How do you evaluate this?

Answer: A. The sampling follows a normal distribution.

              B. Between 25.14 and 30.86

              C. About 95% will contain the true mean and about 5% won't

Step-by-step explanation: A. The sampling is normally distributed because:

B. For a 95% confidence interval: α/2 = 0.025

Since n = 210, use z-score = 1.96

To calculate the interval:

mean ± [tex]z.\frac{s}{\sqrt{n} }[/tex]

Replacing for the values given:

28 ± [tex]1.96.\frac{21}{\sqrt{210} }[/tex]

28 ± [tex]1.96*1.45[/tex]

28 ± 2.84

lower limit: 28 - 2.84 = 25.14

upper limit: 28 + 2.84 = 30.86

Confidence Interval is between 25.14 and 30.86.

C. Confidence Interval at a certain percentage is an interval of values that contains the true mean with a percentage of confidence. In the case of number of times per day students text, 95% of the interval will contain the true mean, while 5% will not contain it.

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

In direct variations, we would have:

[tex]q=kr[/tex]

Where k is some constant.

Since this is indirect variation, instead of that, we would have:

[tex]q=\frac{k}{r}[/tex]

To determine the equation, find k by putting in the values for q and r:

[tex]10=\frac{k}{2.5}\\k=2.5(10)=25[/tex]

Now plug this back into the variation:

[tex]q=\frac{25}{r}[/tex]

The answer is D.

Answer:

Even set = {HTT, THT, TTH, TTT}

Step-by-step explanation:

We are given that three coins are tossed; the result is at most one head.

And we have to find the sets of elements that are included in the sample space.

Firstly, as we know that when three coins are tossed, the total number of cases formed is 8.

Let Head on the coin be represented by 'H' and the Tail on the coin be represented by 'T'.

So, the sample space so formed is;

S = {HHH, HTH, HHT, THH, THT, TTH, HTT, TTT}

Now, our event is at most one head. So, the sample space for the favorable event is given by;

Even set = {HTT, THT, TTH, TTT}

In this, three cases are of head occurring only once and one case is of head not appearing in three tosses of a coin.

Complete Question

The  complete question is shown on the first uploaded image

Answer:

The 90% confidence interval is  [tex][108.165 ,112.895][/tex]

The  95%  confidence interval is [tex][107.7123 ,113.3477][/tex]

The  correct option is  D

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  48

     The sample  mean is  [tex]\= x = \$ 110.53[/tex]

    The standard deviation is  [tex]\sigma = \$ 9.96[/tex]

Considering first question

  Given that the confidence level is  90% then the level of significance is mathematically represented as

            [tex]\alpha = (100 - 90)\%[/tex]

           [tex]\alpha = 0.10[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

          [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = ZZ_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.645 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.365[/tex]

The  90% confidence interval is  

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

=>    [tex]110.53 - 2.365 < \mu < 110.53 + 2.365[/tex]

=>    [tex]108.165 < \mu < 112.895[/tex]

Considering second question

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

            [tex]\alpha = (100 - 95)\%[/tex]

           [tex]\alpha = 0.05[/tex]

The  critical value  of  [tex]\frac{\alpha }{2}[/tex] from the  normal distribution table is  

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

Generally the margin of error is mathematically represented as

            [tex]E = Z_{ \frac{x}{y} } * \frac{\sigma}{ \sqrt{n} }[/tex]

             [tex]E = 1.96 * \frac{9.96}{ \sqrt{ 48} }[/tex]

             [tex]E = 2.8177[/tex]

The  95% confidence interval is  

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

=>    [tex]110.53 - 2.8177 < \mu < 110.53 + 2.8177[/tex]

=>    [tex]107.7123 < \mu < 113.3477[/tex]

Answer:

13.85

Step-by-step explanation:

U use the pythagorean theorem

So 2^2 + x^2 = 14^2

Simplify the equation: 4+x^2=196

--> x^2=192

--> x=13.85

-Hope this helps :)

9514 1404 393

Answer:

  c.  8√3

Step-by-step explanation:

The Pythagorean theorem applies.

