Michael is using a rotating


sprinkler to water his lawn. The


sprinkler rotates in a complete


circle. It sprays water at most 8


feet. Find the area of the lawn


that is watered. Use 3. 14 for π. Show Your Work

Herbert will earn $63,417 for his tenth year of work which is calculated using compound interest formula.

After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4.5% each year. This means that every year, Herbert's salary will increase by 4.5% of his previous year's salary. For example, if his salary in the first year is $50,000, his salary in the second year will be $52,250, and so on.

To find out Herbert's salary for his tenth year of work, we need to use compound interest formula. The formula is:

A = P(1 + r)ⁿ

Where:
A = Final amount (salary in the tenth year)
P = Initial amount (salary in the first year)
r = Annual interest rate (4.5%)
n = Number of years (10)

Substituting the values in the formula, we get:

A = $50,000(1 + 0.045)¹⁰
A = $63,417

Therefore, Herbert will earn $63,417 for his tenth year of work. It is important to note that the increase in salary is a result of compound interest, which means that the salary growth rate accelerates over time. This is a good incentive for Herbert to stay with the company and work hard.

Know more about compound interest here:

https://brainly.com/question/14295570

#SPJ11

a) To express ∂z/∂u and ∂z/∂v as functions of u and v, we first need to express z directly in terms of u and v. We are given that:

z = tan^-1(x/y)

And that:

x = ucosv
y = usinv

Substituting these expressions for x and y into the equation for z, we get:

z = tan^-1((ucosv)/(usinv))
z = tan^-1(cotv)

Now we can use the chain rule to find ∂z/∂u and ∂z/∂v:

∂z/∂u = ∂z/∂cotv * ∂cotv/∂u
∂z/∂v = ∂z/∂cotv * ∂cotv/∂v

To find ∂cotv/∂u and ∂cotv/∂v, we use the quotient rule:

∂cotv/∂u = -cosv/u^2
∂cotv/∂v = -csc^2v

Substituting these into the chain rule expressions, we get:

∂z/∂u = (-cosv/u^2) * (1/(1+cot^2v))
∂z/∂v = (-csc^2v) * (1/(1+cot^2v))

Simplifying these expressions using trig identities, we get:

∂z/∂u = (-cosv/u^2) * (1/(1+(cosv/usinv)^2))
∂z/∂v = (-1/sinv^2) * (1/(1+(cosv/usinv)^2))

b) To evaluate ∂z/∂u and ∂z/∂v at (u,v) = (1.3, pi/6), we simply plug in these values into the expressions we derived in part (a):

∂z/∂u = (-cos(pi/6)/(1.3)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))
∂z/∂v = (-1/sin(pi/6)^2) * (1/(1+(cos(pi/6)/(1.3*sin(pi/6)))^2))

Simplifying these expressions using trig functions, we get:

∂z/∂u = (-sqrt(3)/1.69^2) * (1/(1+(sqrt(3)/1.3)^2))
∂z/∂v = (-4) * (1/(1+(sqrt(3)/1.3)^2))

Plugging in the values and evaluating, we get:

∂z/∂u ≈ -0.5167
∂z/∂v ≈ -1.5045
To answer this question, we'll first express z directly in terms of u and v, and then apply the chain rule to find the partial derivatives ∂z/∂u and ∂z/∂v.

Given:
z = tan^(-1)(x/y)
x = u*cos(v)
y = u*sin(v)

First, let's express z in terms of u and v:
z = tan^(-1)((u*cos(v))/(u*sin(v)))

Now, we can simplify the expression:
z = tan^(-1)(cot(v))

Next, we'll find the partial derivatives using the chain rule:

a) ∂z/∂u:
Since z doesn't have a direct dependence on u, we have:
∂z/∂u = 0

b) ∂z/∂v:
∂z/∂v = -csc^2(v)

Now let's evaluate the partial derivatives at the given point (u,v) = (1.3, π/6):

∂z/∂u(1.3, π/6) = 0
∂z/∂v(1.3, π/6) = -csc^2(π/6) = -4

So, the partial derivatives at the given point are:
∂z/∂u = 0 and ∂z/∂v = -4.

To learn more about derivatives visit;

/brainly.com/question/30365299

#SPJ11

The probability P(2 or fewer) is 0.678.

To find the probability of 2 or fewer successes in a binomial experiment with 10 trials and a success probability of 0.2, we can use the binomial probability formula:

P(2 or fewer) = P(0) + P(1) + P(2)

where P(0), P(1), and P(2) represent the probabilities of getting 0, 1, or 2 successes, respectively.

P(0) = (10 choose 0) * 0.2^0 * 0.8^10 = 0.1074
P(1) = (10 choose 1) * 0.2^1 * 0.8^9 = 0.2684
P(2) = (10 choose 2) * 0.2^2 * 0.8^8 = 0.3020

Therefore,

P(2 or fewer) = 0.1074 + 0.2684 + 0.3020 = 0.6778

Rounded to at least three decimal places, the probability P(2 or fewer) is 0.678.

To learn more about Probability

https://brainly.com/question/24870672

#SPJ11

This is a binomial probability problem, where the number of trials (n) is 15, the probability of success (p) is 0.75, and we want to find the probability of at least 12 successes.

We can use the binomial probability formula to calculate this:

P(X >= 12) = 1 - P(X < 12)

P(X < 12) = sum[k=0 to 11] (n choose k) * p^k * (1-p)^(n-k)

where n choose k is the binomial coefficient, which represents the number of ways to choose k items out of n.

Using a calculator or statistical software, we can calculate:

P(X < 12) = sum[k=0 to 11] (15 choose k) * 0.75^k * 0.25^(15-k) = 0.0278 (rounded to four decimal places)

Therefore,

P(X >= 12) = 1 - P(X < 12) = 1 - 0.0278 = 0.9722

So the probability that the football player will kick at least 12 field goals in the next 15 tries is approximately 0.9722, or about 97.22%

To know more aboutman  probability refer here

https://brainly.com/question/34187875#

#SPJ11

The dilation is (x, y) → (2x, 2y). So, the correct answer is D).

Let the coordinates of point C be (x, y). Then, the distance from the origin to point C is given by the distance formula

OC = √(x² + y²)

The corresponding side lengths are

CG = 16 - x

CD = √((x - 0)² + (y - 0)²)

The scale factor is the ratio of corresponding side lengths

CG/CD = 2

Therefore,

16 - x = 2*√(x² + y²)

Solving for y, we get

y = √(13x² - 64x + 256)

If we assume that point G corresponds to point C, then the center of dilation is the origin and the rule that represents the dilation is

(x, y) → (2x, 2y)

Therefore, the answer is

(x, y) → (2x, 2y)

So, the correct answer is D).

To know more about dilation:

https://brainly.com/question/936148

#SPJ4

--The given question is incomplete, the complete question is given

" Quadrilateral ABCD is dilated about the origin into quadrilateral EFGH so that point G is located at (16,8). scale factor is 2.

Which rule represents the dilation?

Select one

(x, y) → (18x, 18y)

(x, y) → (x+8, y+4)

(x, y) → (12x, 12y)

(x, y) → (2x, 2y) "--

The nearest tenth how many miles is alshleys house from Bridget house is  AB = √[(xB-xA)² + (yB-yA)²]

The nearest tenth how many miles is Ashley’s house from carlys house is AC = √[(xC-xA)² + (yC-yA)²]

The distances from Ashley's house to both Bridget's house and Carly's house, we can compare them and see which one is shorter.

To find the distance between Ashley's house and Bridget's house, we need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Bridget's house is located at point B. We can use the distance formula to find the distance between A and B:

distance AB = √[(xB-xA)² + (yB-yA)²]

Here, xA and yA represent the coordinates of Ashley's house, and xB and yB represent the coordinates of Bridget's house. The formula calculates the square root of the sum of the squares of the differences between the x-coordinates and y-coordinates of the two points.

To find the distance between Ashley's house and Carly's house, we again need to know the coordinates of both locations. Let's say Ashley's house is located at point A, and Carly's house is located at point C. We can use the same distance formula as before:

distance AC = √[(xC-xA)² + (yC-yA)²]

Here, xC and yC represent the coordinates of Carly's house. Plug in the values and calculate the distance to the nearest tenth of a mile.

To determine whose house Ashley lives closest to, we need to calculate the distances from Ashley's house to both Bridget's house and Carly's house. Whichever house has the shorter distance will be the closer one.

To find the difference between the two distances, we can subtract the smaller distance from the larger distance.

To know more about distance here

https://brainly.com/question/4199102

#SPJ4

So the equivalent expression that matches one of the answer choices is option C, 100c/3d.

In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a value. An expression can represent a single number or a more complex calculation, and it can be written using symbols, variables, and/or numbers.

Here,

To simplify the given expression, we need to multiply the two binomials using the distributive property:

(10c6d - 5)(2c - 5d/4)

= 10c * 2c + 10c * (-5d/4) - 5 * 2c - 5 * (-5d/4)

= 20c² - 25cd + 10c + 25/4 d

None of the answer choices match this expression exactly, but we can simplify it further. Factoring out a common factor of 5 from the last two terms, we get:

20c² - 25cd + 10c + 25/4 d

= 5(4c² - 5cd + 2c + 5/4

20c/3 * 5d/4

= 100c/3d

To know more about expression,

https://brainly.com/question/30091997

#SPJ1

Evaluating an exponential function A(x) = 160*(1.03)ˣ we can see that in 30 years she will have:

$388.36

We know that the initial investment is 160, and the rate per year is 3%.

Then after x years, the value is given by the exponential function.

A(x) = 160*(1.03)ˣ

The amount of money in the account after 30 years is what we get if we evaluate the equation in x = 30, then we will get:

A(30) = 160*(1.03)³⁰

A(30) = 388.36

In 30 years she will have a total amount of 388.36 dollars.

Learn more about exponential functions:

https://brainly.com/question/2456547

#SPJ1

Answer:107

Step-by-step explanation:8*17-29=107 so our answer is 107

Answer:

  (C)  Neither

Step-by-step explanation:

You want to know if the function values in the table represent an even function, and odd function, or neither.

An Even function is symmetrical about the y-axis:

  f(-x) = f(x)

An Odd function is symmetrical about the origin:

  f(-x) = -f(x)

The attached graph of the given points shows the function has no symmetry at all.

The table represents neither an even nor odd function.

Answer:

Neither

Step-by-step explanation:

In an even function, f(x) = f(-x).

Look at x = 2 and x = -2.

f(2) = -4; f(-2) = 2

Since f(2) ≠ f(-2), the function is not even.

In an odd function, f(x) = -f(-x).

Look at f(2) and f(-2).

f(2) = -4; f(-2) = 2

Since f(2) ≠ -f(-2), the function is not odd.

Answer: C  Neither

The circumference of the circle is 6.28 kilometers if the diameter of the circle is 2 kilometers and assuming the value of π is 3.14 kilometers.

The diameter of the circle = 2 kilometers

The circumference of a circle is calculated by using the formula,

C = π *d

where,

C = circumference of a circle

d = diameter of the circle

π = Constant value = 3. 14 Km

Substituting the above-given values into the equation, we get:

C = π*d

C = 3.14 x 2 km

C = 6.28 km

Therefore, we can conclude that the circumference of the circle is 6.28 kilometers.

To learn more about the circumference of the circle

https://brainly.com/question/25945520

#SPJ4

Answer:

34.65 mi²

Step-by-step explanation:

Area of parallelogramam = b · h

b = 6.3 mi

h = 5.5 mi

Let's solve

6.3 · 5.5 = 34.65 mi²

So, the area of the shape is 34.65 mi²

Answer:

Let's start by assigning some variables to the unknowns:

Let's call the price of one taco "t".

