Triangle G Y K is shown. Angle G K Y is a right angle. Angle K G Y is 60 degrees and angle G Y K is 30 degrees. The length of G K is 27.
Given right triangle GYK, what is the value of tan(G)?

One-half
StartFraction StartRoot 3 EndRoot Over 2 EndFraction
StartFraction 2 StartRoot 3 EndRoot Over 3 EndFraction
StartRoot 3 EndRoot

Answers

Answer 1

The value of tanG is √3

What is trigonometric ratio?

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

The value of KY

Tan 30 = 27/KY

1/√3 = 27/KY

KY = 27√3

Tan G = 27√3/27

tanG = √3

therefore the value of tanG is √3

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Related Questions

A gardener has a rectangular vegetable garden that is 2 feet longer than it is wide. The area of the garden is at


least 120 square feet.


Enter an inequality that represents all possible widths, w, in feet of the garden

Answers

This is the inequality that represents all possible widths, w, in feet of the garden is W^2 + 2W - 120 ≥ 0

The area of a rectangle is given by the formula A = L x W, where A is the area, L is the length, and W is the width. In this problem, we are given that the garden is rectangular and that the length is 2 feet longer than the width, so we can write L = W + 2.

We are also told that the area of the garden is at least 120 square feet, so we can write:
A = L x W ≥ 120
Substituting L = W + 2, we get:
(W + 2) x W ≥ 120

expanding the left side, we get:
W^2 + 2W ≥ 120
Rearranging, we get:
W^2 + 2W - 120 ≥ 0

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Solve for X pleaseee!!!

Answers

The answer
X=10
If you want Another way

6x-7=10x-47
We move all terms to the left:
6x-7-(10x-47 =0
We get rid of parentheses
6x-10X+47-7=0
We add all the numbers together, and all t
-4X+40=0
We move all terms containing x to the left
-4X=-40
x=-40/-4
X=+10

17 Question Evaluate y=−4(5)x y = − 4 ( 5 ) x for x

Answers

The equation y=−4(5)x y = − 4 ( 5 ) x can be simplified to y = -20x. This equation is a linear function with a slope of -20. As x increases, y decreases at a rate of 20 units for every one unit increase in x. Therefore, the value of y will decrease rapidly as x increases.

Use cylindrical coordinates to evaluate the triple integral ∫∫∫√(x^2 + y^2) dV where E is the solid bounded by the
circular paraboloid z = 9 - (x^2 + y^2) and the xy-plane.

Answers

The value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.

To evaluate the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex], where E is the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane, we can use cylindrical coordinates. In cylindrical coordinates, the equation of the paraboloid becomes:

[tex]z = 9 - (r^2)[/tex]

The limits of integration are:

0 ≤ r ≤ 3 (since the paraboloid intersects the xy-plane at z = 0 when r = 3)

0 ≤ θ ≤ 2π

0 ≤ z ≤ 9 - (r^2)

The triple integral becomes:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r√(r^2) dz dθ dr[/tex]

Simplifying, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π ∫0^(9-r^2) r^2 dz dθ dr[/tex]

Evaluating the innermost integral, we get:

∫[tex]0^(9-r^2) r^2 dz = (9-r^2)r^2[/tex]

Substituting this back into the triple integral, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 ∫0^2π (9-r^2)r^2 dθ dr[/tex]

Evaluating the remaining integrals, we get:

∫∫∫[tex]E √(x^2 + y^2) dV = ∫0^3 (9r^2 - r^4) dθ[/tex]

= 2π [243/5]

= 486π/5

Therefore, the value of the triple integral ∫∫∫[tex]E \sqrt{(x^2 + y^2)} dV[/tex] dV over the solid bounded by the circular paraboloid [tex]z = 9 - (x^2 + y^2)[/tex] and the xy-plane is 486π/5.

