The amount of time people spend exercising in a given week follows a normal distribution with a mean of 3.8 hours per week and a standard deviation of 0.8 hours per week.
i) Which of the following shows the shaded probability that a person picked at random exercises less than 2 hours per week?
ii) What is the probability that a person picked at random exercises less than 2 hours per week? (round to 4 decimal places)
iii) Which of the following shows the shaded probability that a person picked at random exercises between 2 and 4 hours per week?
iv) What is the probability that a person picked at random exercises between 2 and 4 hours per week? (round to 4 decimal places)
Answers
Answer:
i and iii) In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4
ii) [tex]P(X<2)=P(\frac{X-\mu}{\sigma}<\frac{2-\mu}{\sigma})=P(Z<\frac{2-3.8}{0.8})=P(z<-2.25)[/tex]
And using the normal standard table or excel we got:
[tex]P(z<-2.25)=0.0122[/tex]
iv) [tex]P(2<X<4)=P(\frac{2-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{4-\mu}{\sigma})=P(\frac{2-3.8}{0.8}<Z<\frac{4-3.8}{0.8})=P(-2.25<z<0.25)[/tex]
And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:
[tex]P(-2.25<z<0.25)=P(z<0.25)-P(z<-2.25)= 0.5987-0.0122= 0.5865[/tex]
Step-by-step explanation:
Let X the random variable that represent amount of time people spend exercising in a given week, and for this case we know the distribution for X is given by:
[tex]X \sim N(3.8,0.8)[/tex]
Where [tex]\mu=3.8[/tex] and [tex]\sigma=0.8[/tex]
Part i and iii
In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4
Part ii
We are interested on this probability:
[tex]P(X<2)[/tex]
We can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we have:
[tex]P(X<2)=P(\frac{X-\mu}{\sigma}<\frac{2-\mu}{\sigma})=P(Z<\frac{2-3.8}{0.8})=P(z<-2.25)[/tex]
And using the normal standard table or excel we got:
[tex]P(z<-2.25)=0.0122[/tex]
Part iv
We want this probability:
[tex]P(2<X<4)[/tex]
Using the z score formula we got:
[tex]P(2<X<4)=P(\frac{2-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{4-\mu}{\sigma})=P(\frac{2-3.8}{0.8}<Z<\frac{4-3.8}{0.8})=P(-2.25<z<0.25)[/tex]
And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:
[tex]P(-2.25<z<0.25)=P(z<0.25)-P(z<-2.25)= 0.5987-0.0122= 0.5865[/tex]
Related Questions
The number 12,089 is:
< 12,098.
= 12,098.
> 12,098.
None of these choices are correct.
Answers
Answer:
< 12,098
Step-by-step explanation:
Because yes
...........
It is <12,098
One of them is correct
There are 4,500 pounds of fruit in john’s store. 1200 pounds of the fruit is apples and half as much is mangoes. The weight of pears is three times the weight of mangoes. If the rest of the fruits are grapefruits, what is the total weight of grapefruits?
Answers
Answer:
the total weight of the grapefruits is 2100 pounds
Step-by-step explanation:
apples = a
mangoes = a/2
weight of pears=3*a/2
grapefruits=g
a+a/2=1200
3/2a=1200
1.5a=1200
a=800
800+400+1200+g=4500
g=2100
Therefore, the total weight of the grapefruits is 2100 pounds
I hope this helped and have a good rest of your day!
a rectangle has length x + 9 and width 2x - 1. What is the area of the rectangle?
Answers
Answer:
A = 2x^2 + 17x -9
Step-by-step explanation:
A = LW
L = x + 9
W = 2x - 1
A = (x+9)(2x-1)
FOIL
A = 2x^2 + 18x - x - 9
A = 2x^2 + 17x -9
find the percent if the whole is 4700 and the part is 305 and one half.
round to nearest tenth
Answers
Answer:
6.5%
Step-by-step explanation:
305.5/4700=0.065=6.5%
(−4)−(−2)–{(−5)–[(−7)+(−3)–(−8)]}
Thanks 90 POINTS!!!!
Answers
Answer:
1
Step-by-step explanation:
(−4)−(−2)–{(−5)–[(−7)+(−3)–(−8)]}
PEMDAS
Work from the inside out
Change subtracting negatives to adding
(−4)+2–{(−5)–[(−7)+(−3)+8)]}
(−4)+2–{(−5)–[(-2)]}
(−4)+2–{-5+2}
(−4)+2–(−3)
Changing to adding
(−4)+2+3
-2+3
1
To approach the runway, a pilot of a small plane must begin a 5 degree descent starting from a height of 1407 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?
Answers
Answer:
3.0 miles
Step-by-step explanation:
The tangent of the angle relates the opposite side (altitude) to the adjacent side (distance to runway):
tan(5°) = (altitude)/(distance to runway)
Then we have ...
distance to runway = (1407 ft)/(tan 5°) ≈ 16,082 ft
In miles, that is ...
distance to runway = (16082 ft)/(5280 ft/mi) = 3.0458 mi
The pilot is 3.0 miles from the runway at the start of his approach.
Which statement(s) can be interpreted from the equation for a real estate value, V 228,000(1.03)' where V) represents the value of the real estate and t represents the time in years?
The equation is an exponential growth equation
The equation is an exponential decay equation
The equation is neither exponential decay nor exponential growth
$228.000 represents the initial cost of a real estate that appreciates 3% per year over the course of years
$228.000 represents the initial cost of a real estate that appreciates 30% per year over the course of years
$228.000 represents the initial cost of a real estate that depreciates 3% per year over the course of t years
$228.000 represents the initial cost of a real estate that depreciates 30% per year over the course of years
Answers
Answer:
The statements that are true for this equation are:
- The equation is an exponential growth equation.
- $228.000 represents the initial cost of a real estate that appreciates 3% per year over the course of years.
Step-by-step explanation:
We have the equation
[tex]V= 228,000(1.03)^t[/tex]
Where V: value of the real state and t: time in years.
As t is always positive in this case, and 1.03 is larger than 1, the value V will rise exponentially. The equation is an exponential growth equation.
The difference in value for each year is:
[tex]\dfrac{V_{t+1}}{V_t}=\dfrac{1.03^{t+1}}{1.03^t}=1.03^{t+1-t}=1.03\\\\\\V_{t+1}-V{t}=1.03V_t-V_t=0.03V_t[/tex]
We can conclude that the value increases each year 0.03 (3%) from the previous year value, starting from $228,000 in the year t=0.
$228.000 represents the initial cost of a real estate that appreciates 3% per year over the course of years.
NEED HELP PLS
You were shown into a great cavern. “Including yourself, there are 350 people in this cavern,” the genie said.
You looked around and said, “These don’t look like people, they look like mummies.”
“Yes they are mummies, little one. If you can’t solve my next puzzle, you may become one of them. You will join the mummies. Then you will all line up in a single line. I will go down the line and count 1, 2, 3, 4, 5, 6, and so on. Every even numbered person (or mummy) will step out of line. Whenever I reach the end of the line, I will go back to the beginning of the line and continue counting from wherever I left off. The even numbers will still step out of line. The last person or mummy left in line will get the buried treasure. You can stand anywhere you want, but choose wisely.”
The genie then shouted, “Line up,” as you worked furiously trying to figure out what position to be in. The mummies all began to shuffle into position. The genie turned to you and said, “Well, where do you wish to stand?”
What position in line is the lucky winner?
Answers
Answer:
First
Step-by-step explanation:
The first person in the line will always have an odd position, not an even one. They will be the only one left.
Select all the ordered pairs that are in the solution set for the inequality graphed below.
Question 2 options:
(0, 0)
(1, -2)
(-2, 3)
(1, 6)
Answers
Answer:
(0,0)
Step-by-step explanation:
I think thats the only answer because the line goes through that point.
Which value of k will make this relationship NOT a function? {(−7, 2), (−1, 0), (4, 8), (k, 0)}
Answers
Answer:
In this example, if k = -7, this relationship is not a function, since x = -7 would have both y = 2 and y = 0.
Step-by-step explanation:
Requirement to be a function:
For a relationship to be a function, all values of x must have only one corresponding value of y.
In this question:
For x = -7, y = 2
For x = -1, y = 0
For x = 4, y = 0
For x = k, y = 0
A value of x must not have more than 1 value of y.
In this example, if k = -7, this relationship is not a function, since x = -7 would have both y = 2 and y = 0.
Suppose you regress the natural log of total family expenditures on household size using observations of households from the 2013 Consumer Expenditure Survey:
. reg Intotexppq fam_size
Source SS df MS Number of obs = 6,766
Model F(1, 6764) = 634.72
Residual Prob > F = 0.0000
R-squared = 0.0858
Adj R-squared = 0.0857
Total | 5540.26944 6,765 818960744 Root MSE = .86534
Intotexppp | Coef. Std. Err. t P>I t I |[95% Conf. Interval]
fam_size | .1767089 .007014 25.19 0.000
cons | .0203324 404.71 0.000
From the information given, you should be able to answer the following questions about the regression:
• (4) Interpret your estimate of the coefficient on family size.
• (4) Compute the 95% confidence interval for the coefficient on family size.
• (6) Compute the estimate of the intercept of the regression line.
• (5) Compute the Explained Sum of Squares and Residual Sum of Squares of the model.
• (6) How would you assess whether the error terms in your model were homoskedastic or heteroskedastic? Include a picture if you need to.
Answers
Answer:
Step-by-step explanation:
Please check below in the attached, you will see answer to given questions, thank you, I hope it helps.
Is the quotient of 5 and 1/2 greater than or less than 5? Explain your answer in complete sentences.
Answers
Answer: Greater than 5
Step-by-step explanation:
The quotient of 5 and .5 is 10.
5/0.5 = 10
Whenever you divide a whole number by a fraction, the quotient will always be larger than the whole number
The radius of a circle is 7 cm.find its area to the nearest 10th
Answers
Answer:
A = 153.9 cm^2
Step-by-step explanation:
The formula for the area of a circle of radius r is A = (pi)(r)^2.
Here, with r = 7 cm, the area is A = (pi)(7 cm)^2 = 49(pi)(cm)^2, or (to the nearest 10th): A = 153.9 cm^2
Solve the following: 2(5x-3)
Answers
Answer:
The vale of x is 3/5.
Step-by-step explanation:
First you have to expand out :
[tex]2(5x - 3)[/tex]
[tex] = 2(5x) - 2(3)[/tex]
[tex] = 10x - 6[/tex]
Next you have to solve it by adding 6 to both sides :
Let expression = 0,
[tex]10x - 6 = 0[/tex]
[tex]10x - 6 + 6 = 0 + 6[/tex]
[tex]10x = 6[/tex]
[tex]x = \frac{6}{10} [/tex]
[tex]x = \frac{3}{5} [/tex]
Lennox was curious if triangles \triangle ABE△ABEtriangle, A, B, E and \triangle DCE△DCEtriangle, D, C, E were similar, so she tried to map one figure onto the other using a reflection and a dilation. Lennox concluded: "It's not possible to map \triangle DCE△DCEtriangle, D, C, E onto \triangle ABE△ABEtriangle, A, B, E using a sequence of rigid transformations and dilations, so the triangles are not similar." What error did Lennox make in her conclusion?
Answers
Answer:
There is no error. This is a correct conclusion.
Step-by-step explanation:
If a sequence of rigid transformations
(translations, reflections, and rotations) and dilations can map △DCE onto △ABE, then the figures are similar.
Notice that both triangles are right triangles (at vertices B and C), with line AB and DC being the longer legs.
Therefore, if the triangles are similar, we should be able to map each pair of corresponding points onto each other with rigid transformations and dilations:
D should be mapped onto A.
C should be mapped onto B.
E should be mapped onto itself.
Lennox used a reflection across line BE and a dilation about E to get △DCE as close as possible to △ABE. But still, point D did not map onto point A.
So we can conclude that it's not possible to map △DCE onto △ABE using a sequence of rigid transformations and dilations.
Lennox concluded:
"It's not possible to map △DCE onto △ABE using a sequence of rigid transformations and dilations, so the triangles are not similar."
There is no error. This is a correct conclusion.
Answer:
there is no error
Step-by-step explanation:
I took the quiz on Khan and got it correct!
What is the median? I need this turned in aaa on but I don’t get it
Answers
Answer: 7,500 passengers
Step-by-step explanation: Let's put the numbers from least to greatest...
5,000, 6,000, (7,000, 8,000,) 9,000, 10,000
Since there is an even number of numbers we will have two medians for the time being...
