A square with side length
�
cc has an area of
81
8181 square centimeters. The following equation shows the area of the square.
�
2
=
81
c
2
=81

Answer:

$41,320

Step-by-step explanation:

We can use algebra to solve for the annual pay of the fourth worker. Let x be the annual pay of the fourth worker. Then we can set up an equation based on the given information:

(42,998 + 49,972 + 50,510 + x) / 4 = 46,200

We can simplify and solve for x by multiplying both sides by 4:

42,998 + 49,972 + 50,510 + x = 184,800

Subtracting the sum of the other three workers' pay from both sides:

x = 184,800 - 42,998 - 49,972 - 50,510

Simplifying and solving:

x = 41,320

Therefore, the annual pay of the fourth worker was $41,320.

The correct answer is : Part A: The angle of elevation from the top of the shadow to the top of the lamppost is 0 degrees.

Part B: The length from the top of the lamppost to the top of its shadow cannot be determined without knowing the value of [tex]\frac{\theta}{2}[/tex], the current angle of elevation.

Part A: To determine the angle of elevation from the top of the shadow to the top of the lamppost, we can use trigonometry. Let's denote the angle of elevation as θ.

In a right triangle, the tangent of an angle is equal to the ratio of the length of the opposite side to the length of the adjacent side. In this case, the opposite side is the height of the lamppost (5 feet), and the adjacent side is the length of the shadow (8 feet).

Using the tangent function:

[tex]\(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{8}\)[/tex]

To find θ, we can take the inverse tangent (arctan) of both sides:

[tex]\(\theta = \arctan\left(\frac{5}{8}\right)\)[/tex]

The value of θ can be calculated using a scientific calculator or by referencing trigonometric tables.

          |

          |\

          | \

          |  \

          |   \

          |    \

          |     \

-----------+------\

      Lamp Post    \

          |         \

          | Shadow    \

          |____________\

Part B: To find the length from the top of the lamppost to the top of its shadow when the angle of elevation is half of the current angle (θ/2), we can use trigonometry again.

Let's denote the new length of the shadow as x. We want to find x when the angle of elevation is θ/2.

Using the tangent function again:

[tex]\(\tan\left(\frac{\theta}{2}\right) = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{x}\)[/tex]

Rearranging the equation to solve for x:

[tex]\(x = \frac{5}{\tan\left(\frac{\theta}{2}\right)}\)[/tex]

Substituting the value of θ from Part A:

[tex]\(x = \frac{5}{\tan\left(\frac{\arctan\left(\frac{5}{8}\right)}{2}\right)}\)[/tex]

Evaluating the expression on the right-hand side will give us the approximate length from the top of the lamppost to the top of its shadow at half the angle of elevation.

      Lamp Post

          |

          |\

          | \

          |  \

          |   \

          |    \

          |     \

          |______\

          |  x   \

          |________\

          | Shadow

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The measure of the unknown angle or arc are 142 degrees, 65 degrees and 36 degrees

Figure 1

The measure of the angle is calculated as

Angle 1 = 1/2 * 284 degrees

Evaluate the expression

Angle 1 = 142 degrees

Figure 2

The measure of the angle is calculated as

Angle 1 = 1/2 *(72 + 58) degrees

Evaluate the expression

Angle 1 =  65 degrees

Figure 3

The measure of the angle is calculated as

Angle 1 = 1/2 *(138 - 66) degrees

Evaluate the expression

Angle 1 = 36 degrees

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The corrected function that represent the height of the plant is h(s) = 0.004s + 37.

Using the provided growth rate, the plant's height, h, can be described as a function of the number of hours of sunshine, s:

h(s) = 0.004s + 37

This function indicates that the plant's height increases by 0.004 millimeters every hour of sunlight, starting at a height of 37 cm.

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Answer:

5024 flowers spaced every three inches are needed to surround the circular garden with a 200 ft radius.

