Simplifying Fractions
Simplify each fraction to its lowest terms.
1) 9 =
18
8) 4 =
16
15)
21 =
63
2) 8 =
10
9) 18 =
36
16)
30 =
84
6
3) =
8
6
10) =
42
50
17) =
125
4) 5 =
20
13
11) =
39
72
18) =
108
18
5) =
24
21
12) =
28
49
19) =
112
6
6) =
9
12
7) =
15
63
13) =
77
36
14) =
40
4
240
20) =
320
120
21) =
150
Answer:
1)1/2
8)1/4
15)1/3
2)4/5
9)1/2
16)17/40
3)3/4
10)1/7
17)2/5
4)1/4
11)1/3
18)2/3
5)3/4
12)3/4
19)7/16
6)2/3
7)4/5
13)9/11
14)9/10
20)3/4
21)4/5
I tried (in your order and replace / with = if you want)
Suppose c(x) = x3 - 24x2 + 30,000x is the cost of manufacturing x items. Find a production level that will minimize the average cost per item of making x items.
Answer:
hence the required minimum production level is 12units
Step-by-step explanation:
Given the cost function expressed as c(x) = x^3 - 24x^2 + 30,000x
The average cost function will be c(x)/x
Dividing the cost function through by x
Average cost function = c(x)/x = x³/x - 24x²/x + 30,000x/x
Average cost function = x²-24x + 30,000
A(x) = x²-24x + 30,000
If the average cost is minimized, hence dA/dx = 0
dA/dx = 2x - 24
0 = 2x - 24
-2x = -24
Divide both sides by -2
-2x/-2 = -24/-2
x = 12
For the second deriviative
d²A/dx² = 2 which is greater than zero
Hence a production level that will minimize the average cost per item of making x items is 12
The production level that will minimize the average cost per item of making x items is x = 12
How to obtain the minimum value of a function?To find the minimum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
Putting those values of x in the second rate of function, if results in negative output, then at that point, there is maxima. If the output is positive then its minima and if its 0, then we will have to find the third derivative (if it exists) and so on.
For this case, the function in consideration is: [tex]c(x) = x^3 - 24x^2 + 30000x[/tex]
This is cost function for x items' manufacturing.
The average cost per item would be c(x) / x
This gives us a function a(x) as:
[tex]a(x) = c(x)/x = x^2 -24x + 30000[/tex]
For finding the minimum of a(x), getting its first two derivatives as:
[tex]a'(x) = 2x - 24\\a''(x) = 2 > 0[/tex]
Equating first rate to 0,
[tex]a'(x) = 2x - 24 = 0[/tex] critical point.
Since second rate is positive, the point x = 12 is point of minima, and since only one critical point is there, it is the point on which a(x) is minimum.
Thus, the production level that will minimize the average cost per item of making x items is x = 12
Learn more about minima and maxima of a function here:
https://brainly.com/question/13333267
On a snow day, Owen created two snowmen in his backyard. Snowman A was built to
a height of 60 inches and Snowman B was built to a height of 42 inches. The next day,
the temperature increased and both snowmen began to melt. At sunrise, Snowman
A's height decrease by 6 inches per hour and Snowman B's height decreased by 3
inches per hour. Let A represent the height of Snowman At hours after sunrise and
let B represent the height of Snowman Bt hours after sunrise. Graph each function
and determine the interval of time, t, when Snowman A is taller than Snowman B
Answer:
The equations for each function:
A(t) = 60 - 6tB(t) = 42 - 3tThe lines plotted, see attached
The point at which both the snowmen have same height:
60 - 6t = 42 - 3t6t - 3t = 60 - 423t = 18t = 6The required interval is
t = [0, 6)HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP HELP I NEED HELP ASAP
HELP I NEED HELP ASAP
Answer:
B. 25%
Step-by-step explanation:
Total 16 students
4 scored above 90
so 4/16= 0.25
Answer: 25%
plz mark me as brainliest.
please helpppppp i will mark you braliest
Answer:
0.3
Explanation:
you multiply all numbers together to get 0.3
An expression is shown. 2(3/5x+3) - (2/3x-1) create an equivalent expression without parenthesis
Answer:
6/5x -2/3x + 4
Step-by-step explanation:
Simplify the equation
6/5x + 3 -2/3x + 1
6/5x -2/3x + 4
not simplified all the way, but is just exquivalent
Answer 1 13/15x + 5 if simplified or 28/15x + 5 non-simplified
Step-by-step explanation:
2(3/5x+3) = 6/5x + 6 (also can simplfy to 1 1/5x +6)
6/5x + 2/3 = 18/15 + 10/15 = 28/15x ( also can to 1 13/15x)
6-1=5
A cylindrical cookie jar has a volume of 904.23 cubic inches. It is 8 inches tall. What is the radius of the cookie jar? Round your answer to the nearest inch.
Answer:
Answer:
r = 6 in
Step-by-step explanation:
The volume of a cylinder of radius r and height or length h is
V = πr²h.
Here, we need to solve for the radius; we get:
V
------------- = r²
πh
904.23 in³
This works out to r² = ----------------- = 35.97 in²
π(8 in)
Finally, take the square root of this result to find the radius, r:
r = √35.97 in² = 6 inches
Use the box method to distribute and simplify (5x – 3) (-4x – 5). Drag and drop
the terms to the correct locations of the table.
(5x – 3) (- 4x – 5)
NEED HELEOEO
Answer:
your answer is below
-20x +15
e Fill in the char...
Fill in the chart converting between fractions, decimals, and percents.
Fraction
Decimal
Percent
1
8
1.125
What belongs in the cell circled in red?
PLEASE HELP!! DUE SOON!!!
Find the surface area of the sphere (I can't upload the pic but I'll give the radius).
Radius 7 m
A. 56π m²
B. 784π m²
C. 392π m²
D. 196π m²
Answer:
D
Step-by-step explanation:
This is because the formula is 4×pi×r^2
So 4×pi×7^2
(7^2=49) now plug that in: 4×pi×49
Combine like terms: 4×49=196
Plug that into the equation: 196pi
Given the function y = -5x + 4, what is the range of the function if the domain is {-2, 0, 5}?
Answer:
90 hours
Step-by-step explanation:
{14, 4, -21} is the range of the function if the domain is {-2, 0, 5}
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
To find the range of the function, we need to plug each value in the domain into the given function and see what output (y-value) we get.
When x = -2:
y = -5(-2) + 4 = 14
When x = 0:
y = -5(0) + 4 = 4
When x = 5:
y = -5(5) + 4 = -21
So the range of the function is {14, 4, -21}.
Learn more about function here:
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{67, 68, 68, 71, 73, 73, 73, 74, 74, 74, 74, 75, 75, 77, 78, 79, 79, 80, 80}
What is the mode of the data?
68
71
74
75
Answer:
74
Step-by-step explanation:
Mode is the number that shows up the most in the data.
HELP PLEASE 15 POINTS
Answer:
b
Step-by-step explanation:
Given that Δ DEF and Δ ACB are congruent then corresponding angles are congruent.
ACB and DEF , that is ∠ B and ∠ F are corresponding
B
6x+7
3x+c
2x-1
What is the value of c in degrees
Answer:
1.x=15
2.<A=29
Step-by-step explanation:
(2x-1)+(3x+9)+(6x+7)=180
2x-1+3x+9+6x+7=180
11x+15=180
11x=180-15
11x=165
x=165/11
x=15
2.<A=2x-1
<A=2*15-1
<A=30-1
<A=29
In a first aid kit, the ratio of large bandages to small bandages is 1 to 6. Based on this ratio, how many small bandages are in a kit of 140 bandages?
At a birthday party, the ratio of pizza slices to kids is 3:2. At a larger party there are 30 kids. If the ratio of pizza slices to kids stays the same, how many pizza slices will be needed?
Answer:
90:60
Step-by-step explanation:
3x30= 90
2x30= 60
In a 30% off sale, the price of an item is reduced by £27.
What is the original cost of the item?
Answer: the original cost of the item is 90$
Step-by-step explanation:
30% off of the item = 27$
27 dollar is 30% of the item
thus 27 = 0.30X
0.30X = 27
time both side by 10
3X = 270
270/3 = 90
Given are the first three terms of a sequence that is either arithmetic or geometric. If the sequence is arithmetic, find a1 and d. If a sequence is geometric, find a1 and r. 1/6,1/12,1/24
Answer:
a1 = 1/6
r = 1/2
Step-by-step explanation:
Given the sequence
1/6,1/12,1/24
The sequence is a geometric sequence since they have a common ratio
r = 1/12÷1/6 = 1/24 ÷ 1/12
r = 1/12 * 6/1 = 1/24 * 12/1
r = 1/2
Since a1 is the first term, hence a1 is 1/6 and common ratio r is 1/2
Suppose that a certain movie earns $3,000,000 in ticket sales. If 60% goes to the movie studio and 40% goes to theatres: Movie studios will get $ of the total revenue Theatres will get $ of the total revenue.
Jimmy draws a triangle with sides of length 4, 10, and 8. He says that his triangle is acute because when you square the sides and use the pythagorean theorem, 16+ 100 64. Therefore the third side is "too small" to be the hypotenuse, making the triangle acute. You agree or disagree with jimmy? Explain and justify your answer.
Answer:
yes, it is an acute triangle because all angles are less than 90 degrees.
Step-by-step explanation:
The drawing of a building, shown below, has a scale of 2 inches to 8.5 feet.
What is the actual height, in feet, of the house?
Answer:
36 1/8 feet
Step-by-step explanation:
x = height of house in feet
2"/8.5' = 8/5"/x
cross-multiply:
2x = 72.25
x = 36.125 or 36 1/8
Zapisz w postaci jednej potęgi (zapisz obliczenia):
32 * 83 : 42 =
0,0014 *0,012 : 0,13 =
(53 * 252)4 =
27 * 253 *83 * 510 =
211 * 67 : 37 =
Zapisz w postaci notacji wykładniczej i odwrotnie:
403000000 =
2,4 * 109 =
0,00000509 =
5,015 * 10-5 =
Answer:
1. 62,3
2. 0,000129230769
3. 53424
4. 257027760
5. 382,081081
6. ?
7. 261,6
8. ?
9. 45,15
Tyrone wants a new 53 inch television for his bedroom. He plans to put the TV in a space that is 42 inches wide. Tyrone knows the TV is rectangular and has a height of 28 inches.
Enter True or False: The 53 inch TV will fit in the space_________
The width of the TV is _______inches.
Answer:
False
Step-by-step explanation:
Helpp plzz with the one on the top I will mark brainliest
Answer:Its D i hope
Step-by-step explanation:
What is the area of KDL to the nearest tenth of a square inch? Use special right triangles to help find the height. Show
your work
Answer:
8
Step-by-step explanation:
This is a 45-45 traingle which mean that the two sides that aren't the hyptonouse are equal (because their angles are equal)
We will let x equal the length of one of the sides
we have
x²+x²=(4√2)²
2x²=32
x²=16
x=4
this means that the length of the two missing sides are 4
Now using the area of a traingle formula we can solve for the area
A=.5*b*h
.5*4*4=8
.5*4*4
Emma bought a sweater at the sale price of $50. The original cost of the sweater was $80. What percent represents the discount that Emma received when buying the sweater?
Answer:
The percentage represented is 37.5%
(d) Time T, in minutes, for a train journey of
a hours b minutes
Answer:
you didnt give a clear question
Step-by-step explanation:
wth
A computer game company conducts a survey of random sample of customers to determine their favorite type of game. The results of the survey are shown below based on the survey results how many customers are expected to prefer fantasy games out of the 1,000 customers?
Answer:
1.6% of customers
Step-by-step explanation:
Identify the figure. Then state how many bases, faces, edges, and vertices there are.
Name:
Bases:
Faces:
Edges:
Vertices:
Answer:
name: pentagonal pyramid
bases: one
faces: 5
edges: 10
vertices: 6
Step-by-step explanation:
Pls help ASAP I will do anything
Answer:
Imma guess
8^3 + 12
Step-by-step explanation: