Assume that the assumptions and conditions for inference with a two-sample t-test are met. Test the indicated claim about the means of the two populations. State your conclusion. Researchers wanted to compare the effectiveness of a water softener used with a filtering process to that of a water softener used without filtering. Ninety locations were randomly divided into two groups of equal size. Group A locations used a water softener and the filtering process, while group B used only the water softener. At the end of three months, water samples were tested at each location for softness level. (Water softness was measured on a scale of 1 to 5, with 5 being the softest water.) The results were as follows.
Group A (water softener and filtering)
xbar1 = 2.1
s1 = 0.7
Group B ( water softener only)
xbar2 = 1.7
s2 = 0.4
Using a 5% significance level, determine whether there is a difference between the two types of treatments.
H0: μ1 - μ2 = 0
Ha: μ1 - μ2 ≠ 0
Test statistic t = 3.328, P-value = 0.0014, DF = 69.97
A. Since the P-value is less than 0.05, we accept the null hypothesis and conclude that there is no difference in the softness level achieved from the two processes.
B. Since the P-value is less than 0.05, we are unable to reject the null hypothesis; there is insufficient evidence to conclude that there is a difference in the softness level achieved by the two processes.
C. Cannot draw a conclusion from the information given.
D. Since the P-value is less than 0.05, we reject the null hypothesis and conclude that there is a difference in the softness level achieved by the two processes.
E. Since the P-value is less than 0.05, we reject the alternative hypothesis and conclude that there is no significant difference in the softness level achieved by the two processes.

The probability that the 12-sided solid gets 3 , 9 or 11 is P ( A ) = 1/4 and the expected number of times is n = 45

The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible

Probability = number of desirable outcomes / total number of possible outcomes

The value of probability lies between 0 and 1

Given data ,

Let the probability that the the 12-sided solid gets 3 , 9 or 11 be P ( A )

Now , the value of P ( A ) is

Let the number of outcomes when rolling a 12-sided solid = 12

The number of times the solid is rolled = 180 times

So , the total number of outcomes = 12 x 180 = 2160

And , the probability of getting a 3 = 1/12

The probability of getting a 9 = 1/12

The probability of getting a 11 = 1/12

So , the total probability of getting a 3 , 9 or 11 = 3/12 = 1/4

The total expected number of times = 45

Hence , the probability is 1/6

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Answer:

y is the total the pens produced at the factory   each week

Step-by-step explanation:

total pens produced at the factory each week   = y   (=52,000)

3/4 of the total are red ( 39,000)

Answer:

B) 4

Step-by-step explanation:

(x-1+2)^2=(x-1)^2+(2x-4)^2

(x+1)^2=(x-1)^2+(2x-4)^2

x^2+2x+1=x^2-x+1+4x^2-16x+16

0= 4x^2-18x+17-2x-1

4x^2-20x+16=0/4

x^2-5x+4=0

(x-4)(x-1)=0

x-4=0

x=4

hope it helps..

have a great day!!

Answer: v=85/11

Step-by-step explanation: Cross multiply to get 11v=85, divide both sides by 11, and you get v=85/11.

Hope that this helped! Have a great day!!

9514 1404 393

Answer:

  45.6°

Step-by-step explanation:

The attached result was found by typing "arccos(7/10) in degrees" into a web browser search box.

Your calculator can give you the same result. The inverse cosine function often shares a key with the cosine function. It is often marked as cos⁻¹. Be sure that the angle mode is set to degrees, not radians.

Answer:

$6.39

Step-by-step explanation:

100-20=80 then divided by 100 which is .80

.8 times 7.99 is 6.39

hope this helps

Answer:

[tex](\sqrt{2})^3[/tex]

Step-by-step explanation:

Given the expression

[tex](x - \frac{1}{x} )^3[/tex]

Simplify

[tex](\frac{x^2-x}{x} )^3[/tex]

Given that x = 1+√2

Substitute

[tex](\frac{(1+\sqrt{2} )^2-(1+\sqrt{2} )}{1+\sqrt{2} } )^3\\=( \frac{1+2\sqrt{2} +2 - 1 - \sqrt{2}}{1+\sqrt{2}} )^3\\= (\frac{\sqrt{2}+2}{1+\sqrt{2}})^3 \\Rationalize\\= (\frac{\sqrt{2}-2+2-2\sqrt{2}}{1-2})^3 \\=( \frac{-\sqrt{2}}{-1})^3 \\= (\sqrt{2})^3\\ \\[/tex]

Answer:

CAN I ASWER THIS

Step-by-step explanation:

OKAY THANKS

Hold on, our servers are swamped. Wait for your answer to fully load.

Answer:

Both are equal to each other.

Step-by-step explanation:

[tex] \frac{10}{10} = 1[/tex]

[tex] \frac{6}{6} = 1[/tex]

Answer:

None of them are bigger than the other, they are equal to each other.

[tex] \frac{10}{10 } = \frac{6}{6} \\ 1 = 1[/tex]

Answer: Question 5 is 167

Question 6 is 70

Question 7 is 115

Step-by-step explanation:   For these ones you want to subtract from 180 by the number it gives you. For an example If m<2=13 and find m<4 it would be like this 180-13=167.

Answer:

c

5x=5x so when five Cross the=sign

5x-5x=0

Answer:

∠1 = 67°

∠2 = 67°

∠3 = 113°

Step-by-step explanation:

∠3 = 113°

∠1 = ∠2

∠1 + ∠2 + ∠3 + 113° = 360°

∠1 = (360 - 113 - 113)/2 = 67°

Answer:

B) 12

Step-by-step explanation:

Range is when u subtract the minimum value to the maximum value:

1st period:

Max = 98

Min = 60

Range = max - min

Range = 98 - 60

Range = 38

2nd period:

Max = 96

Min = 70

Range = 96 - 70

Range = 26

Difference between the ranges of the 2 periods:

38 - 26 = 12

Answer:you will end up with 350.00 dollars left

Step-by-step explanation: you are spending money on the thing that you are buying

Answer:

$13912.50

Step-by-step explanation:

First you find how much carpet you need by finding the area of the room.

18.75*28= 525ft^2

Then multiply the amount of carpet needed by 26.50 to find the total cost.

525*26.50= 13912.50

Hope this helps!

Answer: The answer is 194

Answer:

17x5=85

25x6=150

35x10=350

350+150+85=585

answer=585

Answer:

option 2: 15

Step-by-step explanation:

ΔBOA is a right angled triangle.

By Pythagoras theorem,

[tex] {oa}^{2} = {bo}^{2} + {ba}^{2} [/tex]

[tex] {oa}^{2} = { {9}^{2} } + {12}^{2} [/tex]

[tex] {oa}^{2} = 81 + 144 [/tex]

OA = √225

OA = 15

Answer:

3 feet

Step-by-step explanation:

The area of banner is 3 because A = l * w. So 2 * 1 1/2. Is 3 feet. Make sure to include the ft. Unit.

Answer:

x = 99°

Step-by-step explanation:

first: find the supplement to 123°:

180 - 123 = 57°

second: since all triangle interior angles total a80°:

180 - 42 - 57 = 81°

third: x = the supplement to 81°, so, x = 180 - 81 = 99°

Answer:

Hans Lipperhey made the telescope

Answer:

Hans lipperhey and Lyman Spitzer

Answer:

[tex]\frac{x^2}{3} - \frac{x}{3} - 44 =\frac{(x -12)(x+ 11)}{3}[/tex]

Step-by-step explanation:

Given

[tex]\frac{x^2}{3} - \frac{x}{3} - 44[/tex]

Required

Solve

Take LCM

[tex]\frac{x^2 - x - 132}{3}[/tex]

Expand

[tex]\frac{x^2 +11 x -12x- 132}{3}[/tex]

Factorize:

[tex]\frac{x(x+11) -12(x+ 11)}{3}[/tex]

[tex]\frac{(x -12)(x+ 11)}{3}[/tex]

Hence:

[tex]\frac{x^2}{3} - \frac{x}{3} - 44 =\frac{(x -12)(x+ 11)}{3}[/tex]

Answer:

21 + x = 35

x = 14

Hope this helps :)

Answer:

Cos 68

Step-by-step explanation:

Given the expression 2cos² 34° - 1, we are to expression as a single trig ratio.

Let the angle be theta

Recall that sin²theta + cos²theta = 1

sin²theta  = 1 - cos²theta ... 1

also Cos 2theta = Cos²theta - sin²theta  ... 2

Substitute 1 into 2

Cos 2theta = Cos²theta - (1-cos²theta)

Cos 2theta = Cos²theta - 1 + cos²theta

Cos 2theta = 2Cos²theta - 1

Replace theta with 34

Cos 2(34)= 2Cos²(34)- 1

Cos 68 = 2Cos²(34)- 1

Hence the single trig expression is Cos 68

Answer:

Solution Given :

apothegm [a]=9in

perimeter [p]=13.1×5=65.5in

given

A=1/2 aP=1/2×9×65.5=294.75in²

Answer:

y = 1/4x - 2

Step-by-step explanation:

If two lines are parallel to each other, they have the same slope.

The first line is y = 1/4x. Its slope is 1/4. A line parallel to this one will also have a slope of 1/4.

Plug this value (1/4) into your standard point-slope equation of y = mx + b.

y = 1/4x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (4, -1). Plug in the x and y values into the x and y of the standard equation.

-1 = 1/4(4) + b

To find b, multiply the slope and the input of x (4)

-1 = 1 + b

Now, subtract 1 from both sides to isolate b.

-2 = b

Plug this into your standard equation.

y = 1/4x - 2

This equation is parallel to your given equation (y = 1/4x) and contains point (4, -1)

Hope this helps!

Answer:

Step-by-step explanation:

3x+4(-0.5x+8)=36

3x-2x+32=36

X=36-32

X=4