1. Nancy is walking around a circular track with a radius of 45 feet. If she walks the equivalent of 210 degrees, find the total distance she has walked around the track to the nearest foot.

2. A windshield wiper blade is 18 inches long. Calculate the area covered by the blade as it rotates through an angle of 122 degrees. Round your answer ti the nearest square inch.

3. A spray irrigation system waters a section of a farmer's field. If the water shoots a distance of 75 feet, what is the area that is watered as the sprinkler rotates through an angle of 80 degrees? Round your answer to the nearest square foot.

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

(1)

The distance walked ( arc length ) is calculated as

arc = circumference of circle × fraction of circle

     = 2πr × [tex]\frac{210}{360}[/tex]

     = 2π × 45 × [tex]\frac{21}{36}[/tex]

     = 90π × [tex]\frac{7}{12}[/tex]

     ≈ 165 ft ( to the nearest foot )

(2)

The area (A)  covered is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{122}{360}[/tex]

   = π × 18² × [tex]\frac{61}{180}[/tex]

   = 324π × [tex]\frac{61}{180}[/tex]

    ≈ 345 in² ( to the nearest square inch )

(3)

The area (A) is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{80}{360}[/tex] ( r is the distance shot by sprinkler )

   = π × 75² × [tex]\frac{8}{36}[/tex]

   = 5625π × [tex]\frac{2}{9}[/tex]

   ≈ 3927 ft² ( to the nearest square foot )

Answer 2

Answer:

9514 1404 393

Answer:

top down: 1, 5, 6, 4, 8, 2, 3, 7

Step-by-step explanation:

It appears the expected order may be ...

__

Write the formula for the arc length of a circle with central angle, θ, in degrees.

\textit{Arc Length}=\dfrac{\theta}{360^{\circ}}\cdot 2\pi rArc Length=

360

θ

⋅2πr

Replace 360° with 2π radians.

\dfrac{\theta}{360^{\circ}}=\dfrac{\theta}{2\pi}

360

θ

=

θ

Replace the angle ratio in degrees with the angle ratio in radians.

\textit{Arc Length}=\dfrac{\theta}{2\pi}\cdot 2\pi rArc Length=

θ

⋅2πr

Simplify by cancelling

\textit{Arc Length}=\theta rArc Length=θr


Related Questions

Jim’s backyard is rectangular with dimensions of 75 feet by 120 feet. He is planning to designate part of the yard to plant a vegetable garden. The garden will be a similar rectangle, using a scale factor of 2/5. How much fencing will he need if he wants to enclose the garden on all four sides?
He will need __________ feet of fence.

Answers

Answer:

15.6 feet of fence

Answer:

The answer is 45 ft. I hope i helped <3

Step-by-step explanation:

Help me please, thank you :)​

Answers

Answer:

300 children

Step-by-step explanation:

half hour: 25 children

1 hour: 25×2= 50 children

6 hours: 50×6= 300 children

hope it helps ☺️!

300 kids in 6 hours

What is the missing value for the probability distribution table ?
X 1 2 3 4 5
P(X) 0.05 0.35 0.15 0.2

Answers

The answer is 0.3 cause when you subtract all of it you can get it

Proving the Sum of the Interior Angle Measures of a Triangle Is 180

Answers

What Do you need help?

The sum of the interior angles of a triangle is 180° is proved below.

We are given that;

To prove angle sum property of triangle

Now,

There are different ways to prove that the sum of the interior angles of a triangle is 180°. Here are three common proofs:

Proof : Using parallel lines and alternate interior angles

Since the line PQ is parallel to the side BC, and AB and AC are transversals, we can use the property that alternate interior angles are congruent.

Therefore, we have:

∠QAC = ∠ACB

∠PAB = ∠ABC

Adding these equations, we get:

∠QAC + ∠PAB = ∠ACB + ∠ABC

But ∠QAC + ∠PAB is a straight angle, which measures 180°. So, we have:

180° = ∠ACB + ∠ABC

Adding ∠CAB to both sides, we get:

180° + ∠CAB = ∠ACB + ∠ABC + ∠CAB

Simplifying, we get:

180° = ∠ACB + ∠ABC + ∠CAB

Hence, by the triangles the answer will be given above.

