Mathematics College

(a^3 / 4)^2
Simplify

Answers

Answer 1
Well, you can change this to (a^3/4)(a^3/4), which is equal to a^6/16, because a^3 times a^3=a^6, and 4 times 4=16.
I hope this helps!
-Raiden
Answer 2
Multiply the exponents in (a^3/4)^2 =a^3/2 simplified 





Related Questions

What is the quotient? x-1/7x2-3x-9

Answers

The quotient of the expression (x - 1)/(7x² - 3x - 9) cannot be determined

How to determine the quotient of the expression

From the question, we have the following parameters that can be used in our computation:

(x - 1)/(7x² - 3x - 9)

From the above, we have

degree of the numerator = 1

degree of the denominator = 2

The degree of the numerator is less than the degree of the denominator

This implies that the quotient of the expression cannot be determined

If the diameter of a penny is 19.05 millimeters and the width of each penny is 1.52 millimeters, what is the approximate volume of the roll of pennies? Use 3.14 for π and round your answer to the nearest tenth.

Answers

we know that
[volume of the roll of pennies]=pi*r²*h
r=19.05/2-----> 9.525 mm
h=1.52 mm
[volume of the roll of pennies]=pi*(9.525)²*1.52---> 433.02 mm³----> 433 mm³

the answer is
433 mm³

Answer:

Volume of cylindrical roll of penny = 433 mm³ ( nearest tenth).

Step-by-step explanation:

Given : diameter of a penny is 19.05 millimeters and the width of each penny is 1.52 millimeters.

To find : volume of the roll of pennies.

Solution : We have given that

Diameter of a penny =  19.05 millimeters.

Width of each penny = 1.52 millimeters.

Volume of cylindrical roll of penny = pi * r² * h

Where, r = radius , h =height

Radius = [tex]\frac{Diameter}{2}[/tex]

Radius=   [tex]\frac{19.05}{2}[/tex].

Radius = 9.525 mm

Plugging the values of r , h and pi = 1.14.

Volume of cylindrical roll of penny = pi * r² * h

Volume of cylindrical roll of penny =3.14 * (9.525)² * 1.52

Volume of cylindrical roll of penny = 433.02 mm³

Volume of cylindrical roll of penny = 433 mm³ ( nearest tenth).

Therefore, Volume of cylindrical roll of penny = 433 mm³ ( nearest tenth).

A ____________ is a graph that uses adjacent rectangles to display frequencies, or relative frequencies, of quantitative data values. box-and-whisker plot histogram convenience sample mean absolute deviation

Answers

The correct answer is: Histogram

Explanation:
In simple terms histogram is a graph that consists of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval. It represents the distribution of the numerical data. Hence the correct answer is histogram as it conforms to the explanation about graph given in the question. 

When paying off debts ,you should ___ .
A. pay the minimum
B.pay as much as possible
C.pay slightly more than the minimum
D.pay exactly half of what you owe

Answers

B: because you will have to pay an little more when u have the money
Answer:

B.pay as much as possible

Step-by-step explanation:

Debts are unpaid money that a person owes to its lenders. The lender can be any bank or any other financial institution or any person.

Long accumulated debts on banks, if not paid, can result in a person filing for bankruptcy. So, it is always good if you pay your debts on time.

Paying minimum or slightly more than minimum amount will result in paying more in the near future. It is possible that if you always pay minimum amount, you will not be able to clear debts anytime soon.

So, its best that if you have money, always pay as much as possible to get rid of your debt.  

given the function, f(x)=(x^3)-(3x^2)+(64x)-192 find the zeros

Answers

There are a few ways to find the zeros. I am going to use the grouping method.

NOTE: GCF = Greatest Common Factor

The function: [tex]f(x) = x^3 - 3x^2 + 64x - 192[/tex] 

Lets group [tex]x^3 - 3x^2[/tex] and [tex]64x - 192[/tex]

Factor [tex]x^3 - 3x^2[/tex]
Find GCF
GCF = [tex]x^2[/tex]

Divide out the GCF [tex]x^2[/tex]
[tex]\frac{x^3 - 3x^2}{x^2} = (x - 3)[/tex]

Factor From:
[tex]x^2(x - 3)[/tex]

Now factor 64x -192
GCF of 64 and 192 = 64
Factor out 64 from 64x - 192
[tex]\frac{64x - 192}{64} = (x - 3)[/tex]

Factor Form:
[tex]64(x - 3)[/tex]

Now that we have factored the groups, bring them together.
[tex] x^2(x-3)[/tex]
[tex] 64(x-3)[/tex]

[tex]x^2(x-3) + 64(x-3)[/tex]

Since (x-3) is the GCF of [tex]x^2(x-3) + 64(x-3)[/tex], factor (x-3) out.
[tex]\frac{x^2(x-3) + 64(x-3)}{(x-3)} = x^2 + 64[/tex]

Factor Form:
[tex](x-3)(x^2 + 64)[/tex]

Now set [tex](x^2 + 64)(x-3)[/tex] to zero and solve for x.
[tex](x^2 + 64) = 0[/tex]
[tex]x^2 = - 64[/tex]

Take the square root of both sides of the equal sign:
[tex]\sqrt{x^2} = \sqrt{-64}[/tex]
[tex]x = \sqrt{-64}[/tex]
[tex]x = \pm 8i[/tex]

Now for (x-3)
x - 3 = 0
x - 3 + 3 = 3
x = 3

The zeros and answers:
[tex]x = -8i[/tex]
[tex]x = 8i[/tex]
x = 3




The diameter of a small gear is 16cm. This is 2.5 cm more than 1/4 of the diameter of a larger gear. What is the diameter of the larger g!ear

Answers

The problem statement tells us ...
  16 cm = 2.5 cm + (1/4)*(large gear diameter)

We can subtract 2.5 cm and multiply by 4 to find the large gear diameter.
  13.5 cm = (1/4)*(large gear diameter)
  54 cm = (large gear diameter)

The diameter of the larger gear is 54 cm.

A plane left Chicago at 8 A.M. At 12 P.M., the plane landed in Los Angeles, which is 1,700 miles away.

If the plane travels at a constant rate, how many miles did it travel per hour?


Answers

first find the amount of time:
 12 pm - 8 am = 4 hours

now divide the total miles traveled by the amount of time travleed:

1700 miles / 4 hours = 425 miles per hour

Form a sequence that has two arithmetic means between -13 and 89. a. -13, 33, 43, 89 c. -13, 21, 55, 89 b. -18, -36, -72, -144 d. -18, -81, -144

Answers

Form a sequence that has two arithmetic means between -13 and 89. a. -13, 33, 43, 89 c. -13, 21, 55, 89 b. -18, -36, -72, -144 d. -18, -81, -144

Solution:

Since  it has to be between -13 and 89, letter d and b are not anymore considered to be the answer.

for a:
33-(-13)=46=d
43-33=10=d the value for this d is different from the two sequence,
89-43=46=d
they have different value for d, thus this is not the answer!

for c:
21-(-13)=34=d
55-21=34=d
89-55=34=d

they have the same value for d, thus the correct answer is  c. -13, 21, 55, 89

what does life expectancy measure

Answers

Life expectancy is an indication of how long a person can anticipate living. It provides a measure of the number of years remaining in a person's life at a particular age, provided death rates do not change.

Hope this helps! :)

To prepare for the party, the host made a large batch of punch. The recipe makes 8 gallons of punch. How many cups of punch can be served from this batch?

A. 24
B. 128
C. 64

Answers

B- 128 cups of punch from this batch

Naoya read a book cover to cover in a single session, at a rate of 55 pages per hour. After 4 hours, he had 350 pages left to read. Let P(t), left parenthesis, t, right parenthesis denote the number of pages to read P as a function of time t (measured in hours). Write the function's formula

Answers

Final answer:

The function's formula that represents the number of pages Naoya has left to read at time t would be P(t) = 570 - 55t.

Explanation:

From the information given we know that Naoya reads at a rate of 55 pages per hour. After 4 hours of reading, he still has 350 pages left to read. This means that before he started reading, he had (55 pages/hour * 4 hours + 350 pages) = 570 pages in total. Since he reads at constant rate, the function that describes the remaining pages to read would be P(t) = 570 - 55t, where t represents the time in hours and P(t) is the number of pages left to read.

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A woman is looking for a bigger square office. She finds an office twice the area of her current office. if the perimeter of her current office is 88feet, how many square feet is the new office?

Answers

The woman's new office has twice the area of her current office. By calculating the side length of the current square office from the perimeter and then finding the area, we determine the new office's area to be 968 square feet.

The question asks about calculating the area of a larger office which is twice the area of the woman's current office. Knowing the current office perimeter allows us to find the side length of the current square office and use it to calculate the area of both the current and the new office.

Calculate the side length of the current office from the given perimeter. The formula for the perimeter of a square is 4 × side length. Given that the perimeter is 88 feet, we divide by 4 to find that the side length of the current office is 22 feet. (88 ÷ 4 = 22)To find the area of the current office we square the side length (side length × side length). Thus, the area is 22 feet × 22 feet = 484 square feet.The new office has twice the area of the current one, so its area is 2 × 484 square feet = 968 ft².

The area of the new, larger office is 968 ft².

Use the drop-down menus to identify the method used to collect data for each scenario. Daniel used the Internet to research the number of tornados reported in the United States each year for the past 10 years. Mia asked 20 random students at her school how many hours they spend on the computer each day. Beatriz recorded the number of customers entering a store for each hour interval.

Answers

The answers are published data, survey, and observational study in that order on elearning for anyone still wondering.

Answer:


Step-by-step explanation:

Given:

1) Daniel used the Internet to research the number of tornados reported in the United States each year for the past 10 years.

Published data - Already recorded data used

2)  Mia asked 20 random students at her school how many hours they spend on the computer each day.

Survey by Random sampling -- since a small size of whole population selected at random

3) Beatriz recorded the number of customers entering a store for each hour interval.

This is observational data because data was collected after really observing and recording the number of customers entering a store for each hour interval.

What is the complete factorization of r2 - 6r - 9s2 + 9? A) (r - 3 + 3s)(r - 3 - 3s) B) (r + 3 + 3s)(r - 3 - 3s) C) (r - 3 + 3s)(r - 3 + 3s)

Answers

[tex]r^2-6r-9s^2+9=r^2-6r+9-9s^2=r^2-2\cdot r\cdot3+3^2-9s^2\\\\\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\=(r-3)^2-9s^2=(r-3)^2-(3s)^2\\\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(r-3-3s)(r-3+3s)\to A[/tex]
Final answer:

We have factorized the expression 'r2 - 6r - 9s2 + 9' into (r - 3)^2 - (3s)^2 and then used the difference of squares formula to find the factorization as (r - 3 + 3s)(r - 3 - 3s). So the correct answer is option A)

Explanation:

The question asked for the complete factorization of the expression r2 - 6r - 9s2 + 9. To factorize this, we can rewrite it into the formula form of a perfect square, which is a^2 - 2ab + b^2 = (a - b)^2.

Our expression fits this form when a = r and b = 3s. Following this, we can rewrite the expression as (r - 3)^2 - (3s)^2 = (r - 3 + 3s)(r - 3 - 3s). Therefore, the correct answer is option A) (r - 3 + 3s)(r - 3 - 3s)

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On the 4th of July, the probability of a person having a car accident is 0.08. What is the probability of a person driving while intoxicated or having a car accident if the probability of a person driving while intoxicated is 0.25 and the probability of a person having a car accident while intoxicated is 0.13?

Answers

The correct answer is D, 0.20. You add the probabilities of either situation occurring and subtract the probability of both of them occurring.
The answer is 0.20

0.25 + 0.08 - 0.13 = 0.20

hey can you please help me posted picture of question

Answers

For this case we have the following function:
 f (c) = (9/5) c + 32
 Substituting the value of c = 20 we have:
 f (20) = (9/5) (20) + 32
 Rewriting we have:
 f (20) = (9) (4) + 32
 f (20) = 36 + 32
 f (20) = 68
 Answer:
 The conversion for this case is given by:
 f (20) = 68
 option A

hey can you please help me posted picture of question

Answers

The correct answer is option D

The solution is shown below:

[tex] x^{2} +16 \\ \\ = x^{2} +(4)^{2} \\ \\ = x^{2} -(-1)(4)^{2} \\ \\ = x^{2} -i^{2} (4)^{2} \\ \\ = x^{2} -(4i)^{2} \\ \\ =(x+4i)(x-4i) [/tex]

Find the pair of numbers whose sum is 46 and whose product is a maximum.

Answers

To solve this problem you must apply the proccedure shown below:

 1. Let's call:

 x the first number and and the other number 46-x

 2. Then, the product of both numbers is:

 y=x(46-x)

 3. When you apply the distributive property, you obtain:

 y=46x-x^2

 4. As you can see, the coefficient of x^2 is negative, this means that the maximun value is at the vertex of the parabola.

 5. Then, you have:

 h=-b/2a
 h=-46/2(-1)
 h=23   (x coordinate)

 6.Then:

  y=46x-x^2
 y=46(23)-(23)^2
 y=529

 Therefore the answer is: 23 and 529.

 

The lengths of infants at birth in a certain hospital are normally distributed with a mean of 18 inches and a standard deviation of 2.2 inches. find the probability that an infant selected at random from this hospital measures between 16 and 21 inches.

Answers

Mean, m = 18 in
Standard deviation, SD = 2.2 in
Range: 16 ≤ X ≤ 21 in

Calculating Z value,
Z = (X-m)/SD

Then,
Z1 = (16-18)/2.2 ≈ -0.91
Z2 = (21-18)/2.2 ≈ 1.36
From Z table, and at Z1 = -0.91, and Z2 = 1.36;
P(16) = 0.1814
P(21) = 0.9131

Therefore,
P(16≤X≤21) = 0.9131 - 0.1814 = 0.7317
The probability that a child selected randomly measures between 16 and 21 in is 0.7317.

hey can you please help me posted picture of question

Answers

Each leaf on the tree diagram represents a possible combination. So we are to find the total number of combinations for the given scenario. 

There are 5 ways to select the pant, 7 ways to select a shirt and 3 ways to select the shoes.

Total number of combinations will be the product of all these ways the dress items can be selected.

So, number of combination of outfits = 5 x 7 x 3 = 105 

Therefore, option B gives the correct answer

how will the volume of the pyramid change if each side is multiplied by a factor of 1/2

Answers

we know that
[volume of a original cone]=(1/3)*pi*r²*h

[volume of a dilated cone]=(1/3)*pi*(r/2)²*(h/2)--->(1/8)* [(1/3)*pi*r²*h]
so
[volume of a dilated cone]=(1/8)* [volume of a original cone]

the answer is
the volume of the cone will be reduced one eighth

Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now?

Answers

Helen is 16 and Jane is 8

Let the age of the Jane be [tex] x [/tex]

So age of Helen =  [tex] x [/tex] + 8

Twenty years ago,

Age of Jane = [tex] x [/tex] - 20

And age of Helen = [tex] x [/tex] + 8 - 20 = [tex] x [/tex] - 12

Helen was three times as old as Jane

[tex] x [/tex] - 12 = 3 ([tex] x [/tex] - 20)

[tex] x [/tex] - 12 = 3 [tex] x [/tex] - 60

Add - 3[tex] x [/tex] on both sides,

[tex] x [/tex] - 3 [tex] x [/tex] - 12 = 3 [tex] x [/tex] - 3 [tex] x [/tex] - 60

-2[tex] x [/tex] - 12 = - 60

Add  12 on both sides

-2[tex] x [/tex] - 12  + 12 = - 60 + 12

-2[tex] x [/tex] = - 48

Divide both side by -2

[tex] \frac{-2x}{-2}=\frac{-48}{-2} [/tex]

[tex] x [/tex] = 24

Age of Jane = 24 yrs

Age of Helen = 32 yrs



Solve for y in terms of x.

2/3y - 4 = x


Please help . Time is critical for me in school rn

Answers

Answer:

[tex]y=\frac{3}{2}(x+4)[/tex]

Step-by-step explanation:

We are given

[tex]\frac{2}{3}y-4=x[/tex]

Since, we have to solve for y

so, we will isolate y on anyone side

Firstly, we add both sides by 4

[tex]\frac{2}{3}y-4+4=x+4[/tex]

[tex]\frac{2}{3}y=x+4[/tex]

Multiply both sides by 3

[tex]3\times \frac{2}{3}y=3\times(x+4)[/tex]

[tex]2y=3\times(x+4)[/tex]

now, we can divide both sides by 2

and we get

[tex]y=\frac{3}{2}(x+4)[/tex]

what does 1/2x+30=55 equals?

Answers

Subtract 30 from both sides.

[tex] \frac{1}{2}x = 25 [/tex]

Multiply both sides by 2 to get x by itself.

[tex]x = 50[/tex]

The answer is x = 50.
1/2x+30=55
        -30   -30
1/2x=25
   *2    *2
x=50.

Apply the commutative property to 13 × 7 × 21 to rearrange the terms and still get the same solution

Answers

The given terms can be arranged in 3! = 6 ways. The other 5 are ...
  13 × 21 × 7
  7 × 13 × 21
  7 × 21 × 13
  21 × 7 × 13
  21 × 13 × 7
Any of these arrangements will give the same answer, 1,911.
Final answer:

The commutative property in mathematics says that the order in which numbers are multiplied doesn't change the product. For example, using the commutative property, the product of 13 x 7 x 21 will be the same as 7 x 21 x 13, which is 1911.

Explanation:

The commutative property is a fundamental concept in Mathematics which states that for multiplication and addition, numbers can be moved around (or commuted) without changing the result. For example, if you have the multiplication problem 13 * 7 * 21, thanks to the commutative property, you can rearrange this problem to: 7 * 21 * 13 or 21 * 13 * 7 or any other arrangement of these three numbers, and the result will remain the same.

Let’s see this in action:
Original arrangement: 13 * 7 * 21 = 1911
Changed arrangement: 7 * 21 * 13 = 1911
As you can see, regardless of how the terms were rearranged, the answer remained the same, thus demonstrating the commutative property.

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dose any one know these 4 answer i am raly struggling and i need the help asap

Answers

I can help.

Remember that the equation for circumference is 2(pi)(r). For the first question, we are given the circumference, 235.5 cm. So, we can reverse this equation to find the radius, so 235.5=2(pi)(r). We divide 235.5 by 2 to get 117.25, and then divide it by pi to get approximately 37.5 cm. Now we multiply by 2 to find the diameter since d=2r, and the diameter is about 75 cm, or D.

We can do the same thing for the second question, so 141.3=2(pi)(r), or 70.65=(pi)(r). Dividing this by pi results in r=22.5 ft, D. again.

Now we can do the same for the third question, and make the equation 47.1=2(pi)(r), or 23.55=(pi)(r). Now divide by pi and get r=7.5. Multiplying this by 2 for diameter yields 15 in, or B.

For the last problem, you do 157=2(pi)(r), or 78.5=(pi)(r). Dividing 78.5/pi=25. So, r=25 m, or A.

Hope this helps!


can someone help me!!!

Answers

let s the side of fabric square and A area of fabric square:

s=√A

s=√2940

s1= 54.22

s 2= √62

s2= 7.9

e is correct

hey can you please help me posted picture of question

Answers

The appropriate selection is ...
  D. x

_____
This is the purpose and meaning of an inverse function. Using inverse functions is the way we solve equations involving functions. They "undo" the effect of the function.
The answer is D. x

In mathematics, an inverse function (or anti-function) is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x, and vice versa. I.e., f(x) = y if and only if g(y) = x.





determine 7th term in the geometric sequence whose first term is 5 and whose common ratio is 2.

Answers

[tex]\bf n^{th}\textit{ term of a geometric sequence} \\\\ a_n=a_1\cdot r^{n-1}\qquad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ a_1=5\\ r=2\\ n=7 \end{cases} \\\\\\ a_7=5\cdot 2^{7-1}\implies a_7=5\cdot 2^6\implies a_7=320[/tex]

The 7th term of the geometric sequence with the first term being 5 and a common ratio of 2 is calculated using the formula Tn = [tex]a * r^{n-1}[/tex]. The 7th term is found to be 320.

The question asks us to determine the 7th term in a geometric sequence where the first term is 5 and the common ratio is 2. The formula for the nth term of a geometric sequence is given by
Tn = [tex]a * r^{n-1}[/tex], where Tn is the nth term, a is the first term, r is the common ratio, and n is the term number. Substituting the given values into the formula, we can find the 7th term as follows:
T7 = [tex]5 * 2^{(7-1)}[/tex] = 5 * 2⁶ = 5 * 64 = 320. Hence, the 7th term of the geometric sequence is 320.

what is the slope of the line

Answers

slope = 4/1 = 4

hope it helps
Slope triangle is rise/run so count how many times it goes up (4) and how many times it goes to the right (or left if it is negative) so that is one. 

4/1= 4 
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