Using the normal distribution, it is found that there is a 0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem, the parameters are given as follows:
[tex]\mu = 8.4, \sigma = 1.8, n = 32, s = \frac{1.8}{\sqrt{32}} = 0.3182[/tex]
The probability that their mean repair time is less than 8.9 hours is the p-value of Z when X = 8.9, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.9 - 8.4}{0.3182}[/tex]
Z = 1.57
Z = 1.57 has a p-value of 0.9418.
1 - 0.9418 = 0.0582.
0.0582 = 5.82% probability that their mean repair time is less than 8.9 hours.
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What was his mistake?
Circle the first line.
His mistake was: He substituted y from 2nd equation in 1st equation incorrectly. There is a minus sign before y and it wasn't taken into the account.
The correct steps are:
2x - y = 18
2x - (4x + 2) = 18
2x - 4x - 2 = 18
-2x - 2 = 18
-2x = 20
x = -10
y = 4x + 2
y = 4(-10) + 2
y = -40 + 2
y = -38
Work out the perimeter of the shaded shape.
3cm
8cm
5cm
7cm
The diagram is not drawn to scale.
Answer:
23 because ya
Step-by-step explanation:
uesssssdssssssss
can someone please answer this fast! thanks
Answer:
The choice C.
[tex] {x}^{ \frac{5}{2} } [/tex]
Step-by-step explanation:
[tex] \frac{ {x}^{3} }{ \sqrt{x} } = \frac{ {x}^{3} }{ {x}^{ \frac{1}{2} } } = {x}^{3} \times {x}^{ - \frac{1}{2} } \\ = {x}^{3 \times - \frac{1}{2} } = {x}^{ \frac{5}{2} } [/tex]
Or ;
[tex] \frac{ {x}^{3} }{ \sqrt{x} } = {x}^{2} \sqrt{x} = {x}^{2} \times {x}^{ \frac{1}{2} } \\ = {x}^{2 + \frac{1}{2} } = {x}^{ \frac{5}{2} } [/tex]
help please dont know how to do this
if f(x) = 4x²-2 then f(-3) is
Step-by-step explanation:
We are going to plug -3 into the equation of f(x) = 4x²-2.
f(-3) = 4(-3)²-2
f(-3)=36-2
f(-3)=34
The answer to this question is 34.
I hope this helps!! :)
Need help with this
n = 66
Step-by-step explanation:
you can make a proportion 3/99 = 2/x
[tex] \frac{3}{99} = \frac{2}{x} [/tex]
99 * 2= 198
3 * x = 3x
so the equation would be 198 = 3x
than do 198 ÷ 3 on ur calculator
so x (or n in this context) would equal 66
A Clothing shop sold 140 Jackets an d 60 rain coats during the winter sale . Find the ratio of the number of raincoats sold to the Jackets sold.
Answer:
3:7
Step-by-step explanation:
60 ratio 140
Divide both sides by 10
6 ratio 14
Divide both sides by 2
3 ratio 7
3:7 ✔️
Pls help! I will give brainliest! And pls no links. What is 29 oz to Ib?
Answer:
1.8125 lb(pounds)
Step-by-step explanation:
there are 16 oz in 1 lb
so 29/16 = 1.8125
Simplify the expression (10 + 3i)(10 - 3i).
Answer:
109
Step-by-step explanation:
[tex]\textbf{Assuming}~ i ~\textbf{as the imaginary unit, where}~ i = \sqrt{-1}~ \textbf{and}~ i^2 = -1\\\\\textbf{Given that,}\\\\~~~(10+3i)(10-3i)\\\\=10^2 -(3i)^2~~~~~~~~~~;\textbf{Difference of two squares} ~a^2 -b^2 = (a+b)(a-b)\\\\=100-9i^2\\\\=100-9(-1)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;{i^2 = -1}\\\\=100+9\\\\=109[/tex]
[tex](a-b)(a+b)=a^2-b^2[/tex]
Therefore
[tex](10 + 3i)(10 - 3i)=100-9i^2[/tex]
A quadrilateral is formed by the points a(1, -1), b(0, 3), c(5, 5), and d(6, 1). plot the points and use the distance formula to find the lengths of all 4 sides. what type of quadrilateral is this?
