When you board a Ferris wheel your feet are 1 foot off the ground. At the highest point of the ride, your feet are 99 feet above the ground. It takes 30 seconds for the ride to complete one full revolution. Write a trigonometric equation for your height above the ground at t seconds after the ride starts.

Answer:3048.7804878

Step-by-step explanation:

I took the same test p.s. you may need to round.

The descriptions that can describe more than one triangle are

This is further explained below.

Generally, An angle is a figure produced in Euclidean geometry by two rays, which are referred to as the sides of the angle, and which have a common endpoint, which is referred to as the vertex of the angle. The plane that includes two rays will always contain the angles that are generated by the beams. Another way that angles are created is when two planes cross with one another. These particular angles are referred to as dihedral angles.

In conclusion, Measurements of 40 degrees, 60 degrees, and 80 degrees in relation to one another may define more than one triangle.

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We know that the candle will have 15 cubic inches of wax, this is the volume.

Now, if the candle's height is twice its diameter, then we express

Additionally, the volume of a cone is

Where pi=3.14. Also, we know that the radius is half the diameter, so we'll use the following expression

Replacing all, we have

The radius should be 1.5 inches long.

Then, we find the height

The height should be 6.1 inches long.

Answer: 4

Step-by-step explanation:

Use the triangle to the right to find the measure of the side the two triangles share. That side is 8.06 roughly and squared it’s 65. I used the 65 to solve for b in a^2 + b^2 = c^2

65 + b^2 = 81

b^2 = 16

b = 4

Answer:

I'm pretty sure it's opposite if I'm wrong just tell me

Opposite, because this would be the result of a reflection over the y-axis

Answer:

6miles

Step-by-step explanation:

They can go 6 miles because 26-2=24 24/6=4 4x6=24 so they can go 6 miles

Answer:

6 miles is the maximum amount they can afford

minus 2 from 26

2-26=24

then divide the total amount by 4

24/4= 6

Answer: 1 4/5 feet

Step-by-step explanation:

Length of the strip of yellow paper = 9 feet.

Number of streamers that were cut = 5

Length of each streamer will then be:

= Length of the strip of yellow paper = 9 feet / Number of streamers that were cut

= 9 feet / 5

= 1 4/5 feet

To find the limit as t approaches infinity for the given functions, we need to analyze the behavior of each term as t gets larger and larger. The limits for the given terms are -7, 7π/2, and 0, respectively.

For the first term, 7t^2 / (7-t^2), we can see that as t increases, the denominator (7-t^2) will dominate the expression, causing the fraction to approach 0. Therefore, the limit of this term as t approaches infinity is 0.

For the second term, 7tan^-1(t), we can use the fact that the inverse tangent function approaches pi/2 as its input approaches infinity. Therefore, the limit of this term as t approaches infinity is 7(pi/2) = 7(1.57) ≈ 10.99.

For the third term, (7-e^-2t) / t, we can see that the denominator will dominate as t approaches infinity, causing the fraction to approach 0. Therefore, the limit of this term as t approaches infinity is 0.

To find the limit of the entire expression, we simply add up the limits of each term. Therefore, the limit as t approaches infinity for the given function is approximately 10.99.

To find the limit as t approaches infinity for the given terms, we'll consider each term separately:

1. lim(t→∞) 7t^2 / (7 - t^2)
As t approaches infinity, both the numerator and the denominator grow infinitely large. To analyze this, we can divide both the numerator and the denominator by t^2:
lim(t→∞) (7t^2/t^2) / (7/t^2 - 1)
This simplifies to lim(t→∞) 7 / (-1) = -7.

2. lim(t→∞) 7tan^(-1)(t)
As t approaches infinity, tan^(-1)(t) approaches π/2 (or 90 degrees). Thus, the limit is 7 * π/2.

3. lim(t→∞) (7 - e^(-2t))/t
We can apply L'Hopital's Rule to this term, as it is of the form 0/∞ or ∞/∞. Differentiating the numerator and the denominator, we get:
lim(t→∞) (0 - (-2)e^(-2t))/(1)
As t approaches infinity, e^(-2t) approaches 0, and the limit becomes 0.

So, the limits for the given terms are -7, 7π/2, and 0, respectively.

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The estimated amount of carbon-14 when t = 1,000 years is approximately 34.196 grams.

The decay of carbon-14 follows an exponential decay model, which can be expressed as:

A(t) = A₀ * \(e^(-kt)\)

Where:

- A(t) is the amount of carbon-14 at time t

- A₀ is the initial amount of carbon-14

- k is the decay constant

The half-life of carbon-14 is given as 5715 years. The decay constant (k) can be calculated using the formula:

k = ln(2) / half-life

k = ln(2) / 5715

Now we can rewrite the equation as:

A(t) = A₀ * \(e^(-(ln(2) / 5715) * t)\)

We are given that 10,000 years after t₀, the amount of carbon-14 is 3 grams. So we can substitute t = 10,000 and A(t) = 3 into the equation:

3 = A₀ *\(e^(-(ln(2) / 5715) * 10,000)\)

To find the initial amount A₀, we rearrange the equation:

A₀ = 3 /\(e^(-(ln(2) / 5715) * 10,000)\)

Now we can estimate the amount of carbon-14 when t = 1,000:

A(1,000) =\(A₀ * e^(-(ln(2) / 5715) * 1,000)\)

Substituting the value of A₀ into the equation and evaluating it will give us the estimated amount of carbon-14 when t = 1,000 years. Rounding the answer to three decimal points will provide the final result.

Therefore, the estimated amount of carbon-14 when t = 1,000 years is approximately 34.196 grams.

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Answer:

first box is 24

second is -5

third is -6

Step-by-step explanation:

The number of wild bears the naturalist can relocate per month is 2 wild bears.

Number of wild bears relocated by the naturalist = 12 wild bears

Time taken by the naturalist to relocate these wild bears = 6 months

Thus the number of bears the naturalist can relocate in 1 month can be found out by using unitary method

This implies that the number of bears relocated by the naturalist in 1 month or per month = 12 / 6 = 2 wild bears

Thus the number of wild bears the naturalist can relocate per month is 2 wild bears .

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Answer:

D

Step-by-step explanation:

This is because the angle are corresponding which mean they are on the same side and are the same number

Hope this Helped

Yes, the given equation y = 2x² - 3x + 4 defines the variable y as a function of x.

A quadratic equation is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

The quadratic equation y = 2x² - 3x + 4 is showing y as the function of the variable x. The graph of the equation is attached with the answer below. in which the latex is at ( 0.75, 2.875).

Therefore, the given equation y = 2x² - 3x + 4 defines the variable y as a function of x.

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Given:

Initial number of participants = 128

During each round, half of the players are eliminated.

To find:

The number of players remain after 5 rounds.

Solution:

It is given that, the initial number of participants is 128 and during each round, half of the players are eliminated.

If half of the players are eliminated, then half of the players are remained.

So, the initial value is 128 and the decay factor is \(\dfrac{1}{2}\).

The general exponential decay model is:

\(y=a(b)^x\)

Where, a is the initial value and b is the decay factor.

Putting \(a=128\) and \(b=\dfrac{1}{2}\) in the above model, we get

\(y=128\left(\dfrac{1}{2}\right)^x\)

Here, y is the number of remaining players after x rounds.

Substituting \(x=5\), we get

\(y=128\left(\dfrac{1}{2}\right)^5\)

\(y=128\left(\dfrac{1}{32}\right)\)

\(y=4\)

Therefore, the required model is \(y=128\left(\dfrac{1}{2}\right)^x\) and the number of players remain after 5 rounds is 4.

Answer:

3+3+3+3+3+3+3+3+3=27

Step-by-step explanation:

just add it together.

The equation of a line passing through the point (5,-3) and parallel to 6x+3y=-12 is y =-2x+7.

Parallel lines are those that never intersect. As a result, two parallel lines must have the same slope but different intercepts (if they had the same intercepts, they would be identical lines).

The equation of the line is 6x+3y=-12.

6x+3y=-12​

3y =-12-6x

y = -2x-4    

The slope of this line is -2.

Because parallel lines have the same slope, the new line will also have a slope of -2.

You now have a point (5,-3) and a slope; thus, use the Point-Slope form to solve the equation of a line.

y-y₁= m(x-x₁)

y+3 = -2(x -5)

y+3 = -2x+10

y =-2x+7

The equation of a line passing through the point (5,-3) and parallel to 6x+3y=-12 is y =-2x+7.

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The required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let 'a' be the cost per gallon of fuel in the year 2000, and 'b' be the inflation rate per year. If the rate of inflation is constant then
After 7 year inflation = 7b
Cost of fuel in 2007 = a + 7b

Now,
according to the question
Change in cost of fuel
= cost in 2007 - cost in 2000
= a + 7b - a
= 7b

Thus, the required, in 2007 the price per gallon was 7b more than the price of a gallon of fuel in the year 2000. Where b is the inflation factor.

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The type of armored cable listed under UL 4 with permitted conductor sizes of 14 AWG through 1 AWG only is Type AC Cable.

Type AC Cable is also known as armored cable or BX cable, and it is a type of electrical wiring that consists of two or more insulated conductors that are wrapped in a flexible metal sheath. The metal sheath provides protection against physical damage and also serves as a grounding conductor.

UL 4 is a standard for Armored Cable and it covers various types of armored cables, including Type AC cable. UL 4 specifies the construction, performance, and testing requirements for armored cables. It also includes requirements for the thickness and composition of the metal sheath, as well as the thickness and type of insulation on the conductors.

In summary, Type AC Cable is the type of armored cable that is listed under UL 4 and has permitted conductor sizes of 14 AWG through 1 AWG only.

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The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Answer:

32

Step-by-step explanation:

First you're going to change 20% to a decimal which would be 0.20

Next, multiply .20 by 40

You should get 8

Subtract 8 from 40

You're answer is 32

The probability that James will take the same mode of transportation twice is 1/9.

To find the probability that James will take the same mode of transportation twice, we need to calculate the probability of each individual transportation option and then multiply them together.

In the morning, James has 3 transportation options: bus, cab, or train. Since he randomly chooses his ride, the probability of selecting any particular option is 1 out of 3 (assuming all options are equally likely).

Therefore, the probability of James selecting the same transportation mode in the morning and evening is 1/3.

Hence, the probability that James will take the same mode of transportation twice is 1/3 multiplied by 1/3:

P(same mode of transportation twice) = 1/3 * 1/3 = 1/9.

Therefore, the probability that James will take the same mode of transportation twice is 1/9.

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Answer: D

Step-by-step explanation:

the second one cant be it because its negative and it would end in a negative result and 3,1 is equal to 2x-5 on the graph

Done!

Answer:

(a) - Refer to the step-by-step explanation.

(b) - Displacement of the object.

Step-by-step explanation:

To estimate the gradient of the graph at t = 2, we need to look at the slope of the line at that specific point. The gradient represents the rate of change of speed with respect to time.

Part (a) - Estimate of the gradient at t = 2:

To find an estimate of the gradient at t = 2, we can draw a tangent line to the curve at that point and determine its slope. If you could provide the specific values of speed (m/s) at different times around t = 2 (e.g., the speeds at t = 1.9 and t = 2.1), we can calculate the slope using the formula:

Slope = (Change in speed) / (Change in time).

With the additional information, we can proceed to estimate the gradient at t = 2.

Part (b) - The area under the graph represents the displacement or distance traveled.

The area under the speed-time graph corresponds to the distance or displacement traveled by the object. Since speed is the rate of change of distance, the area under the graph gives us the total distance covered during the given time interval. To calculate the area under the graph, you can divide it into individual shapes (rectangles, triangles, etc.) or use integrals and find their respective areas. Then, summing up these areas will give you the total distance traveled.

Answer:

D. Multiply the second equation by 5

The best answer would have been to multiply the first equation by 1

I hope it helps