  14² = s² + 2²

  s = √(14² -2²) = √192 = 8√3

The length of the remaining side is 8√3.

Answer:

the like terms are:

3x+8x+x+y+8

12x+y+8

Answer:

The like terms are

3x, 8x, x

Step-by-step explanation:

3x+8x+y+x+8

The like terms are

3x, 8x, x

They are the terms that are in terms of the first power of x

Answer:

Step-by-step explanation:

12 eggs in one box

12 boxes = 1 crate

12 x 12 = 144 eggs

144 x 24 crates = 3456 eggs

Answer:

3,456 eggs

Step-by-step explanation:

There are 12 eggs in one box and 12 boxes in one crate. To find out how many eggs are in a crate, multiply 12 and 12

12*12=144

144 eggs in one crate.

We want to find out what how many eggs are in 24 creates. We know there are 144 eggs in 1 crate. Therefore, we can multiply 144 and 24.

144*24=3,456

There are 3,456 eggs in 24 crates.

Answer:

The correct answer will be option b

Step-by-step explanation:

We know that x = rcos( θ ), and y = rsin( θ ), so let's rewrite this polar equation.

r = 4( x / r ) + 2( y / r ),

r = 4x / r + 2y / r,

r = 4x + 2y / r,

r / 1 = 4x + 2y / r ( Cross - Multiply )

4x + 2y = r²

We also know that r² = x² + y², so let's substitute.

x² + y² = 4x + 2y,

x² - 4x - 2y + y² = 0,

Circle Equation : ( x - 2 )² + ( y - 1 )² = ( √5 )²,

Solution : ( x - 2 )² + ( y - 1 )² = 5

Triangle PQR=TSR

PROVED

Answer:

Image provided is correct, thank you!

Answer:

If the null hypothesis is true in a chi-square test, discrepancies between observed and expected frequencies will tend to be small enough to qualify as a common outcome.

Step-by-step explanation:

Here in this question, we want to state what will happen if the null hypothesis is true in a chi-square test.

If the null hypothesis is true in a chi-square test, discrepancies between observed and expected frequencies will tend to be small enough to qualify as a common outcome.

This is because at a higher level of discrepancies, there will be a strong evidence against the null. This means that it will be rare to find discrepancies if null was true.

In the question however, since the null is true, the discrepancies we will be expecting will thus be small and common.

[tex]\displaystyle\\(a+b)^n\\T_{r+1}=\binom{n}{r}a^{n-r}b^r\\\\\\(x+2)^7\\a=x\\b=2\\r+1=5\Rightarrow r=4\\n=7\\T_5=\binom{7}{4}x^{7-4}2^4\\T_5=\dfrac{7!}{4!3!}\cdot x^3\cdot16\\T_5=16\cdot \dfrac{5\cdot6\cdot7}{2\cdot3}\cdot x^3\\\\T_5=560x^3[/tex]

Answer:

[tex]\large \boxed{560x^3}[/tex]

Step-by-step explanation:

[tex](x+2)^7[/tex]

Expand brackets.

[tex](x+2) (x+2) (x+2) (x+2) (x+2) (x+2) (x+2)[/tex]

[tex](x^2 +4x+4) (x^2 +4x+4) (x^2 +4x+4)(x+2)[/tex]

[tex](x^4 +8x^3 +24x^2 +32x+16)(x^3 +6x^2 +12x+8)[/tex]

[tex]x^7 +14x^6 +84x^5 +280x^4 +560x^3 +672x^2 +448x+128[/tex]

The fifth term is 560x³.

Answer:

1700

Step-by-step explanation:

pls thnx and mark me brainliest

Answer:

Step-by-step explanation:

The determinant of the coefficient matrix is ...

  [tex]D=\left|\begin{array}{ccc}2&5&3\\4&-1&-4\\-5&-2&6\end{array}\right|\\\\=2(-1)(6)+5(-4)(-5)+3(4)(-2)-2(-4)(-2)-5(4)(6)-3(-1)(-5)\\\\=-12+100-24-16-120-15=\boxed{-87}[/tex]

The other determinants are found in similar fashion after substituting the constants on the right for each of the above matrix columns, in turn.

