How do I simplify the expression

The calculation of the probability and interpretation of the difference in mean and the relation to level of significance between and the treatment and control groups are as follows;

Question 1;   Part A

The probability that the treatment group mean is greater than the control group mean by 8 points or more is 3.6%

The completed statement is as follows;

The significance level is set at 5%, and the probability of the result is 3.6%, which is lower than significance level. The result is statistically significant

Part B

The result is statistically significant, which implies that spraying the corn plant with the new type of fertilizer does increase the growth rate

Question 2; Part A

The probability of the treatment group mean is lower than the control group mean by 15 points or more is 7.8%

The completed statement is as follows;

The significance level is set at 5%, and the probability of the result is 7.8% which is higher than the significance level. The result is not statistically significant

Part B;

The result is not statistically significant which implies that wearing a watch does not make people manage their time better

The reason for the above solutions is as follows;

Question 1;

The known parameters;

The significance level of the test, α = 5%

The frequencies of the difference in mean between the treatment and control groups given in the table

The number of randomizations, ∑f = 1,000

The required parameter

The probability of the treatment group mean is greater than the control group mean by 8 points or more

The significance of the result

The comparison between the given level of significance and the probability

Method

We find the probability for the required difference in mean from the data given in the table

The probability that the treatment group mean is greater than the control group mean by 8 points or more is given by the following formula;

[tex]\mathbf{P(8 \ or \ more) = \dfrac{\sum f(8 \ or \ more)}{\sum f}}[/tex]

From the table, we have;

∑f(8 or more) = 26 + 8 + 2 = 36

∑f = 1 + 10 + 28 + 58 +...+ 114 + 57 + 28 + 8 + 2 = 1,000

Therefore;

[tex]P(8 \ or \ more) = \dfrac{36}{1,000} = 0.036 = 3.6\%[/tex]

The probability, P(8 or more) 3.6%

Given that the significant level, α = 5% is higher than the probability of 3.6%, the result is statistically significant

Part B

The true statement is that the result is statistically significant, which implies that spraying the corn plant with the new type of fertilizer does increase the growth rate

Question 2;

The known parameters are;

The significance level of the test, α = 5%

The frequencies of the difference in mean between the treatment and control groups given in the table

The number of randomizations, ∑f = 1,000

The required parameter

The probability of the treatment group mean is lower than the control group mean by 15 points or more

The significance of the result

The comparison between the given level of significance and the probability

Method

Using the method from Question 1, we have;

Part A

[tex]\mathbf{P(15 \ or \ more) = \dfrac{\sum f(15 \ or \ less)}{\sum f}}[/tex]

From the table, we have;

∑f(15 or more) = 50 + 18 + 10 = 78

∑f = 10 + 18 + 50 + 127 + 195 + 226 + 180 + 117 + 48 + 17 + 12 = 1,000

Therefore;

[tex]P(15 \ or \ more) = \dfrac{78}{1,000} = 0.078 = 7.8\%[/tex]

The probability, P(15 or more) = 7.8%

Given that the significant level, α = 5% is lower than the probability of 7.8%, the result is not statistically significant

Therefore, we have;

The significance level is set at 5%, and the probability of the result is 7.8% which is higher than the significance level. The result is not statistically significant

Part B

The true statement is that the result is not statistically significant which implies that wearing a watch does not make people manage their time better

Learn more about hypothesis testing here;

https://brainly.com/question/4232174

Question 1;  

Part A

The significance level is set at 5%, and the probability of the result is 3.6%, which is less than the significance level. The result is statistically significant

Part B

A) The result is statistically significant, which implies that spraying the corn plants with the new type of fertilizer does increase the growth rate.

Question 2;

Part A

The significance level is set at 5%, and the probability of the result is 7.8% which is higher than the significance level. The result is NOT statistically significant

Part B;

B) The result is not statistically significant, which implies that wearing a watch does not help people manage their time better.

Answer: About 27.49

Step-by-step explanation:

You use the laws of tangent within a triangle to find x:

[tex]tan(32)=\frac{opposite}{adjacent}= \frac{x}{44}\\ \\x=44*tan(32)=27.49425...[/tex]

The coldest time of day in Mumbai is 5 hours after midnight.

Since the average temperature t hours after midnight in Mumbai, India, is given by:

T(t)=24.5-5.5sin((2pi(t+1))/24)

We have that

T(t) = 24.5 - 5.5sin((2π(t+1))/24)

The coldest time of day is when T(t) is minimum.

T(t)  is minimum when 5.5sin((2π(t+1))/24) is minimum where t is the coldest time of day at minimum temperature, T(t).

Since for a sine function, -1 ≤ sinФ ≤ 1, the minimum value of sinФ = -1.

So, T(t) = 24.5 - 5.5sin((2π(t+1))/24) is minimum when

5.5sin((2π(t+1))/24) is minimum.

Also, -5.5sin((2π(t+1))/24) = 5.5 × -1 at minimum temperature T(t)

So, 5.5 × -1 = 5.5 × -sin((2π(t+1))/24)

So, -sin((2π(t+1))/24) = -1

sin((2π(t+1))/24) = 1

Taking inverse sine of both sides, we have

sin⁻¹sin((2π(t+1))/24) = sin⁻¹(1)

((2π(t+1))/24) = π/2

Multiplying both sides by 24, we have

(2π(t+1))/24 × 24 = π/2 × 24

(2π(t+1)) = 12π

Dividing both sides by 2π, we have

2π(t+1)/2π = 12π/2π

t + 1 = 6

t = 6 - 1

t = 5 hours

So, the coldest time of day in Mumbai is 5 hours after midnight.

Learn more about average temperature here:

https://brainly.com/question/19388300

Answer:

2107

Step-by-step explanation:

In this type of question we have to follow these steps

1) Find the biggest number in interval which is divisible by seven

For this question it is 196

2)Find the smallest number in interval which is divisible by seven

For this question it is 105

3) Then subtract 105 from 196

196-105=91

4) Divide 91 by seven

91:7=13

5)Lastly we have to add 1 to the 13

13+1=14

So we found that we have 14 different numbers that divisible by seven in this interval. So next steps will be about sum of them

To find them sum we have a formula:

  (biggest number + smaller number) x number of terms / 2

      (196+105) x 14 /2  = 2107

Answer:

0

Step-by-step explanation:

We can use the slope formula to find the slope

m = ( y2-y1)/(x2-x1)

    = (3-3)/(-3-3)

    = 0/-6

    =0

Answer:

m = 0

Step-by-step explanation:

Use the slope formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}\\[/tex]

[tex]\frac{3-3}{3-(-3)}\\\\ \frac{0}{6}\\\\0[/tex]

Therefore, the slope of the line is 0.

*Note that if the y values do not change as x changes, it is evidence that the slope is 0.*

Answer:

C

Step-by-step explanation:

3(17x-6.5) =108

=17x-6.5=36

=17x =36 +6.5

= 17x=42.4

=x =2.5

Answer:

x= 2.5

Step-by-step explanation:

3(17x-6.5)=108

Divide each side by 3

3/3(17x-6.5)=108/3

17x - 6.5 = 36

Add 6.5 to each side

17x-6.5+6.5=36+6.5

17x = 42.5

Divide by 17

17x/17 = 42.5/17

x= 2.5

Answer:

1.6<x<9.6

Step-by-step explanation:

Triangle says the sum of any 2 sides is bigger than the third.

Assume a,b,c are side measurements of a triangle.

So if you know two sides a and b then the third number, c, is such that |b-a|<c<a+b.

So just add the given numbers and find the positive difference.

5.6+4=9.6

5.6-4=1.6

Answer:

k = -20.

Step-by-step explanation:

Do the division:

4x  ) 12x^2 + kx ( 3x

       12x^2 + k/4

So k/4 = - 5

k = -20.

Answer:

-3

Step-by-step explanation:

for this function you have to replace -1 were there's x in the function h(x)=2x-1

h(-1)=2(-1)-1

=-2-1

=-3

hope this helps

Answer:

8 inches

Step-by-step explanation:

A rhombus is a four sides quadrilateral with the four sides equal in length

A rhombus has 4 equal sides and the diagonal bisect at right angles

Adjacent sides = 9/2 = 4.5

we are to determine the value of the hypotenuse given the adjacent side and angle (108/2) = 54

Cos 54 = adjacent / hypotenuse

0.58778 = 4.5 / hypotenuse

hypotenuse = 4.5 / 0.58778

=7.6559

= 8 inches

Answer:

r = 11

Step-by-step explanation:

Hi there!

This scenario represents a linear relation, given the equation [tex]m=rp+k[/tex].

Linear equations are typically written in the form [tex]y=mx+b[/tex], where m is the slope and b is the y-intercept. As you can see, [tex]y=mx+b[/tex] and the given equation [tex]m=rp+k[/tex] share the same form.

This makes r the slope. This is also stated in the question, as r is the amount of money ($) paid per page.

The ordered pairs in the table represents points on a graph, if we were to graph this. For example, (9, 308) and (12, 341) both fall on the graph of this relation.

To solve for r, we must solve for the slope using the slope equation:

[tex]r=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

We can use any two points from the table in this equation. For example, (9, 308) and (12, 341):

[tex]r=\displaystyle \frac{341-308}{12-9}\\\\r=\displaystyle \frac{33}{3}\\\\r=11[/tex]

Therefore, the value of r is 11.

I hope this helps!

Answer:

Area of parallelogram = 21

Step-by-step explanation:

A = BH

Plug in

A = 7×3

Solve

A = 21

The answer will be 21.

Answer:

Does the answer help you?

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

Explanation:

The result of [tex]g^{-1}(-8)[/tex] is the same as trying to find x in [tex]g(x) = -8[/tex]

Draw a horizontal line through -8 on the y axis. This horizontal line intersects the curve at point P. From point P, move upward until you reach the x axis. You should get to 7 on the x axis. Therefore, the solution to [tex]g(x) = -8[/tex] is [tex]x = 7[/tex]. In other words, [tex]g(7) = -8[/tex]. This ultimately means [tex]g^{-1}(-8) = 7[/tex]

Refer to the diagram below.

Answer:

A reflection of the point across the line y = -x

Step-by-step explanation:

General rule for reflection across line  y = -x is

(a,b) -------> (-b , -a)

Answer:

Step-by-step explanation:

There are 30 possible combinations of teachers.

Given that at Tubman Middle School, there are 6 English teachers and 5 science teachers, to determine, if each student takes one English class and one science class, how many possible combinations of teachers are there, the following calculation must be performed:

To calculate possible combinations, the number of options A must be multiplied by the number of options B. Thus, the calculation would be as follows.

Therefore, there are 30 possible combinations of teachers.

Learn more about combinations in https://brainly.com/question/24180105.

Answer: C. 6x+18

Step-by-step explanation:

Use the distributive property

First multiply 6 times x which is 6x

Then multiply 6 times 3 which is 18

Keep the sign the same

Therefore, this should give you 6x+18

Answer:

a

Step-by-step explanation:

assuming theyre asking you to graph y = (x-2)(x+3)  -cant see the signs in your photo

the x-intercepts would be 2 and -3 , so option a!

Answer:

56 litres

Step-by-step explanation:

let x be the amount when the container is full.

1/8x + 35 = 3/4x

-5/8x = -35

x = 56

Answer:

A) 1 day=500, 2 day=250, 10 days=0.9765

B) 1 year=365 days, 1000*(1/2)^(365)=1.33*(10)^(-107)

Step-by-step explanation:

Disclaimer: When writing this on the paper use the theta symbol, I'm using x since I'm on mobile.

2.

i).

[tex] \sin(x) \tan(x) \sec(x) = \tan {}^{2} (x) [/tex]

[tex] \sin(x) \sec(x) \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \sin(x) \frac{1}{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \frac{ \sin(x) }{ \cos(x) } \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \tan( x) ) \tan(x) = \tan {}^{2} (x) [/tex]

[tex] \tan {}^{2} (x) = \tan {}^{2} (x) [/tex]

iii).

[tex] \sec {}^{2} (x) (1 - \sin {}^{2} ( x ) ) = 1[/tex]

[tex] \sec {}^{2} (x) ( \cos {}^{2} (x) ) = 1[/tex]

[tex] \frac{1}{ \cos {}^{2} (x) } \cos {}^{2} (x) = 1[/tex]

[tex]1 = 1[/tex]

v).

[tex] \cot {}^{2} (a) - \cos {}^{2} (a) = \cot {}^{2} (a) \cos {}^{2} (a) [/tex]

[tex] \frac{ \cos{}^{2} (x) }{ \sin {}^{2} (x) ) } - \cos {}^{2} (x) [/tex]

Factor out cosine

[tex] \cos {}^{2} (x) ( \frac{1}{ \sin {}^{2} (x) } - 1) [/tex]

Simplify

[tex] \cos {}^{2} (x) ( \frac{1 - \sin {}^{2} (x) }{ \sin(x) } [/tex]

[tex] \cos {}^{2} (x( \frac{ \cos {}^{2} (x) }{ \sin {}^{2} (x) } ) = [/tex]

[tex]( \cos {}^{2} ( x ) ( \cot {}^{2} (x) )[/tex]

Answer:

5.41 m

Step-by-step explanation:

First, let's find a side length by taking the square root of the area.

117/64 ^ 1/2 = 1.352...

Next, we need to multiply by 4.

1.352... x 4 = 5.408...

= approximately 5.41

Answer:

Step-by-step explanation:

Step-by-step explanation:

= 4x-x+5x+1+8-2

=8x+7

proved##

Answer:

B847,030

Step-by-step explanation:

y=95,000(1.2)^x

2025 - 2013 = 12

y=95,000(1.2)^12

y=847029.54258

Answer:

[tex]9[/tex]

Step-by-step explanation:

Recall the exponent property [tex]\frac{a^b}{a^c}=(a)^{b-c}[/tex].

Therefore, simplify:

[tex]\frac{3^4}{3^2}=3^{4-2}=3^2=\boxed{9}[/tex]

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]9[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Calculating the Answer...}}\\\\\frac{3^4}{3^2}\\------------\\\text{Keep in mind: } \frac{m^a}{m^b} = m ^{a-b}\\\\\rightarrow \frac{3^4}{3^2}\\\\\rightarrow 3^{4-2}\\\\\rightarrow 3^2\\\\\rightarrow 3 * 3\\\\\rightarrow \boxed{9}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

x         -2     3     8     13

f^-1(x)  -1    0     1        2

Step-by-step explanation:

The inverse function has the input as the output and the output as the input

x         -2     3     8     13

f^-1(x)  -1    0     1        2

Answer: C

Step-by-step explanation: In this problem, we're given a function

in the form of a chart and we're asked to find the inverse of the function.

To find the inverse of a function, we simply switch

the x and y values in each point.

In other words, the point (-1, -2) becomes (-2, -1),

the point (0, 3) becomes (3, 0), the point (1, 8) becomes (8, 1),

and the point (2, 13) becomes (13, 2).