Help please? and steps

Which describes how to find the solution to 3p < 14?

Flura [38]

Answer:

p < 14/3

Step-by-step explanation:

5 0

3 years ago

Find the area of the shaded regions. Give your answer as a completely simplified exact value in terms of π (no approximations).

Lapatulllka [165]

Hello!

The formula for the area of a sector can be written as follows:

Area = $\frac{1}{2}$ $r^{2}$ (R)

In the above formula, “r” represents the radius while “R” represents the radian measure of a sector. The radius is given to us in the image above as 10 inches. However, we still need the radian measure of the two sectors. To find this measure, we can use the following conversion:

1 degree = $\frac{pi}{180}$ radians

Because the two sectors have a given measure of 72 degrees, we need to multiply both sides of the above conversion by 72:

72 degrees = $\frac{72pi}{180}$

Reduce the fraction on the right side of the equation:

72 degrees = $\frac{2pi}{5}$

We now have the radian measure of both sectors. Now simply insert this and any other known values into the “area of a sector” formula above:

Area = $\frac{1}{2}$ $10^{2}$ ( $\frac{2pi}{5}$ )

Simplify the right side of the equation to get the following answer:

Area = 20 pi

We have now proven that the area of one sector is equal to 20 pi.

If, however, you need the combined area of the two identical sectors, simply multiply the proven area by 2 to get a total area of 40 pi.

I hope this helps!

3 0

3 years ago

Southwest Co-op produces bags of fertilizer, and it is concerned about impurity content. It is believed that the weights of impu

Harman [31]

Answer:

a) 0.216

b) 0.1587

c) 0.369

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 12.2 grams

Standard Deviation, σ = 2.8 grams

We are given that the distribution of weights of impurities per bag is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(contains less than 10 grams of impurities)

P(x < 10)

$P( x < 10) = P( z < \displaystyle\frac{10 - 12.2}{2.8}) = P(z < -0.7857)$

Calculation the value from standard normal z table, we have,

$P(x < 10) =0.216= 21.6\%$

b) P(contains more than 15 grams of impurities)

P(x > 15)

$P( x > 15) = P( z > \displaystyle\frac{15 - 12.2}{2.8}) = P(z > 1)$

$= 1 - P(z \leq 1)$

Calculation the value from standard normal z table, we have,

$P(x > 610) = 1 - 0.8413 = 0.1587 = 15.87\%$

c) P(contains between 12 and 15 grams of impurities)

$P(12 \leq x \leq 15) = P(\displaystyle\frac{12 - 12.2}{2.8} \leq z \leq \displaystyle\frac{15-12.2}{2.8}) \\\\= P(-0.0714 \leq z \leq 1)\\\\= P(z \leq 1) - P(z < -0.0714)\\= 0.841 - 0.472 = 0.369 = 36.9\%$

$P(12 \leq x \leq 15) = 36.9%$

d) The mean divide the data in exactly two parts. Since 15 is farther away from the mean as compared to 10, the probability obtained in part (b) is smaller as compared to probability obtained in part (a).

5 0

4 years ago

Please help really important for my grade :(

Licemer1 [7]

Answer:

≈ 50.7 cm²

Step-by-step explanation:

The area (A) of Δ XYZ is calculated as

A = $\frac{1}{2}$ bh ( b is the base and h the perpendicular height ), that is