If m∠AOD = (7x − 5)° and m∠BOC = (3x + 15)°, what is m∠BOC?
A. 5°
B. 30°
C. 39°
D.60°

The complex number (cos π/4 + i sin π/4)³ can be written in a trigonometric form as (cos π³/64 + i sin π³/64).

We have,

De Moivre's theorem states that for any non-zero complex number

z = r(cosθ + i sinθ) and any positive integer n.

z^n = r^n (cos nθ + i sin nθ)

In this case,

We have z = cos π/4 + i sin π/4 and n = 3.

So we can apply de Moivre's theorem as follows:

z³ = (cos π/4 + i sin π/4)³

= cos³ π/4 + 3i cos² π/4 sin π/4 - 3 cos π/4 sin² π/4 - i sin³ π/4

= (cos³ π/4 - 3 cos π/4 sin² π/4) + i (3 cos² π/4 sin π/4 - sin³ π/4)

We can simplify the real and imaginary parts using the trigonometric identities:

cos³ θ - 3 cos θ sin² θ = cos 3θ

3 cos² θ sin θ - sin³ θ = sin 3θ

So we get:

z³ = cos 3π/4 + i sin 3π/4

= cos π³/4 + i sin π³/4

Therefore,

The complex number (cos π/4 + i sin π/4)³ can be written in a trigonometric form as (cos π³/64 + i sin π³/64).

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The complete question:

Use de Moivre's theorem to write the complex number in trigonometric form (cos π/4 + i sin π/4)³

(cos π³/64 + i sin π³/64)

Note that where the above qualities of a right triangle are given the value of BC in it's simples radical is 11√2.

Here we simply applied the trigonometric rule.

BC = a / Sin (Ф)

Where a = 11 and
Ф = 45

So

BC = 15.55635 = 11√2

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The sum of all the perfect squares between $15$ and $25$, inclusive, minus the sum of all the other integers between $15$ and $25$, inclusive, is [tex]$-164$[/tex].

To find the sum of all the perfect squares between $15$ and $25$, we need to list them out: $16$, $25$. The sum of these perfect squares is $16+25=41$.

To find the sum of all the other integers between $15$ and $25$, we can use the formula for the sum of an arithmetic series. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms. In this case, the first term is $16$ and the last term is $25$, so there are $10$ terms. The average of the first and last term is [tex]$\frac{16+25}{2}=20.5$[/tex]. Therefore, the sum of all the other integers between $15$ and $25$ is $20.5\times 10 = 205$.

Now we can subtract the sum of all the other integers from the sum of the perfect squares to get our final answer: $41-205 = -164$.

Therefore, the sum of all the perfect squares between $15$ and $25$, inclusive, minus the sum of all the other integers between $15$ and $25$, inclusive, is $-164$.

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For a sample for manufacturing process will increase the mean acceptable transmission distance, the correct test statistic value is t = 2.36. So, option(a) is right one.

We have a sample of a type of light-carrying fiber optic cable, and the research team wants to investigate whether modifications in the manufacturing process will increase the diameter. Then sample mean, [tex] \bar X [/tex] = 60.3 km

Population mean, μ = 58 km

Standard deviation, σ = 4.35 km.

Sample size, n = 20

Let's consider the population is normally distributed. We have to determine the value of test statistic that is t-score.

Test statistic : From the normal distribution the t-score formula for mean difference is, [tex]t =\frac{ \bar X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

Substitute all known values in above formula, [tex]t = \frac{ 60.3 - 58 }{\frac{ 4.35}{\sqrt{20}}} [/tex]

[tex]= \frac{ 2.3 }{ \frac{4.35}{\sqrt{20}}} [/tex]

= 2.3646 ~ 2.36

Hence, required test statistic value is 2.36.

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Complete question:

A certain type of fiber optic cable transmits light at a mean distance of 58 km. A research team wishes to investigate if a modification in the manufacturing process will increase the mean acceptable transmission distance. A sample of twenty batches of cable produced under the new process is tested. The sample mean is 60.3 km with a sample standard deviation of 4.35 km. Assume the population is normally distributed. The correct test statistic is

a) t= 2.36

b) t=−2.36

c) z=4.45

d) z=2.36

e) z=−2.36

The equation to represent the relationship is x - 3y + 9 = 0.

