What is the perimeter of a fence 18 yards by 10 yards??

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

Reika [66]

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.

3 0

2 years ago

Assume that all six outcomes of a six-sided number cube have the same probability. What is the theoretical probability of each r

Margarita [4]

Hey there! I am on the same one. :) I will help you out a little.

Assume that all six outcomes of a six-sided number cube have the same probability. What is the theoretical probability of each roll?
• 1: 1/6
• 2: 2/6
• 3: 3/6
• 4: 4/6
• 5: 5/6
• 6: 6/6

Using the uniform probability model you developed, what is the probability of rolling an even number?
1/6 Roll a number cube 25 times. Record your results here.

 1st toss=6 2nd toss=4 3rd toss=6 4th toss=6 5th toss=3 6th toss=3 7th toss=4 8th toss=2 9th toss=6 10th toss=5 11th toss=1 12th toss=4 13th toss = 5 14th toss =1 15th toss=4 16th toss=2 17th toss=2 18th toss=2 19th toss=6 20th toss=5 21st toss=3 22nd toss=4 23rd toss=3 24th toss=3 25 toss=5
How many results of 1 did you have? __2____________ How many results of 2 did you have? ____4__________ How many results of 3 did you have? ____5__________ How many results of 4 did you have? ______5________ How many results of 5 did you have? ______4________ How many results of 6 did you have? ______5________
Based on your data, what is the experimental probability of each roll? 1. 2/25 or 0.08

2. 4/25 or 0.16

3. 5/25 or 0.24

4. 5/25 or 0.2

5.4/25 or 0.16

6. 5/25 or 0.2Using the probability model based on observed frequencies, what is the probability of rolling an even number? 3/6 = ½ or 0.5
Was your experimental probability different than your theoretical probability? Why or why not? It somewhat is! The denominator is 25 for the experimental probability, and 6 for the theoretical probability.
Have a lovely day! Cheerio. :)

8 0

2 years ago

Read 2 more answers

Find the surface area of x^2+y^2+z^2=9 that lies above the cone z= sqrt(x^@+y^2)

Mashcka [7]

The cone equation gives

$z=\sqrt{x^2+y^2}\implies z^2=x^2+y^2$

which means that the intersection of the cone and sphere occurs at

$x^2+y^2+(x^2+y^2)=9\implies x^2+y^2=\dfrac92$

i.e. along the vertical cylinder of radius $\dfrac3{\sqrt2}$ when $z=\dfrac3{\sqrt2}$ .

We can parameterize the spherical cap in spherical coordinates by

$\mathbf r(\theta,\varphi)=\langle3\cos\theta\sin\varphi,3\sin\theta\sin\varphi,3\cos\varphi\right\rangle$

where $0\le\theta\le2\pi$ and $0\le\varphi\le\dfrac\pi4$ , which follows from the fact that the radius of the sphere is 3 and the height at which the sphere and cone intersect is $\dfrac3{\sqrt2}$ . So the angle between the vertical line through the origin and any line through the origin normal to the sphere along the cone's surface is

$\varphi=\cos^{-1}\left(\dfrac{\frac3{\sqrt2}}3\right)=\cos^{-1}\left(\dfrac1{\sqrt2}\right)=\dfrac\pi4$

Now the surface area of the cap is given by the surface integral,

$\displaystyle\iint_{\text{cap}}\mathrm dS=\int_{\theta=0}^{\theta=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}\|\mathbf r_u\times\mathbf r_v\|\,\mathrm dv\,\mathrm du$
$=\displaystyle\int_{u=0}^{u=2\pi}\int_{\varphi=0}^{\varphi=\pi/4}9\sin v\,\mathrm dv\,\mathrm du$
$=-18\pi\cos v\bigg|_{v=0}^{v=\pi/4}$
$=18\pi\left(1-\dfrac1{\sqrt2}\right)$
$=9(2-\sqrt2)\pi$

3 0

2 years ago

Alex is creating an outdoor structure out of two 12 foot boards. The boards must have an angle of elevation

Whitepunk [10]

Answer:

5.0 ft - 5.6 ft

Step-by-step explanation:

Given that the structure is to be made using two 12 foot boards, then we expect the total perimeter to be equal to (2*12)= 24 ft.

Using the angle of elevation, 40° and the width of 8 ft then you can apply the formula for tangent of a triangle where ;

Tan α = opposite side length/adjacent length

Tan 40°= h/8

h= 8 tan 40° = 6.71 ft

Applying the cosine of an angle formula to find the length of the sliding side

Cosine β = adjacent length /hypotenuse

Cosine 40°= 8/ sliding side length

sliding side length = 8/cosine 40° =10.44 ft

Checking the perimeter = 10.44 +8+6.71= 25.15 ft

This is more than the total lengths of the boards, so you need to adjust the height as;

24 - 18.44 = 5.56 ft ,thus the height should be less or equal to 5.56 ft

h≤ 5.6 ft

6 0

2 years ago

The cost of a jacket increased from $85.00 to $94.35. What is the percentage increase of the cost of the jacket?

Serggg [28]

It's an 11% increase. To find this, you have to subtract 85 from 94.35 and then you divide that difference by the original amount. In this case it's 85. After that, you get .11. Then you just turn it into a percent.

8 0

2 years ago