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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

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;

https://brainly.com/question/14850029

Answer:

90

Step-by-step explanation:

it its a 45 45 90 triangle

Answer:

time interval when Tree A is taller than Tree B is;

t > 5 years

Step-by-step explanation:

Tree A;

Initial height = 24 inches

Increase in height per year = 6 inches per year

Thus, for t years after being planted, height is;

A = 6t + 24

Tree B;

Initial height = 39 inches

Increase in height per year = 3 inches per year

Thus, for t years after being planted, height is;

B = 3t + 39

For tree A to be taller than tree B, then it means thay;

A > B

Thus;

6t + 24 > 3t + 39

Subtract 3t from both sides to get;

6t - 3t + 24 > 39

3t + 24 > 39

3t > 39 - 24

3t > 15

Divide both sides by 3 to get;

t > 5

Thus, time interval when Tree A is taller than Tree B is; t > 5

Answer:

8

Step-by-step explanation:

As it's an isosceles right triangle, it's sides are equal, say x. x^2+x^2=(4*sqrt(2))^2. x=4, Area is (4*4)/2=8

Answer:

B

Step-by-step explanation:

Given

4x² - 72x = 0 ← factor out 4 from each term

4(x² - 18x) = 0

To complete the square

add/subtract (half the coefficient of the x- term)² to x² - 18x

4(x² + 2(- 9)x + 81 - 81) = 0

4(x - 9)² - 4(81) = 0

4(x - 9)² - 324 = 0 ( add 324 to both sides )

4(x - 9)² = 324 ( divide both sides by 4 )

(x - 9)² = 81 ( take the square root of both sides )

x - 9 = ± [tex]\sqrt{81}[/tex] = ± 9 ( add 9 to both sides )

x = 9 ± 9

Then

x = 9 - 9 = 0

x = 9 + 9 = 18

Answer:0,18

Step-by-step explanation:

its right

Step-by-step explanation:

Step 1: 12x-6= 1

step 2:12x=7

Answer:

they have it on calculator soup

Step-by-step explanation:

Answer:

D. 31<m<43

Step-by-step explanation:

45 x 5 = 225 which is the age of the 5 joggers altogether.

55 x 2 = 110 which is the age of the 2 joggers together.

3m + 110 = 225 then solve for m so,

3m = 115

m = 38.3333

so hence, m is greater than 31 but less than 43.

answer: D

3 sec²(θ) - 5 tan(θ) - 4 = 0

Recall the Pythagorean identity,

cos²(θ) + sin²(θ) = 1.

Multiplying both sides by 1/cos²(θ) gives another form of the identity,

1 + tan²(θ) = sec²(θ).

Then the equation becomes quadratic in tan(θ):

3 (1 + tan²(θ)) - 5 tan(θ) - 4 = 0

3 tan²(θ) - 5 tan(θ) - 1 = 0

I'll solve by completing the square.

tan²(θ) - 5/3 tan(θ)) - 1/3 = 0

tan²(θ) - 5/3 tan(θ) = 1/3

tan²(θ) - 5/3 tan(θ) + 25/36 = 1/3 + 25/36

(tan(θ) - 5/6)² = 37/36

tan(θ) - 5/6 = ±√37/6

tan(θ) = (5 ± √37)/6

Take the inverse tangent of both sides:

θ = arctan((5 + √37)/6) + nπ   or   θ = arctan((5 - √37)/6) + nπ

where n is any integer

Answer:

False

Step-by-step explanation:

well i think that the answer from my calculations

Answer:

0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

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

The average price for a movie in the United States in 2012 was $7.96. Assume the population st. dev. is $0.50.

This means that [tex]\mu = 7.96, \sigma = 0.5[/tex]

Sample of 30:

This means that [tex]n = 30, s = \frac{0.5}{\sqrt{30}}[/tex]

What is the probability that the sample mean will be between $7.75 and $8.20?

This is the p-value of Z when X = 8.2 subtracted by the p-value of Z when X = 7.75.

X = 8.2

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{8.2 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]

[tex]Z = 2.63[/tex]

[tex]Z = 2.63[/tex] has a p-value of 0.9957

X = 7.75

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{7.75 - 7.96}{\frac{0.5}{\sqrt{30}}}[/tex]

[tex]Z = -2.3[/tex]

[tex]Z = -2.3[/tex] has a p-value of 0.0107.

0.9957 - 0.0157 = 0.985

0.985 = 98.5% probability that the sample mean will be between $7.75 and $8.20.

