Write your answers in the spaces provided.
1 Adam works for a car trading company.
He has this information about the number of cars sold by the company in the
first six months of 2017
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DO NOT WRITE IN THIS AL
Jan
Feb
Mar
Apr
May
Jun
31
28
46
52
44
62
Number of cars sold
Adam says
The mean number of cars sold each month in this period was
more than 42
The number of cars sold in June 2017 was more than of the number
of cars sold from the beginning of January to the end of June.
DO NOT WRITE IN THIS AREA
DO NOT WRITE IN THIS AREA
(a) Is Adam correct?
Show why you think this.​

Answer:

69.12

Step-by-step explanation:

12x5.76

Answer

69

Step-by-step explanation:

12×5.75=69

Answer:

a)  c. 90.

b) The margin of error of the point estimate is of 6.19 minutes.

c) The minimum sample size needed to obtain this amount of precision is 289.

Step-by-step explanation:

(a) Which of the following numbers gives the value of the point estimate?

The value of the point estimate is the sample mean, of 90 minutes. So the answer is given by option c.

(b) Using the information given above, calculate the margin of error (in minutes) of the point estimate. Assume we would like to estimate the population mean with 95% confidence.

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0639.

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

Here, we have [tex]s = 15, n = 25[/tex]. So

[tex]M = T\frac{s}{\sqrt{n}}[/tex]

[tex]M = 2.0639\frac{15}{\sqrt{25}}[/tex]

[tex]M = 6.19[/tex]

The margin of error of the point estimate is of 6.19 minutes.

Question c:

College students tend to watch sports between 0 and 120 minutes per day, which means that the standard deviation for population can be estimated as the standard deviation of an uniform distribution with [tex]a = 0, b = 120[/tex]. This standard deviation is:

[tex]\sigma = \sqrt{\frac{(b-a)^2}{12}}[/tex]

Then

[tex]\sigma = \sqrt{\frac{(120-0)^2}{12}}[/tex]

[tex]\sigma = 34.64[/tex]

Minimum sample size:

Now, since we have an estimate for the standard deviation of the population, we use the z-distribution.

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 - 0.95}{2} = 0.025[/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 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The minimum sample size is n for which M = 4. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]4 = 1.96\frac{34.64}{\sqrt{n}}[/tex]

[tex]4\sqrt{n} = 1.96*34.64[/tex]

[tex]\sqrt{n} = \frac{1.96*34.64}{4}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*34.64}{4})^2[/tex]

[tex]n = 288.1[/tex]

Rounding up:

The minimum sample size needed to obtain this amount of precision is 289.

Answer: x = -3

Step-by-step explanation:

2 x 2 + x - 1 = 0

4 + x - 1 = 0

3 + x = 0

x = -3

Answer:

X=-3

Step-by-step explanation:

See steps below:)

Answer:

13

Step-by-step explanation:

4w-10=42

4w=52

w=52/4

w=13

Answer:

x=10

Step-by-step explanation:

I guess solve for x

5x=50

x=10

Answer:

x=10

Step-by-step explanation:

Subtract to 25 from both sides

5x+25-25=75-25

so 75- 25 is 50

then ur left with 5x=50 so u divide because 5 is by x which means multipy so u do the opposite which is divding

5÷50 =10

Complete question is;

A leasing firm claims that the mean number of miles driven annually, u , in its leased cars is less than 12800 miles. A random sample of 50 cars leased from this firm had a mean of 12499 annual miles driven. It is known that the population standard deviation of the number of miles driven in cars from this firm is 3140 miles. Is there support for the firm's claim at the 0.05 level of significance?

Perform a one-tailed test.

null hypothesis?

alternative hypothesis?

type of test statistic?

value of the test statistic?

the p-value?

Can we support the leasing firm’s claim that the mean number of miles driven annually is less than 12800 miles?

Answer:

A) Null hypothesis; μ ≥ 12800

Alternative hypothesis; μ < 12800

B) type of test statistic: z-score test

C) test statistic; z = -0.678

D) p - value = 0.2489

E) No, we can't support the leasing firms claim

Step-by-step explanation:

We are given;

Population mean; μ = 12800 miles

Sample mean; x¯ = 12499 miles

Sample size; n = 50

Population standard deviation; σ = 3140

Let's define the hypothesis;

Null hypothesis; μ ≥ 12800

Alternative hypothesis; μ < 12800

The alternative hypothesis is the claim.

Since sample size is greater than 30, we will use z-score test.

Formula for z-score;

z = (x¯ - μ)/(σ/√n)

z = (12499 - 12800)/(3140/√50)

z = -0.678

From online p-value from z-score calculator attached, using z = -0.678 with one tailed hypothesis and significance value of 0.05,we have;

p - value = P(z < -0.678) = 0.2489

The p-value is greater than the significance value, so we will fail to reject the null hypothesis and conclude that there is no sufficient information to support the leasing firm's claim

Answer:

2X2

Step-by-step explanation:

Answer: 10

Step-by-step explanation: 5 x 2 = 10

                                             5 + 5 = 10

Answer:

About 220 of the students scored less than 96

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

Mean of 156 and a standard deviation of 23.