7,000 + 8,000 = 15,000
15,000 ÷ 2 = 7,500
Therefore, the median is 7,500, there are 7,500 passengers in total.
I hope this helps!
SOMEONE HELP ????
Select steps that could be used to solve the equation 1+ 3x = -x+4
Answers
Answer:
a) add x , subtract 1 and divide by 4
The solution of given equation [tex]x = \frac{3}{4}[/tex]
Step-by-step explanation:
Given equation 1+3 x = -x +4
Add 'x' on both sides , we get
1 + 3 x + x = - x + x +4
1 + 4 x = 4
Subtract '1' on both sides , we get
1+4 x -1 = 4 -1
4 x = 3
Dividing '4' on both sides, we get
[tex]\frac{4x}{4} = \frac{3}{4}[/tex]
[tex]x = \frac{3}{4}[/tex]
Final answer:-
The solution of given equation [tex]x = \frac{3}{4}[/tex]
WILL MARK YOU AS BRAINLIEST HELP PLZ
Answers
Answer:
896+32=928in
Step-by-step explanation:
Based on the graph, explain why or why not
Answers
Answer:
No the given factors won't work. They are the opposite of what they should be.
Step-by-step explanation: The "zeros" of the graph are (-5,0) and (2,0) If you use substitute those x values in the factors, (-5-5) or (2+2) and put them into the function the results are false.
To get f(x)=0 the factors should be (x+5) and (x-2)
Question 3 (1 point)
The Base of a prallelogram is is multiplied by 3 and the height is multiplied by 6. The area of the new paralellogram is multiplied by
Answers
Answer: The area of the new parallelogram is multiplied by 18
Step-by-step explanation: Let the base and the height of the original parallelogram be ' x '
Base of the parallelogram = x
Height of the parallelogram = x
Area of parallelogram = l × b = lb
= x × x = x²
∴ Area of the original parallelogram = x²
∴ The base is multiplied by 3 = 3x
The height is multiplied by 6 = 6x
∴ Area of new parallelogram = 3x × 6x = 18x²
∴ The area of the new parallelogram is multiplied by = 18x²/ x²
= 18
Please mark this as brainliest
How many blocks with dimensions of 1/3 x1 x1 can fit in a unit cude
Answers
Answer:
3
Step-by-step explanation:
1 / (1/3) = 3
Ruth has pennies and dimes in her pocket. The number of dimes is twelve less than twice the number of pennies. Let p represent the number of pennies. Write an expression for the number of dimes.
Answers
I hope that helps!
What is the residual of a week in which a barrel of crude oil costs $60 and a barrel of jet fuel costs $78?
Answers
Answer:
residual cost = $24.57
Step-by-step explanation:
The residual is the difference between the observed value of y and the predicted value of y. The least square regression equation was used to predict cost in dollars per barrel of jet fuel from the cost , in dollars ,per barrel of crude oil. The residual value is the difference between the observed or measured value and the predicted value of the regression model . The predicted value is gotten from the regression equation.
y = 2 + 6/7 x
where
x = cost of a barrel of crude oil
x = $60
y = 2 + 6/7 × 60
y = 2 + 360/7
y = 2 + 51.4285714286
y = 53.4285714286
y = $53. 43
predicted cost = $53. 43
Measured cost = $78
residual = observed value - predicted value
residual = 78 - 53.43
residual cost = $24.57
The residual of a week in which a barrel of crude oil costs $60 and a barrel of jet fuel costs $78 is $24.57
What is the residual value?The residual value is the difference between the observed or measured value and the predicted value of the regression model.
Given that a barrel of crude oil costs $60 and a barrel of jet fuel costs $78.
According to the question, we have;
y = 2 + 6/7 x
where x = the cost of a barrel of crude oil
x = $60
Substitute;
y = 2 + 6/7 × 60
y = 2 + 360/7
y = 2 + 51.4285714286
y = 53.4285714286
y = $53. 43
The predicted cost is $53. 43
Measured cost = $78
Then the residual = observed value - predicted value
The residual = 78 - 53.43
Residual cost = $24.57
Hence, the residual of a week in which a barrel of crude oil costs $60 and a barrel of jet fuel costs $78 is $24.57
Learn more about equations here;
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The complete question is
The residual is the difference between the observed value of y and the predicted value of y. The least square regression equation was used to predict the cost in dollars per barrel of jet fuel from the cost, in dollars, per barrel of crude oil. The predicted value is gotten from the regression equation. What is the residual of a week in which a barrel of crude oil costs $60 and a barrel of jet fuel costs $78?
I NEED HELP QUICK PLEASE Segment Line segment X Y is dilated using a scale factor of Two-thirds through P. Which segment shows the correct result of the dilation?
Point P is the center of dilation. Line a is 4 units from point P, line B is 2 units from line a, line c is 2 units from line b, line d is 2 units from line c, line X Y is 2 units from line d.
line a
line b
line c
line d
Answers
Answer:
C
Step-by-step explanation:
Since lines a, b, c, d, and XY are all parallel to each other, and are a part of the same triangle, they are all similar. Thus, we can compare rates -- the distance between P to Y is 12, and 2/3 of 12 is 8, so we need to find that length, which is C
The segment of line c shows the correct result of the dilation. Hence, the correct answer is option C.
What is dilation?Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
Since lines a, b, c, d, and XY are all parallel and part of the same triangle, they are all similar. Thus, we can compare rates the distance between P to Y is 12, and 2/3 of 12 is 8, which is C.
Hence, the correct answer is option C.
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help me with this plissssss
Answers
Answer: 1st and 3rd 2nd and fourth hope this helps :3
Step-by-step explanation:
Rearrange the equation so u is the independent variable.
-12u + 13 = 8w - 3
y = __
15 POINTS HELP ME !
Answers
Answer: U = 8w-16/-12
Step-by-step explanation:
-12u + 13 = 8w -3
-12u + 13 - 13 = 8w -3 -13
-12u = 8w -16
u = 8w - 16/ -12
Find the GCF of 260,80,50
Answers
Answer:
10
Step-by-step explanation:
Please help
There are 7 seats in the first row of a theater, 9 seats in the second row, and 11 seats in the third row. This pattern continues for each row in the theater. Write a rule for an, the number of seats in the nth row.
Answers
Answer:
an=n+2
Step-by-step explanation:
UJUU J
Given p(a) = (a^4 - 6a^3 + 3a^2 + 26a – 24) = 0
a) Check by the remainder or factor theorems which of these is a factor of the polynomial
p(a): (a - 1), (a - 2) or (a + 4).
b) By the remainder theorem, state the remainder when p(a) is divided by the binomial
which are not its factors.
c) Use the factor from (a) to divide p(a) by long division.
d) Use the factor from (a) to divide p(a) by synthetic division. (your answer should
correspond with that from (c)).
Answers
Answer:
Plese read the complete procedure below:
Step-by-step explanation:
The polynomial is p(a) = (a^4 - 6a^3 + 3a^2 + 26a – 24)
a)
1 -6 3 26 -24 | 1
1 -5 -2 24
1 -5 -2 24 0
The remainder is zero, then (a-1) is a factor of the polynomial
b)
1 -6 3 26 -24 | 2
2 -8 10 72
1 -4 5 36 48
When p(a) is divided by (a-2) the remainder 28/p(a)
1 -6 3 26 -24 | - 4
-4 40 172 -792
1 -10 43 198 -816
When p(a) is divided by (a-2) the remainder -816/p(a)
c) I attached an image of the long division below:
A bag contains white marbles and green marbles, 52 in total. The number of white
marbles is 3 less than 4 times the number of green marbles. How many white marbles
are there?
Answers
Answer:
Step-by-step explanation:
I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget ro thank me...
There are 41 white marbles in the bag.
Let's assume the number of green marbles is represented by "x". According to the given information, the number of white marbles is 3 less than 4 times the number of green marbles.
Number of white marbles = 4x - 3
The total number of marbles is given as 52, so we can write the equation:
Number of white marbles + Number of green marbles = Total number of marbles
(4x - 3) + x = 52
Combining like terms:
5x - 3 = 52
Adding 3 to both sides:
5x = 55
Dividing both sides by 5:
x = 11
Therefore, the number of green marbles is 11.
To find the number of white marbles:
Number of white marbles = 4x - 3
= 4 * 11 - 3
= 44 - 3
= 41
Hence, there are 41 white marbles.
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