Decide all proper subsets of A { 8 ,7 ,6 ,5 ,4 ,3 ,2 ,1} = A 1- { 4 ,3 ,2 ,1} 2- { } 3- { 9 ,8 ,7 } 4- { 11 ,2} 5- { 5 }

Answer:

The 95% confidence interval for the difference in population means is (−26.325175  , 36.325175)

Step-by-step explanation:

Given that :

sample size n₁ = 36

sample mean [tex]\over\ x[/tex]₁ = 83

standard deviation [tex]\sigma[/tex]₁ = 5

sample size n₂ = 49

sample mean [tex]\over\ x[/tex]₂= 78

standard deviation [tex]\sigma[/tex]₂ = 3

The objective is to construct a 95% confidence interval for the difference in the population means

Let the population means be [tex]\mu_1[/tex]  and  [tex]\mu_2[/tex]

The 95% confidence interval or the difference in population means can be calculated by using the formula;

[tex](\overline{x_1} - \overline{x_2}) \pm t_{\alpha /2} \ \times s_{p}[/tex]

where;

the pooled standard deviation  [tex]s_{p} = \dfrac{(n_1-1)s_1^2+(n_2-1)s^2_2}{n_1+n_2-2}[/tex]

[tex]s_{p} = \dfrac{(36-1)5^2+(49-1)3^2}{36+49-2}[/tex]

[tex]s_{p} = \dfrac{(35)25+(48)9}{83}[/tex]

[tex]s_{p} = \dfrac{875+432}{83}[/tex]

[tex]s_{p} = \dfrac{1307}{83}[/tex]

[tex]s_p[/tex] = 15.75

degree of freedom = [tex]n_1 +n_2 -2[/tex]

degree of freedom = 36+49 -2

degree of freedom = 85 - 2

degree of freedom = 83

The Critical t- value 95% CI at df = 83 is

t  critical = T.INV.2T(0.05, 83) = 1.9889

Therefore, for the population mean , we have:

= (83 - 78) ± (1.9889 × 15.75)

= 5 ± 31.325175

= 5  - 31.325175 , 5 + 31.325175

= (−26.325175  , 36.325175)

Answer:

6 1/6 pounds

Step-by-step explanation:

since 2/3 coverted into sixths is 4/6, and 14-6 is 8, and 1/2 into sixths is 3/6, 4/6-3/6 is 1/6. You put the whole in the front and you have 6 1/6

Answer:

0.44

Step-by-step explanation:

11/25 = 0.44 = 44%

Answer:

11/25

Step-by-step explanation:

since there are 25 students, there will be 25 choices, and the 25 will be the denominator

and there are 11 guys so there will be 11 choices of guys and the 11 will go on top

Answer:

7≤r≤12

Step-by-step explanation:

The domain is the values that the input takes

The input goes from 7 to 12

7≤r≤12

Answer: Choice B) [tex]7 \le r \le 12[/tex]

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

Explanation:

The domain is the set of allowed x inputs of a function.

How far to the left can we go on this red line? That would be x = 7.

How far to the right? That would be x = 12.

We can have x equal anything between 7 and 12, including both endpoints. We include the endpoints because they are filled in circles (as opposed to open holes).

So the domain is [tex]7 \le x \le 12[/tex]. If we replace x with r, then we update that inequality into [tex]7 \le r \le 12[/tex]. This replacement happens because r is along the horizontal x axis.

area of Arc subtending [tex]360^{\circ}[/tex] (i.e. the whole circle) is $\pi r^2$

so area of Arc subtending $\theta^{\circ}$ is, $\frac{ \pi r^2}{360^{\circ}}\times \theta^{\circ}$

$\theta =72^{\circ}$ so the area enclosed by one such arc is $\frac{\pi (10)^272}{360}$

abd there are 2 such arcs, so double the area.

[tex] \LARGE{ \underline{ \boxed{ \rm{ \purple{Solution}}}}}[/tex]

For solving this question, Let's know how to find the area of a sector in a circle?

[tex] \large{ \boxed{ \rm{area \: of \: sector = \frac{\theta}{360} \times \pi {r}^{2} }}}[/tex]

Here, Θ is the angle of sector and r is the radius of the circle. So, let's solve this question.

