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brilliants [131]

3 years ago

10

Neil has 3 partially full cans of white paint.They contain 1/3 gallon,1/5 gallon,and 1/2 gallon of paint.About how much paint do

es neil have in all
more than 2 gallons, less than 1 1/2 gallons, between 1 1,2 and 2 gallons

1 answer:

Wittaler [7]3 years ago

4 0

Answer:

less than 1 1/2 gallons

Step-by-step explanation:

1/3 + 1/6 = 1/2, so the sum of the three cans is more than 1 by the difference between 1/5 and 1/6. That difference is 1/30 gallon. The sum is 1 1/30 gallons, which is less than 1 1/2 gallons.

__

A suitable common denominator is 2·3·5 = 30. Then the sum of the fractions is ...

1/3 + 1/5 + 1/2

= 10/30 + 6/30 + 15/30

= 31/30 = 1 1/30 . . . . . less than 1 1/2

In decimal, 1/3 ≈ 0.333, 1/5 = 0.200, 1/2 = 0.500, so the sum is ...

0.333 +0.200 +0.500 = 1.033

which is less than 1.5.

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5 0

3 years ago

Manuel earns $7.25 per hour helping his neighbor. Last month he earned $348. Choose the correct equation and solution which dete

zysi [14]

Answer:

Number of hours= 48 hours

Step-by-step explanation:

Giving the following information:

Hourly rate= $7.25

Total earned= $348

<u>To calculate the number of hours worked, we need to use the following formula:</u>

Total earned= hourly rate*number of hours

number of hours= total earned / hourly rate

number of hours= 348 / 7.25

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6 0

3 years ago

Find the expansion of cos x about the point x=0

ycow [4]

Answer:

Cos x = 1 - $\frac{x^2}{2!}$ + $\frac{x^4}{4!}$ - $\frac{x^6}{1!}$ + ...

Step-by-step explanation:

We use Taylor series expansion to answer this question.

We have to find the expansion of cos x at x = 0

f(x) = cos x, f'(x) = -sin x, f''(x) = -cos x, f'''(x) = sin x, f''''(x) = cos x

Now we evaluate them at x = 0.

f(0) = 1, f'(0) = 0, f''(0) = -1, f'''(0) = 0, f''''(0) = 1

Now, by Taylor series expansion we have

f(x) = f(a) + f'(a)(x-a) + $\frac{f''(a)(x-a)^2}{2!}$ + $\frac{f'''(a)(x-a)^3}{3!}$ + $\frac{f''''(a)(x-a)^4}{4!}$ + ...

Putting a = 0 and all the values from above in the expansion, we get,

Cos x = 1 - $\frac{x^2}{2!}$ + $\frac{x^4}{4!}$ - $\frac{x^6}{1!}$ + ...

8 0

3 years ago

Set A={1,2,3,4,5,6} two numbers from set A are selected at random without replacement and their sum recorded how many different

wolverine [178]

The minimum sum is 3 and the maximum is 11. So there are 9 different possible sums.
There are 30 ways to get these 9 different sums.
The table below shows all outcomes.

1 2 3 4 5 6
———————————-
1 | X 3 4 5 6 7
2 | 3 X 5 6 7 8
3 | 4 5 X 7 8 9
4 | 5 6 7 X 9 10
5 | 6 7 8 9 X 11
6 | 7 8 9 10 11 X

6 0

3 years ago

Last year, Keiko had $20,000 to invest. She invested some of it in an account that paid %7 simple interest per year, and she inv

erma4kov [3.2K]

Answer:

$P_2 = \$6,000\\P_1 = \$14,000$

Step-by-step explanation:

The formula of simple interest is:

$I = P_0rt$

Where I is the interest earned after t years

r is the interest rate

$P_0$ is the initial amount

We know that the investment was $20,000 in two accounts

_______________________________________________

<u><em>For the first account</em></u> r = 0.07 per year.

Then the formula is:

$I_1 = P_1r_1t$

Where

$P_1$ is the initial amount in account 1 at a rate $r_1$ during t = 1 year

$I_1 = P_1(0.07)(1)\\\\I_1 = 0.07P_1$

<u><em>For the second account </em></u>r = 0.05 per year.

Then the formula is:

$I_2 = P_2r_2t$

Where

$P_2$ is the initial amount in account 2 at a rate $r_2$ during t = 1 year

Then

$I_2 = P_2(0.05)(1)\\\\I_2 = 0.05P_2$

We know that the final profit was I $1,280.

So

$I = I_1 + I_2=1,280$

Substituting the values $I_1$ , $I_2$ and I we have:

$1,280 = 0.07P_1 + 0.05P_2$

As the total amount that was invested was $20,000 then

$P_0 = P_1 + P_2 = 20,000$

Then we multiply the second equation by -0.07 and add it to the first equation:

$0.07P_1 + 0.05P_2 = 1.280\\.\ \ \ \ \ \ \ \ +\\-0.07P_1 -0.07P_2 = -1400\\-------------$

$-0.02P_2 = -120\\\\P_2 = 6,000$

Then $P_1 = 14,000$

4 0

3 years ago