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pychu [463]
3 years ago
11

Alex bought a new aquarium. He is in the process of setting it up. The aquarium is in the shape

Mathematics
1 answer:
KengaRu [80]3 years ago
4 0

Answer:

39.00%

Step-by-step explanation:

Given

Dimension: 36⅞ by 19 by 24⅝

Volume of Water = 6039in³

Required

What percent of the volume of the aquarium is filled with water?

First, we need to calculate the volume of the aquarium.

This is calculated by multiplying the dimensions of the aquarium

Volume = 36⅞ * 19 * 24⅝

Volume = 295/8 * 19 * 197/8

Volume = 1104185/64

Volume = 17252.89

The percent filled with water is calculated using the following formula:

%Percent = (Volume of water * 100%)/(Volume of aquarium)

%Percent = (6039 * 100%)/(17252.89)

%Percent = (603900%)/(17252.89)

%Percent = 39.00% (approximated)

Hence, the water occupies 39.00% of the aquarium

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Here is the solution of the given problem above.
First, let's analyze the question. 
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What we are going to do is to divide 9/10 pound to 3.
so 9/10 divided by 3 and we get 9/30 and to simplify that, 3/10.
So per 1/3 of the bag, there is 3/10 pound. 
To get the weight for 2/3 of the bag, we multiply 3/10 by 2 and we get 6/10 or to simplify it, it is 3/5. Therefore, the 2/3 bag weights 3/5 pound. Hope this answer helps.
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Subtract 3.5 from both sides:

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An English professor assigns letter grades on a test according to the following scheme. A: Top 15% of scores B: Scores below the
lisabon 2012 [21]

Answer:

59 to 66

Step-by-step explanation:

Mean test scores = u = 74.2

Standard Deviation = \sigma = 9.6

According to the given data, following is the range of grades:

Grade A: 85% to 100%

Grade B: 55% to 85%

Grade C: 19% to 55%

Grade D: 6% to 19%

Grade F: 0% to 6%

So, the grade D will be given to the students from 6% to 19% scores. We can convert these percentages to numerical limits using the z scores. First we need to to identify the corresponding z scores of these limits.

6% to 19% in decimal form would be 0.06 to 0.19. Corresponding z score for  0.06 is -1.56 and that for 0.19 is -0.88 (From the z table)

The formula for z score is:

z=\frac{x-u}{\sigma}

For z = -1.56, we get:

-1.56=\frac{x-74.2}{9.6}\\\\ x = 59

For z = -0.88, we get:

-0.88=\frac{x-74.2}{9.6}\\\\ x = 66

Therefore, a numerical limits for a D grade would be from 59 to 66 (rounded to nearest whole numbers)

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3 years ago
For the function f(x) = 7/2x-16, what is the difference quotient for all nonzero values of h?
sergey [27]

Answer:

\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}

Step-by-step explanation:

Given

f(x) = \frac{7}{2}x - 16

Required

The difference quotient for h

The difference quotient is calculated as:

\frac{f(x + h) - f(x)}{ h}

Calculate f(x + h)

f(x) = \frac{7}{2}x - 16

f(x+h) = \frac{7}{2}(x+h) - 16

f(x+h) = \frac{7}{2}x+ \frac{7}{2}h- 16

The numerator of \frac{f(x + h) - f(x)}{ h} is:

f(x + h) - f(x) =  \frac{7}{2}x+ \frac{7}{2}h- 16 -(\frac{7}{2}x - 16)

f(x + h) - f(x) =  \frac{7}{2}x+ \frac{7}{2}h- 16 -\frac{7}{2}x + 16

Collect like terms

f(x + h) - f(x) =  \frac{7}{2}x  -\frac{7}{2}x + \frac{7}{2}h- 16 + 16

f(x + h) - f(x) = \frac{7}{2}h

So, we have:

\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h \div h

Rewrite as:

\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}h * \frac{1}{h}

\frac{f(x + h) - f(x)}{ h} = \frac{7}{2}

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2 years ago
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