A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 50 microwaves that are 5 years old, 12% needed repairs at a=.04 can you reject the makers claim that no more than 10% of its microwaves need repair during the first five years of use?

Answer:

The 95% confidence interval is  [tex]84.83< \mu < 90.37[/tex]

Step-by-step explanation:

From the question we are told that

    The  sample size is  [tex]n = 113[/tex]

     The sample mean is  [tex]\= x = 87.6[/tex]  

      The standard deviation is  [tex]\sigma = 15[/tex]

Given that the confidence level is  95% then the level of significance is mathematically represented as

            [tex]\alpha = 100 - 95[/tex]

             [tex]\alpha = 5\%[/tex]

             [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value  is  

              [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically evaluated as

              [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma}{ \sqrt{n} }[/tex]

=>          [tex]E = 1.96 * \frac{ 15}{ \sqrt{113} }[/tex]

=>          [tex]E = 2.77[/tex]

The  95% confidence interval is mathematically represented as

          [tex]\= x - E < \mu < \= x + E[/tex]

substituting values

        [tex]87.6 - 2.77< \mu < 87.6 + 2.77[/tex]

        [tex]84.83< \mu < 90.37[/tex]

Answer:

Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.

Step-by-step explanation:

From the question we are told that

     The sample size is  n =  500

     The sample proportion is  [tex]\r p = 0.57[/tex]

     The  95% confidence interval is (0.5266, 0.6134)

Looking at the 95% confidence level interval we see that the sample proportion is within the interval and given that the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.

Answer:

50k

Step-by-step explanation:

Answer:

A) Null Hypothesis; H0: μ = $41,500

Alternative hypothesis; H1: μ > $41,500

B) Reject H0 is t > 2.821433

C) t = 1.79

D) there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average

Step-by-step explanation:

A) The hypotheses is given as;

Null Hypothesis; H0: μ = $41,500

Alternative hypothesis; H1: μ > $41,500

B) From online t-score calculator attached using significance level of 0.01 and DF = n - 1 = 10 - 1 = 9, we have;

t = 2.821433

Normally, when the absolute value of the t-value is greater than the critical value, we reject the null hypothesis. However, when the absolute value of the t-value is less than the critical value, we fail to reject the null hypothesis.

Thus, if t > 2.821433, we will reject the null hypothesis H0.

C) Formula for the test statistic is;

t = (x' - μ)/(s/√n)

We have, μ = 41500, x' = 47500, s = 10600, n = 10

t = (47500 - 41500)/(10600/√10)

t = 1.79

D) So, 1.79 is less than the t-critical value of 2.821433. Thus, we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average

Answer:

A. 30

Step-by-step explanation:

The interquartile range for a box and whiskers plot, is the value from the right side of the box minus the value of the left side of the box.

In this case at the far right side of the box it is at 130, at the far left side of the box it is at 100.

130-100=30

Answer:

[tex]\huge\boxed{IQR = 30}[/tex]

Step-by-step explanation:

Q1 = 130 (Left hand edge of the box)

Q3 = 100 (Right Hand edge of the box)

Interquartile Range = Q3-Q1

IQR = 130-100

IQR = 30

Answer:

D

Step-by-step explanation:

The ratio of yellow paint to blue paint is 4:3. We can make the largest amount of green paint by using all of the 20 quarts of yellow paint so we have to solve for x in 4:3 = 20:x, since 4 * 5 = 20, 3 * 5 = x so we use 15 qts of blue paint, therefore we will have 20 + 15 = 35 qts of green paint.

Answer:

D

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Let T be triangle, C the circle and S the square.

● T + T + T = 30

● 3T = 30

Divide both sides by 3

● 3T/3 = 30/3

● T = 10

So the triangle has a value of 10.

●30 T + C + C = 20C + S + S = 13T +C ×S/2

Add like terms together

●30 T + 2C = 20C +2S= 13T + C×S/2

Replace T by its value (T=10)

● 300 + 2C = 20C + 2S = 130 + C×S/2

Take only this part 20C + 2S = 130 + C × S/2

● 20C + 2S = 130 + C×S/2 (1)

Take this part (300+2C = 20C+2S) and express S in function of C

● 20C + 2S = 300 + 2C

Divide everything by 2 to make easier

● 10 C + S = 150+ C

● S = 150+C-10C

● S = 150-9C

Replace S by (5-9C) in (1)

● 20C + 2S = 130 + C×S/2

● 20C + 2(150-9C) = 130 +C× (150-9C)/2

● 20C + 300-18C= 130 + C×(75-4.5C)

● 2C + 300 = 130 + 75 -4.5C^2

● 2C +300-130 = 75C - 4.5C^2

● 2C -75C + 170 = -4.5C^2

● -73C + 170 = -4.5C^2

Multiply all the expression by -1

● -4.5C^2 +73C+ 170= 0

This is a quadratic equation, so we will use the discriminant method.

Let Y be the discriminant

● Y = b^2-4ac

● b = 73

● a = -4.5

● c = 170

● Y = 73^2 - 4×(-4.5)×170= 8389

So the equation has two solutions:

● C = (-b +/- √Y) /2a

√Y is approximatively 92

● C = (-73 + / - 92 )/ -9

● C = 18.34 or C = -2.11

Approximatively

● C = 18 or C = -2

■■■■■■■■■■■■■■■■■■■■■■■■■

● if C = 18

30T + 2C = 300 + 36 = 336

● if C = -2

30T + 2C = 300-4 = 296

Step-by-step explanation:

Ellen - 115/23

Classmates and Ellen got = 5 each

Answer:

[tex]Area=\frac{1}{2} (B\,+\,b)\,h[/tex]

Step-by-step explanation:

The grassy area is that of a trapezoid, so recall the formula for the area of a trapezoid:

[tex]Area=\frac{1}{2} (Base\,+\,base)\,height[/tex]

where:

Base stands for the larger base (in our case the dimension "B" in the attached image)

base stands for the shorter base parallel to the largest Base (in our case the dimension "b" in the attached image)

and

height stands for the distance between bases (in our case the dimension "h" in the attached image.

Therefore the formula for the area of the grassy section becomes:

[tex]Area=\frac{1}{2} (Base\,+\,base)\,height\\Area=\frac{1}{2} (B\,+\,b)\,h[/tex]

Answer:

1/2 (b+b) h

here is the actual picture

Answer:

  [tex]\dfrac{2x-11}{x-2}[/tex]

Step-by-step explanation:

Simplify the fractions, then add.

  [tex]-\dfrac{7}{x-2}+\dfrac{2x}{x}=\dfrac{-7}{x-2}+2=\dfrac{-7}{x-2}+\dfrac{2(x-2)}{x-2}\\\\=\dfrac{2x-4-7}{x-2}=\boxed{\dfrac{2x-11}{x-2}}[/tex]

_____

Note that this comes with the restriction that x ≠ 0.

Answer:

0.8989

Step-by-step explanation:

Using the Newton's Raphson approximation formula.

Xn+1 = Xn - f(Xn)/f'(Xn)

Given f(x) = x³-2x+2

f'(x) = 3x²-2

If the initial value X1 = 2

X2 = X1 - f(X1)/f'(X1)

X2 = 2 - f(2)/f'(2)

f(2) = 2³-2(2)+2

f(2) = 8-4+2

f(2) = 6

f'(2) = 3(2)²-2

f'(2) = 10

X2 = 2- 6/10

X2 = 14/10

X2 = 1.4

X3 = X2 - f(X2)/f'(X2)

X3 = 1.4 - f(1.4)/f'(1.4)

f(1.4) = 1.4³-2(1.4)+2

f(1.4) = 2.744-2.8+2

f(1.4) = 1.944

f'(1.4) = 3(1.4)²-2

f'(1.4) = 3.880

X3 = 1.4- 1.944/3.880

X3 = 1.4 - 0.5010

X3 = 0.8989

Hence the value of X3 is 0.8989

Answer: 669

Step-by-step explanation:

Given, In a Gallup poll of randomly selected​ adults, 66% said that they worry about identity theft.

i.e. The proportion of adults said that they worry about identity theft. (p) = 0.66

Sample size : n= 1013

Then , Mean for the sampling distribution of sample proportion  = np

= (1013) × (0.66)

= 668.58 ≈ 669  [Round to the nearest whole number]

Hence, the mean of those who do not worry about identify theft is closest to​ 669 .

Answer:

35°

Step-by-step explanation:

If BCD is 75, then BCA is 105.

105+40=145

180-145=35

So ABC is 35°

Answer:

At first, we have 3 expressions that are equal.

[tex]3(2+7) - 9 \cdot 7= 3+8 \cdot 2 \cdot 2 - 4[/tex]

[tex]6+21 - 63= 3+32 - 4[/tex]

[tex]-36=31[/tex]

[tex]-36\neq 31[/tex]

This is not true.

Answer:

the least integer for n is 2

Step-by-step explanation:

We are given;

f(x) = ln(1+x)

centered at x=0

Pn(0.2)

Error < 0.01

We will use the format;

[[Max(f^(n+1) (c))]/(n + 1)!] × 0.2^(n+1) < 0.01

So;

f(x) = ln(1+x)

First derivative: f'(x) = 1/(x + 1) < 0! = 1

2nd derivative: f"(x) = -1/(x + 1)² < 1! = 1

3rd derivative: f"'(x) = 2/(x + 1)³ < 2! = 2

4th derivative: f""(x) = -6/(x + 1)⁴ < 3! = 6

This follows that;

Max|f^(n+1) (c)| < n!

Thus, error is;

(n!/(n + 1)!) × 0.2^(n + 1) < 0.01

This gives;

(1/(n + 1)) × 0.2^(n + 1) < 0.01

Let's try n = 1

(1/(1 + 1)) × 0.2^(1 + 1) = 0.02

This is greater than 0.01 and so it will not work.

Let's try n = 2

(1/(2 + 1)) × 0.2^(2 + 1) = 0.00267

This is less than 0.01.

So,the least integer for n is 2

In this exercise we have to use the knowledge of Taylor Polynomial to calculate the requested function, this way we will have;

the least integer for n is 2    

The function given in this exercise corresponds to:

[tex]f(x) = ln(1+x)[/tex]

knowing that the x point will be centered on:

[tex]x=0\\Pn(0,2)\\Error < 0.01[/tex]

By rewriting the equation we have to:

[tex][[Max(f^{(n+1)} (c))]/(n + 1)!] *0.2^{(n+1)} < 0.01[/tex]

So doing the derivatives related to the first function given in the exercise we have to:

[tex]f(x) = ln(1+x)[/tex]

Following this we have to:

[tex]Max|f^{(n+1)} (c)| < n![/tex]

Thus, error is;

[tex](n!/(n + 1)!) * 0.2^{(n + 1)} < 0.01[/tex]

[tex](1/(n + 1))* 0.2^{(n + 1)} < 0.01[/tex]  

Let's try n = 1

[tex](1/(1 + 1)) *0.2^{(1 + 1)} = 0.02[/tex]

This is greater than 0.01 and so it will not work. Let's try n = 2

[tex](1/(2 + 1)) * 0.2^{(2 + 1)} = 0.00267[/tex]

This is less than 0.01. So,the least integer for n is 2.

See more about Taylor polynomial at brainly.com/question/23842376

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

Answer:

There is not sufficient evidence to support a claim of linear correlation between the two variables.

Step-by-step explanation:

(a)

The scatter plot for the provided data is attached below.

(b)

The hypothesis to test significance of linear correlation between the two variables is:

H₀: There is no linear correlation between the two variables, i.e. ρ = 0.

Hₐ: There is a significant linear correlation between the two variables, i.e. ρ ≠ 0.

(c)

Use the Excel function: =CORREL(array1, array2) to compute the correlation coefficient, r.

The correlation coefficient between the number of internet users and the award winners is,

r = 0.786.

The test statistic value is:

[tex]t=r\sqrt{\frac{n-2}{1-r^{2}}}[/tex]

  [tex]=0.786\times\sqrt{\frac{6-2}{1-(0.786)^{2}}}\\\\=2.5427\\\\\approx 2.54[/tex]

Thus, the test statistic is 2.54.

(d)

The degrees of freedom is,

df = n - 2  

  = 6 - 2

  = 4

Compute the p-value as follows:

[tex]p-value=2\cdot P(t_{n-2}<2.54)=2\times 0.032=0.064[/tex]

*Use a t-table.

p-value = 0.064 > α = 0.05

The null hypothesis will not be rejected.

Thus, it can be concluded that there is not sufficient evidence to support a claim of linear correlation between the two variables.

Answer:

6.14 inches

Step-by-step explanation:

The one side of the dollar bill is 6.14 inch. The 6.14 inches of the dollar approximates the 156.1 mm. When Malia measures the longer side of a dollar bill from her rule it will be approximately 6.14 inches in length. The ruler normally has inches and cm sides. Very few rulers have mm scales. The most probable scale that malia would have measure is in inches.

Answer:

x = -2.6, x = 2.6

Step-by-step explanation:

The graph crosses the x-axis at approximately 2.6 and -2.6.

The required approximate solution of the function graphed is x = -2.6 and 2.6.

Given that,
A graph of a function is plotted, and the solution of the function is to be determined.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

The graph is a demonstration of curves that gives the relationship between the x and y-axis.

Here, the solution of the function is that value of x where the function terminates to zero, So the given curve terminates to zero at two places at x = -2.6 and x = 2.6 from the observation of the graph.

Thus, the required approximate solution of the function graphed is x = -2.6 and 2.6.

Learn more about function here:

brainly.com/question/21145944

#SPJ2

Answer:

117 cm³

Step-by-step explanation:

To find the volume of a rectangular prism, we can simply multiply the length, width and height so the answer is 13 * 3 * 3 = 117 cm³.

Answer:

117 cubic centimeters

Step-by-step explanation:

Assuming that the stick of butter is a perfect rectangular prism, we can calculate the volume by simply multiplying the length, width, and the height as modeled by the volume equation:

V = LWH

For this, the L = 13cm, W = 3cm, and H = 3cm

So our volume in cubic centimeters will be:

V = LWH

V = (13cm) * (3cm) * (3cm)

V = (13cm) * (9cm^2)

V = 117 cm^3

So the volume of the stick of butter is 117 cubic centimeters.

Cheers.

Answer:

  g(x) = 4, 6, 9, 13.5 for the x-values given

Step-by-step explanation:

The table and graph are attached.

Answer:

1

Step-by-step explanation:

Hello, please consider the following.

First, we develop and move everything to the left side, then we solve the equation, using the discriminant.

Finally, we get the expression of the two solutions and we can conclude.

[tex](x+1)(x+2)=(x+3)\\\\<=> x^2+3x+2-x-3=0\\\\<=>x^2+2x-1=0\\\\\Delta=b^2-4ac=4+4=8\\\\x_1=\dfrac{-2-\sqrt{8}}{2}=\dfrac{-2-2\sqrt{2}}{2}=-1-\sqrt{2}\\\\x_2=\dfrac{-2+\sqrt{8}}{2}=-1+\sqrt{2}[/tex]

So, m=-1 and n = 2

m+n = -1 + 2 = 1

Thank you

The value of m + n is 1.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 - 9 is an equation.

We have,

(x + 1)(x + 2) = x + 3

x² + 2x + x + 2 = x + 3

x² + 3x + 2 - x - 3 = 0

x² + 2x - 1 = 0

This is in the form of ax² + bx + c = 0

a = 1, b = 2, and c = -1

Now,

Using the determinant.

x = -b ± √(b² - 4ac) / 2a

x = -2 ± √(4 + 4) / 2

x = (-2 ± 2√2) / 2

x = (-1 ± √2)

x = -1 + √2

x = -1 - √2

Now,

The solutions can be written in the form of (m + √n) and (m - √n).

This means,

m + √n = -1 + √2

m - √n = -1 - √2

m = -1 and n = 2

Now,

m + n

= -1 + 2

= 1

Thus,

m + n is 1.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:

-54 is a integer and rational number

Step-by-step explanation:

Step-by-step explanation:

A rotation about point A a reflection across the line containing AR a reflection across the line containing AQ a rotation about point R

Answer:

A rotation about point A

Step-by-step explanation:

I am taking the test if it is wrong I will add a comment

Answer:

a.H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

Step-by-step explanation:

Formulate the null and alternative hypotheses as

a) H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test

Here ∝= 0.005

For alpha by 2 for a two tailed test Z∝/2 = ± 1.96

Standard deviation = s= 3.5 pounds

n= 49

The test statistic used here is

Z = x- x`/ s/√n

Z= 69.1- 70 / 3.5 / √49

Z= -1.80

Since the calculated value of Z= -1.80 falls in the critical region we reject the null hypothesis.

b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

d) If standard deviation is 1.75 pounds

The test statistic used here is

Z = x- x`/ s/√n

Z= 69.1- 70 / 1.75 / √49

Z= -3.6

This value does not fall in the critical region.

d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

e) If the sample mean is 69 pounds

Z = x- x`/ s/√n

Z= 69.1- 69 / 3.5 / √49

Z= 0.2

This value falls in the critical region

e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.

Answer:

Sum : 65

Step-by-step explanation:

In this notation, n is our starting value, and hence we start at 3 and go to 7. Given the set of values : { 3, 4, 5, 6, 7 }, we can substitute in our expression " 4n - 7 " for n and solve. The sum of these values is our solution.

4( 3 ) - 7 = 12 - 7 = 5,

4( 4 ) - 7 = 16 - 7 = 9,

4( 5 ) - 7 = 20 - 7 = 13,

Our remaining values for n = 6 and n = 7 must then be 17 and 21. This is predictable as we have an arithmetic series here, the common difference being 4. As you can see 9 - 5 = 4, 13 - 9 = 4, 17 - 13 = 4, 21 - 17 = 4.

Therefore we have the series { 5, 9, 13, 17, 21 }. This adds to an answer of 65.

Answer:

(C) 1 and 3

Step-by-step explanation:

Corresponding angles are angles that are at the same corner at the different intersections.

We can see that 1 is on the bottom right corner of the bottom line, now we need to see what angle is at the bottom right corner of the top line?

That's 3.

So 1 and 3 are congruent because they are corresponding.

Hope this helped!

Answer:

approximately x = 38

Step-by-step explanation:

The maximum profit is the vertex of the profit graph parabola. The maximum occurs at approximately x = 38.

The solution is x = 38

The location on the profit function parabola where the profit from sales of the phone cases is a maximum is given by x = 38

A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line

The equation of the parabola is given by

( x - h )² = 4p ( y - k )

where ( h , k ) is the vertex and ( h , k + p ) is the focus

y is the directrix and y = k – p

The equation of the parabola is also given by the equation

y = ax² + bx + c

where a , b , and c are the three coefficients and the parabola is uniquely identified

Given data ,

Let the revenue, cost, and profit functions for a line of cell phone cases be given as two parabolic functions R ( x ) and P ( x )

The maximum profit is given by the parabolic function R ( x )

The profit is represented by = y

The price per phone is represented by = x

Now , when y is maximum ,

The value of y = $ 2,250,000

The value of x when y = $ 2,250,000 is x = 38

So , the value of x from the parabola where profit is maximum is x = 38

Therefore,  the value of x = 38

Hence , the value of x from the function is x = 38

To learn more about parabola click :

https://brainly.com/question/24042022

#SPJ2

Answer:

Evaluate 8P6 P 6 8 using the formula nPr=n!(n−r)! P r n = n ! ( n - r ) ! . 8!(8−6)! 8 ! ( 8 - 6 ) ! Subtract 6 6 from 8 8 . 8!(2)! 8 ! ( 2 ) ! Simplify 8!(2)! 8 !

Step-by-step explanation:

evaluate" usually means to put a value in for the variable, but you don't give us a value for p. also, it is unclear if you ...

The value of the expression [tex]^8P_6[/tex] is 20160.

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order.

The value of the expression is calculated as:-

[tex]^8P_6=\dfrac{8!}{8!-6!}=\dfrac{8!}{2!}[/tex]

[tex]^8P_6 =\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2}{2}[/tex]

[tex]^8P_6[/tex] = 20160

Hence, the value is 20160.

To know more about permutations follow

https://brainly.com/question/4658834

#SPJ5

False!

The answer is: False.

Whomever stated the answer is "true" is wrong.