Convert: 31 ft = _yd__ft

The area watered by the sprinkler is 1117.0 sq. feet. The sprinkler sprays in a circular direction with an angle of 80° and a radius of 40 feet.

Given that,

The sprinkler sprays over a distance of 40 feet i.e., r = 40 feet

The sprinkler rotates at an angle of 80°

So, the area watered by the sprinkler is

= [tex]\frac{80}{360}[/tex] × π × r²

= 0.22 × π × (40)²

= 1117.0 sq. feet

Therefore, the area is 1117.0 sq. feet.

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The area watered by the sprinkler is approximately [tex]\(286.48\)[/tex] square feet, calculated from [tex]\(A = \frac{8100}{9\pi}\).[/tex]

Step 1:

Recognize that the sprinkler's watered area forms a sector of a circle.

Step 2:

Calculate the radius [tex](\(r\))[/tex] of the circle using the formula for the arc length: [tex]\(s = r\theta\)[/tex], where [tex]\(s\)[/tex] is the arc length and [tex]\(\theta\)[/tex] is the angle in radians.

Step 3:

Convert the given angle of 80 degrees to radians: [tex]\(80^\circ \times \frac{\pi}{180} = \frac{4\pi}{9}\)[/tex] radians.

Step 4:

Substitute the given arc length [tex]\(s = 40\)[/tex] feet and angle [tex]\(\theta = \frac{4\pi}{9}\)[/tex] into the formula to find [tex]\(r\): \(40 = r \times \frac{4\pi}{9}\).[/tex]

Step 5:

Solve for [tex]\(r\): \(r = \frac{40 \times 9}{4\pi} = \frac{90}{\pi}\)[/tex] feet.

Step 6:

Calculate the area [tex](\(A\))[/tex] of the sector using the formula: [tex]\(A = \frac{1}{2} r^2 \theta\).[/tex]

Step 7:

Substitute the values of [tex]\(r\)[/tex] and [tex]\(\theta\)[/tex] into the formula: [tex]\(A = \frac{1}{2} \times \left(\frac{90}{\pi}\right)^2 \times \frac{4\pi}{9}\)[/tex].

Step 8:

Simplify the expression to find the area: [tex]\(A = \frac{8100}{9\pi} \approx 286.48\)[/tex] square feet.

Therefore, the area watered by the sprinkler is approximately [tex]\(286.48\)[/tex] square feet.

[tex]x+40=3x\\2x=40\\x=20[/tex]

For this case we have by definition of angles between secant lines that:

[tex]x + 40 = 3x[/tex]

Also, the angle between T and V is equal to the angle between S and W.

Returning to the question, we have to:

[tex]x + 40 = 3x[/tex]

We must know the value of "x":

Subtracting 3x on both sides of the equation we have:

[tex]x-3x + 40 = 0[/tex]

Subtracting 40 from both sides of the equation:

[tex]-2x = -40[/tex]

Dividing between -2 on both sides of the equation:

[tex]x = \frac {-40} {- 2}\\x = 20[/tex]

So, the value of x is 20

Answer:

[tex]x = 20[/tex]

Answer:

z = [tex]\frac{y-x}{3y-x}[/tex]

Step-by-step explanation:

2x+6yz=2xz+2y  (rearrange so that z is on one side)

6yz - 2xz = 2y - 2x   (divide both sides by 2)

3yz - xz = y - x   (factor our z from LHS)

z (3y - x) = y - x

z = [tex]\frac{y-x}{3y-x}[/tex]

Final answer:

Kevin can safely take sacks weighing up to 308.33 pounds each in the elevator, provided he takes six sacks at a time and the elevator's capacity is 2,000 pounds with Kevin weighing 150 pounds.

Explanation:

The student's question is asking for the maximum weight of each sack of grain that Kevin can deliver on the elevator, given the elevator's weight capacity and the additional weight of Kevin himself. To answer this question, we need to consider the weight that the elevator can hold minus Kevin's weight, and then determine how much weight is left for the sacks of grain.

The elevator has a capacity of 2,000 pounds, and Kevin weighs 150 pounds. This means the total weight that the elevator can carry in addition to Kevin is:

2000 pounds (elevator capacity) - 150 pounds (Kevin's weight) = 1850 pounds (available for sacks)

If Kevin needs to deliver six sacks at a time, we can divide the total available weight by six to find the maximum weight for each sack:

1850 pounds / 6 sacks = approximately 308.33 pounds per sack

Therefore, the weight of each sack must be 308.33 pounds or less for Kevin to safely use the elevator without exceeding its capacity.

Answer:

- 768

Step-by-step explanation:

Substitute n = 8 into the explicit formula, that is

[tex]a_{8}[/tex] = 6 × [tex](-2)^{7}[/tex] = 6 × - 128 = - 768

Answer:

it is 21 because 9+10=19+2=21-10=11+10=21 its magic

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

9 + 10 = 19

It is impossible for it to be 21.

10

9

----

1 9

Hope this helps.

Alice.

Answer:

Distributive law of multiplication

Step-by-step explanation:

Answer:

Step-by-step explanation

A: No it is not the inverse law of multiplication which has something to do with division.

B: is your answer.

C: It is not the commutative Law. An example of that would be a*b =b*a

D: Identity of multiplication is 1.

Answer:

x = 2

Step-by-step explanation:

Given

1 + x = 7 - 2x ( add 2x to both sides )

1 + 3x = 7 ( subtract 1 from both sides )

3x = 6 ( divide both sides by 3 )

x = 2

Answer:

9 hr

Step-by-step explanation:

vary directly means you should think about a constant being multiply to one variable to get another variable.

So we have E=kH

where E=earnings and H=hours and k is the constant of proportionality

So they give us when H=7 we have E=77 giving us 77=k(7) which means the constant of proportionality is 11

So that means no matter what the E and H are k is 11

So we have the equation is E=11H

Replace E with 99 and solve for H

99=11(H)

So H=9

9 hours

Answer:

V=4/3 πr3

I belive it is.

Answer:

V=121.5pi cm^2

Step-by-step explanation:

V=(4/3)*pi*r^3

V=(4/3)*pi*91.125

V=121.5pi cm^2

Answer:

20

Step-by-step explanation:

100% - 20% = 80%.

80% of 25 = 25 x 0.8 = 20

When the number 25 is decreased by 20%, the result is 20.

To find the result when the number $25 is decreased by 20%, we need to calculate 20% of 25 and subtract that from 25.

20% of 25 is (20/100) x 25 = 5.

Subtracting 5 from 25, we get the result as 20.

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Answer:

[tex]\large\boxed{f^{-1}(x)=\dfrac{3x+51}{2}=\dfrac{3}{2}x+\dfrac{51}{2}}[/tex]

Step-by-step explanation:

[tex]f(x)=\dfrac{2x}{3}-17\to y=\dfrac{2x}{3}-17\\\\\text{exchange x to y and vice versa:}\\\\x=\dfrac{2y}{3}-17\\\\\text{solve fro y:}\\\\\dfrac{2y}{3}-17=x\qquad\text{add 17 to both sides}\\\\\dfrac{2y}{3}=x+17\qquad\text{multiply both sides by 3}\\\\2y=3x+51\qquad\text{divide both sides by 2}\\\\y=\dfrac{3x+51}{2}=\dfrac{3}{2}x+\dfrac{51}{2}[/tex]

Step-by-step explanation:

75.99 ×.0625=4.749

75.99+4.75(because I rounded)=

$80.74 total cost incase you have another step

75.99 ×.0625 = 4.749

I rounded to get 4.75.

75.99 + 4.75 = $80.74

$80.74 - $75.99 = $4.75

Answer: $4.75

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

Explanation:

There are 6 red marbles out of 10+6+3 = 19 total. So 6/19 is the probability of picking one red marble. If that marble is not replaced, then we have 6-1 = 5 red marbles left out of 19-1 = 18 total. The probability of picking another red is 5/18

We have 6/19 as the probability of picking red the first time, then 5/18 as the probability of picking another red marble. The first marble is not put back, and that marble is not replaced.

--------------------------

In terms of math notation, we can say

A = event of picking red on the first selection

B = event of picking red on the second selection

P(A) = 6/19

P(B|A) = 5/18

P(A and B) = P(A)*P(B|A)

P(A and B) = 6/19 * 5/18

Answer:

It's between C and D. I would say it's D.

Step-by-step explanation:

Hope my answer has helped you!

By: Syrenity Holford

if you multiply the number of necklaces sold by 4 for all 4 values in the first column of the table then you should get the value in the second column of the table

Table {4} represents the correct function that represents the profit function.

A function is a relation between a dependent and independent variable. We can write the examples of function as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that Sara sells beaded necklaces she makes a profit of 4 dollars every necklace she sells.

Assume that she sells {x} necklaces in total. So, we can write the function for Sara's profit as -

y = 4x

We can see that table {4} is represented by the profit function.

Therefore, table {4} represents the correct function that represents the profit function.

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Answer:

0.625 is a decimal and 62.5/100 or 62.5% is the percentage for 10/16.

Step-by-step explanation:

Please mark brainliest and have a great day!

[tex]\text{Hey there!}[/tex]

[tex]\frac{10}{16}=10\div16= 0.625[/tex]

[tex]\boxed{\boxed{\text{Answer: 0.625}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

[tex]|\Omega|=16\cdot15=240\\|A|=4\cdot3=12\\\\P(A)=\dfrac{12}{240}=\dfrac{1}{20}=5\%[/tex]

1/2, 3/8, 5/16, 9/12, and 30/64. Hope this helped!

Answer: 1/2, 9/12, 3/8, 5/16, 15/32

Step-by-step explanation:

(divide 3) 9/12 (divide 3)

                =3/4

(divide 2)30/64 (divide 2)

              =15/32

Answer:

Step-by-step explanation:

2/3 yard          2 yd

--------------- = ---------------- = 1/6 yd / piece

4 pieces        12 pieces

Alternatively:  Use inches:

 24 inches

------------------ = 6 inches/piece   = 1/6 yd / piece

 4 pieces

Answer:

-2 + i

Step-by-step explanation:

v = -3i

w = 2 - 4i

v - w =

= -3i - (2 - 4i)

= -3i - 2 + 4i

= -2 + i

The given value of  v = -3i and w = 2-4i, so v-w = -2 + i.

Given: v = -3i, w = 2-4i

To find: v - w

Solution:

Substitute the values of v and w into the expression v - w.

v - w = -3i - (2-4i)

v - w = -3i - 2 + 4i

v - w = -2 + i

Answer:

a) $2248.75

Step-by-step explanation:

Susan pays $0.3 per $100

For $483000, she pays $1449 insurance annually : Calculation shown below

483000/100 x 0.3 = $1449

Monthly instalments of the insurance premium for 12 months :

annual insurance premium/ 12 months

1449/12 = $120.75

Monthly mortgage payments = $2128

Monthly total payments = monthly mortgage payments + monthly insurance premium instalment.

                                       = 1449 + 120.75

                                       = $2248.75

!!

[tex]a_n=3n-10[/tex]

Answer:

an = -7 + (n - 1) 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since it's a division we need to look for a common factor to cancel

so first we try to break the numbers to there prime factors

[tex]\frac{\sqrt{10} }{4\sqrt{8} } = \frac{\sqrt{2.5} }{4\sqrt{2.2.2} }[/tex]

So , now we try to factors that are common in top and bottom

[tex]= \frac{\sqrt{2} \sqrt{5}}{4\sqrt{2}\sqrt{4} }[/tex]

common factor is sqrt 2 so lets cancel it

we get

[tex]\frac{\sqrt{5} }{4\sqrt{4} }[/tex]

[tex]\frac{\sqrt{5} }{8}[/tex]

Answer:

Add the two equations together to eliminate y

Step-by-step explanation:

X+y=3

4x-y=7

I would use elimination since one equation has +y and one equation has -y

Add the two equations together

X+y=3

4x-y=7

-------------------

5x = 10

Answer: (4.5, 6.5) is your solution

Step-by-step explanation:

You need either the x term or the y term to be the same in both equations so you can eliminate them...

8x=2y+5

6x=2y+14

Now you can subtract the two equations...

2x=9

Divide 9 by 2....

x=4.5 or 4 1/2

Plug in x into one of the original equations to find y...

13.5=y+7

Subtract 7 from 13.5...

6.5=y

Answer:

$ 0.30

Step-by-step explanation:

Given:

Average daily balance = $20

Daily period rate = 0.05%

Number of days in a cycle = 30 days

The formula to calculate the monthly Finance Charge is:

Monthly finance charge = Balance x APR x (Number of days)/365

We are given the Daily period Rate which is calculated as:

Daily period rate = APR/365

Therefore, we can write the above equation as:

Monthly finance charge = Balance x Daily Periodic Rate x Number of days

Using the given values, we get:

Monthly finance charge = 20 x 0.0005 x 30 = $ 0.30

Therefore, the monthly finance charge would be $ 0.30

Answer:

The answer is $0.30 or 30 cents

Step-by-step explanation:

From the question Given, we recall the following statement

The monthly finance charge if the average daily balance =$20

The daily periodic rate is =0.05%

The number of days in the cycle is =30

We solve for the monthly finance charge

We apply  the monthly Finance Charge formula:

Monthly finance charge = Balance x APR x (Number of days)/365

Thus,

20 x  0.05% = 0.01

0.01 x 30 days = 0.30  

Therefore the monthly finance charge is = $0.30 or 30cents or 30¢

Martha should start planning early for her college expenses by seeking advice from school counselors, creating a budget, and researching financial aid such as grants, scholarships, and loans. She should be proactive in understanding the costs associated with her post-graduation lifestyle and utilize tools like the Reality Check to create a comprehensive plan.

Martha can take several important steps to ensure she has money to pay for college, which she should start thinking about as she enters high school. These steps include:

Additionally, she should consider exploring different post-secondary options like college, trade schools, or military service, all of which can influence the type and amount of financial planning needed.

Talking to parents and using resources like the Jumpstart Coalition's Reality Check will help Martha gain insights into the cost of her desired lifestyle post-graduation and plan accordingly to ensure she can afford her education and future expenses.

Answer:

14 cm²

Step-by-step explanation:

Using the formula given to calculate the area

with b = 7 and h = 4, then

A = [tex]\frac{1}{2}[/tex] × 7 × 4 = 0.5 × 28 = 14 cm²

Answer:

a = -2 and b=4 and c = -4

Step-by-step explanation:

the center is : A(1 ; -2)

B(1 ; 1) in this circle so ; AB= r  (  ridus)...r =3

note :

an equation of the circle Center at the A(1,-2) and ridus : r is :

(x-1)² +(y+2)² = 3²  

x²-2x+1  +y²+4y +4-9 =0

x²+y² -2x+4y -4 = 0   so : a = -2 and b=4 and c = -4