How do you do this problem?
Find the exact values of sin(2u), cos(2u), and tan(2u) using the double-angles formulas. cot(u)=-3, 3pi/2 < u < 2pi

The mean (µ) and standard deviation (σ) of the binomial distribution with n=202 and p=0.44 are 88.88 and 7.8959, respectively. The probability of obtaining x=53 is approximately 0.0561, and the z-score for x=37 is -6.55.

To find the mean (µ) and standard deviation (σ) of the binomial distribution, we use the formulas µ = np and σ = sqrt(np(1-p)), where n is the number of trials and p is the probability of success.

Given n = 202 and p = 0.44, we can calculate the mean and standard deviation as follows:

µ = 202 * 0.44 = 88.88 (rounded to 2 decimal places)

σ = sqrt(202 * 0.44 * (1 - 0.44)) = 7.8959 (rounded to 4 decimal places)

Now, let's suppose we want to find the probability of obtaining a specific value of x, let's say x = 53. We can use the formula for the binomial probability:

\(P(x) = C(n, x) * p^x * (1 - p)^{n - x}\)

Substituting the values, we have:

\(P(53) = C(202, 53) * (0.44)^{53} * (1 - 0.44)^{202 - 53}\)

Using a binomial calculator or software, we can find the probability as approximately 0.0561 (rounded to 4 decimal places).

Finally, if we want to calculate the z-score for a given value of x, we can use the formula:

z = (x - µ) / σ

For x = 37, the z-score would be (37 - 88.88) / 7.8959 = -6.55 (rounded to 2 decimal places).

In conclusion, for a binomial distribution with n = 202 and p = 0.44, the mean is 88.88 and the standard deviation is 7.8959. The probability of obtaining x = 53 is approximately 0.0561. The z-score for x = 37 is -6.55.

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Step-by-step explanation:

It is not a scalene triangle

because the third angle is 69⁰

Explanation: 180-(69+42)

180-111

69

The probability of getting a difference in sample means xF − xM of at least 1 minute is 0.1160 or 11.60%.

To find the probability of getting a difference in sample means xF − xM, we need to use the Central Limit Theorem.

For the female students, the sample mean running time x¯f follows a normal distribution with a mean of 8.8 minutes and a standard deviation of 3.3 minutes divided by the square root of 8 (since we are selecting 8 students). Similarly, for the male students, the sample mean running time x¯m follows a normal distribution with a mean of 7.3 minutes and a standard deviation of 2.9 minutes divided by the square root of 8.

Now, we need to find the difference in sample means xF − xM or we want to find the probability of getting a difference of at least 1 minute between the sample means of the two populations.

Using the formula for the difference in sample means, we have:

xF − xM = 8.8 - 7.3 = 1.5

The standard deviation of the difference in sample means is the square root of the sum of the variances of the two populations, which is:

sqrt[(3.3^2/8) + (2.9^2/8)] = 1.255

The z-score for a difference of 1.5 minutes is:

z = (1.5 - 0) / 1.255 = 1.195

Using a standard normal table or a calculator, we can find that the probability of getting a z-score of 1.195 or greater is approximately 0.1160.

Therefore, the probability of getting a difference in sample means xF − xM of at least 1 minute is 0.1160 or 11.60%.

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Here you go. We just did this in my class

In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

A normally distributed phenomenon using standard nomenclature can be described as follows:

A dataset is said to be normally distributed if it follows a bell-shaped curve, which is symmetrical around the mean (µ) and characterized by its standard deviation (σ). In standard nomenclature, a normally distributed dataset is represented as \(N(µ, σ^2)\), where µ is the mean and \(σ^2\)is the variance (square of the standard deviation).

For example, if we consider the heights of adult males in a large population, we may observe that the distribution is normally distributed with a mean height (µ) of 175 cm and a standard deviation (σ) of 10 cm. In this case, the nomenclature for this normally distributed phenomenon would be N(175, 100), as the variance is \(10^2 = 100\).

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Answer:

See image

Step-by-step explanation:

The researcher could use statistical analysis to compare the proportion of accidents that occur among older employees (e.g., those over 50 years old).

The proportion that occurs among younger employees (e.g., those under 30 years old).

If the proportions are similar, then the data would suggest that older and younger employees are equally prone to having accidents.

To determine whether older and younger employees are equally prone to having accidents.

The researcher at the light manufacturing plant would need to analyze the data collected on accident types and age of the employees involved in the accidents.

If the proportions are different, then the data would suggest that one age group is more prone to accidents than the other.

It is important to note that other factors, such as job type, experience level, and physical condition, could also influence the likelihood of accidents. Therefore, the researcher should also consider these factors when analyzing the data.

to ascertain if employees of different ages are similarly prone to accidents.

The light manufacturing plant researcher would have to examine the information gathered on accident kinds and the ages of the personnel involved in the incidents.

The data would indicate that one age group is more prone to accidents than the other if the proportions were different.

It is significant to remember that additional elements, such as work kind, amount of expertise, and physical condition, may also affect the chance of mishaps.

As a result, when the researcher analyses the data, they should also take these things into account.

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By collecting data, calculating and comparing percentages, and analyzing accident types, we can investigate whether older and younger employees are equally prone to having accidents at the manufacturing plant for random sample.

We will look at the data from the researcher's investigation at the light manufacturing plant. They classified a random sample of accidents by type and age of the employee.

Step 1: Collect data on the total number of accidents involving older and younger employees, as well as the types of accidents they were involved in.

Step 2: Calculate the percentage of accidents involving older employees and the percentage involving younger employees.

Step 3: Compare the percentages and determine if there is a significant difference between the accident rates for older and younger employees.

Step 4: Analyze the types of accidents each group is involved in to see if there are any patterns or trends that may suggest a higher risk for either age group.

By following these steps, we can investigate whether older and younger employees are equally prone to having accidents at the manufacturing plant.

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If 54 oranges cost 36 naira, then the cost of 3 oranges​ is 2 naira

Unitary method is a method of solving problems by finding the value of one unit and then using that value to find the value of a given number of units

To find the cost of 3 oranges, we can use unitary method which involves finding the cost of one orange and then multiplying it by 3.

Let's first find the cost of one orange

54 oranges cost 36 naira

So, 1 orange will cost:

1/54 of 36 naira = (36/54) naira = (2/3) naira

Now, we can find the cost of 3 oranges by multiplying the cost of one orange by 3

Cost of 3 oranges = 3 x (2/3) naira = 2 naira

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Answer:

No solution

Step-by-step explanation:

5x - (-x + 3) = -3 + 6x + 6     Distributive property ( the negative sign in front of the parentheses is -1 even if it doesn’t say.

5x + x - 3 = -3 + 6x + 6        Combine like terms

6x - 3 = 3 + 6x

Answer: No solution

It is no solution because 6x - 3 is not equal to 6x + 3.

I hope this helped and please mark me as brainliest!

Btw you are smart. You just have to try your best! :) Keep trying!

Answer:

\(P=\frac{C}{4} -5\)

Step-by-step explanation:

Step one:

given

cost  per drive= $20

additional fee per person= $4

let the number of persons be p

and the total cost be C

The total cost function is expressed as

\(C=20+4p\)

Step two:

Required:

We want to make P subject of the cost function

Take 20 to the other side we have

C-20=4p

divide through by 4

P=C-20/4

simplify

P=C/4-5

\(P=\frac{C}{4} -5\)

The location of the solutions of the inequality are quadrant in I, III, and IV

An inequality is a non-equal comparison between quantities, variables or mathematical expressions.

The specified inequality is; \(y \leq\dfrac{2}{3} \cdot x-4\)

The line of the inequality is a straight line that has a positive slope.

The y-intercept is at (0, -4)

The x-intercept is found as follows;

\(y=\dfrac{2}{3} \cdot x-4\)

\(0 =\dfrac{2}{3} \cdot x-4\)

\(4 =\dfrac{2}{3} \cdot x\)

x = 6

The x-intercept = (0, 6)

The graph therefore from quadrant III enters quadrant IV at (0, -4), then enters into quadrant I at the x-intercept (0, 6)

The solution of the inequality, found by the coordinates of the intercepts and the path through of  the line of the inequality are in I, III, and IV

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There are 12 cells or groups in a 3 × 4 ANOVA design.

So, the answer is option B.

This design involves three levels of one independent variable and four levels of another independent variable, resulting in 12 unique combinations or cells.

Each cell represents a specific condition or treatment group in the study, and the dependent variable is measured for each group.

ANOVA, or analysis of variance, is a statistical method used to compare means between groups to determine if there are significant differences. Understanding the number of cells or groups in the design is important for planning the study and interpreting the results accurately.

Hence,the correct answer is B.

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The correct option answer is C , that is Entry 12 represents The cost of goods manufactured transferred to Finished Goods

Given that, the T-account below Work In Process 30,000 (12) Bal. 270,000  90,000  70,000  110,000

We have,  Total work in progress (WIP) before Transfer =

                           30,000 + 90,000 +70,000 + 110,000 = $300,000

And the ending work in progress (WIP)  = 30,000

It clearly means that 270,000 (300,000 - 30,000) of goods has been transferred to finished goods inventory.

Therefore, the balance entry represents that the cost of goods manufactured transferred to Finished Goods.

The required question's table of T-account is attached below.

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Answer:

2x^2

Step-by-step explanation:

2x * x = 2x^2

Thus, Brian's average speed for the whole journey from Ashton to Oldham is 34.29 mph.

Average, also known as mean, is a measure of central tendency in statistics that represents the typical value of a set of numbers. It is calculated by adding up all the numbers in the set and then dividing the sum by the total number of values in the set. For example, if you want to

Given by the question.

To calculate the average speed of Brian's whole journey, we need to use the formula:

average speed = total distance ÷ total time

We know the distance between Ashton and Lees is 12 miles, and we also know the speed at which Brian drove this part of the journey: 40 mph. Using the formula:

time taken = distance ÷ speed

we can calculate that it took Brian:

time taken from Ashton to Lees = 12 miles ÷ 40 mph = 0.3 hours

We also know the distance between Lees and Oldham is 12 miles, and the speed at which Brian drove this part of the journey: 30 mph. Again using the formula:

time taken from Lees to Oldham = 12 miles ÷ 30 mph = 0.4 hours

So, the total distance Brian covered from Ashton to Oldham is:

total distance = distance from Ashton to Lees + distance from Lees to Oldham

total distance = 12 miles + 12 miles = 24 miles

The total time Brian spent on the journey is:

total time = time taken from Ashton to Lees + time taken from Lees to Oldham

total time = 0.3 hours + 0.4 hours = 0.7 hours

Now we can use the formula for average speed:

average speed = total distance ÷ total time

average speed = 24 miles ÷ 0.7 hours

average speed = 34.29 mph

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Answer:

The equation is:

f(x) = Ix + 3I - 2

Step-by-step explanation:

For a function like:

f(x) = Ix - kI + c

k is the x-value where the vertex is, and c is the y-value where the vertex is.

In the graph we can see that the vertex is in the point (-3, -2)

then:

x-value = -3 = k

y-value = -2 = c

Replacing those in the equation for the function:

f(x) = Ix - (-3)I - 2

f(x) = Ix + 3I - 2

Answer:

G- 1/5

Step-by-step explanation:

When doing probability questions, you want to take the amount of what you are looking for and put it over the total. In this case, the total amount of t-shirts would be 15. If we are looking for the sports t-shirts, the fraction would be 3/15, which then simplifies down to 1/5.

Hope this helps! :)

Answer:

G 1/5

Step-by-step explanation:

3/15 - > 1/5

The no.of sports t-shirts divided by the total t-shirts

Answer:

There are 182.88 cm in 6 feet, given that 1 inch = 2.54 cm.

Step-by-step explanation:

Given that 1 inch = 2.54 cm, how many centimeters are there in 6 feet?

12 inches = 1 foot

We have 6 feet, so:

6 feet x 12 inches = 72 inches

If 1 inch is 2.54 cm, multiply by the number of inches by 2.54 to get the number of cm.

2.54 x 72 = 182.88

There are 182.88 cm in 6 feet, given that 1 inch = 2.54 cm.

The function f(x) = 1/4x³ is constant when the intercept is 0

Polynomials are sums of terms of the form k⋅xⁿ, where k is any number and n is a positive integer.

the graph of a polynomial function is a smooth continuous curve.

The y-intercept is the point where the graph crosses the y-axis and can be found by substituting x = 0. The x-intercepts are points where the graph crosses the x-axis and can be found by making the function equal to zero and solving for x.

therefore f(0) = 1/4 0³ = 0

therefore the y- intercept of the function is 0

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The temperature at an altitude of 11,000 ft will be 47.6 degrees Fahrenheit.

We are given that the airplane is on the ground level at a temperature of 59.7 Fahrenheit. After every 1,000 feet, there will be a drop in temperature of 1.1 degrees Fahrenheit. It means that initially, the temperature was 59.7 degrees F and we have to find the temperature when the airplane has covered a distance of 11,000 Ft.

When the airplane is at ground level, the height is 0 feet with a temperature of 59.7 degrees F. Later, the airplane climbs into the sky at an altitude of 11,000 feet.

1,000 feet = 1.1 deg F drop

11,000 feet = 1.1 * 11 degree F drop

= 12.1 degrees F drop

The temperature will decrease 11 times.

Temperature at 11,000 feet altitude = 59.7 - 12.1

= 47.6 degrees F

Therefore, the temperature at an altitude of 11,000 ft will be 47.6 degrees Fahrenheit.

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The complete question is "Suppose there is a 1.1deg F drop in temperature for every 1000 feet an airplane climbs into the sky. If the temperature on the ground is 59.7deg F, what will be the temperature at an altitude of 11,000 ft? "

The solution to the given differential equation with the initial condition y(2) = 14 is y = (1/3)x² - (2/9)x + (2/9).

