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MrMuchimi
3 years ago
14

Sam and Charley have a rectangular swimming pool that is 8 feet wide and 14 feet long. They are going to build a tile border aro

und the pool of uniform width. They have 75 square feet of tile. How wide is the border?
Mathematics
1 answer:
aniked [119]3 years ago
7 0

Answer:

The border is 1.5 feet wide

Step-by-step explanation:

The rectangular pool is 8 feet wide and 14 feet long.

Area of pool = (8 × 14) square feet

= 112 square feet.

The pool they are going to build is 75 square feet of tile. Let the width of this pool be x.

Then Length of pool + length of sidewalk = 14 + 2x

Width of pool + width of sidewalk = 8 + 2x

Then

(14 + 2x)(8 + 2x) - 112 = 75

112 + 28x + 16x + 4x² - 112 = 75

4x² + 44x - 75 = 0

Solving this using the quadratic formula

x = [-b ± √(b² - 4ac)]/2a

Where a = 4, b = 44, c = -75

x = [-44 ± √(44² - 4×4×(-75))]/2×4

= [-44 ± √(3236)]/8

= (-44 ± 56)/8

Ignoring the negative value for x

x = (-44 + 56)/8

= 12/8

= 1.5

The border is 1.5 feet wide

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Step-by-step explanation:

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3 0
3 years ago
A researcher was interested in seeing how many names a class of 38 students could remember after playing a name game After playi
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Answer:

Proportion of the students recalled more than 15 names is 91.77%.

Step-by-step explanation:

We are given that a researcher was interested in seeing how many names a class of 38 students could remember after playing a name game After playing the name game, the students were asked to recall as many first names of fellow students as possible.

The mean number of names recalled was 19.41 with a standard deviation of 3.17.

<em>Let X = number of names recalled</em>

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The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

Now, proportion of the students recalled more than 15 names is given by = P(X > 15 names)

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