Answer:
a) [tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]
b) [tex]n=24[/tex]
Step-by-step explanation:
From the question we are told that:
Rate r=90 units per hour
Setup cost =20
Operating Cost =26
Units=40000
Generally the equation for Total cost is mathematically given by
[tex]Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}[/tex]
[tex]T_n=20n+\frac{11556}{n}\\\\T_n=\frac{20n^2+11556}{n}.....equ 1[/tex]
Differentiating
[tex]T_n'=\frac{n(40n)-(40n^2+11556)}{n_2}\\\\T_n'=\frac{20n^2-11556}{n^2}.....equ 2[/tex]
Equating equ 1 to zero
[tex]0=\frac{20n^2+11556}{n}[/tex]
[tex]n=24[/tex]
Therefore
Substituting n
For Equ 1
[tex]T_n=\frac{20(24)^2+11556}{24}[/tex]
F(n)>0
For Equ 2
[tex]T_n'=\frac{20(24)^2-11556}{24^2}[/tex]
F(n)'<0
In this problem, assume that the probability that a person is born on a given day is 1/365. (For simplicity, ignore Feb 29.) In a group of 100, what is the expected number of pairs of people who have the same birthday
Answer:
the expected number of pairs of people who have the same birthday is 14
Step-by-step explanation:
The computation of the expected number of pairs of people who have the same birthday is as follows:
= 100 (100 - 1) ÷ 2 × 365
= 100 × 99 ÷ 730
= 9900 ÷ 730
= 13.5616
= 14
Therefore, the expected number of pairs of people who have the same birthday is 14
An empty density bottle weighs 24gm. When completely filled with water it weighs 52 gm, when completely filled with a brine solution. Its weighs 56 gm calculate: a) Volume of bottle b) Density of brine solution
Step-by-step explanation:
Density = weight / volumeWater density = 1 gm/cm³a) Weight of the water:
52 - 24 = 28 gmVolume of bottle:
28 gm : 1 gm/cm³ = 28 cm³b) Weight of brine:
56 - 24 = 32 gmDensity of brine:
32 gm : 28 cm³ ≈ 1.14 gm/cm³Use the Unit Circle to find the exact value of the trig function. Cos(45)
1/2
√2/2
√3/-2
1
In a unit circle a line reaching from origin to the circle's circumference specifies the trigonometric functions.
A point where the line which comes from origin to the circumference intersecting it has coordinates [tex](\cos\theta,\sin\theta)[/tex].
In our case [tex]\theta=45^\circ[/tex] which lifts the line up by 45 degrees and makes it intersect circumference at [tex](\cos45^\circ,\sin45^\circ)[/tex].
In the upper right quadrant the angle between x and y axis is 90 degrees so a line coming in at angle of 45 degrees would split the quadrant in half, that means sine and cosine 45 degrees will be equal.
As you may noticed a point has coordinates cos, sin which means the distance between 0 and y coordinate where the point on a circle is, is called [tex]\cos\theta=\cos45^\circ[/tex].
Because cosine 45 degrees is so simple in interpretation it has a known value of [tex]\cos45^\circ=\sin45^\circ=\frac{\sqrt{2}}{2}[/tex].
Hope this helps :)
Solve 3(x + 2) > x.
answer
Answer:
Step-by-step explanation:
3(x + 2) > x
3x + 6 > x
3x - 3x + 6 > x - 3x
6 > -2x
6/-2 < -2x/-2
-3< x
PLEASE HELP ASAP!!! (answer in decimal)
Answer:
re send it
Step-by-step explanation:
ty
i 0 -i
8. If P=0 -i i
-i i 0
pois ecual to
then PQ is equal to
and Q=00
i -i.
(-2 2
1 -1
1
2 -2
-1
1
(1)
(
2)
-1
2 -2
-1 1
(3)
1 0 0
0 1 0
0 0 1
(4)
Answer:
-2 maybe
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
A sequence is defined by the recursive function f(n + 1) = f(n) – 2.
If f(1) = 10, what is f(3)?
1
6
8
30
Answer:
f(3) = 6
Step-by-step explanation:
If f(1)=10, then f(1+1)=f(1)-2
f (2) = 10 - 2 = 8
Therefore f(3) = f(2) - 2 = 8 - 2 = 6
After conducting a survey of all her classmates, Midge discovers that the amount of money everyone spends buying books each month has a mean of $30. What does the mean say about the amount her classmates spend on books?
Half of her classmates spend exactly $30 per month buying books.
Half of her classmates spend more than $30 per month buying books.
The majority of her classmates spend $30 per month buying books.
If the amount spent on books per month by all her the classmates is leveled, that amount would be $30.
Answer:
If the amount spent on books per month by all her the classmates is leveled, that amount would be $30.
Step-by-step explanation:
The mean is the average amount calculated by finding the sum of a certain group of numbers, then dividing it.
This can be described as "leveling" the amount, since it is the total average.
So, the mean of $30 in this situation means that the average amount that her classmates spend on books is $30.
The correct answer is that If the amount spent on books per month by all her the classmates is leveled, that amount would be $30.
Answer:
Your answer is D
Step-by-step explanation:
Please give top guy brainiest
f(x)=|x| to the graph of g(x)=∣∣4+x∣∣?
t "To Do" list has four items: 1) Organize email folders 2) Create a schedule for next month 3) Help a coworker and 4) Answer a customer inquiry. Which item should you probably do first ? a) Answer a customer inquiry b) Organize email folders c) Help a coworker d) Create a schedule for next month
Answer:
I think A) Answer a customer inquiry
Step-by-step explanation:
Because customers come first
Question 3 of 10
Which angle in ABC has the largest measure?
2
С
A
B.
C.
D. Cannot be determined
Answer:
Step-by-step explanation:
C
What is the GCF of the expression 7xyz - 21xyz + 49yz + 14yz2?
Answer:
7yz
Step-by-step explanation:
You can take 7yz common from all the terms in the given expression
Answered by GAUTHMATH
Production possibilities curve graph
Answer:
?????????????????:))
so sánh 198*202 và 200^2
Step-by-step explanation:
198×202=39,996
200×200=40,000
hence,
39,9996 < 40,000
hope it helps
An unknown number becomes 30 when rounded to the nearest ten. Which could NOT be the unknown number?
A. 24
B. 25
C. 28
D. 31
Answer:
A. 24
Step-by-step explanation:
Five and above rounds up
so 25,26,27,28,29 rounds up to 30
We leave it alone when 4 or less
34,33,32,31,30 remains at 30
24 would not round to 30
A kite is a ........... quadrilateral
Answer:
yes
Step-by-step explanation:
The complete sentence is,
A kite is a convex quadrilateral.
We have to given that,
To find a kite is which type of a quadrilateral.
We know that,
A quadrilateral known as a kite has four sides that may be divided into two pairs of neighboring, equal-length sides.
The two sets of equal-length sides of a parallelogram, however, are opposite one another as opposed to being contiguous.
Hence, The complete sentence is,
A kite is a convex quadrilateral.
Learn more about quadrilateral visit:
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What would be an appropriate domain if the function hin) gives the number
of man-hours it takes to assemble n engines in a factory in a day, subject to a
maximum of 300 engines?
Answer:
assuming that you are NOT allowed to build 1/2 of an engine or that you dont destroy any of them in the process of building them ...
"all positive integers less than or equal to 300"
Step-by-step explanation:
I’m having trouble with this
Answer:
this will give you the answer: for cylinder
V = 3×2^2×7 = 84cm
this will give you the answer for cone:
V = 3× 2^2 × 6/3 = 24cm
then we just add
84 + 24 = 108cm^3
Step-by-step explanation:
hope it helps!
Temperatures in northern Canada ranged as high as 37°F one summer. That same year the lowest temperature was −28°F. What was the range of temperatures for the year?
Answer:
65 degrees
Step-by-step explanation:
Find the range of temperatures by finding the difference between the lowest and highest temperatures:
37 - (-28)
37 + 28
= 65
So, the range of temperatures was 65 degrees
(SAT PREP) Find the value of x in each of the following excersises
Answer:
The answer is 155.
Step-by-step explanation:
We can find the remaining parts of the triangle angles.
[18].Simplify (TTE): x(2x+y+5) - 2(x²+xy+5) + y(x + y)
Answer:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
Step-by-step explanation:
Given
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Required
Simplify
We have:
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y)[/tex]
Open brackets
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²+xy+5x - 2x\²-2xy-10 + xy + y\²[/tex]
Collect like terms
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 2x\²- 2x\²+xy-2xy+ xy+5x -10 + y\²[/tex]
[tex]x(2x+y+5) - 2(x\²+xy+5) + y(x + y) = 5x -10 + y\²[/tex]
beverly found a magic bean if she puts it in the soil every single day it will grow 4 cm after how many days will it grow 14.56 meters tall?
Answer:
It will take 364 days
Step-by-step explanation:
First, convert:
1 meter = 100 cm
14.56 meters = 1456 cm
1456 cm is how tall it is at the end, to find out how many days it takes to grow, divide 1456 by 4 (how much it grows every day).
1456/4 = 364 days
The number of days to grow by 14.56 meters is 364 days.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
The number of days to grow is 14.56 meters will be calculated as:-
1 meter = 100 cm
14.56 meters = 1456 cm
1456 cm is how tall it is at the end, to find out how many days it takes to grow, divide 1456 by 4 (how much it grows every day).
1456/4 = 364 days
Therefore, the number of days will be 364.
To know more about Expression follow
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Matt and his siblings bought their mom her favorite perfume for her birthday. They gave the cashier $80. The cashier gave them back 1 ten-dollar bill, 1 five-dollar bill, 8 dimes, and 1 nickel as change. How much did the perfume cost?
Answer:
$64.15
Step-by-step explanation:
to solve this problem, first we should figure out how much money that the cashier gave them back, and then subtract that from $80 (which was what Matt and his siblings gave the cashier) to find out how much the perfume cost.
it is given that:
they gave the cashier $80.
the cashier gave them back 1 ten-dollar bill ($10), 1 five-dollar bill ($5), 8 dimes ($0.80 or 80 cents) , and 1 nickel ($0.05 or 5 cents)
$10+$5+$0.80+$0.05=$15.85
the total amount of money that the cashier gave them back is $15.85
to find how much the perfume cost:
$80-$15.85=$64.15
so, the perfume cost $64.15
Mrs. Hanson has 3 pies for a party. She calculates that if she splits the pies evenly among the guests, they will each receive
1/6
of a pie. How many guests are there?
Answer:
18 guests.
Step-by-step explanation:
To find the number of guests, we can simply divide 1/6 from 3. The result gives us 18.
Write the point-slope form of an equation of the line through the points (-4, 7) and (5, 3).
Answer:
[tex]y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)[/tex]
OR
[tex]y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex]m[/tex] is the slope and [tex](x_1,y_1)[/tex] is a point that falls on the line
1) Determine the slope (m)
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-4, 7) and (5, 3):
[tex]m=\frac{\displaystyle 3-7}{\displaystyle 5-(-4)}\\\\m=\frac{\displaystyle 3-7}{\displaystyle 5+4}\\\\m=\frac{\displaystyle -4}{\displaystyle 9}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 4}{\displaystyle 9}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex] as [tex]m[/tex]:
[tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)[/tex]
2) Plug a point into [tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)[/tex]
Because we're given two points, there are two ways we can write this equation:
[tex]y-y_1=-\frac{\displaystyle 4}{\displaystyle 9}(x-x_1)\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x-(-4))\\\\y-7=-\frac{\displaystyle 4}{\displaystyle 9}(x+4)[/tex]
OR
[tex]y-3=-\frac{\displaystyle 4}{\displaystyle 9}(x-5)[/tex]
I hope this helps!
A bookkeeper needs to post the cost of the desk and the chair into his records. The cost of the desk is fives times the cost if the chair. The total cost of the desk and the chair is $720, what is the cost of the chair?
Answer:
120
Step-by-step explanation:
720÷6
why?
becoz 6= 1+5
1 is the cosy of the chair
5 is the cost of the desk
Write the equation of a line in slope intercept form that passes through the two points. 4,-1 and 6,-7
A line has an equation of,
[tex]y=mx+n[/tex].
m is called a slope
n is called y-intercept
We are also given two points [tex](x_1,y_1)=(4,-1),(x_2,y_2)=(6,-7)[/tex].
We begin with computing the slope,
[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-7-(-1)}{6-4}=\frac{-7+1}{2}=\frac{-6}{2}=\boxed{-3}[/tex]
We have computed the slope m and our equation is almost done,
[tex]y=-3x+n[/tex]
Next step is to find out what y-intercept n is. I will use point [tex](4,-1)[/tex] and insert x and y it into already known equation, then solve for n,
[tex]-1=-3(4)+n[/tex]
[tex]-1=-12+n\implies n=\boxed{11}[/tex]
The reason I can insert coordinates of a point as x and y is because this particular point is in the line described by equation,
[tex]\boxed{y=-3x+11}[/tex]
Hope this helps. :)
!!!Please help!!!
What is the following quotient?
96
B
O 2.13
4.
2.V22
12
Solve the triangle.
9514 1404 393
Answer:
b = 757.7 mA = 17.2°C = 14.3°Step-by-step explanation:
From the law of cosines, you can find the length of side b to be ...
b = √(a² +c² -2ac·cos(B))
b = √(184041 +128164 -307164cos(148.5°)) ≈ √574105.36
b ≈ 757.7
__
From the law of sines, you can find the measure of angle C to be ...
C = arcsin(c/b·sin(B))
C ≈ arcsin(358/757.7·sin(148.5°)) ≈ arcsin(0.246872)
C ≈ 14.3°
A = 180° -148.5° -14.3°
A = 17.2°
_____
Some graphing calculators have built-in triangle-solving functions. Apps are available for the purpose for phone or tablet. The screenshot shows a web site that does a nice job of solving the triangle.
Write the ratio as a fraction in simplest form
4.5 hr to 4 hr
9514 1404 393
Answer:
9/8
Step-by-step explanation:
To clear the fraction in the ratio 4.5 to 4, you can multiply both numbers by 2. This gives you the reduced ratio 9 to 8. As a fraction, that is 9/8.
