We will address this word problem step by step while explaining every step. We will use substitution method.
Let n be the number of nickels.
Let q be the number of quarters.
We are told: q + n = 80 ,call this equation1
Also we know the dollar values: 0.25q + 0.05n = 14.60...

The decimal number 4372.254257 can be written in scientific notation as 4.372254257 × 10^3
The conversion rules are that the first number is between 0 and 10 and the second number is raised to the tenth power.

This is picking 5 out of 52 balls without replacement.
So it is 52 * 51 * 50 * 49 * 38 = 311,875,200
So the answer is c) 311,875,200

Since multiplying and addition fractions is known to be inherently difficult, I'll break it down into steps:
Step 1) Let's start by creating an algebraic expression of the word question:
We want the total, so this is = 2 * 1/5 + 9 * 1/20 + 5 * 1/4
Step 2) Adding fractions...

If a line is parallel to another line, both have the same slope.
We know the first line is y = 2x -5
For the second line, we can use formula y=mx + b,
We must have slope m=2, and we need to find b the y-intercept.
We get y=2x+b and we need to find b
b is the y intercept...

To solve this, we will use this property of logarithms:
If x= a ^ y
then log a (x) = y , where a is the base
So if e^9 = y , or y = e^9
then log e (y) = 9
NB: log e (y) is also referred to as the natural log of y, or ln y.
So it can also be written...

Convert to minutes = 4*60+29= 240+29 = 269 minutes
3*60+10 = 190 minutes
For Monday, 269 = 5L + 4P
For Tuesday, 190 = 4L + 2P (Let's multiply this equation by 2, then subtract the top equation from the resulting equation)
380 = 8L + 4P
269...

a) Let's write the algebraic equations:
Profit = Band pay - 3*Ticket cost
Each band member's pay = Profit / Number of people
b) Now we solve:
Profit = $1250 - 3*$150 = $1250 - $450 = $800
The band made $800 Profit.
Each band member's pay = $800/5 = $160...

The length of the brass grip-strip that encircles the manhole cover is simply the circumference of the circle.
The circumference of a circle is solved by this formula: C = pi * D (which is the same as 2 * pi * r)
= 3.142 * 3 = 9.426 ft.
So the length is approximately 9.4( when...

The house should be priced at $113.89 /sq ft * 1800 sq ft = $205,002.
This is approximately $205,000 if rounded.

If the number of workers decreased two times, it would be 6-2 = 4 workers.
This is a ratio problem:
6 workers /22 hrs = 4 / x
x = 22 * 4 / 6 = 14.67 hours
It would take the remaining workers 14.67 hours.

We need to convert everything to feet or convert everything to inches.
If we choose feet.
18 inches is 18/12 = 1.5 feet
6/1.5 = 4/x
x = 1.5 * 4 / 6 = 18/12 * 4/6
x = 1 ft
The chair needs to be 1 ft or 12 inches high.

Let's say the item price is $10. (Just choose any convenient number for this.)
So 40% off means it now costs: (1-0.40) * $10 = $6
An additional 20% means it now costs: (1-0.20) * $6 = $4.8 (NOTE: Remember that we have to use the already discounted price)
So the final price is what percent...

You need to correct the choices.
The correct range answer should be:
C is greater than 25; C is real

The question is essentially:
how many 3/4 yard runners can you make with 18 yards fabric?
So we divide:
18 yards / (3/4 yards)
= 18 * (4/3) = 6* 4 = 24.
Manuel can make up to 24 runners.
So a, b, c, and d should be marked.

I assume that the 324 represents the area of the fabric in square feet.
Area = pi * r^2
324 = 3.142 * r^2
r = sqrt ( 324/ 3.142 )
Radius = 10.15 ft
This can be rounded to 10.2 ft

The solution to this problem depends on what 'change' means. If it means lower denomination coins like quarters, dimes, nickels, and pennies then here is the solution for largest change.
We want to maximize our number of coins, but minimize the total value above $2.00.
Solution:
Person...

This question seems to be missing some information.
1 foot + k = 3W ??
W * L = 24 feet
Provide the missing information and we will help.

To minimize labor costs, we want the optimal mix of level I and level II workers. This way we will stay within our desired hours constraint and also produce our desired number of items per week.
Let m be the hours used by level I workers
Let n be the hours used by level II workers...

This is a trick question and you have to gather just the relevant information and solve.
NOTE: The fact that 31 adults saw the movie is irrelevant to the question that is asked.
Step 1: Gather relevant information
So 164 children saw movie in morning
And 125 children saw...