Mathematics College

Product of prime factors for 60 = 2x2x3x5
How do i write this in index form?
I have tried by simplifying so it is 2 to the power of 2 x 3 x 5
It stills says it is incorrect, anyone know?

Answers

Answer 1
The prime factors of 60
60 = 2,2,3,5
Index Form =  [tex]2^2 \times 3 \times 5[/tex]
They might want something like below for the index form
[tex]2^2 \times 3^1 \times 5^1[/tex]
Answer 2
Final answer:

The correct index form for the product of prime factors of 60, which is 2x2x3x5, is 2^2 x 3 x 5.

Explanation:

The product of prime factors for 60 is indeed 2x2x3x5. To write this in index form, we group the same numbers together and count how many there are. Then we use the base and exponent form to write it. Here, 2 is repeated twice. So, 2x2 can be written as 2^2. The primes 3 and 5 are each given once, so, we do not write powers for them. Therefore, the correct index form is 2^2 x 3 x 5.

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Related Questions

Molly's Custom Kitchen Supplies sells handmade forks and spoons. It costs the store $1.70 to buy the supplies to make a fork and $1.30 to buy the supplies to make a spoon. The store sells forks for $5.60 and spoons for $5.40. Last April Molly's Custom Kitchen Supplies spent $37.90 on materials for forks and spoons. They sold the finished products for a total of $147.20. How many forks and how many spoons did they make last April?

Answers

Since the amount of money it costs for the forks are 1.70f (if f is the number of forks, due to that we add 1.70 for each fork) and the spoons is 1.30s (with s being the number of spoons), the total money spent is
1.7f+1.3s=37.9 and the total money made is
5.6f+5.4s=147.20 dollars (since forks sell for 5.6 dollars and spoons 5.4)

Multiplying the first equation by -5.4/1.3 and adding it to the second, we end up with -1.46153846154f=-10.2307692308 and by dividing both sides by -1.46153846154, we get f=7. Plugging that into 1.7f+1.3s=37.9, we get 1.7*7+1.3s=37.9. Subtracting 1.7*7 from both sides and then dividing them by 1.3, we end up with (37.9-1.7*7)/1.3=s=20

Raffle tickets are being sold for a fundraiser. The function a(n) relates the amount of money raised to the number of tickets sold, n. 

It takes as input the number of tickets sold and returns as output the amount of money raised. 

a(n) = 3n – 15 

Which equation represents the inverse function n(a), which takes the money raised as input and returns the number of tickets sold as output?


Answers

Answer:

For apex it is N(a)= [tex]\frac{a+15}{3}[/tex]

Final answer:

To find the inverse function, solve the equation a = 3n - 15 for n. The inverse function is n(a) = (a + 15) / 3.

Explanation:

To find the inverse function, we need to solve the equation n(a) = 3n - 15 for n.

Step 1: Replace n(a) with a: a = 3n - 15

Step 2: Solve for n.

Add 15 to both sides of the equation.a + 15 = 3nDivide both sides of the equation by 3.(a + 15) / 3 = n

Therefore, the inverse function is n(a) = (a + 15) / 3.

Ms.Smith has 132 stickers to give to her students.Shehas 5 students.If she gives the same number of stickers to each of her students how many stickers will she have leftover

Answers

If Ms. Smith hands out 130 of her stickers between all 5 of her students each will have 26. Which means she will have 2 remaining
She'll have 24.6 stickers left over because you divide the 132 stickers with the 5 students

Solve 8d + 4d – 5d – 4 = 3d.

Answers

8d + 4d - 5d - 4 = 3d
12d - 5d - 4 = 3d
7d - 4 = 3d
7d = 3d + 4
4d = 4
d = 1
8d+4d-5d-4=3d
 7d-4=3d
 7d-3d=4
 4d=4
 d=1

A flea weighs 8 decigrams, and an ant weighs 3 milligrams. How much more does a flea weigh than an ant?

Answers

now, a decigram is "deci" one tenth of a gram, 1/10 gram.

whilst a milligram is "milli" one thousandth of a gram, 1/1000 gram

now, the flea is 8 of those decigrams thus is 8 * (1/10) grams

the ant is 3 of those milligrams thus 3 * (1/1000) grams

let's find their difference.

[tex]\bf 8\left( \frac{1}{10} \right)\implies \cfrac{8}{10}\implies \stackrel{decigrams}{\cfrac{4}{5}} \\\\\\ 3\left( \frac{1}{1000} \right)\implies \stackrel{milligrams}{\cfrac{3}{1000}}\\\\ -------------------------------\\\\ \cfrac{4}{5}-\cfrac{3}{1000}\impliedby \textit{our LCD is 1000}\implies \cfrac{(200\cdot 4)-3}{1000}\implies \cfrac{800-3}{1000} \\\\\\ \cfrac{797}{1000}\implies 797\left( \frac{1}{1000} \right)\implies 797~milligrams[/tex]

Answer:

797 milligrams

Step-by-step explanation:

Hope this helps!

The second angle of a triangular kite is four times as large as the first. The third angle is 45 degrees more than the sum of the other two angels. Find the measurement of the second angle.

Answers

the  ANSWER is
92.5 degrees
because second angle = 4x = 4*17.5 = 70 deg
so 
third angle = 5x+5 = 5*17.5 + 5= 92.5 deg

Need help solving this :/

Answers

[tex]\bf \begin{array}{cccll} x&171x-337778&\textit{internet users}\\ ----&-------&------\\ 2004&171(2004)-337778&4906\\ 2005&171(2005)-337778&5077\\ 2006&171(2006)-337778&5248\\ 2007&171(2007)-337778&5419\\ 2008&171(2008)-337778&5590\\ 2009&171(2009)-337778&5761\\ 2010&171(2010)-337778&5932\\ \end{array}[/tex]

now, that's using the table of values, let's do so using N = 5932

[tex]\bf N=171x-337778\implies 5932=171x-337778 \\\\\\ 5932+337778=171x\implies 343710=171x\implies \cfrac{343710}{171}=x \\\\\\ 2010=x[/tex]

What is the answer to the distributative operation of 85 divided by 5

Answers

85(2)+85(3)=255 but if u divide it normally it would be 17

Create a table of data for two different linear functions. The table should use the same values of x for both functions. Based on your table, will the graphs of these two functions intersect? Explain your answer. 40 POINTS

Answers

3x + 1 = y

x: 1 | 2 | 3  |
------|---|--- |----------------
y: 4 | 7 | 10|

so make points at (1,4) (2,7) and (3,10), and connect them to get the line

4x + 1

x: 1 | 2 | 3
----------------
y: 5 | 9 | 13

Make points at (1,5) (2,9) and (3,13)

IF they do not intersect yet, continue making points until they intersect. Make note of the point in which they intersect, and that is your answer

hope this helps

A company manufactures photo cells it uses the expression

Answers

What expression it’s not completed

expand and simplify: 5(x-3)+2(2x+1)

Answers

First you have to distribute.
5(x - 3) + 2(2x + 1)
5x - 15 + 4x + 2
Then you combine like terms.
9x - 13
This is your final answer. I hope this helps love! :)
5(x-3)+2(2x+1)
5x-15 +2(2x+1)
 5x-15 +4x +2
      9x-13

9x-13 is your answer

Carly sold 18 rolls of wrapping paper. that is 2 time as many as may rolls as Jasmine sold.

Answers

Jasmine sold 9 rolls.
18x2 would equal 36 if its a word problem that's supposed to be solved. hope it helps!


The environment club is selling indoor herbs gardens for Earth Day. Each member is encouraged to sell at least 10 gardens. You sell 3 on Monday and 4 on Tuesday. Write and solve an inequality to find the possible number of gardens you can sell to reach your goal.

Answers

The inequality is looking for a value of "at least 10" gardens. This means something "greater than or equal to" 10 (>=10). After selling 3 on Monday plus 4 on Tuesday, this leaves "x" to be sold to reach the goal. By setting this on the same side as the 7, we can create the inequality to find out how many more are needed, at minimum, to reach our stated goal: 7 + x >= 10, which, when subtracting the 7 out from both sides of the inequality, leaves x >= 3 gardens.

A bank offers a money market account paying 4.9% interest compounded semiannually. A competing bank offers a money market account paying 4.8% interest compounded daily. Which account is the better investment?

Answers

Assume $1000 at 4.9% semi-annually = $1,049.60
Assume $1000 at 4.8% daily =  $1,049.17

Let's try a bigger number $50'000 4.9% semi-annually $52,480.01
                                           $50,000 4.8% daily =              $52,458.37
It's a wash, the question is how long will you be investing, that might make a difference. I calculated 12 Millions over 6 years and bank A would be the better choice. Semi-annual compounded at 4.9%

what two consecutive numbers the square root of 10 between

Answers

[tex]\bf \sqrt{10}\approx 3.162278 \\\\\\ \boxed{3}\text{\textemdash\textemdash\textemdash}3.162278\text{\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash\textemdash}\boxed{4}[/tex]

Evaluate the integral. (remember to use absolute values where appropriate. use c for the constant of integration.) 2 (t + 2)(t − 6) dt

Answers

do you mean 2(t+2)(t-6) dt?
if yes then,
expanding you have
2 { t² -4t -12} dt
2 ∫ t²-4t-12 dt
2 [ t³ -4t² -12t +c]

In a steel titanium alloy, 360 grams of steel were required to make 1200 grams of the alloy. How much titanium was required to make 1600 grams of the alloy?

Answers

check mathematics app

What is the probability that the selected consumer is 35–55 years old or likes crunchicles?

Answers

Final answer:

The probability that a selected consumer is 35–55 years old or likes crunchicles is 0.5.

Explanation:

To determine the probability that the selected consumer is 35–55 years old or likes crunchicles, we need to add the probabilities of these two events happening individually and subtract the probability of both events happening. Let's assume the probability of a randomly selected consumer being 35–55 years old is 0.4 and the probability of a randomly selected consumer liking crunchicles is 0.3. The probability of a randomly selected consumer being both 35–55 years old and liking crunchicles is 0.2. Therefore, the probability that the selected consumer is 35–55 years old or likes crunchicles is:

P(35-55 or crunchicles) = P(35-55) + P(crunchicles) - P(35-55 and crunchicles)

= 0.4 + 0.3 - 0.2 = 0.5

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A microwave is placed on top of two boxes. One box is 2 feet 5 inches tall the other box is 3 feet 11 inches tall and the microwave is 3 feet 3 inches tall. How tall are they combined ?

Answers

Okay, so looking at the numbers.
1 foot =12 inches 

2*12= 24+5= 29 inches

Second box
3*12= 36+3=39

Adding both of those numbers, 29 and 39 you get 68 inches.

So, if you combine the boxes, you get 5 feet and 8 inches.

The answer in inches is 68, and the answer in feet and inches is 5 feet, 8 inches.

Hope this helps!

3(2x+4)-7=-2(x-5)+3x what does x equal? A.1 B.-1 C.-5 D.5

Answers

Solve for x:3 (2 x + 4) - 7 = 3 x - 2 (x - 5)
3 (2 x + 4) = 6 x + 12:6 x + 12 - 7 = 3 x - 2 (x - 5)
Add like terms. 12 - 7 = 5:6 x + 5 = 3 x - 2 (x - 5)
-2 (x - 5) = 10 - 2 x:6 x + 5 = 3 x + 10 - 2 x
3 x - 2 x = x:6 x + 5 = x + 10
Subtract x from both sides:(6 x - x) + 5 = (x - x) + 10
6 x - x = 5 x:5 x + 5 = (x - x) + 10
x - x = 0:5 x + 5 = 10
Subtract 5 from both sides:5 x + (5 - 5) = 10 - 5
5 - 5 = 0:5 x = 10 - 5
10 - 5 = 5:5 x = 5
Divide both sides of 5 x = 5 by 5:(5 x)/5 = 5/5
5/5 = 1:x = 5/5
5/5 = 1:Answer: x = 1

2x + y = -2
x + y = 5
 The x-coordinate of the solution to the system shown is _____.
 -7
-3
3
7

Answers

Subtract equation (2) from equation (1)
Subtract the like terms (ie subtract straight down)

2x - x = 1x = x
y - y = 0y = 0 so the y terms go away
-2 - 5 = -7

We end up with x = -7

Answer:

-7

Step-by-step explanation:

Hello Brainly,
Please send the details for the area of each shape.
Sincerely,
Leanoriaia

Answers

This type of problems are solved by partitioning the figure into rectangles, whose areas we can find easily.

Picture 1)

From the point denoted by E, draw two altitudes towards the sides AG and AC.

Since ED is 3, then BC is 3. Thus, AB=4-3=1. 

Since EF is 1, then HG is 1, so AH=3-1=2.


The area of the figure is equal to the area of rectangle ACDH + the area of the square HEFG.

That is, the area of the figure is 4*2+1*1=8+1=9 (square in).

Picture 2)

As in the first part, draw the altitudes EB and EH from point E.

GF is 5, so AB is 5. This means that BC=7-5=2 (in).

FE is 3, so GH is 3, that is HA=6-3=3.

Thus, Area(figure)=Area(ABFG)+Area(BCDE)=5*6+2*3=30+6=36 (square in.)

Answer: 9 (square in); 36 (square in.)

Find two positive numbers whose product is 81 and whose sum is a minimum. (if both values are the same number, enter it into both blanks.)

Answers

Answer:

The two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.

Step-by-step explanation:

81 is divisible by 1 and 81, since 81/1 = 81 and 81/81 = 1.

81 is divisible by 3 and 27, since 81/3 = 27 and 81/27 = 3.

81 is divisible by 9, since 81/9 = 9.

Their sums are.

81 + 1 = 82.

3 + 27 = 30

9 + 9 = 18.

So the two positive numbers whose product is 81 and whose sum is a minimum are 9 and 9.

Answer:

The two positive numbers will be 9 and 9.

Step-by-step explanation:

Let the two positive numbers be x and y.

It is given that the product of the number is 81 the sum of them is minimum.

So, the product can be written as [tex]xy=81[/tex].

The sum can be written as [tex]x+y=x+\dfrac{81}{x}[/tex]. It is required to minimize the sum.

Differentiate the sum as,

[tex]x+y=x+\dfrac{81}{x}\\1+y'=1-\dfrac{81}{x^2}=0\\x^2=81\\x=9\\y=\dfrac{81}{x}\\y=9[/tex]

Now, the second derivative of the sum will be,

[tex]y''=2\times \dfrac{81}{x^3}>0[/tex]

So, the second derivative is positive and hence, the sum will be minimum at x=9.

Therefore, the two positive numbers will be 9 and 9.

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Which expression is equivalent to 6 – (–8)?

Answers

[tex] 6 -(-8)[/tex] 

[tex]6+8 [/tex] 

[tex]=14[/tex]

The expression 6 – (–8) will be equivalent to 14.

What is an expression?

An expression is a combination of some mathematical symbol such that arithmetic operator and variable such that all are constrained and create an equation.

In other meaning, expression is very useful to determine the end or root value of constraint.

For example 3x +5y

The constraint of expression is represented as = or <, >.

Given the expression,

6 – (–8)

By multiplication,

Negative signs become positive

6 – (–8) = 6 + 8 = 14

Hence "The expression 6 – (–8) will be equivalent to 14.".

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What is a point estimate of the difference between the mean annual premium in pennsylvania and the national mean (to the nearest dollar)?

Answers

Given that the mean annual premium for automobile insurance in the United States is $1503 and that a sample of 25 automobile insurance policies from the state of Pennsylvania showed a mean annual premium of $1440

Then the point estimate of the difference between the mean annual premium in pennsylvania and the national mean (to the nearest dollar) is $1,440 - $1,503 = -$63.
Final answer:

A point estimate is a single value used to estimate an unknown parameter. The point estimate of the difference between the mean annual premium in Pennsylvania and the national mean can be calculated by taking the difference between the two means.

Explanation:

A point estimate is a single value that is used to estimate an unknown parameter of a population. In this case, the point estimate of the difference between the mean annual premium in Pennsylvania and the national mean can be calculated by taking the difference between the two means. Let's say the mean annual premium in Pennsylvania is $1000 and the national mean is $1500. The point estimate of the difference would be $1500 - $1000 = $500.

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If 3 tons of flower bed mulch cost $480, what is the price per pound?

Answers

1 ton = 2,000 pounds 
3 tons = 6,000 pounds
$480/6,000 = 0.08 
per pound is $0.08

Mike has $880 in his savings account and adds $24 per week. at the same time, leslie has $520 in his savings account and adds $36.00 per week. how long will it take leslie to have the same amount as mike?

Answers

30 weeks

880+24x=mike
520+36x=leslie

880+24x = 520+36x

360=12x
x=30 weeks

The question asked what is 1/4 % of 2000

Answers

1/4% of 2000 is 5

Hope this helps!
do u mean 25% if so its 500 if u mean .25% then 5

How to divide 715÷25 using partial quotient

Answers

Attached a solution and showed work.

Lisa drew a picture of a boat. She used the scale 1 inch: 6.5 feet the boat in her picture is 7:25 inches long. What is the length, in feet of the actual boat?

Answers

Okay. So, using the scale, we can solve for the length of the actual boat by writing and solving a proportion. Let’s write it out like this: 1/6.5 = 7.5/x. This is because you’re looking for the real length of the boat, so the x would be lined up horizontally with 6.5, as shown in the proportion. Let’s cross multiply. 6.5 * 7.5 is 48.75. 1 * x is 1x. 48.75 = 1x. Now, let’s divide each side by 1 to isolate the “x”. When you do that, you get x = 48.75. There. The length of the actual boat is 48.75 feet.
you can write this as a proportion  1 inch is to 6.5 feet as 7.25 in is to X               1/6.5 = 7.25/X                     7.25 times 6.5 = X           X = 47.125 feet
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