A ballasted roof is flat and covered with gravel to hold the roofing material in place. Adam plans to cover the roof in the diagram with gravel.
30 ft.
21 ft.
13 ft.
57 ft.
27 ft.
52 ft.
The area that Adam plans to cover with gravel is
weight of gravel on the roof will be
If the weight of the gravel is 12 pounds per square foot, the total
ling
2,702 square feet
Next
2,374 square feet
2,222 square feet
2,031 square feet

Answer:

C: 40 teaspoons.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

This is a straight proportion question. Many things can be solved with a proportion. This is a good example of what is possible.

Formula

3 teaspoons       x

======              =========

36 cookies        480 cookies

Notice that in the end, the units of teaspoons will be left. Multiply both sides by 480

3 teaspoons * 480 cookies

=======================            =  X

36 cookies

Notice the cookies cancel

3 teaspoons * 480

===============     =  x

36

x = 1440/36 teaspoons.

x = 40 teaspoons

answer: C

This is basically in the form y = mx+b with m = 1/3 as the slope and b = 3 as the y intercept. I'm using f(x) in place of y to indicate function notation.

==========================================

Work Shown:

The goal is to solve for y.

x - 3y = -9

-3y = -9-x ... subtracting x from both sides

-3y = -x-9

y = (-x-9)/(-3) .... dividing both sides by -3

y = -x/(-3) - 9/(-3) ... break up the fraction

y = (1/3)x + 3 .... simplify

f(x) = (1/3)x + 3 .... replace y with f(x)

｡☆✼★ ━━━━━━━━━━━━━━  ☾  

First find the area of the sector.

For that, use this equation:

area = [tex]\frac{x }{360} * \pi r^{2}[/tex]

where 'x' is the angle and 'r' is the radius

Sub the values in

area = [tex]\frac{56}{360} * \pi15^2[/tex]

Solve:

area = [tex]35\pi[/tex]

It is easier to keep it in terms of pi until the end

Now, calculate the area of the triangle within the sector

area = 1/2 ab x sinC

where 'a' and 'b' are the radius (side lengths) and C is the angle

thus,

area = 1/2(15 x 15) x sin(56)

area = 93.27 (to 2 d.p)

Now subtract the area of the triangle from the area of the sector

[tex]35\pi[/tex] - 93.27 = 16.6857

This would give you a final answer of 16.69 units^2

Have A Nice Day ❤    

Stay Brainly! ヅ    

- Ally ✧    

｡☆✼★ ━━━━━━━━━━━━━━  ☾

a function will not have any repeating x values...they all have to be different...they can have repeating y values, just not repeating x values.

so ur answer is : { (-1,5), (-2,6), (-3,7) }...u see how there is no repeating x values....this is a function....the other 3 are not.

Answer:

y=x+2

Step-by-step explanation:

I have included a graph with the equation and both points on it (click/tap on it to see the full picture.)

Answer: y= x+2

Step-by-step explanation:

Answer:

[tex]y=\sqrt{55}[/tex]

which agrees with answer A

Step-by-step explanation:

Notice there are three right angle triangles for which we can apply the Pythagorean theorem:

In the small triangle at the bottom we have the Pythagorean theorem rendering:

(a)

[tex]5^2+y^2=x^2\\x^2=25+y^2[/tex]

in the second right angle triangle on top of the previous one, if we call the vertical side on the right side "z", we have:

(b)

[tex]11^2+y^2=z^2\\z^2=121+y^2[/tex]

and finally in the large right angle triangle:

(c)

[tex]z^2+x^2=16^2\\z^2=256-x^2[/tex]

We can combine equations b and c to obtain:

[tex]121+y^2=256-x^2\\x^2+y^2=256-121=135\\x^2=135-y^2[/tex]

and then combine this and (a) to get:

[tex]25+y^2=135-y^2\\2\,y^2=135-25\\2y^2=110\\y^2=55\\y=\sqrt{55}[/tex]

Answer:

6.1

Step-by-step explanation:

use law of cosines

d² = e² + f² - 2ef cos D

d² = 9² + 10² - 2(9)(10) cos 37

d² = 81 + 100 - 143.75

d² = 37.25

d = 6.1

Answer:

A. The graph of g(x) is vertically compressed by a factor of 3.

Step-by-step explanation:

When there is a fraction, that means that there is a veritcal dilation.

Hope this helps! Good luck!

So if we think of a test tube, it looks sort of like a cylinder. This means that its cross-section would be a circle. To find out how many turns a piece of thread would make around the test tube, we need to find the circumference of the test tube, then divide the length of the string by the circumference.

Step 1) Find the circumference

C = pi x diameter

C = 3.14 x 3

C = 9.42

Step 2) Divide the length of the string by the circumference

90.42 / 9.42 = 9.5987

The string would make approximately 9.60 turns around the test tube.

Hope this helps!! :)

Answer:

A. [tex] 3 {}^{9} [/tex]

Step-by-step explanation:

[tex]3 {}^{4} \times {3}^{5} = {3}^{4 + 5} = 3 {}^{9} [/tex]

Hope this helps ;) ❤❤❤

Answer:

[tex]\boxed{3^9}[/tex]

Step-by-step explanation:

[tex]3^5 \times 3^4[/tex]

Apply the law of exponents : [tex]a^b \times a^c = a^{b+c}[/tex]

The exponent product rule states that, when multiplying two exponents that have the same base, you can add the exponents.

[tex]3^{5+4}[/tex]

[tex]3^9[/tex]

Answer:

-3

Step-by-step explanation:

Well to find the common ratio we need to figure out,

what * 2/3 = -2.

To find that we do -2 ÷ 2/3

= -3

To check -2 * -3 should be 6 which it is.

Thus,

the common ratio is -3.

Hope this helps :)

Answer:

-3

Step-by-step explanation:

Common ratio = 2nd term ÷ 1 st term

                        = -2 ÷ 2/3

                       = [tex]-2 * \frac{3}{2}\\\\[/tex]

                        = -3

Answer:

64/9

Step-by-step explanation:

(8/3) ^2

( 8/3) * (8/3)

64/9

64/9 is the answer <3<3 Hope this helps

Answer:

[tex]10[/tex]

Step-by-step explanation:

[tex]f(x)=-x^2+6x+1[/tex]

x coordinate:

[tex]\frac{-b}{2a}[/tex]

[tex]a=-1\\b=6[/tex]

[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]

y-coordinate:

[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]

Answer:

10

Step-by-step explanation:

Answer:

The function f(x) = IxI works as follows:

if x ≤ 0, then IxI = -x

if x ≥ 0, then IxI = x

notice that if x = 0, then I0I = 0 = -0

Now, we want that:

IxI = x

Then we have that x must be greater or equal than zero:

x ≥ 0.

To represent it in the number line, you should use a black dot in the zero an shade all the right region:

__-2__-1__0__1__2__3__4__5__6__....

Answer:

The answer to your question is given below.

Step-by-step explanation:

To which of the above expression is a sum or difference of cube, or not a sum or difference of cube, we shall do the following simplification:

Note: The Cube root of a particular number is simply a multiplication of an identical number in three places.

64x³ – 216

64 has a cube root of 4 and 216 has a cube root of 6. Therefore, the above expression can be written as:

4³x³ – 6³

(4x)³ – 6³

64x³ – 216 = (4x)³ – 6³

Therefore, 64x³ – 216 can be expressed as a difference of cube.

8x^9 + 27

8 has a cube root of 2, x^9 has a cube root of x³ and 27 has a

cube root of 3. Therefore, the above expression can be written as:

2³(x³)³ + 3³

(2x³)³ + 3³

8x^9 + 27 = (2x³)³ + 3³

8x^9 + 27 can be expreessed as a sum of cube

x³ + 125

125 has a cube root of 5. Therefore, the above expression can be written as:

x³ + 5³

x³ + 125 = x³ + 5³

x³ + 125 can be expressed as a sum of cube

36x³ + 121

36 and 121 has no cube root. Therefore, the above expression is not a sum or difference of cube.

x^6 – 16

x^6 has a cube root of x² and 16 has no cube root. Therefore, the above expression is not a sum or difference of cube.