We have the table

Input (x)     Output (y)

      3              4

      6              5

      9              6

     12              7

     15              8

So, the equation can be formed as

(y - 4) = (5-4)/ (6-3) (x-3)

y - 4 = 1/3 (x -3)

3y - 12 = x - 3

x - 3y - 3 + 12 =0

x - 3y + 9 = 0

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The measure of length of x from the similar triangles is x = 10

Given data ,

Let the first triangle be ΔABC

Let the second triangle be ΔACD

Now , AC is the common side of the triangle

And , they are similar triangles

So , the corresponding sides are in the same ratio

And , x / 5 = 20 / x

On cross multiplying , we get

x² = 100

Taking square roots on both sides , we get

x = 10

Hence , the length of side is x = 10

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The probability of getting a multiple of 4 or a multiple of 7 is 0.267

There are three multiples of 4 (4, 8, 12) and two multiples of 7 (7, 14) on the spinner.

However, 8 is a common multiple of 4 and 7, so it is counted twice. Thus, there are 4 outcomes that are either a multiple of 4 or a multiple of 7: 4, 7, 8, and 12.

The total number of possible outcomes is 15, since there are 15 sectors on the spinner.

Therefore, the probability of getting a multiple of 4 or a multiple of 7 is:

P(multiple of 4 or multiple of 7) = number of favorable outcomes / total number of possible outcomes

= 4 / 15

≈ 0.267

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Answer:

the answer is 1/3

To solve the given initial value problems, we need to find the general solution of the differential equation dy/dt = -2t and then use the initial condition to determine the particular solution for each problem.

a. y(0) = -1:

We can start by separating the variables and integrating both sides of the equation:

dy/dt = -2t

dy = -2t dt

Integrating both sides, we get:

y = -t^2 + C

where C is the constant of integration. To find the particular solution that satisfies the initial condition y(0) = -1, we substitute t=0 and y=-1 into the general solution:

-1 = -0^2 + C

C = -1

Therefore, the particular solution is:

y = -t^2 - 1

b. y(0) = 5:

Following the same steps as above, we have:

dy/dt = -2t

dy = -2t dt

Integrating both sides, we get:

y = -t^2 + C

where C is the constant of integration. To find the particular solution that satisfies the initial condition y(0) = 5, we substitute t=0 and y=5 into the general solution:

5 = -0^2 + C

C = 5

Therefore, the particular solution is:

y = -t^2 + 5

In summary, the solutions to the given initial value problems are:

a. y = -t^2 - 1

b. y = -t^2 + 5

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To determine if a series is convergent or divergent, we need to analyze the behavior of the sequence of its partial sums. If the sequence approaches a finite limit as we add more and more terms, then the series is convergent. Otherwise, if the sequence either grows without bound or oscillates, then the series is divergent.

Without any specific series to consider, it's hard to give a definitive answer. However, in general, there are various techniques and tests we can use to evaluate the convergence or divergence of a series. Some common ones include the comparison test, the ratio test, the root test, the integral test, and the alternating series test.

If the series is convergent, we can also try to find its sum by using formulas or manipulations that express the series in a simpler form. For example, if the series is a geometric series, then we can use the formula for its sum. If the series is a telescoping series, then we can use partial fraction decomposition or other algebraic tricks to cancel out most of the terms.

Overall, the analysis of series convergence and divergence is an important topic in calculus and mathematical analysis, with many applications in physics, engineering, finance, and other fields.

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The graph is attached in the solution.

Given that, the equation t = 4c represents the number of tires t for c cars,

Here,

t is the dependent variable and c is the independent variable.

To plot the graph, find the coordinates by the values of c and getting the corresponding values of t, then plot those points on the graph, join the line.

The straight line obtained will be the graph of the equation.

Hence, the graph is given in the solution.

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A planning phase for an engineering component generated 80 engineering drawings. The QA team randomly selected 8 drawings for inspection. This exercise can BEST be described as example of random sampling.

The exercise can be described as an example of random sampling, which is a statistical technique used to select a subset of individuals or items from a larger population, in a way that each member of the population has an equal chance of being selected. In this case, the 80 engineering drawings represent the population, and the QA team randomly selecting 8 of them for inspection is a form of random sampling.

By selecting the drawings randomly, the QA team can get an unbiased representation of the population and make inferences about the quality of the engineering component as a whole based on the inspection results of the selected subset.

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The row where three consecutive entries occur in the ratio 3:4:5 is row 7 in Pascal's Triangle.

To find the row in Pascal's Triangle where three consecutive entries occur in the ratio 3:4:5, we can use the property of Pascal's Triangle, where each entry is the sum of the two entries above it.
Let's denote the three consecutive entries in the ratio as 3x, 4x, and 5x. Since these are consecutive entries, we can use the following relationships from Pascal's Triangle:
1. 4x = C(n, k) = C(n-1, k-1) + C(n-1, k), where C(n, k) represents a binomial coefficient.
2. 3x = C(n-1, k-1) and 5x = C(n-1, k).
Now, we can write the equation:
4x = 3x + 5x => x = 3C(n-1, k-1) = 5C(n-1, k).
We can see that 3 divides C(n-1, k) and 5 divides C(n-1, k-1). Let's try different values of n until we find the smallest integer that fits this condition.
For n = 6:
C(5, 1) = 5, which is divisible by 5.
C(5, 2) = 10, which is not divisible by 3.
For n = 7:
C(6, 1) = 6, which is not divisible by 5.
C(6, 2) = 15, which is divisible by 3.

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Yes, that is correct. Collaboration is the process of working together with others, in this case, the customer, to achieve a common goal or find a mutually satisfying solution. It involves active listening, sharing ideas and information, and finding a compromise that meets the needs and goals of everyone involved.

Collaboration is a cooperative process where two or more parties work together to achieve a common goal. In the context of customer service, collaboration involves working with the customer to identify and solve problems, and to find mutually satisfying solutions that meet both the customer's needs and the organization's objectives.

Collaboration requires active listening, effective communication, and a willingness to work together to find solutions. It involves acknowledging the customer's concerns and understanding their perspective, as well as providing relevant information and options to help them make informed decisions.

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Sin-1(0) is equivalent to either 0 radians or π radians, depending on the context of the problem.The sine function is defined as the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

It ranges from -1 to 1 and is zero at 0 radians and at every multiple of π radians (π, 2π, 3π, etc.). The inverse sine function or sin-1, also known as arcsine, gives the angle whose sine is equal to a given value.In this case, sin-1(0) represents the angle whose sine is zero. Since the sine function is zero at 0 radians and at every multiple of π radians, sin-1(0) is equivalent to either 0 radians or π radians. These are the only two possible solutions for sin-1(0), as the sine function is positive in the first and second quadrants and negative in the third and fourth quadrants, where it takes on nonzero values. In summary, sin-1(0) is equivalent to either 0 radians or π radians, depending on the context of the problem.

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The turning point (or vertex) of the quadratic equation y = x^2 + 14x - 3 is:

(-7, -52)

The turning point is also called the vertex. To find it we can complete squares, remember the perfect square trinomial:

(a + b)^2 = a^2 + 2ab + b^2

Here we have:

y = x^2 + 14x - 3

Completing squares we will get:

y = x^2 + 2*7*x - 3

Add in both sides 7^2 to get:

y + 7^2 = x^2 + 2*7*x + 7^2 - 3

y = (x + 7)^2 - 3 - 49

y = (x + 7)^2 - 52

Then the vertex is at (-7, -52), that is the turning point.

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To solve this problem, we can use the law of total probability and the definition of conditional probability. Let's start by calculating the probabilities of the first ball being red or green:

Pr(R1) = (31)/(31+16+12) = 31/59

Pr(G1) = (16+20+24)/(31+16+12) = 28/59

(a) Pr(R2) = Pr(R2|R1)Pr(R1) + Pr(R2|G1)Pr(G1)

To calculate the conditional probabilities, we need to consider two cases:

If the first ball is red (R1), we pick the second ball from box B, which has 12 red balls and 20 green balls:

Pr(R2|R1) = 12/32

Pr(G2|R1) = 20/32

If the first ball is green (G1), we pick the second ball from box C, which has 24 red balls and 16 green balls:

Pr(R2|G1) = 24/40

Pr(G2|G1) = 16/40

Plugging these values into the formula, we get:

Pr(R2) = (12/32)(31/59) + (24/40)(28/59) = 65957/173420

(b) Pr(G2) = 1 - Pr(R2) = 107463/173420

(c) Pr[R2|R1] = 12/32 (as calculated above)

(d) Pr[R2|G1] = 24/40 (as calculated above)

(e) Pr[G2|G1] = 16/40 (as calculated above)

(f) Pr[G2|R1] = 20/32 = 5/8 (complementary to Pr[R2|R1])

Therefore, the answers are:

(a) Pr(R2) = 65957/173420

(b) Pr(G2) = 107463/173420

(c) Pr[R2|R1] = 12/32

(d) Pr[R2|G1] = 24/40

(e) Pr[G2|G1] = 16/40

(f) Pr[G2|R1] = 5/8

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The steps necessary to put he equation, x² - 3x + 27 = 8x - 3 in standard form is D. add 3 to both sides and subtract 8x from both sides

The standard form of quadratic equation is ax² + bx + c = 0, where 'a' is the leading coefficient and it is a non-zero real number.

Hence, let's represent x² - 3x + 27 = 8x - 3 in standard form as follows:

x² - 3x + 27 = 8x - 3

Therefore, the two steps that are necessary to make the quadratic equation in standard form is add 3 to both sides and subtract 8x from both sides

Hence,

x² - 3x - 8x + 27 + 3 = 8x - 8x - 3 + 3

x² - 11x + 30 = 0

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A researcher needs a sample size of 629 to estimate the passing rate of Stats courses at FIU with a margin of error of 3% and a confidence level of 90%.

To estimate the passing rate of Stats courses at FIU with a margin of error of 3% and a confidence level of 90%, we need to calculate the appropriate sample size.

Here's a step-by-step explanation:

1. Identify the key terms: In this problem, the margin of error is 3% (0.03), the confidence level is 90% (z-score corresponding to 90% is 1.645), and the estimated passing rate is 70% (0.7).

2. Convert the passing rate and margin of error to proportions: The passing rate (p) is 0.7, and the margin of error (E) is 0.03.

3. Calculate the standard deviation (SD) for the proportion: SD = √(p(1-p)) = √(0.7(1-0.7)) = √(0.21) ≈ 0.458.

4. Determine the required sample size (n) using the formula: n = (z² * SD²) / E², where z is the z-score corresponding to the desired confidence level (1.645 for 90% confidence).

5. Plug in the values: n = (1.645² * 0.458²) / 0.03² ≈ (2.706 * 0.209) / 0.0009 ≈ 0.565 / 0.0009 ≈ 628.89.

6. Round up the result to the nearest whole number: Since you cannot have a fraction of a person in your sample, round up to the nearest whole number, which is 629.

In conclusion, a researcher needs a sample size of 629 to estimate the passing rate of Stats courses at FIU with a margin of error of 3% and a confidence level of 90%.

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(i) To calculate the probability that the time between buses will be at least 20 minutes,

we need to find the area under the exponential distribution curve for values greater than or equal to 20.

Using the formula for the exponential distribution, we have: P(X ≥ 20) = 1 - P(X < 20) = 1 - e^(-20/20) = 1 - e^(-1) ≈ 0.632, Therefore, the probability that the time between buses will be at least 20 minutes is approximately 0.632.

(ii) To calculate the probability that the time between buses will exceed 20 minutes but will be less than 30 minutes,

we need to find the area under the exponential distribution curve between 20 and 30. Using the formula for the exponential distribution, we have:

P(20 < X < 30) = ∫[from 20 to 30] λe^(-λx) dx
               = [-e^(-λx)] from 20 to 30
               = [-e^(-30/20) + e^(-20/20)]
               ≈ 0.117

Here, T represents the inter-arrival time, λ is the rate parameter (1/mean), and t is the time we want to calculate the probability for. In this case, λ = 1/20 and t = 20 minutes.

P(T >= 20) = e^(-1/20 * 20) = e^(-1) ≈ 0.368

We want to find P(20 < T < 30), which can be calculated as P(T <= 30) - P(T <= 20).

P(T <= 30) = 1 - e^(-1/20 * 30) ≈ 0.776
P(T <= 20) = 1 - e^(-1/20 * 20) ≈ 0.632

P(20 < T < 30) = 0.776 - 0.632 ≈ 0.144

So, the probability that the time between buses will exceed 20 minutes but be less than 30 minutes is approximately 0.144 or 14.4%.

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Answer:4x32 givea you

Step-by-step explanation:

To find P(AC), we need to remember that the probability of an event and its complement always adds up to 1. So, P(AC) = 1 - P(A) = 1 - 0.7 = 0.3.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

P(A or AC) is the probability that either event A occurs or its complement occurs. Since these two events are mutually exclusive (they cannot both happen at the same time), we can use the addition rule of probability to find P(A or AC) = P(A) + P(AC) = 0.7 + 0.3 = 1.

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Answer: 9.01 is the answer

Step-by-step explanation: Because when you add the number in the square you can split the number you add to the nearest sum to the number you get in the outcum.

Answer:

The answer to your problem is, B. Player B is the most consistent, with an IQR of 1.5.

Step-by-step explanation:

Steps in which we need to answer

We know the first table be represented as A.

A = { 2 , 1 , 3 , 8 , 2 , 1 , 4 , 3 , 1 }

mean of A = 25/9 = 2.778

We know the second table be represented as B.

B = { 2 , 3 , 1 , 3 , 2 , 2 , 1 , 3 , 6 }

mean of B = 23/9 = 2.5556

The standard deviation of B = 1.5

Which can conclude to the answer.

Thus the answer to your problem is, B. Player B is the most consistent, with an IQR of 1.5.

The probability that in a randomly selected hour, the number of calls is 2 is approximately 0.133 or 13.3%.

The number of calls received by a car towing service follows a Poisson distribution with an average of 18 calls per day (per 24-hour period). To find the mean number of calls per hour, divide the daily average by the number of hours in a day: 18 calls/day ÷ 24 hours/day = 0.75 calls/hour.

Now, to calculate the probability that in a randomly selected hour, the number of calls is 2, we can use the formula for the Poisson distribution:

P(X=k) = (e^(-λ) * λ^k) / k!

where P(X=k) is the probability of having k calls, λ is the mean number of calls per hour (0.75 in this case), k is the desired number of calls (2), e is the base of the natural logarithm (approximately 2.718), and k! is the factorial of k.

Plugging in the values, we get:

P(X=2) = (e^(-0.75) * 0.75^2) / 2!

P(X=2) ≈ (0.472 * 0.5625) / 2 ≈ 0.133

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Amir's search for Hassan and the blue kite occurs in the novel "The Kite Runner" by Khaled Hosseini. The two men Amir encounters mock Hassan primarily because of his Hazara ethnicity, which is a marginalized and discriminated group in Afghanistan.

Hassan's social status is further complicated by the fact that he is Amir's family's servant, emphasizing the existing class differences between them. The novel portrays the social and cultural tensions in Afghanistan during that period, highlighting the disparities between the dominant Pashtun ethnic group, which Amir belongs to, and the Hazara minority. These disparities manifest in various forms of prejudice, including mockery, which further emphasizes the power dynamics at play.

In this particular scene, the men's mockery of Hassan is an attempt to belittle and demean him, thereby reinforcing the status quo that supports their own position within the social hierarchy. Amir's reaction to the situation also sheds light on his  internal struggle with loyalty, friendship, and personal identity.

In conclusion, the men mock Hassan due to his Hazara ethnicity and his position as a servant in Amir's household, reflecting the societal prejudices and power imbalances present in Afghanistan during that time.

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The distance that you will travel if you will drive at given speed for the following situations are 120 km, 330km, 69km, 60km, and 234km respectively.

Calculating distance involves using the formula:

distance = rate x time

Where "rate" is the speed at which you're traveling, measured in units of distance per unit of time (such as kilometers per hour or miles per minute), and "time" is the duration of your travel in those units of time (such as hours or minutes).

To find the distance, simply multiply the rate by the time. For example, if you're traveling at 60 kilometers per hour for 2 hours, your distance would be:

distance = 60 km/h x 2 h = 120 km

So in this case, you would travel 120 kilometers.

Similarly,

Distance = (Speed) x (Time) = 55 km/h x 6 h = 330 km

Distance = (Speed) x (Time) = 46 km/h x 1.5 h = 69 km

Distance = (Speed) x (Time) = 80 km/h x (45 min/60 min) = 60 km

Distance = (Speed) x (Time) = 78 km/h x 3 h = 234 km

Thus, the distances are 120 km, 330km, 69km, 60km, and 234km respectively.

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Calculate the distance that you will travel is you will

drive for the following situations. Write your answers on a separate sheet of

paper.

1. 3 hours at 40km/h

2. 6 hours at 55km/h

3. 1.5 hours at 46km/h

4. 45 minutes at 80km/h

5. 3 hours at 78km/h​

To find the 75th term of the sequence consisting of positive integers that can be expressed as a sum of distinct powers of 3. Thus, the 75th term of the sequence is $111$.

To find the 75th term of the sequence consisting of positive integers that can be expressed as a sum of distinct powers of 3, we can use the base-3 (ternary) numeral system. The 75th term can be represented as the 74th number in base-3 without a digit 2 (as it will require subtraction to form distinct powers of 3).

The 74th number in base-10 is represented as $74_{10}$, which when converted to base-3 is $2202_3$. Since we need to avoid the digit 2, we can carry out the operation similar to addition with carry-over: $2202_3 + 1111_3 = 10310_3$.

Now, we can convert $10310_3$ back to base-10: $(1 \times 3^4) + (0 \times 3^3) + (3 \times 3^2) + (1 \times 3^1) + (0 \times 3^0) = 81 + 0 + 27 + 3 + 0 = 111$.

Thus, the 75th term of the sequence is $111$.

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The null and alternative hypotheses are H₀ = μ ≥ 6 and H₁ = μ < 6.

Given that, the mean GPA of students in colleges is different from 2.0 (out of 4.0).

H₀: μ = 2.0 and H₁: μ ≠ 2.0

So,

We test the likelihood of the statement being true in order to decide whether to accept or reject our alternative hypothesis. Since, the question wants to test if the college student take less than six years to graduate on average, then we take, H₀ = μ ≥ 6.

And,

WE determine whether to accept or reject based on the likelihood of the null hypotheses being true, so we then take H₁ = μ < 6.

Hence, the null and alternative hypotheses are H₀ = μ ≥ 6 and H₁ = μ < 6.

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The revolutions the wheel will have to make before the car comes to a complete stop are approximately 25.5 revolutions.

To find out how many revolutions the wheel will have to make before the car comes to a complete stop, we need to use the information provided about the distance and diameter of the wheel.

First, we need to convert the diameter from centimeters to meters: 61 centimeters = 0.61 meters.

Next, we can use the formula for the circumference of a circle: C = πd, where C is the circumference and d is the diameter.

So the circumference of the wheel is: C = π(0.61m) = 1.92m.

Now we can use the distance the car can stop in, 49 meters, to calculate the number of revolutions of the wheel:

49m ÷ 1.92m/rev ≈ 25.5 revolutions.

Therefore, the wheel will have to make approximately 25.5 revolutions before the car comes to a complete stop.

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The probability of both the socks and the t-shirt being white is 21/44.

The probability of selecting a white pair of socks from the drawer is 6/11. The probability of selecting a white t-shirt from the drawer is 7/8. To find the probability of both events occurring together, we multiply the two probabilities:
P(white socks and white t-shirt) = (6/11) * (7/8) = 0.4773
Therefore, the probability of randomly selecting one pair of white socks and one white t-shirt from the drawer is approximately 0.4773 or 47.73%.
Hi there! To find the probability that both the socks and the t-shirt you randomly select are white, you'll need to multiply the individual probabilities for each item being white.
For the socks, there are 6 white pairs out of a total of 11 pairs. So, the probability of selecting a white pair is 6/11.
For the t-shirts, there are 7 white ones out of a total of 8. So, the probability of selecting a white t-shirt is 7/8.
Now, multiply these probabilities together: (6/11) * (7/8) = 42/88. Simplify the fraction to get 21/44.
So, the probability of both the socks and the t-shirt being white is 21/44.

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