Step-by-step explanation:
The formula for the circumference (C) of a circle is:

C = 2 * π * r

Given a radius of 200 ft

C = 2 * 3.14 * 200

C = 6.28 * 200

C = 1256 ft

with each flower spaced every 3 inches apart. Convert the spacing to feet (1 ft = 12 inches)

Divide the circumference by the spacing between the flowers:

Number of flowers = C / spacing

Number of flowers = 1256 / (1/4)

Number of flowers = 1256 * 4

Number of flowers = 5024

Part A: The equation that can be used to determine the dimensions, in meters, of the field is 5500 = 2x² + 10x

Part B: width is 50 meters.

The formula for calculating the area of a rectangle is expressed with the equation;

A = lw

Such that the variables are expressed as;

We then have that;

l = 2x + 10

Substitute the values

5500 = (2x + 10)(x)

expand the bracket

5500 = 2x² + 10x

2x² + 10x - 5500

x² + 5x - 2750

x² + 55x - 50x - 2750

x(x + 55) - 50(x + 55)

x = 50 meters

Length = 2(50) + 10

Length = 100 + 10 = 110 meters

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The demand will drop by 741 T-shirts per dollar increase in price.

We will use derivative of p formula with respect to q to find how fast the demand will drop [tex]dp/dq = -50/\sqrt{q^3}[/tex]

At the initial price of $10, the corresponding demand is:

p = 5 + 100/√q = 10

Solving for q, we get:

q = 10000/9

Now, we will find rate of change of demand as the price increases by differentiating the demand formula with respect to p:

[tex]\frac{dq}{dp} = -1/\frac{dp}{dq}[/tex]

At p = 10, we have:

dq/dp = -1/(-50/√(10000/9)^3)

dq/dp = -1/(-0.00135)

dq/dp = 740.740740741

dq/dp = 741.

Full question:

Demand for your tie-dyed T-shirts is given by the formula p = 5+ 100/ √ q  where p is the price in dollars you can charge to sell q T-shirts per month. If you currently sell T-shirts for $10 each and you raise price by $1 each month, how fast will the demand drop?

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Answer:

256r^6/t^9

Step-by-step explanation:

start by dividing or simplifying the numbers on the fraction.

4096/16 = 256

Now you multiply the powers on top with the power outside the parenthesis. So (r^-2t^3)^-3

so you now have r^6 t^-9

your equation looks like 256 r^6 t^-9/r^0

But you can't have negative numbers for your powers so we are going to add/subtract with the bottom of the fraction. There are no t's to add/subtract so the t's move to the bottom and become positive. the r has a 0 power so it goes away.

Your equation is now. 256r^6/t^9

Hope that made sense. Good luck!

Answer:

Choice B

Step-by-step explanation:

Peter had no money left to give to his children and each child received $0.

Let's start by finding the amount of money Peter had initially:

Initial money = Money is given to wife + Money spent on TV + Remaining money

Initial money = $1400 + $400 + Remaining money

Initial money = $1800 + Remaining money

Next, we need to find the amount of money Peter had left after giving $1400 to his wife and spending $400 on a TV set:

Remaining money = Initial money - Money is given to wife - Money spent on TV

Remaining money = ($1800 + Remaining money) - $1400 - $400

Remaining money = $1800 + Remaining money - $1800

Remaining money = $0

This means that Peter spent all his money on his wife and the TV set, so he had no money left to give to his children.

Therefore, each child received $0.

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Answer:

A. 10x + y - 2 Ans

B. Solution

(3x + 4) + (y - 5) + ( 7x - 1) =0

grouping

(3x + 7x) + (y) + (4 - 5 - 1) =0

10x + y -2 =0

therefore

perimeter is 10x + y - 2

Nate is a supply-sider economist. As such, Nate predicts that the deregulation of industries would result in increased economic growth, efficiency, and productivity.

Supply-side economics is an economic theory that focuses on policies aimed at stimulating economic growth and productivity by focusing on the supply side of the economy.

It emphasizes the importance of factors such as tax cuts, deregulation, and incentives for businesses and individuals to promote investment, production, and innovation.

Supply-side economists believe that by reducing barriers and costs for businesses, such as lowering taxes and reducing regulations, there will be increased incentives for economic activity, leading to higher output, job creation, and overall economic prosperity.