We have,

By using formula,

⇛ Area of shaded region = 2 × Area of each sector

⇛ Area of shaded region = 2 × Θ/360° × πr²

⇛ Area of shaded region = 2 × 72°/360° × 22/7 × 10²

⇛ Area of shaded region = 2/5 × 100 × 22/7

⇛ Area of shaded region = 40 × 22/7

⇛ Area of shaded region = 880/7 inch. sq.

⇛ Area of shaded region = 125.71 inch. sq.

☄ Your Required answer is 125.71 inch. sq(approx.)

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Complete Question

The complete question is shown on the first uploaded image

Answer:

Yes  the test  suggest that the true average percentage of organic matter in such soil is something other than 3%

Step-by-step explanation:

From the question we are told that

  The  sample mean is  [tex]\= x = 2.482\%[/tex]

  The  standard deviation is [tex]\sigma = 1.614[/tex]

   The  standard error is [tex]SE = 0.295[/tex]

     The  sample size is [tex]n = 30[/tex]

   The  level of significance is  [tex]\alpha = 0.05[/tex]

  The  null hypothesis is [tex]H_o : \mu = 3\%[/tex]

   The  alternative hypothesis is  [tex]H_a : \mu \ne 3\%[/tex]

Now  the degree of freedom is evaluated as

       [tex]df = n - 1[/tex]

       [tex]df = 30 - 1[/tex]

       [tex]df = 29[/tex]

The test statistics is mathematically evaluated as

         [tex]t = \frac{ 2.482 - 3}{ 0.295}[/tex]

         [tex]t = -1.756[/tex]

The p-value is obtained from the the student t -distribution table , the value is  

        [tex]p-value = P( T \le t)= 2 * t_{ t, df } = t_{ -1.756 , 29 } = 2 *0.0448= 0.0896[/tex]

The reason for the 2 in the equation is because the test is a two -tailed test i.e  -1.756 and  1.756

Given that the [tex]p-value > \alpha[/tex] then we fail to reject the null hypothesis

Hence the test the suggest that the true average percentage of organic matter in such soil is something other than 3%

Answer:

83

Step-by-step explanation:

1∇2= (2+2^1)

=2+2=4

(4)∇3= (2+3^4)

=2+81

=83

Answer:

D: 450 miles

Step-by-step explanation:

So we know that Officer Jacobi drove 180 miles, which represents 40% of the total distance driven. In other words, 40% of the total distance traveled is 180. Thus (let D be the total distance traveled):

[tex]0.4D=180[/tex]

This equation is basically saying that 40% (0.4) of the total distance driven is 180 miles. To solve for the total distance D, we can divide both sides by 0.4. Thus:

[tex]0.4D=180\\D=450[/tex]

So the answer is D or 450 miles.

Note that there isn't a specific formula you would use. These types of problems require you to write out an equation yourself.

Answer:

-0.00411522633

Step-by-step explanation:

Contribution per head

Option A

Answer:

14 miles

Step-by-step explanation:

Since we know that the distance of the paths from Cedarburg to Allenville is 22 and 13/16 miles, and we know the distance from Cedarburg to Lakeside is 8 and 13/16 miles.

We know that the total distance is made up of the distance from C to L and L to A.

So 22 and 13/16 = 8 and 13/16 + L to A

We can subtract 22 and 13/16 by 8 and 13/16 to get 14 miles.

Hope this helps.

Answer:

B

Step-by-step explanation:

x can not be greater than (1,325-270)/26 because $270 is fixed for the rental

Answer:

-5

Step-by-step explanation:

y = -0.5x + [?]

The equation is put in slope intercept form

slope intercept form: y = mx + b

where m = slope and b = y intercept

We want to find the y intercept.

the y intercept is the value of y when x = 0

looking at the table when x = 0, y = -5 so the y intercept is -5.

In other words -5 belongs in [?]

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day

Step-by-step explanation:

We are given that a website developer wished to analyze the clicks per day on their newly updated website.

The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.

Let [tex]\mu[/tex] = mean number of clicks per day.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day

Here, the null hypothesis states that the mean number of clicks per day is 200 clicks a day.

On the other hand, the alternate hypothesis states that the mean number of clicks per day is different than 200 clicks a day.

Hence, this is the correct null and alternative hypotheses.

Answer: Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Step-by-step explanation:

Let [tex]\mu[/tex] be the mean number of clicks per day.

Given, a website developer wished to analyze the clicks per day on their newly updated website.

The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.

i.e. he wants to check either [tex]\mu=200\text{ or }\mu\neq 200[/tex]

Since a null hypothesis is a hypothesis believes that there is no difference between the two variables whereas an alternative hypothesis believes that there is a statistically significant difference between two variables.

So,  Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Hence, the required null and alternative hypotheses.

Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Step-by-step explanation:

Here are some examples of ten integers (in this case prime numbers) chosen from 2 to 24;

2, 3, 5, 7, 9, 15, 17, 19, 21, 23

Lets take for example the integers 15 and 21, they have a common divisor 3 which is greater than 1. Which implies that the number 3 can divide through 15 and 21 without a remainder, that is, 21 ÷ 3 = 7, 15 ÷ 3 = 5. Also note that 3 is a divisor of 9.

Therefore, we could right say that within any set of ten integers chosen from 2 through 24, there are at least two integers with a common divisor greater than 1.

Answer:

3

Step-by-step explanation:

a is 4 and 3 is x so 4+3=7

Answer: a=2 {x=3} r=1.         2(3)+ 1= 7

Step-by-step explanation:

Answer:

The answer is A 15,840, because 5,280 x 3 is equivalent to A

Answer:

A. x = 15,840 feet.

Step-by-step explanation:

[tex]\frac{5280 feet}{1 mile} =\frac{x feet}{3 miles}[/tex]

[tex]\frac{5280}{1} =\frac{x}{3}[/tex]

1 * x = 5,280 * 3

x = 15,840 feet

So, your answer is A. x = 15,840 feet.

Hope this helps!

Answer:

126°

Step-by-step explanation:

If that angle is 27, so is angle a.

180-27-27=126

Answer:

I think the answer is 4 boys

Step-by-step explanation:

Let the no of boys be y.

No. of girls = 11

= 3 + 2y (equation)

3 + 2y = 11

3 - 3 + 2y = 11 - 3

2y = 8

2y/2 = 8/2

y = 4

Boys = 4

Answer:

15

Step-by-step explanation:

Complementary angles add to 90 degrees

8x+27 + 6x-21 = 90

Combine like terms

14x+6 = 90

Subtract 6 from each side

14x+6-6 = 90-6

14x = 84

Divide by 14

14x/14 = 84/14

x=6

We want angle B

B = 6x-21 = 6*6-21 =36-21 = 15

Answer:

(a) 36.36%

(b) 0.36%

(c) 0.06%

Step-by-step explanation:

Given that the time intervals measured with a stopwatch have an uncertainty of about 0.2 s.

We want to know what is the percent uncertainty of a hand-timed measurement of:

(a) 5.5 s

Percentage = (0.2/5.5) × 100

≈ 36.36%

(b) 55 s

Percentage = (0.2/55)×100

≈ 0.36%

(c) 5.5 min

5.5 min = 5.5 × 60 s

= 330 s

Percentage = (0.2/330)×100

≈ 0.06%

Answer:

72[tex]\sqrt{3}[/tex] units²

Step-by-step explanation:

The area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )

Here b = ST = a = 12 and h = RS

To calculate RS use the tangent ratio in the right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex] , thus

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{RS}{ST}[/tex] = [tex]\frac{RS}{12}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 12 )

RS = 12[tex]\sqrt{3}[/tex]

Thus

A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex] units²

Answer:

Step-by-step explanation:

NO perimeter does not map directly to area....

take a square with side of 5 ... area is 5*5 which  is 25 perimeter is 20

if you now take a rectangle with long side 8 and short side 2

the perimeter is 20 but the area is 16

It's the third option.

Completing the square yields

x ² + 9x + 7 = 0

(x ² + 9x + 81/4) + 7 = 81/4

(x + 9/2)² + 7 = 81/4

Now solving for x gives

(x + 9/2)² = 53/4

x + 9/2 = ± √(53/4) = ± √53/2

x = (-9 ± √53)/2

Answer:

x = -2 or x = 2

Step-by-step explanation:

The solution is the points of intersection of the line and the parabola.

x = -2 or x = 2

Answer:

x = -2 and  x=2

Step-by-step explanation:

The solution to the system is where the two graphs intersect

The meet at x = -2 and  x=2

Answer:

A

Step-by-step explanation:

The first term of the sequence is 4, the common difference is 3. So the equation of this sequence is 4+(n-1)*3 or 1+3*n. Plug in n=100

Answer:

582-600

1,234-1,200

640-600

770-800

1,104-1,100