What is the value of S
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Answer:

The point estimate for the true difference between the population means is of -2.62 years.

The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.

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.

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]

Subtraction of normal variables:

When we subtract normal variables, the mean is the subtraction of the mean, while the standard deviation is the square root of the sum of variances.

A sample of 138 cars owned by students had an average age of 5.13 years. The population standard deviation for cars owned by students is 3.45 years.

This means that:

[tex]\mu_{s} = 5.13, \sigma_{s} = 3.45, n = 138, s_s = \frac{3.45}{\sqrt{138}} = 0.2937[/tex]

A sample of 111 cars owned by faculty had an average age of 7.75 years.  The population standard deviation for cars owned by faculty is 2.08 years.

This means that [tex]\mu_{f} = 7.75, \sigma_{f} = 2.08, n = 111, s_f = \frac{2.08}{\sqrt{111}} = 0.2658[/tex]

Difference between the true mean ages for cars owned by students and faculty.

s - f

Mean:

[tex]\mu = \mu_s - \mu_f = 5.13 - 7.75 = -2.62[/tex]

This is the point estimate for the true difference between the population means.

Standard deviation:

[tex]s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2937^2+0.2658^2} = 0.3961[/tex]

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 - 0.95}{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 = zs = 1.96*0.3961 = 0.78[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is -2.62 - 0.78 = -3.4

The upper end of the interval is the sample mean added to M. So it is -2.62 + 0.78 = -1.84

The 95% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -3.4 years and -1.84 years.

Answer:

9490 species

Step-by-step explanation:

Hope this helps! You take 5.1% of 10,000 which is 510. Then you take 10,000-510= 9490

Answer:  there are more than 12,500 species of ants today like right now

Step-by-step explanation:

Answer:

-47

Step-by-step explanation:

that's the correct answer

Answer:

Choice C

Step-by-step explanation:

You find the ratio, so every if 4 McDonalds is $28 thats 4:28

You find the unit rate 1:x

divide each side by 4 and the unit rate is 7. Graph c shows cordinate (1,7)

Answer: I'm assuming that there were multiple choices provided for this question.. but just to help you, when a number is within the absolute value, it changes any number to a positive:

|-2.6| = 2.6

So any number higher than that work for this question :-)

Answer:

24

Step-by-step explanation:

Answer:

3/12

Step-by-step explanation:

Answer:

2/6

Step-by-step explanation:

it is equal to 1/3. The others are equal to 1/4 and 1/24 so 1/3 is the largest

Answer:

MNO no se estoy en 6th y no se pero esta es mi respuesta espero y me la saco bien

The  sequence of transformations T(–2, 4) ry-axis ry-axis T(2, –4) can be used to map triangle MNO onto M"N"O".

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The given sequence of transformations is:

T(–2, 4) - translation by (-2, 4)

ry-axis - reflection across the y-axis

ry-axis - reflection across the y-axis

T(2, –4) - translation by (2, -4)

We can check whether this sequence of transformations maps triangle MNO onto M"N"O" by applying each transformation to the coordinates of triangle MNO in order:

T(–2, 4) maps M(5,-4) to M'(3,0), N(3,-2) to N'(1,2), and O(1,-3) to O'(-1,1).

ry-axis reflects M'(-3,0) to M"(-3,0), N'(1,2) to N"(-1,2), and O'(-1,1) to O"(1,1).

ry-axis reflects M"(-3,0) back to M"(-3,0), N"(-1,2) back to N"(-1,2), and O"(1,1) back to O"(1,1).

T(2, –4) maps M"(-3,0) to M'(-1,-4), N"(-1,2) to N"(1,-2), and O"(1,1) to O"(3,-3).

The resulting coordinates M'(-1,-4), N'(1,-2), and O'(3,-3) are the coordinates of triangle M"N"O".

Therefore, the given sequence of transformations T(–2, 4) ry-axis ry-axis T(2, –4) can be used to map triangle MNO onto M"N"O".

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Answer:

The total leaves on the 7th tree is, 127.

Explanation:

A sequence is defined as a set of integers arranged in a specific order. A series, on the other hand, is defined as the sum of a sequence's elements.

Step by step:

The total leave will be on  7th tree are calculated.

Multiply term 2 and add term 1, to get the next digit.

According, to the question:

[tex]1[/tex]×[tex]2+1=3[/tex]

[tex]3[/tex]×[tex]2+1=7[/tex]

[tex]7[/tex]×[tex]2+1=15[/tex]

[tex]15[/tex]×[tex]2+1=31[/tex]

[tex]31[/tex]×[tex]2+1=63[/tex]

[tex]63[/tex]×[tex]2+1=127[/tex]

Hence, the 7th tree will have a total of 127 leaves.

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Answer:

0.7880

Step-by-step explanation:

0.7883

Hope it helps!

Answer:

I think they took 3 * 3 is equals to 9

3 * 5 equals to 15

3 * 7 equals to 21

and 3 * 9 equals to 27.

Step-by-step explanation:

can can you realise that they skipped 3 * 4 3 * 6 and 3 * 8 and the difference between 9 and 15 is 6 meaning there's a gap of 6 at each sequence so I guess my answer is 3 and + 3 if it's not if this is not the answer please tell me if it is not matching with your book tell me so that i can ask the people around me. answer 3n + 3

Answer:

360

Step-by-step explanation:

length times width of the base then multiply by the height of the prism.

(4)(9)10

Answer: 3/4 + 7/12 - (-4) = 3/4 + 7/12 + 4 (two minuses make a plus)

3/4 + 7/12 + 4/1 = 9/12 + 7/12 + 48/12           (4 = 4/1 or 4 divided by 1)  

(to add the fractions the denominators need to be the same. Multiply both the denominator and numerator by the same number)

(9+7+48)/12 = 64/12 = 5 and 1/3 or 16/3

We can also get this answer by leaving the 4 as a whole number:

9/12 + 7/12 +4 = 16/12 + 4 = 1 and 1/3 + 4 = 5 and 1/3

If you put the sum in a calclator you also get 5 and 1/3.

Hope this helps :)

Answer:

-16/3 = -5.3333333333

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

If these two lines are parallel, they have the same slope, which is -2.

Answer:

6) 9 3/5

7) 1/50

8) 28/45

Step-by-step explanation:

6) 8÷5/6=8x6/5=48/5=9 3/5

7) 1/5÷10=1/50

8) 7/5÷9/4=7/5x4/9=28/45

Answer:

i think c

Step-by-step explanation:

Answer:

The angles are adjacent and x=100

Answer:

71

Step-by-step explanation:

The square represents 90 degrees.

A triangle’s three angles ALWAYS adds up 180.

To find the missing angle:

180 - 90 = 90

90 - 19 = 71.

Therefore, the answer is 71

Answer:

$16.50

Step-by-step explanation:

Take the total price, convert the percentage to a decimal and multiply the two together.

329.97*0.05=16.498

Round to the nearest cent.

$16.50

Answer:

346.47

Step-by-step explanation:

the equation is: 329.97 * 5/100 + 329.97

= 16.4985 +329.97=346.4685

rounding to the nearest cent we get 346.47

Answer:

Its 2

Step-by-step explanation:

(39-7) / 4^2

32 / 4^2

32 / 2^4

2^5 / 2^4 divide which gets you

2

Answer:

21 times

Step-by-step explanation:

Answer:

20 Times

Step-by-step explanation:

Answer:

c = 24

Step-by-step explanation:

Angle c is supplementary to 146 and their sum is 180

c + 146 = 180 subtract 146 from both sides

c = 34

Answer:

$9.24

Step-by-step explanation:

1.68÷2=0.84

1.68×5+0.84=9.24

Answer:

length = 8 ft

width = 5 ft

Step-by-step explanation:

width = w

length = w + 3

Area of rectangular garden = 40 square feet

length  *width = 40

(w + 3) *w = 40

w*w + 3*w = 40

w² + 3w = 40

w² + 3w - 40 = 0

w² + 8w - 5w - 8*5 = 0

w(w + 8) - 5 (w +8) =0

(w + 8) (w - 5) = 0

w - 5 = 0       {Ignore w + 8 =0, as measurement will not be in -ve}

w = 5 ft

l = 5 + 3

l = 8 ft

Answer:

57

Step-by-step explanation:

60*0.95 = 57

Answer:

57 pounds is 95 percent of the limit.

Step-by-step explanation:

Answer:

a) 0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.

Step-by-step explanation:

A sequence of Bernoulli trials composes the binomial distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that a selected component is non-defective is 0.8

This means that [tex]p = 0.8[/tex]

a) Three non-defective components in a batch of seven components.

This is P(X = 3) when n = 7. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{7,3}.(0.8)^{3}.(0.2)^{4} = 0.0287[/tex]

0.0287 = 2.87% probability that three non-defective components in a batch of seven components.

b) 8 non-defective components are drawn before the first defective component is chosen.

Now the order is important, so the we just multiply the probabilities.

8 non-defective, each with probability 0.8, and then a defective, with probability 0.2. So

[tex]p = (0.8)^8*0.2 = 0.0336[/tex]

0.0336 = 3.36% probability that 8 non-defective components are drawn before the first defective component is chosen.