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Serga [27]
3 years ago
14

Rob and Amy each improved their yards by planting rose bushes and shrubs. They bought their supplies from the same store. Rob sp

ent $100 on 8 rose bushes and 5 shrubs. Amy spent $112 on 8 rose bushes and 8 shrubs. What is the cost of one rose bush and the cost of one shrub?
Mathematics
1 answer:
Damm [24]3 years ago
3 0

Answer:

  • shrub: $4
  • rose bush: $10

Step-by-step explanation:

Amy bought 3 more shrubs than Rob, and paid $12 more. Thus, each shrub must cost $12/3 = $4.

Rob's 5 shrubs cost him $4×5 = $20, so the $80 remainder of his $100 total cost paid for 8 rose bushes. Then the cost of one rose bush is ...

... $80/8 = $10

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An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corne
lawyer [7]

Answer:

The dimensions of the resulting box that has the largest volume is 1.3 inches x 1.3 inches

Step-by-step explanation:

Card board size is L= 14 inches and

W = 6 inches

Let x be the size of equal squares cut from 4 corners and bent into a box whose size is now;

L = 14 − 2x , W = 6 −2x and h = x inches.

Volume of the box is given as;

V = (14 −2x)(6−2x)x

V =(4x² − 40x + 84)x

= 4x³ − 40x² + 84x.

Now, for the maximum value,

dV/dx =0

Thus,

dv/dx = 12x² - 80x + 84 = 0

Using quadratic formula

x = [-(-80) ± √(-80²) - 4(12 x 84)]/(2 x 12)

x = [80 ± √(6400 - 4032)]/24

x = (80 + 48.66)/24 or (80-48.66)/24

x = 5.36 or 1.31

Looking at the two values, 1.31 would be more appropriate because if we use 5.36,we will get a negative value of the width (W).

Thus, x = 1.31 inches

Let us use the Second Derivative Test to verify that V has a local maximum at x = 1.31.

Thus;

d²v/dx² = 24x - 80 = 24(1.31) - 80 = -48.56

This is less than 0 and therefore, the volume of the box is maximized when a 1.31 inch by 1.3 inch square is cut from the corners of the cardboard sheet.

3 0
3 years ago
Washington (CNN) About three-quarters of Americans (77%) approve of President Donald Trump's decision to meet with North Korean
snow_tiger [21]

Answer:

b. The margin of error would decrease.

Step-by-step explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

M = z\frac{\sigma}{\sqrt{n}}

In which z is related to the confidence level, \sigma is the standard deviation of the population and n is the size of the sample.

This means that the margin of error is inversely proportional to the size of the sample, which means that if the sample size increases, the margin of error decreases.

In this question, the sample size is increased, leading to a smaller margin of error. So the correct answer is given by option b.

8 0
2 years ago
Find the diameter of a circle with an area of 6767 square centimeters.
scZoUnD [109]
  • Area=6767cm²

Diameter be d

Radius be r

  • πr²=6767
  • r²=6767/π
  • r²=2155
  • r=46.4cm

Diameter=2r=46.4(2)=92.8cm

6 0
2 years ago
Read 2 more answers
Find fourth proportional of 6, 9, 18. Please say me correct answer
olganol [36]
A: 3

Good luck on everything
4 0
2 years ago
The area of a rectangle is 44m. The height is 11/3m. What is the length?
iogann1982 [59]

Width of the rectangle is 12m

<u>Explanation:</u>

<u></u>

Area of rectangle = 44m

height = \frac{11}{3}m

area of rectangle = length X breadth

44 = \frac{11}{3} X b\\b = 12m

Therefore, width of the rectangle is 12m

4 0
3 years ago
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