This means that [tex]\mu = 156, \sigma = 23[/tex]

Proportion that scored less than 96:

p-value of Z when X = 96. So

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

[tex]Z = \frac{96 - 156}{23}[/tex]

[tex]Z = -2.61[/tex]

[tex]Z = -2.61[/tex] has a p-value of 0.00453.

About how many of the students scored less than 96?

0.00453 out of 48592.

0.00453*48592 = 220.1.

Rounding to the closest integer:

About 220 of the students scored less than 96

Answer:

220

Step-by-step explanation:

#platolivesmatter

Answer:

D

Step-by-step explanation:

Answer:

42

Step-by-step explanation:

39+39 = 78

162 - 78 = 2 lengths =84

84/2 = 42

Answer:

A and C

Step-by-step explanation:

The triangle given has three equal sides and three equal angles.

Since the sum of a triangle = 180°, therefore, each angle equals 60°

Thus, we can conclude that the triangle is an acute triangle because an acute triangle has all three sides measuring less than 90°. This implies that all it's angles are acute angles.

Also, since all its sides are equal and the same as well as it's three angles, based on this, we can equally say the triangle is an equilateral triangle.

The triangle can be referred to as an acute triangle and also as an equilateral triangle.

Answer:

y

=

3

√

−

2

a

x

y

=

−

3

√

−

2

a

x

Step-by-step explanation:

Answer:

[tex] a^{5} [/tex]

Step-by-step explanation:

Given the mathematical expression;

a⁸/a³

To rewrite the expression in the form [tex] a^{m} [/tex]

We would have to apply the law of indices.

[tex] Law \; of \; division = \frac {a^{x}}{a^{y}} = a^{x - y} [/tex]

[tex] Law \; of \; division = \frac {a^{8}}{a^{3}} = a^{8 - 3} [/tex]

[tex] a^{m} = a^{8 - 3} = a^{5} [/tex]

Answer: 15850

Step-by-step explanation:

if johns account has 10000 dollars then each year he'll be making at 3.25% interest that's a total of $325 each year therefore in 18 years he'll have made 325 X the 18 years which you turn hall to 5850 as interest but now the question is it asking how much will John have in his account after 18 years at the yearly simple interest of the 3.25 there for the total will be 15850 dollars

the clock lost 2 seconds per day

Answer:

Where are the statements?

Step-by-step explanation:

Where are the statements?

Step-by-step explanation:

Answer:

1: true

2: false

Step-by-step explanation:

1: congruent = equal while supplementary = 180-degrees

2: congruent angles= vertical angles, corresponding angles, alternate interior angles, & alternate exterior angles

Answer:

yes it does. good job on your A.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

Answer:

-5

Step-by-step explanation:

To find the common difference, take the second term and subtract the first term

-2 - 3 = -5

Check with the third term and the second term

-7 - (-2) = -7 +2 = -5

The common difference is -5

Answer:

girls

Step-by-step explanation:

an outlier is a number that is greater than the others.

boys doesnt have and outlier because the highest number has other numbers near it, while girls doesn't.

Answer: Choice C

exact length = sqrt(26) units

approximate length = 5.10 units  

=======================================================

Work Shown:

We can use the distance formula.

A = (x1,y1) = (2,2)

B = (x2,y2) = (1,-3)

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(2-1)^2 + (2-(-3))^2}\\\\d = \sqrt{(2-1)^2 + (2+3)^2}\\\\d = \sqrt{(1)^2 + (5)^2}\\\\d = \sqrt{1 + 25}\\\\d = \sqrt{26}\\\\d \approx 5.0990195\\\\d \approx 5.10\\\\[/tex]

The distance from A to B is exactly sqrt(26) units which approximates to 5.10 units. This distance represents the length of chord AB.

Answer:

A

Step-by-step explanation:

because box is filled with four out of six and the second is filled with three out of six. So, you subtract the second one from the first one. I HOPE IT HELPS

Answer:

its e because i have done it before

Step-by-step explanation:

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Answer:

Difference = 250 students

Step-by-step explanation:

Let the total number of students be x.

Given the following data;

% driving = 30%

% riding = 60%

% walking = 10%

Number of students driving = 375

First of all, we would determine the total number of students.

Total = 30/100 * x = 375

0.3x = 375

Total, x = 375/0.3

Total, x = 1250 students.

Next, we determine the number of students walking;

Walking = 10/100 * 1250

Walking = 12500/100

Walking = 125 students

Finally, we would determine many more students drive to school than walk to school;

Difference = 375 - 125

Difference = 250 students

Step-by-step explanation:

I am assuming you want x? if so :

5x+12=6x-10

-x = -22

x =22

if u wanted angle J :

plug x back in

5(22)+12 = 122

subtract 180-122

J = 58°

Answer: person above me is correct

Step-by-step explanation:

Answer:

x = 12

Step-by-step explanation:

= 6 * (1/6 x)

= (6) * (2)

x = 12

Hope this helps....

Have a good day ahead :)

Answer:

The awnser is D) X=12

Step-by-step explanation:

Sorry if its blurry:<

Answer:

V = πr²h

V = 3.14 (5cm)²(7 cm)

V = 3.14 (25cm²) ( 7 cm)

V = 3.14 (175 cm³)

V = 549.50 cm³