The EverGlow nuclear power plant releases water into Lake Fishbegone every afternoon at 4:51 p.m. Environmental researchers are concerned that fish are being driven away from the area around the plant. They believe that the temperature of the water discharged may be a factor. The data table below gives the temperature of the water released by the plant and the measured distance (in meters) from the outflow pipe of the plant to the nearest fish found in the water on several randomly chosen afternoons. A scatterplot of the data and the least-squares regression line are given.
What is the slope of the least-squares regression line? *
A. -74.704
B. 5.791
C. 12.196
D. 0.946
Answers
9514 1404 393
Answer:
B. 5.791
Step-by-step explanation:
The slope of the line is the coefficient of x in its equation. The equation is ...
ŷ = -74.704 +5.791x
The coefficient of x, the slope, is 5.791.
Related Questions
Identify the slope of the line using the 2 points
(8,-7), (6,17)
12
-12
12
12
Answers
In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A shipment is acceptable if at least 440 of the 500 bearings meet the specification. Assume that each shipment contains a random sample of bearings. a. What is the probability that a given shipment is acceptable? b. What is the probability that more than 285 out of 300 shipments are acceptable? c. What proportion of bearings must meet the specification in order that 99% of the shipments are acceptable?
Answers
Answer:
(a) 0.94
(b) 0.20
(c) 90.53%
Step-by-step explanation:
From a population (Bernoulli population), 90% of the bearings meet a thickness specification, let [tex]p_1[/tex] be the probability that a bearing meets the specification.
So, [tex]p_1=0.9[/tex]
Sample size, [tex]n_1=500[/tex], is large.
Let X represent the number of acceptable bearing.
Convert this to a normal distribution,
Mean: [tex]\mu_1=n_1p_1=500\times0.9=450[/tex]
Variance: [tex]\sigma_1^2=n_1p_1(1-p_1)=500\times0.9\times0.1=45[/tex]
[tex]\Rightarrow \sigma_1 =\sqrt{45}=6.71[/tex]
(a) A shipment is acceptable if at least 440 of the 500 bearings meet the specification.
So, [tex]X\geq 440.[/tex]
Here, 440 is included, so, by using the continuity correction, take x=439.5 to compute z score for the normal distribution.
[tex]z=\frac{x-\mu}{\sigma}=\frac{339.5-450}{6.71}=-1.56[/tex].
So, the probability that a given shipment is acceptable is
[tex]P(z\geq-1.56)=\int_{-1.56}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}}=0.94062[/tex]
Hence, the probability that a given shipment is acceptable is 0.94.
(b) We have the probability of acceptability of one shipment 0.94, which is same for each shipment, so here the number of shipments is a Binomial population.
Denote the probability od acceptance of a shipment by [tex]p_2[/tex].
[tex]p_2=0.94[/tex]
The total number of shipment, i.e sample size, [tex]n_2= 300[/tex]
Here, the sample size is sufficiently large to approximate it as a normal distribution, for which mean, [tex]\mu_2[/tex], and variance, [tex]\sigma_2^2[/tex].
Mean: [tex]\mu_2=n_2p_2=300\times0.94=282[/tex]
Variance: [tex]\sigma_2^2=n_2p_2(1-p_2)=300\times0.94(1-0.94)=16.92[/tex]
[tex]\Rightarrow \sigma_2=\sqrt(16.92}=4.11[/tex].
In this case, X>285, so, by using the continuity correction, take x=285.5 to compute z score for the normal distribution.
[tex]z=\frac{x-\mu}{\sigma}=\frac{285.5-282}{4.11}=0.85[/tex].
So, the probability that a given shipment is acceptable is
[tex]P(z\geq0.85)=\int_{0.85}^{\infty}\frac{1}{\sqrt{2\pi}}e^{\frac{-z^2}{2}=0.1977[/tex]
Hence, the probability that a given shipment is acceptable is 0.20.
(c) For the acceptance of 99% shipment of in the total shipment of 300 (sample size).
The area right to the z-score=0.99
and the area left to the z-score is 1-0.99=0.001.
For this value, the value of z-score is -3.09 (from the z-score table)
Let, [tex]\alpha[/tex] be the required probability of acceptance of one shipment.
So,
[tex]-3.09=\frac{285.5-300\alpha}{\sqrt{300 \alpha(1-\alpha)}}[/tex]
On solving
[tex]\alpha= 0.977896[/tex]
Again, the probability of acceptance of one shipment, [tex]\alpha[/tex], depends on the probability of meeting the thickness specification of one bearing.
For this case,
The area right to the z-score=0.97790
and the area left to the z-score is 1-0.97790=0.0221.
The value of z-score is -2.01 (from the z-score table)
Let [tex]p[/tex] be the probability that one bearing meets the specification. So
[tex]-2.01=\frac{439.5-500 p}{\sqrt{500 p(1-p)}}[/tex]
On solving
[tex]p=0.9053[/tex]
Hence, 90.53% of the bearings meet a thickness specification so that 99% of the shipments are acceptable.
The manufactures bearings.
As per the question, the process that a manufacturer bears 90% of the bearings and meet the thickness specifications. The shipment consists of 500 bearings. The shipment if taken has a least 440 and 500 bearings.
the answer is 0.94, 0.20, and 90.53%.
The assumption is that each shipment is randomly taken in a sample of bearings. The chances or the probability that that given shipment are acceptable are 0.94% and the probability that they are more than 285 out of the 300 bearings is 0.205. The part of bearings that must meet the specifications in order to be 99% of shipments is 90.5%.Learn more about the manufactures bearings.
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What value is equivalent to 52 + 53 − 54?
Answers
Answer:
51
Step-by-step explanation:
Answer: 51
Step-by-step explanation:
Evaluate
Suppose that a company's profit (in terms of q, the number of units sold) is given by the model
P(q) = 4q2 + 241q - 530. Find the profit when 20 units are sold.
Answer: P =
dollars.
Answers
7.51 rounded to the nearest tenth
Answers
Answer:
7.5
Step-by-step explanation:
Answer:
7.5
Step-by-step explanation:
I am a senior so I am right
Select the locations on the number line to plot the points 5, 3, and −2
Answers
Answer:
To find the points, remember the definition of distance or difference.
First, the 5 is easy to find, is in the extreme right.
Now, the next number is 3.
The difference between 3 and 5 is:
3 - 5 = - 2
This means that the place of the 3 will be 2 units at the left of the 5.
The next number is -2
The difference between -2 and 5 is:
-2 - 5 = -7
This means that the -2 is located 7 units at the left of the 5.
Below is an image of the located points in a number line.
Sophia has fabric to make banners for school she needs 1 and 1/4 yards of fabric for each Banner she has made 4 banners and has 2 and a 1/2 yards of fabric left over how much fabric did she begin with
Answers
Answer: 7 and a 1/2
Step-by-step explanation: 1 and 1/4 times4 = 5 plus 2 and a 1/2 = 7 and a 1/2
by 2013 the money spent on internet advertising in the country was projected to exceed the amount spent on tv advertising if it is estimated that 0.6 million dollars more will be spent on internet advertising and 2013 and the total amount spent on internet and tv advertising is expanded to be $120 billion dollars find the amount of money for projected to be spent on each medium
Answers
Answer:
72 dollars
Step-by-step explanation:multiplrf the two
i’m sure they are right, believe in ur self!!!!!!
how can I solve this equation
49x^2 - 14x + 1 <= 0
Answers
(adding for limit)
Step-by-step explanation:
(7x)^2 - 2×7x×1 +1^2 =0
(7x-1)^2 =0
7x-1=0
7x=1
x= 1\7
Rapid Rental Car charges a $40 rental fee, $15 for gas, and $0.25 per mile driven. For the same car, Capital Cars charges $45 for rental and gas, and $0.35 per mile. For how many miles is the rental cost at both companies the same?