9514 1404 393

Answer:

  (b)  -1

Step-by-step explanation:

The graph shows the difference between the two expressions is zero at x=-1.

__

Additional comment

For finding solutions to polynomial equations, I like to put them in the form f(x)=0. Most graphing calculators find zeros (x-intercepts) easily. Sometimes they don't do so well with points where curves intersect. Also, the function f(x) is easily iterated by most graphing calculators in those situations where the root is irrational or needs to be found to best possible accuracy.

Answer:

The answer is b: -1

Step-by-step explanation:

good luck!

Answer: A (x+1)(x+2)(x+5)

Step-by-step explanation:

Answer:

X(-12,-7)

Step-by-step explanation:

This is the answer to your problem. I hope it helps. I don't know how to explain it sorry.

Answer:

D. 65°

Step-by-step explanation:

It is so because the triangle is isosceles, two identical sides and two equal angles.

Answer:

x > 21

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

x + 34 > 55

Step 2: Solve for x

Answer:(2,5)

Step-by-step explanation:   watch this video

https://youtu.be/l78P2Xi68-k

9514 1404 393

Answer:

  x = 7

  y = 5

Step-by-step explanation:

The applicable rule of exponents is ...

  a^-b = 1/a^b

__

For a=-j and b=7,

  (-j)^-7 = 1/(-j)^7   ⇒   x = 7

For a=k and b=-5,

  k^-5 = 1/k^5   ⇒   y = 5

Given:

The heights (in inches) of students in a third-grade class are:

39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

To find:

The median height.

Solution:

The given data set is:

39, 37, 48, 49, 40, 42, 48, 53, 47, 42, 49, 51, 52, 45, 47, 48

Arrange the data set in ascending order.

37, 39, 40, 42, 42, 45, 47, 47, 48, 48, 48, 49, 49, 51, 52, 53

Here, the number of observations is 16. So, the median of the given data set is:

[tex]Median=\dfrac{\dfrac{n}{2}\text{th term}+\left(\dfrac{n}{2}+1\right)\text{th term}}{2}[/tex]

[tex]Median=\dfrac{\dfrac{16}{2}\text{th term}+\left(\dfrac{16}{2}+1\right)\text{th term}}{2}[/tex]

[tex]Median=\dfrac{8\text{th term}+9\text{th term}}{2}[/tex]

[tex]Median=\dfrac{47+48}{2}[/tex]

[tex]Median=\dfrac{95}{2}[/tex]

[tex]Median=47.5[/tex]

Therefore, the median height of the students is 47.5 inches.

Step-by-step explanation:

[tex]\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}[/tex]

[tex]=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}[/tex]

[tex]=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha[/tex]

Question :

Required solution :

Here we would be considering L.H.S. and solving.

Identities as we know that,

By using the identities we gets,

[tex] : \: \implies \: \sf{ \dfrac{sin \: \alpha }{cos \: \alpha} \: + \: \dfrac{cos \: \alpha }{sin \: \alpha} }[/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin \: \alpha \times sin \: \alpha }{cos \: \alpha \times sin \: \alpha} \: + \: \dfrac{cos \: \alpha \times cos \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]

[tex] : \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \times sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \times \: cos \: \alpha } } [/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha }{cos \: \alpha \: sin \alpha} \: + \: \dfrac{cos {}^{2} \: \alpha }{sin \: \alpha \: cos \: \alpha } } [/tex]

[tex]: \: \implies \: \sf{ \dfrac{sin {}^{2} \: \alpha \: + \: cos {}^{2} \alpha}{cos \: \alpha \: sin \alpha} } [/tex]

Now, here we would be using the identity of square relations.

By using the identity we gets,

[tex] : \: \implies \: \sf{ \dfrac{1}{cos \: \alpha \: sin \alpha} }[/tex]

[tex]: \: \implies \: \sf{ \dfrac{1}{cos \: \alpha } \: + \: \dfrac{1}{sin\: \alpha} }[/tex]

[tex]: \: \implies \: \bf{sec \alpha \: cosec \: \alpha}[/tex]

Answer:

AB is correct as It is the shorter parallel line

as the line measures 6 units.

Step-by-step explanation:

The polygon is a trapezoid / (trapezium Eng/Europe)

We see the given coordinates  (2, 6) - (-4, 6) = x-6 y 0 = x = 6units

as x always is shown as x - 6  as  x= 6

We can also show workings as y2-y1/x2-x1 = 6-6/-4-2 0/-6

y = 0  x = 6 = 6 units as its horizontal line.

when y is 6-6 = 0 then we know the line is horizontal for y = 0.

The difference of the measures -4 to 2 is 6units so if no workings we just add on from -4 to 2 and find the answer is 6 units long.

When looking at diagonal lines we still group the x's and y's and make the fraction whole.

When looking for solid vertical lines that aren't shown here we use the y values if showing workings and show x =0 to cancel out.

Answer:

Step-by-step explanation:

2/3y=1/4 this means 3y=8 then you divide both sides by 8 you will get the value of y =8/3

Answer:

"0.250" is the appropriate answer.

Step-by-step explanation:

Given:

New car sample,

= 1453

Preferred foreign,

= 363

Now,

The amount of new automobile purchasers preferring foreign cars will be approximated as:

= [tex]\frac{363}{1453}[/tex]

= [tex]0.250[/tex]

Answer:

hello

as probability is equal to number of favourable outcomes/total number of out comes,

Step-by-step explanation:

=7/10

HOPES THAT IT HELPS YOU

PLEASE MARK ME AS BRAINLIEST

Answer:

1 / 9

Step-by-step explanation:

Choosing with replacement means that the first draw from the lot is replaced before another is picked '.

Number of Blue marbles = 2

Number of red marbles = 4

Total number of marbles = (2 + 4) = 6

Probability = required outcome / Total possible outcomes

1st draw :

Probability of picking blue = 2 / 6 = 1 /3

2nd draw :

Probability of picking blue = 2 / 6 = 1/3

P(1st draw) * P(2nd draw)

1/3 * 1/3 = 1/9

Given:

Distance traveled by sprinter = 200 m

Time taken by sprinter = 20.03 seconds

To find:

The sprinter's average speed rounded to 4 sf.

Solution:

We know that,

[tex]\text{Average speed}=\dfrac{\text{Distance}}{\text{Time}}[/tex]

It is given that, the sprinter travels a distance of 200 m in a time of 20.03 seconds.

[tex]\text{Average speed}=\dfrac{200}{20.03}[/tex]

[tex]\text{Average speed}=9.985022466[/tex]

[tex]\text{Average speed}\approx 9.985[/tex]

Therefore, the average speed of the sprinter is 9.985 m/sec.

Answer:

9.985

Step-by-step explanation:

Answer:

Distributive Property means you can multiply the outside and inside of parenthesis.

Addition Property... means you can add the same value to both sides of the equation without changing it.  In this case you add 3x.

Subtraction Property... same as addition property, but with subtraction.  In this case subtract 10 from both sides.

Division property...  same as addition and subtraction properties but with division.  In this case divide both sides by 8.  

Technically the addition property can be used for the subtract 10 because you just add -10 and multiplication property could be used for the division, because you just multiply both sides by 1/8, but for the purpose of this equation, you would say subtraction and division.

Answer:

a) 0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg.

b) The weight that is exceeded by 98% of the bags is of 45.9 kg.

c) 0.0125 = 1.25% probability that two weigh more than 53kg and one weighs less than 53kg.

Step-by-step explanation:

The first two questions are solved using the normal distribution, while the third is solved using the binomial distribution.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The weight X kg of a bag can be modeled by a normal distribution with mean 50kg and standard deviation 2kg.

This means that [tex]\mu = 50, \sigma = 2[/tex]

a. Find the probability that a randomly selected bag weighs more than 53kg.

This is 1 subtracted by the p-value of Z when X = 53. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{53 - 50}{2}[/tex]

[tex]Z = 1.5[/tex]

[tex]Z = 1.5[/tex] has a p-value of 0.9332.

1 - 0.9332 = 0.0668.

0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg.

b. Find the weight that is exceeded by 98% of the bags.

This is the 100 - 98 = 2nd percentile, which is X when Z has a p-value of 0.02, so X when Z = -2.054.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-2.054 = \frac{X - 50}{2}[/tex]

[tex]X - 50 = -2.054*2[/tex]

[tex]X = 45.9[/tex]

The weight that is exceeded by 98% of the bags is of 45.9 kg.

c. Three bags are selected at random. Find the probability that two weigh more than 53kg and one weighs less than 53kg.

0.0668 = 6.68% probability that a randomly selected bag weighs more than 53kg means that [tex]p = 0.0668[/tex]

3 bags means that [tex]n = 2[/tex]

Two above 53kg, which means that we want P(X = 2). So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{3,2}.(0.0668)^{2}.(0.9332)^{1} = 0.0125[/tex]

0.0125 = 1.25% probability that two weigh more than 53kg and one weighs less than 53kg.