Let's call the price of one burrito "b".

With these variables, we can write two equations based on the information given in the problem:

5t + 2b = 13.25 (equation 1)

3t + 2b = 10.75 (equation 2)

We now have two equations and two variables. We can use algebra to solve for t and b. One way to do this is to eliminate b by subtracting equation 2 from equation 1:

(5t + 2b) - (3t + 2b) = 13.25 - 10.75

Simplifying this equation, we get:

2t = 2.5

Dividing both sides by 2, we get:

t = 1.25

So the price of one taco is $1.25.

Now that we know the price of one taco, we can substitute this value into one of the equations to solve for b. Let's use equation 1:

5t + 2b = 13.25

Substituting t = 1.25, we get:

5(1.25) + 2b = 13.25

Simplifying this equation, we get:

6.25 + 2b = 13.25

Subtracting 6.25 from both sides, we get:

2b = 7

Dividing both sides by 2, we get:

b = 3.5

So the price of one burrito is $3.5.

Therefore, the price of one taco is $1.25 and the price of one burrito is $3.5.

To know more about variables refer here

https://brainly.com/question/17344045#

#SPJ11

Answer:

f(-2) = 9

Step-by-step explanation:

f(x) = -3x + 3                       Solve for f(-2)

f(-2) = -3(-2) + 3

f(-2) = 6 + 3

f(-2) = 9

Possible options for z could be:

1) z = -6

2) z = -7

These are two possible options for z that satisfy the given inequality.

Given that the opposite of z is greater than 5, we can write this as an inequality:

-z > 5

To find the possible options for z, we can follow these steps:

Step 1: Multiply both sides of the inequality by -1 to solve for z. Remember to flip the inequality sign when multiplying by a negative number:

z < -5

Step 2: Choose two values for z that satisfy the inequality z < -5.

Possible options for z could be:

1) z = -6
2) z = -7

These are two possible options for z that satisfy the given inequality.

Learn more about inequality,

https://brainly.com/question/30681777

#SPJ11

We can start by integrating both sides of the differential equation to obtain:

∫f '(x) dx = ∫([tex]5x^2 - x^2/5[/tex]) dx

f(x) = (5/3)[tex]x^3[/tex] - (1/15) [tex]x^5[/tex] + C

where C is the constant of integration.

To find the value of C, we can use the initial condition f(1) = 0:

f(1) = (5/3)[tex](1)^3[/tex] - (1/15) [tex](1)^5[/tex] + C = 0

Simplifying this equation gives:

C = (1/15) - (5/3)

C = -2/9

Therefore, the solution to the initial value problem f '(x) = 5[tex]x^2[/tex] − [tex]x^2[/tex]/5 , f(1) = 0 is:

f(x) = (5/3) [tex]x^3[/tex] - (1/15) [tex]x^5[/tex] - (2/9)

Learn more about initial value problem

https://brainly.com/question/30547172

#SPJ4

the formula for ak, we can set up a system of linear equations using the given values for ao, aj, and Ak+1.

Let x = ak-1 and y = ak. Then we have:

2 = a0 = x
4 = a1 = y
Ak+1 = 10ak-1 + 9ak

Substituting x and y, we get:

Ak+1 = 10(2) + 9(4) = 56

So we have the system of equations:

x = 2
y = 4
y = 10x + 9y

Rewriting the third equation, we get:

-10x + y = 0

Adding the first two equations, we get:

x + y = 6

Solving this system of equations, we get:

x = 2
y = 4

Therefore, ak = 4 for all k > 0.

