Each box of Fred’s Fudge is constructed from 2 triangles and 3 rectangles. What is the shape of each box?

injured runners train on a special track at a rehabilitation center. The track is a square with a half circle on its left and ri

diamong [38]

Answer:

The length of the track is approximately 51.7 ft

The track has three sides of the square and the distance round a half of a complete circle

Step-by-step explanation:

The given track shape and measurements are;

The shape on the left side of the track = Square

The shape on the right side of the track = Half circle

The area of the square on the the left side of the track = 128 square feet

Therefore, from the area, A, of a square of side length, s, which is s × s, and letting the side length of the square = s, we have;

Area of the square portion of the track = s × s = s² = 128 ft²

Therefore, s = √(128 ft²) = 8·√(2) ft.

Whereby the side length of the square is bounded by the diameter of the half circle, we have;

Length of the diameter of the half circle = s = 8·√(2) ft.

The length of the perimeter of the half circle = π·D/2 = π × 8·√(2)/2 = π × 4·√(2) ≈ 17.77 ft.

The perimeter of the track, which is the length of the track is made up of the three sides of the square opposite to the half circle and the circumference of the half circle.

Therefore;

The length of the track = 3 × 8·√(2) ft + π × 4·√(2) ft. = 4·√2×(π+6) ≈ 51.7 ft

The length of the track ≈ 51.7 ft

Which gives;

The track has three sides of the square and the distance round a half of a complete circle.

5 0

2 years ago

A survey of the students in Lance’s school found that 58% of the respondents want the school year lengthened, while 42% think it

alina1380 [7]

The margin of error of a given statistic is an amount that is allowed for in case of miscalculation or change of circumstances.

It is usually the radius or half of the width of the confidence interval of that statistic.

Given that a survey of the students in Lance’s school found that 58% of the respondents want the school year lengthened, while 42% think it should remain the same. The margin of error of the survey is ±10%.

This means that 58% ± 10% of the respondents want the school year lengthened, while 42% ± 10% think it should remain the same.

Thus, from 48% to 68% of the respondents want the school year lengthened, while from 32% to 52% think it should remain the same. 

Therefore, according to the survey data, at least 32% of students want the duration of the school year to remain unchanged, and at least 48% want the school year to be lengthened.

7 0

2 years ago

The population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard dev

Vladimir [108]

Answer:

Probability that the average length of a sheet is between 30.25 and 30.35 inches long is 0.0214 .

Step-by-step explanation:

We are given that the population of lengths of aluminum-coated steel sheets is normally distributed with a mean of 30.05 inches and a standard deviation of 0.2 inches.

Also, a sample of four metal sheets is randomly selected from a batch.

Let X bar = Average length of a sheet

The z score probability distribution for average length is given by;

Z = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)