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3 years ago

Junior wanted to ride a roller coaster at Six Flags. The sign says you have to be 48 inches to ride the roller

Mathematics

1 answer:

OLEGan [10]3 years ago

8 0

Answer:

90 feet per second.

Step-by-step explanation:

If it moves 540 feet in 6 seconds, than it moves 540/6=90feet per second.

Not sure what the height requirement has to do with this problem or what 'unit rate' is specifically referring to so this may not be the answer you're looking for but I hope this helped anyway!

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A group of rowdy teenagers near a wind turbine decide to place a pair of pink shorts on the tip of one blade, they notice the sh

Paladinen [302]

The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9

Question: The likely missing parameters in the question are;

The time at which the shorts are at the maximum height, t₁ = 10 seconds

The time at which the shorts are at the minimum height, t₂ = 25 seconds

The general form of a sinusoidal function is A·sin(B(x - h)) + k

Where;

A = The amplitude

The period, T = 2·π/B

The horizontal shift = h

The vertical shift = k

The parent equation of the sine function = sin(x)

We find the values of the variables, A, B, h, and k as follows;

The given parameters of the sinusoidal function are;

The maximum height = 16 meters at time t₁ = 10 seconds

The minimum height = 2 meters at time t₂ = 25 seconds

The time it takes the shorts to complete a cycle, (maximum height to maximum height), the period, T = 2 × (t₂ - t₁)

∴ T = 2 × (25 - 10) = 30

The amplitude, A = (Maximum height- Minimum height)/2

∴ A = (16 m - 2 m)/2 = 7 m

The amplitude of the motion, A = 7 meters

T = 2·π/B

∴ B = 2·π/T

T = 30 seconds

∴ B = 2·π/30 = π/15

B = π/15

At t = 10, y = Maximum

Therefore;

sin(B(x - h)) = Maximum, which gives; (B(x - h)) = π/2

Plugging in B = π/15, and t = 10, gives;

((π/15)·(10 - h)) = π/2

10 - h = (π/2) × (15/π) = 7.5

h = 10 - 7.5 = 2.5

h = 2.5

The minimum value of a sinusoidal function, having a centerline of which is on the x-axis, and which has an amplitude, A, is -A

Therefore, the minimum value of the motion of the turbine blades before, the vertical shift = -A = -7

The given minimum value = 2

The vertical shift, k = 2 - (-7) = 9

Therefore, k = 9

Therefore;

The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9

More can be learned about sinusoidal functions on Brainly here;

brainly.com/question/14850029

6 0

3 years ago

A student researcher compares the ages of cars owned by students and cars owned by faculty at a local state college. A sample of

diamong [38]

Answer:

The point estimate for the true difference between the population means is 0.13.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

Step-by-step explanation:

To solve this question, before building the confidence interval, we need to understand the central limit theorem and subtraction between normal variables.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When we subtract two normal variables, the mean is the subtraction of the means while the standard deviation is the square root of the sum of the variances.

A sample of 263 cars owned by students had an average age of 7.25 years. The population standard deviation for cars owned by students is 3.77 years.

This means that:

$\mu_s = 7.25, \sigma_s = 3.77, n = 263, s_s = \frac{3.77}{\sqrt{263}} = 0.2325$

A sample of 291 cars owned by faculty had an average age of 7.12 years. The population standard deviation for cars owned by faculty is 2.99 years.

This means that:

$\mu_f = 7.12, \sigma_f = 2.99, n = 291, s_f = \frac{2.99}{\sqrt{291}} = 0.1753$

Difference between the true mean ages for cars owned by students and faculty.

Distribution s - f. So

$\mu = \mu_s - \mu_f = 7.25 - 7.12 = 0.13$

This is also the point estimate for the true difference between the population means.

$s = \sqrt{s_s^2+s_f^2} = \sqrt{0.2325^2+0.1753^2} = 0.2912$

90% confidence interval for the difference:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.9}{2} = 0.05$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.05 = 0.95$ , so Z = 1.645.

Now, find the margin of error M as such

$M = zs = 1.645*0.2912 = 0.48$

The lower end of the interval is the sample mean subtracted by M. So it is 0.13 - 0.48 = -0.35 years

The upper end of the interval is the sample mean added to M. So it is 0.13 + 0.48 = 0.61 years.

The 90% confidence interval for the difference between the true mean ages for cars owned by students and faculty is between -0.35 years and 0.61 years.

5 0

3 years ago

Find the mean (average) of the data. Answer to the nearest hundredth.

Rainbow [258]

Answer:

31.86

Step-by-step explanation:

add them all up and then divide by how many numbers there are to get the mean

5 0

4 years ago

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Explain How can you describe a proportional relationship with a number? NO TROLL ANSWERS!!

Rom4ik [11]

Answer:

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

hope this helps

3 0

3 years ago

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If a= 2 ,b= 5 and c= 9, find i) 2a( b+c) ii) abc

klio [65]

Answer:

i) 56

ii) 90

Step-by-step explanation:

i) 2a (b + c) where a = 2 b = 5 and c = 9

2(2) ((5) + (9))

2(2) (14)

(4) (14)

56

ii) abc

(2)(5)(9)

90

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3 years ago

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