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valentina_108 [34]
2 years ago
5

To complete bookshelves, a customer at your store needs to purchase vertical brackets to attach to the wall. The customer wants

the shelving to be 9 feet high and 10 feet long. The wall brackets come in 48-inch and 60-inch sections. The 48-inch sections cost $12.95; the 60-inch sections cost $16.95. The brackets should be 1 foot from each end and no more than 24 inches apart. What will be the total cost of the brackets, before tax?
Mathematics
1 answer:
stiks02 [169]2 years ago
8 0
We are given with
height = 9 feet
length = 10 feet
wall brackets:
48-in costing $12.95
60-in costing $16.95
distance of brackets from ends = 1 foot
maximum distance between brackets= 24 inches

The brackets are
48/12 = 4 feet
and
60/12 = 5 feet

One of each must be used to cover the height of the shelf

The length of the shelf is
60 inch
subtracting 1 in from each side for the allowance
60 - 2 = 58 in
Dividing by 24 inches
58/24 = 2.41 ~ 3 

The total cost is
($12.95 + <span>$16.95) * 3 = $89.7
The total cost of the brackets is </span>$89.7
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Tempestt graphs a function that has a maximum located at (-4, 2). Which could be her graph?
son4ous [18]

Answer:

Here's what I get  

Step-by-step explanation:

Assume the function is a parabola.

The function has a maximum, so the parabola opens downward.

The maximum is at (-4,2), so the maximum is in the second quadrant.

The figure may look like the diagram below.

3 0
2 years ago
The length of the day in Boulder (Latitude 40 N) can be modeled approximately by l(t) = −3 cos ( 2π 365 (t + 10)) + 12 where l i
Harman [31]

Answer:

(a) I(355)=9

(b) I'(265)=−0.05163

(c) The l′(t) is largest at 81.25.

Step-by-step explanation:

The given function is

I(t)=-3\cos (\frac{2\pi}{365}(t+10))+12

where I(t) the length of the day in Boulder and l is given in hours and t is the day of the year.

(a)

Substitute t=355 in given function.

I(355)=-3\cos (\frac{2\pi}{365}(355+10))+12

I(355)=-3\cos (2\pi)+12

I(355)=-3(1)+12

I(355)=9

Therefore, the value of I(355) is 9. It means the length of the day in Boulder is 9 hours at 355 day of the year.

(b)

Differentiate the given function with respect to t.

I'(t)=-3(-\sin (\frac{2\pi}{365}(t+10)))(\frac{2\pi}{365})

I'(t)=\frac{6\pi}{365}\sin (\frac{2\pi}{365}(t+10))

Substitute t=265 in the above function.

I'(t)=\frac{6\pi}{365}\sin (\frac{2\pi}{365}(265+10))

I'(265)\approx −0.05163

Therefore, the value of I'(265) is −0.05163. It means the length of the day in Boulder decreased by 0.05163 hours at 265 day of the year.

(c)

Differentiate the I'(t) function with respect to t.

I''(t)=\frac{6\pi}{365}\cos (\frac{2\pi}{365}(t+10))(\frac{2\pi}{365})

I''(t)=\frac{12\pi^2}{(365)^2}\cos (\frac{2\pi}{365}(t+10))

Equate I''(t)=0 to find critical points.

\frac{12\pi^2}{(365)^2}\cos (\frac{2\pi}{365}(t+10))=0

\cos (\frac{2\pi}{365}(t+10))=0

\cos (\frac{2\pi}{365}(t+10))=\cos (\frac{\pi}{2})

On comparing both sides we get

\frac{2\pi}{365}(t+10)=\frac{\pi}{2}

t+10=\frac{\pi}{2}\times \frac{365}{2\pi}

t+10=\frac{365}{4}

t=\frac{365}{4}-10

t=81.25

Check the value of the function I'''(t) at t=81.25.

Since I'''(81.25)=-0.0000153, therefore the value of l′(t) is largest at 81.25.

4 0
2 years ago
The table shows the shipping costs for items of different values. A 2-column table with 4 rows. The first column is labeled tota
Lisa [10]

A strong positive correlation.

Step-by-step explanation:

The question requires you to calculate the correlation coefficient and then make a conclusion about its value.

Form a table as shown where x is cost of items and y is shipping cost

x               y           xy                   x²         y²

25           5.99       149.8          625         35.9

45            8.99       404.6       2025        80.8

50            8.99      449.5         2500       80.8

70            10.99      769.3         4900       120.8

190           34.96     1773.2        10050      318.3 ------sum

The formula for correlation coefficient follows;

r=n(∑xy)-(∑x)(∑y) ÷ √{[n∑x²-(x)²] [n∑y²-(y)²]}

where n=4

r=4(1773.2)-(190)(34.96) ÷ √{[4(10050)-190²] [4(318.3)-34.96²]}

r=450÷ √{4100*51)

r=450÷√209100

r=450÷457.3

r=0.98409

The value of r indicates a stronger positive correlation

Learn More

Correlation coefficient :brainly.com/question/12528676

Keywords :shipping costs,cost of items, strength of the model

#LearnwithBrainly

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2 years ago
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MakcuM [25]

its the first answer x + y = 29, 5x + 2y = 100

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2 years ago
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You and a friend buy two fruit smoothies and leave a tip. You split the total and your half comes to $3.60. What percent tip (in
Bezzdna [24]

the amount they paid includes the price of the two smoothies and tip

since the friends are splitting the bill in 2, then each friend pays only half the amount

each friend pays $ 3.60 each

so the total amount they both paid is 3.60 x 2 = $ 7.20

the cost of one smoothie - $3

therefore the cost of the 2 smoothies - 3 x 2 = $ 6

so they paid 7.20 but the bill was only 6 dollars

so the difference in the 2 amounts is the value of the tip they left

tip = 7.20 - 6 = 1.20

so the percentage of the tip is - tip amount / value of the bill x 100 %

percentage = 1.20 / 6.0 x 100 % = 20 %

they left 20 % of the bill as a tip

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2 years ago
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