Mathematics High School

Which expression is equivalent to (m^5n/pq^2)^4

Answers

Answer 1

[tex]\left( \cfrac{m^5n}{pq^2}\right)^4 = \cfrac{(m^5n)^4}{(pq^2)^4}= \cfrac{m^{20}n^4}{p^4q^8} [/tex]

Answer 2

Answer

Find the expression is equivalent to

[tex](\frac{m^{5}n}{pq^{2}})^{4}[/tex]

To prove

As the expression is given in the question as follow .

[tex]=(\frac{m^{5}n}{pq^{2}})^{4}[/tex]

By using the exponent properties of the raise a power to a power

[tex](x^{a})^{b} = x^{ab}[/tex]

than the above expression becomes

[tex]=\frac{(m^{5}n)^{4}}{(pq^{2})^{4}}\\ =\frac{(m^{5})^{4}n^{4}}{p^{4}(q^{2})^{4}}[/tex]

[tex]=\frac{m^{20}n^{4}}{p^{4}q^{8}}[/tex]

Thus the expression is equivalent to

[tex]=(\frac{m^{20}n^{4}}{p^{4}q^{8}})[/tex]

Related Questions

Simplify the expression 3^5*6^-6/3^3*6^-4

A. 180
B. 5/2
C. 1/4
D. 3/20

Answers

3^5*6^-6/3^3*6^-4
= 3^(5-3) 6^(-6+4)
=3^2 6^-2
= 9/36
= 1/4

answer

C. 1/4

Solve each proportion. Show your work

Answers

a)
2x/7 = 12/14
x=6

I don't know b i am sorry

(2x)/7 = 12/14
cross multiply
(2x)(14) = (7)(12)
28x = 84
x = 84/28
x = 3

3 / (x - 1) = 5/7
cross multiply
5(x-1) = (7)(3)
5x - 5 = 21
5x = 21 + 5
5x = 26
x = 26/5 or 5.2

I won tickets to a trip for four to the Super Bowl. I have eight friends but I can only bring three of them. In how many ways can I form my Super Bowl party?

Answers

[tex]8C3=\dfrac{8!}{3!5!}=\dfrac{6\cdot7\cdot8}{2\cdot3}=56[/tex]

Answer:

Step-by-step explanation:

Joshua is 25 years old and has a high risk job making $72,000 a year. The insurance company charges him an extra 20% on top of his premium rate because of his job. If Joshua wants a policy that will replace five years of his salary, what is the annual premium for the cheapest policy?

Answers

I believe is $6,644...

Find the product of 543.1187 and 100

Answers

That would be 54311.87

solve for b, then find the value of b when a = 3.
4a=2b-7

a. -9/2
b. 5/2
c. 19/2
d. 17

Answers

4a=2b-7
4(3) = 2b - 7
12 = 2b - 7
2b = 12 + 7
2b = 19
b = 19/2

answer
c. 19/2

Your answer will be 19/2

Corrugated Specialties produces boxes of all kinds, and they manufacture an average of 67,000 shirt-size boxes per month. In November, they were told to increase production by 35%. How many shirt-size boxes will they produce in November? Hint: This question requires two calculations. A. 91,125 B. 23,625 C. 23,450 D. 90,450

Answers

The answer is A because p=production in november p=67000 +35%(67000)+0.35(67000)p=67000+2345p=90450

The production increased by
67,000×0.35=23,450

So they will produce in November
67,000+23,450=90,450....answer

Slope (12,-18),(11,12)

Answers

If you are trying to find the slope using only these two points then you should first take note of what your X and Y values are. For instance, 12 & 11 are your X values and -18 & 12 are your Y values. Knowing this you can now find your slope by doing y2-y1/
x2-x1. You will get the fraction -30/1 or -30 which is your slope. Hope that made sense!

Final answer:

The slope of the line passing through the points (12, -18) and (11, 12) is calculated using the formula for slope (y2 - y1) / (x2 - x1). The result is -30.

Explanation:

The subject of this question is Mathematics, more specifically the topic of 'Slope of a Line'. The grade level appears to be High School.

To answer the question 'Find the slope for the given coordinates (12,-18) and (11,12)', we use the formula to calculate the slope between two points which is (y2 - y1) / (x2 - x1). Let's take (12, -18) as (x1, y1) and (11, 12) as (x2, y2). Now we just input the values into the formula:

Slope (m) = (12 - (-18)) / (11 - 12).

This simplifies to Slope (m) = 30 / -1 = -30.

So, the slope of the line passing through the points (12, -18) and (11, 12) is -30.

Learn more about Slope of a Line here:

https://brainly.com/question/14511992

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identify the graph of the equation. What is the angle of rotation for the equation? 13x^2+6sprt3xy+7y^2-16=0

Answers

We are given the equation:

13x^2 + 6√3 xy + 7y^2 - 16 = 0

Based on the general equation of conic sections:

Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0,

A = 13
B = 6√3
C = 7
D = 0
E = 0
F = -16

So we can find the graph of the equation by solving for the discriminate B^2 - 4AC

B^2 - 4AC, substitute given:

(6^2 * 3) - 4 (13 * 7) = -256

since the discriminate is less than zero, the graph could be a circle or a parabola. In this case, the values of A and C are not equal, then our graph is a parabola.

Answer:

The answer is ellipse; 30° ⇒ answer (d)

3. what is the simplified form of x+4/7 - x+3/x+5

Answers

(x + 4) (x+5) (x + 3) 7 x^2 + 2x - 1
------- * ----- - ----------- * --- = --------------------
7 (x+5) (x + 5) 7 7( x + 5)

The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.

What is Algebra?

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]

Simplify the expression, then we have

⇒ [(x + 4) / (7)] - [(x + 3) / (x + 5)]

⇒ [(x + 4)(x + 5) - 7(x + 3)] / [7(x + 5)]

⇒ [x² + 9x + 20 - 7x - 21] / [7(x + 5)]

⇒ (x² + 2x - 1) / 7(x + 5)

The expression [(x + 4) / (7)] - [(x + 3) / (x + 5)] in simplified form will be (x² + 2x - 1) / 7(x + 5). Then the correct option is A.

More about the Algebra link is given below.

https://brainly.com/question/953809

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Benny bought 5 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 43 cards left. How many cards did Benny start with?

Answers

81 cards 43x2=86 86-5=81

What is the 7th term of the geometric sequence where a1 = -5 and a5 = -1,280?

Answers

Any geometric sequence can be expressed as:

a(n)=ar^(n-1), a=initial term, r=common ratio, n=term number.

Here we are give the initial term so we have to solve to solve for the common ratio...

a(5)=-1280 and a(1)=-5 so

-1280=-5r^(5-1)

-1280=-5r^4

256=r^4

256^(1/4)=r

4=r, so our sequence is:

a(n)=-5(4^(n-1)), so the 7th term is:

a(7)=-5(4^6)

a(7)= -20480

What would a monthly payment be on a purchase of a $10,000 car at a 5.9% for 4 years?

Answers

The current monthly pay can be calculated as follows;
A=p(1/r/100)^n
A=10000
r=5.9/12=0.5%
10000=p(1+0.5/100)^(4*12)
10000=p(1.005)^48
p=10000/(1.005)^48
p=7,871
the monthly payment will be:
7871/12
=$655.92

Answer:

$234.39

Step-by-step explanation:

A restaurant offers a choice of 2 soups, 3 entrees, and 5 desserts. how many different meals consisting of a soup, an entree, and a dessert are possible?

Answers

multiply all of the numbers

Braces are used in interval or roster notation?

Answers

Braces, also called curly brackets in used to list the elements of a set in a roster notation.

While parenthesis is used in interval notation.

What is the following sum in simplest form? sqrt 8 + 3 sqrt2 + sqrt 32
\

Answers

[tex] \sqrt{8} +3 \sqrt{2}+ \sqrt{32} =\\\\ \sqrt{4*2}+3 \sqrt{2}+ \sqrt{16*2}=\\\\2 \sqrt{2}+3 \sqrt{2}+4 \sqrt{2}=\\\\ \boxed{9 \sqrt{2} } [/tex]

Answer:-[tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.

Explanation:-

Given sum :- [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}[/tex]

To simplify, rewrite the numbers inside the root in the product of primes, we get

[tex]\Rightarrow\sqrt{2\times2\times2}+3 \sqrt{2}+ \sqrt{2\times2\times2\times2\times2}\\\\\Rightarrow\sqrt{2^2\times2}+3 \sqrt{2}+ \sqrt{4\times4\times2}\\\\\Rightarrow\sqrt{2^2}\sqrt{2}+3 \sqrt{2}+ \sqrt{4^2\times2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+\sqrt{4^2}\sqrt{2}\\\\\Rightarrow2\sqrt{2}+3\sqrt{2}+4\sqrt{2}=9\sqrt{2}[/tex]

Thus [tex]\sqrt{8}+3 \sqrt{2}+ \sqrt{32}=9\sqrt{2}[/tex] in the simplest form.

A randomly generated list of numbers from 0 to 4 is being used to simulate an event, with the number 4 representing a success. What is the estimated probability of a success?

A.75%
B.60
C.25%
D.40%

Answers

The solution would be like this for this specific problem:

Given:

{0, 1, 2, 3, 4}
Success = 2, 3, and 4

Solution:

Success = 3 numbers
Sample = 5

= 3 / 5

= .6

= .6 * 100%

= 60%

So, the estimated probability of a success based from the randomly generated list of numbers being used to simulate an event is 60%.

To add, the measure of the likelihood that an event will occur is called probability and it is quantified as a number between 0 and 1, where, loosely speaking, 0 indicates impossibility and 1 indicates certainty.

Given the equation 2x + 4 = 4x − 2, select the reasoning that correctly solves for x.

Add 2, subtract 2x, then divide by 2.
Add 2, subtract 4x, then divide by −2.
Subtract 4, subtract 2x, then divide by −2.
Subtract 4, subtract 4x, then divide by 2.

Answers

Answer:

Number One / Letter A

Step-by-step explanation:

Add 2, subtract 2x, then divide by 2.

Hope This Helps!

The sum of two numbers is 61.61. if three times three times the smaller number is subtracted from the larger? number, the result is 5.5. find the two numbers.

Answers

x + y = 61
y - 3x = 5...y = 3x + 5

x + (3x + 5) = 61
4x + 5 = 61
4x = 61 - 5
4x = 56
x = 56/4
x = 14

y - 3x = 5
y - 3(14) = 5
y - 42 = 5
y = 42 + 5
y = 47

ur 2 numbers are 14 and 47

Am I doing this right?

Answers

For which one, and are you just finding the volume

The value of the cumulative standardized normal distribution at z is 0.8770. the value of z is

Answers

The value of z would be 1.16

Final answer:

To find the z-score corresponding to a cumulative area of 0.8770 in a standard normal distribution, one can look up this area in a z-table or use statistical software, yielding a z-score of approximately 1.15.

Explanation:

The question involves finding the value of z in a standard normal distribution given that the cumulative area to the left of z is 0.8770.

The z-score is a measure that describes the position of a raw score in terms of its distance from the mean, measured in standard deviations.

To find the value of z corresponding to an area of 0.8770, one would typically use a z-table or statistical software. The z-table lists areas to the left (cumulative probabilities) for different z-values.

For an area of 0.8770, the z-score is approximately 1.15. This calculation is based on the standard normal distribution, where the mean is 0 and the standard deviation is 1.

House is 50.0 ft long and 26 ft wide and has 8.0-ft- m high ceilings. what is the volume of the interior of the house in cubic meters and in cubic centimeters?

Answers

560 cm to the power of 2

Aiden calculated the area of triangle QRS below by finding half the product of 1.5 and 1.1.

Answers

His error is the second choice.
Aiden should have calculated
area = (1.1 * 5.4) / 2
because triangle area = half the base times the altitude.

Answer: The correct option is

(B) Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.

Step-by-step explanation: Given that Aiden calculated the area of triangle QRS by finding half the product of 1.5 and 1.1.

We are to select the correct option which states the error made by Aiden.

The AREA of a triangle is given by

[tex]A=\dfrac{1}{2}\times \textup{base}\times \textup{altitude},[/tex]

where the altitude is perpendicular to the base.

In ΔQRS, the length of the base is given by

b = QS = 0.9 + 4.5 = 5.4 units

and

the length of the altitude is given by

h = 1.1 units.

So, the area of the triangle QRS will be

[tex]A=\dfrac{1}{2}\times b\times h=\dfrac{1}{2}\times 5.4\times 1.1[/tex]

Therefore, the area of ΔQRS will be calculated by finding half the product of 1.1 and 5.4.

So, Aiden made the error by finding half the product of 1.5 and 1.1, because 1.5 line is not perpendicular to 1.1 line.

Thus, Aiden should have found half the product of 1.1 and 5.4 because the 1.5 line is not perpendicular to 1.1 line.

Option (B) is correct.

the price of 9-volt batteries is increasing according to the function below, where t is years after January 1, 1980. During what year will the price reach $4? use formula P(t)=1.1*e^0.047t A.)2007 B.)2005 C.)2003 D.)2009

Answers

4=1.1e^(0.047t) divide both sides by 1.1

40/11=e^(0.047t) take the natural log of both sides

ln(40/11)=0.047t divide both sides by 0.047

t=ln(40/11)/0.047

t≈24.5

1980+24.5

2007.5

So during 2007 the price will reach $4.

Answer:

The option A.) 2007 is correct

Step-by-step explanation:

The formula which is to be used is given :

[tex]P(t) = 1.1\cdot e^{0.047t}[/tex]

where P(t) is the function of time t and t is the time in years after January 1 , 1980

Now, we need to find the year when the price will reach $4

So, substituting P(t) = 4 and finding the value of t from the given equation.

[tex]\implies 4=1.1\cdot e^{0.047t}\\\\\implies 3.64=e^{0.047t}\\\\\text{Taking natural log ln on both the sides}\\\\\implies \ln 3.64=\ln e^{0.047t}\\\\\implies 1.29=0.047\cdot t\\\\\implies t = 27.49[/tex]

So, t = 27.49 which is approximately equals to 27.5 years

So, 27.5 years after January 1, 1980 is the year 2007

Hence, The price will reach $4 in the year 2007

Therefore, The option A.) 2007 is correct

(15 POINTS) A student is chosen at random from a school. Why are the events "choosing a student of age group 5−10" and "choosing a student of age group 11−15" mutually exclusive?
a) They are independent.
b) They are dependent.
c) A student can belong to only one age group.
d) A student can belong to both the age groups.

Answers

they would indepedent a

In probability, you study the chances, odds or likelihood of the event occurring. This is determined by dividing the number of possibilities to the total number of events. But terms may come up such as 'mutually exclusive'. Suppose, event A is for students ages 5-10, while event B is for students ages 11-15. The events A and B are said to be mutually exclusive when they do not intersect or meet at some point. In other words, when a student is in group A, he cannot be in group B because that becomes invalid and untrue. That seems logical because a student cannot be both 6 years old and 12 years old, right?

Hence, the answer to this question is letter C.

PLEASE HELP

Probability allows a person to effectively measure the risks in selecting one alternative over others.

True
False

Answers

In order to mitigate and reduce the likelihood that the risk event will occur, the risk must be identified and analyzed. The process is called risk mitigation. The concept of probability occupies an important place in the risk management and decision-making process. The statement "Probability allows a person to effectively measure the risks in selecting one alternative over others" is true. It also called probabilistic modelling.

The sum of two consecutive integers is 111. find the largest of these integers

Answers

divide 111 in half

111/2 = 55.5

take the whole number above and below 55.5

so you get 55 and 56

55 + 56 = 111

56 is the larger one

PLEASE HELP!!!
The first two steps in determining the solution set of the system of equations, y = –x2 + 4x + 12 and y = –3x + 24, algebraically are shown in the table. Which represents the solution(s) of this system of equations? (3, 15) (–4, 36) (3, 15) and (4, 12) (–3, 33) and (–4, 36)

Answers

y = –x2 + 4x + 12
y = –3x + 24
so
–x2 + 4x + 12 = –3x + 24

x^2 -7x + 12 = 0
(x - 4)(x - 3) = 0
x - 4 =0; x =4
x - 3 = 0; x= 3

y = –3x + 24 = -3(3) + 24 = -9+24 = 15 (when x = 3)
y = –3x + 24 = -3(4) + 24 = -12+24 = 12 (when x = 4)

answer
(3, 15) and (4, 12)

Answer:

Step-by-step explanation:

or (3, 15) and (4, 12)

If you start with a number divide it by 4 then multiply it by two you end up with 8 squared

Answers

8 squared = 64

(x/4)*2 = 64

divide x/4 by 2 to get x/2=64

now multiply both sides by 2 to get x=128

x = 128

How to convert decimal to binary by hand?

Answers

You have to divide decimal number by 2 and then to write the reminder. Then you have to continue to divide the result by 2 and so on. At the end you have to read all those reminders ( numbers 0 and 1 ) backwards and you will get the binary number. Example: Convert 10 ( decimal ) to binary.
10 : 2 = 5 |   0
5 : 2 = 2 |   1
2 : 2 = 1 |   0
1 : 2 = 0 |   1
                        ↑
Finally: 10 ( decimal ) = 1010 ( binary )

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