A random sample of 1000 people was taken. Four hundred fifty of the people in the sample favored Candidate AT. The 95% confidence interval for the true proportion of people who favor Candidate A is a. .424 to .476. b. .419 to .481. c. .40 to .50. d. .45 to .55.

Answer:

y = -3x + 3

[tex]y=\frac{1}{3}x-7[/tex]

Step-by-step explanation:

Slope of a line passing through two points ([tex]x_1, y_1[/tex]) and [tex](x_2, y_2)[/tex] is determined by the formula,

Slope = [tex]\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

If these points are (0, 3) and (3, -6),

Slope of the line passing through these lines = [tex]\frac{3+6}{0-3}[/tex] = (-3)

Equation of the line which passes through (0, 3) and slope = (-3),

y - y' = m(x - x')

y - 3 = (-3)(x- 0)

y - 3 = -3x

y = -3x + 3

Now slope of another line that passes through (3, -6) and (0, -7),

m' = [tex]\frac{(-6+7)}{(3-0)}[/tex]

m' = [tex]\frac{1}{3}[/tex]

Equation of the line that passes through (0, -7) and slope = [tex]\frac{1}{3}[/tex]

y - (-7) = [tex]\frac{1}{3}(x-0)[/tex]

y + 7 = [tex]\frac{1}{3}x[/tex]

y = [tex]\frac{1}{3}x-7[/tex]

Therefore, system of linear equations are,

y = -3x + 3

[tex]y=\frac{1}{3}x-7[/tex]

Answer: m=-3/2

Step-by-step explanation:

To find the slope, we use the formula [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]. With our given points, we can directly plug them into the formula.

[tex]m=\frac{9-6}{-5-(-3)} =\frac{3}{-2}[/tex]

Our slope is m=-3/2.

Answer:

7 toy cars

Step-by-step explanation:

If there are 35 toy vehicles, then there will be 7 cars

(Divide) 35/5

Answer:

1/100

Step-by-step explanation:

Since the numerators are all the same, the lowest value will depend on the denominators. The greater the denominator, the lower the value. Thus, the answer is 1/100

Answer:

A. Using a 90% confidence level (instead of 95%)

D. Using a sample size of 90 employees (instead of 60)

Step-by-step explanation:

The margin of error of a confidence interval is given by:

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

In which z is related to the confidence level, [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

The higher the margin of error, the less precise the confidence interval is.

We have:

A 95% confidence interval, with a sample of 60.

We want to make it more precise:

Two options, decrease z(decrease the confidence level), or increase n(increase the sample size).

So the correct options are:

A. Using a 90% confidence level (instead of 95%)

D. Using a sample size of 90 employees (instead of 60)

Answer:

  340 square feet

Step-by-step explanation:

If we "unwrap" the painted surface from the shed, it will have the shape shown in the attachment. It is essentially a 40' by 8' rectangle with two 10' wide by 2' high triangles added.

The rectangle area is ...

  A = LW = (40 ft)(8 ft) = 320 ft²

The total area of the two triangles is ...

  A = 2(1/2)bh = (10 ft)(2 ft) = 20 ft²

Then the painted area is ...

  total area = 320 ft² +20 ft²

  total area = 340 ft²

[tex] \frac{x}{ {1}^{3} - 3x + {3x} - {x}^{3} } [/tex]

Answer:

68% of these phones last 3.87 years.

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

The average lifetime of a certain new cell phone is 3.4 years.

This means that [tex]m = 3.4, \mu = \frac{1}{3.4} = 0.2941[/tex]

So

[tex]P(X \leq x) = 1 - e^{-0.2941x}[/tex]

68% of these phones last how long (in years)?

This is x for which:

[tex]P(X \leq x) = 0.68[/tex]

[tex]P(X \leq x) = 1 - e^{-0.2941x}[/tex]

Then

[tex]0.68 = 1 - e^{-0.2941x}[/tex]

[tex]e{-0.2941x} = 0.32[/tex]

[tex]\ln{e{-0.2941x}} = \ln{0.32}[/tex]

[tex]-0.2941x = \ln{0.32}[/tex]

[tex]x = -\frac{\ln{0.32}}{0.2941}[/tex]

[tex]x = 3.87[/tex]

68% of these phones last 3.87 years.

Answer:

Step-by-step explanation:

The data for the test are the differences between the head circumferences of the older twin girls and that of their sisters

μd = mean head circumferences of the older twin girls minus the mean head circumferences of the sisters

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

It is a left tailed test

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 25 - 1 = 24

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

Where

xd = difference in sample means

μd = difference in population means

sd = standard deviation of the difference

From the information given,

xd = 50.23 - 49.96 = 0.27

t = (0.27 - 0)/(1/√25)

t = 1.35

We would determine the probability value by using the t test calculator.

p = 0.095

Since alpha, 0.05 < than the p value, 0.095, then we would fail to reject the null hypothesis.

