \(5\sqrt{2}~ h\)

And the fencing cost for the hypotenuse would be,

= 10/ h

So, the total cost of fencing C would be,

\(C = \frac{10}{h} + 5\sqrt{2}~ h\\\\C = \frac{10 + 5\sqrt{2}~ h^2}{h}\)

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The function f(n)=−48⋅(-¼)^n is a geometric sequence

The recursive definition of f(n) is f(1) = 12;  f(n) = f(n - 1) . -¼

The function is given as:

f(n)=−48⋅(-¼)^n

Calculate f(1)

f(1)=−48⋅(-¼)^1

This gives

f(1) = 12

Calculate f(2)

f(2)=−48⋅(-¼)^2

This gives

f(2) = -3

Calculate the common ratio (r)

r = f(2)/f(1)

So, we have:

f = -3/12

Simplify

r = -1/4

Recall that: r = f(2)/f(1)

This gives

-1/4 = f(2)/f(1)

Make f(2) the subject

f(2) = -1/4* f(1)

Express 1 as 2 - 1

f(2) = -1/4* f(2 - 1)

Substitute 2 for n

f(n) = -1/4* f(n - 1)

Rewrite as:

f(n) = f(n - 1) . -¼

Hence, the recursive definition of f(n) is f(1) = 12;  f(n) = f(n - 1) . -¼

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Answer:*

Step-by-step explanation:

Answer:

$0.05

Step-by-step explanation:

1.25/25=0.05

Answer:

Area of given figure = 197.48 mi² (Approx.)

Step-by-step explanation:

Note;

Divide given figure into a semi-circle, rectangle, and square

Given:

Radius = 8 mi

Length of rectangle = 11 mi

Width of rectangle = 8 mi

Side of square = 3 mi

Find:

Area of given figure

Computation:

Area of given figure = Area of semi-circle + Area of rectangle + Area of square

Area of given figure = (π/2)(r²) + [L x B] + Side²

Area of given figure = (3.14/2)(8²) + [11 x 8] + 3²

Area of given figure = (1.57)(64) + [88] + 9

Area of given figure = 100.48 + [88] + 9

Area of given figure = 197.48 mi² (Approx.)

Multiplying by 1/2 at both sides, we get:

This means that f(x) is compressed by a factor of 1/2 to be transformed into g(x)