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The length of side AD is,

⇒ AD = 16

We have to given that;

The given figure is a right triangular prism.

In the prism:

• DF = 22 in.

• EG = 11 in.

• Volume of the prism = 1936 cubic in.

Since, Volume of right triangular prism is,

V = 1/2 (bh) x L

Substitute all the values we get;

V = 1/2 (22 × 11) × AD

1936 = 121 × AD

AD = 16

Thus, The length of side AD is, 16

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Plot twist:

The answer is actually is 16

Step-by-step explanation:

15/10 = 1.5)       24/1.5 = 16

The answer is 16

If leg a is the missing side, then transform the equation to the form where a is on one side and take a square root: a = √(c² - b²)

If leg b is unknown, then: b = √(c² - a²)

For hypotenuse c missing, the formula is: c = √(a² + b²)

The truth of the remaining statements, you would need to examine the proportions of seniors and freshmen who like UCLA, the overall proportion of the student body cheering for UCLA, and the number of seniors cheering for UCLA out of the total number of surveyed students.

To determine which statements are true, you need to refer to the data in the two-way table. The table should provide information on the number or proportion of students from each class (freshmen, sophomores, seniors) who will be cheering for each team (UCLA, USC). Based on this information, you can evaluate the statements.

For example, if the table shows that out of 100 freshmen surveyed, 59% will be cheering for UCLA, then the first statement would be true. Similarly, if the table shows that out of 100 sophomores surveyed, 79% will be cheering for USC, then the second statement would be true.

To determine the truth of the remaining statements, you would need to examine the proportions of seniors and freshmen who like UCLA, the overall proportion of the student body cheering for UCLA, and the number of seniors cheering for UCLA out of the total number of surveyed students.

Once you have the actual data from the two-way table, you can compare it to the statements and identify which ones are true.

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Answer:

The third one is rectangular pyramid.

Step-by-step explanation:

The third one is rectangular pyramid because it has a rectangle on the bottom.

In the short run, the firms in a competitive industry will earn positive profits because, the market price is higher than the minimum of the average cost curve. The Option A is correct

When the market price is between P4 and P6, firms in a competitive industry are able to earn positive profits in the short run because the price is above their average variable cost (AVC) but below their average total cost (ATC).

This means that firms are covering their variable costs and also making a contribution towards their fixed costs. As a result, they are earning positive profits. But, in the long run the firms will enter the industry and increase supply causing market price to decrease towards P4 where firms earn zero economic profits in the long run.

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Answer:

48

Step-by-step explanation:

When looking at this you know that all the angle are a full 360. Knowing this you see that both side are the same. So that means they both are 48.

Answer:

Step-by-step explanation:

f(x) = x^8 + 6x^7 + 7x^6
     = x^6 ( x^2 + 6x + 7)
     = x^6 (x =  [tex]\frac{-6 +- \sqrt{36 - 28} }{2}[/tex] )

     = x^6 (x =  -3 +- [tex]\sqrt{2}[/tex] )    =   0

     =  x = 0    or         x = -3 +- [tex]\sqrt{2}[/tex]

Answer:

(a) Average rate of change of volume during the 60 seconds it takes to empty: -9 m^3/s

(b) Volume of the balloon after 40 seconds: 270 m^3

(c) Instantaneous rate of change of volume at 40 seconds: -67.5 m^3/s

Step-by-step explanation:

(a) The average rate of change of volume during the 60 seconds it takes to empty can be calculated by finding the change in volume over the change in time:

Average rate of change = (V(60) - V(0)) / (60 - 0)

where V(60) is the volume of the balloon at 60 seconds and V(0) is the volume at 0 seconds. Substituting these values into the equation V(t) = 540(1 - t/60)^3, we get:

V(60) = 0

V(0) = 540

So, the average rate of change of volume is:

Average rate of change = (0 - 540) / (60 - 0) = -9 m^3/s

(b) The volume of the balloon after 40 seconds can be found by substituting t = 40 into the equation V(t) = 540(1 - t/60)^3:

V(40) = 540(1 - 40/60)^3 = 270 m^3

Therefore, the volume of the balloon after 40 seconds is 270 m^3.

(c) The instantaneous rate of change of volume at 40 seconds can be found by taking the derivative of the volume function with respect to time:

dV/dt = -540(3/60)(1 - t/60)^2

Substituting t = 40 into this equation, we get:

dV/dt | t=40 = -540(3/60)(1 - 40/60)^2 = -67.5 m^3/s

Therefore, the instantaneous rate of change of volume at 40 seconds is -67.5 m^3/s.

Answer:the product of - 3/8 and - 4/12 is 0.125.

Natalie is 2 meters taller than the statue.

Calculating the distance in height between Natalie's head and the statue's peak is necessary.

According to the information provided, Natalie is located 8 meters from the statue, and Natalie's head is 10 meters from the top of the monument.

With the aid of the comparable triangles idea, we can establish the ratio shown below:

(height of statue) / (distance to statue) = (height difference) / (distance to Natalie's head)

Let's denote the height of the statue as "H" and the height difference as "D." The proportion can be written as:

H / 8 = D / 10

To find the height difference (D), we can rearrange the equation:

D = (H / 8) * 10

Given that the distance between the top of the statue and Natalie's head is 10 meters, we can substitute this value into the equation:

10 = (H / 8) * 10

Dividing both sides by 10:

1 = H / 8

Multiplying both sides by 8:

H = 8

Therefore, the height of the statue is 8 meters.

We deduct Natalie's height (10 meters) from the statue's (8 meters) height to find the height gap between the two:

Height difference = Statue's height - Natalie's height

= 8 - 10

= -2

The negative value indicates that Natalie's height is 2 meters taller than the statue.

Therefore, Natalie is 2 meters taller than the statue.

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Answer:

This equation is a perfect square binomial so you would just square root the front and then square root the back to get (9x+7)(9x-7)

Step-by-step explanation:

The front is 81x^2 and the back is 49 which are both perfect squares.

The given polynomial, 81x^2 - 49, is a difference of perfect squares. To factor it completely, we can use the formula a^2 - b^2 = (a + b)(a - b).

In this case, a^2 = 81x^2 and b^2 = 49. Taking the square root of both sides, we have a = 9x and b = 7.

Therefore, the value of a is 9x and the value of b is 7.

To factor the polynomial completely, we use the formula (a + b)(a - b). Substituting the values of a and b, we have:

(9x + 7)(9x - 7)

The product of the prime factors is (9x - 7)(9x + 7).

I hope this helps!

Answer:

To find the value of x, we need to add up all the sides of the shape and set them equal to the perimeter:

x + 9 + x + 2 + x + 6 + 2x - 4 = 94

Combining like terms, we get:

5x + 13 = 94

Subtracting 13 from both sides, we get:

5x = 81

Dividing both sides by 5, we get:

x = 16.2

Therefore, the value of x is 16.2 cm.

Step-by-step explanation:

Answer:

translation (5, 0)

Step-by-step explanation:

the blue has been translated 5 units to the right (x-axis). no change on y-axis. this translation is (5,0)

* 5 will be above the 0. hard to do with the formatting options on here

Using the graph the problem is soled as follows

a. The concentration of the drug in 8 hours is 24 mg/L

b. The concentration of the drug is increasing from 0 to 2 hours and the concentration of the drug is decreasing from 2 to 20 hours

c. The maximum concentration occurred in 2 hours and the maximum concentration at this time is 64 mg/L

d. The time required for the drug concentration to reduce to 16 mg/L is 8 hours.

at maximum it was at 2 hours while at 16 mg/L it was at 10 hours. by subtraction we have

10 - 2 = 8 hours

e. The graph will predict values close to zero but not equal to zero

f. The concentration of the drug is summarized as follows

The concentration rise to its peak which is 64 mg/L at 2 hours and after this time, the concentration is on a steady decline. at 20 hours it is at about 2 mg/L and continued decreasing

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