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 $400 and standard deviation $20. How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?
Answer:
$425.6 should be budgeted for weekly repairs and maintenance.
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 $400 and standard deviation $20.
This means that [tex]\mu = 400, \sigma = 20[/tex]
How much should be budgeted for weekly repairs and maintenance to provide that the probability the budgeted amount will be exceeded in a given week is only 0.1?
This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.28 = \frac{X - 400}{20}[/tex]
[tex]X - 400 = 20*1.28[/tex]
[tex]X = 425.6[/tex]
$425.6 should be budgeted for weekly repairs and maintenance.
If a + b = 2 and a - b = -4 what is the value of ab A. 5 B. -5 c.3 D. -3
Answer:
D
Step-by-step explanation:
Given the 2 equations
a + b = 2 → (1)
a - b = - 4 → (2)
Add the equations term by term to eliminate b
2a + 0 = - 2
2a = - 2 ( divide both sides by 2 )
a = - 1
Substitute a = - 1 into (1) and solve for b
- 1 + b = 2 ( add 1 to both sides )
b = 3
Then
ab = - 1 × 3 = - 3 → D
Answer:
option d
Step-by-step explanation:
a+b=2. ,. a-b = -4
a= 2-b
substituting values, we get
(2-b) - b = -4
2 -b -b =-4
2 -2b =-4
-2b = -4-2
2b= 6
b =3
a = 2-3
a= -1
ab = 3×-1
ab = -3
PLZZ HELP ME ITD MEAN THE WORLD
Answer: 33/3
Step-by-step explanation:
I don't know the question is weird but it probably is 33/3
-7 2/3 + (-5 1/2) + 8 3/4
Answer:
the answer would be -1339/24
What is the value of the rational expression
2x+1
when x = 5?
Step-by-step explanation:
2x+1
x = 5
2(5)+1
=10+1=11
Answer:
2(5)+1
10+1
11
Hope This Helps!!!
If i= square root of -1, what is the value of i^3
Answer:
[tex] - i[/tex]
Step-by-step explanation:
Set up equation.
[tex]i {}^{3} = y[/tex]
[tex] {i}^{2 } \times i = y[/tex]
[tex] - 1 \times i = y[/tex]
[tex] - i = y[/tex]
4.2kg of oranges are £8.76. How much does 2kg cost
Answer:
x = 4.17
Step-by-step explanation:
We can use a ratio to solve
4.2 k 2 k
---------------- = ---------------
8.76 x
Using cross products
4.2 * x = 2 * 8.76
4.2x =17.52
Divide by 4.2
x=4.17
Answer:
2kg cost £4.18
Step-by-step explanation:
4.2 kg of oranges cost £8.76
:. 1 kg of orange cost £8.76/4.2 = £2.09
2kg cost 2 × £2.09 = £4.18
In a community of 9,400 people the number of women exceeds the number of men by 1,500.Find the ratio of men to women in the community
Answer:
Step-by-step explanation:
x +(x+1500) = 9400
2x + 1500 = 9400
2x = 7900
x=3950 (men)
y = 5450 (woman)
5450 :3950
109:79
Find the area of the shape.
Answer:
Step-by-step explanation:
(1) At the local nursery, 1/2 of the plants for sale are flowers and another 1/10 of them are
bushes. What fraction of the plants for sale are either flowers or bushes?
Answer:
6/10
Step-by-step explanation:
Look at is a whole. Half the plants are flowers, and just a few are bushes. That leaves other plants that are neither.
We can find a total amount of plants that are either flowers or bushes by combining the two.
Because 1/2 and 1/10 are not currently combinable, you must find a common denominator. This common denominator is 10. If you multiply 2 by 5, you'll get 10.
[tex]\frac{1}{2} +\frac{1}{10}[/tex]
[tex]\frac{5}{1} (\frac{1}{2} )+\frac{1}{10}[/tex]
[tex]\frac{5}{10} +\frac{1}{10}[/tex]
[tex]\frac{6}{10}[/tex]
This means that 6/10 of the whole number of plants are either flowers or bushes. You could also say it means that 4/10 of the plants are something other than flowers or bushes.
I hope this helped :)
Which function can represent the height, y, of the railing in inches according to the horizontal distance in inches, x, from the top of the stairs? y = –StartFraction 3 Over 4 EndFractionx + 36 y = –3x + 36 y = StartFraction 3 Over 4 EndFractionx + 36 y = 3x + 36
Answer:
[tex]y = 36 - \frac{3}{4}x[/tex]
Step-by-step explanation:
The missing parameters are:
[tex]h = 36in[/tex] --- height of rails
The rate of decrement is: 9 [tex]inches[/tex] for [tex]every[/tex] 12 [tex]horizontal[/tex] [tex]inches.[/tex]
Required
The function
First, we represent the rate (r) as a fraction.
[tex]r = -\frac{9}{12}[/tex] ---- negative, because it decreases
Simplify
[tex]r = -\frac{3}{4}[/tex]
So, the function is:
[tex]y = h + r * x[/tex]
Where:
[tex]x \to[/tex] distance from top
So, we have:
[tex]y = 36 - \frac{3}{4}x[/tex]
HELP ASAPPPP!!!!!!!
Find the y-intercept of the line y-7x= -3
Answer:
y - intercept = - 3
Step-by-step explanation:
The equation of a line is typically written as y=mx + b where m is the slope and b is the y-intercept.
Given :
y - 7x = - 3
y = 7x - 3 [ convert to standard line equation form ]
Therefore , y - intercept = - 3
Answer:
-3
This is the y intercept because when you re-arrange the equation to form y=mx+c, the y-intercept( c) is -3.
Which expression is equivalent
Answer:
[tex]\sqrt[6]{2\\}[/tex]
Step-by-step explanation:
Rewriting
2 ^1/2 ÷ 2 ^ 1/3
We know a^ b ÷ a^c = a^ (b-c)
2 ^ (1/2 -1/3)
Getting a common denominator
2^ ( 3/6 - 2/6)
2^ 1/6
[tex]\sqrt[6]{2\\}[/tex]
Answer:
[tex]\sqrt[6]{2}[/tex]
Step-by-step explanation:
We can start by writing the expression as one power of two, and then comparing it to the options. The square root of two is the same and [tex]2^{\frac{1}{2} }[/tex] and the cube root of two is the same as [tex]2^{\frac{1}{3} }[/tex]. Therefore, we can rewrite the expression:
[tex]\frac{2^{\frac{1}{2} }}{2^{\frac{1}{3} }}[/tex]
Now, to write them as one power of two, we can use the quotient rule which states, [tex]\frac{x^m}{x^n} = x^{m-n}[/tex]:
[tex]2^{\frac{1}{2} -\frac{1}{3}}[/tex]
We just need to subtract 1/3 from 1/2 to get:
[tex]2^{\frac{1}{6} }[/tex]
This is the same as the 6th root of 2, which is the second option.
Given m||n, find the value of x.
Answer:
x = 15
Step-by-step explanation:
The two angles add to a straight line, so they add to 180
6x-5 + 6x+5 = 180
Combine like terms
12x = 180
Divide by 12
12x/12 =180/12
x =15
Answer:
x = 15
Step-by-step explanation:
Two angles are supplementary and their sum is 180
6x + 5 + 6x - 5 = 180 add like terms
12x = 180 divide both sides by 12
x = 15
Hannah lost four points on a test and earned four points on an extra credit question what does the sum of 0 mean in the description of this situation?
Answer:
Is that it's not about the answers and the questions
holaaandaaa cuanto es 22+22
Step-by-step explanation:
22+22=44
Es una pregunta fácil, incluso un niño pequeño puede responder a esto.
John is buying new shoes. He finds the shoes he wants on sale for 30%, and the original price is $88. How much will he pay for the shoes?
Answer:
61.6 dollars
Step-by-step explanation:
So, lets go over what we know:
The shows orginally cost 88 dollars.
They are 30% less than that.
This basically means that the shoes will cost 70 percent of their orginal price.
We can basically find the new cost by multiplying the 88 dollars by the 70 percent.
Or, multiplying 88 by 0.7, which is the decimal form of 70%.
88*0.7=61.6
How did I get this?
Multiply 80 by 0.7:
7*8=56
We have 0.7 so it = 5.6
However, it's tens place is 80, not 8, so it will be = 56
It is the same thing in the ones place, however it is 8 not 80, so it will be 0.7*8
= 5.6
56+5.6=61.6
So 61.6 is our answer.
Hope this helps!
Answer:
$61.60
Step-by-step explanation:
the other answer is correct.
just to add some explanation about the % considerations.
we know $88 is 100%
in order to get any other % value, we need to divide the original value by 100 (that gives us 1%), and then multiply with the number of % we want to have - in our example 70, as the discount is 30% (so the remaining part is 70% of the original price).
so, in order to get 70% we actually have to do the above things and divide by 100 and multiply by 70.
70% = (100% / 100) × 70 = 100% × 70 / 100
70 / 100 = 0.7 (that is how answer 1 actually got that multiplication factor)
70% = 100% × 0.7
70% = $88 × 0.7 = $61.60
Two friends Vicky and Love start a business together. They decided to share their capitals depending upon the variable
expenditure. The capital of the two
partners together is given by polynomial 6x+10x -35, which is the product of
their individual share factors.
On the basis of the above information,
answer the following questions.
i) The total expenditure of Vicky and Love
when x = 10 is (in )
(a) 375 (b) 475
(c) 575 (d) 675
(ii) The shares of the Vicky and Love
individually is
(a) 2x +7, 3x -
5
(b) 3x -5, 2x +7
(c) Both (a) and (b)
(d) None of the above
(iii) The value of x, when their shares are
equal
(a) 12 (b) 10
(c) 8 (d) 6
(iv) The value of x, when their total share is
equal tob0
7
(a)- (b) 3
(c) Both (a) and (b) (d) None of these
(v) The sum of their expenditure is
(a) 5r -2 (b)5x+2 (c) 4x-2 (d) 4x+2
The distance needed to stop a car, d, varies directly as the square of the speed, s, at which it is travelling. A car travelling at a speed of 70 km/h requires a distance of 40 m to make a stop. What distance is required to stop a car travelling at 80 km/h?
Answer:
52.24 km
Step-by-step explanation:
Given that,
The distance needed to stop a car, d, varies directly as the square of the speed, s, at which it is travelling.
d = ks²
Where
k is constant
When s₁ = 70 km/hr, d₁ = 40 m, s₂ = 80 km/hr, d₂ = ?
So,
[tex]\dfrac{d_1}{d_2}=\dfrac{s_1^2}{s_2^2}\\\\d_2=\dfrac{d_1s_2^2}{s_1^2}\\\\d_2=\dfrac{40\times 80^2}{70^2}\\\\d_2=52.24\ km[/tex]
So, the new distance is 52.24 km.
Type the correct answer in each box.
Please answer max 10 min, I have a test.
Given a room is 12 feet by 10 feet and we have a circular rug with a radius of 3 feet, calculate the amount of floor left uncovered by the circular area rug in a rectangular living room
Step-by-step explanation:
floor = 12*10= 120 sq ft
rug = r² = 9 Пr2
120-9π = 91.74 sq ft
A girl runs 2 km in 1 hour . How long will she take to ran 500 m ?
Answer:
1/4 he
Step-by-step explanation:
Answer:
1/4 hour
Step-by-step explanation:
convert 2 km to m
1 km = 1000m
2 km = 2*1000 m
=2000 m
distance time taken
2000 m 1 hour
500 m let be x
2000/500 = 1/x
do cross multiplication
500*1 = 2000*x
500/2000 = x
1/4 = x
There are 14 birds sitting on a wire. One-half of the birds are black. How many black birds are sitting on the wire?
Answer:
7
Step-by-step explanation:
There are 14 birds sitting on the wall
One half of the birds are black
Therefore the number of black birds can be calculated as follows
= 14×1/2
= 14×0.5
= 7
Hence 7 birds are black
The Naturally Made Bath and Body store pays $550 a month for rent and utilities. The average cost for its products to be manufactured is about $3.00 an item. If the average price for a product sold in the store is $5.50, what will the break-even point be?
Answer:
Break-even point is at quantity 220.
Step-by-step explanation:
Given the rent amount that is fixed cost for the store = $550
The average cost of the goods = $3
The average price of the goods = $5.50
Let the total number of break-even items = Q
Thus, total revenue = 5.50 x Q = 5.50Q
At break-even, TR = TC
5.50Q = FC + VC
5.50Q = 550 + 3Q
5.50Q - 3Q = 550
2.50Q = 550
Q = 550 / 2.50
Q = 220
Thus break-even point is at quantity 220.
pls help me solve pls show how you got the answer
Answer:
$348
Step-by-step explanation:
Unit rate:
Sales clerk: $12/h
Assistant manager: 1/2 x 12= $6/h
Manager: 2 1/2 x 12= $30/h
Now for how long they will work (7.25 hours long):
Sales clerk: 12 x 7.25= $87
Assistant manager: 6 x 7.25= $43.5
Manager: 30 x 7.25= $217.5
In total: 87 + 43.5 + 217.5= $348 is paid in one day for each of the employees when they work 7.25 hours.
I hope this will help qwq
says hint: divide, i dunno
distance= rate * time
distance/rate=time
(2.4 *10^20)/ (1.2*10^5) = 2 * 10^15 seconds
Need help on this!! Will give 20 points!!!
Answer:
80 mm
Step-by-step explanation:
1/p + 1/20 = 1/16
Subtract 1/20 from both sides
1/p = 1/16 - 1/20
Use 160 as common denominator
1/p = 10/160 - 8/160
1/p = 2/160
1/p = 1/80
Cross multiply
80 = p
80 mm
What is the completely factored form of this polynomial?
x^4- 8x^2 + 16
A. (X+2)^2(x-2)^2
B. (x^2-4)^2
C. (x^2+4)(x+2)(x-2)
D. (x+2)(x-2)
Answer:
A. (x + 2)²(x - 2)²
Step-by-step explanation:
x⁴ - 8x² + 16 =
(x² - 4)(x² - 4) =
(x - 2)(x + 2)(x - 2)(x + 2) =
(x - 2)²(x + 2)²
how do i solve this
[tex] {x}^{6} [/tex]
Answer:
You did give anything to solve
Step-by-step explanation:
x⁶ is just a single term
If you had posted an equation like
x⁶ = 64
Take the cube root of both side
x² = 4
Take the square root of both sides
x = ± 2
6. A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again. If the ball continues to rebound and fall in this manner, find the total distance the ball has travelled after it hits the ground the 5th time. This may be answered in decimal form. Round your answer to 2 decimal places.
Answer:
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.
Step-by-step explanation:
Geometric sequence:
In a geometric sequence, the quotient of consecutive terms is the same. The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term and [tex]q[/tex] is the common ratio.
A super-bouncy-ball is thrown 25m into the air. The ball falls, rebounds to 70% of the height of the previous bounce and falls again.
This means that:
[tex]q = 0.7, a_1 = 25*0.7 = 17.5[/tex]
Then
[tex]a_n = a_1q^{n-1}[/tex]
[tex]a_n = 17.5(0.7)^{n-1}[/tex]
First 5 terms:
[tex]a_1 = 17.5[/tex]
[tex]a_2 = 17.5(0.7)^{2-1} = 12.25[/tex]
[tex]a_3 = 17.5(0.7)^{3-1} = 8.58[/tex]
[tex]a_4 = 17.5(0.7)^{4-1} = 6[/tex]
[tex]a_5 = 17.5(0.7)^{5-1} = 4.2[/tex]
Find the total distance the ball has travelled after it hits the ground the 5th time.
[tex]T = 17.5 + 12.25 + 8.58 + 6 + 4.2 = 48.53[/tex]
The total distance the ball has travelled after it hits the ground the 5th time is of 48.53m.
