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Juliette [100K]
1 year ago
14

6-Mr. Lofters has 7/8 of a gallon of blue paint. He needs to distribute the blue paint out equally to his students. If Mr. Lofte

rs pours 1/16 of a gallon of blue paint into each cup, how many cups of blue paint can he get? IMAGINE WHAT IS HAPPENING IN THE PROBLEM. WHAT OPERATION WILL BE INVOLVED? WHICH NUMBER WILL GO FIRST? LOOK FOR KEYWORDS. DO YOU REMEMBER THE FISH SONG?? YOU'LL REALLY FLIP IF YOU DON'T GET THIS ONE RIGHT.
Mathematics
1 answer:
Liula [17]1 year ago
4 0

We need to distribute 7/8 of a gallon into cups of 1/16 of a gallon. It means that to know the number of cups, we need to divide 7/8 into 1/16.

So, let's remember how to make a division between two fractions:

\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}

Then, the division of 7/8 into 1/16 is equal to:

\frac{\frac{7}{8}}{\frac{1}{16}}=\frac{7\cdot16}{8\cdot1}=\frac{112}{8}=14

Therefore, he gets 14 cups of blue paint.

Answer: 14 cups

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The population of a small town in Ohio was 3,800 people in I. It has slowly been decreasing at a rate of 25% per year. What will
MrRa [10]

Answer:

676 assuming the population is 3800 in 2019. If it's a different year then change t.

Step-by-step explanation:

P(t) = P_{0} (1+r)^t \\\\P(6) = 3800(1-.25)^6 \\=P(6) = 3800(.75)^6\\=676


3 0
3 years ago
For the composite function, identify an inside function and an outside function and write the derivative with respect to x of th
alexira [117]

Answer:

The inner function is h(x)=4x^2 + 8 and the outer function is g(x)=3x^5.

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

Step-by-step explanation:

A composite function can be written as g(h(x)), where h and g are basic functions.

For the function f(x)=3(4x^2+8)^5.

The inner function is the part we evaluate first. Frequently, we can identify the correct expression because it will appear within a grouping symbol one or more times in our composed function.

Here, we have 4x^2+8 inside parentheses. So h(x)=4x^2 + 8 is the inner function and the outer function is g(x)=3x^5.

The chain rule says:

\frac{d}{dx}[f(g(x))]=f'(g(x))g'(x)

It tells us how to differentiate composite functions.

The function f(x)=3(4x^2+8)^5 is the composition, g(h(x)), of

     outside function: g(x)=3x^5

     inside function: h(x)=4x^2 + 8

The derivative of this is computed as

\frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=3\frac{d}{dx}\left(\left(4x^2+8\right)^5\right)\\\\\mathrm{Apply\:the\:chain\:rule}:\quad \frac{df\left(u\right)}{dx}=\frac{df}{du}\cdot \frac{du}{dx}\\f=u^5,\:\:u=\left(4x^2+8\right)\\\\3\frac{d}{du}\left(u^5\right)\frac{d}{dx}\left(4x^2+8\right)\\\\3\cdot \:5\left(4x^2+8\right)^4\cdot \:8x\\\\120x\left(4x^2+8\right)^4

The derivative of the function is \frac{d}{dx}\left(3\left(4x^2+8\right)^5\right)=120x\left(4x^2+8\right)^4.

3 0
4 years ago
The output is eleven more then the input
enot [183]
The input is known as x and the output is known as y in math.
So you’re stating that we’re making the equation equal the output, y, and we’re adding based off of the word “more”. Now that we know we’re adding, we have to find what we are adding together. We are adding x and 11 is that it equals y. Note that x and y could be many different variables and values.
Y= x+11
5 0
3 years ago
F = <img src="https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B5%7D" id="TexFormula1" title="\frac{9}{5}" alt="\frac{9}{5}" align="absmi
zaharov [31]

Answer:

888

Step-by-step explanation:

8 0
3 years ago
The soccer team collected $800 at a car wash fundraiser. They charged $5.00 for small vehicles and $10.00 for longer vehicles. T
Dahasolnce [82]

There are 160 small cars that were washed because u divide

800/ 5= 160. :P

Hope this helps you!!

4 0
3 years ago
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