ZABD and DBC are supplementary angles
What is the measure of x?
x = [?]
D
As
x 78
B
>C
Angles are not chanm to scale

Answer:

1. The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).

2. The point estimate for the true difference between the population means is of -1872.

Step-by-step explanation:

Before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction of Normal Variables:

When two normal variables are subtracted, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 212 brakes using Compound 1 yields an average brake life of 47,895 miles. The population standard deviation for Compound 1 is 1590 miles.

This means that [tex]\mu_1 = 47895, \sigma_1 = 1590, n = 212, s_1 = \frac{1590}{\sqrt{212}} = 109.2[/tex]

A sample of 180 brakes using Compound 2 yields an average brake life of 49,767 miles. The population standard deviation for Compound 2 is 4152 miles.

This means that [tex]\mu_2 = 49767, \sigma_2 = 4152, n = 180, s_2 = \frac{4152}{\sqrt{180}} = 309.47[/tex]

True difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2.

This is the distribution 1 - 2. So

[tex]\mu = \mu_1 - \mu_2 = 47895 - 49767 = -1872[/tex]

This is also the point estimate for the true difference between the population means, which is question 2.

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{109.2^2+309.47^2} = 328.17[/tex]

90% confidence interval

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = zs = 1.645*328.17 = 539.84[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is -1872 - 539.84 = -2411.84

The upper end of the interval is the sample mean added to M. So it is -1872 + 539.84 = -1332.16.

The 90% confidence interval for the true difference between average lifetimes for brakes using Compound 1 and brakes using Compound 2 is (-2411.84, -1332.16).

Step-by-step explanation:

Slope = m

y - y° = m(x - x°)

m(x - x°) = y - y°

m = (y - y°)/(x - x°)

y intercept x = 0

... and I don't know :")

Answer:

ds/dt = kN(N-S)

Step-by-step explanation:

Given

Total number of student = N

number of students who have seen the program = S

Number of students who have not seen the program = N-S

The product of the number of students who have seen the program and the number of students who have not seen the program = N(N-S)

If the rate of number of students who have seen a new television program increases at a rate proportional to the product of the number of students who have seen the program and the number of students who have not seen the program, then:

ds/dt = kN(N-S)

k is the proportionality constant

Answer:

Its also 30 degrees

Step-by-step explanation:

That shape is a vertical angle. This means that is 2 was 150 degrees, than 4 would also be 150 degrees. This means that if 1 is 30, then 3 is...... eh you get the idea. its 30 degrees.

P.S: Your welcome :)

Answer:

x = 30

Step-by-step explanation:

All triangle angles add up to 180 so:

x + 3x + 2x = 180

6x = 180

x = 30

Answer:

180°

Step-by-step explanation:

180

The total number of degrees in which has the triangle ABC been rotated counterclockwise about the origin is 180 degrees.

The transformation of a figure around a point, either clockwise or counterclockwise, is called rotation. A figure's coordinate point changes when it rotates.

About the origin, the triangle ABC has been rotated. The new triangle A'B'C' is created as a result. In the graph below,

The vertex B' points have the same but negative coordinates,

The vertex of B of the original figure points on the same line.

The coordinate point of B is (5,8).

The coordinate points of B' is (-8,-5).

The same will goes for the A and C points of the triangle

Thus the change in coordinate point after the rotation is,

coordinates of B = (5,8)

coordinates of B' = (-5, -8)

The same will follow with A and C

This is the rotation rule of 180 degrees counterclockwise.

Therefore, The triangle ABC has been rotated 180 degrees counterclockwise in all with respect to the origin.

Learn more about the rotation of figures here;

brainly.com/question/26249005

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Answer:

108

Step-by-step explanation:

50 + 4 = 54

54 x 2 = 108

We have two types of textbooks. Let's use "x" to represent the number of math textbooks and "y" to represent the number of history textbooks.

Altogether, the bookseller sold 240 math and history textbooks. So:

x + y = 240

Now, the number of history textbooks sold was 72 less than the number of math books sold. So:

y = x - 72

Now we can substitute for y in the equation and solve:

x + y = 240

x + (x - 72) = 240

2x - 72 = 240

2x = 312

x = 156

The bookseller sold 156 math textbooks.

Since y = x - 72, he must have sold 84 history textbooks.

Let's check our answers:

x + y = 240

156 + 84 = 240

That is true, so we did get the correct answers.

Answer:

28/64

Step-by-step explanation:

7/16 = 14/32 = 28/64

9514 1404 393

Answer:

  10π meters

Step-by-step explanation:

The circumference of the island is given by ...

  C = πd

For the given diameter, the circumference is ...

  C = π(20 m) = 20π m

The penguin swam half that distance, so swam ...

  (1/2)(20π m) = 10π m

The penguin swam 10π meters.

Answer:

+12 +1

Step-by-step explanation:

Answer:

an = 33n + 37

Step-by-step explanation:

I took the test.

Answer:

5(3+4) = - 35

Step-by-step explanation:

-5(3 + 4)

-5 × 3 + (-5) × 4

-15 + (- 20)

-15 - 20 = - 35

Thus, The value of the expression

-5(3+4) is - 35

-TheUnknownScientist

Answer:

100 sq ft

Step-by-step explanation:

triangle has a base of 25 and a height of 8

A = bh/2

A = 8 x 25 / 2

A = 100

Answer:

$2.10

Step-by-step explanation:

8.40÷4=2.1

Therefore, the price for 1 lb of grapes is $2.10.

Answer:

25%

Step-by-step explanation:

Since we know that the markdown is $20 by subtracting 80-60 , we find out what percent of 20 is 80. To do that you do 20/80, which is 0.25, or 25 percent.

Answer:

A. [tex] \frac{5}{6}\pi x^2 [/tex]

Step-by-step explanation:

Central angle of shaded part

[tex] \theta = 360\degree-60\degree= 300\degree[/tex]

Radius (r) = x unit

Area of the shaded part of [tex] \odot K[/tex]

[tex] = \frac{\theta}{360\degree} \times \pi r^2 [/tex]

[tex] = \frac{300\degree}{360\degree} \times \pi x^2 [/tex]

[tex] = \frac{5}{6}\pi x^2 [/tex]

Answer:

x=13

Step-by-step explanation:

3(x-10)=x+4

3x-30=x-4

3x=x+26

2x=26

x=13

Answer:

20%

Step-by-step explanation:

Total number of children = 20

Number of children who chose oatmeal = 4

Percentage of children who chose oatmeal :- [tex] \frac{Number \: of \: children \: who \: chose \: oatmeal}{Total \: number \: of \: children} \times 100[/tex]

[tex] = > \frac{4}{20} \times 100 [/tex]

[tex] = > 20\%[/tex]

Answer:

15 - 2x = 3

Step-by-step explanation:

Let x be the amount of days that have passed.

15 - 2x gives the amount at any day number x.

15 - 2x = 3 represents the day when you had 3 bottles left.

Answer:

2 solutions

Step-by-step explanation:

Answer:

x = 113

Step-by-step explanation:

Since the shape is a quadrilateral, the angles add up to 360 so:

x + 87 + 113 + 47 = 360

x + 247 = 360

x = 360 - 247

x = 113

Answer:

C) If the null hypothesis were true, there is a 2 percent chance of obtaining a chi-square value of at least 7.82.

Step-by-step explanation:

The value of the chi-square test statistic was 7.82 and the p- value is 0.02. This means that if the null hypothesis were true there is a 2 percent chance of obtaining a chi square value of at least 7.82

The p- value is defined as obtaining the test statistic under H0 as extreme as observed.

When the p- value is less than 0.05 in the chi square goodness fit test it means that the null hypothesis is rejected.

There fore option C is the best answer.

A)There is a 2 percent chance that the company's claim is correct.

B) There is a 2 percent chance of obtaining a chi-square value of at least 7.82.

C) If the null hypothesis were true, there is a 2 percent chance of obtaining a chi-square value of at least 7.82.

D) If the null hypothesis were true, there is a 2 percent chance that the company's claim is correct.

E)  If the null hypothesis were true, there is a 2 percent chance of obtaining a chi-square value of 7.82.

The p-value is defined as obtaining the test statistic under H₀ as extreme as observed. Then the correct option is C.

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

The value of the chi-square test statistic was 7.82 and the p-value is 0.02. This means that if the null hypothesis were true if there is a 2% chance of obtaining a chi-square value of at least 7.82.

The p-value is defined as obtaining the test statistic under H₀ as extreme as observed.

Thus, the correct option is C.

More about the null hypotheses and the alternative hypotheses link is given below.

https://brainly.com/question/9504281

The expression 5²/3 can be written without exponents as the fraction 25/3 or 8.33 approximately to 2 decimal place.

Whole numbers include all natural numbers and 0 and can be expressed as exponents and fractions. Exponent is the method of expressing numbers in terms of powers while fractions a fraction represents a part of a whole or, more.

The expression 5²/3 having an exponent can be rewritten as follows:

5²/3 = (5 × 5)/3

5²/3 = 25/3

Therefore, without using exponents the fraction 25/3 or 8.33 approximately to 2 decimal place is the same as the expression 5²/3.

Learn more about exponents here: https://brainly.com/question/11975096

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Answer:

%6.8

Step-by-step explanation:

The five members of the Roberts family went to a high school soccer game. The total cost was $44.

They paid $10 less because they used a $10 coupon, how much was the cost per person?

members in the family = 5

total cost = $44

cost per person = 44/5

= $8.8

Now, they got $10 coupon so they paid $10 less.

therefore,

New total cost = $44-$10

= $34

New per person cost = $34/5

= $6.8

Answer:

they paid $8.80 cents per person without coupan but with coupon they paid $6.80

Step-by-step explanation:

i divied 44 by 5 to get $8.80 without cupon but woth coupan is subracted 34 divied by 5 and got $6.80.

Answer:

-10x-15

Step-by-step explanation:

So first we start off with 5(-2x-3)

Next, we distribute the 5 to the -2x to get -10x.

Next, we distribute the 5 to the -3 to get -15.

Therefore,

-10x-15 is correct

Answer:

-10x-15

Step-by-step explanation:

It's 10x-15, because you just need to simplify it.

It is the same thing as (5 x (-2x)) - (5 x 3), if you use the distributive property.

that is the same as -10x-15

Answer:

Wins _16____. Losses _12____.

Step-by-step explanation:

Since they played 24 games, the wins and losses must add to 24.

Wins     losses

24           0

23           1

22           2

21            3

20           4

19            5

18           6

17            7

16            8            

15            9

14            10

13            11

12           12

11            13

10           14

9           15

They won 4 more than they lost is 16 W and 12 L.

Answer:

Tank is a tank and a cat is a cat.

Step-by-step explanation: