Little bit more math hw

Little Bit More Math Hw

Answers

Answer 1

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

For these kind of problems, simply take the denominator and compare it to zero. Then solve the equation.

[tex]x+2=0\\\\\Rightarrow x=-2[/tex]       By subtracting 2 from both sides!

Best Regards!


Related Questions

WHat is the solution to the system of linear equations graphed below answers 3 1/2-4

Answers

Answer:

(3 1/2, -4)

Step-by-step explanation:

The solution is the point on the graph that the two lines intersect.  The point that the lines intersect in the graph is (3 1/2, -4).

Answer:

3 1/2 , -4

Step-by-step explanation:

yes

what number has 7 ten thousands, 1 thousand, 1 hundred, and no ones?

Answers

Answer:

[tex]71,100[/tex]

Step-by-step explanation:

If you are trying to find a number that is written in word form, we can just use place values to find what goes where.

A number is broken down into this:

Ten thousands, thousands, hundreds, tens, ones.

If they have 7 ten thousands, the first digit will be a 7.

If they have 1 thousand, the second digit will be a 1.

If they have 1 hundred, the third digit will be a 1.

Since nothing is stated about tens, we assume it's value is 0.

And since there are no ones, it's value is 0.

So:

71,100.

Hope this helped!

Solve x/2 = 3x/4 + 5 (make sure to type the number only)

Answers

Answer:

x= -20

Step-by-step explanation:

x/2=3x/4+5

Multiply both sides of the equation by 4, the least common multiple of 2,4.

2x=3x+20

Subtract 3x from both sides.

2x−3x=20

Combine 2x and −3x to get −x.

−x=20

Multiply both sides by −1.

x=−20

algebra pyramid please answer !! be the first to be marked as a brainliest .

Answers

Answer:

The first pyramid:

      63x

  39x  24x  

23x  16x  8x

The second pyramid:

     162x

 82x  80x  

4x  78x  2x

The third pyramid:

     12a+2b

9a+b   3a+b  

9a     b     3a

The fourth pyramid:

      -19a

  -5a   -14a  

3a   -8a  -6a

   

Step-by-step explanation:

All that an alegbra pyramid is is adding the two terms below it.

So you can see how I added the terms that lied below each number, such as in number 1:  I added 23x and 16x to get me 39x, and I added 16x and 8x to get me 24.

Hope this helped!

Find the common ratio for the following sequence. Type a numerical answer in the space provided. If necessary, use the
/ key to represent a fraction bar. Do not type spaces in your answer.
2,-2, 2, -2, ...

Answers

Answer:

-1

Step-by-step explanation:

the common ratio in this geometric series is -1

An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm, how many of these components should she consider to be 90% sure of knowing the mean will be within ± 0.1 ±0.1 mm?

Answers

Answer:

She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

Step-by-step explanation:

We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.

And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.

As we know that the margin of error is given by the following formula;

The margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]  

Here, [tex]\sigma[/tex] = standard deviation = 3.6 mm

         n = sample size of components

         [tex]\alpha[/tex] = level of significance = 1 - 0.90 = 0.10 or 10%

         [tex]\frac{\alpha}{2} = \frac{0.10}{2}[/tex] = 0.05 or 5%

Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]  

                  0.1 mm        =  [tex]1.645 \times \frac{3.6}{\sqrt{n} }[/tex]

                    [tex]\sqrt{n} = \frac{3.6\times 1.645}{0.1 }[/tex]

                    [tex]\sqrt{n}[/tex] = 59.22

                     n = [tex]59.22^{2}[/tex] = 3507.0084 ≈ 3507.

Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

ax+r=7 , solve for x

Answers

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:

Examine the two triangles. Are the triangles congruent? Justify your conclusions. If they are congruent, complete the following statement: "Yes, triangle __ congruent to triangle __ giving a detailed explanation of your reasoning. If they are not congruent, explain why you think so. Be specific in your answer and make sure to show your work.

Answers

Answer: The triangles are not congruent

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

Explanation:

For triangle DEF, the missing angle D is

D+E+F = 180

D+80+60 = 180

D+140 = 180

D = 180-140

D = 40

While the missing angle K in triangle JKL is

J+K+L = 180

80+K+50 = 180

K+130 = 180

K = 180-130

K = 50

---------------------

The three angles for triangle DEF are

D = 40E = 80F = 60

The three angles for triangle JKL are

J = 80K = 50L = 50

We don't have all the angles matching up. We need to have the same three numbers (the order doesn't matter) show up for both triangles in order for the triangles to be congruent. This is because congruent triangles have congruent corresponding angles.

The only pair that matches is E = 80 and J = 80, but everything else is different. So there is no way the triangles are congruent.

Notice how triangle JKL has two congruent base angles (K = 50 and L = 50), so this triangle is isosceles. Triangle DEF is not isosceles as we have three different angles, so this triangle is scalene.

Jaime went to the mall with $42. If he bought a T-shirt and had $18 left, how much did the T-shirt cost Jaime in dollars?

Answers

Answer:

$24

Step-by-step explanation:

You simply do $42-$18

=24

Answer:

$24

Step-by-step explanation:

At the start, Jaime had $42. In order to find out how much the T-shirt he purchased costs, we must subtract 18 from 42.

42 - 18 = 24

Jaime spent $24 on the T-shirt.

Which of the following is the solution to the inequality below? -5x — 10 -6 B. x > -2 C. x <-6 D. x < -2

Answers

Answer:

x > -6

Step-by-step explanation:

-5x — 10 < 20

Add 10 to each side

-5x — 10+10 < 20+10

-5x < 30

Divide each side by -5, remembering to flip the inequality

-5x/-5 > 30/-5

x > -6

Answer:

x>-6

Step-by-step explanation:

[tex]-5x - 10 < 20\\\\\mathrm{Add\:}10\mathrm{\:to\:both\:sides}\\\\-5x-10+10<20+10\\\\\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\\\left(-5x\right)\left(-1\right)>30\left(-1\right)\\\\\mathrm{Simplify}\\\\5x>-30\\\\\mathrm{Divide\:both\:sides\:by\:}5\\\\\frac{5x}{5}>\frac{-30}{5}\\\\x>-6[/tex]

In the figure below, circle O has a central ángel of 120 degrees. what is the area shaded of the circle in terms of ,r, the radius? Leave your answer in terms of pi.

Answers

Answer:

the area of a section of a circle is [tex]\frac{1}{360}[/tex]* Θ * (area of the circle)

the theta/360 tells us the amount of circle currently in question

so , the answer will be 1/3 pi r^2        [A]

A TV Dinner Company Sells Three Types Of Dinners: A Chicken Dinner For $10, A Beef Dinner For $11, Or A Fish Dinner For $12. At One Particular Grocery Store, They Sold 200 Dinners For A Grand Total Of $2138. Required:a. If they sold three times as many chicken dinners as they did fish, then how many of each kind of dinner did they sell?b. Find the equation of the quadratic function that passes through the points (−1, 9), (2, 6), and (3, 17). Write your answer in the form y = ax2+bx+c.

Answers

Answer:

a) The company sold 93 Chicken dinners, 76 Beef dinners and 31 Fish dinners.

b) [tex]y=3x^{2}-4x+2[/tex]

Step-by-step explanation:

a)

In order to solve part a of the problem, we must start by setting our variables up:

C=# of Chicken dinners

B=# of Beef dinners

F=# of Fish dinners

Next we can use these variables to build our equations. We start by taking the fact that they sold a total of 200 dinners. The sum of all the variables should add up to that so we get:

C+B+F=200

Then the problem tells us the price of each dinner and the total amount of money they made from selling the dinners that day:

"A TV Dinner Company Sells Three Types Of Dinners: A Chicken Dinner For $10, A Beef Dinner For $11, Or A Fish Dinner For $12. For A Grand Total Of $2138"

So we can use this information to build our second equation:

10C+11B+12F=2138

We have two equations now but three variables, so we need an additional equation so we can finish solving this. The problem tells us that:

"they sold three times as many chicken dinners as they did fish"

which translates to:

C=3F

so now we have enough information to finish solving the problem. We can start by substituting the last equation into the previous two equations so we get:

C+B+F=200

3F+B+F=200

4F+B=200

and

10C+11B+12F=2138

10(3F)+11B+12F=2138

30F+11B+12F=2138

42F+11B=2138

So now we can take the two bolded equations and solve them simultaneously. We can solve them by using any method we wish. Let's solve it by substitution.

We start by solving the first equation for B so we get:

B=200-4F

and now we substitute it into the second equation:

42F+11(200-4F)=2138

and now we solve for F

42F+11(200-4F)=2138

42F+2200-44F=2138

-2F=2138-2200

[tex]F=\frac{-62}{-2}[/tex]

F=31

So now that we know the value of F, we can find the values of the rest of the variables so we can take the previous equations to figure this out:

B=200-4F

B=200-4(31)

B=200-124

B=76

and finally:

C=3F

C=3(31)

C=93

So

The company sold 93 Chicken dinners, 76 Beef dinners and 31 Fish dinners.

b) For the second part of the problem we need to build a system of equations to find the equation we are looking for. We were given three points:

(-1,9), (2,6) and (3,17)

so we need to substitute each of the points on the given quadratic equation so we get:

[tex]9=a(-1)^{2}+b(-1)+c[/tex]

eq.1:  [tex]9=a-b+c[/tex]

[tex]6=a(2)^{2}+b(2)+c[/tex]

eq. 2:  [tex]6=4a+2b+c[/tex]

[tex]17=a(3)^{2}+b(3)+c[/tex]

eq. 3:  [tex]17=9a+3b+c[/tex]

So now that we have our three equations we can solve them simultaneously to get the values of a, b and c by using the method you feel more comfortable with. Let's solve it by elimination:

So let's take the first equations and let's subtract them:

[tex]9=a-b+c[/tex]

[tex]-6=-4a-2b-c[/tex]

-------------------------------

3=-3a-3b

And now we repeat the process with the first and third equations:

[tex]9=a-b+c[/tex]

[tex]-17=-9a-3b-c[/tex]

-------------------------------

-8=-8a-4b

So now we have two new equations we can solve simultaneously, but they can be simplified by dividing the first one into -3 and the second one into -4 so they become:

a+b=-1

2a+b=2

We can now solve them by substitution. Let's solve the first one for a and then let's substitute it into the second equation:

a=-1-b

let's substitute

2(-1-b)+b=2

and solve for b

-2-2b+b=2

-b=4

b=-4

Now we can find a:

a=-1-b

a=-1+4

a=3

and now we can find c:

c=9-a+b

c=9-3-4

c=2

So we can use these answers to build our equation:

[tex]y=ax^{2}+bx+c[/tex]

[tex]y=3x^{2}-4x+2[/tex]

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 9 hours of burning, a candle has a height of 25.4 centimeters. After 23 hours of burning, its height is 19.8 centimeters. What is the height of the candle after 22 hours?

Answers

Answer:

Suppose that the height (in centimeters) of a candle is a linear function of

the amount of time (in hours) it has been burning.

After 11 hours of burning, a candle has a height of 23.4 centimeters.

After 30 hours of burning, its height is 12 centimeters.

What is the height of the candle after 13 hours?

:

Assign the given values as follows:

x1 = 11; y1 = 23.4

x2 = 30; y2 = 12

:

Find the slope using: m = %28y2-y1%29%2F%28x2-x1%29

m = %2812-23.4%29%2F%2830-11%29 = %28-11.4%29%2F19

:

Find the equation using the point/slope formula: y - y1 = m(x - x1)

y - 23.4 = -11.4%2F19(x - 11)

y - 23.4 = -11.4%2F19x + 125.4%2F19

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 23.4

y = -11.4%2F19x + 125.4%2F19 + 444.6%2F19

y = -11.4%2F19x + 570%2F19

y = -11.4%2F19x + 30, is the equation

:

What is the height of the candle after 13 hours?

x = 13

y = -11.4%2F19(13) + 30

y = -148.2%2F19 + 30

y = -7.8 + 30

y = 22.2 cm after 13 hrs

Solve and graph the inequality. 45x + 5 < −3

Answers

Answer:

x < -8/45

Step-by-step explanation:

Step 1: Write out inequality

45x + 5 < -3

Step 2: Subtract both sides by 5

45x + 5 - 5 < -3 - 5

45x < -8

Step 3: Divide both sides by 45

45x/45 < -8/45

x < -8/45

Step 4: Graph

Which of the following is the correct equation for the distance formula for the points (x1, y1) and (x2,y2)?
A. D=sqrt (x2-x1)^2+(y2-y1)^2
B. D=sqrt (x2-y2)^2+(y1-x1)^2
C. D=sqrt -(y2-y1)^2+(x2-x1)^2
D. D=sqrt (x1-x2)^2+(y2-y1)^2

Answers

Answer:

  A. D=sqrt( (x2-x1)^2+(y2-y1)^2 )

Step-by-step explanation:

The distance between two points is the root of the sum of the squares of the differences in their corresponding coordinates. The equation of choice A is the usual formulation.

__

Comment on answer choices

Because the square of a number is the same as the square of its opposite, the formula in choice D is also correct.

Answer the question that follow about the given sequence. “Does not exist” and “none” are valid answers. Blank answers will be counted incorrect. -33, -27, -21, -15, … a. Arithmetic/Geometric/Neither? b. State the Common Ratio or Common Difference. c. Find the explicit formula for the nth term d. Find the recursive formula for the nth term e. Value of the 10th term f. ∑ notation for the Infinite Series. g. Sum of the Infinite Series.

Answers

Answer:

it's an arithmetic sequence with common difference 6An=6n-39, A10=21Sn=3n'2-(39/2)n

4(c+3) =4+c+c+c+c+17

Answers

4c +12 = 4+4c+17
-4c -4c
12 =4+c+17
12=21+c
-21
-9=c
idk if this is what ur looking for?

You are studying for your final exam of the semester up to this point you received 3 exam scores of 61% 62% and 86% to receive a grade of c and the class you must have an average exam score between 70% and 79% for all four exams including the final find the widest range of scores that you can get on the final exam in order to receive a grade of C for the class 63 to 100% 71 to 100% 68 to 97

Answers

There will be a total of 4 test scores including the final exam. To get a 70, the 4 tests need to equal 4 x 70 = 280 points , to be 79, they have to equal 4 x 79 = 316 points.

The 3 already done = 61 + 62 + 86 = 209 points.

The final exam needs to be between :

280 -209 = 71

316 -209 = 107. The answer would be between 71 and 100%

There are 30 colored marbles inside a bag. Six marbles are yellow, 9 are red, 7 are white, and 8 are blue. One is drawn at random. Which color is most likely to be chosen? A. white B. red C. blue D. yellow Include ALL work please!

Answers

Answer:

red

Step-by-step explanation:

Since the bag contains more red marbles than any other color, you are most likely to pick a red marble

16% of 242 = ?
Please help me solve this

Answers

Answer:

16% of 242 = 38.72

Step-by-step explanation:

16% = 16/100 = 0.16

242 * 0.16 = 38.72

Answer:

38.72

Step-by-step explanation:

242 * .16 = 38.72

Question: Complete the point-slope equation of the line through (1,3)and (5,1). Use exact numbers. Equation: y-3=(Answer ?)

Answers

Answer:

y - 3 = -1/2(x - 1)

Step-by-step explanation:

Hey there!

Well point slope form is,

[tex]y - y_{1} = m(x - x_{1})[/tex]

We can use the point (1,3)

y - 3 = m(x - 1)

Now we need to find slope with the following formula,

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex], we’ll use the points (1,3) and (5,1).

[tex]\frac{1-3}{5-1}[/tex]

-2/4

Slope or m = -1/2

y - 3 = -1/2(x - 1)

Hope this helps :)

Which values of x are point(s) of discontinuity for this function? Function x = –4 x = –2 x = 0 x = 2 x = 4

Answers

Answer:

x=0 and x=2

Step-by-step explanation:

We need to check at each  point where the function changes definition

At x= -2

On the left side  -4   on the right side = -( -2)^2 = -4  continuous

At  x=0

The point is not defined since neither side has an equals sign

discontinuous

x =2

on the left side 2^2 =4  on the right side 2

It is discontinuous

Answer:

x = 0

x = 2

Step-by-step explanation:

Edge 2020

~theLocoCoco

The set of natural numbers is: infinite finite

Answers

Answer:

A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number.

Step-by-step explanation:

Answer:

Finite

Step-by-step explanation:

please give me brainliest

The value (in dollars) of an airplane depends on the flight hours as given by the formula V= 1,800,000 - 250x . After one year, the value of the plane is between $1,200,000 and $1,300,000. Which range for the flight hours does this correspond to?

a. 1800 <= x <= 2100
b. 2200<= x <= 2500
c. 1500<= x <= 1800
d. 2000<= x <= 2400

Answers

Answer:

D

Step-by-step explanation:

To determine the range we must solve this inequality;

● 1200000<1800000-250x<1300000

Substract 1800000 from both sides.

● 1200000-1800000<1800000-250x<1300000-1800000

● -600000< -250x < -500000

Divide both sides by 250

● -600000/250 < -250x/250 < -500000/250

● -2400 < -x < -2000

Multiply both sides by -1 and switch the signs

● 2000 < x < 2400

The correct option is D. 2000<= x <= 2400

Given, the value of an airplane depends on the flight hours,

[tex]V= 1800000-250x[/tex], here x is the flight hours.

We have to calculate the range of x After one year.

Since, [tex]V= 1800000-250x[/tex]

[tex]250x=1800000-V\\\\x=\dfrac{1800000-V}{250}[/tex]

Since the value of the plane is between $1,200,000 and $1,300,000. So,

[tex]x=\dfrac{1800000-1200000}{250}[/tex]

[tex]x=\dfrac{600000}{250}[/tex]

[tex]x=2400\\[/tex]

When V is 1300000 then x will be,

[tex]x=\dfrac{1800000-1300000}{250} \\[/tex]

[tex]x=\dfrac{500000}{250}[/tex]

[tex]x=2000[/tex]

Hence the range of x will be from 2000 to 2400.

The correct option is D. 2000<= x <= 2400.

For more details on range follow the link:

https://brainly.com/question/10185991

Raul and his friends each way 1/20 of a ton are standing on a truck scale . The total weight shown by the scale is 3/4 of a ton . How can I find the total number of people on the scale when Raul and his friends are weighed?

Answers

Answer: There are 15 friends.

Step-by-step explanation:

We know that there is N friends (N is the number that we are looking for)

Each friend weights 1/20 ton.

Now, the weight of the N friends together is N times 1/20 ton.

Then we have:

N*(1/20) ton = 3/4 ton

We solve this for N.

First multiply both sides by 20.

20*N*(1/20) = N = 20*(3/4) = 60/4 = 15

Answer:

I can find the total number of people by dividing the total weight by the weight of one person.

Step-by-step explanation:

1. Quadratics: The path of the longest shot put by the Women’s track team at Sun Devil U is modeledby h(x) = -0.015x2 + 1.08x + 5.8, where x represents the horizontal distance from the start and h(x) isthe height of the shot put above the ground. (Both x and h(x) are measured in feet.)a. [3 pts] Determine h(24). Round your answer to 2 decimal places.

Answers

Answer:

23.08 feet

Step-by-step explanation:

If  the path of the longest shot put by the Women’s track team at Sun Devil U is modeled by h(x) = -0.015x² + 1.08x + 5.8 where x represents the horizontal distance from the start and h(x) is the height of the shot put above the ground, to determine h(24), we will have to substitute x = 24 into the modeled equation as shown;

[tex]h(x) = -0.015x^2 + 1.08x + 5.8\\\\if \ x = 24;\\\\h(24) = -0.015(24)^2 + 1.08(24) + 5.8\\\\h(24) = -0.015(576)+25.92+5.8\\\\h(24) = -8.64+31.72\\\\h(24) = 23.08\\[/tex]

Hence the value of the height at the horizontal distance of 24 feet is 23.08 feet to 2 decimal place.

Solve this and get 12 points

Answers

Answer:

9

Step-by-step explanation:

First, find x. Since x is the average of the three number, add the three up and then divided by three. Thus:

[tex]x=\frac{13+-16+6}{3}=3/3=1[/tex]

y is the cube root of 8. Thus:

[tex]y=\sqrt[3]{8}=2[/tex]

So:

[tex]x^2+y^3\\=(1)^2+(2)^3\\=1+8=9[/tex]

Answer:

ljih

Step-by-step explanation:

Points A( − 1, 7), B(2, 19), and C(3, y) are on the same line. Find y.

Answers

Answer: y=23

Step-by-step explanation:

If Points and A,B and C lines on the same line then they will have the same slopes so since we have the coordinates of  A and B we will use the to write an equation in slope intercept form.

To write it in slope intercept form we will need to find the slope and the y intercept.

To find the slope you will find the change in the y coordinates and divide it by the change in the x coordinates.

Using the coordinates (-1,7) and (2,19)  the y coordinates are 7 and 19 and the x coordinates are -1 and 2.

Slope :  [tex]\frac{7-19}{-1-2} \frac{-12}{-3} = 4[/tex]   In this case the slope is 4 so we will use that to find the y intercept by using point A coordinate.

  The slope intercept formula says that y=mx +b  where me is the slope and b is the y intercept.

 7=4(-1) + b  

7 = -4 + b

+4   +4

 b= 11       The y intercept is 11.

Now we can write the whole equation as y=4x + 11   .

To answer the question now, where we need to find y , we will plot the x coordinate which is 3 into the equation and solve for y.

 y = 4(3) + 11  

y = 12 + 11

 y = 23

What two rational expressions sum to [tex]\frac{4x+2}{x^{2}-9+8 }[/tex] Enter your answer by filling in the boxes. Enter your answer so that each rational expression is in simplified form.

Answers

Answer:

[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]

Step-by-step explanation:

Given

[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]

Required

Fill in the gaps

Going by the given parameters, we have that

[tex]\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}[/tex]

[tex]x^2 - 9x + 8[/tex], when factorized is [tex](x-1)(x-8)[/tex]

Hence; the expression becomes

[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}[/tex]

Combine Fractions

[tex]\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}[/tex]

Simplify the denominators

[tex]4x + 2 = A + B[/tex]

By direct comparison

[tex]A = 4x[/tex]

[tex]B = 2[/tex]

Hence, the complete expression is

[tex]\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}[/tex]

Answer:4x+2/x2−9x+8 = −6/7(x−1) + 34/7(x−8)

Twelve dieters lost an average of 13.7 pounds in 6 weeks when given a special diet plus a "fat-blocking" herbal formula. A control group of twelve other dieters were given the same diet, but without the herbal formula, and lost an average of 10.7 pounds during the same time. The standard deviation of the "fat-blocker" sample was 2.6 and the standard deviation of the control group was 2.4. Find the 95% confidence interval for the differences of the means.

Answers

Answer:

The 95% confidence interval is   [tex]0.88 < \mu_1 - \mu_2 < 5.12[/tex]

Step-by-step explanation:

From the question we are told that

   The  sample mean for fat-blocking [tex]\= x_1 = 13.7[/tex]

     The  sample size  for fat-blocking  [tex]n = 12[/tex]

      The standard deviation for  fat-blocking is [tex]\sigma_1 = 2.6[/tex]

      The  sample mean for control group is  [tex]\= x _2 = 10.7[/tex]

      The  sample size  for control group is [tex]n_2 = 12[/tex]

      The standard deviation for control group is [tex]\sigma _2 = 2.4[/tex]

Given that the confidence level is  95% then the level of significance can me mathematically evaluated as

                 [tex]\alpha = 100 - 95[/tex]

                 [tex]\alpha = 5 \%[/tex]

                    [tex]\alpha =0.05[/tex]

Generally the degree of freedom is mathematically represented as

           [tex]df = n_1 + n_2 - 2[/tex]

substituting values

           [tex]df = 12 +12 - 2[/tex]

           [tex]df = 22[/tex]

Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of  22 form the students t-distribution , the value is  

                [tex]t_{\frac{\alpha }{2}, df } = 2.074[/tex]

Generally the margin of error is mathematically represented as

            [tex]E = t_{\frac{\alpha }{2}, df } * \sqrt{ \frac{\sigma^2_1 }{n_1 } + \frac{\sigma^2_2 }{n_2 } }[/tex]

substituting values

            [tex]E = 2.07 4 * \sqrt{ \frac{ 2.6^2 }{12 } + \frac{2.4^2 }{12 } }[/tex]

           [tex]E = 2.12[/tex]

the 95% confidence interval for the differences of the means is mathematically represented as

        [tex]\= x_1 - \= x_2 - E < \mu_1 - \mu_2 < \= x_1 - \= x_2 + E[/tex]

substituting values

       [tex]13.7 - 10.7 - 2.12 < \mu_1 - \mu_2 < 13.7 - 10.7 + 2.12[/tex]

      [tex]0.88 < \mu_1 - \mu_2 < 5.12[/tex]

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