Therefore, at 5% significance level, the difference is not significant

[tex]-95/5=-19[/tex]

[tex]70/-2=-35[/tex]

[tex]-18 \times 10=-180[/tex]

[tex]27 \times -3=-81[/tex]

Answer:

a. -19

b. -35

c. -180

D. -81

please see the attached picture for full solution

hope it helps....

Good luck on your assignment....

Answer:

x = -5/2

Step-by-step explanation:

3 ^ ( 4x-5) = (1/27) ^( 2x+10)

Rewriting 1/27 as 3^-3

3 ^ ( 4x-5) = (3^-3) ^( 2x+10)

We know that a^b^x = a^(b*c)

3 ^ ( 4x-5) = (3) ^(-3*( 2x+10))

3 ^ ( 4x-5) = (3) ^( -6x-30)

The bases are the same so the exponents are the same

4x-5 = -6x-30

Add 6x to each side

10x -5 = -30

Add 5 to each side

10x -5+5 = -30+5

10x = -25

Divide each side by 10

10x/10 = -25/10

x = -5/2

Answer:

5/2 or 2.5

Step-by-step explanation:

3^(4x - 5) = (3^- 3)^(2x + 10)

3^(4x - 5) = (3)^(- 3 * (2x + 10))

3^(4x - 5) = (3) ^( - 6x - 30)

4x - 5 = - 6x - 30

10x = - 25

= - 25/10

= - 5/2 or 2.5

Hope this helps!

Answer:

see below

Step-by-step explanation:

You can remove one or more of the other color marbles to increase the probability of drawing a green marble

or

You can add  one or more green marbles to have more green marbles in the bag

Answer:

a)0.8280

b)0.7691

c)0.4503

Step by step Explanation:

It was Given that 13% of all steel shafts produced by a certain process are nonconforming but can be reworked (rather than having to be scrapped).Each shaft is independent of the other and probability for non conforming is the same for each trial.

If X the denote the number among these that are nonconforming and can be reworked. Then

n =200 and

p = 0.13

Then, CHECK THE ATTACHMENT FOR DETAILED EXPLATION

4 miles

Step-by-step explanation:

if you travel 8 in 1 hour just cut it in half

8 * 1/2 = 4

Answer:

y=-2/3x-2

Slope: -2/3

Y intercept: -2

Answer:

14.3%

Step-by-step explanation:

There is only one four out of 7 total numbers.

1/7 = 0.142857 = 14.29%

We are given 7 numbers.

4 is only one card in that 7 card set so, 1/7.

1/7 = 0.1428

0.1428 * 100% = 14.28%

Therefore, the answer is roughly 14.3%

Best of Luck!

Answer:

2/6, 4/12, 8/24, 16/48, 32/96 ect....

Step-by-step explanation:

I hope this helps I really didnt know if this is what you were asking about

Answer:

Step-by-step explanation:

Answer: (x,y)=(14/4,0)

Step-by-step explanation:

y=-2(x-3)(2)+2

Clear the brackets

y=-2(2x-6)+2

y=-4x+12+2

y=-4x+14

To get the x-intercept y=0

0=-4x+14

4x=14

x=14/4

(x,y)=(14/4,0)

Answer:

a. The claim is that the amount of television watched per day last year by the average person differed from that in 2005.

b. The critical values are tc=-1.729 and tc=1.729.

The acceptance region is defined by -1.792<t<1.729. See the picture attached.

c. Test statistic t=0.18.

The null hypothesis failed to be rejected.

d. At a significance level of 10%, there is not enough evidence to support the claim that the amount of television watched per day last year by the average person differed from that in 2005.

e. The 95% confidence interval for the mean is (2.29, 7.23).

Step-by-step explanation:

We have a sample of size n=20, which has mean of 4.76 and standard deviation of 5.28.

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{20}(1+4.6+5.4+. . .+6.2)\\\\\\M=\dfrac{95.2}{20}\\\\\\M=4.76\\\\\\s=\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2\\\\\\s=\dfrac{1}{19}((1-4.76)^2+(4.6-4.76)^2+(5.4-4.76)^2+. . . +(6.2-4.76)^2)\\\\\\s=\dfrac{100.29}{19}\\\\\\s=5.28\\\\\\[/tex]

a. This is a hypothesis test for the population mean.

The claim is that the amount of television watched per day last year by the average person differed from that in 2005.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=4.55\\\\H_a:\mu\neq 4.55[/tex]

The significance level is 0.1.

The sample has a size n=20.

The sample mean is M=4.76.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=5.28.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.28}{\sqrt{20}}=1.181[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{4.76-4.55}{1.181}=\dfrac{0.21}{1.181}=0.18[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=20-1=19[/tex]

The critical value for a level of significance is α=0.10, a two tailed test and 19 degrees of freedom is tc=1.729.

The decision rule is that if the test statistic is above tc=1.729 or below tc=-1.729, the null hypothesis is rejected.

As the test statistic t=0.18 is within the critical values and lies in the acceptance region, the null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the amount of television watched per day last year by the average person differed from that in 2005.

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=4.76.

The sample size is N=20.

The standard error is s_M=1.181

The degrees of freedom for this sample size are df=19.

The t-value for a 95% confidence interval and 19 degrees of freedom is t=2.093.

The margin of error (MOE) can be calculated as:

[tex]MOE=t\cdot s_M=2.093 \cdot 1.181=2.47[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=M-t \cdot s_M = 4.76-2.47=2.29\\\\UL=M+t \cdot s_M = 4.76+2.47=7.23[/tex]

The 95% confidence interval for the mean is (2.29, 7.23).

Answer:

1. 0.9836 = 98.36% probability that your survey will provide a sample proportion within ±0.03 of the population proportion

2. 0.7698 = 76.98% probability that your survey will provide a sample proportion within ±0.015 of the population proportion.

Step-by-step explanation:

Normal probability distribution

When the distribution is normal, we use the z-score formula.

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

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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

In this question, we have that:

[tex]p = 0.1, n = 575[/tex]

So

[tex]\mu = 0.1, s = \sqrt{\frac{0.1*0.9}{575}} = 0.0125[/tex]

1. What is the probability that your survey will provide a sample proportion within ±0.03 of the population proportion?

This is the pvalue of Z when X = 0.1 + 0.03 = 0.13 subtracted by the pvalue of Z when X = 0.1 - 0.03 = 0.07. So

X = 0.13

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

By the Central Limit Theorem

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

[tex]Z = \frac{0.13 - 0.1}{0.0125}[/tex]

[tex]Z = 2.40[/tex]

[tex]Z = 2.40[/tex] has a pvalue of 0.9918

X = 0.07

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

[tex]Z = \frac{0.07 - 0.1}{0.0125}[/tex]

[tex]Z = -2.40[/tex]

[tex]Z = -2.40[/tex] has a pvalue of 0.0082

0.9918 - 0.0082 = 0.9836

0.9836 = 98.36% probability that your survey will provide a sample proportion within ±0.03 of the population proportion.

2. What is the probability that your survey will provide a sample proportion within ±0.015 of the population proportion?

This is the pvalue of Z when X = 0.1 + 0.015 = 0.115 subtracted by the pvalue of Z when X = 0.1 - 0.015 = 0.085. So

X = 0.115

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

[tex]Z = \frac{0.115 - 0.1}{0.0125}[/tex]

[tex]Z = 1.2[/tex]

[tex]Z = 1.2[/tex] has a pvalue of 0.8849

X = 0.085

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

[tex]Z = \frac{0.085 - 0.1}{0.0125}[/tex]

[tex]Z = -1.2[/tex]

[tex]Z = -1.2[/tex] has a pvalue of 0.1151

0.8849 - 0.1151 = 0.7698

0.7698 = 76.98% probability that your survey will provide a sample proportion within ±0.015 of the population proportion.

Answer:

Option E is correct.

The expected number of meals expected to be served on Wednesday in week 5 = 74.2

Step-by-step Explanation:

We will use the data from the four weeks to obtain the fraction of total days that number of meals served at lunch on a Wednesday take and then subsequently check the expected number of meals served at lunch the next Wednesday.

Week

Day 1 2 3 4 | Total

Sunday 40 35 39 43 | 157

Monday 54 55 51 59 | 219

Tuesday 61 60 65 64 | 250

Wednesday 72 77 78 69 | 296

Thursday 89 80 81 79 | 329

Friday 91 90 99 95 | 375

Saturday 80 82 81 83 | 326

Total number of meals served at lunch over the 4 weeks = (157+219+250+296+329+375+326) = 1952

Total number of meals served at lunch on Wednesdays over the 4 weeks = 296

Fraction of total number of meals served at lunch over four weeks that were served on Wednesdays = (296/1952) = 0.1516393443

Total number of meals expected to be served in week 5 = 490

Number of meals expected to be served on Wednesday in week 5 = 0.1516393443 × 490 = 74.3

Checking the options,

74.3 ≈ 74.2

Hence, the expected number of meals expected to be served on Wednesday in week 5 = 74.2

Hope this Helps!!!

Answer:

MODE IS WHEN A NUMBER APPEARS MORE OFTEN IN A SET OF NUMBERS

Step-by-step explanation:

Example 2,3,8,6,5,3,4 , the mode is 3 because it appears more often

Have a great day

Answer:

let’s make a Unit rate.

$20/4 hours = $5 per hour

So you earn $5 in 1 hour if you earn $20 in 4 hours.

hope this helps and pls mark me brainliest if it did ;)

Answer:

$5

Step-by-step explanation:

Let's set up a proportion using the following setup.

money/hours=money/hours

We know that $20 is earned in 4 hours. We don't know how much is earned in 1 hour, so we can say $x is earned in 1 hour.

$20/4 hours= $x/1 hour

20/4=x/1

x/1 is equal to x.

20/4=x

Divide 20 by 4.

5=x

$5 is earned in 1 hour.

Answer: 44°

Step-by-step explanation:

Measures of the angles of a triangle

= 180°

Therefore, 180 - 105 + 31 = 44°

The measure of the third angle is 44 degrees.

We have,

To find the measure of the third angle in a triangle, we can use the fact that the sum of the measures of all three angles in a triangle is always 180 degrees.

Let's denote the measure of the third angle as "x".

We are given that the measures of the other two angles are 105 degrees and 31 degrees.

Using the sum of angles in a triangle, we can set up the equation:

105 + 31 + x = 180

Simplifying the equation:

136 + x = 180

To isolate "x", we subtract 136 from both sides of the equation:

x = 180 - 136

x = 44

Therefore,

The measure of the third angle is 44 degrees.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ2

Answer:

He has 16 moose photos

Step-by-step explanation:

He has 4 bear photos since 4 times 4 equals 16. The eagle photos would have to be 30, which is divisible by 6.

16 moose+4 bear+30 eagle=50 photos

Answer:

a) X ~ N(70,12)

b) ¯ x ~ N(70,1.6971)

c) For a single tire, 0.0541 = 5.41% probability that the number of miles (in thousands) before it will need replacement is between 72.1 and 73.8. For the 50 tires tested, 0.0950 = 9.50% probability that the average miles (in thousands) before need of replacement is between 72.1 and 73.8.

d) No

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

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

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.

a. What is the distribution of X ?

Single tire, so normal with mean [tex]\mu = 70[/tex], standard deviation [tex]\sigma = 12[/tex]

So X ~ N(70,12).

b. What is the distribution of ¯ x ?

Sample of 50.

By the Cental Limit Theorem, the mean stays the same.

The standard deviation will be [tex]s = \frac{12}{\sqrt{50}} = 1.6971[/tex]

So

¯ x ~ N(70,1.6971)

c. f a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 72.1 and 73.8.

This is the pvalue of Z when X = 73.8 subtracted by the pvalue of Z when X = 72.1. So

X = 73.8

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

[tex]Z = \frac{73.8 - 70}{12}[/tex]

[tex]Z = 0.32[/tex]

[tex]Z = 0.32[/tex] has a pvalue of 0.6255

X = 72.1

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

[tex]Z = \frac{72.1 - 70}{12}[/tex]

[tex]Z = 0.18[/tex]

[tex]Z = 0.18[/tex] has a pvalue of 0.5714

0.6255 - 0.5714 = 0.0541

For a single tire, 0.0541 = 5.41% probability that the number of miles (in thousands) before it will need replacement is between 72.1 and 73.8.

For the 50 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 72.1 and 73.8

50 tires, so by the Central Limit Theorem, we use s in the z-score formula.

X = 73.8

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

[tex]Z = \frac{73.8 - 70}{1.6971}[/tex]

[tex]Z = 2.24[/tex]

[tex]Z = 2.24[/tex] has a pvalue of 0.9875

X = 72.1

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

[tex]Z = \frac{72.1 - 70}{1.6971}[/tex]

[tex]Z = 1.24[/tex]

[tex]Z = 1.24[/tex] has a pvalue of 0.8925

0.9875 - 0.8925 = 0.0950

For the 50 tires tested, 0.0950 = 9.50% probability that the average miles (in thousands) before need of replacement is between 72.1 and 73.8.

d. Is the assumption that the distribution is normal necessary?

Sample size of 30 or larger(in this case, 50), so the assumption is not necessary.

Answer:

Roots

Step-by-step explanation:

Solve for

x

by simplifying both sides of the equation, then isolating the variable.

x=0

Answer:

translation

Step-by-step explanation:

To map Triangle DEF onto Triangle GHJ, a transformation is needed to be done.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent. Hence all the three sides and three angles are congruent.

Triangle D E F is shifted down and to the right to form triangle G H J.  Hence to map Triangle DEF onto Triangle GHJ, a transformation is needed to be done.

Find out more on Congruent triangles at: https://brainly.com/question/1675117

Answer:

the answer is the first option