The simplified form of the expression is a⁻¹²/8b⁶
Simplifying an expressionFrom the question, we are to simplify the given expression
The expression is
a raised to the negative fourth power over quantity 2 times b squared end quantity all cubed
That is,
(a⁻⁴/2 × b²)³
Simplifying the expression
(a⁻⁴/2 × b²)³
= a⁻⁴ˣ³/(2³ × b²ˣ³)
= a⁻¹²/(8 × b⁶)
= a⁻¹²/8b⁶
Hence, the simplified form of the expression is a⁻¹²/8b⁶
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A pet shop sold 20 rabbits for $192. some of the rabbits sold for $7 each and the rest for $11 each. how many rabbits were sold at each price?
There are 7 rabbits sold for $7 and 13 rabbits sold for $11.
Substitution method:
In the substitution method, we must substitute the value of one given variable in terms of the other given variable and find the solution.
Given,
A pet shop sold 20 rabbits for $192.
Some of the rabbits sold for $7 each and the rest for $11 each.
Here we need to find the number of rabbits sold in each case.
Let us consider x be the number of rabbits sold for $7 and y be the number of rabbits sold for $11.
We know that, the total number of rabbits sold = 20.
So, it can be written as,
=> x + y = 20
Here we have to rewritten this equation as,
=> x = 20 - y ----------------------(1)
We know that, total amount for sold rabbits = 192
So, it can be written as,
=> 7x + 11y = 192 -----------------------(2)
Apply the value of x to equation (2),
Then we get,
=> 7(20 - y) + 11y = 192
=> 140 - 7y + 11y = 192
=> 4y + 140 = 192
=> 4y = 192 - 140
=> 4y = 52
=> y = 52/4
=> y = 13.
Apply the value of y on the equation (1),
Then we get,
=> x = 20 - y
=> x = 20 - 13
=> x = 7
Therefore, there are 7 $7 rabbits and 13 $11 rabbits are sold.
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PLEASE HELP ASAP!!!!!!!!!
Use PEMDAS to solve the following problem: 60* 10-8* (3* 2) What is left after completing the first step of PEMDAS
Answer:60*10-8*6
Step-by-step explanation: after you complete the first step which is perenthesis you are left with 60*10-8*6
The first step is the parenthesis. the left after completing the first step of PEMDAS is answer 552.
How to determine the first step?The equation is given as:
60* 10-8* (3* 2)
Using PEMDAS, the first step is to open the brackets by multiplication So, we have:
60* 10-8* (3* 2)
60* 10-8*6
Then multiply the rest and subtract.
600- 48 = 552
Hence, the first step is the parenthesis. the left after completing the first step of PEMDAS is answer 552.
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A bookstore offered mystery bags each containing 12 books. The quantity of each type of book was the same in
each mystery bag. A shopper bought 3 mystery bags and found that 6 books were spy novels.
Based on this information, which prediction can the shopper make about buying mystery bags in the future?
A.There will be 4 more spy novels in 8 bags than in 6 bags
B.There will be 2 more spy novels in 6 bags than in 4 bags.
C.There will be 1 more spy novel in 9 bags than in 8 bags.
D.There will be 6 more spy novels in 10 bags than in 8 bags.
The prediction thay the shopper can make about buying mystery bags in the future is A.There will be 4 more spy novels in 8 bags than in 6 bags.
How to calculate the value?Since the shopper bought 3 mystery bags and found that 6 books were spy novels, it means that there are 6/3 = 2 spy novels in each bag.
There, the prediction thay the shopper can make about buying mystery bags in the future is that there will be 4 more spy novels in 8 bags than in 6 bags.
This is because there's an extra 2 bags which will be equal to 4 spy novels
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help!!! 50 points!!!!
Answer:
Less than and -97
Step-by-step explanation:
Answer: -17
Step-by-step explanation:
find the value by using the systematic of expressions then exponent it then factorize it by using prime numbers
Find the area of the region inside the circle r=4cos(theta) and outside the circle r=2.
Area of the region inside the circle r=4cos(theta) and outside the circle r=2 is 4π/3 + 2√3
What is the polar curve?A form created using the polar coordinate system is called a polar curve. Points on polar curves have varying distances from the origin (the pole), depending on the angle taken off the positive x-axis to calculate distance. Both well-known Cartesian shapes like ellipses and some less well-known shapes like cardioids and lemniscates can be described by polar curves.
r = 1 − cosθsin3θ
Polar curves are more useful for describing paths that are an absolute distance from a certain point than Cartesian curves, which are good for describing paths in terms of horizontal and vertical lengths. Polar curves can be used to explain directional microphone pickup patterns, which is a useful application. Depending on where the sound is coming from outside the microphone, a directional microphone will take up sounds with varied tonal characteristics. A cardioid microphone, for instance, has a pickup pattern like a cardioid.
The area between two polar curves can be found by subtracting the area inside the inner curve away from the area inside the outer curve.
The figure attached shows the bounded region of the two graphs. The red curve is r=4cos(θ) and the blue curve is r=2.
The points of intersection of the two curves are
θ = π/3 and 5π/3
The area is calculated as follows:
Since the bounded region is symmetric about the horizontal axis, we will find the area of the top region, and then multiply by 2, so as to get the total area.
A = 2 [tex]\(\int_{0}^{\pi /3}[/tex] ½ (4 cos (θ)² − ½ (2)² dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 16 cos2 (θ) − 4dθ
= [tex]\(\int_{0}^{\pi /3}[/tex] 8 (1+cos(2θ)) − 4dθ
=[tex]\(\int_{0}^{\pi /3}[/tex] 4 + 8 cos (2θ) dθ
= [4θ + 4sin (2θ)] [tex]\(\int_{0}^{\pi /3}[/tex]
= 4π/3 + 2√3
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Find an equation of the line through (3,4) and parallel to y = 2x + 2: y =____. (Type your answer in slope-intercept form.)
Answer:
y = 2x - 2
Step-by-step explanation:
y = 2x + 2
4 = 2(3) + c
4 = 6 + c
c = -2
y = 2x - 2
The line is parallel so slope remains same but intercept changes.
A sheet of paper contains a list of 5 double-digit prime numbers.
Their mean is 31, while their median and mode is 29.
The largest number is 41.
Show how you can discover the 5 prime numbers written on the sheet.
the five prime number are 19,29,29,37,41
mean =sum of observations / total number of observation
= 19+29+29+37+41 /5
= 155/5
=31
median = (n+1) / 2 th term n is number of term and n is odd
= (5+1) /2 th term
= 3 rd term
= 29
mode = the value that appears most in the data
= 29
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424 divided by 3243.6
Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbl
Which number sentence tells the story of how many marbles he had left ?
The number of marbles left in the pocket after losing is 29 { after narrating the story in numerical sentences}
Given that Tran bought 25 marbles and put them in his pocket with 10 other marbles. He had a hole in his pocket and lost 6 marbles. and asked to narrate the story in numerical form
Total number of marbles Tran bought=25 marbles
Total number of marble Tran has before buying new marbles=10 marbles
Total number of marbles after buying new marbles=35 marbles
Given that he lost 6 marbles because of the hole in his pocket
Therefore, the Total number of marbles left=35-6
The total number of marbles left=29 marbles.
Therefore, The number of marbles left in the pocket after losing is 29 { after narrating the story in numerical sentences}
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Use the two examples that you provided in question 5 to describe how those trace elements have been introduced into our diets and/or personal hygiene habits.
Peaches, beans, spinach, and pistachios are dietary sources of iron. We get iodine via seaweed, shrimp, eggs, salt, and dairy products in our diet.
What do dietary trace elements do?
Minerals known as trace elements or trace metals are minor levels of which are found in living tissues. Some of them are known to be nutritionally necessary, some might be (but the evidence is merely speculative or sparse), and the rest are regarded as nonessential.What are trace elements give two examples?
Essential trace elements of the human body include zinc (Zn), copper (Cu), selenium (Se), chromium (Cr), cobalt (Co), iodine (I), manga- nese (Mn), and molybdenum (Mo).
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[tex]\sqrt[3]{x} = 3[/tex]
Answer:
x = 27
Step-by-step explanation:
You need to cube each side.
[tex]\sqrt[3]{x} ^{3}[/tex] = [tex]3^{3}[/tex]
x = 27
Joe works as a pianist in a local restaurant. He makes $8.50 an hour. He was able to work 45 hours last week. How much money did he make that week?
Answer: $382.50
Step-by-step explanation:
8.50 x 45 = 382.50
8 children have to share two thirds of a watermelon equally what part of the whole watermelon would each child get
Each child would get 1/12 th part of the whole watermelon.
For given question,
8 children have to share two thirds of a watermelon equally .
This means we need to equally distribute 2/3 of whole watermelon to 8 children.
To divide 2/3 part of of a watermelon equally into 8 parts, we need to divide 2/3 by 8.
(2/3) ÷ 8
= [tex]\frac{(\frac{2}{3} )}{8}[/tex]
We know that in 8 = 8/1
So, we rewrite the denominator of above fraction as,
[tex]\frac{(\frac{2}{3} )}{8} \\\\= \frac{(\frac{2}{3} )}{(\frac{8}{1} )} \\\\=\frac{2}{3} \times \frac{1}{8} \\\\=\frac{1}{12}[/tex]
This means, each child will get 1/12 part of the whole watermelon.
Therefore, each child would get 1/12 part of the whole watermelon.
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You want to make 20 plates and have 30 bags of shredded cheese. How can you determine how much cheese to put on each plate so that each plate has the same amount of shredded cheese?
The amount of cheese in each plate = 1.5x
There are 30 bags of shredded cheese.
Let 'x' be the quantity of cheese in each bag. Then,
The total quantity of cheese in 30 bags = 30x
Number of plates = 20 plates
We need to determine the quantity of cheese put on each plate so that each plate has the same amount of shredded cheese.
For this we just need to divide the total amount of shredded cheese by the number of plates.
The equal amount of cheese in each of 20 plates = 30x/20
= 3x/2
= 1.5x
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Write two ratio that are equivalent to 4:5
Answer:
8:10, 12:15
Step-by-step explanation:
A power company calculates a person's monthly bill from the number of
kilowatt-hours (kwh), x, used.
the function b(x)
The bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.
The given functions are
b(x) = 0.15x; x ≤ 360
b(x) = 0.10(x - 360) + 54; x > 360
What is the function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.
For a person who uses 560 kWh, it means that:
x > 360
So, we use the following function to determine the bill
b(x) = 0.10(x - 360) + 54
Substitute 560 for x
b(560) = 0.10(560 - 360) + 54
⇒b(560) = 74
Hence, the bill for a person who uses 560 kWh in a month is $74. Therefore, option D is the correct answer.
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Your question is incomplete, probably the complete question/missing part is:
A power company calculates a person's monthly bill from the number of kilowatt-hours ( Nh), x, used. The function b(x)= 0.15x, and x≤360. 0.10(x-360)+54, and x>360 determines the bill. How much is the bill for a person who uses 560 kWh in a month? A. $84 B. $54. $64 D. $74.
Find the slope of the lines containing the following points
(-2, 1) & (-5,5)
The slope of the lines containing the following points (-2, 1) & (-5,5) is [tex]\frac{-4}{3}[/tex].
As per the question statement, two points lie (-2, 1) & (-5,5) on a line.
We are supposed to find the slope of the line.
To solve this question, we need to know the formula to calculate the Slope of line passing through two points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] which is given by
[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]
Since given in the question statement, our concerned points are (-2, 1) & (-5,5), we can consider [tex][x_{1}=(-2)] , [x_{2}=(-5)], [y_{1}=1][/tex] and [tex][y_{2}=5][/tex].
Using these values into above mentioned formula, we get,
Slope (m) = [tex]\frac{5-1}{[(-5)-(-2)]}=\frac{4}{-3}=\frac{-4}{3}[/tex].
Slope of a line: In mathematics, the slope or gradient of a line is a value that describes both, direction and the steepness of the line.To learn more about Slope of lines, click on the link below.
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Translate the sentence into an equation.
Four times the sum of a number and 3 is 2.
Use the variable w for the unknown number.
The problem is:
y = -2(x-3)^2
Please help me find the;
Vertex,
X-Intercepts,
and the Axis of Symmetry
Alg 2, Intercept, Vertex form.
The Vertex is at (3, 0)
The Axis of symmetry is; x = 3
The x-intercept is; x = 3
What is the Vertex and Axis of Symmetry?
We are given the quadratic equation as;
y = -2(x - 3)²
Expanding this gives us;
y = -2(x² - 6x + 9)
y = -2x² + 12x - 18
x coordinate of vertex = -b/2a = -12/(2 * -2) = 3
y coordinate of vertex = f(3) = -2(3)² + 12(3) - 18 = 0
Vertex is at (3, 0)
Axis of symmetry is the x coordinate of vertex = -b/2a = -12/(2 * -2) = 3
x-intercepts is gotten by finding the roots which are; x = 3 and 3
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The ages of three friends are represented by three consecutive odd integers. If the youngest of
the three is represented by m, express the sum of the ages of the three friends.
Solving the Question
We're given:
m is the smallest age.This means that the consecutive odd integers will be m + 2 and m + 4.
If we add all their ages, it will look like this:
[tex]m+(m+2)+(m+4)\\= m+m+2+m+4\\= 3m+2+4\\= 3m+6[/tex]
Answer[tex]3m+6[/tex]
When milgram conducted his first series of experiments with a sample of 20- to 50-year-old men, he found that over 60 percent of them:____.
When Milgram conducted his first series of experiments with a sample of 20- to 50-year-old men, he found that over 60 percent of them: went all the way to 450 volts.
What is the Milgram experiment?Milgram's experiment examined if authority affected submission. Stanley Milgram, a Yale University psychologist, carried out several obedience tests in the 1960s that produced some providing more opportunities.
Milgram discovered that more than 60% of the men in his sample of 20 to 50-year-olds who participated in his initial series of trials reached 450 volts.
As a result, when Milgram conducted his first series of experiments with a sample of 20- to 50-year-old men, he found that over 60 percent of them: went all the way to 450 volts.
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help!! struggling with geometry and work is due tmrw
Answer:
SK: 32
Step-by-step explanation:
Subtract SY - KY to find SK
45 - 13 = 32
∠A and \angle B∠B are complementary angles. If m\angle A=(x-19)^{\circ}∠A=(x−19) ∘ and m\angle B=(3x+1)^{\circ}∠B=(3x+1) ∘ , then find the measure of \angle B∠B.
Answer:
∠ B = 82°
Step-by-step explanation:
complementary angles sum to 90° , then
∠ A + ∠ B = 90 , that is
x - 19 + 3x + 1 = 90
4x - 18 = 90 ( add 18 to both sides )
4x = 108 ( divide both sides by 4 )
x = 27
Then
∠ B = 3x + 1 = 3(27) + 1 = 81 + 1 = 82°
Evaluate each function.
41) k(t)=t-4; Find (10)
The value of k(10) is 6.
A function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has precisely one output and the output can be linked to its input.A relationship between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output.Each function has a range, co-domain, and domain. The given function is k(t).k(t) = t-4Here, the value of k(t), depends upon the value of 't'. k(t) is the dependent variable whereas 't' is the independent variable. Substitute the value of 't' by 10.k (10) = 10-4k (10) = 6To learn more about functions, visit :
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If mPQY = 4x – 7 and mRQY = 2x + 25, solve for x. Show all your work. Please help me. I would appreciate it. Thanks. x s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s s d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d d
The value of x is 27°, m∠=PQY=101° and m∠RQY=79°.
Given that, m∠PQY= 4x-7 and m∠RQY = 2x+25 are linear pairs of angles.
What are linear pairs of angles?Linear pairs of angles are formed when two lines intersect each other at a single point. The angles are said to be linear if they are adjacent to each other after the intersection of the two lines. The sum of angles of a linear pair is always equal to 180°.
Now, m∠PQY+m∠RQY=180°
⇒4x-7+2x+25=180°
⇒6x+18=180°
⇒6x=162
⇒x=27°
So, m∠=PQY=4x-7
=101°
and m∠RQY=2x+25
=79°
Therefore, the value of x is 27°, m∠=PQY=101° and m∠RQY=79°.
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Answer:
27
Step-by-step explanation:
which of the following expressions has a coefficient of 10 and a constact of 5
Answer:
2
Step-by-step explanation:
a car dealer claims that buying a new car sam will pay 20% less for gas than for the car he currently owns. the car sam currently drives cost 15% less to gas than dons car. don pays 800$ per year for gas car. assume all cars will be traveling the same distance. how much does he pay for his current car?
Help pls and pls give explanation!
Sam pays 680$ per year for his current car and will pay 544$ per year if he buys the new car as per dealer's claim.
According to the question statement, A car dealer claims that buying a new car Sam will have to pay 20% less for gas than for the car he currently owns. The car Sam currently drives costs 15% less to gas than Don's car. Don pays 800$ per year for gas car. It is assumed that all cars will be travelling the same distance.
We are supposed to find out how much will Sam pay for his current car.
To solve this question, we need to know about the concept of percentage of any number.
Don currently pays 800$ per year on gas.
Sam pays 15% less than what Don pays, Therefore the money Sam is paying currently will be 800$ minus 15% of 800$ i.e.,
= [tex]800 - \frac{15}{100} *800[/tex]
= [tex]800-120[/tex]
= [tex]680[/tex]$
680$ per year is the money Sam is spending currently.
If he buys the new car, according to the claim of dealer, he will pay 20% less than what he is paying currently i.e., 680$ - 20% of 680$
= [tex]680-\frac{20}{100} *680\\[/tex]
= [tex]680 - 136[/tex]
= [tex]544[/tex]$
Therefore, Sam pays 680$ per year on gas on his current car but if he buys the new car he will pay 544$ per year on gas.
Percentage: In math, a percentage is a number or ratio that can be expressed as a fraction of 100 i.e., if we are supposed to find 20% of 80 then [tex]\frac{20}{100} *80=16[/tex]If you wish to learn more about percentage, click the link given below:
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What is this called ,
, <--- That is called a comma
Help i am so confused and I need this asap!!
Answer:
25 tickets were purchased ahead of time
Explanation and Check part below
Hope this helps :)
Step-by-step explanation:
1)
25
× 11
------
275
2)
625
-275
--------
350
3)
350 ÷ 14 = 25
Check:
350 (dollars from purchased ahead of time)
+275 (dollars from purchased at the door)
--------
$ 625 (total ticket sales stated in the word problem)
Melissa bought a new dishwasher for$1,200. The manufacturer is offering a 15% rebate. How much will the dishwasher cost after the rebate?
Answer:
$1020.00
Step-by-step explanation:
15% means 15/100 divide by 100 and you get .15
.15 x 1200 gives us the rebate. The rebate is 180. We subtract that from 1200. 1200 -180 = 1020
Another way to think about this, is that we are taking 15% off we are leaving on 85%
.85 x 1200 = 1020