Summary:

Sum or Difference of cubes

64x³ – 216

8x^9 + 27

x³ + 125

Not a Sum or Difference of cubes

36x³ + 121

x^6 – 16

Answer:

look at attached picture

Answer:

(x - 1)² + (y - 2)² = 20

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given the endpoints, then the centre is at the midpoint

C = [ [tex]\frac{-3+5}{2}[/tex], [tex]\frac{0+4}{2}[/tex] ] = (1, 2 )

The radius is the distance from the centre to either of the 2 endpoints.

Use the distance formula to find r

r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (1, 2) and (x₂, y₂ )= (- 3, 0)

r = [tex]\sqrt{(-3-1)^2+(0-2)^2}[/tex]

  = [tex]\sqrt{(-4)^2+(-2)^2}[/tex]

  = [tex]\sqrt{16+4}[/tex]

  = [tex]\sqrt{20}[/tex]

Thus equation of circle is

(x - 1)² + (y - 2)² = ([tex]\sqrt{20}[/tex] )² , that is

(x - 1)² + (y - 2)² = 20

Answer:

5/6π.

Step-by-step explanation:

The following data were obtained from the question:

Radius (r) = 12 cm

Area (A) = 60π cm²

Centre angle in radian (∅) =...?

Since we are to look for the centre angle in radian, the area of the sector will be given by:

A = ½r²∅

Inputting the values of the area, A and radius, r, the centre angle, ∅ can be obtained as follow:

A = ½r²∅

60π = ½ × 12² × ∅

60π = ½ × 144 × ∅

60π = 72 × ∅

Divide both side by 72

∅ = 60π/72

∅ = 5/6π

Therefore, the centre angle measured in radian is 5/6π.

Answer:

An example of a prism could be a an amazon box to represent a rectangular prism.  As the height, length, or width of the box increases, the volume increases allowing more items to fit within the box.

An example of a cone would be an ice cream cone.  As the height or the radius of the cone increases, the more volume the cone can hold, meaning more ice cream for you.

An example of a cylinder could be a cup.  As the height or the radius of the cup increases, the larger the volume.  More drink for you.

An example of a sphere would be a soccer ball.  As the radius increases, the volume of the ball increases.  Hence, larger soccer balls have a bigger radius than smaller soccer balls.  This allows for different varients of the ball to be created (i.e., youth, highschool, college, pro).

Note, the volume can also be decreased by simply shrinking the measurements instead of increasing them.

Step-by-step explanation:

Let's simply look at the equations of each shape.

Volume of a prism = base * height

Volume of a cone = Pi * r^2 * (height/3)

Volume of a cylinder = Pi * r^2 * height

Volume of a sphere = (4/3) Pi r^3

Notice that the volumes of prisms, cones, and cylinders directly correlate to height.  As height increases, the volume increases.  The sphere is unique in that the height is 2 * radius; however, the volume is related to the cube of the radius.  Consider if you expanded the radius of the sphere, the volume will increase.

Answer:

Increase or decrease the dimensions of objects. See below for an explanation!

Step-by-step explanation:

An amazon box, which is a rectangular prism, is an example of a prism. If you increase the height, length, or width of the box, you can fit more stuff inside.

A cup is an example of a cylinder; by increasing the height or radius of the cup, you can fit more of a drink inside.

An icecream cone is an example of a cone; if the height or radius were increased, you might fit more ice cream inside.

A soccer ball is an example of a sphere; increasing the radius makes it larger, and various sizes are available for different levels.

You may also shrink the dimensions for each of these objects to make them smaller.

Hope this helps!

Answer:

The expected value for the insurance company is $392.20.

Step-by-step explanation:

The expected value of a random variable, X is:

[tex]E(X)=x\cdot P(X)[/tex]

It is provided that a life insurance company sells a $100,000 one year term life insurance policy to a 30-year old male for $475.

The probability that the male survives the year is, P(S) = 0.999172.

Then the probability that the male does not survives the year is:

P (S') = 1 - P (S)

        = 1 - 0.999172

P (S') = 0.000828

The amount the company owes the male if he survives is, S = $475.

The amount the company owes the male if he does not survives is,

S' = $475 - $100,000 = -$99525.

Compute the expected value for the insurance company as follows:

[tex]E(\text{Insurance Company})=S\cdot P(S)+S'\cdot P(S')[/tex]

                                     [tex]=(475\times 0.999172)+(-99525\times 0.000828)\\=474.6067-82.4067\\=392.20[/tex]

Thus, the expected value for the insurance company is $392.20.

Answer:

The answer is B CPCT

Step-by-step explanation:

In an isosceles triangle ΔHKJ with

Construct KM, a bisector of the base HJ.

to prove:

in ΔKHM and ΔKJM

bisects      [Given]

Segment bisectors states that a line or segment which cuts another line segment into two equal parts.

then, by definition of Segment bisector :

       [Given]

Reflexive property of congruence that any geometric figure is congruent to itself.

  [by definition of Reflexive property of congruence]

SSS(Side-Side-Side) Postulates states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

therefore, by SSS postulates

ΔKHM  ΔKJM

By CPCT [Corresponding Part of congruent Triangle]

         proved!

hope i helped

-lvr

Answer: On the 20th day, he will give $5242.88

Step-by-step explanation: This is a geometric series with elements:

initial value ([tex]a_{0}[/tex]) = 0.01

ratio = 2

At the twentieth day means the 20th term, i.e. n = 20.

To determine that term, use the formula: [tex]a_{n} = a_{0}.r^{n-1}[/tex]

Substituing terms:

[tex]a_{20} = 0.01.2^{20-1}[/tex]

[tex]a_{20} = 0.01.2^{19}[/tex]

[tex]a_{20} = 0.01.524288[/tex]

[tex]a_{20} = 5242.88[/tex]

Then, on the 20th day, your uncle gave to you $5242.88

Answer:

The proportion of college students who work​ year-round is 58%.

Step-by-step explanation:

The claim made by the education researcher is that 58​% of college students work​ year-round.

A random sample of 400 college​ students, 232 say they work​ year-round.

To test the researcher's claim use a one-proportion z-test.

The hypothesis can be defined as follows:

H₀: The proportion of college students who work​ year-round is 58%, i.e. p = 0.58.

Hₐ: The proportion of college students who work​ year-round is 58%, i.e. p ≠ 0.58. C

Compute the sample proportion as follows:

 [tex]\hat p=\frac{232}{400}=0.58[/tex]

Compute the test statistic value as follows:

 [tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.58-0.58}{\sqrt{\frac{0.58(1-0.58)}{400}}}=0[/tex]

The test statistic value is 0.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

Compute the p-value for the two-tailed test as follows:

 [tex]p-value=2\times P(z<0)=2\times 0.5=1[/tex]

*Use a z-table for the probability.

The p-value of the test is 1.

The p-value of the test is very large when compared to the significance level.

The null hypothesis will not be rejected.

Thus, it can be concluded that the proportion of college students who work​ year-round is 58%.

Answer:

[tex] d = 123 [/tex]

Step-by-step explanation:

The given figure above is an inscribed quadrilateral with all four vertices lying on the given circle, thereby forming chords each.

Therefore, the opposite angles of the above quadrilateral are supplementary.

This means:

[tex] c + 31 = 180 [/tex] , and

[tex] d + 57 = 180 [/tex]

Find the measure of d:

[tex] d + 57 = 180 [/tex]

Subtract 57 from both sides.

[tex] d + 57 - 57 = 180 - 57 [/tex]

[tex] d = 123 [/tex]

Answer:

Please check explanation

Step-by-step explanation:

Here, we want to do a matching.

We shall be matching the given statements with the features we have on the graph

Hence we shall be looking closely at the graph to answer the questions.

The y-intercept is the point at which the graph touches the y-axis

And it was at -3 degrees celsius at the beginning of the day.

The temperature was above zero between 8am and 8pm. The matching statement is that it is increasing or decreasing interval

We can see that the graph rose from 8am before it finally comes to zero at 8pm

Positive or negative interval matches with it was getting warmer between 2am and 2pm.

While temperature was lowest at 2am, we can see a peak at 2pm.

Answer:

1,1,3,1,1

Step-by-step explanation:

Answer:

0       1

1        1

2       3

3       1

4       1

Step-by-step explanation:

You would just count how many 0 there are in the set and there are 1 and you would put in by 0. For 1 there are 1, for 2 there are 3, for 3 there are 1, and for 4 there are 1.

Step-by-step explanation:

Use law of sines.

16 / sin 39° = BC / sin 120°

BC ≈ 22.02

Greetings from Brasil...

Here we cant use calculator..... It seems that in the USA the use of a scientific calculator is allowed

Let's use Senos Law in Any Triangle

(AC/SEN B) = (BC/SEN A)

16/SEN 39 = BC/SEN 120     sen 120 = sen 60 = √3/2

16/0,63 = BC/(√3/2)

0,63BC = 16√3/2

BC = 8√3/0,63

Answer:

30%

Step-by-step explanation:

Total population=15,000

kantipur=9000

gorkhapatra= 7500

Both magazine=40%

n(k intersection g)=40% of 15,000

=0.4*15,000

=6,000

n(k) =9000

n(g)=7500

n(A union B)= n(k) + n(g) -n(k intersection g)

=9000+7500-6000

=10,500

Population who do no read= Total population - n(A union B)

=15000-10500

=4500

Percentage population who do not read both magazine

=4,500/15,000 * 100

=0.3 * 100

=30%

Answer:

The total surface area of cone is 70π cm² or 219.9 cm².

Step-by-step explanation:

Given that the formula of total surface area of cone is T.S.A = πr² + πrl where r represents radius and l is slant height. So you have to substitute the values :

[tex]t.s.a = \pi {r}^{2} + \pi{r}l[/tex]

[tex]let \: r = 5 \: , \: l = 9[/tex]

[tex]t.s.a = \pi {(5)}^{2} + \pi(5)(9)[/tex]

[tex]t.s.a = 25\pi + 45\pi[/tex]

[tex]t.s. a = 70\pi \: or \: 219.9 \: [/tex]

Answer:

Micah's solution is wrong

Step-by-step explanation:

Micah solves a linear equation and concludes that x = 0 is the solution. His work is shown below.

(1 – 3x) = 4(– + 2)

0 = x

Which statement is true about Micah’s solution?

Micah’s solution is wrong.

There are no values of x that make the statement true.

Micah’s solution is correct, and the value of x that makes the statement true is 0.

Micah should have divided by .

Micah should have subtracted

Solution

First solve for the value of x

Given

(1 – 3x) = 4(– + 2)

It could mean;  (1 – 3x) = 4(+ 2)

or  

(1 – 3x) = 4(-2)

In the first option (1 – 3x) = 4(+ 2)

1 – 3x = 4(+ 2)

1-3x= 8

-3x=8-1

-3x=7

x= -7/3  

In the second option

(1 – 3x) = 4(-2)

1-3x= -8

-3x= -8-1

-3x = -9

x= 3

 x= 3 0r -7/3

The values of x that make the statement true are 3 and -7/3

Micah's solution of x=0 is wrong

Answer:

A. Micah’s solution is wrong. There are no values of x that make the statement true.

Step-by-step explanation:

Answer with explanation:

Given: Charlie is laying down mulch in his front yard. It takes Charlie 4 minutes to lay down 11 cubic yards of mulch and  16 minutes to lay down 44 cubic yards of mulch.

Here, Time(Independent variable (x)) is directly proportion to the Volume of mulch(dependent variable (y)) lied by Charlie.

Let k be the constant of proportionality, such that

[tex]k=\dfrac{y}{x}[/tex]

For x= 4 and k= 11, [tex]k=\dfrac{11}{4}[/tex]

Required equation: [tex]y=\dfrac{11}{4}x[/tex]                        

Two points are given in question: (4,11) , (16,44).

Take x= 8 , [tex]y=\dfrac{11}{4}(8)=22[/tex]i.e. point (8,22)

Similarly, for x= 12, y=33 i.e. point (12, 33)

For x= 20 , y= 55 i.e. point (20,55)

Five data points: (4,11) , (16,44), (8,22),  (12, 33), (20,55).

Now, we plot these points on graph and join them

Answer:

Here

Step-by-step explanation: