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ivann1987 [24]
3 years ago
15

Find the dimensions of the rectangle with area 289 square inches that has minimum perimeter, and then find the minimum perimeter

.
Mathematics
1 answer:
nalin [4]3 years ago
4 0
 <span>To minimize the perimeter you should always have a square. 
sqrt(289) = 17 
The dimensions should be 17 X 17 

To see , try starting at length 1, and gradually increase the length. 
The height decreases at a faster rate than the length increases, up until you reach a square. 

Or if you want to use algebra, Say the width is 17-x 
Then the length is 289/(17-x) 

Now, this is bigger than 17+x, as shown here: 
289/(17-x) > 17+x 
289 > 289 - x^2 
which is true. 
so the perimeter would be bigger than 2 * (17- x + 17 + x) = 2 * (2 * 17) = 4 * 17 

Again, the dimensions should be a square. 17 X 17.</span>
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Data set D does not contain the value 128, which is the median value.

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Let sugar be the explanatory variable and calories be the response variable; which scenario best describes ŷ = 57 + 2.5x?
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Answer: Choice E)

The amount of calories in fruit juice increases by 2.5 for every one gram of sugar. The calorie amount estimated by this model is 57 if there are zero grams of sugar.

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x = amount of sugar (in grams)

y = number of calories in the juice

ŷ = estimate of y, so its the estimate of calories in the juice

The regression equation rearranges to ŷ = 2.5x + 57

This is in the form y = mx+b where m = 2.5 is the slope and b = 57 is the y intercept.

The slope tells us what the rate of change is. Specifically, it tells us how much the amount of calories (y) is going up each time the amount of sugar (x) goes up. Each time x goes up by 1, y goes up by 2.5

The y intercept 57 is the starting or initial amount of calories. If you have 0 grams of sugar, the lowest amount of sugar possible, then you start off with 57 calories. We can see this by plugging x = 0 into ŷ = 2.5x + 57 (you should get ŷ = 57). Visually, the y intercept is where the line crosses the y axis.

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