Kalon and his friend Marna own a chimney sweep service company. Working together, they can clean a chimney in 1 5/7 hours. If it takes Kalon 4 hours to clean a 20-foot chimney by himself, how long does it take Marna to clean the same size chimney by herself?

Answers

Answer 1

Answer: So to set up the equation we have:4M4+M=127
28M=12(4+M)
28M=48+12M
28K−12M=48
(28−12)M=48
16K=48
M=4816
M=3So Marna can clean the chimney alone in 3 hours

Answer 2

Answer:

Final answer:

To find the time it takes for Marna to clean a 20-foot chimney by herself, we first determine the combined and individual rates of Marna and Kalon. We then subtract Kalon's rate from the combined rate to find Marna's rate and subsequently her individual cleaning time which is 3 hours.

Explanation:

The subject of this question is Mathematics, specifically dealing with the concept of rates and time. To solve this problem, we first need to express the combined rate of Kalon and Marna working together. The combined rate is expressed as 1 job per 1 5/7 hours, which simplifies to 7/12 of a chimney per hour.

Kalon's individual rate is 1 job per 4 hours, this simplifies to 1/4 of a chimney per hour. The formula we'll use is (1/Marna's time) = combined rate - Kalon's rate. Therefore, Marna's rate will be (7/12 - 1/4), simplified to 1/3 of a chimney per hour. Hence, Marna would require 3 hours to clean a 20-foot chimney by herself.

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A store sells 8 cans of fruit cocktail for $22. How much would it cost you to buy 7 cans of fruit cocktail ?It would cost $_______

It took John 12 hours riding his bike to make the round trip to his uncle's. If he averaged 20 mph out and 30 mph back, how long did he travel each way? (Round answer to nearest tenth.)

Answers

I belive it would be 7 hours going and 5 hours coming back

Let d = dist traveled one way
Write a time equation;
time = dist/speed
d/20+d/30 = 12

Mukul has $3.75 in quarters, dimes and nickels in his pocket. he has five more dimes than quarters and nine more nickels than quarters. how many of each coin are in his pocket?

Answers

Answer:

There are 7 coins of quarters , 12 coins of dimes and 16 coins of nickels .

Step-by-step explanation:

Mukul has $3.75

1 dollar = 100 cents

3.75 dollar = 375 cents

Let he has x coins of quarters

Since we are given that he has five more dimes than quarters.

So, Dimes = x+5

Since we are given that he has nine more nickels than quarters .

So, nickels = x+9

Now 1 quarter = 25 cents

So, x quarter = 25 x cents

1 dime = 10 cents

So, (x+5) dimes = 10(x+5) cents

1 nickel = 5 cents

So, (x+9) nickels = 5(x+9) cents.

Since he had 375 cents in total .

$\Rightarrow 25 x+ 10(x+5) +5(x+9)=375$

$\Rightarrow 25 x+ 10x+50 +5x+45=375$

$\Rightarrow 40 x+95=375$

$\Rightarrow 40 x=375-95$

$\Rightarrow 40 x=280$

$\Rightarrow x=(280)/(40)$

$\Rightarrow x=7$

Thus there are 7 coins of quarters

Coins of dimes = x+5=7+5=12

Coins of nickels = x+9=7+9 =16

Hence there are 7 coins of quarters , 12 coins of dimes and 16 coins of nickels .

Their should be 18 dimes and 8 quarters

Find the roots of f(x)=dx^2+ex+f by completing the square.

Answers

Answer and workings in the attachment below.

What is being done to the variable in the equation y + 8.5 = 17.2?

Answers

The value of the variable y in the equation y + 8.5 = 17.2 is 8.7.

What is an expression?

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equation for the variable y is y + 8.5 = 17.2. The value of the y will be calculated as,

y + 8.5 = 17.2

y = 17.2 - 8.5

y = 8.7

Therefore, the value of the variable y in the equation y + 8.5 = 17.2 is 8.7.

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Answer:

the answer is that the number 8.5 is going to be subtracted.

Step-by-step explanation:

It says in the lesson when a number is going to b added it must be subtracted if the number is going to be subtracted it is going to be added.

so 17.2 - 8.5 = Y. There you go. Welcome.

Verify the basic identity. What is the domain of validity? cot theta = cos theta csc theta

Answers

Both sides can be the domain of validity since both are just simple but what we are going to change is the right side.
Let us review that $cot \alpha = (cos \alpha )/(sin \alpha )$ and $csc \alpha = (1)/(sin \alpha )$ .
So, to prove the following identity:
$cot \alpha =cos \alpha csc \alpha$
Let us substitute the value of csc with respect to sin.
$cot \alpha =cos \alpha * (1)/(sin \alpha )$
$cot \alpha = (cos \alpha )/(sin \alpha )$
$cot \alpha =cot \alpha$

Answer:

The domain of validity of the given identity is:

All real numbers except nπ where n belongs to integers.

Step-by-step explanation:

We are asked to prove the trignometric identity:

$\cot \theta=\cos \theta\csc \theta$

We know that:

$\cot \theta=(\cos \theta)/(\sin \theta)$

Hence, the function cotangent is defined where the denominator is not zero i.e. all the real numbers except where sine function is zero.

We know that the zeros of sine function are of the type: nπ where n belongs to integers.

Also, we can write the expression by:

$\cot \theta=\cos \theta\cdot (1)/(\sin \theta)$

We know that cosecant function is the reciprocal of the sine function.

i.e.

$\csc \theta=(1)/(\sin \theta)$

Hence, we get:

$\cot \theta=\cos \theta\cdot \csc \theta$

There are 8 students in a small class. To make a team, the names of the 2 of them will be drawn from a hat. How many different teams of 2 students are

Answers

use slot method
2 slots

8 choices for first slot
7 choices for second (since 1 is in 1st slot)
8 times 7=56

56 ways to make 2 person teams

The first name can be any one of the 8.
   For each of those . . .
The second name can be any one of the remaining 7.

Total number of ways that 2 names can be drawn = (8 x 7) = 56 .

But . . .

Each team can be drawn in two different ways . . .
   -- Smith first, then Cohen
   -- Cohen first, then Smith.

So, among the 56 ways to draw 2 names, you will find
each possible pair of names drawn twice, in the opposite
order.

The number of different 2-member teams is (56 / 2) = 28 .

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