Answer:
(A) A 95% confidence for the population mean is [$332.16, $447.84] .
(B) If the confidence level in part (a) changed from 95% to 99%, then the margin of error for the confidence interval would increase.
(C) If the sample size in part (a) changed from 19 to 22, then the margin of error for the confidence interval would decrease.
(D) A 99% confidence interval for the proportion of students who purchase used textbooks is [0.363, 0.477] .
Step-by-step explanation:
We are given that 19 students are randomly selected the sample mean was $390 and the standard deviation was $120.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = $390
s = sample standard deviation = $120
n = sample of students = 19
[tex]\mu[/tex] = population mean
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.101 < [tex]t_1_8[/tex] < 2.101) = 0.95 {As the critical value of t at 18 degrees of
freedom are -2.101 & 2.101 with P = 2.5%}
P(-2.101 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.101) = 0.95
P( [tex]-2.101 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.101 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.101 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.101 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.101 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.101 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]\$390-2.101 \times {\frac{\$120}{\sqrt{19} } }[/tex] , [tex]\$390+2.101 \times {\frac{\$120}{\sqrt{19} } }[/tex] ]
= [$332.16, $447.84]
(A) Therefore, a 95% confidence for the population mean is [$332.16, $447.84] .
(B) If the confidence level in part (a) changed from 95% to 99%, then the margin of error for the confidence interval which is [tex]Z_(_\frac{\alpha}{2}_) \times \frac{s}{\sqrt{n} }[/tex] would increase because of an increase in the z value.
(C) If the sample size in part (a) changed from 19 to 22, then the margin of error for the confidence interval which is [tex]Z_(_\frac{\alpha}{2}_) \times \frac{s}{\sqrt{n} }[/tex] would decrease because as denominator increases; the whole fraction decreases.
(D) We are given that to estimate the proportion of students who purchase their textbooks used, 500 students were sampled. 210 of these students purchased used textbooks.
Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;
P.Q. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion students who purchase their used textbooks = [tex]\frac{210}{500}[/tex] = 0.42
n = sample of students = 500
p = population proportion
Here for constructing a 99% confidence interval we have used a One-sample z-test statistics for proportions
So, 99% confidence interval for the population proportion, p is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5%
level of significance are -2.58 & 2.58}
P(-2.58 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 2.58) = 0.99
P( [tex]-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
P( [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.99
99% confidence interval for p = [ [tex]\hat p-2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] , [tex]\hat p+2.58 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ]
= [ [tex]0.42 -2.58 \times {\sqrt{\frac{0.42(1-0.42)}{500} } }[/tex] , [tex]0.42 +2.58 \times {\sqrt{\frac{0.42(1-0.42)}{500} } }[/tex] ]
= [0.363, 0.477]
Therefore, a 99% confidence interval for the proportion of students who purchase used textbooks is [0.363, 0.477] .
3C - 2/7 -5c-8/4=1/14
Justine and Meagan played a trivia game. Justine answered a question incorrectly and lost 7 points. Then Meagan answered correctly and got the opposite score. Which is the correct way to represent that “the opposite of Justine’s score was equal to Meagan’s score
Answer:
[tex]m = -j[/tex], or in this case, [tex]m=-(-7)[/tex]
Step-by-step explanation:
Assuming that Justine's score is represented by [tex]j[/tex] and Meagan's score is represented by [tex]m[/tex], we know that [tex]j[/tex] will always be the opposite of [tex]m[/tex].
To represent opposite, we put a negative sign before the variable.
This makes the current number, even if it's negative, the opposite value.
Let's test it out.
Since Justine's score is -7, substituting it into the equation makes it [tex]m=-(-7)[/tex]. We know that two negatives make a positive, so [tex]m=7[/tex].
Now let's assume Justine's score is 7. Plugging it into the equation, we get [tex]m=-(7)[/tex]. That's the same thing as [tex]m = -1(7)[/tex], and -1 times 7 is -7.
Hope this helped!
i will rate you brainliest
Answer:
First option
Step-by-step explanation:
Common ratio is greater than 1
Mike took clothes to the cleaners three times last month. First, brought 4 shirts and of slacks and paid $11.45. Then brought 7 shirts, 2 pairs of slacks, and 2 sports and paid $35.39. Finally, brought 5 shirts and 2 sports and paid $21.43 . How much was charged for each shirt, each pair of slacks, and each sports coat?
Complete Question:
Mike took clothes to the cleaners three times last month. First, brought 4 shirts and 1 pair of slacks and paid $11.45. Then brought 7 shirts, 2 pairs of slacks, and 2 sports and paid $35.39. Finally, brought 5 shirts and 2 sports and paid $21.43 . How much was charged for each shirt, each pair of slacks, and each sports coat?
Answer:
The charges
For each Shirt = $1.49
For each pair of slacks = $5.49
For each sports coat = $6.99
Step-by-step explanation:
Let Shirt = a
Let pair of slacks = b
Let sports coat = c
First, brought 4 shirts and 1 pair of slacks and paid $11.45
= 4a + b = 11.45 ..........Equation 1
b = 11.45 - 4a
Then brought 7 shirts, 2 pairs of slacks, and 2 sports and paid $35.39
= 7a + 2b + 2c = 35.39.........Equation 2
5 shirts and 2 sports and paid $21.43
5a + 2c = 21.43............Equation 3
Hence:
4a + b = 11.45 ..........Equation 1
7a + 2b + 2c = 35.39.........Equation 2
Using elimination method
Multiply Equation 2 by the coefficient of b = 1 in Equation 1
Multiply Equation 1 by the coefficient of b = 2 in Equation 2
8a + 2b = 22.9 .......Equation 4
7a + 2b + 2c = 35.39.........Equation 2
Subtracting Equation 2 from Equation 4
= a - 2c = -12.49 ........Equation 5
a = -12.49 + 2c
Subtituting -12.49 + 2c for a in Equation 3
5a + 2c = 21.43............Equation 3
5(-12.49 + 2c) + 2c = 21.43
= -62.45 + 10c + 2c = 21.43
Collecting like terms
10c + 2c = 21.43 + 62.45
12c = 83.88
c = 83.88/12
c = 6.99
5a + 2c = 21.43............Equation 3
Substituting 6.99 for c in Equation 3
5a + 2(6.99) = 21.43
5a + 13.98 = 21.43
5a = 21.43 - 13.98
5a = 7.45
a = 7.45/5
a = 1.49
4a + b = 11.45 ..........Equation 1
Substituting 1.49 for a in Equation 1
4(1.49) + b = 11.45
b = 11.45 - 4(1.49)
b = 11.45 - 5.96
b = 5.49
Therefore, since the charges
For each shirt = a
The charges for each Shirt = $1.49
For each pair of slacks = b
The charges for each pair of slacks = $5.49
For each sports coat = c
The charges for each sports coat = $6.99
Một cuộc điều tra tại một đô thị cho kết quả: 20% dân số dùng một loại sản phẩm A, 50% dân số
dùng một loại sản phẩm B, 15% dân số dùng cả hai loại A và B. Chọn ngẫu nhiên một người dân
trong đô thị đó, tìm xác suất để:
a. Người đó dùng sản phẩm A hoặc B.
b. Người đó không dùng sản phẩm A cũng không dùng sản phẩm B.
c. Người đó chỉ dùng đúng một trong hai loại sản phẩm A hoặc B.
d. Người đó chỉ dùng duy nhất sản phẩm A.
From a group of 11 people, 4 are randomly selected. What is the probability the 4 oldest people in the group were selected
The probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
Given that:
Find how many ways the 4 oldest people can be selected from the group.
Since the 4 oldest people are already determined, there is only 1 way to select them.
n = 11 (total number of people in the group) and k = 4 (number of people to be selected).To calculate the probability, to determine the total number of ways to select 4 people from the group of 11. This can be found using the combination formula:
Number of ways to choose k items from n items :
C(n,k) = n! / (k!(n-k)!)
Calculate the total number of ways to select 4 people from the group:
Plugging n and k value from given data:
C(11,4 )= 11! / (4!(11-4)!)
On simplifications gives:
C(11, 4) = 330.
Calculate the probability:
Probability = Number of ways 4 oldest people selected / Total number of ways to select 4 people
Plugging the given data:
Probability = 1 / 330
Probability ≈ 0.00303 or 0.303%.
Therefore, the probability that the 4 oldest people in the group were selected is based on combinatorics is 0.00303 or 0.303%.
Learn more about probabilities here:
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The perimeter of a triangle is 93 centimeters. If two sides are equally long and the third side is 9 centimeters longer than the others, find the lengths of the three sides.The length of each of the two equally long sides is ____ ▼ square centimeters centimeters and the length of the longer side is ____ ▼ square centimeters. centimeters.
Answer:
28 & 37 cm
Step-by-step explanation:
Perimeter(P)=9 cm
Let the equal sides(a) be x cm, then third side(b)=(x+9)cm
We have,
P=Sum of all sides
93=a+a+b
or,93=2a+(x+9)
or,93=2x+x+9
or,93-9=3x
or,84/3=x
therefore, x=28
Now,
Length of equal sides=x=28cm
Therefore, The length of each of the two equally long sides is 28 cm
The length of the longer side=(x+9)=28+9=37cm
Answer:
the other person is correct
Step-by-step explanation:
i put in the answers and i passed
100 pointer and will mark brainliest thank you. Hi! I ask that you provide a digital scatter plot image of this graph and predict the line of best fit and make sure to sketch it on the graph aswell. Thank you. Arm Span (inches) Height (inches) 58 60 49 47 51 55 19 25 37 39 44 45 47 49 36 35 41 40 46 50 58 61 And then provide the answers to these questions about the scatter plot which variable did you plot on the x-axis, and which variable did you plot on the y-axis? Explain why you assigned the variables in that way. Write the equation of the line of best fit using the slope-intercept formula y = mx + b. Show all your work, including the points used to determine the slope and how the equation was determined. What does the slope of the line represent within the context of your graph? What does the y-intercept represent Test the residuals of two other points to determine how well the line of best fit models the data. Use the line of best fit to help you to describe the data correlation. Using the line of best fit that you found, approximate how tall is a person whose arm span is 66 inches According to your line of best fit, what is the arm span of a 74-inch-tall person
I used arm span as the x-axis and height as the y-axis; arm span is the independent variable because height is typically dependent on arm span. Although the opposite could be argued for.
The equation of the line of best fit is y= 12+(7/9)x. To get the slope I used the points (37,39) and (19,25). The slope is therefore 14/18=7/9. The slope represents that height increases by 7/9 inches when arm span increases by 1 inch. The y-intercept 12 represents roughly the height when arm size is very small. I tested the residuals of the points (47,49) and (58,61). The respective predictions are 48.556 and 57.111. The respective residuals are then (49-48.556)=0.444 and (61-57.111)=3.889. It seems that the line models the data well until the x values get larger, where the performance decreases. The line of best fit with its positive slope indicates that there is a positive correlation with arm span and height.
Using the model, a person with arm span 66 inches has a height of 12+(7/9)*66= 63.333 inches. A person with 74 inches height has an estimated arm span of 62*9/7= 79.714 inches.
The equation of best fitted line is given as follows
[tex]\rm y = 0.955x+ 3.787 \\with \; R^2 = 0.951[/tex]
The y intercept 3.787 represents the height of that is independent of Arm span.
The height of the person whose arm span is 66 inches is 66.817 inch.
The arm span of a person whose height is 74 inches is 73.52 inch
According to the given data the arm span and heights are given in inches
Using Microsoft excel we can draw the scatter plot of both the variables such that arm span is on X axis and Height is on Y axis
The image for the excel work done showing calculations and scatter plot is attached.
Now we can fit the linear tread line and to find out the equation of fitted line just tick on the " show equation" line option of trend line fitting
The equation of best fitted line is given as follows
[tex]\rm y = 0.955x+ 3.787 .....(1) \\with \; R^2 = 0.951[/tex]
Slope of line of best fit = 0.955
So we can conclude that height (Y) is related to Arm span according to equation (1)
Equation (1) shows the equation of line of best fit for the given data
The y intercept 3.787 represents the height of that is independent of Arm span.
So the height of the person whose arm span is 66 inches is given following
[tex]\rm y = 0.955 \times 66+ 3.787 \\y = 66.817 \; inch[/tex]
Similarly the arm span of a person whose height is 74 inches
[tex]\rm 74 = 0.955x +3.787 \\x = 73.52 \; inches[/tex]
For more information please refer to the link given below
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If (x^2−1)/(x+1) = 3x + 5, then x + 3 =
(A) -3
(B) -2
(C) 0
(D) 2
(E) 4
Evaluate b h for b = 12 and h = 2 . 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.
Answer:63
Step-by-step explanation:
What number should replace the question mark?
Answer:
1 Cruz it makes sense I hope this helps tho
Help please!??!!?!?
9514 1404 393
Answer:
a) CP = SP/1.1
b) CP = $59.50
c) GST = $5.95
Step-by-step explanation:
a) Divide by the coefficient of CP.
SP = 1.1×CP
CP = SP/1.1
__
b) Use the formula with the given value.
CP = $65.45/1.1 = $59.50
__
c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.
GST = SP -CP = $65.45 -59.50 = $5.95
GST = CP×0.10 = $59.50 × 0.10 = $5.95
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
Answer:
Both functions have the same slope.The origin is the y-intercept for the function expressed in the table.The table and the graph express an equivalent function.Step-by-step explanation:
Both functions have the same slope
The slope is m in the equation; y =mx+c which is the formula for a straight line.
m = change in Y/change in x
Using 2 points: (1,3/4) and ( 4,3) from the table;
= (3 - 3/4) / ( 4 - 1)
= 2.25/3
= 0.75 which is 3/4 which is the same as the slope of the function in the equation.
The origin is the y-intercept for the function expressed in the table.
Slope of function in table is known to be 0.75. Find c to complete equation.
3 = 0.75 ( 4) + c
3 = 3 + c
c = 0
c is the y-intercept. The origin of a line is 0 so if c is 0 then the origin is the y intercept.
The table and the graph express an equivalent function.
The function for the table as calculated is;
y = 0.75x + 0
y = 0.75x
This is the same as the function for the equation for the graph which is y = 3/4x.
Answer:Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The table and the graph express an equivalent function.
Step-by-step explanation:
Compare the linear functions expressed below by data in a table and by an equation.
A 2-column table with 4 rows. Column 1 is labeled x with entries negative 6, negative four-thirds, 1, 4. Column 2 is labeled y with entries negative StartFraction 9 Over 2 EndFraction, negative 1, three-fourths, 3. y = three-fourths x.
Which of the following statements are true? Select all that apply.
If the equation were graphed, it would be a horizontal line.
Both functions have the same slope.
The origin is the y-intercept for the function expressed in the table.
The linear equation does not have a y-intercept.
The table and the graph express an equivalent function.
The number of unique visitors to the college website can be approximated by the formula N(t)=410(1.32)t where t represents the number of years after 1997 when the website was created. Approximate to the nearest integer the number of unique visitors to the college website in the year 2020.
Answer:
243212
Step-by-step explanation:
Substitute the given value of t into the given formula. To find t, subtract 1997 from 2020.
2020−1997=23
Now substitute 23 into the equation for t and calculate.
N(t)N(23)==≈410(1.32)t410(1.32)23243,212
The number of unique visitors to the college website in the year 2020 was approximately 243,212.
Select the table representing a linear function. (Graph them if necessary.)
O A. x 0
7
2 3
y 1 2 56
B. х 0
7
3
2
0
y -2 -1
-1
O c. xo
1
N
3
y 10 12 14 16
-OD. x 0 1 2 3
y 5 3 1 2
Answer:
Option C
Step-by-step explanation:
the linear equation y = 2x+10 matches with option c
which of the following best describes the bases of a cylinder? A. Congruent B. Polygons C. Parallel D. Discs (Check All That Apply)
Answer:
A. Congruent and D. Discs
Step-by-step explanation:
You won't see a cylinder that doesn't have congruent bases
Look at the shape of the bases and look at a disc compare their shape
We can describe the bases of a cylinder as congruent.
What is the volume of cylinder?The volume of cylinder is given by -
V = πR²h
Given is to describe the bases of a cylinder.
The cylinders are uniform in cross - section. Therefore, the bases of the cylinder will have the same area. So, we can conclude that the given bases are congruent.
Therefore, we can describe the bases of a cylinder as congruent.
To solve more questions on cylinders, visit the link below-
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Use the graph showing Debra's account balance to answer the question that follows. ^
About how long will it take for Debra's account balance to equal $60?
A - 6 months
B - 6 years
C - 3 months
D - 3 years
Answer: 2 years
Step-by-step explanation:
In the given graph, we have
Account Balance ($) on y-axis
Time (years) on x-axis.
To know the time taken to get a balance of $60 , we check the point corresponding to 60 at y-axis and then join it to the line of the function and stop.
Then from there we drop a line to x-axis.
We get x=2.
That is it will take 2 years to get $60 balance in Debra's account.
So the correct answer is 2 years.
Help me with this question plz
9514 1404 393
Answer:
17
Step-by-step explanation:
The points at the ends of the interval are ...
(0, f(0)) = (0, 0)
(7, f(7)) = (7, 119)
The average rate of change is given by the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (119 -0)/(7 -0) = 119/7 = 17
At an airport, 76% of recent flights have arrived on time. A sample of 11 flights is studied. Find the probability that no more than 4 of them were on time.
Answer:
The probability is [tex]P( X \le 4 ) = 0.0054[/tex]
Step-by-step explanation:
From the question we are told that
The percentage that are on time is p = 0.76
The sample size is n = 11
Generally the percentage that are not on time is
[tex]q = 1- p[/tex]
[tex]q = 1- 0.76[/tex]
[tex]q = 0.24[/tex]
The probability that no more than 4 of them were on time is mathematically represented as
[tex]P( X \le 4 ) = P(1 ) + P(2) + P(3) + P(4)[/tex]
=> [tex]P( X \le 4 ) = \left n } \atop {}} \right.C_1 p^{1} q^{n- 1} + \left n } \atop {}} \right.C_2p^{2} q^{n- 2} + \left n } \atop {}} \right.C_3 p^{3} q^{n- 3} + \left n } \atop {}} \right.C_4 p^{4} q^{n- 4}[/tex]
[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{11- 1} + \left 11 } \atop {}} \right.C_2p^{2} q^{11- 2} + \left 11 } \atop {}} \right.C_3 p^{3} q^{11- 3} + \left 11 } \atop {}} \right.C_4 p^{4} q^{11- 4}[/tex]
[tex]P( X \le 4 ) = \left 11 } \atop {}} \right.C_1 p^{1} q^{10} + \left 11 } \atop {}} \right.C_2p^{2} q^{9} + \left 11 } \atop {}} \right.C_3 p^{3} q^{8} + \left 11 } \atop {}} \right.C_4 p^{4} q^{7}[/tex]
[tex]= \frac{11! }{ 10! 1!} (0.76)^{1} (0.24)^{10} + \frac{11!}{9! 2!} (0.76)^2 (0.24)^{9} + \frac{11!}{8! 3!} (0.76)^{3} (0.24)^{8} + \frac{11!}{7!4!} (0.76)^{4} (0.24)^{7}[/tex]
[tex]P( X \le 4 ) = 0.0054[/tex]
Help please I need answers for these questions
I think because the angles are corresponding/opposite to each other u equate them to 180°
Find an equation for the surface consisting of all points P in the three-dimensional space such that the distance from P to the point (0, 1, 0) is equal to the distance from P to the plane y
Answer:
x^2 +4y +z = 1
Step-by-step explanation:
Surface consisting of all points P to point (0,1,0) been equal to the plane y =1
given point, p (x,y,z ) the distance from P to the plane (y)
| y -1 |
attached is the remaining part of the solution
A woman bought some large frames for $17 each and some small frames for $6 each at a closeout sale. If she bought 18 frames for $141, find how many of each type she bought. She bought ____ large frames.
Answer:
3 large frames
Step-by-step explanation:
Let the large frames she bought be x in number and small frames be y in number.
ATQ, 17x+6y=141 and x+y=18. Solving it, we will get x=3 and y=15. So she bought 3 large frames
A cubical sandbox has a volume of 91.125 cubic inches. What is the side length of the
sandbox?
Hey there! I'm happy to help!
To find the volume of a cube, you simply cube the side length (multiply it by itself three times). This is because all of the sides of a cube are the same and if you multiply the length by the width by the height it is the same number multiplied by itself three times.
We already know that the volume is 91.125 cubic inches. To find the side length, we simply do the cube root on our calculator, which tells us what number we cube to get 91.125.
∛91.125=4.5
Therefore, the side length of the sandbox is 4.5 inches.
I hope that this helps! Have a wonderful day! :D
a wolf population of 850 wolves is increasing by 7% each year. Find the wolf population after 7 years
Answer:
1,267 wolvesStep-by-step explanation:
Initial population of wolf = 850 wolves
If the wolves increases by 7% each year, yearly increment will be 7% of 850
= 7/100 * 850
= 7*8.5
= 59.5 wolves.
This shows that the wolves increases by 59.5 each year.
