The weekly amount of money spent on maintenance and repairs by a company was observed, over a long period of time, to be approximately normally distributed with mean $440 and standard deviation $10. How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.05
Answer:
$456.45 should be budgeted.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean $440 and standard deviation $10.
This means that [tex]\mu = 440, \sigma = 10[/tex]
How much should be budgeted for weekly repairs and maintenance so that the probability the budgeted amount will be exceeded in a given week is only 0.05?
This is x for which
P(X > x) = 0.05
So this is the 100 - 5 = 95th percentile, which is X when Z has a pvalue of 0.95, so X when Z = 1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 440}{10}[/tex]
[tex]X - 440 = 10*1.645[/tex]
[tex]X = 456.45[/tex]
$456.45 should be budgeted.
Find the volume of a pyramid with a square base, where the area of the base is
8.3 m² and the height of the pyramid iş 9.8 m. Round your answer to the nearest
tenth of a cubic meter.
Answer: 27.1 cubic meters
Step-by-step explanation: The area for finding the volume of a pyramid is V=1/3 Bh, where B= base, and h=height. To substitute in the numbers from the problem, you get V=1/3 times 8.3 times 9.8. 9.8 times 8.3 is 81.34. 81.34 times 1/3 rounds to 27.1.
Solve for t: F =2t+k/3g
Answer:
[tex]F = \frac{2t + k}{3g} \\3Fg = 2t+k\\3Fg - k = 2t\\t = \frac{3Fg - k}{2}[/tex]
A triangle has an area of 37.5 inches the height of the triangle is 20 inches what is the length of the base of the triangle?
Answer:
base = 3.75 inches
Step-by-step explanation:
37.5 = 20b/2
37.5 = 10b
b = 3.75
Calculator
13 in
94
7.5 in.
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final
answer to the nearest tenth.
Answer:
9165.0
Step-by-step explanation:
13*94*7.5 = 9165.0
Determine the measures of the following; (SOMEONE PLS) :v
arc AC=27°
arc BD=33°
arc CB=120°
hope it helps you ❣❣Mark me as brainliest
Cup G has a diameter of 4 in. and a height of 8 in. Find the volume of Cup G.
Answer:
32pi
Radius=1/2 Diameter
radius=2
Area of circle= pi*radius^2= 4pi
4pi*8=32 pi
I need help what's the answer anyone?
Answer:
B
Step-by-step explanation:
Element X is a radioactive isotope such that its mass decreases by 59% every day. If an experiment starts out with 390 grams of Element X, write a function to represent the mass of the sample after tt days, where the hourly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage rate of change per hour, to the nearest hundredth of a percent.
The function representing the mass of Element X after t days is [tex]{\text} M(t) = 390 * (0.41)^t[/tex], and the percentage rate of change per hour is 2.46%.
Given:
Initial mass = 390 grams
Rate of decay = 59% = 0.59
The general form of an exponential decay function is:
[tex]{\text}y = a (1 - r)^t[/tex]
So, the function to represent the mass of the sample after t days would be:
[tex]{\text} (t) = 390 * (1 - 0.59)^t[/tex]
Simplifying this equation gives
[tex]M(t) = 390 * (0.41)^t[/tex]
Now, the hourly rate of change is
Hourly rate of change = 0.59 / 24
= 0.024583
= 2.46% per hour.
Therefore, the function is [tex]{\text} M(t) = 390 * (0.41)^t[/tex]and the rate of change is 2.46%.
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Use the equation below to find y, if m=6, x=4, and b= 15. y=mx-b
Answer:
9
Step-by-step explanation:
Y = MX-B,
therefore Y = (6*4) - 15,
so Y = 24 - 15
Y = 9
sarah walks 1/4 mile every 1/2 hour
Answer:
To find ratio mph (miles PER hour), we can write the information given as a fraction. (The miles will go on top and the number of hours will go on the bottom).
1/2=.5 miles
1/4-.25 miles
So we have .5miles/.25 hours
From here, we can do 2 things: divide to get 2miles/hour or you can see that you can reduce the fraction (.5/2=.25 and .25/.25=1). So again we get 2/1 miles per hour OR 2 mph
Hope that helps,
Gracie
Find the perimeter of the triangle to the right
9514 1404 393
Answer:
76.5 units
Step-by-step explanation:
This is an interesting question. The side lengths are proportional to the sine of the opposite angle. So, we can find a scale factor for the given length by adding the sines of the angles and dividing by the sine of the angle opposite the given side.