To find lim kak, we can use the formula for ak:

lim kak = lim 4 = 4

So the limit of ak as k approaches infinity is 4.
To find the formula for a_k using linear algebra, we can first form a system of linear equations using the given recurrence relation:

a_(k+1) = 10a_(k-1) + 9a_k

Since we know a_0 = 2 and a_1 = 4, we can start by finding a_2:

a_2 = 10a_0 + 9a_1 = 10(2) + 9(4) = 20 + 36 = 56

Next, we can find a_3 using a_1 and a_2:

a_3 = 10a_1 + 9a_2 = 10(4) + 9(56) = 40 + 504 = 544

Now, we can represent this system of linear equations in matrix form:

[ [ 1  0 ]   [ a_0 ]   [  2 ]
 [ 0  1 ] * [ a_1 ] = [  4 ]
 [ 10 9 ] * [ a_2 ] = [ 56 ]  
 [ 10 9 ] * [ a_3 ] = [ 544 ] ]

We can then use methods of linear algebra such as Gaussian elimination, Cramer's rule, or matrix inversion to solve the system and find a_k.

However, this particular system does not provide a direct formula for a_k. Moreover, as the given information doesn't suggest a converging series, we cannot determine the limit as k approaches infinity (lim k→∞ a_k).

To know more about  linear equations click here:

brainly.com/question/29739212

#SPJ11

John threw the javelin 3 standard deviations below the mean

An equation is an expression that shows how numbers and variables using mathematical operators.

The z score shows by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean) / standard deviation

Given that John threw 106 feet. The average throw was 130 ft. The standard deviation was 8 feet. Hence:

z = (106 - 130) / 8

z = -3

John threw 3 standard deviations below the mean

Find out more on equation at: https://brainly.com/question/22688504

#SPJ1

a = 5

b = 4

c= 0

Therefore, the equation for graph C is Y = a ^b + c

Y = 5 ^4 + 0

A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.

Graphs are a popular tool for graphically illuminating data relationships. A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.

Learn more about graphs at: https://brainly.com/question/19040584

#SPJ1

The probability of the spinner not landing on red and then landing on red is 7/64.

The probability chance that the spinner will not land on red then land on red is calculated as follows;

The probability of the spinner not landing on red is 1 - 1/8 = 7/8.

To find the probability that the spinner will not land on red and then land on red, we multiply the probabilities:

(7/8) x (1/8) = 7/64

Learn more about probability here: https://brainly.com/question/24756209

#SPJ4

Yes, there is reason to doubt the randomness of the jury selection based on the information provided.

Given data:

Out of the 20 potential jurors, 8 were African American and 12 were white. The probability of randomly selecting an African American juror from the pool of potential jurors would ideally be 8/20, which simplifies to 2/5 or 40%. However, the actual jury selected had only 1 African American member out of 6 jurors, which is significantly lower than the expected 40% if the selection were truly random.

This deviation from the expected probability raises questions about the randomness of the selection process. The observed outcome appears to be disproportionately skewed against the representation of African American jurors. While random variations can occur, the extent of the deviation in this case warrants further investigation into the jury selection process to determine if there were any biases or factors influencing the outcome.

To learn more about probability, refer:

https://brainly.com/question/17089724

#SPJ12

Answer:

40%

Step-by-step explanation:

[tex] \frac{48}{120} \times 100 = 40[/tex]

Answer:

40%

Step-by-step explanation:

To find out what percentage of 2 hours is 48 minutes, we need to first convert both values to the same unit of time, such as minutes.

2 hours is equal to 120 minutes (2 x 60).

So, the fraction of 2 hours that is represented by 48 minutes is:

48/120

Simplifying this fraction by dividing both the numerator and denominator by 12, we get:

4/10

Multiplying the numerator and denominator by 10 to convert this fraction into a percentage, we get:

40%

Therefore, 48 minutes is 40% of 2 hours.

Since G is a cyclic group of order m, there exists an element g in G such that the subgroup generated by g contains all elements of G. We denote this subgroup by <g>. The order of <g> is equal to the order of g, which is a divisor of m. Hence, there exists an integer k such that m = kg.

Now, consider the element [tex]g^{(k/d)[/tex]. Since ([tex]g^k[/tex]) generates G and d is a divisor of k, ([tex]g^k/d[/tex]) is an element of <g>. Therefore, the subgroup generated by [tex]g^{(k/d)[/tex] is a subgroup of <g> with order d.

To show that this subgroup has order d, suppose that there exists an integer r such that [tex](g^{(k/d)})^r[/tex] = [tex]g^{(kr/d)[/tex] = e, where e is the identity element of G. This means that kr/d is an integer multiple of k, which implies that r is a multiple of d. Thus, the order of [tex]g^{(k/d)[/tex] is d, and the subgroup generated by [tex]g^{(k/d)[/tex] has order d.

Therefore, we have shown that if G is a cyclic group of order m and d | m, then G must have a subgroup of order d, which is generated by an element of the form [tex]g^{(k/d)[/tex], where g is a generator of G and m = kg.

To know more about cyclic group, refer to the link below:

https://brainly.com/question/30327236#

#SPJ11

There are several transformations that can be applied to a pentagon in order to map it onto itself. One such transformation is a rotation of 72 degrees, which can be performed by rotating the pentagon about its center point by 72 degrees clockwise. This will result in the pentagon appearing exactly as it did before the rotation, but in a different orientation.

Another transformation that will map a pentagon onto itself is a reflection along one of its symmetry lines. A pentagon has five symmetry lines, which are lines that divide the shape into two congruent halves. Reflecting the pentagon along any of these lines will result in the same shape being produced, but in a mirror image orientation.

Finally, a translation can also be used to map a pentagon onto itself. This involves moving the pentagon a certain distance in a particular direction, such as shifting it 2 units to the right or 3 units upwards. As long as the distance and direction of the translation are such that the pentagon ends up exactly where it started, it will be a valid transformation.

Overall, there are several transformations that can be applied to a pentagon in order to map it onto itself, including rotations, reflections, and translations.

To know more about transformations refer here

https://brainly.in/question/15660713#

#SPJ11

To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.

We are given a population growth model with a recursive rule and an initial population. Let's break down the information and find the population at any given term n.

Recursive rule: Pₙ = Pₙ₋₁ + 50
Initial population: P₀ = 30

Now let's find the population at any term n, using the recursive rule:

Step 1: Determine the base case, which is the initial population.
P₀ = 30

Step 2: Apply the recursive rule to find the next few terms.
P₁ = P₀ + 50 = 30 + 50 = 80
P₂ = P₁ + 50 = 80 + 50 = 130
P₃ = P₂ + 50 = 130 + 50 = 180

Step 3: To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50

Using this recursive rule and the initial population, you can find the population at any given term n.

Learn more about recursive rule,

https://brainly.com/question/29508048

#SPJ11

The perimeter and area of the shape is 18cm² and 12cm respectively.

The perimeter of a shape is the total measurement of all the edges of a shape. Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The perimeter of the shape = 4+4+5+5 = 8 +10

= 18cm.

The area of the shape is = b×h

the base = 4cm and height is 3cm

A = 4× 3

= 12cm²

therefore the perimeter and the area of the shape is 18cm² and 12cm² respectively.

learn more about area and perimeter from

https://brainly.com/question/28978432

#SPJ1

Candace is flipping the coin 5 times.

The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.

The theoretical probability of flipping tails on any single flip of a fair coin is 1/2, since there are two equally likely outcomes (heads or tails) on each flip.

If Candace is flipping the coin a certain number of times and the theoretical probability of flipping tails on all flips is 1/32, we can set up the equation:

[tex](1/2)^n[/tex] = 1/32

where n is the number of times Candace is flipping the coin.

We can simplify this equation by taking the logarithm of both sides:

[tex]log((1/2)^n) = log(1/32)[/tex]

Using the property of logarithms that [tex]log(a^b) = b*log(a)[/tex], we can rewrite the left-hand side as:

n*log(1/2) = log(1/32)

We can simplify the logarithms using the fact that log(1/a) = -log(a), so:

n*(-log(2)) = -log(32)

Dividing both sides by -log(2), we get:

n = -log(32) / log(2)

Using a calculator, we find:

n ≈ 5

Therefore, Candace is flipping the coin 5 times.

Learn more about probability on:

https://brainly.com/question/13604758

#SPJ4