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3 years ago

6 feet 12 feet What is the area of the given composite shape?

Mathematics

1 answer:

Reika [66]3 years ago

3 0

Answer:

choice A; 128.52 square feet

Step-by-step explanation:

This shape is made up of a semi-circle and a rectangle. The area of the rectangle will be 12*6 = 72 sq ft.

The formula for area of a circle is $\pi$ * $r^{2}$ . also r=radius. We are given the diameter, 12 feet. The radius is diameter/2, so the radius of the circle will be 6 feet.

Since pi is infinite we round it to 3.14.

Plug in the values and our expression will be (3.14* $6^{2}$ )/2 because it is a semi-circle. Simplify that to (3.14*36)/2 = 113.04/2 = 56.52 sq ft.

Remember to add the area of the rectangle and semi-circle. 72 + 56.52 = 128.52 sq ft.

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The life times of light bulbs produced by a particular manufacturer have a mean of 1,200 hours and a standard deviation of 400 h

Nezavi [6.7K]

Answer:

a. 1200hours

b. σ² = 400² =160000hour

c. standard error = 133.33

d. for 9 lightbulb it is likely that 9*0.146 = 1.31 bulbs will have lives of fewer than 1,050 hours?

Step-by-step explanation:

mean of 1,200 hours

σ, a standard deviation of 400 hours.

Sample size, N = nine bulbs,

a) mean of the sample mean lifetime: is given as 1,200 hours

b) variance of the sample mean is the square of the σ, a standard deviation of 400 hours.

σ² = 400² =160000hours

c) What is the standard error of the sample mean?

The standard deviation of a sampling distribution of mean values is called the standard error of the means,

standard error of the means, σx = σ √N

The formula for the standard error of the means is true for all values infinite number of sample, N.

σx = σ √N

=400 √9 = 400/3 =133.3333

d) the probability that, on average, those nine lightbulbs have lives of fewer than 1,050 hours

The area under part of a normal probability curve is directly proportional to probability and the value is calculated as

z = ( x₁−x) /σ

where z = propability of normal curve

x₁ = variate mean = 1050hours

x = mean of 1200hours

σ = standard deviation = 400

applying the formula,

z= (1050-1200)/400

z = 150/400 =0.375

Using a table of partial areas beneath the standardized normal curve (see Table of normal curve, a z-value of 0.375 corresponds to an area of 0.1460 between the mean value.

Thus the probability of a lightbulbs having lives of fewer than 1,050 hours is 0.1460.

for 9 lightbulb it is likely that 9*0.146 i.e. 1.31 bulbs will have lives of fewer than 1,050 hours?

8 0

3 years ago

Simply<br> (2k-9)^2+(k+2)^2=(2k+1)^2+(k-8)^2

vova2212 [387]

The square of a binomial expands as follows:

$(a+b)^2=a^2+2ab+b^2$