After 7 years, increment will be equivalent to 59.5 * 7 = 416.5
The wolf population after 7 years = Initial population + Increment after 7 years
= 850 + 416.5
= 1266.5
≈ 1267 wolves
Hence the population of the wolves after 7 years is approximately 1,267 wolves
If the random variable X is normally distributed with mean of 50 and standard deviation of 7, find the 9th percentile.
Answer:
The 9th percentile is 40.52.
Step-by-step explanation:
We are given that the random variable X is normally distributed with a mean of 50 and a standard deviation of 7.
Let X = the random variable
The z-score probability distribution for the normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean = 50
[tex]\sigma[/tex] = standard deviation = 7
So, X ~ Normal([tex]\mu=50, \sigma^{2} = 7^{2}[/tex])
Now, the 9th percentile is calculated as;
P(X < x) = 0.09 {where x is the required value}
P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-50}{7}[/tex] ) = 0.09
P(Z < [tex]\frac{x-50}{7}[/tex] ) = 0.09
Now, in the z table the critical value of x that represents the below 9% of the area is given as -1.3543, i.e;
[tex]\frac{x-50}{7}=-1.3543[/tex]
[tex]x-50=-1.3543 \times 7[/tex]
[tex]x=50 -9.48[/tex]
x = 40.52
Hence, the 9th percentile is 40.52.
I need help with this
Answer:
The fraction that represents the heart in the diagram shown is 7/3
Step-by-step explanation:
For this problem, we have to find the fraction expressed by the number line in the diagram shown.
First off, we know that the fraction will be between 2 and 3. Second, we know that each little dash between 2 and 3 represents 1/6.So, let's use this information to find the fraction.
Since the heart is two dashes away from 2, then this part of the fraction is 2/6 which can also be simplified to 1/3.
2 1/3
Since we can not have a mixed fraction, then we are going to turn this mixed number into an improper fraction. We do this by multiplying 2 with the denominator (which is 3) and adding the numerator (which is 1) to that product. Our denominator will stay the same in the final fraction.
2 1/3 = 7/3
So, the fraction represented by the heart is 7/3
Answer:
16/7
Step-by-step explanation:
There are 7 divisions between the numbers 2 and 3
So the denominator is 7
The heart is at the second mark
We are past the 2 mark so it is
2 2/7
Changing this from a mixed number to an improper fraction
(7*2+2) /7
16/7
Solve this and I’ll give u 5 stars and brainleist
Answer:
notice: temperature rises quickly at sunrise, and drops before sunsetwonder: whether this location is shaded by mountains later in the dayStep-by-step explanation:
notice
The temperature starts off below zero in the early morning and stays cold until the sun comes up. Then it warms rapidly to an above zero temperature that peaks in early afternoon. Once the sun gets lower, the temperature starts cooling off again. (The daily temperature range of 25-27 degrees is pretty typical for partly-cloudy sky conditions and stable weather.)
wonder
We wonder if this isn't a location that is on the east- or north-side of a mountain, or in a mountain valley, where the sun hits it early and is shaded later in the day. (The topo map attached seems to show it is in such a location.)
write the first 10 multiples of 2 and 3 and find LCM.
Answer:
multiples of 2 2,4,6,8,10,12,14,16,18,20
multiples of 3 3,6,9,12,15,,18,21,24,27,30
Step-by-step explanation:
Lcm is 6
A farmer wishes to construct a fence around his rectangular field. The farmer has 150 feet of fence and
wishes to have the length be three more than the width. What is the width of the field. Make sure and
include feet in your answer.
Help
Answer:
The width is 36 feet
Step-by-step explanation:
If the width of the fence is x then its length is x+3.
The perimeter is 150 feet, so we have the equation:
2(x + x + 3) = 150
4x + 6 = 150
x = 144/4 = 36 feet
T= 2pi times the sqrt of l/g (l=2.0m; g= 10m/s^2
Answer:
v (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?
Step-by-sv (m/s) a(m/s2). √. ½. 0. ¼. √. -¼. Movimiento circular y M.A.S. Un punto se mueve ... como la que se ilustra en la figura, llamada onda cuadrada. ... Movimiento Armónico Simple I. Una partícula cuya masa es de 1 g vibra con movimiento ... Multiplicando por el Periodo de oscilación del sistema T (con ... distancia de 10 m?tep explanation: