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2 years ago

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you have 1200 feet of fencing enclose a rectangular region and subdivide it into three smaller rectangular regions by placing tw

o fences parallel to one of the sides. Express the area of the enclosed rectangular region, as a function of the length the fence that divides the rectangular region, x

1 answer:

miss Akunina [59]2 years ago

8 0

Answer:

400

Step-by-step explanation:

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(SAT Prep) An airplane has leveled off (is flying horizontally) at an altitude 12000 feet. When the airplane is at point P its p

serious [3.7K]

Answer:

m∠PRT = 114°

m∠T = 37°

m∠RPT = 29°

Step-by-step explanation:

This question is incomplete (without a picture) ; here is the picture attached.

In this picture, an airplane is at an altitude 12000 feet.

When the plane is at the point P, pilot can observe two towns at R and T in front of plane.

We have to find the measure of ∠PRT, ∠T and ∠RPT.

Form the figure attached segment PS is parallel to RT and PR is a transverse.

We know that internal angles formed on one side of the parallel lines by a transverse are supplementary.

Therefore, x + 66 = 180

x = 180 - 66 = 114°

∠PRT = x = 114°

m∠RPT = m∠SPR - m∠SPT

= 66 - 37

= 29°

Since m∠PRT + m∠T + m∠RPT = 180°

114 + ∠T + 29 = 180

143 + ∠T = 180

∠T = 180 - 143

∠T = 37°

8 0

3 years ago

Read 2 more answers

Calculate the sample standard deviation and sample variance for the following frequency distribution of hourly wages for a sampl

lidiya [134]

Answer:

(a) The sample variance is 16.51

(a) The sample standard deviation is 4.06

Step-by-step explanation:

Given

$\begin{array}{cc}{Class} & {Frequency} & 8.26 - 10.00 & 20 &10.01-11.75 & 38 &11.76 - 13.50& 36 & 13.51-15.25 &25&15.26-17.00 &27 &\ \end{array}$

Solving (a); The sample variance.

First, calculate the class midpoints.

This is the mean of the intervals.

i.e.

$x_1 = \frac{8.26+10.00}{2} = \frac{18.26}{2} = 9.13$

$x_2 = \frac{10.01+11.75}{2} = \frac{21.76}{2} = 10.88$

$x_3 = \frac{11.76+13.50}{2} = \frac{25.26}{2} = 12.63$

$x_4 = \frac{13.51+15.25}{2} = \frac{28.76}{2} = 14.38$

$x_5 = \frac{15.26+17.00}{2} = \frac{32.26}{2} = 16.13$

So, the table becomes:

$\begin{array}{ccc}{Class} & {Frequency} & {x} & 8.26 - 10.00 & 20&9.13 &10.01-11.75 & 38 &10.88&11.76 - 13.50& 36 &12.63& 13.51-15.25 &25&14.38&15.26-17.00 &27 &16.13\ \end{array}$

Next, calculate the mean

$\bar x = \frac{\sum fx}{\sum f}$

$\bar x = \frac{20*9.13 + 38 * 10.88+36*12.63+25*14.38+27*16.13}{20+38+36+25+27}$

$\bar x = \frac{1845.73}{146}$

$\bar x = 12.64$

Next, the sample variance is:

$\sigma^2 = \frac{\sum f(x - \bar x)^2}{\sum f - 1}$

So, we have:

$\sigma^2 = \frac{20*(9.13-12.63)^2 + 38 * (10.88-12.63)^2 +...........+27 * (16.13 -12.63)^2}{20+38+36+25+27-1}$

$\sigma^2 = \frac{2393.6875}{145}$

$\sigma^2 = 16.51$

The sample standard deviation is:

$\sigma = \sqrt{\sigma^2}$

$\sigma = \sqrt{16.51}$

$\sigma = 4.06$

6 0

3 years ago

Heather and her family are going to the grand opening of a new amusement park. There is a special price on tickets this weekend.

Likurg_2 [28]

56 + 16.80 = 72.80!!!!!!!!!!!!!

4 0

3 years ago

Read 2 more answers

What is the answer to this equation |x−1|+5=2

barxatty [35]

Answer:

No solutions

Step-by-step explanation:

Isolate the absolute value:

|x−1| + 5 = 2

Subtract 5 from both sides:

|x-1| = -3

Since an absolute value can never be equal to a negative number, there are no solutions.

6 0

3 years ago

Read 2 more answers

Please help me with this pleaseee

torisob [31]

Answer:

x = 88.2

Step-by-step explanation:

The angle at the top of the triangle = 90° - 10° = 80°

and the left side of the triangle is x ( opposite sides of a rectangle )

Using the tangent ratio in the right triangle

tan80° = $\frac{opposite}{adjacent}$ = $\frac{500}{x}$

Multiply both sides by x

x × tan80° = 500 ( divide both sides by tan80° )

x = $\frac{500}{tan80}$ ≈ 88.2

5 0

3 years ago