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Tom Jones, a mechanic at Golden Muffler Shop, is able to install new mufflers at an average rate of 3 per hour (exponential distribution). Customers seeking this service, arrive at the rate of 2 per hour (Poisson distribution). They are served first-in, first-out basis and come from a large (infinite population). Tom only has one service bay.



a. Find the probability that there are no cars in the system.


b. Find the average number of cars in the system.


c. Find the average time spent in the system.


d. Find the probability that there are exactly two cars in the system

Answers

a. To find the probability that there are no cars in the system, we need to use the formula for the steady-state probability distribution of the M/M/1 queue:
P(0) = (1 - λ/μ)
where λ is the arrival rate (2 per hour) and μ is the service rate (3 per hour).
P(0) = (1 - 2/3) = 1/3 or 0.3333
Therefore, the probability that there are no cars in the system is 0.3333.

b. To find the average number of cars in the system, we can use Little's Law:
L = λW
where L is the average number of cars in the system, λ is the arrival rate (2 per hour), and W is the average time spent in the system.
We can solve for W by using the formula:
W = 1/(μ - λ)
W = 1/(3 - 2) = 1 hour
Therefore, the average number of cars in the system is:
L = λW = 2 x 1 = 2 cars

c. To find the average time spent in the system, we already calculated W in part b:
W = 1 hour

d. To find the probability that there are exactly two cars in the system, we need to use the formula for the steady-state probability distribution:
P(n) = P(0) * (λ/μ)^n / n!
where n is the number of cars in the system.
P(2) = P(0) * (λ/μ)^2 / 2!
P(2) = 0.3333 * (2/3)^2 / 2
P(2) = 0.1111 or 11.11%
Therefore, the probability that there are exactly two cars in the system is 11.11%.

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Hudson is designing a new board game, and is trying to figure out all the possible


outcomes. How many different possible outcomes are there if he spins a spinner with


three equal-sized sections labeled Walk, Run, Stop and spins a spinner with 5 equal-


sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday?

Answers

There are 15 different possible outcomes when Hudson spins both spinners in his board game.

To determine the total number of possible outcomes when Hudson spins both spinners, you need to multiply the number of outcomes on the first spinner (Walk, Run, Stop) by the number of outcomes on the second spinner (Monday, Tuesday, Wednesday, Thursday, Friday).

Step 1: Determine the number of outcomes on the first spinner. There are 3 outcomes: Walk, Run, and Stop.

Step 2: Determine the number of outcomes on the second spinner. There are 5 outcomes: Monday, Tuesday, Wednesday, Thursday, and Friday.

Step 3: Multiply the number of outcomes from both spinners. 3 outcomes on the first spinner multiplied by 5 outcomes on the second spinner equals 15 total possible outcomes.

So, there are 15 different possible outcomes when Hudson spins both spinners in his board game.

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Help Asap due Tomorrow in morning. Thanks if you help!

Answers

Answer: C. 54cm^2

Step-by-step explanation:

Break the shape into 2 pieces and multiply the sides. ex. 12 by 2 and 8 by 5 and then add the 2 answers to get 54cm

Help there is a picture of it

Answers

Answer:

5 19/20 miles

"Consider the following function: f(x,y)=y^5 ln(−2x^4+3y^5) find fx and fy"

Answers

From the function f(x,y)=y⁵ ln(−2x⁴+3y⁵).  The value of  fx = -10x³y⁵ / (-2x⁴ + 3y⁵) and

fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]

To find fx, we differentiate f(x,y) with respect to x, treating y as a constant:

fx = d/dx [y⁵ ln(-2x⁴ + 3y⁵)]

Using the chain rule and the derivative of ln u = 1/u, we have:

fx = y⁵ * 1/(-2x⁴ + 3y⁵) * d/dx [-2x⁴ + 3y⁵]

Simplifying and applying the power rule of differentiation, we get:

fx = -10x³y⁵ / (-2x⁴ + 3y⁵)

Similarly, to find fy, we differentiate f(x,y) with respect to y, treating x as a constant:

fy = d/dy [y⁵ ln(-2x⁴ + 3y⁵)]

Using the chain rule and the derivative of ln u = 1/u, we have:

fy = y⁴ * ln(-2x⁴ + 3y⁵) * d/dy [(-2x⁴ + 3y⁵)]

Applying the power rule of differentiation and simplifying, we get:

fy = 15y⁴ ln(-2x⁴ + 3y⁵)

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Solve the optimization problem. Maximize P= xy with x + 2y = 26.
P=

Answers

The optimization problem has a maximum value of P when x = 13 and y = 6.5. The maximum value of P = 13 * 6.5 = 84.5.

To solve the optimization problem and maximize P = xy with the constraint x + 2y = 26, follow these steps:

1. Express one variable in terms of the other using the constraint: x = 26 - 2y

2. Substitute the expression for x into the objective function P: P = (26 - 2y)y

3. Differentiate P with respect to y to find the critical points: dP/dy = 26 - 4y

4. Set the derivative equal to zero and solve for y: 26 - 4y = 0 => y = 6.5

5. Plug the value of y back into the expression for x: x = 26 - 2(6.5) => x = 13

6. Check the second derivative to confirm it's a maximum: d²P/dy² = -4 (since it's a constant negative, this confirms it's a maximum)

Thus, the optimization problem has a maximum value of P when x = 13 and y = 6.5. The maximum value of P = 13 * 6.5 = 84.5.

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In 1990, Jane became a real estate agent. Eight years later, she sold a house for $144,000. Eleven years later, she sold the same house for $245,000. Write an equation that represents the value of the house (V) related to the number of years (t) since Jane became a real estate agent. (Hint: Be careful! The second sale of the house was 11 years after the first sale which was 8 years after she became a real estate agent! That means the second sale took place 19 years after she became an agent!)

Answers

Let's break down the information given in the problem:

- Jane became a real estate agent in 1990.

- She sold a house 8 years later (in 1998) for $144,000.

- She sold the same house 11 years after that sale (in 2009), which is 19 years after she became an agent, for $245,000.

To write an equation that represents the value of the house (V) related to the number of years (t) since Jane became a real estate agent, we can use the information from the two sales to find the rate of change in the value of the house over time. We can use this rate of change to write an equation in point-slope form:

V - V1 = m(t - t1)

where V1 is the value of the house at time t1, m is the rate of change in the value of the house, and t is the time since Jane became a real estate agent.

Using the two sales, we can find the rate of change in the value of the house as follows:

m = (V2 - V1) / (t2 - t1)

where V2 is the value of the house at the second sale, t2 is the time of the second sale (19 years after Jane became an agent), V1 is the value of the house at the first sale, and t1 is the time of the first sale (8 years after Jane became an agent).

Substituting the given values, we get:

m = ($245,000 - $144,000) / (19 - 8) = $10,100 per year

Now we can use the point-slope form equation to find the value of the house at any time t since Jane became a real estate agent. Let's choose 1990 as our initial time (t1), so V1 = $0:

V - 0 = $10,100 (t - 0)

Simplifying, we get:

V = $10,100t

Therefore, the equation that represents the value of the house (V) related to the number of years (t) since Jane became a real estate agent is V = $10,100t. Note that this equation assumes a constant rate of change in the value of the house over time, which may not be accurate in real life.

When angela and walker first started working for the​ supermarket, their weekly salaries totaled ​$550. now during the last 25 years walker has seen his weekly salary triple angela has seen her weekly salary become four times larger. together their weekly salaries now total ​$2000. write an algebraic equation for the problem. how much did they each make 25 years​ ago?

Answers

Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

Let's assign variables to represent Angela and Walker's salaries 25 years ago. Let A be Angela's salary 25 years ago and W be Walker's salary 25 years ago.

Using the information given in the problem, we can set up two equations:

A + W = 550 (their total salary 25 years ago)
4A + 3W = 2000 (their total current salary)

To solve for A and W, we can use substitution or elimination. Let's use substitution.

From the first equation, we can rearrange to solve for A:

A = 550 - W

Substitute this into the second equation:

4(550 - W) + 3W = 2000

Distribute the 4:

2200 - 4W + 3W = 2000

Simplify:

W = 800

Now that we know Walker's salary 25 years ago was $800, we can plug that into the first equation to solve for Angela's salary:

A + 800 = 550

A = -250

Uh oh, a negative salary doesn't make sense in this context. We made a mistake somewhere.

Let's go back to our original equations and try elimination instead:

A + W = 550
4A + 3W = 2000

Multiplying the first equation by 4, we get:

4A + 4W = 2200

Subtracting the second equation from this, we get:

W = 200

Now we can plug this into either equation to solve for A:

A + 200 = 550

A = 350

So Angela made $350 per week 25 years ago and Walker made $200 per week 25 years ago.

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You get a job as a nurse. Your salary for the first year is $74,000. You will
receive a 1.2% increase every year. If you could save your entire salary, how
much money would you have in 5 years? Round to the nearest cent (2 decimal
places). Hint: What is a₁? What is r? Then use the formula for a finite
geometric series.

Answers

Answer: The amount of money you would have in 5 years if you could save your entire salary with a 1.2% increase every year would be $87,357.41.

Explanation:

The initial term, a₁, is $74,000, and the common ratio, r, is 1 + 1.2% = 1.012. To find the sum of the first 5 terms, we use the formula for a finite geometric series:

S₅ = a₁(1 - r⁶)/(1 - r)

Plugging in the values, we get:

S₅ = $74,000(1 - 1.012⁵)/(1 - 1.012) = $87,357.41 (rounded to the nearest cent)

Therefore, if you save your entire salary, you would have approximately $87,357.41 in 5 years with a 1.2% increase every year.

What do you think causes the percent of filers to jump so dramatically between the under-18 group and the 18-26 group?

Answers

The significant increase in the percent of filers between the under-18 group and the 18-26 group can be attributed to various factors, including age, income, and financial independence.



Firstly, individuals under the age of 18 are typically considered minors and are often dependent on their parents or guardians for financial support. As a result, they may not have any significant income that requires them to file taxes, and their income might be included in their parent's or guardian's tax return. This leads to a lower percentage of filers in the under-18 group.


On the other hand, the 18-26 age group marks the transition into adulthood, where individuals begin to gain financial independence. Many start working full-time jobs or attend college, where they may earn income through part-time jobs or internships. This increased income leads to a higher percentage of filers in the 18-26 group, as they are now responsible for filing their own tax returns.


Furthermore, the age range of 18-26 also coincides with the period where individuals are more likely to have various income sources. This includes scholarships, grants, and student loans for those attending college. These additional income sources may also contribute to the increased percentage of filers in this age group.


Lastly, as individuals become more financially independent, they may become more aware of tax benefits and deductions available to them, such as educational credits or deductions for student loan interest. This newfound awareness could encourage more people within the 18-26 age group to file taxes, leading to a higher percentage of filers.


In conclusion, the dramatic jump in the percent of filers between the under-18 group and the 18-26 group can be attributed to factors such as increased financial independence, diverse income sources, and greater awareness of tax benefits and deductions.

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The unit cube is divided into identical rectangular prisms. What is the volume of one of the identical prisms?

Answers

Note that the Volume of one prism = (1/16) unit³

How did we reach the above conclusion?

The given volume of the cube, v₁ = 1 unit cube

The height of the unit cube, h₁ = 1 unit

The length of the unit cube, w₁ = 1 unit

The height of the unit cube, l₁ = 1 unit

The number of identical prism located along the height = 2 identical prism

The number of identical prism located along the width = 2 identical prism

The number of identical prisms located along the length = 4 identical prism

Therefore;

The height of each identical rectangular prism that make up the unit cube, h₂ = h₁/2 = 1/2 unit

Similarly, for each identical rectangular prism, we have;

The width, w₂ = w₁/2 = 1/2 unit

The length, l₂ = l₁/4 = 1/4 unit

The volume of each one of the identical rectangular prism, v₂ = h₂ × w₂ × l₂



⇒  v₂ = 1/2 unit × 1/2 unit × 1/4 unit = 1/16 unit³

So it is correct to state that the volume of one of the identical rectangular prisms = (1/16) unit³.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

See attached image.

Find the inverse for each relation: 4 points each


1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)}


2. {(4,2),(5,1),(6,0),(7,‐1)}


Find an equation for the inverse for each of the following relations.


3. Y=-8x+3


4. Y=2/3x-5


5. Y=1/2x+10


6. Y=(x-3)^2


Verify that f and g are inverse functions.


7. F(x)=5x+2;g(x)=(x-2)/5


8. F(x)=1/2x-7;g(x)=2x+14

Answers

The inverse for each relation:

1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)} - {(-2, 1), (3, 2), (-3, 3), (2, 4)}

2. {(4,2),(5,1),(6,0),(7,‐1)} - {(2, 4), (1, 5), (0, 6), (-1, 7)}

3. Inverse equation: y=(-1/8)x+3/8

4. Inverse equation: y=3/2x+15/2

5. Inverse equation: y=2x-20

6. Inverse equation: y=[tex]x^{(1/2)}+3[/tex]

7. Since fog(x) = gof(x) = x, f and g are inverse functions.

8. Since fog(x) = gof(x) = x, f and g are inverse functions.

1. To find the inverse of the relation, we need to swap the positions of x and y for each point and then solve for y.

{(1, -2), (2, 3), (3, -3), (4, 2)}

Inverse: {(-2, 1), (3, 2), (-3, 3), (2, 4)}

2. Again, we swap x and y and solve for y.

{(4, 2), (5, 1), (6, 0), (7, -1)}

Inverse: {(2, 4), (1, 5), (0, 6), (-1, 7)}

3. To find the inverse equation for y=-8x+3, we swap x and y and solve for y.

x=-8y+3

x-3=-8y

y=(x-3)/-8

Inverse equation: y=(-1/8)x+3/8

4. To find the inverse equation for y=2/3x-5, we swap x and y and solve for y.

x=2/3y-5

x+5=2/3y

y=3/2(x+5)

Inverse equation: y=3/2x+15/2

5. To find the inverse equation for y=1/2x+10, we swap x and y and solve for y.

x=1/2y+10

x-10=1/2y

y=2(x-10)

Inverse equation: y=2x-20

6. To find the inverse equation for y=(x-3)², we swap x and y and solve for y.

x=(y-3)²

[tex]x^{(1/2)}=y-3[/tex]

[tex]y=x^{(1/2)}+3[/tex]

Inverse equation: [tex]y=x^{(1/2)}+3[/tex]

7. To verify that f(x)=5x+2 and g(x)=(x-2)/5 are inverse functions, we need to show that fog(x)=gof(x)=x for all x in the domain of f and g.

fog(x) = f(g(x)) = f((x-2)/5) = 5((x-2)/5) + 2 = x

gof(x) = g(f(x)) = g(5x+2) = ((5x+2)-2)/5 = x/5

Since fog(x) = gof(x) = x, f and g are inverse functions.

8. To verify that f(x)=1/2x-7 and g(x)=2x+14 are inverse functions, we need to show that fog(x)=gof(x)=x for all x in the domain of f and g.

fog(x) = f(g(x)) = f(2x+14) = 1/2(2x+14) - 7 = x

gof(x) = g(f(x)) = g(1/2x-7) = 2(1/2x-7) + 14 = x

Since fog(x) = gof(x) = x, f and g are inverse functions.

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To celebrate halloween, lacey's class is making candy necklaces. lacey is helping pass out string from a 50-yard-spool. she gives 30 inches of string to each student. if there are 24 students in her class, how many yards of string will be leftover?

Answers

The class will use 20 yards of the 50-yard spool, leaving 30 yards of string leftover.

This leftover string could be used for future projects or saved for another occasion.

Lacey's class will use a total of 720 inches (30 inches per student x 24 students) of string for the candy necklaces.

To convert this to yards, we divide by 36 (since there are 36 inches in a yard). 720 inches ÷ 36 = 20 yards

It's important to note that when working with different units of measurement, it's necessary to convert them to the same unit before performing calculations.

In this case, we converted inches to yards in order to determine the amount of string used by the class. By doing so, we were able to determine how much string was leftover in yards, which is a more appropriate unit of measurement for a spool of string.

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The value of y varies directly with x. which function represents the relationship between x and y if y = 18/5 when x = 24

Answers

The function that represents the relationship between x and y is y = 3/20 x

Since y varies directly with x, we can write the relationship between x and y as

y = kx

where k is the constant of proportionality.

y = 18/5 when x = 24

Substituting these values into the equation, we get:

18/5 = k(24)

Simplifying this equation, we get:

k = (18/5) / 24

k = (18/5 × 24)

k = 18/120

We can simplify this expression to:

k = 3/20

Therefore, the function that represents the relationship between x and y is y = 3/20 x

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I need someone to do this for me rq

Answers

Answer:

Step-by-step explanation:

The triangle area= 1/2 * the perpendicular height * breath

                           = 1/2*2*(3/4)

                          =0.75

A ball is dropped from a window at a height of 36 feet. the function h(x) = -16x2 + 36 represents the height (in feet) of the ball after x seconds. round
to the nearest tenth.
how long does it take for the ball to hit the ground?

Answers

It takes about 1.5 seconds for the ball to hit the ground.

How to calculate the time for ball to hit the ground?

To find how long it takes for the ball to hit the ground, we need to find the value of x when h(x) = 0, since the height of the ball is 0 when it hits the ground. We can set -16x²+36 = 0 and solve for x:

-16x²+ 36 = 0

Dividing both sides by -16:

x² - 2.25 = 0

Adding 2.25 to both sides:

x²= 2.25

Taking the square root of both sides (we can ignore the negative root since time cannot be negative):

x = √(2.25) ≈ 1.5

Therefore, it takes about 1.5 seconds for the ball to hit the ground.

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can someone did this step by step correctly and not give the wrong answer
A cylinder has the net shown.

net of a cylinder with diameter of each circle labeled 3.8 inches and a rectangle with a height labeled 3 inches

What is the surface area of the cylinder in terms of π?

40.28π in2

22.80π in2

18.62π in2

15.01π in2

Answers

40.28 in2 hope it helps

A right triangle is shown. The length of the hypotenuse is 4 centimeters and the lengths of the other 2 sides are congruent.
The hypotenuse of a 45°-45°-90° triangle measures 4 cm. What is the length of one leg of the triangle?

2 cm
2 StartRoot 2 EndRoot cm
4 cm
4 StartRoot 2 EndRoot cm

Answers

Answer:

The length of one leg of this right triangle is 4/√2 = 2√2 cm.

In the shown figure, DE←→
is parallel to side BC¯¯¯¯¯¯¯¯
in triangle ABC
. If m∠B=52
°, what is m∠DAB
?


m∠DAB
=
°

Answers

Answer:

In triangle ABC, m∠BAC = 50°. If m∠ACB = 30°, then the triangle is triangle. If m∠ABC = 40°, then the triangle is triangle. If triangle ABC is isosceles, and AB = 6 and BC = 4, then AC =

Answer:

52 degrees

Step-by-step explanation: because i looked and they looked the same so i put 52 and it was right

A large apartment complex has 1,500 units, which are filling up at a rate of 10% per month. If the


apartment complex starts with 15 occupied units, how many months will pass before the complex


has 800 occupied units? (Assume logistic growth). Round to the nearest tenth.


0. 58 months


15. 7 months


1. 3 months


47. 3 months

Answers

After about 15.7 months, the apartment complex will have 800 occupied units.

Logistic growth is a type of growth in which the growth rate of a population decreases as the population size approaches its maximum value. In this case, the apartment complex has a maximum capacity of 1500 units.

Starting with 15 occupied units and growing at a rate of 10% per month, the number of occupied units can be modeled by a logistic function.

To find the number of months it takes to reach 800 occupied units, we need to solve for the time when the logistic function equals 800.

Let P(t) be the number of occupied units at time t (in months), then we have:

P(t) = 1500 / (1 + 1485[tex]e^{(-0.1t)}[/tex])

We want to find t such that P(t) = 800. Solving for t, we get:

t = -10 ln(1 - 4/37) ≈ 15.7 months

This means that after about 15.7 months, the apartment complex will have 800 occupied units.

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PLEASE HELP!!!!!!! Two lines, E and F, are represented by the equations given below. Line E: 5x + 5y = 40 Line F: x + y = 8 Which statement is true about the solution to the set of equations? (4 points) Question 2 options: 1) It is (40, 8). 2) It is (8, 40). 3) There is no solution. 4) There are infinitely many solutions.

Answers

Answer: (4)

Step-by-step explanation:

Two lines E and F are same.

5x + 5y = 40

x + y = 8

Deviding both hands of E by 5,

we get F's equation.

So every single point on the line x+y=8

represents the solution of the given system.

Use the normal approximation to find the indicated probability. the sample size is n, the population proportion of successes is p, and x is the number of successes in the sample.
n = 81, p = 0.5: p(x ≥ 46)
group of answer choices

0.1210

0.1335

0.8790

0.1446

Answers

We know that the indicated probability is approximately 0.1210.

To use the normal approximation, we need to check if the conditions for a normal approximation are met. In this case, we have:

np = 81 * 0.5 = 40.5 ≥ 10
n(1-p) = 81 * 0.5 = 40.5 ≥ 10

Since both conditions are met, we can use the normal approximation to find the probability.

First, we need to find the mean and standard deviation of the sampling distribution of sample proportions:

mean = np = 81 * 0.5 = 40.5
standard deviation = sqrt(np(1-p)) = sqrt(81 * 0.5 * 0.5) = 4.5

Next, we need to standardize the value of x:

z = (x - mean) / standard deviation
z = (46 - 40.5) / 4.5 = 1.22

Finally, we can use a standard normal table or calculator to find the probability:

P(z ≥ 1.22) = 0.1118

Therefore, the answer is approximately 0.1210.

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The diameter of a wheel is 3 feet witch of the following is closest to the area of the whee

Answers

The area of the wheel is approximately 7.07 square feet.

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius of the circle. In this case, the diameter of the wheel is given as 3 feet, so the radius is half of that, which is 1.5 feet.

Substituting the value of the radius into the formula, we get A = π(1.5)^2. Simplifying this expression gives us approximately 7.07 square feet. Therefore, the closest answer to the area of the wheel is 7.07 square feet.

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Make a table of values in a graph for fabian's income inexpenses the expenses e to make n cakes per month is given by the equation E = 825 + 3.25n the income I for selling n Cakes given by the equation I equals 8.20 n also graphic and make a table

Answers

The table of values in a graph for fabian's income in expenses is

n            E(n)

0           825

1            828.25

2           831.5

4          838

Making a table of values in a graph for fabian's income inexpenses

From the question, we have the following parameters that can be used in our computation:

The expenses E to make n cakes per month is given by the equation

E = 825 + 3.25n

Next, we assume values for n and calculate E

Using the above as a guide, we have the following:

E = 825 + 3.25(0) = 825

E = 825 + 3.25(1) = 828.25

E = 825 + 3.25(2) = 831.5

E = 825 + 3.25(4) = 838

So, we have

n            E(n)

0           825

1            828.25

2           831.5

4          838

This represents the table of values

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Circle A is located at (6, 5) and has a radius of 4 units. What is the equation of a line that is tangent to circle A from point C (2, 8)? x = 2 y = −0. 75x + 9. 5 y = 1. 33x + 1. 66 x = 8

Answers

We can use the point-slope form of the equation of a line to find the equation of the tangent line.

How to find the equation of the line that is tangent to circle A from point C (2, 8)?

To find the equation of the line that is tangent to circle A from point C (2, 8), we need to first find the point of tangency, which is the point where the line intersects the circle.

Point C (2, 8) is outside the circle, so the tangent line will be perpendicular to the line connecting the center of the circle to point C and will pass through point C.

Step 1: Find the center of the circle

The center of the circle A is at (6, 5).

Step 2: Find the slope of the line connecting the center of the circle to point C

The slope of the line connecting the center of the circle (6, 5) and point C (2, 8) is:

m = (8 - 5) / (2 - 6) = -3/4

Step 3: Find the equation of the line perpendicular to the line from Step 2 passing through point C

The slope of the line perpendicular to the line from step 2 is the negative reciprocal of the slope:

m_perp = -1 / (-3/4) = 4/3

Now we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y - 8 = (4/3)(x - 2)

Simplifying, we get:

y = (4/3)x + 4.67

So the equation of the line that is tangent to circle A from point C (2, 8) is y = (4/3)x + 4.67.

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The number of views on a viral video can be modeled by the function
G(t) = 15(4)+3. Write an equivalent function of the form G'(t) = abt.

Answers

An equivalent function of the form G'(t) = abt for the given function G(t) = 15(4)+3 is: G'(t) = 63 * 1.

What is an equivalent function?

An equivalent function refers to a mathematical function that has the same output values or behavior as another function but may have a different mathematical expression or representation. In other words, two functions are considered equivalent if they produce the same results for the same inputs, even though they may be expressed differently in terms of mathematical notation, variables, or parameters.

According to the given information:

To write an equivalent function of the form G'(t) = abt, we need to rearrange the given function G(t) = 15(4)+3 into a format that matches the form G'(t) = abt.

The given function G(t) = 15(4)+3 can be simplified as follows:

G(t) = 60 + 3

G(t) = 63

Now, we can see that G(t) is a constant function with a constant value of 63. To express it in the form G'(t) = abt, we can rewrite it as:

G'(t) = 63 * 1

So, an equivalent function of the form G'(t) = abt for the given function G(t) = 15(4)+3 is:

G'(t) = 63 * 1

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