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Neporo4naja [7]
3 years ago
6

A rain gutter is made from sheets of aluminum that are 16 inches wide by turning up the edges to form right angles. Determine th

e depth of the gutter that will maximize its​ cross- sectional area and allow the greatest amount of water to flow. What is the maximum​ cross-sectional area?
Mathematics
1 answer:
blsea [12.9K]3 years ago
8 0

Answer:

Depth of the rain gutter is 8 inches

Step-by-step explanation:

Let’s assume ‘x’ is the depth of the rain gutter

Then the width of the rain gutter can be written as 16 - 2x

Cross sectional area

A = depth x width

Substitute values

A = x*(16 - 2x)

A = 16x – 2x^2

Now according to axis of symmetry for maximum area x = -b/2a

x = -16/2*(-2)

x = 4 inches depth of rain gutter, substitute the value of x to get

Width of rain gutter 16 – 2(4) = 8 inches

Area of the rain gutter for maximum water flow

A = 4 * 8

A = 32 square inch.

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These box plots show the prices for two different brands of shoes.
nignag [31]

Answer: Choice C

The interquartile range (IQR) for brand A, $10, is less than the IQR for brand B, $20.

===========================================================

Explanation:

Let's go through the answer choices one by one to see which is true and which is false. Also, we'll see which is helpful when it comes to the spread.

----------------------

Choice A

The IQR is found by subtracting the values of Q1 and Q3, which are the left and right edges of the box in that order.

For boxplot A, we have an IQR = Q3-Q1 = 80-70 = 10.

So we can immediately rule out choice A because the IQR for boxplot A is not 20, but instead it's 10.

----------------------

Choice B

The statement made in choice B is true, since the center vertical lines represent the median, but it's not useful to determine the spread. The median only tells us the center of the distribution. It doesn't tell us how spread out the distribution is.

Imagine you didn't have access to the graph. Now if you're told that the median for brand A is larger than brand B's median, then you'd probably think boxplot A is more spread out; however, the boxplot diagram shows the opposite is the case.

So again the median isn't used here. We can rule out choice B.

----------------------

Choice C

This statement is true. We subtract the box edge values to get the IQR values for each boxplot

For brand A we have IQR = Q3-Q1 = 80-70 = 10

For brand B we have IQR = Q3-Q1 = 70-50 = 20

This is the answer we're after.

The IQR is one tool we can use to measure the spread. The range is another option. We could also use the variance or the standard deviation (two slightly similar ideas) to measure the spread.

As you can see from the diagram, the larger the IQR, the more spread out the data will be.

----------------------

Choice D

This is false because earlier we've shown 10 is the IQR for brand A.

7 0
3 years ago
The price of a math book is 50$, but you have only 35$ with you. If you get a discount of 20%, how much money do you need to bor
tino4ka555 [31]

Answer:

Step-by-step explanation:

The original price of the math book is

50$, The amount of money that you have with you is $35.

If you get a discount of 20%, it means that you get 20% of $50. This is expressed as

20/100 × 50 = 0.2 × 50 = $10

The new cost of the math book is determined by subtracting the discount from the original price. It becomes

50 - 10 = $40

Since the amount that you have with you is $35, the amount that you need to borrow in order to buy the math book is

40 - 35 =$5

6 0
3 years ago
Let f(x) = log3(x) and g(x) = 3x.
QveST [7]

Answer with Step-by-step explanation:

We are given that

f(x)=log_3(x)

g(x)=3x

a.We have to find g(f(x))

g(f(x))=g(log_3(x))

g(f(x))=3log_3(x)

b.We can see that

f(x) is logarithm function and g(x) is linear function.

But , the composition function gof(x) is also logarithmic function.

The composition function gof(x) is 3 times the function f(x).

5 0
2 years ago
Festus bought a computer at $736.34, Apple iPad at $249.99, and a printer at 381.23. The sales tax rate is %6. What is the total
tatuchka [14]

The total purchase price including sales tax will be $1449.6136

<em><u>Explanation</u></em>

Festus bought a computer at $736.34, Apple iPad at $249.99 and a printer at $381.23

So, the <u>total price of all three items</u> =(736.34+249.99+381.23) dollar = 1367.56 dollar.

The sales tax rate is 6%. So, <u>the amount of sales tax</u> =(1367.56*0.06) dollar= 82.0536 dollar.

Thus, the total purchase price including sales tax will be:  (1367.56 + 82.0536) dollar = 1449.6136 dollar

6 0
3 years ago
Shira has 20 books on her bookshelf. Of those 15 are about horses, the rest are nature books. What fraction of Shiras books are
givi [52]

Answer:

1/4

Step-by-step explanation:

15 out of the 20 books are horses. 5 of those are nature. 5/20 is the fraction, but can be simplified to 1/4

6 0
3 years ago
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