The type of quadrilateral is rectangle.
What is distance formula?
The distance between coordinate P(x1 , y1) and coordinate Q(x2 , y2) is calculated using the distance formula: d = √[(x2 - x1)² + (y2 - y1)²]
Given coordinates: a(1, -1), b(0, 3), c(5, 5), and d(6, 1).
ab= √(0-1)² + (3+1)²
ab= √17
bc= √(5-0)² + (5-3)²
bc= √29
cd= √(6-5)² + (1-5)²
cd= √17
da=√(6-1)² + (1+1)²
da= √29
ac=√(5-1)² + (5+1)²
ac= √16+36
ac= √52
bd =√(6-0)² + (1-3)²
bd= √36+4
bd= √40
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Answer:
PARALLELOGRAM
Step-by-step explanation:
opposite sides are congruent, but it doesn't have 4 right angles or 4 congruent sides; this means it's a parallelogram (and not a rectangle or rhombus)
An isosceles trapezoid has base lengths of 12 in and 18 in. If the area of the larger shaded triangle is 72 square inches, find the area of the smaller shaded triangle.
Answer:
32 in²
Step-by-step explanation:
length ratio = [tex]\frac{12}{18}[/tex] = [tex]\frac{2}{3}[/tex]
area ratio = ([tex]\frac{2}{3}[/tex] )² = [tex]\frac{4}{9}[/tex]
smaller area = 72 × [tex]\frac{4}{9}[/tex] = 8 × 4 = 32 in²
The area of the smaller shaded triangle is approximately 31.98 square inches.
The area of a triangle is given by the formula: A = 1/2 * base * height. In an isosceles trapezoid, the two parallel sides are equal in length. In this case, the base lengths of the trapezoid are 12 inches and 18 inches.
To find the area of the larger shaded triangle, we need to determine its base and height.
The base of the larger shaded triangle is the same as the length of the larger base of the trapezoid, which is 18 inches.
Let's denote the height of the larger shaded triangle as h1. Using the formula for the area of a triangle, we have: 72 = 1/2 * 18 * h1 To solve for h1, we can multiply both sides of the equation by 2 and divide by 18: 2 * 72 = h1 h1 = 144 / 18 h1 = 8 inches
So, the height of the larger shaded triangle is 8 inches. Now, let's find the area of the smaller shaded triangle. The base of the smaller shaded triangle is the same as the length of the smaller base of the trapezoid, which is 12 inches. Let's denote the height of the smaller shaded triangle as h2. Using the formula for the area of a triangle, we have: A = 1/2 * base * height A = 1/2 * 12 * h2
We don't know the value of h2, but we do know that the two shaded triangles are similar because they have equal angles. This means that the ratio of the heights of the two triangles is the same as the ratio of their bases. The ratio of the bases of the two triangles is 18/12 = 3/2.
So, the ratio of the heights of the two triangles is also 3/2.
To find the height of the smaller shaded triangle, we can set up a proportion: h2 / 8 = 2/3 Cross-multiplying, we have: 3 * h2 = 8 * 2 3 * h2 = 16 h2 = 16 / 3 h2 = 5.33 (rounded to two decimal places)
So, the height of the smaller shaded triangle is approximately 5.33 inches.
Now, we can find the area of the smaller shaded triangle using the formula: A = 1/2 * base * height A = 1/2 * 12 * 5.33 A = 31.98 square inches (rounded to two decimal places)
Therefore, the area of the smaller shaded triangle is approximately 31.98 square inches.
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A membership at a yoga studio costs $35 per month.
Write an equation for the cost of the membership,that you pay if you keep your membership for months.
Answer:
35×(m)=c
Step-by-step explanation:
m=months
c=cost
Suppose the length and the width of the sandbox are doubled.
The percentage change in perimeter is 100%.
The percentage change in area is 300%
How to find perimeter and area?The perimeter of the sandbox = 2l + 2w
where
l = lengthw = widthTherefore,
perimeter = 2(10) + 2(6)
perimeter = 20 + 12 = 32 ft
The area of the sand box = lw
area = 10 × 6 = 60 ft²
If the length and width are doubled,
length = 2(10) = 20 ft
width = 2(6) = 12 ft
hence,
perimeter = 2(20) + 2(12) = 40 + 24 = 64 ft
area = 12 × 20 = 240 ft²
Therefore,
percentage change in perimeter = 64 - 32 / 32 × 100 = 100%
percentage change in area = 240 - 60 / 60 × 100 = 18000 / 60 = 300%
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Germaine measured the height of a plant, H, in centimeters (cm) as a function of days, d, since he planted it in
his yard. The following table shows his data.
d 0 2 4 6 8 10 12
H(d) 8.2 9.6 11.0 12.4 13.8 15.2 16.6
What is the rate of change of the function?
O 1.7 cm per day
O 8.4 cm per day
O 1.4 cm per day
O 0.7 cm per day
The rate of change of the function the height of a plant is gotten as; D: 0.7
How to find the rate of change?To find the rate of change, we will use the formula;
Rate of change = (y2 - y1)/(x2 - x1)
From the given table, we can solve for the rate of change by picking two consecutive points to get;
Rate of change = (9.6 - 8.2)/(2 - 0)
Rate of change = 1.4/2
Rate of change = 0.7
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Suppose we want to assess the effect of a one-day SAT prep class at a 5% level of significance. Scores on the SAT writing exam can range from 200 to 800. A random sample of 50 students takes the SAT writing test before and after a prep class. We test the hypotheses: : : where is the mean of the difference in SAT writing scores (after minus before) for all students who take the SAT prep class. The sample mean is 5 with a standard deviation of 18. Since the sample size is large, we are able to conduct the T-Test. The T-test statistic is approximately 1.96 with a P-value of approximately 0.028. What can we conclude
The conclusion is that since the value of 0.028 is less than 0.05 so we reject the null hypothesis at 5% level of significance and conclude that the mean of the difference in SAT writing scores for all students who take SAT prep class is equal to 0.
What is a null hypothesis?A null hypothesis is a hypothesis that there is no significant difference between specified populations, any observed difference being due to sampling error.
Here, the effect of a one-day SAT prep class at a 5% level of significance was assessed. Since the value of 0.028 is less than 0.05 so we reject the null hypothesis at 5% level of significance and conclude that the mean of the difference in SAT writing scores for all students who take SAT prep class is equal to 0.
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If tan theta = -3/4 and theta is in Quadrant IV, cos2theta =, and tan2theta =
Step-by-step explanation:
please mark me as brainlest
In a group of friends were to eat 13 candies, there would be 8 candies left. if each friend were to eat 15 candies, all the candies would be gone. how many friends are there?
Answer:
4
Step-by-step explanation:
from 13 to 15 you added two more so you have to do 8 divided by 2 which is 4
(8 x 10^5) x (8 x 10^5)
Find the product write your answer in scientific notation
Answer:
6.4 x 10¹¹
Step-by-step explanation:
(8 x 10⁵)(8 x 10⁵) = 6.4 x 10¹¹
find the value of y when x=3
y=10-3x
Answer:
y=1
Step-by-step explanation:
In order to solve this problem, you have to substitute 3 in for x. Then you would multiply 3 by 3, which equals 9. Subtract 9 from 10, equals 1.
I included a picture so you can see the work.
Hope this helped!
Solve the inequality.