Learn more about the triangles;

https://brainly.com/question/2773823

#SPJ4

6. Slope =
Y-Intercept
Equation in slope-intercept form:

Answers

Slope = 0.5x
Y intercept = 1
Equation: 0.5x +1

determine whether the triangles are congruent by sss sas asa aas or hl.

Answers

Answer:

sas :)

Step-by-step explanation:

There were 30 cars and 20 trucks in the parking garage. What is the ratio of cars to total vehicles?
A. 3 to 2
B. 7 to 2
C. 3 to 5
D. 2 to 3

Answers

I believe C. 3 to 5!

y = 6x + 11
2x - 3y = 7

Answers

2x - 3(6x +11) = 7
2x - 18x +33= 7
-16x = -26
x =13/8

A bank's loan officer rates applicants using their FICO credit score. The ratings are normally distributed with a mean of 711 and a standard deviation of 80. Find the credit score which separates the lower 80% from the top 20%. g

Answers

Answer:

The answer is "778"

Step-by-step explanation:

Given value:

[tex]\to \mu= 711\\\\\to \sigma= 80\\\\\to P(Z >0.84) = 0.20\\\\\to z = 0.84[/tex]

The formula for z-score:

[tex]\to x = z \times \sigma + \mu \\\\\to x = 0.84 \times 80 + 711 \\\\ \to x=67.2 +711\\\\ \to x= 778.2\\\\ \to x= 778[/tex]

A science fair poster is a rectangle 4 feet long and 3 feet wide. What is the area of the poster in square inches?
Be sure to include the correct unit in your answer.
in
in?
in?
G
Х
?

Answers

4x3=12 the poster is 12 feet^2 but now you have to convert it into inches. 12 inches=1 foot so you multiply 12x12 =144 so the poster is 144in^2

What is the range of fx) = 3^x

Answers

Answer: For the cubic function f(x)=x3 f ( x ) = x 3 , the domain is all real numbers because the horizontal extent of the graph is the whole real number line. The same applies to the vertical extent of the graph, so the domain and range include all real numbers.

Step-by-step explanation:

Evaluate each arithmetic series described (find the sum).
15
(13 – 5n)
=
n=1
Helppppp

Answers

Answer:

120

Step-by-step explanation:

Answer:

120

Step-by-step explanation:

first figure out parenthesis

replace n for 1 then you get 13-5, and you get 8.

then you just have to multiply 15 x 8.

then you get 120

Evaluate 12²- 4 (6) + 1/ 11²

Answers

Answer:

On a calculator you would get 120.008264463

other wise know as 120 1/121

Consider the inequity

Answers

Answer:

What inequality??

Step-by-step explanation:

Answer:

where?

Step-by-step explanation:

Determine the equation for the line that passes through (2,-1) and (6,5)
Write in point slope form
Write in slope intercept form
Write in standard form

Answers

Answer with explanation:

The equation of a line passing through (a,b) and (c,d) is given by :-

[tex](y-b)=\dfrac{d-b}{c-a}(x-a)[/tex]

Equation of line passing through (2,-1) and (6,5) is given by :-

[tex](y-(-1))=\dfrac{5-(-1)}{6-2}(x-2)\\\\\Rightarrow\ (y+1)=\dfrac{6}{4}(x-2)[/tex]

[tex]\\\\\Rightarrow\ (y+1)=\dfrac{3}{2}(x-2)\ \ \ \ \ \text{[point slope form} : (y-y_1)=m(x-x_1)] \\\\\Rightarrow\ y+1=\dfrac{3}{2}x-3\\\\\Rightarrow\ y=\dfrac32x-4\ \ \ \ \ [\text{ slope intercept form} : y= mx+c]\\\\\Rightarrow\ 2y= 3x-2\times4\\\\\Rightarrow\ 2y=3x-8\\\\\Rightarrow\ 3x-2y=8 \ \ \ \ [\text{Standard form : Ax + By = C}][/tex]

Solve 8a – 15 – 6a + 3a = 85

Answers

Answer:

a = 20

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Step-by-step explanation:

Step 1: Define

8a - 15 - 6a + 3a = 85

Step 2: Solve for a

Combine like terms:                    5a - 15 = 85Isolate a term:                              5a = 100Isolate a:                                       a = 20

If you are buying at item at a store for a price of $66, and there is a 5.1% tax added on top, what would be the total amount due at the register, to the nearest cent?​

Answers

Answer:

$69.37

Step-by-step explanation:

Before Tax Price: $66.00

Sale Tax: 5.10% or $3.37

After Tax Price: $69.37

PLEASE HELP it would be appreciated!!!!

Answers

Answer:

B 15

Step-by-step explanation:

Since the triangle has two same side lengths you can calculate that the other two are 54°.

Answer:

D. 33

Step-by-step explanation:

(3x+9)=72=180

3x + 81     = 180

subtract 81 from both sides

3x =180

divide 3 from both sides to get the x alone

x=33

Mark me brainliest by clicking the button at the bottom of this answer next to comments

thnk youuu

What is the value of the missing exponent in the equation 7.4 ÷ 10= 0.074?

Answers

the answer is 0.74 not 0.074

Step-by-step explanation:

7.4 ÷ 10 = 0.74

Solve the following system of equations.
2x +y = 3 = 3
2 = 2y - 1 - 1

Answers

Answer:   or (1,1)

Step-by-step explanation:

You can apply the Method of substitution.

Knowing that   (second equation), you can substitute it into the first equation and solve for the variable y:

Now you need to substitute  into the second equation  to calculate the value of the variable x. Then:

Then, the solution is:

or (1,1)

Don’t PUT A Random Answer PLEASE

Answers

Answer:

314

Step-by-step explanation:

Answer:

ok I won't

Step-by-step explanation:

What is the Slope?
4x + y = 1

Answers

Answer:

m=-4

Step-by-step explanation:

Answer:

take 1 - 4 you should get answer

Step-by-step explanation:

4x + y = 1

Solve 4h = 92 for h.

h = ___

Answers

Answer:

H= 23

Step-by-step explanation:

92 divided by 4 will give you 23

Answer:

h = 23

Step-by-step explanation:

Divide each term by 4 and simplify.

A particle moves along a line so that its velocity at time t is
v(t) = t2 − t − 20
(measured in meters per second).
(a) Find the displacement of the particle during
3 ≤ t ≤ 10.

(b) Find the distance traveled during this time period.

Answers

Just trying to get my points up

I don't know how to do this plz help

Answers

144-100 = 44. You take the square root of 44 and you get the number 12, which is the only rational number out of the list. Therefore, the answer is E.

Cindy bought 3 burgers and 2 soft drinks for $10.50. At the same restaurant, Sean bought 4 burgers and 3 soft drinks for 14.50. How much does 1 burger cost

Answers

Answer:

To much to count

Step-by-step explanation:

Help me please I need assistance!​

Answers

Answer:

84ft

Step-by-step explanation:

one side of the house is 14 units

since 1unit=6ft

Length of one side of her house= 14(6)=84ft

Find the value of x
Please help

Answers

Answer:

x=67

Step-by-step explanation:

Two ways to solve it:

1st way: Just looking at it, x is definitely not 180° because it’s to big of an angle, it is definitely not 113° because it’s still to big of an angle, and it’s also not 90° because it doesn’t form a right angle. So it must be 67°.

2nd way: Since two angles in a straight line add up to 180°, you can subtract 113° from 180° to find what x is. You can tell that 180° - 113° is equal to 67°

So either way, the answer is: x=67

Hope this helped! :)

67 according to the vertical angle postulate

(Giving brainliest)

Solve five ninths plus four sixths.

A) sixty six fifty fourths
B) ten fifteenths
C) thirty ninths

Answers

Answer:

C

Step-by-step explanation:

Make it the same denominator so you can add them (18.)
Multiply 5/9 by 2 and multiply 4/6 by 3.
10/18 + 12/18 = 22/18.
Since there is not 22/18 listed, you can use this fraction as a proportion. The only proportion that can be evident is answer A, as when you multiply 22/18 by 3, you get 66/54.
Your answer is A.

11. A tank is being filled up with water. At t=0, we know that the tank holds 150 gallons of
water, and after one hour ( t=1) , it holds 180 gallons of water.
a) Assuming that the volume of water in the tank, V, is a linear function of time, t, in hours,
find a formula for V ( linear function)

b) BY what percent did the volume of water increase from t=0 to t= 1?

Answers

Answer:

V = 30t + 15020%

Step-by-step explanation:

Given

Initial volume = 150 galVolume after 1 hour = 180 gal

a) The volume formula will be:

V = 30t + 150

As 150 is y-intersect (volume at zero time) and the rate of change (the slope) is 30 gal per hour

b) Increase of volume by percent:

30 gal increase on top of 150 gal

30/150*100% = 20%

Answer:

20%

Step-by-step explanation:

The volume formula is V = 30t + 150 → where 150 is y-intersect and the slope is 30 gals per hour

So you can do:

30 gals of increase on top of the 150 gals to get:

30/150×100%  which equals 20%

:)

Other Questions
You decided to join a fantasy Baseball league and you think the best way to pick your players is to look at their Batting Averages.You want to use data from the previous season to help predict Batting Averages to know which players to pick for the upcoming season. You want to use Runs Score, Doubles, Triples, Home Runs and Strike Outs to determine if there is a significant linear relationship for Batting Averages.You collect data to, to help estimate Batting Average, to see which players you should choose. You collect data on 45 players to help make your decision.x1 = Runs Score/Times at Batx2 = Doubles/Times at Batx3 = Triples/Times at Batx4 = Home Runs/Times at Batx5= Strike Outs/Times at BatInterpret the slope(s) of the significant predictors for Batting Average (if there are any).See Attached Excel for Data.Baseball data.xlsxDoubles/Times at Bat Triples/times at bat HR/Times at Bat SO/Times at Bat0.049 0.012 0.013 0.0860.039 0.013 0.002 0.0620.045 0.021 0.013 0.0740.043 0.001 0.03 0.0320.044 0.011 0.07 0.0760.047 0.018 0.05 0.0070.036 0.008 0.012 0.0950.03 0.006 0.003 0.1450.05 0.008 0.061 0.1120.041 0.005 0.014 0.1240.047 0.012 0.009 0.1110.058 0.01 0.011 0.070.041 0.009 0.005 0.0650.037 0.003 0.004 0.1380.058 0.014 0.011 0.0320.05 0.012 0.05 0.060.04 0.008 0.049 0.2330.038 0.013 0.003 0.0680.06 0.016 0.085 0.1580.066 0.021 0.037 0.0830.051 0.02 0.012 0.040.052 0.008 0.054 0.0950.037 0.003 0.043 0.1350.063 0.026 0.01 0.0310.054 0.027 0.01 0.0480.025 0.006 0 0.0610.044 0.003 0.022 0.1510.063 0.02 0.037 0.0810.045 0.008 0 0.2520.053 0.017 0.013 0.070.041 0.007 0.051 0.2640.057 0.03 0.017 0.0580.029 0.007 0.011 0.1880.034 0.019 0.005 0.0140.038 0.006 0.015 0.1420.068 0.016 0.022 0.0920.042 0.009 0.066 0.2110.052 0.008 0.054 0.0950.049 0.007 0.038 0.1010.044 0.007 0.002 0.2050.037 0.003 0.004 0.1380.061 0.002 0.012 0.1470.049 0.012 0.021 0.130.026 0.011 0.002 00.053 0.005 0.039 0.115Question 4 options:There are no significant predictors.When you hold Double, Triples, Home Runs and Strike Outs constant, as Runs Score increases by 1, your Batting Average will increase by .109/Times at Bat.When you hold Runs Score, Triples, Home Runs and Strike Outs constant, as Doubles increases by 1, your Batting Average will increase by .313/Times at Bat.When you hold Runs Score, Doubles, Triples, and Home Runs constant, as Strike Outs increase by 1, your Batting Average will decrease by .052/Times at Bat.When you hold Double, Triples, Home Runs and Strike Outs constant, as Runs Score increases by 1, your Batting Average will increase by .225/Times at Bat.When you hold Runs Score, Triples, Home Runs and Strike Outs constant, as Doubles increases by 1, your Batting Average will increase by .358/Times at Bat.When you hold Runs Score, Doubles, Triples, and Home Runs constant, as Strike Outs increase by 1, your Batting Average will decrease by .389/Times at Bat.When you hold Double, Triples, Home Runs and Strike Outs constant, as Runs Score increases by 1, your Batting Average will increase by .447/Times at Bat.When you hold Runs Score, Triples, Home Runs and Strike Outs constant, as Doubles increases by 1, your Batting Average will increase by .991/Times at Bat.When you hold Runs Score, Doubles, Triples, and Home Runs constant, as Strike Outs increase by 1, your Batting Average will decrease by .285/Times at Bat. i need a lot of help on this please!!! 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