The three angles are ...
43°, 63° and 74° (the supplement of the sum of the other two)
So, the scale factor mentioned above is ...
(sin(43°) +sin(63°) +sin(74°))/sin(74°) ≈ 2.636396
Then the perimeter of the triangle is ...
(2.636396)(29) ≈ 76.5 . . . units
Triangle ABC has vertices A (6, 1), B (1,7), and C (-3, -2). The translation to create triangle A'B'C' is (x, y) + (x-1, y +2).
Which of the following will be the coordinates of the vertices of triangle A'B'C?
A (5,2), (0, -4), (0,9)
B (5,3), (0, -4), (0,8)
C (5,3), (0,9), (-4,0)
D (5,2), (1, -3), (0,9)
Answer:
I think C is the answer
15 Points, please give full equation on how you answer.
3) Suppose you deposit $10,000 in a savings account that pays interest at an annual rate of 5%
compounded quarterly. How many years will it take for the balance in your savings account to reach
$12,000?
9514 1404 393
Answer:
3.67 years
Step-by-step explanation:
The amount is found using the compound interest formula.
A = P(1 +r/n)^(nt)
for principal P invested at annual rate r compounded n times per year for t years.
We can solve this for t:
A/P = (1 +r/n)^(nt) . . . . divide by P
log(A/P) = (nt)log(1 +r/n) . . . . take the logarithm
t = log(A/P)/(n·log(1 +r/n)) . . . . divide by the coefficient of t
Filling in the given values, we find ...
t = log(12000/10000)/(4·log(1 +0.05/4)) ≈ 3.6692
It will take about 3.67 years for the balance to reach $12,000.
Answer:
the answer is 3.67 years
Determine the scientific notation for the number.
124,900,000,000
Answer: 1.249 × 10^11
Step-by-step explanation:
The coordinate point F(-8, 0) after a dilation with scale factor of 0.25, centered at the origin, becomes the point
O (-2,0)
O (-2, 0.25)
O (2, 0.25)
O (2,0)
Answer:
[tex](-2,\, 0)[/tex].
Step-by-step explanation:
Dilate a point [tex](x,\, y)[/tex] by a scale factor of [tex]r[/tex] with [tex](a,\, b)[/tex] as the center, and the resultant point would be at [tex](a + r\, (x - a),\, b + r\, (y - a))[/tex].
In this question:
Point to dilate: [tex](x,\, y) = (-8,\, 0)[/tex].
Scale factor: [tex]r = 0.25[/tex].
Center of dilation: [tex](a,\, b) = (0,\, 0)[/tex].
The resultant point would be:
[tex](0 + 0.25\, (-8 - 0),\, 0 + 0.25\, (0 - 0))[/tex], which simplifies to [tex](-2,\, 0)[/tex].
Help please some one
Answer:
i dont know im just doing this for the points
6. If a person adopts a pet, it's either a cat or a dog. 25% of the time, it's a cat and 75% of the time, it's a dog. If you meet someone at the shelter that adopted three pets, what's the probability that they got either: three cats or three dogs? Show your calculation and give your single answer as a decimal.
Answer:
0.0156 probability that they got three cats.
0.4219 probability that they got three dogs.
Step-by-step explanation:
For each person there are only two possible outcomes. Either they adopted a dog, or a cat. The probability of a person adopting a cat or a dog is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Three people:
This means that [tex]n = 3[/tex]
What's the probability that they got three cats?
25% of the time it's a cat adopted, which means that [tex]p = 0.25[/tex]
This is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.25)^{3}.(0.75)^{0} = 0.0156[/tex]
0.0156 probability that they got three cats.
What's the probability that they got three dogs?
75% of the time it's a dog adopted, which means that [tex]p = 0.75[/tex]
This is P(X = 3). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{3,3}.(0.75)^{3}.(0.25)^{0} = 0.4219[/tex]
0.4219 probability that they got three dogs.
find the area of this polygon - PLZZZZZ HELP I WILL GIVE 30 points T^T
Answer:
82 m should be correct i hope
Step-by-step explanation:
A certain company sends 50% of its overnight mail parcels via express mail service E1. Of these parcels, 1% arrive after the guaranteed delivery time (denote the event late delivery by L). Suppose that 10% of the overnight parcels are sent via express mail service E2 and the remaining 40% are sent via E3. Of those sent via E2 on 2% arrive late, whereas 5% of the parcels handled by E3 arrive late.
A. If a record of an overnight mailing is randomly selected from the company's file, what is the probability that the parcel went via El and was late?
B. What is the probability that a randomly selected parcel arrived late?
C. If a randomly selected parcel has arrived on time, what is the probability that is was not sent via E1?
Answer:
A. 0.005 = 0.5% probability that the parcel went via El and was late
B. 0.027 = 2.7% probability that a randomly selected parcel arrived late.
C. 0.8148 = 81.48% probability that is was not sent via E1
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
A. If a record of an overnight mailing is randomly selected from the company's file, what is the probability that the parcel went via El and was late?
50% are chosen via E1, and of those, 1% were late. So
[tex]p = 0.5*0.01 = 0.005[/tex]
0.005 = 0.5% probability that the parcel went via El and was late
B. What is the probability that a randomly selected parcel arrived late?
1% of 50%(via E1)
2% of 10%(via E2)
5% of 40%(via E3).
So
[tex]p = 0.01*0.5 + 0.02*0.1 + 0.05*0.4 = 0.027[/tex]
0.027 = 2.7% probability that a randomly selected parcel arrived late.
C. If a randomly selected parcel has arrived on time, what is the probability that is was not sent via E1?
Conditional Probability.
Event A: Late
Event B: Not sent via E1
0.027 = 2.7% probability that a randomly selected parcel arrived late, which means that [tex]P(A) = 0.027[/tex]
Late and not sent via E1:
2% of 10%(via E2)
5% of 40%(via E3).
So
[tex]P(A \cap B) = 0.02*0.1 + 0.05*0.4 = 0.022[/tex]
Desired probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.022}{0.027} = 0.8148[/tex]
0.8148 = 81.48% probability that is was not sent via E1
A school buys 1,950 pencils. The pencils are sold in boxes, with 30 pencils in each box. If each box costs $4.05, what is the total cost, in dollars, that the school will pay for the pencils?
What type of transformation
has this figure made
Answer:
translation
Step-by-step explanation:
a rotation would make it horizontal which it is not
reflection would flip it its not fliped.
There for its translation
hope this helps
i
You are given the difference of the numbers of boys and girls in a class and the ratio of boys to girls. How many boys
and how many girls are in the class?
4 more girls; 9 for every 13
There are
boys and
girls in the class.
Answer:
Maybe they are all 13s th am sure
Question 3 (1 point)
If a ball has a density of 3 grams per cubic centimeter and a mass of 6.2 grams, what
is the volume of the ball? Round your answer to the nearest tenth.
I
Answer:
tydghhhhhhhhhhhhhhhhhhhhhhh
Step-by-step explanation:
hv
i need help with this one
Answer:
I
Step-by-step explanation:
PLEASE HELP DUE IN 3 minutes
Answer:
41-50
Step-by-step explanation:
Answer: 41-50
Step-by-step explanation:
It is the lowest one so it occurred less frequently.
Hope this helps :)
The rectangular pyramid below has a height of 6 inches what is the volume of the pyramid? A. 18 cubic inches
B. 40 cubic inches
C. 120 cubic inches
D. 360 cubic inches
The Volume of rectangular Pyramid whose height inches is 40 cubic inches.
What is the Volume of rectangular pyramid?
The volume of the rectangular pyramid is defined as the capacity of the rectangular pyramid. In geometry, a rectangular pyramid is a three-dimensional geometric shape that has a rectangular base and four triangular faces that are joined at a vertex.
Here, height of pyramid = 6 inches
base area = 4 X 5 = 20 sq. inches
Volume of rectangular pyramid = 1/3 × Base Area × height
= 1/3 X 20 X 6
= 120 / 3
= 40 cu. inches
Thus, the Volume of rectangular Pyramid whose height inches is 40 cubic inches.
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What is the measure of x? Please help!
Answer:
x =√[y²+(27)²] = √[ z² - 3² +(27)²]
Step-by-step explanation:
step 1) x=√[y²+(27)²]
step 2)
We find y
z²=y²+3² → y² = z² - 3²
step 3) x = √[ z² - 3² +(27)²]
can anyone help me with #1?
Answer:
x = 16.1 in
Step-by-step explanation:
Using sin law
sin44 / x = sin98/ 23in
x = 16.1 in (nearest tenth)