−13x+10>17
Which inequality represents the solutions to this inequality?
a) x<7x<7
b) x>−21x>−21
c) x<−21x<−21
d) x>7x>7
The solution to inequality is less than the negative of 21. Then the correct option is C.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The inequality is given below.
−(1/3)x + 10 > 17
Then the solution to the inequality will be
−(1/3)x + 10 > 17
−(1/3)x > 17− 10
−(1/3)x > 7
When the sign is changed then the equality sign also changed.
(1/3)x < −7
x < − 21
The value of x is less than the negative of 21.
Thus, the correct option is C.
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How many units is -14 away from 0
Answer:
14
Step-by-step explanation:
|-14|=14
is this true or false? please help
Answer:
true jufhjjzjsjjajajw
On a coordinate plane, a circle has a center at (negative 2, 0). Point (negative 2, 4) lies on the circle.
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
Does the point (1, StartRoot 7 EndRoot) lie on the circle shown?
Explain.
Yes, the distance from (–2, 4) to (1, ) is 4 units.
Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.
No, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is not 4 units.
No, the distance from (–2, 4) to (1, StartRoot 7 EndRoot) is not 4 units.
The correct answer to where the point(1, StartRoot 7 EndRoot) lies on the circle is A. Yes, the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units
What is a Coordinate Plane?This refers to the tool that is used to graph points on a two-dimensional plane that intersects two number lines.
Hence, given the information in the given diagram, there is a coordinate plane that shows a circle at the center that has certain values on the y and x-axis.
We can state that the point (1, StartRoot 7 EndRoot) lies on the circle shown because the distance from (–2, 0) to (1, StartRoot 7 EndRoot) is 4 units.
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Answer: A on edge
Step-by-step explanation:
because i said so
You move left 5 units. You end at (-1, 5). Where did you start?
Answer:
(4,5)
Step-by-step explanation:
Hello!
If you move 5 units to the left, you change the x-value in (x, y) by -5.
Let the original x-value be x:
x - 5 = -1x = 4The original x-value is 4. Since you didn't change the y-value (up/down), you can keep the same y-value for the coordinate.
The original point was at (4,5)
Answer:
You started at (4, 5)
Step-by-step explanation:
The first number of coordinate pair is x. you started at the right and THEN moved the the left, as stated in the question. So -1 + 5 is 4.
So you started at (4, 5)
A cashier earns $7 an hour. if x is the number of hours worked, which function represents the cashier’s earnings? y = 7x y = x superscript 7 y = startfraction 7 over x endfraction y = 7
Answer:
y=7x
Step-by-step explanation:
The job pays $7 per 1 hour so to find out how much money you get for x hours, you would multiply the hourly rate ($7) by the amount of hours (x)
Answer:
y=7x
Step-by-step explanation:
edge review 2022
Which of the following best describes the pattern in the diagram shown below? 2 3 O A. As you move from left to right, the number of points in the star decreases by 1. OB. As you move from left to right, the number of points in the star increases by 1. O C. As you move from right to left, the number of points in the star increases by 1. O D. As you move from left to right, the number of points in the star remains the same.
Annie choose a red shirt at random. what is the likelihood that the shirt's large, given that it's red?
The likelihood that the shirt is large given that it is red is 14.29%
What is the probability?Probability determines the likelihood that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The likelihood that the shirt is large given that it is red = number of large red shirts / total number of red shirts
5/35 = 14.29%
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How do I solve for y on this?
(4x-6)° and (x+6y)° are both 90° because they are perpendicular, so:
4x-6= 90
4x= 96
x= 24
x+6y=90
24+6y=90
6y=66
y=11
What is the solution to this system of equations?
Answer:
C
Step-by-step explanation:
C. x=7, y=5
(5)(5)(5)(5)(5)(5) i do not understand what that means or what am i supposed to do
Answer:
Your supposed to multiply 5*5*5*5*5*5 so the answer is 15,625