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3 years ago

5

There are 5 gallons of distilled water in science supplies. If 8 students each use an equal amount of distilled water and there

is 1 gallon left in supplies, how much will each student get?

1 answer:

Maurinko [17]3 years ago

7 0

Answer:

0.5 gallon

Step-by-step explanation:

let x refer to students

5 = 8x + 1

8x = 4

x= 0.5 gallon

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What is 0.66666666666 as a fraction

stellarik [79]

To turn $0.(6)=0.6666...$ into a fraction you should do such steps:

1 step. Set up an equation by representing the repeating decimal with a variable. Using your example, you will let x represent the repeating decimal 0.(6), so you have x=0.666... .

2 step. Identify how many digits are in the repeating pattern, or n digits. Multiply both sides of the equation from Step 1 by $10^n$ to create a new equation. Again, using your example, you see that the repeating pattern consists of just one digit: 6. Now multiply both sides of the equation by $10^1 = 10$ . Thus, you have $10x = 10 \cdot 0.666...$ or $10x = 6.666....$ .

3 step. Subtract the equation in Step 1 from the equation in Step 2. Notice that when we subtract these equations, our repeating pattern drops off. Therefore, $10x-x=6.666...-0.666...\\ 9x=6$ .

4 step. You now have an equation that you can solve for x and simplify as much as possible, using x as a fraction: $9x = 6$ . If you divide both sides by 9, you get $x=\dfrac{6}{9}$ . When simplified, you get that $x=\dfrac{2}{3}$ .

Answer: $0.(6)=0.666... =\dfrac{2}{3}$ .

8 0

3 years ago

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What is the difference between (Picture 1) and (picture 2)? A. 0 B. 2 C. 5 D. 6

Vesnalui [34]

Answer:

The difference between the picture is 0 , option A .

Step-by-step explanation:

Given two figures as :

In figure A

The expression is 1 + 3 n , where n lies from 0 to 4

So , let f (n) = 1 + 3 n

Or,f ( n ) = 1 + 3 ×0 = 1 + 0 = 1

f ( 1 ) = 1 + 3 ×1 = 1+ 3 = 4

f ( 2 ) = 1 + 3 ×2 = 1+ 6 = 7

f ( 3 ) = 1 + 3 ×3 = 1+ 9 = 10

f ( 4 ) = 1 + 3 ×4 = 1+ 12 = 13

so, summation of ( 1 + 3 n ) from n = 0 to 4 = 1 + 4 + 7 + 10 + 13 = 35

In figure B

The expression is 3 i - 5 , where i lies from 2 to 6

So , let g (i) = 3 i - 5

Or,g ( 2 ) = 3 ×2 - 5 = 6 - 5 = 1

g ( 3 ) = 3 ×3 - 5 = 9 - 5 = 4

g ( 4 ) = 3 ×4 - 5 = 12 - 5 = 7

f ( 5 ) = 3 ×5 - 5 = 15 - 5 = 10

f ( 6 ) = 3 ×6 - 5 = 18 - 5 = 13

so, summation of ( 3 i - 5 ) from i = 2 to 6 = 1 + 4 + 7 + 10 + 13 = 35

So, The difference between the summation of functions f(n) - g(i) is

f(n) - g(i) = 35 - 35

I.e f(n) - g(i) = 0

Hence The difference between the picture is 0 , option A . Answer

4 0

3 years ago

Please help lol

Alborosie

Step-by-step explanation:

first bro + 2nd bro + 3rd bro

x + (x+2) + (x+4) = 93

x = 87/3

x= 29

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3 years ago

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Help with 5b please . thank you.

Allushta [10]

Answer:

See explanation

Step-by-step explanation:

We are given f(x)=ln(1+x)-x+(1/2)x^2.

We are first ask to differentiate this.

We will need chain rule for first term and power rule for all three terms.

f'(x)=(1+x)'/(1+x)-(1)+(1/2)×2x

f'(x)=(0+1)/(1+x)-(1)+x

f'(x)=1/(1+x)-(1)+x

We are then ask to prove if x is positive then f is positive.

I'm thinking they want us to use the derivative part in our answer.

Let's look at the critical numbers.

f' is undefined at x=-1 and it also makes f undefined.

Let's see if we can find when expression is 0.

1/(1+x)-(1)+x=0

Find common denominator:

1/(1+x)-(1+x)/(1+x)+x(1+x)/(1+x)=0

(1-1-x+x+x^2)/(1+x)=0

A fraction can only be zero when it's numerator is.

Simplify numerator equal 0:

x^2=0

This happens at x=0.

This means the expression,f, is increasing or decreasing after x=0. Let's found out what's happening there. f'(1)=1/(1+1)-(1)+1=1/2 which means after x=0, f is increasing since f'>0 after x=0.

So we should see increasing values of f when we up the value for x after 0.

Plugging in 0 gives: f(0)=ln(1+0)-0+(1/2)0^2=0.

So any value f, after this x=0, should be higher than 0 since f(0)=0 and f' told us f in increasing after x equals 0.

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2 years ago

Write the equation in point slope form that describes the line given by the two points (2,1) and (2,-2) are on a line. then conv

Aleonysh [2.5K]

Answer: There is no way we can find the point slope form of two points together since only one point is needed for point slope.

Step-by-step explanation: However the slope of these two points is undefined which means not even a slope-intercept equation would be possible for these two points.

Hope this helps!

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3 years ago

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