Those determinants are ...

  [tex]D_x=\left|\begin{array}{ccc}21&5&3\\-13&-1&-4\\0&-2&6\end{array}\right|=174[/tex]

  [tex]D_y=\left|\begin{array}{ccc}2&21&3\\4&-13&-4\\-5&0&6\end{array}\right|=-435[/tex]

  [tex]D_z=\left|\begin{array}{ccc}2&5&21\\4&-1&-13\\-5&-2&0\end{array}\right|=0[/tex]

The solutions are ...

  x = 174/-87 = -2

  y = -435/-87 = 5

  z = 0

That is, (x, y, z) = (-2, 5, 0).

Answer:

7.15 miles

Step-by-step explanation:

4/5 of a mile is equivalent to .8 miles.

32.95

-25.8

7.15

Answer:

Step-by-step explanation:

39.95 - 25.80 = 7.15 miles

Answer:

Option  A

Step-by-step explanation:

2001 can be divided by 3, 23, and 29 without remainders. This means that the three numbers are prime divisors of 2001.

2001/3 = 667

2001/23 = 87

2001/29 = 69

The sum of the prime divisors is 55.

3 + 23 + 29 = 55

Option A should be the correct answer.

Hope this helps.

Answer:

[tex]\boxed{4x + 3y}[/tex]

Step-by-step explanation:

Hey there!

Well 4x + 3y cannot be added together because they are 2 different variables.

4x + 3y = 4x + 3y

So 4x + 3y simplified is,

Hope this helps :)

Step-by-step explanation:

To solve for x, we set up our equation like this:

7x - 7 = 4x + 14

Next, we subtract 4x from the right side to cancel it out and then subtract 4x from the left side.

7x (-4x) - 7 = 4x (-4x) + 14

3x - 7 = 14

Then, we add 7 on both sides (to cancel the -7 out and place it on the right)

3x - 7 (+7) = 14 + 7

3x = 21

Finally, we divide both sides by 3 to isolate our variable, x.

3x ÷ 3 = x

21 ÷ 3 = 7

Our final answer: x = 7

Answer:

x = 2/3 or x = -2/5

Step-by-step explanation:

15x^2 - 4x - 4 = ?

factor the left side of the expression and set factors equal to zero:

(3x-2)(5x+2)=0

3x - 2 =0 or 5x + 2 =0

3x =2 or 5x = -2

x = 2/3 or x = -2/5

Answer:

Step-by-step explanation:

Using the value for calculating the confidence interval as given;

CI = xbar + Z*σ/√n

xbar  is the mean = 37.14+42.86/2

xbar= 80/2

xbar = 40

Z is the z-score at the 90% confidence = 1.645

σ is the standard deviation

n is the sample size = 35

Given the confidence interval CI as [37.14, 42.86]

Using  the maximum value of the confidence interval to get the value of the standard deviation, we will have;

42.86 =  xbar + Z*σ/√n

42.86 = 40 + 1.645* σ/√35

42.86-40 = 1.645*σ/√35

2.86 = 1.645*σ/√35

2.86/1.645 = σ/√35

1.739 = σ/√35

1.739 = σ/5.92

σ= 1.739*5.92

σ = 10.295

Hence, the sample standard deviation of a pair of jeans is 10.295

Answer:

63.5

Step-by-step explanation:

Answer:

25, 2.45, 8, -0.84, -2

Step-by-step explanation:

negative is a least number

positive is a greater number

Positive number-8, 25, 2.45

Negative number-(-2), -0.84

ordering number from greatest to least:

25, 2.45, 8, -0.84, -2

-2 is smallest then -0.84 because 2 is bigger then 0.84. It is opposite with the positive number.

The bigger the positive number the biggest it is. While the bigger the negative number the smallest it is.

Answer:

Step-by-step explanation:

The numbers are:

● 8

● -2

● 25

● 2.45

● -0.84

To make it easy classify the positive numbers apart and the negatives ones alone

● 2.45<8< 25

● -2 < -0.84

25 is the greatest and -2 is the least

● 25 > 8 > 2.45 > -0.84 > -2

Answer:

48

Step-by-step explanation:

Janet - 12 = Cody

60 - 12 = Cody

60 - 12 = 48

Answer:

A) one-sample t-test

B) two sample t-test

C) two sample t-test

Step-by-step explanation: The one - sample t-test is used to determine the existence of a statistical difference between a sample mean and a given population mean. The one sample t test is only capable of making comparison between a singular sample mean and an established value. Such is the case in (A) where the aim is to determine if a group of night workers sleep for 8 hours.

The other two cases however, involves making comparison between the sample means of two different groups, this requires the use of a two independent sample t-test

For a one-sample t test:

(Sample mean - population mean) / standard error.

Sample mean = s

Population mean = p

Sample size = n

For a two sample t-test :

[(s2 - s1) - (p2 - p1)] ÷ √[(sd1^2/n1) + (sd2^2/n2)]

Answer:

The 95% CI is   [tex]2.108 < \mu < 2.892[/tex]

Step-by-step explanation:

From the question we are told that

   The  population mean [tex]\mu = 2.5[/tex]

    The standard deviation is  [tex]\sigma = 0.8[/tex]

Given that the confidence level is  95% then the level of confidence is mathematically evaluated 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 values 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]

here we would assume that the sample size is  n =  16 since the person that posted the question did not include the sample size

  So    

               [tex]E = 1.96* \frac{0.8}{\sqrt{16} }[/tex]

               [tex]E = 0.392[/tex]

The  95% CI is mathematically represented as

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

substituting values

              [tex]2.5 - 0.392 < \mu < 2.5 + 0.392[/tex]

substituting values

              [tex]2.108 < \mu < 2.892[/tex]

Answer:

$188.91

Step-by-step explanation:

$999*.09=$89.91

$89.91+$99=$188.91

Answer:

ŷ = 0.964X1 - 0.336X2 + 13.066

b1 = 0.964 which is the unit change in the value of y when x1 changes.

b2 = - 0.336 which is the unit change in the value of y when x2 changes

Step-by-step explanation:

Y

10

11

15

15

20

23

27

32

X1

1

5

5

9

7

11

16

21

X2

16

11

14

11

1

8

7

3

The general form of a multiple regression equation is in form:

ŷ = b1x1 + b2x2 + c

Where,

ŷ = predicted or dependent variable

b1 and b2 = slope or gradient Coefficient for the independent or predictor variables x1 and X2 respectively.

c = intercept (constant)

Using the online multiple regression calculator, the model obtained by Inputting the values is written below:

ŷ = 0.964X1 - 0.336X2 + 13.066

Value of b1 = 0.964 which is the unit change in the value of y when x1 changes.

Value b2 = - 0.336 which is the unit change in the value of y when x2 changes

Answer:

D. The zeros are the hot dog prices that give $0.00 profit (no profit).

Step-by-step explanation:

Given the function  y=-2(x-3)² + 4

The zeros of the function are the points at which the graph of the function crosses the x axis if plotted. y is the daily profit (in hundreds of dollars) and x is the price of the hot dog. To find the zeros, we substitute x = 0 and solve.

Therefore:  y=2(x-3)² + 4

0 = 2(x-3)² + 4

-2(x² - 6x + 9) + 4 = 0

-2x² + 12x - 18 + 4 = 0

2x² - 12x + 18 - 4 = 0

2x² - 12x + 14 = 0

2(x² - 6x + 7) = 0

x² - 6x + 7 = 0

Solving the quadratic equation gives:

x = 3 + √2 and x = 3 - √2

This means that the graph crosses x at 3 + √2 and 3 - √2.

The zeros of the function are 3 + √2 and 3 - √2. The zeros of the function is the point where y = 0, that is the point that the hot dog prices that give $0.00 profit (no profit).

you can only see values of [tex] x[/tex] Ranging from $-3$ to $3$ and they're included, so domain is $[-3,3]$

and $y$ values ranging from $-2$ to $4$ but $-2$ is not included so range is $(-2,4]$