Solve for b.
b-c+d/8 = a

In one sweep, the area covered by the sprinkler is 77.19 sq ft (approx). The area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

We know that a rotating sprinkler can reach up to 14 feet through a 300-degree angle. Area covered by the sprinkler in one sweep = area of the sector whose radius = 14 feet and angle = 300°Area of sector = (θ / 360) × πr²Where θ = 300°, r = 14 ftArea of sector = (300/360)× π(14)²= 77.19 sq ft (approx) Therefore, the area covered by the sprinkler in one sweep is 77.19 sq ft (approx).

We need to find the total area of the lawn that receives water from this sprinkler. The sprinkler rotates 360 degrees, so it will cover a full circle whose radius is 14 feet. Area of a circle = πr²= π(14)²= 615.752 sq ft (approx) Therefore, the area of the lawn, to the nearest square foot, that receives water from this sprinkler is 616 sq ft (approx).

To know more about area visit:-

https://brainly.com/question/1631786

#SPJ11

The integral for the volume of the solid is:

V = ∫[0,8] 2π(12 - x)(9x - x²) dx.

The method of cylindrical shells can be used to compute an integral for the volume of a solid obtained by rotating the region bounded by the curves y = 10x - x², y = x about the line x = 12.

The rotation axis is x = 12, which is a vertical line that passes through the point (12, 0).

The next step is to determine the integration's limits. At x = 0 and x = 8, the curves y = 10x - x² and y = x intersect. We'll integrate with respect to x, so the integration range will be from x = 0 to x = 8.

We can now apply the formula for the volume of a cylindrical shell:

V = 2πrhΔx

where r denotes the distance from a point on the curve to the axis of rotation, h denotes the height of the shell, and x denotes the thickness of the shell.

We have the following solutions to our problem:

r = 12 - x (the distance between x = 12 and a point on the curve)

h = y2 - y1 = (10x - x²) - x = 9x - x²

Δx = dx

As a result, the integral for the solid's volume is:

dx = V = [0,8] 2(12 - x)(9x - x²).

To know more about Integral visit:

brainly.com/question/30376753

#SPJ1

The probability that Emme answers exactly 3 questions correctly is 0.1961.

Since each question has four answer choices and only one is correct, the probability of Emme randomly guessing the correct answer for each question is 1/4 = 0.25. Emme needs to answer exactly 3 out of the 9 questions correctly, so we use the binomial distribution with n = 9 and p = 0.25 to calculate the probability:

P(X = 3) = (9 choose 3) * (0.25)^3 * (0.75)^6

Using a calculator, we get:

P(X = 3) = 0.1961

Therefore, the probability that Emme answers exactly 3 questions correctly is 0.1961.

To know more about probability refer here:

https://brainly.com/question/30034780#

#SPJ11

The mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

We have,

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the mean absolute deviation (MAD), we need to first calculate the mean of the given data set:

mean = (4 + 5 + 7 + 9 + 8) / 5 = 6.6

Next, we calculate the deviation of each data point from the mean:

|4 - 6.6| = 2.6

|5 - 6.6| = 1.6

|7 - 6.6| = 0.4

|9 - 6.6| = 2.4

|8 - 6.6| = 1.4

Then we find the average of these deviations, which gives us the mean absolute deviation:

MAD = (2.6 + 1.6 + 0.4 + 2.4 + 1.4) / 5 = 1.6

Therefore, the mean absolute deviation of the given data set is 1.6 (rounded to the nearest tenth).

To learn more about mean from the given link:

brainly.com/question/31101410

#SPJ1

Answer:

umm i think it is B.

Step-by-step explanation:

Answer:

no hablo espanol Lo siento

The signed number representation for David losing 15 dollars is -15, indicating a decrease of 15 units in his pocket.

We can use a negative value since he lost money to represent the change of David losing 15 dollars from his pocket using signed numbers. Using a signed number system, we represent positive values as regular numbers and negative values with a minus sign (-) in front of the number. So, in this case, the change can be represented as: -15

The negative sign (-) indicates that David lost 15 dollars. In signed number notation, the minus sign represents a decrease or a loss, while a positive sign (+) represents an increase or a gain.

In summary, the signed number representation for David losing 15 dollars is -15, indicating a decrease of 15 units in his pocket.

To know more about number

https://brainly.com/question/251701

#SPJ2

Answer:

Step-by-step explanation:

I think you mean

x² - 49.

If so it factors to (x +7)(x - 7)

Answer:

I don't know the answer to this question.

Answer:

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Step-by-step explanation:

Answer:

The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

Step-by-step explanation:

Natural Numbers are known as 1, 2, 3, 4, ..., ∞

Now,

For Cube of first six natural numbers

1³ = 1

2³ = 8

3³ = 27

4³ = 64

5³ = 125

6³ = 216

Thus, The cube of first six natural numbers are

1, 8, 27, 65, 125, 216

-TheUnknownScientist

The matrix A = [1 0 0; 0 1 0; 1 1 0] does not span R3. We show that there exists a vector in R3 that cannot be expressed as a linear combination of the columns of A.

To show that the columns of A do not span R3, we need to show that there exists a vector in R3 that cannot be expressed as a linear combination of the columns of A. Let b = [0 0 1]T. We need to show that there do not exist scalars x, y, and z such that Ax = [0 0 1]T.

Ax = [1 0 0; 0 1 0; 1 1 0][x; y; z] = [x; y; x+y]

Setting this equal to b, we get x+y = 1, which is impossible to satisfy for any values of x and y. Therefore, the columns of A do not span R3.

Learn more about Matrix:

https://brainly.com/question/1279486

#SPJ4

The sinU from the triangle is √4/5

To find sinU we have to find the side length ST

By pythagoras theorem we find ST of the triangle

ST²+UT²=SU²

ST²+11=55

ST²=55-11

ST²=44

Take square root on both sides

ST=√44

The sine function is ratio of opposite side and hypotenuse

sinU = √44/55

sinU=√4/5

Hence,  the sinU from the triangle is √4/5

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

Answer:

A. =

B. >

C. >

Step-by-step explanation:

0.30 and 0.3 same

8.3 and 8.09 the " 9 " is in the hundreths place while the " 3 " is in the tenths place

8.34 and 3.88 well 8 is bigger than 3 soo yea

Answer:

Below.

Step-by-step explanation:

5^4/5^7

= 5^(4-7)

= 5^-3 or 1/5^3.

Or we might write it as 1/125.

Answer: 100

hope this helps

The correct function that describes the line segment from P(2,7,3) to Q(3,1,1) is r(t) = ⟨2 + t, 7 - 6t, 3 - 2t⟩; 0 ≤ t ≤ 1.

The function that describes the line segment from point P(2,7,3) to Q(3,1,1), we can use the parametric form of a line. The general form of a line equation is r(t) = ⟨x₀ + at, y₀ + bt, z₀ + ct⟩, where (x₀, y₀, z₀) is a point on the line and (a, b, c) are direction ratios.

1. First, we find the direction ratios by subtracting the coordinates of P from Q:

  a = 3 - 2 = 1

  b = 1 - 7 = -6

  c = 1 - 3 = -2

2. Next, we substitute the point P(2,7,3) into the line equation and simplify:

  r(t) = ⟨2 + t, 7 - 6t, 3 - 2t⟩

3. The parameter t represents the distance along the line segment. Since we want to describe the segment from P to Q, we need t to vary from 0 to 1, ensuring that we cover the entire segment.

4. Comparing the obtained equation with the given options, we find that the correct function is r(t) = ⟨2 + t, 7 - 6t, 3 - 2t⟩; 0 ≤ t ≤ 1.

Therefore, option A, r(t) = ⟨2 - t, 7 + 6t, 3 + 2t⟩; 0 ≤ t ≤ 1, is the correct answer.

Learn more about function  : brainly.com/question/28278690

#SPJ11

The magnetic field generated by the wires at the point (x=4m, y=4m) carrying identical currents of 90A out of the page is 2.50 x \(10^{-6\) T or 2.50 μT.

Hence option b is correct.

According to the given information,

We can use the Biot-Savart Law to calculate the magnetic field generated by these wires at the given point.

Using the formula, we get:

B = (μ0/4π) I [(sinθ1 + sinθ2) / 2] / d,

Where,

μ0 is the permeability of free space (4π x \(10^{-7}\) T m/A),

I is the current (90 A),

θ1 and θ2 are the angles between the wire and the vector pointing from the wire to the given point,

And d is the distance between the wires (8 m).

To find θ1 and θ2, we can use Trigonometry:

θ1 = sin inverse (y/d)

   = sin inverse (4/8) = 30°

θ2 =  sin inverse [(y-d)/d]

     =  sin inverse [(4-8)/8]

     = -30°

Substituting these values into the formula, we get:

B = (4π x \(10^{-7}\) T m/A) 90 A [(sin30° + sin(-30°)) / 2] / 8 m

B = 2.50 x \(10^{-6\)  T

   = 2.50 μT

Therefore, the correct option is (b) 2.50 x  \(10^{-6\)  T (or 2.50 μT).

To learn more about magnetic fields visit:

https://brainly.com/question/14848188

#SPJ4

The complete question is attached below:

Answer:

∠8 = 139°

Step-by-step explanation:

Before we start solving, let's identify the figure to understand the problem.

We are given two parallel lines that are cut by a transversal.

Two lines are parallel if they have the same arrow head marking.

If two parallel lines are cut by a transversal, the following angles are created:

I have attached an image of the different types of angles to this response.

Thus, we can use the types of angles to solve for ∠8.

∠3 and ∠5 are corresponding angles. Therefore, they have the same measure.

Set up the equation to solve for x:

∠3 = ∠5

9x + 14 = 14x - 1 . . . . . . substitute the values

14 = 5x - 1 . . . . . . . . subtract 9x from the LHS and RHS

15 = 5x . . . . . . . . . . add 1  to the LHS and RHS

∴ 3 = x . . . . . . . . . . . . divide the LHS and RHS by 5 to isolate x

Now that we know what x is, we can substitute it into the value of ∠3.

∠3 = 9x + 14

∠3 = 9(3) + 14 . . . . substitute the values

∠3 = 27 + 14 . . . . . compute

∴ ∠3 = 41

∠3 and ∠8 are adjacent angles. Therefore, they add up to 180°.

Set up the equation to solve for ∠8:

∠8 + ∠3 = 180

∠8 + 41 = 180 . . . . substitute the known values

∴ ∠8 = 139° . . . . . subtract 41 from the LHS and RHS to isolate ∠8

⭐if this response helped you, please mark it the "brainliest"!⭐

Answer:

Step-by-step explanation:

180-54=139 so 8 equals 139

The distance of the flowerbed to the hive is 864 feet.

The resulting displacement between two places is defined as distance. It is sometimes referred to as a line segment. It is determined using the conventional distance formula. This allows for the examination of the characteristics like intercepts and slope.

Calculate the time and distance using the provided inputs, as per the question.

Here, the common formula for speed is applied: Distance times speed (Time)

Let's assume that the distance is now d.

Thus, it takes d/12 seconds to go directly from a flower bed to a hive.

Likewise, it takes d/8 seconds to go from the flower bed to the hive.

And the bee spent a total of: 22-19 = 3min. = 180 seconds.

The formula is now expressed as follows: d/12 + d/8 = 180 20d = (180)(12)(8) =(9)(96) d= 864 feet.

To learn more about the distance from the given link:

https://brainly.com/question/23848540

#SPJ9

The odds that the number rolled is not greater than or equal to 5 are 40%.


- There are 10 possible outcomes when rolling a 10-sided die, labeled 1-10.
- Half of these outcomes are greater than or equal to 5, which means there are 5 outcomes that meet this criteria.
- Therefore, the other half of the outcomes are not greater than or equal to 5, which also equals 5 outcomes.
- To calculate the odds of rolling a number not greater than or equal to 5, we divide the number of outcomes that meet this criteria (5) by the total number of possible outcomes (10).
- This gives us a probability of 0.5, which is equal to 50%.
- To convert this probability to odds, we divide the probability of rolling a number not greater than or equal to 5 (0.5) by the probability of rolling a number greater than or equal to 5 (also 0.5).
- This gives us odds of 1:1 or 1/1, which simplifies to 1.

Therefore, the odds that the number rolled is not greater than or equal to 5 are 40% or 1 in 1.

To know more about probability visit:

brainly.com/question/31828911

#SPJ11

a) 2 sin(11°) cos(11°) simplifies to sin(22°) using the double-angle formula for sine;

(b) 2 sin(3) cos(3) simplifies to sin(6) using the double-angle formula for cosine.

The expressions using the double-angle formula.
(a) 2 sin(11°) cos(11°)
Using the double-angle formula for sine, sin(2x) = 2 sin(x) cos(x), we can rewrite the expression as:
sin(2 * 11°) = sin(22°)
So, 2 sin(11°) cos(11°) simplifies to sin(22°).
(b) 2 sin(3) cos(3)
Similarly, using the double-angle formula for sine, we can rewrite the expression as:
sin(2 * 3) = sin(6)
So, 2 sin(3) cos(3) simplifies to sin(6).

Note that in general, double-angle and half-angle formulas can be used to simplify expressions involving trigonometric functions.

These formulas allow us to express a function in terms of another function with an argument that is either twice or half the original argument, which can often simplify calculations or allow us to apply other identities.

For similar question on double-angle formula.

https://brainly.com/question/29056772

#SPJ11

(a) The simplified expression is: sin(22°)/2

(b) The simplified expression is: sin(6)

simplify these expressions by using either a double-angle formula or a half-angle formula. Let's start with part (a):

To simplify 2 sin(11°) cos(11°), we can use the double-angle formula for sine: sin(2θ) = 2 sin(θ) cos(θ). If we let θ = 11°, we get:

sin(2(11°)) = 2 sin(11°) cos(11°)

Simplifying the left-hand side gives us:

sin(22°) = 2 sin(11°) cos(11°)

So, we can rewrite 2 sin(11°) cos(11°) as sin(22°)/2.

For part (b), we can use the double-angle formula for cosine: cos(2θ) = cos²(θ) - sin²(θ). If we let θ = 3, we get:

cos(2(3)) = cos²(3) - sin²(3)

Simplifying the left-hand side gives us:

cos(6) = cos²(3) - sin²(3)

So, we can rewrite 2 sin(3) cos(3) as (cos(6) + sin²(3))/2 = sin(6).
Visit here to learn more about double-angle formula:

brainly.com/question/30402422

#SPJ11

Answer:

B

Step-by-step explanation:

To find how many picture are in the yearbook, multiply the number of pages of the yearbook by the number of pictures on one page. This is 32 times 8:

There are 256 picture in the yearbook.

Answer:

y = 2x - 3

i just know this is correct, so trust me :)

The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

You should perform x trials until you observe a success.

We have given that,

There are exactly two possible outcomes success and failure.

We have to determine the following is NOT a common characteristic of a binomial distribution.

By process of elimination:-

A binomial experiment is a statistical experiment that must meet certain requirements

All trials are independent.

There are a fixed number of n trials.

The probability of success, p, is the same for each trial.

To learn more about the probability visit:

brainly.com/question/24756209

#SPJ1

The scale of the map can be written as:

1cm to 20km

We want to find the distance that 1 cm in the map representes in the real world.

We know the relation:

3cm = 60km

We want to get a 1 in the left side, then we can divide both sides by 3 to get:

1cm = 60km/3

1cm = 20km

Then the scale of the map is 1cm to 20km

Learn more about scales at:

https://brainly.com/question/25722260

#SPJ1

The last year when the population was more than 250,000 was 2005.

What is the natural logarithm?

The natural logarithm, denoted by ln(x), is a mathematical function that gives the logarithm of a number x with respect to the base e, where e is the mathematical constant approximately equal to 2.71828.

We can start by setting up the equation p = 250, where p represents the population in thousands. Then, we can solve for t, the number of years since 2000:

\(250 = 90*(34)^t\)

\((34)^t = 250/90\)

\((34)^t = 2.777...\)

Taking the natural logarithm of both sides, we get:

t ln(34) = ln(2.777...)

t = ln(2.777...)/ln(34)

t ≈ 4.4

So, the population was more than 250,000 in the year 2000 + 4.4 ≈ 2004.4, which we can round up to 2005.

Therefore, the last year when the population was more than 250,000 was 2005.

To learn more about the natural logarithms visit:

https://brainly.com/question/23129841

#SPJ1

Answer:

3 3/4

Step-by-step explanation:

m > 650 miles

A mileage over 650 miles makes company A cheaper than B.

1) Gathering the data

Company A

$127 (unlimited mileage)

Company B

$75 + 0.08m

2) To find out the mileage that makes Company A cheaper than Company B, we can write out the following:

3) Hence when we drive over 650 miles the Company A becomes cheaper than B.

Answer:

23.3 mpg

Step-by-step explanation:

For the unit rate of miles per gallon (mpg)

140 miles / 6 gallons = 23 1/3   mpg  = 23.3 mpg

The required ratio as a unit rate is 23.3 mi/gal, which is determined by dividing the number of miles by the number of gallons.. The correct answer is option (a).

To express each ratio as a unit rate (mi/gal), we need to divide the number of miles by the number of gallons.

The units rate can be calculated as:

Units rate = number of miles / the number of gallons.

Unit rate = 140 miles / 6 gallons

Apply the division operation to get:

Unit rate = 23.3 mi/gal

Thus, the required ratio as a unit rate is 23.3 mi/gal.

Hence, the correct answer is option (a).

To learn more about the rate click here :

https://brainly.com/question/12786410

#SPJ3

Answer:

D

Step-by-step explanation:

Answer: Five more than two times x

Step-by-step explanation:

2x + 5 = y

2(1) + 5 = 2 + 5 = 7

2(2) + 5 = 4 + 5 = 9

2(3) + 5 = 6 + 5 = 11

2(4) + 5 = 8 + 5 = 13