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coldgirl [10]
1 year ago
14

The greatest common divisor of two positive integers less than $100$ is equal to $3$. Their least common multiple is twelve time

s one of the integers. What is the largest possible sum of the two integers?
Mathematics
1 answer:
tangare [24]1 year ago
3 0

Answer:

129

Step-by-step explanation:

Let a and b be two numbers.

We have been given that the greatest common divisor of two positive integers less than 100 is equal to 3. We can represent this information as GCD(a,b)=3.

Their least common multiple is twelve times one of the integers. We can represent this information as LCM(a,b)=12a.

Now, we will use property GCD(x,y)*LCM(x,y)=xy.

Upon substituting our given values, we will get:

3*12a=ab

36a=ab

Switch sides:

ab=36a

\frac{ab}{a}=\frac{36a}{a}

b=36

Now, we need to find a number less than 100, which is co-prime with 12 after dividing by 3.

The greatest multiple of 3 less than 100 is 99, but it is not co-prime with 12 after dividing by 3.

Similarly 96 is also not co-prime with 12 after dividing by 3.

We know that greatest multiple of 3 (less than 100), which is co-prime with 12, is 93.

Let us add 36 and 93 to find the largest possible sum of the required two integers as:

36+93=129

Therefore, the required largest possible sum of the two integers is 129.

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At a certain company, loan agents are paid based on the number of loans they close in a day. Based on company records, the numbe
Ilya [14]

Answer:

C. The mean daily salary is greater than $350 per day

Step-by-step explanation:

The computation is shown below:

Y = a + bX

where,

Y = money made by a random selected

a = $150

b = $50

X = number of loan

Now

E(x) = (1 × 0.05) + (2 × 0.10) + (3 × 0.22) + (4 × 0.30) + (5 × 0.18) + (6 × 0.12) + (7 × 0.03)

= 3.94

Now

E(y) = $150 + ($50 × 3.94)

= $347

hence, the option C is not correct

4 0
1 year ago
Read 2 more answers
How many distinct 9-letter words starting with “i” can be formed from the word “committee”?
Nikitich [7]

We have already chosen "i" to be the first letter. This means that we still have 8 letters that we can use as the second letter. Once that letter is chosen, we still have 7 letters that we can use as the third letter, and so on. This means we have

8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 8!

ways of choosing the remaining 8 letters.

<u>However,</u> some of the 8 available letters are equal: we have 2 m's, 2 t's and 2 e's. This means that we overcounted the number of words on the reasoning above. We can correct the counting by dividing three times by 2!, one time for each of the repeated letters.

The final answer is

\dfrac{8!}{2! \times 2! \times 2!} = \dfrac{40320}{8} = 5040.

7 0
1 year ago
Find the percent of change if the original price is $246.95 and the new price is $199.95. Round to nearest tenth of a percent if
Grace [21]

Answer:

<h3>Percentage change = 19%</h3>

Step-by-step explanation:

Since the new price is lesser than the original price the percentage change will be a decrease.

To find the percentage change use the formula

Percentage  \:  \: change =  \frac{change}{original  \:  \: quantity}  \times 100

To find the change subtract the new price from the original price

new price = $199.95

original price = $246.95

Change = $246.95 - $ 199.95 = $47

Percentage  \:  \: change =  \frac{47}{246.95}  \times 100

<h3>Percentage change = 19%</h3>

Hope this helps you

3 0
2 years ago
Read 2 more answers
Sometimes a change of variable can be used to convert a differential equation y′=f(t,y) into a separable equation. One common ch
enot [183]

Answer:

y=\frac{-7t^2+22t-7}{7t-22}

Step-by-step explanation:

We are given that

Initial value problem

y'=(t+y)^2-1, y(3)=4

Substitute the value z=t+y

When t=3 and y=4 then

z=3+4=7

y'=z^2-1

Differentiate z w.r.t t

Then, we get

\frac{dz}{dt}=1+y'

z'=1+z^2-1=z^2

z^{-2}dz=dt

Integrate on both sides

-\frac{1}{z}dz=t+C

z=-\frac{1}{t+C}

Substitute t=3 and z=7

Then, we get

7=-\frac{1}{3+C}

21+7C=-1

7C=-1-21=-22

C=-\frac{22}{7}

Substitute the value of C then we get

z=-\frac{1}{t-\frac{22}{7}}

z=\frac{-7}{7t-22}

y=z-t

y=\frac{-7}{7t-22}-t

y=\frac{-7-7t^2+22t}{7t-22}

y=\frac{-7t^2+22t-7}{7t-22}

8 0
2 years ago
Which equation accurately represents this statement? Select three options.
atroni [7]

Complete question:

Which equation accurately represents this statement? Check all that apply.

Negative 3 less than 4.9 times a number, x, is the same as 12.8

A: -3-4.9x=12.8

B: 4.9x-(-3)=12.8

C: 3+4.9x=12.8

D: (4.9-3)x=12.8

E:  12.8=4.9x+3

Answer:

B: 4.9x-(-3)=12.8

C: 3+4.9x=12.8

E:  12.8=4.9x+3

Step-by-step explanation:

The word equation can be expressed mathematically as follows

negative 3  → -3

less than 4.9 times a number , x →  4.9 x - (-3)

is same as 12.8  → 4.9 x - (-3) = 12.8

The equation can be expressed as

4.9 x - (-3) = 12.8

when you open the bracket, you multiply  -3 time  - 1 . MInus times minus is equals to plus. so you get

4.9 x + 3 = 12.8

12.8 = 4.9x+3

3 0
2 years ago
Read 2 more answers
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