Answers
1415236 IDC DCCDSDSDCSDCSDC
Use the geometric probability distribution to solve the following problem. On the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry. Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village. (a) Write out a formula for the probability distribution of the random variable n. (Enter a mathematical expression.) P(n) = p(1 - p)n-1 (b) Compute the probabilities that n = 1, n = 2, and n = 3. (For each answer, enter a number. Round your answers to three decimal places.) P(1) = 0.740 P(2) = 0.192 P(3) = 0.050 (c) Compute the probability that n ≥ 4. Hint: P(n ≥ 4) = 1 − P(n = 1) − P(n = 2) − P(n = 3). (Enter a number. Round your answer to three decimal places.) 0.018 (d) What is the expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry? Hint: Use μ for the geometric distribution and round. (Enter a number. Round your answer to the nearest whole number.) residents
Answers
Answer:
(a) [tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]
(b) P(1) = 0.740, P(2) = 0.192, and P(3) = 0.050.
(c) The probability that n ≥ 4 is 0.018.
(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is 3.
Step-by-step explanation:
We are given that on the leeward side of the island of Oahu, in a small village, about 74% of the residents are of Hawaiian ancestry.
Let n = 1, 2, 3, … represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.
(a) We can observe that the above situation can be represented through the geometric distribution because the geometric distribution states that we will keep on going with the trials until we achieve our first success,
Here also, n represent the number of people you must meet until you encounter the first person of Hawaiian ancestry in the village.
So, the probability distribution of the geometric distribution is given by;
[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1} ; \text{ n} = 1, 2, 3,....[/tex]
where, p = probability that the residents are of Hawaiian ancestry = 74%
(b) The probabilities that n = 1, n = 2, and n = 3 is given by;
[tex]\text{P(n)} = \text{p} \times \text{(1 - p)}^{n-1}[/tex]
P(1) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{1-1}[/tex] = 0.74
P(2) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{2-1}[/tex] = 0.192
P(3) = [tex]\text{0.74} \times \text{(1 - 0.74)}^{3-1}[/tex] = 0.050
(c) The probability that n ≥ 4 is given by = P(n ≥ 4)
P(n ≥ 4) = 1 - P(n = 1) - P(n = 2) - P(n = 3)
= 1 - 0.74 - 0.192 - 0.050
= 0.018
(d) The expected number of residents in the village you must meet before you encounter the first person of Hawaiian ancestry is given by = E(n)
We know that the mean of the geometric distribution is given by;
Mean = [tex]\dfrac{p}{1-p}[/tex] = [tex]\dfrac{0.74}{1-0.74}[/tex]
= [tex]\dfrac{0.74}{0.26}[/tex] = 2.85 or 3 (approx).
one third of a number is greater than one tenth of that same number by 63 what is the number
Answers
Answer:
The answer is 270.
Step-by-step explanation:
This is the answer is because:
If you let the number be x.
x divided by 3 is equal to x divided by 10 plus 63.
x/3 = x/10 +63
So...
x divided by 3 plus x divided by 10 is equal to 63
x/3 +x/10 = 63
Then if you make a commmon denominator...
10x divided 30 plus 3x divided by 30 is equal to 63
10x/30 + 3x/30 = 63
Then...
7x divided by 30 is equal to 63
7x/30 = 63
After that...
x is equal to ( 63 * 30 ) divided by 7
x = (63*30) / 7
So...
x is equal to 9*30
x = 9*30
Finally...
x is equal to 270
x = 270
The race course is 3/4 of a mile long. How many feet long is the race course?
Answers
Answer:
3960 feet
Step-by-step explanation:
Answer:
3,960 feet long
Step-by-step explanation:
1 mile = 5,280 feet
5,280 feet ÷ 4 (because the denominator is 4) = 1,320 feet
1,320 x 3 (the numerator is 3) = 3,960 feet
3/4 of a mile = 3,960 feet
if f(x) = 2x + 4 and g(x) = 6x - 10, find f(4) - g(2)
Answers
Answer:
f(4) - g(2) = 10
Step-by-step explanation:
[tex]f(x) = 2x + 4 \\ f(4) = 2 \times 4 + 4 = 8 + 4 = 12 \\ \\ g(x) = 6x - 10 \\ g(2) = 6 \times 2 - 10 = 12 - 10 = 2 \\ \\ f(4) - g(2) = 12 - 2 \\ \\ \huge \red{ \boxed{ f(4) - g(2) = 10}}[/tex]
can you make an irrational number, a rational number and if possible, how?
Answers
Answer:
The sum of two irrational numbers, in some cases, will be irrational. However, if the irrational parts of the numbers have a zero sum (cancel each other out), the sum will be rational.
decrease 5% by 2205
Answers
Answer:
The answer is,2094.75
Step-by-step explanation:
Percentage decrease = 5% × 2,205
2,205 - Percentage decrease =
2,205 - (5% × 2,205) =
2,205 - 5% × 2,205 =
(1 - 5%) × 2,205 =
(100% - 5%) × 2,205 =
95% × 2,205 =
95 ÷ 100 × 2,205 =
95 × 2,205 ÷ 100 =
209,475 ÷ 100 =
2,094.75
Or to be simpler
You find 5% of 2,205 which is 110.25 then subtract it from 2205 which is 2,094.75 and that 5% of 2,205
In a game you have 1/20 probability of winning $76 and a 19/20 probability of losing $9. What is your expected value?
Answers
Answer:
1
Step-by-step explanation:
The expected value for the given case is $-4.75.
What is probability?Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.
The probability of any event always lies in the close interval of 0 and 1 [0,1].
Given that,
The probability of winning $76 is 1/20.
And, the probability of losing $9 is 19/20.
The expected value for the given probability can be given by taking the product of the probability and the wining or losing amount and then substracting them as,
Expected value = 1/20 × 76 - 19/20 × 9
= 3.8 - 8.55
= -4.75
Hence, the expected value of amount for losing and winning the game is $-4.75.
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Help.-. Plsssssssssss
Answers
Answer:
mDE = 9
Step-by-step explanation:
mCD and mDE must add up to mCE
Step 1: Set up equation
mCD + mDE = mCE
5x + 1 + 3x + 3 = 20
Step 2: Solve for x
Combine like terms: 8x + 4 = 20Subtract 4 on both sides: 8x = 16Divide both sides by 8: x = 2Step 3: Find mDE
mDE = 3x + 3
mDE = 3(2) + 3
mDE = 6 + 3
mDE = 9
What is the difference between 9 and -2?
7
11
-7
-11
Answers
Answer:
7
The difference between 9 a positive number and - 2 a negative number is 7 because the question States 9 - 2.
50 Points
What is the value of y?
Answers
Answer:
y=14
Step-by-step explanation:
measure of a=50degrees b=50 degrees c=(5(14)+10) =80
50+50+80=180
Answer:
Y= 14
Step-by-step explanation:
a=50degrees
b=50 degrees
c=(5(14)+10) =80
50+50+80=180
Answer please I need it ASAP
Answers
Answer:
answer what???
Step-by-step explanation:
The reaction of the body to a dose of medicine can sometimes be represented by an equation of the formR = M^2 (C/2- M/3),where C is a positive constant and M is the amount of medicine absorbed in the blood. If the reaction is a change in blood pressure, R is measured in millimeters of mercury. If the reaction is a change in temperature, R is measured in degrees, and so on. Find dR/dM. This derivative, as a function of M, is called the sensitivity of the body to the medicine.
Answers
Answer:
The derivative is [tex]\frac{dR}{dM} = CM - M^2[/tex]
Step-by-step explanation:
From the question we are told that
The equation representing the reaction is [tex]R = M^2 (\frac{C}{2} - \frac{M}{3} )[/tex]
Generally this equation can be represented as
[tex]R = \frac{C M^2}{2} - \frac{M^3}{3}[/tex]
Generally [tex]\frac{dR}{dM}[/tex] as a function of M is mathematically represented as
[tex]\frac{dR}{dM} = 2 * \frac{C M^{2 - 1 }}{2} + 3 * \frac{M^{3-1}}{3}[/tex]
=> [tex]\frac{dR}{dM} = CM - M^2[/tex]
प्रश्न 5 समीकरण हल कीजिए- (आलेख विधि से नही)
4x-5y+16 =0
2x+y-6 =0
bicol method)
Answers
Answer:
Step-by-step explanation:
Given the simultaneous equation
4x-5y+16 =0 ....... 1
2x+y-6 =0 ...... 2
Let us solve to get the variable x and y:
The equation becomes
4x-5y =-16 ........ * 1
2x+y =6 ...... *2
Using Elimination method
Multiply eqn 1 by 1 and eqn 2 by 2
4x-5y =-16
4x+2y =12
Subtract resulting equation
-5y-2y = -16-12
-7y = -28
solve for y
-7y/-7 = -28/-7
y = 4
Substitute y = 4 into equation 2 to get x
2x+y =6
2x + 4 = 6
2x = 6-4
2x = 2
x = 2/2
x = 1
hence x is 1, y is 4
1/6 times 3/5 in simplist form
Answers
Answer:
0.1
Step-by-step explanation:
what IS the sum 59+23
Answers
Answer:
82
Step-by-step explanation:
59 + 23 = 82
The sum of 59 and 23 is 82
Casey did a science experiment to find out which brand of popcorn popped the most kernels. The first brand had 123 kernels pop. The second brand had 108 kernels pop. To the nearest ten, about how many kernels popped in all?
Answers
Answer:
230
Step-by-step explanation:
The answer is 230 because if you add 123 and 108 together you get 231 but since we are rounding to the nearest 10 it would be 230 because 231 is closer to 230 than it is to 240.
PLEASE HELP WILL MARK BRAINLEIST!
Answers
Answer:
-3.25
Step-by-step explanation:
Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165. The equation represents the $495 total cost that Barbara paid to Dance Unlimited. 495 = 165 + 55 m How many months, m, did Barbara receive dance lessons from Dance Unlimited? F. 2.25 months G. 6 months H. 12 months J. 9 months
Answers
Answer:
G. 6 months
Step-by-step explanation:
1. 495-165 to remove the one-time payment = 330
2. 330/55 to find the number of months = 6
Barbara receive 6 months of dance lessons from Dance Unlimited
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, Barbara signed up for dance lessons at Dance Unlimited. She was charged $55 per month for lessons and a one-time recital fee of $165.
Let m be the no of months and f(m) is the total cost.
∴ f(m) = 55m + 165.
The equation represents the $495 total cost,
∴ 495 = 55m + 165.
55m = 330.
m = 330/55.
m = 6.
Barbara receives 6 months of dance lessons from Dance Unlimited.
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What is the result of 5 divided by 1/5?
Answers
Answer:
15 divided by 1/5 is equal to 1.
If x = − 4, which number line shows the value of |x|?
A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. A dot is shown on a point at 4 tick marks to the left of 0. Above the number line, a bracket is shown extending from a point at 4 tick marks to the left of zero to 0. A horizontal line is shown between the brackets, and 4 is written on the line.
A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. A dot is shown on a point at 4 tick marks to the left of 0. Above the number line, a bracket is shown extending from a point at 4 tick marks to the left of zero to 0. A horizontal line is shown between the brackets, and negative 4 is written on the line.
A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. A dot is shown on a point at 4 tick marks to the left of 0. Above the number line, a bracket is shown extending from a point at 4 tick marks to the left of zero to a point at 4 tick marks to the right of zero. A horizontal line is shown between the brackets, and 4 is written on the line.
A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. A dot is shown on a point at 4 tick marks to the left of 0. Above the number line, a bracket is shown extending from a point at 4 tick marks to the left of zero to a point at 4 tick marks to the right of zero. A horizontal line is shown between the brackets, and negative 4 is written on the line.
Answers
Answer:
B
Step-by-step explanation: