Answers
The simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
How simplification of an expression work?The given expression is [tex](a^0 b^-4 cde^3)^2[/tex]
We know that any number raised to the power of 0 is 1.
Therefore,[tex]a^0 = 1[/tex].
Also, any number raised to the power of -1 is its reciprocal.
Therefore, [tex]b^-4 = 1/b^4[/tex]
Simplifying the above expression we get
[tex](1*1/b^4 * cde^3)^2 = (cde^3/b^4)^2[/tex]
Now, we apply the rule that [tex](a^m * a^n) = a^(m+n)[/tex]
So, [tex](cde^3/b^4)^2 = c^2 d^2 e^6 / b^8)[/tex]
Hence the simplified expression is [tex]c^2 d^2 e^6 / b^8[/tex]
Please note, when an exponent is raised to another exponent, we can multiply the exponents, so [tex](a^m)^n = a^(m*n)[/tex]
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Related Questions
Victoria needs to earn at least an 85 in College Algebra. Only exam scores are used to calculate her grade. Currently she has scored an 82, 81, and 90 this semester. All that remains is the semester exam, which counts twice (counts as two exam grades). She hopes to make an 85 or higher in the class.
Answers
She would need to make two extra grades of 86 each.
What is the average?Here we can see that the average of the scores that Victoria would need to make is an average score of 85 so as to be able to pull through. In this case, we can see that we have the scores; 82, 81, and 90
Let the scores tat we have to count twice be p each and then we have;
85 = 82 + 81 + 90 + p + p/5
85 = 253 + 2p/5
5(85) = 253 + 2p
p = 5(85) - 253/2
p = 86
Hence, the twice scores that need to be earned for Victoria are both 86.
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10,14,18,22,26 find the 12 term of the sequence
Answers
Answer:
30,34,38,42,46,50,54,58,62,66,70
-15 POINTS-
A.
B.
C.
Answers
Answer:
Trapezoid
Step-by-step explanation:
The math
Kana tried to solve the system of equations below. She says there are no solutions. Is Kana correct? Explain your reasoning.
Answers
The solution for the given system of equations:
x = 6 and y = 6.
Kana is incorrect about the solutions of the given equations.
What are algebraic properties?Algebraic expressions and equations follow the same set of rules as numerical expressions and equations. The order of operations is preserved, and the laws governing addition and multiplication still apply.
Associative: a + ( b + c ) = ( a + b ) + c , a ( b c ) = ( a b ) c
Identity: a + 0 = a , a ⋅ 1 = a
Inverse: a + ( − a ) = 0 , a ⋅ 1 a = 1
Distributive: a ( b + c ) = a b + a c
Given equations,
4x-2y=12 -----(a)
2x+2y=24 -----(b)
Multiplying -2 to the equation (b) like kana solution
-2 (2x+2y=24 )
By Distributive property
-2(2x+2y) = -2(24)
- 4x - 4y = - 48 ---------(c)
Now adding equation (a) and equation(c)
4x - 2y = 12
- 4x - 4y = - 48
__+___+____+__
- 6y = -36
⇒ y = 36/6 = 6.
Putting value of y in equation (b).
2(x) + 2(6) = 24
2x + 12 = 24
2x = 24 - 12
2x = 12
x =12/2 = 6
By the above calculation,
Value of x = 6 and
value of y = 6.
Hence, for the system of equations given
the solutions are:
x = 6 and y = 6
which proves that Kana is incorrect that there are no solutions.
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Does the table below represent a proportional relationship? DUE PLSS
A. Yes, because all the ratios of y to x are equal to 2.
B. Yes, because all the ratios of y to x are equal to 3.
C. No, because all the ratios of y to x are not equal.
D. No, because all the numbers are positive.
Answers
Answer: The answer to your question is the letter B. May want to assess it before answering.
Identify each angle pair as Complementary, Supplementary, Adjacent, or Vertical. Select from the drop
down menu. Select the most specific choice.
Answers
Answer:
A. Adjacent
B. Complementary
C. Complementary
Step-by-step explanation:
in the xy-plane what is the y-intercept of the graph of the equation y=(x-2)^2?
Answers
As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.
what is equation ?The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two collinear and an equal marker in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear equation is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). An identity holds true regardless of the value given to the variables.
given
Equation as given:
y = 6 (x - 1/2)(x+3)
To identify the equation's graph's y-intercept
Put x = 0 in place of it in the equation.
y = 6 (0 - 1/2)(0+3)
Apply the math operation, then find y.
y = -9
As a result, the graph of the equation y=(x-2)2 in the xy plane has the y-intercept of y = -9.
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Tell whether the angles are complementary or supplementary. Then find the value of x.
Answers
The angles add up to 180° so the angles are supplementary.
The value of x is 31.
What are corresponding angles?The angles that are in the same position on two parallel lines intersected by a transversal line on the parallel lines.
Corresponding angles are equal.
We have,
From the figure,
Two angles:
3x + 25 and 2x
These two angles form a straight angle.
Now,
3x + 25 + 2x = 180
5x = 180 - 25
5x = 155
x = 31
When the sum of two angles is 90°, then the angles are known as complementary angles.
When the sum of two angles is 180°, then the angles are known as supplementary angles.
Now,
3x + 25
= 3 x 31 + 25
= 93 + 25
= 118
2x
=2 x 31
= 62
Now,
118 + 62 = 180
Thus,
The angles are supplementary.
The value of x is 31.
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I have a question which says:
Increase 32 by 4.4%
Answers
Answer:
increase amount = 32× 4.4%
= 32 × 4.4 ÷ 100
= 32 × 44 ÷ 1000
= 1.408
32 increased by 4.4% = 32 + 1.408 = 33.408
Nina uses 2/3 cup peanuts, 1/2 cup cashews, 3/4 cups pecans, and some raisins in a recipe that makes 2 1/4 cups of trail mix. How many cups of cashews are there per cup of trail mix?
Answers
Answer:
[tex]\frac{2}{9}[/tex]
Step-by-step explanation:
1/2 ÷ 2 1/4
1/2 ÷ 9/4
1/2 x 4/9 = 4/18 = 2/9
Manicure sets at nails by Nina are marked up 47% from the cost of $8.36. What does a manicure set cost in Nina’s store?
Answers
Answer:
The cost of a manicure set in Nina's store is $12.30.
Step-by-step explanation:
To find the cost of the manicure set in Nina's store, you can use the following formula:
Selling price = Cost + Cost * Markup percentage
Substituting the given values into this formula, you get:
Selling price = $8.36 + $8.36 * 47%
To find the value of the markup percentage, you can convert 47% to a decimal by dividing it by 100: 47/100 = 0.47
Then you can use this value in the formula to find the selling price:
Selling price = $8.36 + $8.36 * 0.47
Please Click The Screenshot.
Answers
Answer:
Step-by-step explanation:
70%=0.7
90 X 0.7 = 63
ANSWER IS 63
least common number
( sorry i forgot what its called )
of 598 and 45
Answers
The least common multiple of 598 and 45 is 26, 910
How to find the least common multiple ?To find the least common multiple of 598 and 45, you can use the prime factorization method. This involves finding the prime factors of both 598 and 45 and then multiplying these prime factors when they are in their highest power.
This gives:
598 prime factorization :
2 x 13 x 23 = 598
45 prime factorization :
3 x 3 x 5 = 45
The least common multiple is;
= 2 x 13 x 23 x 3 x 3 x 5
= 26, 910
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9x+12y=-108 Please solve this, but it cannot be in fraction form!!!
Answers
All you have to do is solve this by using substitution or elimination. or in this case, because we don’t have a second equation, we would solve the x-intercept and y-intercept
X=-12
Y=-9
Which of these ratios are equivalent? Choose all that apply.
1) 16:4
2) 2:1
3) 32:2
4) 480:120
5) 4:16
6) 4:1
Answers
The ratios which are equivalent are as follows:
1) 16:4
4) 480:120
6) 4:1
Step-by-step solution:
1) 16:4
[tex]=\frac{16}{4}[/tex]
[tex]=\frac{4}{1}[/tex]
4:1
2) 2:1
[tex]=\frac{2}{1}[/tex]
2:1
3) 32:2
[tex]=\frac{32}{2}[/tex]
[tex]=\frac{16}{1}[/tex]
=16:1
4) 480:120
[tex]=\frac{480}{120}[/tex]
[tex]=\frac{4}{1}[/tex]
=4:1
5) 4:16
[tex]=\frac{4}{16}[/tex]
[tex]=\frac{1}{4}[/tex]
=1:4
6) 4:1
[tex]=\frac{4}{1}[/tex]
=4:1
Therefore, the correct solution to this question is:
1) 16:4
4) 480:120
6) 4:1
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Answer:
16:4 and 480:120 and 4:1 are equivalent.
Step-by-step explanation:
hello i neeed help with my math question 5
Answers
Answer:
Add a file to it.
Step-by-step explanation:
We can't see anything.
A pet shelter has 5 cats and 9 dogs.
Enter the ratios in the boxes.
ratio of cats to all animals:
ratio of dogs to cats:
Answers
The ratio of cats to all animals is 5:14
the ratio of dogs to cats is 9:5
Given-
Cats = 5
Dogs = 9
Total animals = cats+ Dogs
5+9=14
so the ratio of cats to all animals = 5: 14
and dogs to the cats= 9:5
Ratio give the relation between quantities of to identies.
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4) You are hired to work for a company at age 25 and the company has a retirement plan
where you can put up to 6% of your salary into the plan each month and they will match
that amount. Your starting monthly salary is $6,100, assume for simplicity sake you
never get a raise, and the retirement plan guarantees a 6.28% interest rate over the life of
the plan.
Scenario 1: You decide to start the retirement plan right away and you can afford
to put the full amount (6% of your salary) into the plan each month.
a) What is 6% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
Scenario 2: You decide to start the retirement plan right away, but you can only
afford to put 3% of your salary into the plan each month.
a) What is 3% of your salary? _______________
b) Since your company matches what you put into your retirement account, what is the
total amount put into your account each month?
_______________
c) How much money will you have in the retirement account when you reach full
retirement age, the time when you can start taking money out of the account, which is 62
years old? ________________
d) How much money did you put into the account? ________________
e) How much money did your employer put into your account? ________________
f) How much money did your account gain in interest over the years? _______________
What is the difference in the amount of money you will have at age 62 between scenarios
1 and 2? ________________
What is the difference in the amounts of money you put into retirement between
scenarios 1 and 2? _______________
How much more money did you get from your employer in scenario 1 than 2? ________
Answers
6% of the salary is $366
The total amount that would in the retirement account in the account each month is $732.
The amount that would be in the retirement account when you retire is $345,418.50.
The amount of money that you put in the account is $162,504.
The amount of money that the employer put in the account is $162,504.
The interest that was gained over the years is $20,410.50.
3% of the salary is $183.
The total amount that would in the retirement account in the account each month is $366.
The amount that would be in the retirement account when you retire is $172,709.25.
The amount of money that you put in the account is $81,252
The amount of money that the employer put in the account is $81,252
The interest that was gained over the years is $10,205.25.
How much would be in the retirement account?6% of the salary = salary x percentage
6% of the salary = 6% x $6,100
6% of the salary = 0.06 x $6,100 = $366
The amount in your account at the end of the month = amount the company puts + amount you deposit
= $366 + $366 = $732
Amount that would be in your retirement account = (1 + interest rate) x amount in the account
Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year
Amount in the account at retirement = $732 x 12 x (62 -25)
$732 x 12 x 37 = $325,008
Amount in the account at retirement = (1 + 0.0628) x $325,008 = $345,418.50
Amount the employer put in the account = $325,008 \ 2 = $162,504
Interest earned = $345,418.50 - $325,008 = $20,410.50
3% of the salary = salary x percentage
3% of the salary = 3% x $6,100
3% of the salary = 0.03 x $6,100 = $183
The amount in your account at the end of the month = amount the company puts + amount you deposit
= $183 + $183 = $366
Amount that would be in your retirement account = (1 + interest rate) x amount in the account
Amount that would have been deposited in the account at retirement = number of years until retirement x number of months in a year x amount deposited each year
Amount in the account at retirement = $366 x 12 x (62 -25)
$366 x 12 x 37 = $162,504
Amount in the account at retirement = (1 + 0.0628) x $325,008 = $172,709.25
Amount the employer put in the account = $162,504 \ 2 = $81,252
Interest earned = $172,709.25 - $162,504 = $10,205.25
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3 ratios that are equivalent to 15/40
Answers
Answer:
3.8 ,6.16 , 9.24
Step-by-step explanation:
Solve the following mentally 65% of 100
Answers
Answer: 65
Step-by-step explanation:
What is statistics. Explain?
Answers
The science of statistics focuses on creating and researching strategies for gathering, analysing, interpreting, and presenting empirical data.
Research in statistics finds application in almost all scientific domains, and research concerns in the various scientific fields inspire the creation of new statistical methods and theories. Statistics is a very interdisciplinary field. Statisticians use a range of mathematical and computational techniques while creating new approaches and researching the theory that supports such methods. Uncertainty and variation are two key concepts in the study of statistics. In science, as well as more generally in life, there are numerous circumstances where the result is unknown. Sometimes the uncertainty is caused by the fact that the result is still up in the air. Probability is a mathematical language that is used to talk about uncertain events, and it is crucial to statistics. There are numerous causes of variance that can affect any measurement or data collection attempt. By this, we indicate that the result would probably alter if the same measurement was repeated. The goal of statisticians is to comprehend and, whenever feasible, manage the sources of variation.
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Select largest number from 16,48,8
Answers
Answer:
48.
Step-by-step explanation:
8 < 16 < 48
48 > 16 > 8
Answer:
Step-by-step explanation:
Select largest number from 16,48,8
please help!
Use the Fundamental Counting Principle to determine how many kinds of teddy bears you can build if you must choose one of each category.
1) Choose the bear.
2) Choose an accessory.
3) Choose sound option.
Answers
Answer:
Step-by-step explanation:
33
WILL GIVE POINTS
Three Algebra 1 students are comparing how fast their social media posts have spread. Their results are shown in the following table:
Student Amber Ben Carter
Description Amber shared her photo with 3 people. They continued to share it, so the number of shares increases every day, as shown by the function. Ben shared his post with 2 friends. Each of those friends shares with 3 more every day, so the number of shares triples every day. Carter shared his post with 10 friends, who each share with only 2 people each day.
Social Media Post Shares f(x) = 3(4)x
Day Number of Shares
0 2
1 6
2 18 Carter shared his post with 10 friends, who each share with only 2 people each day.
Write an exponential function to represent the spread of Ben's social media post.
Write an exponential function to represent the spread of Carter's social media post.
Graph each function using at least three points for each curve. All graphs should be placed together on the same coordinate plane, so be sure to label each curve. You may graph your equation by hand on a piece of paper and scan your work, or you may use graphing technology.
Using the functions for each student, predict how many shares each student's post will be received on Day 3 and then on Day 10. Justify your answers.
If Amber decides to mail copies of her photo to the 45 residents of her grandmother's assisted living facility, the new function representing her photo shares is f(x) = 3(4)x + 45. How does this graph compare with the original graph of Amber's photo share?
Based on your results, which student's post travels the fastest? How is this shown in the equation form of the functions?
If you had to choose, would you prefer a post with fewer friends initially but more shares, like Amber, or more friends initially but fewer shares? Justify your answer with your calculations from previous questions.
Answers
a. The exponential function to represent the spread of Ben's social media post is f(x) = 2(3)^x
b. The exponential function to represent the spread of Carter's social media post is f(x) = 10(2)^x
c. On Day 3, Ben's post will have 2(3)^3 = 227 = 54 shares, Carter's post will have 10(2)^3 = 108 = 80 shares. On Day 10, Ben's post will have 2(3)^10 = 259049 = 118098 shares, Carter's post will have 10(2)^10 = 101024 = 10240 shares.
d. Adding 45 to the function representing Amber's photo shares changes the function to f(x) = 3(4)x + 45. The new function will shift the graph upward by 45 units.
e. Based on the functions, Ben's post travels the fastest because the base of the exponent, 3, is greater than the base of the exponent, 2, for Carter's post.
f. It depends on the goal of the post. If the goal is to reach a larger audience quickly, then having more friends initially but fewer shares like Carter is preferable. But if the goal is to reach a smaller audience but with a more engaged audience, then having fewer friends initially but more shares like Amber is preferable.
What is exponential function examples?An exponential function is one in which the variable is an exponent. Mathematically, it is defined as f of R in R, such that f(x) = ax, where a ϵ R, a > 0 and a ≠ 1. The graph of this function is a curve obtained by finding some ordered pairs that belong to the function and drawing this curve that passes through them.
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2. Two sidewalks in a park are represented by lines on a coordinate grid.
Sidewalk 1: 3x + 3y = 6
Sidewalk 2: y = x + 6
(a) Find the solution to the system of equations by using the substitution method.
(b) Show ALL of your steps.
Answers
Answer: x is -2 and y is 4 if needed (-2,4) is the origin form
Step-by-step explanation: first we take side walk one we subtract -3x on both sides then you get 3y=-3x+6 divide both by 3 you get y=-x+2 finally we can substitute. substitute y for x+6 you get x+6 = -x+2 do the inverse of -x on both sides you get 2x+6=2 do the inverse of 6 on both sides you get 2x=-4 divide 2 on both sides you get x=-2. substitute x of y=-x+2 to y=-(-2)+2 mult -1 x -2 is 2, 2+2 is four so y= 4 put that together x is -2 and y is 4
Triangle ABC has vertices A(-3, 3), B(2, 5), and C(4, - 3).
a. What is the x-coordinate of the centroid of triangle ABC?
(-,5/3)
Answers
Answer:
Step-by-step explanation:
To find the x-coordinate of the centroid of triangle ABC, we need to take the average of the x-coordinates of the three vertices of the triangle. The x-coordinates of the vertices of triangle ABC are -3, 2, and 4, so the average of these three numbers is (-3 + 2 + 4) / 3 = (3) / 3 = 1.
Therefore, the x-coordinate of the centroid of triangle ABC is 1. The correct answer is (-,1). The given answer (-,5/3) is not the correct x-coordinate of the centroid.
Find the measure of angle A,
Answers
The value of the Angle A is 74.3°.
What is Relation between angle and Side of a triangle?The longest side is in opposition to the longest angle, and the shortest side is in opposition to the smallest angle, respectively.
The opposite of the longest side is the greatest angle, while the opposite of the shortest side is the smallest angle. According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.
The comparable sides are proportionate and the angles are same. The sides that are opposite the same angle are the corresponding sides. For instance, if two triangles have a 90-degree angle on each side, Triangle A's opposing side will match Triangle B's opposite side.
We know:-AB/sin(c)=AC/sin(a)=BC/sin(b)
8/sin(a)=5/Sin37°
Angle= 74.3°.
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A family is canoeing downstream (with the current). Their speed relative to the banks of the river averages 2.75 mi/h. During the return trip, they paddle upstream (against the current), averaging 1.5 mi/h relative to the riverbank. Write and solve a system of equations to find the family’s paddling speed in still water. Let s equal the families paddling speed and c represent the current
a.
s + c = 2.75
s - c = 1.5
2.125 mi/h
c.
s + c = 2.75
c - s = 1.5
.60 mi/h
b.
2.75s = c
1.5s = c
1.725 mi/h
d.
2.75c = s
1.5c = s
30 mi/h
Answers
On solving the provided question, we can say that In still water, a family must paddle at a speed of 2.125 miles per hour.
What is speed?Speed is the amount of distance traveled by an object in one unit of time when it is in motion.
Given that, a family is paddling a boat (with the current). Their average speed in relation to the riverbanks is 2.75 miles per hour. On the way back, they paddle upstream (against the current), moving toward the riverbank at an average speed of 1.5 miles per hour.
Here, Let the family's speed on still water be x and the current's speed be y. Upstream speed is calculated using the formula 1.5 = x - y - - - - (1)
2.75 downstream speed = x + y - - - - (1)
Equations 1 and 2 are solved as follows: 2x = 4.25 and x = 2.125 miles per hour In still water, a family must paddle at a speed of 2.125 miles per hour.
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"what is the median of the following values 9,9,2,8,11,6,4"
Answers
Answer: 8
Step-by-step explanation:
Arrange the data in ascending order, and the median is the middle value. If the number of values is an even number, the median will be the average of the two middle numbers.
Rearrange 9, 9, 2, 8, 11, 6, 4 in ascending order:
2, 4, 6, 8, 9, 9, 11
The number eight appears to be in the very middle, therefore it is the median.
An electronics company can spend no more than $4,000 on raw materials for circuit boards. The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
To summarize the situation, a worker writes the inequality:
10c+20s≤4,000 where c is the number of ounces of copper material and s is the number of ounces of silver material.
Which graph's shaded region shows the possible combinations of raw materials the company can buy?
Answers
The given graph's shaded region shows the possible combinations of raw materials the company can buy.
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
An electronics company can spend no more than $4,000 on raw materials for circuit boards.
And, The raw materials cost $10 per ounce for copper and $20 per ounce for silver.
Here, The inequality for the given condition is,
⇒ 10c + 20s ≤ 4,000
Where, c is the number of ounces of copper material and s is the number of ounces of silver material.
So, The given graph's shaded region shows the possible combinations of raw materials the company can buy.
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