To solve the given differential equation dy/dx + 3y = 8x² with the initial condition y(2) = 14, we can use an integrating factor. The integrating factor is defined as the exponential of the integral of the coefficient of y, which in this case is 3.

First, let's find the integrating factor. The integral of 3 dx is simply 3x. Therefore, the integrating factor is e^(3x).

Next, multiply both sides of the differential equation by the integrating factor:

e^(3x) * dy/dx + 3e^(3x) * y = 8x² * e^(3x).

Now, we can rewrite the left side of the equation using the product rule for differentiation:

d/dx (e^(3x) * y) = 8x² * e^(3x).

Integrating both sides with respect to x, we have:

∫ d/dx (e^(3x) * y) dx = ∫ 8x² * e^(3x) dx.

Integrating the right side gives us:

e^(3x) * y = ∫ 8x² * e^(3x) dx.

To find the integral on the right side, we can use integration by parts. Let's choose u = x² and dv = e^(3x) dx. Then, du = 2x dx and v = (1/3)e^(3x).

Applying the integration by parts formula, we have:

∫ 8x² * e^(3x) dx = (1/3)x² * e^(3x) - ∫ (1/3)(2x) * e^(3x) dx.

Simplifying further, we get:

∫ 8x² * e^(3x) dx = (1/3)x² * e^(3x) - (2/3)∫ x * e^(3x) dx.

We can continue applying integration by parts to evaluate the remaining integral. Choosing u = x and dv = e^(3x) dx, we have du = dx and v = (1/3)e^(3x). Applying the formula again, we get:

∫ x * e^(3x) dx = (1/3)x * e^(3x) - (1/3)∫ e^(3x) dx.

The integral on the right side is a simple exponential integral:

∫ e^(3x) dx = (1/3)e^(3x).

Substituting the results back into the equation, we have:

e^(3x) * y = (1/3)x² * e^(3x) - (2/3)((1/3)x * e^(3x) - (1/3)e^(3x)).

Simplifying further, we obtain:

e^(3x) * y = (1/3)x² * e^(3x) - (2/9)x * e^(3x) + (2/9)e^(3x).

Now, divide both sides of the equation by e^(3x) to solve for y:

y = (1/3)x² - (2/9)x + (2/9).

Therefore, the solution to the given differential equation with the initial condition y(2) = 14 is y = (1/3)x² - (2/9)x + (2/9).

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Given equation of the line ,

\(\implies 4x - 5y +(-1) = 0 \)

Simplify ,

\(\implies 4x - 5y - 1 = 0 \)

Transpose terms to RHS ,

\(\implies 5y = 4x - 1 \)

Divide both sides by 5 ,

\(\implies \boxed{ y =\dfrac{4}{5}x -\dfrac{1}{5}}\)

Now we know the slope intercept form of the line as \( y = mx + c \) we have ,

As we know that the slope of all parallel lines are same . Henceforth ,

The derivative formula for the function g(x) = 15 - 8ln(x) is g'(x) = -8/x.

To find the derivative of g(x), we can use the power rule and the chain rule. The power rule states that the derivative of x^n is n*x^(n-1), and the chain rule allows us to differentiate composite functions.

In this case, g(x) is a combination of a constant function (15) and the natural logarithm function (ln(x)). The derivative of the constant term (15) is 0 since it does not depend on x.

The derivative of the natural logarithm function, ln(x), is 1/x. Therefore, using the chain rule, the derivative of -8ln(x) is -8 * (1/x), which simplifies to -8/x.

Hence, the derivative of g(x) = 15 - 8ln(x) is g'(x) = -8/x.

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The utility function reflects the preferences of your friend, with M and C contributing to their overall happiness. The goal is to determine the minimum income level that allows them to achieve a total utility of 80.

To find the minimum level of income, we need to consider the prices of movie and concert tickets. Given that movie tickets cost $5 each and concert tickets cost $10 each, we can set up the following equation: 10M^0.5 + 2C = 80.

Since the equation represents the total utility, we can solve for M and C by substituting the ticket prices and rearranging the equation. By finding the values of M and C, we can then calculate the minimum income level required for your friend to achieve the desired utility of 80.

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Answer:

J is the answer of the percentage

The function which represents the cost to drive a car from this agency miles x a day is :

C(x) = 15, if 0 ≤ x ≤ 200

      = 15 + 0.05x, if x > 200

Given that,

A car rental agency charges $15 a day for driving a car 200 miles or less.

The function can be written as,

C(x) = 15 if 0 ≤ x ≤ 200

If a car is driven over 200 miles, the renter must pay $0.05 for each mile over 200 driven.

C(x) = 15 + 0.05x, if x > 200

Hence the correct option is D.

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