An environmental engineer is tasked with determining whether a power plant cooling system is heating the water it uses more than allowed by environmental regulations. They measure water temperatures at the cooling system input and the cooling system output for several different days in several different seasons.A data file containing these measurements is HW_PTA 243.csv.Do a statistical analysis on this data to determine if the temperature change between the input and output of the cooling system is different than 6 degrees. What does your analysis indicate?
A) The cooling system changes the temperature of the water by an amount different than 6 degrees.
B) The cooling system changes the temperature of the water by 6 degrees.
Answers
Complete Question
The complete question is shown on the first , second and third uploaded image
Answer:
A
The correct option is A
B
The correct option is H
Step-by-step explanation:
The null hypothesis is [tex]H_o : \mu_1 - \mu_2 = 6[/tex]
The alternative hypothesis is [tex]H_a : \mu_1 - \mu_2 \ne 6[/tex]
The population mean difference is [tex]\mu_d = 6[/tex]
Generally the sample size is n = 15
Generally the sample mean for input temperature is mathematically represented as
[tex]\= x _1 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x _1 = \frac{57.6 + 68.9 + \cdots +60.4 }{15}[/tex]
=> [tex]\= x _1 = 62.57 [/tex]
Generally the sample mean for output temperature is mathematically represented as
[tex]\= x _2 = \frac{\sum x_i }{n}[/tex]
=> [tex]\= x _2 = \frac{65.1+ 74.4 + \cdots +67.3 }{15}[/tex]
=> [tex]\= x _2 = 55.97 [/tex]
Generally the sample mean difference is mathematically represented as
[tex]\= d = 62.57 - 55.97[/tex]
=>[tex]d = 6.6[/tex]
Generally the standard deviation is mathematically represented as
[tex]s_d = \sqrt{\frac{ \sum [d_1 - \= d]^2}{n-1} }[/tex]
=> [tex]s_d = \sqrt{\frac{ [ [57.6 -65.1]- 6.6]^2 +[68.9 -74.4]- 6.6]^2+\cdots + [60.4 -67.3]- 6.6]^2}{15-1} }[/tex]
=> [tex]s_d = 1.732 [/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{6.6 - 6 }{\frac{1.732}{\sqrt{15} } }[/tex]
=> [tex]t = 1.342 [/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n - 1[/tex]
So
[tex]df = 15 - 2[/tex]
=> [tex]df = 14[/tex]
Generally the p-value is mathematically represented as
[tex]p-value = 2 * P(t > 1.342 )[/tex]
Generally from the t -distribution table the probability of 1.342 at a degree of freedom of [tex]df = 28[/tex] is
[tex]P(t > 1.342 ) = 0.10047[/tex]
So
[tex]p-value = 2 * 0.10047[/tex]
=> [tex]p-value = 0.201[/tex]
Generally from the value obtained we see that [tex]p-value > \alpha[/tex] Hence
The decision rule is
Fail to reject the null hypothesis
The conclusion is
The cooling system changes the temperature of the water by 6 degrees
Related Questions
20 points & Brainliest
Why are rotations a rigid motion?
Answers
Answer:
RC,\α is a rigid motion.
Here C, is the rotacenter which is the fixed point and around C all other points move in a fixed distance by the definition of rotation.
the motion follows in a circularmanner with C as the center.
consider a point Q which changes to Q1 after rotation by an angle\alpha
Step-by-step explanation:
When considering rotational motion and subsequently rotational mechanics every point on the body must have same angular velocity and angular acceleration. If the body is not rigid different points on the body will have different angular velocity and angular acceleration.
s x = –4 a valid solution this linear equation? 2x + 9(x – 1) = 8(2x + 2) – 5 No. When –4 is substituted for the variable, the result is a true statement. No. When –4 is substituted for the variable, the result is a false statement. Yes. When –4 is substituted for the variable, the result is a true statement. Yes. When –4 is substituted for the variable, the result is a false statement.
Answers
Answer:your answer is C!
Step-by-step explanation: I got it right
Answer:
c) Yes. When –4 is substituted for the variable, the result is a true statement.
Step-by-step explanation:
i verified with my teacher may i plz get brainliest
#16 What is the product of
3.4 and 15.56?
Answers
Answer:
53.04
Step-by-step explanation:
Answer:
52.904
Step-by-step explanation:
The life span of a graphing calculator manufactured by Texas Instruments has a normal distribution with a mean of 54 months and a standard deviation of 8 months. The company guarantees that any calculator that starts malfunctioning within 36 months of the purchase will be replaced by a new one. You apply the normal model and discover that this is approximately 1.22% of their graphing calculators. Texas Instruments has sold 75 million graphing calculators world- wide. How many of these would you expect to malfunction within 3 months (and thus need to be replaced)? Explain.
Answers
Answer:
The expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.
Step-by-step explanation:
Let X represents the number of graphing calculator that starts malfunctioning within 36 months of the purchase and needs to be replaced by a new one.
It is provided that X follows a normal distribution with a mean of 54 months and a standard deviation of 8 months.
Also, using the normal model it was determined that 1.22% of graphing calculator manufactured by Texas Instruments malfunctions and needs replacement.
That is,
P (X) = 0.0122
Texas Instruments has sold 75 million graphing calculators world- wide.
Compute the expected number of graphing calculators that malfunctions within 3 months and need to be replaced as follows:
E (X) = n × P (X)
= 75 × 10⁶ × 0.0122
= 915000
Thus, the expected number of graphing calculators that malfunctions within 3 months and need to be replaced is 915,000.
3.2654376... Rational or Irrational *
O Rational
O Irrational
Answers
Answer:
its irrational if the number goes on forever my g
Graph the line y=-1/3x+3
Answers
Help!!!
Lines b and c are parallel.
What is the measure of 26?
Answers
Answer:
m∠6 = 54°
Step-by-step explanation:
∠6 is equal to (5x + 9) because they are vertical angles. But, to be able to find the measure of ∠6, you will need to find the value of (5x + 9). So, since ∠5 is equal to (13x + 9) because they are Corresponding Angles, (5x + 9) and (13x + 9) are supplementary because they are a linear pair.
So:
m∠6 = 5x + 9 and
5x + 9 + 13x + 9 = 180°
18x + 18 = 180
18x = 162
x = 9
To find m∠6, plug in values:
m∠6 = 5x + 9
= 5(9) + 9
= 45 + 9
= 54°
Arachnophobia is the fear of spiders. People with arachnophobia suffer to different degrees, but they tend to react intensely to visible signs of the presence of spiders, such as webs. The director of a clinic decides to investigate different treatment types for arachnophobia. She gathers three groups of clients: One group receives in vivo flooding, which involves prolonged or repeated exposure to the actual anxiety-producing stimuli. The second group receives imaginal flooding, which involves the same techniques as in vivo flooding, except the exposure occurs in the client’s imagination. The third group receives no treatment. The results come in, and a statistician conducts an analysis of variance.
The ___________ is that there is no difference between the population means (in other words, there is no treatment effect).
The ___________is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).
Answers
Answer:
1. The null hypothesis is that there is no difference between the population means (in other words, there is no treatment effect).
2. The alternative hypothesis is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).
Step-by-step explanation:
In a statistical analysis, the statistician shares his participants into several groups and administers treatments to them. After administering the treatment, he might want to compare the values obtained to see if there is a difference. If he accepts the null hypothesis as true, that means that there was no difference between the population means. This can also be taken to mean that the result had no difference among the groups.
But if the alternative hypothesis was true, that means that the population means were not all equal and so, there was an effect from the treatment administered.
Answer:
1. The null hypothesis is that there is no difference between the population means (in other words, there is no treatment effect).
2. The alternative hypothesis is that at least one of the population means is different from another (in other words, there is an effect Of at least one Of the treatments).
3
Describe and correct the error a student made when graphing the linear equation y = -3/4x -6
Answers
Answer:
In step 1 the y-intercept should be plotted at (0,-6)
Step-by-step explanation:
Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.
Since the formula is y = -3/4x -6
We just insert a 0 insted of the "x"
y = -3/4(0) -6
y=0-6
y=6
So the y-intercept sould be placed in (0,-6)
That's what he did wrong when graphing the equation.
Answer:
Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.
Step-by-step explanation:
Remember that to find the Y intercept in any linear equation you need to use 0 as your X value, this means taking the formula in the y=mx+b form and replacing X with a 0.
Since the formula is y = -3/4x -6
We just insert a 0 insted of the "x"
y = -3/4(0) -6
y=0-6
y=6
So the y-intercept sould be placed in (0,-6)
That's what he did wrong when graphing the equation.
what is the solution to -3/4x + 2
Answers
Answer: 1/4x(3x+8)
Step-by-step explanation:
hope this helps
let me know if its correct!!
From the table below, determine whether the data shows an exponential function. Explain why or why not.
х
3 1 -1 -3
у
1 2 3 4
a. No; the domain values are at regular intervals and the range values have a common sum 1.
b. No; the domain values are not at regular intervals.
C. Yes; the domain values are at regular intervals and the range values have a common factor 2.
d. Yes; the domain values are at regular intervals and the range values have a common sum 1.
Answers
Answer:
B because the domains repeat themselves so it can not be a function
No; the domain values are not at regular intervals.
The correct option is b.
What is an exponential function?Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.
In an exponential function, the domain values are usually at regular intervals, and the range values have a common factor or a common sum.
In the given data, the domain values are not at regular intervals.
The difference between 3 and 1 is 2, and the difference between 1 and -1 is 2, but the difference between -1 and -3 is -2.
This indicates that the domain values are not at regular intervals, which means that the data cannot be modeled by an exponential function.
Additionally, the range values also do not have a common factor or a common sum. The difference between consecutive y-values is 1, which is not a constant factor or sum.
Therefore, the data cannot be modeled by an exponential function.
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what is the answer for this -6+x=-11
Answers
Answer:
x = -5
Step-by-step explanation:
-6 + x = -11
x = -11 + 6
x = -5
Answer:
x=17
Step-by-step explanation:
17+ -6= 11
pls mark brainlest for real ('>')
Frank plans to spend no more than $85 on plants for his front garden. He purchases a salvia and three azaleas. The azaleas cost $22 each. Let c be the cost for a salvia. Which inequality below could be used to show how much money Frank spent on salvia?
Answers
Answer: 3×22+c≤85
Step-by-step explanation: i think the answer is 3×22+c≤85 because 3x 22 represent the total cost of azaleas + c the cost of salvia is less than or equal to 85 because the buget is 85 and it cannot be greater
Hope this helped
The inequality for the given situation is 66+c ≤ 85.
Given that, Frank plans to spend no more than $85 on plants for his front garden. He purchases a salvia and 3 azaleas. The azaleas cost $22 each.
What is inequality?In mathematics, inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.
Let c be the cost for a salvia.
Three azaleas + A salvia ≤ 85
3×22+c ≤ 85
⇒ 66+c ≤ 85
Therefore, the inequality for the given situation is 66+c ≤ 85.
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CAN YOU PLS ANSWER THIS QUICK!!! WHAT IS THE ANSWER TO THIS MATH EQUATION??? GEOMETRY/COLLEGE!!!
Answers
A junior basketball player has a goal of scoring at least 1,000 points in his high-school career. His team plays twenty games per year, and after two years he has 320 points
Answers
Explanation: 1,000-320=680
680 divided by 2 = 340
find the equation of the graphed function.
f(x)= _________
Answers
Answer:
y =(x+3) ^2
Step-by-step explanation:
The zero is -3 and it is the vertex (-3,0)
Using the vertex form of a parabola where ( h,k) is the vertex
y = a( x-h)^2 +k
y =a(x- -3) ^2+0
y =a(x+3) ^2
We also know another point is ( -1,4)
Substituting that point into the equation
4 = a( -1+3) ^2
4 = a( 2)^2
4 = a*4
Divide each side by 4
1 =a
The equation is
y =(x+3) ^2
What sample size is needed to give a margin of error within in estimating a population mean with 99% confidence, assuming a previous sample had .
Answers
This question is Incomplete
Complete Question
What sample size is needed to give a margin of error within ± 13 in estimating a population mean with 99% confidence, assuming a previous sample had s=116
Answer:
The sample size n = 530 samples
Step-by-step explanation:
Margin of Error formula = z × standard deviation/√n
Margin of Error = ± 13
Standard deviation = 116
z = z score of 99% = 2.58
±13 = 2.58 × 116/√n
Cross Multiply
±13 × √n = 2.58× 116
±13 × √n = 299.28
√n = 299.28/±13
√n = ± 23.0215384615
Square both sides
(√n)² = (±23.0215384615)²
n = 529.991233134
Approximately , n = 530 samples
A composition of transformations maps pre-image EFGH to final image E"F"G"H".
Trapezoid E F G H is shifted down and to the left to trapezoid E prime F prime G prime H prime. Trapezoid E prime F prime G prime H prime is reflected across the line of reflection c to form trapezoid E double-prime F double-prime G double-prime H double-prime.
The first transformation for this composition is [________], and the second transformation is a reflection across line c.
a 180° rotation about point G
a 180° rotation about point H
a translation down and to the left
a translation up and to the right
Answers
Answer:
c. a translation down and to the left
Step-by-step explanation:
As per translation of a graph, the first transformation for this composition is translation down and to the left.
What is the translation of a graph?"A translation of a graph is its rigid movement, vertically or horizontally."
Here, A composition of transformations maps pre-image EFGH to final image E"F"G"H".
Trapezoid E F G H is shifted down and to the left to trapezoid E prime F prime G prime H prime.
Therefore, this transformation for this composition is translation down and to the left, and the second transformation is a reflection across line c.
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how to simplify 2a³ × a⁴
Answers
Answer:
2a⁷
Step-by-step explanation:
you have to add 3 to 4
Write 257% as decimal
Answers
Answer:
please mark brainliest!
Step-by-step explanation:
2.57
Answer:
2.57
Hope this helps! Mark me brainliest
god bless!
Rewrite it as a function and isolate Y.
Answers
Answer: y= -2x + 12
or f (y ) = 6 - [tex]\frac{y}{2}[/tex]
Step-by-step explanation:
just subtract the 2x to get the y alone
What do you think the important skills necessary in solving problems in differential calculus?
Answers
Answer:
idk if this helps but here:
Cutoff points are a crucial piece of calculus and are among the main things that understudies find out about in a calculus class. So, finding the constraint of a capacity implies figuring out what esteem the capacity approaches as it draws nearer and more like a specific point.
Step-by-step explanation:
The price of a sweater was reduced from $20 to $12, By what percentage was the price of the sweater reduced?
Answers
Answer:
40%
Step-by-step explanation:
12 ÷ 20 = .6
You can convert the .6 to a percentage by multiplying it:
.6 x 100 = 60%
If 12 is 60% of 20, then that means 40% was taken away.
Price of the sweater was reduced by 40%.
Given in the question,
Original Price of a sweater is $20.Price of the sweater was reduced from $20 to $12.Percentage reduction in the price from $20 to $12 can be calculated from the expression,
Percentage reduction = [tex]\frac{\text{Change in price}}{\text{Original price}}\times 100[/tex]
= [tex](\frac{20-12}{12})\times 100[/tex]
= [tex]\frac{8}{12}\times 100[/tex]
= 40%
Therefore, price of the sweater was reduced by 40%.
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Find the 15th term of the arithmetic sequence if the first term is -3 and the common difference is 2. Write the equation first, then substitute to find the answer
Answers
Answer:
25.
Step-by-step explanation:
f(x)=-3+2(x-1)
f(15)=-3+2(15-1)
f(15)=-3+2(14)
f(15)=-3+28
f(15)=25
what is the best estimate of 45 percent of 76
Answers
9514 1404 393
Answer:
In order of improvement:
383434.2 (actual value)Step-by-step explanation:
In my engineering experience, a method of estimating should satisfy two requirements:
it should be relatively easy to accomplish mentallyit should provide a means of estimating the error in the estimate__
Multiplication and division by 2 are generally easy to perform mentally.
We note that 45% is about 50%.
50% of 76 is 76/2 = 38 . . . a good starting estimate
45% is down 5% from 50%, so the actual value will be 5/50 = 10% lower than this first estimate
A good second estimate is 38 -0.10(40) = 34.
A better estimate is 38 -3.8 = 34.2, which is the actual value of the expression.
_____
Alternate approach
You could also transform the problem to 76% of 45, which is about 3/4 of 44, or about 33. Figuring the error adjustment on this approach is somewhat more difficult, as it is factors of 1/75 and 1/44 too low. 1 part in 44 is not too difficult to figure, as it is 33/44 = 3/4, so a better estimate is 33.75. It takes a calculator to figure 1 part in 75 of this, which is 0.45. Adding that amount gets you to the actual value of 34.2.
Sammie bought just enough fencing to border either a rectangular plot or a square plot,
shown. The perimeters of the plots are the same. How many feet of fencing did she buy?
(3x + 6) feet.
———————
| |
| | (x - 1) feet
|__________|
(x + 6) feet
___________
| |
| |
| | (x + 6) feet
| |
|__________ |
Sammie bought____feet of fencing.
Answers
Answer:
3.5 feet
Step-by-step explanation:
The question isn't formatted properly.
We have:
(x + 6) feet on each side of the square
(3x + 6) feet horizontally on the rectangle
(x - 1) feet vertically on the rectangular
First, we need to determine the perimeter of the square:
[tex]Perimeter = 4 * Length[/tex]
[tex]Perimeter = 4 * (x + 6)[/tex]
[tex]Perimeter = 4x + 24[/tex]
Next, we determine the perimeter of the rectangle
[tex]Perimeter = 2(Length + Width)[/tex]
[tex]Perimeter = 2(3x + 6 + x - 1)[/tex]
[tex]Perimeter = 2(3x + x+ 6 - 1)[/tex]
[tex]Perimeter = 2(4x+ 5)[/tex]
[tex]Perimeter = 8x+ 10[/tex]
Equate both perimeters:
[tex]8x + 10 = 4x + 24[/tex]
Collect Like Terms
[tex]8x - 4x = 24 - 10[/tex]
[tex]4x = 14[/tex]
Solve for x
[tex]x = 14/4[/tex]
[tex]x = 3.5[/tex]
which expression means 8 less twice a number
8-2n
2n-8
Answers
Answer:
I think 2n-8 because you are taking 8 away from 2 times a number
Step-by-step explanation:
Write a linear equation that passes through the points (1,-6) and (-3, 10) *
HAHAHA HELP PLS
Answers
y=-4x-2
Step-by-step explanation:
Answer:
y= -4x-2
Step-by-step explanation:
10- -6/-3-1
10+6/-3-1
16/-4
-4
Simplify the complex fraction. 8/5 divide by 6 3/4 *
Answers
Step-by-step explanation:
[tex]\frac{8}{5}[/tex]÷6[tex]\frac{3}{4}[/tex]
First, simplify the 6[tex]\frac{3}{4}[/tex] to an improper fraction, which is:
[tex]\frac{27}{4}[/tex]
Next rewrite the equation using the improper fraction:
[tex]\frac{8}{5}[/tex]÷[tex]\frac{27}{4}[/tex]
Now, in order to divide the fraction, we will need to flip the second fraction over, and then multiply the two fractions together. A great way to remember this is the phrase Copy Dot Flip - Copy the first fraction, put a dot for multiplication, and flip the second fraction.
[tex]\frac{8}{5}[/tex]·[tex]\frac{4}{27}[/tex]
Finally, multiply together and simplify/reduce if needed:
The final answer is [tex]\frac{32}{135}[/tex] and no simplification or reduction is needed
free brainlyest if answer 9+10 the right way
Answers
Answer:
19
Step-by-step explanation:
literally if this is wrong i swear
Answer:
19
Step-by-step explanation: