1. Scores made on an aptitude test by employees are approximately normally distributed with mean of 500 and variance of 10,000.
(i) What percentage of those taking the test, score below 225?
(ii) What percentage of the scores fall between 355 and 575?

The graph of the parametric equations x = -2cos(t) and y = -sin(t) within the range 0 ≤ t < 2π is an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis.

To sketch the graph of the parametric equations x = -2cos(t) and y = -sin(t), where 0 ≤ t < 2π, we need to plot the coordinates (x, y) for each value of t within the given range.

1. Start by choosing values of t within the given range, such as t = 0, π/4, π/2, π, 3π/4, and 2π.

2. Substitute each value of t into the equations to find the corresponding values of x and y. For example, when t = 0, x = -2cos(0) = -2 and y = -sin(0) = 0.

3. Plot the obtained coordinates (x, y) on a graph, using a coordinate system with the x-axis and y-axis. Repeat this step for each value of t.

4. Connect the plotted points with a smooth curve to obtain the graph of the parametric equations.

The graph will be an ellipse centered at the origin, with the major axis along the x-axis and a minor axis along the y-axis. It will have a vertical compression and a horizontal stretch due to the coefficients -2 and -1 in the equations.

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Step-by-step explanation:

That is, the event A ∪ B will occur if either A or B occurs. In Example 4.1(a), if A = {g} is the event that the child is a girl and B = {b} is the event that it is a boy, then A ∪ B = {g, b}.

Associative law: (E ∪ F)∪G = E ∪ (F ∪ G)

Distributive law: (E∪F)G=EG∪FG

Commutative law: E ∪ F = F ∪ E

After selling x pints of Boldly Buttered Popcorn icecream and y pints of Lovely Lavender Lemon on the charged of $10 for each, his profit equation is written as P = 6x + 6y = 6( x + y).

We have, Mr. McCoy's new ice cream shop. He sold two flavors of icecream. He sold his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. The quantity of sold Boldly Buttered Popcorn ice cream = x pints

The quantity of sold Lavender Lemon ice cream = y pints

Cost of each pint of ice cream = $4

Selling price of each pint of ice cream

= $10

First, total pints of icecream he sold

= pints of Boldly Buttered Popcorn ice cream+ pints of Lavender Lemon ice cream = ( x + y) pints

Now, Cost of (x + y) pints of ice cream

= $4 ( x + y)

Similarly, selling price of ( x + y ) pints of icecream = $ 10 ( x + y)

As we know, when selling price is greater than cost price then profit will occur. Equation for profit P = selling price - cost price = $ 10 ( x + y) - $4 ( x + y)

= 10 x + 10y - 4x - 4y

P = 6(x + y)

Hence, required equation is 6x + 6y.

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Complete question:

Mr. McCoy's new ice cream shop is doing great! Last month, he sold out of his Boldly Buttered Popcorn ice cream and his Lovely Lavender Lemon ice cream. He sold x pints of Boldly Buttered Popcorn and y pints of Lovely Lavender Lemon. Each pint cost him $4 to make, and he charged $10 for each. Write an equation for his profit or loss on ice cream selling.

Yes, the figure shown in the xy-coordinate plane is a parallelogram because side OP is parallel to side TS and side OT is parallel to side PS

In order for any quadrilateral to be considered a parallelogram, two pairs of its parallel sides must be equal (congruent). Therefore, we would determine the slope of each side by using this mathematical equation:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

For side OP, the slope is given by:

Slope (m) = (b - 0)/(a - 0)

Slope (m) = b/a.

For side TS, the slope is given by:

Slope (m) = (0 - )/(c - (a + c))

Slope (m) = -b/-a = b/a

Therefore, side OP is parallel to side TS.

For side OT, the slope is given by:

Slope (m) = (0 - 0)/(c - 0)

Slope (m) = 0.

For side PS, the slope is given by:

Slope (m) = (b - b)/((a + c) - c)

Slope (m) = 0

In conclusion, the figure shown above is a parallelogram because side OT is parallel to side PS and side OP is parallel to side TS.

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There probability 6C3 = 20 ways to select 3 items from a group of 6 items.

When selecting three items from a group of six items, the total number of combinations is referred to as a combination. Combinations are based on the concept of permutations, which is the number of ways an item can be rearranged. In this case, the number of permutations is 6P3 = 6 / (6 - 3) = 6 * 5 * 4 / 3 * 2 * 1 = 20. This means that there are 20 different combinations of three items that can be selected from the group of six items. To calculate the number of combinations, the formula 6C3 = 6 / (6 - 3) * 3 is used. This formula simplifies to 6 * 5 * 4 / 3 * 2 * 1, which equals 20. Therefore, there are 20 ways to select three items from a group of six items.

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600 degrees is approximately equal to 10.47 radians or 10π / 3 radians when expressed in terms of π.

To convert 600 degrees to radians, we need to use the conversion formula: Radians = (Degrees * π) / 180.

Let's plug in the given value:

Radians = (600 * π) / 180

Simplifying the equation, we have:

Radians = 10π / 3

Now let's express this answer in terms of π and as a decimal rounded to the nearest hundredth.

In terms of π, the answer is 10π / 3 radians. This means that the measure is equal to 10 times the irrational number π divided by 3.

To find the decimal approximation, we substitute the value of π ≈ 3.14:

Radians ≈ (10 * 3.14) / 3

≈ 31.4 / 3

≈ 10.47

Therefore, when rounded to the nearest hundredth, 600 degrees is approximately equal to 10.47 radians or 10π / 3 radians when expressed in terms of π.

This conversion allows us to relate angles measured in degrees to their equivalent measures in radians, which is often useful in mathematical calculations involving trigonometric functions or circular motion.

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Answer:

$66.43

Step-by-step explanation:

In order to see how much one sweater cost you need to divide 47.45 by 5 and you will get 9.49 then after that you will multiply 9.49 by 7 and get 66.43

\(\begin{array}{ccll} sweaters&\$\\ \cline{1-2} 5 & 47.45\\ 7& x \end{array} \implies \cfrac{5}{7}~~=~~\cfrac{47.45}{x} \\\\\\ 5x=7(47.45)\implies x=\cfrac{7(47.45)}{5}\implies x=66.43\)

Answer:

Here is your answer

((3 * 6) ^ 8) ^ 7 =

(18 ^ 8) ^ 7 =

11019960576 ^ 7 = 19736052228807988194997231645899399052500495522364054175325333567307776

Step-by-step explanation:

Answer: 52

15 + 4 (10 - 2 × 5) + 7

15 + 4×(10 - 10) + 7

15 + 0 + 7

= 22

...sorry i thought it was a decimal between 2 and 5

Answer:

22

Step-by-step explanation:

15+4(10-2×5)+7

15+4(10-10)+7

15+4×0+7

15+0+7

15+7

22

50

Step-by-step solution:

    0.3x-42=0.1x-32

    -0.1x

    0.2x-42=-32

                   +42

      0.2x=10

               0.2                

        x=50

Answer:

c

Step-by-step explanation:

Based on the given equation, we can say that as n approaches infinity, the sum ∑ 8/n f (2 + 2j/n) approaches 6. This implies that the average value of the function f(x) over the interval [2,4] is equal to 6.

However, we cannot determine the exact function f(x) without additional information or constraints. The function f(x) and given the following expression: lim ∑ 8/n f(2 + 2j/n) = 6, where the limit is taken as n approaches infinity. Let's break down the expression and see what it represents.
1. "lim" stands for "limit," which means we are examining the behavior of the expression as a certain variable approaches a particular value. In this case, we're looking at what happens when n approaches infinity.
2. "∑" is the summation symbol, which is used to represent the sum of a sequence of terms. Here, the terms depend on the index variable j.
3. "8/n" is a factor in the expression, and it will influence the value of each term in the summation.
4. "f(2 + 2j/n)" is the function f(x) evaluated at the point x = 2 + 2j/n.
Now, let's put it all together:
As n approaches infinity, we are considering the sum of the terms 8/n * f(2 + 2j/n) for each j from 1 to n. The given information states that this sum approaches a limit of 6.
So, for some function f(x), we have:
lim (n→∞) ∑ [8/n f(2 + 2j/n)] = 6

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Answer:

the graph you are looking for should look like this!

Step-by-step explanation:

hope this helped!

(hint* if you are ever in trouble use desmos! its a free online graphing calculator and HELPS SOO much! its what i used to give you the answer, i just typed in the inequality and it tells you the answer)

The shaded region represents the possible solutions of the inequality.

Given is the inequality -

y ≤ (1/2)x - 4

Refer to the graph of the inequality attached. It is showing the inequality being plotted. The shaded region represents the possible solutions of the inequality.

Therefore, the shaded region represents the possible solutions of the inequality.

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The recommended rule to sequence the jobs for minimum flow time is the EDD (Earliest Due Date) rule.

The EDD rule prioritizes jobs based on their due dates, where jobs with earlier due dates are given higher priority. By sequencing the jobs in order of their due dates, the goal is to minimize the total flow time, which is the sum of the time it takes to complete each job.

In this case, applying the EDD rule, the sequence of jobs would be as follows:

D (Due on Friday 10th June)

F (Due on Tuesday 14th June)

E (Due on Wednesday 15th June)

C (Due on Friday 17th June)

G (Due on Thursday 16th June)

H (Due on Saturday 18th June)

A (Due on Monday 13th June)

B (Due on Monday 20th June)

By following the EDD rule, we aim to complete the jobs with earlier due dates first, minimizing the flow time and ensuring timely delivery of the orders.

Therefore, the recommended rule for sequencing the jobs in this scenario is the EDD (Earliest Due Date) rule.

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The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

In the question ,

it is given that ,

a theater sells adult and child tickets for its play .

the cost for 2 adult ticket and 3 child ticket is = $30.75

and the cost for 3 adult tickets and 2 child tickets = $33.00

let the cost of 1 adult ticket = "a"   and

let the cost of 1 child ticket = "c"

So, According to the question ,

the equation to represent both the situation is

2a + 3c = 30.75   and

3a + 2c = 33

Therefore , The system of equations that can be used to represent the cost of each type of ticket is  2a + 3c = 30.75   and 3a + 2c = 33   .

The given question is incomplete , the complete question is

A theater sells adult and child tickets to its plays. 2 adult tickets and 3 child tickets cost $30.75. 3 adult tickets and 2 child tickets cost $33.00. let "a' represent the cost of 1 adult ticket, and "c" represent the cost of 1 child ticket . Write a system of equations can be used to determine the cost of each type of ticket ?

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Step-by-step explanation:

Slope = (y2-y1)/(x2-x1)

Slope = (4-7)/(7-1)

Slope = -3/6

Slope = -1/2

Some part of the regression can be estimated precisely, but it is difficult to predict the effect of individual regressors when there is multicollinearity in the data.Multiple regression models require that variables be independent of one another, otherwise, multicollinearity will occur.

Consider the multiple regression model with two regressors X1 and X2, where both variables are determinants of the dependent variable. You first regress Y on X1 only and find no relationship. However when regressing Y on X1 and X2, the slope coefficient changes by a large amount.

This suggests that your first regression suffers from omitted variable bias. Imperfect multicollinearity implies that it will be difficult to estimate precisely one or more of the partial effects using the data at hand. Imperfect multicollinearity means that there is a strong correlation between the regressors, but they are not perfectly correlated.

As a result, some part of the regression can be estimated precisely, but it is difficult to predict the effect of individual regressors when there is multicollinearity in the data.Multiple regression models require that variables be independent of one another, otherwise, multicollinearity will occur.

When there is multicollinearity in the data, it means that two or more of the variables are highly correlated with one another. In other words, the data may contain redundant information, which can make it difficult to estimate the regression coefficients or partial effects.The dummy variable trap refers to a situation in which one of the variables is a perfect linear combination of the other variables.

This results in the model being unsolvable, and the coefficients cannot be estimated. Heteroskedasticity is the term used to describe when the variance of the residuals is not constant across all values of the independent variables. This means that the predictions of the model may be biased, and the standard errors of the coefficients may be incorrect.

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Answer:

x=1

Step-by-step explanation:

It will be x=1 because once it is at x=1, the parobola is split into 2 EQUAL parts. For example, if you graph this on paper and try to guess the middle and place a line where you want to split it, the line will go at x=1

Thank you :)

The lines given by x = 2t + 1, y = 5t + 5, z = 4t + 5, and x = s + 2, y = 4s + 9, z = -2s + 3 intersect at the point (3, 10, 9). The plane determined by these lines can be found by taking the cross product of the direction vectors of the lines and using one of the points of intersection.

To find the point of intersection of the given lines, we can set the corresponding components equal to each other:

2t + 1 = s + 2

5t + 5 = 4s + 9

4t + 5 = -2s + 3

Solving these equations simultaneously, we find t = 1 and s = 2. Substituting these values back into the equations, we obtain x = 3, y = 10, and z = 9. Therefore, the lines intersect at the point (3, 10, 9). To find the plane determined by these lines, we can take the cross product of the direction vectors of the lines. The direction vectors of the first line are (2, 5, 4), and the direction vectors of the second line are (1, 4, -2). Taking the cross product of these vectors, we get (2 * (-2) - 4 * 4, 4 * 1 - (-2) * 2, 1 * 4 - 1 * 5) = (-12, 8, -1). We can now use the point of intersection (3, 10, 9) and the normal vector (-12, 8, -1) to determine the equation of the plane. The equation of the plane can be written as -12(x - 3) + 8(y - 10) - (z - 9) = 0, which simplifies to -12x + 8y - z + 15 = 0. Therefore, the plane determined by the lines is -12x + 8y - z + 15 = 0.

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Answer:

CE..AE...Segment addition postulate

Step-by-step explanation:

i got these answers from the quiz

Answer:

1.A  

2.C

3.A

Step-by-step explanation:

Edgen2020

The solution set of the inequality 8x + 2 > 34 is x > 4

The system of inequality is given as:

8x + 2 > 34

8x + 2 > 34

From the above system of inequality, we can see that the inequalities in the system are the same.

This means that:

8x + 2 > 34

Subtract 2 from both sides of the inequality

8x > 32

Divide both sides by 8

x > 4

Hence, the solution set of the inequality 8x + 2 > 34 is x > 4

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Answer/step-by-step explanation:

2(x + 5) = 3x + 1

2x + 10 = 3x + 1

Subtract 2x from both sides.

10 = x + 1

Subtract 1 from both sides.

9 = x

3y - 4 = 6 - 2y

Add 2y to both sides.

5y - 4 = 6

Add 4 to both sides.

5y = 10

Divide both sides by 5.

y = 2

3(n + 2) = 9(6 - n)

3n + 6 = 54 - 9n

Add 9n to both sides.

12n + 6 = 54

Subtract 6 from both sides/

12n = 48

Divide both sides by 12.

n = 4

Answer:

i dono actualy

Step-by-step explanation:

soorroorryyy

Answer: I Do not know specifically but If we are talking about rates/per hour the answer is 55 Per hour

Step-by-step explanation:

165 miles ÷ 3 hours because It may be talking about rates. Per "HOUR"

x(x−1)/ 5

sorry if incorrect

Answer; present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

The present value of $12,200 to be received 4 years from today can be calculated using the formula for present value. The formula is:

Present Value = Future Value / (1 + Discount Rate)^n

Where:
- Future Value is the amount to be received in the future ($12,200 in this case)
- Discount Rate is the interest rate used to discount future cash flows (5 percent in this case)
- n is the number of periods (4 years in this case)

Plugging in the given values into the formula:

Present Value = $12,200 / (1 + 0.05)^4

Calculating the exponent first:

(1 + 0.05)^4 = 1.05^4 = 1.21550625

Dividing the future value by the calculated exponent:

Present Value = $12,200 / 1.21550625

Calculating the present value:

Present Value = $10,027.51

Therefore, the present value of $12,200 to be received 4 years from today, with a discount rate of 5 percent, is $10,027.51.

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Step-by-step explanation:

Answer:

3. f' ( x) = 5

4. d= 69.21

I hope i helped

The correct option is Simple Linear Regression. Simple Linear Regression is NOT considered to be a Time-Series method of forecasting. The other methods are Time-Series method.

Time-Series analysis is a technique for forecasting future values based on previous observations. It includes various methods such as Moving Average, Exponential Smoothing, Seasonality Analysis, and Multiplicative/Additive Decomposition. Simple Linear Regression, on the other hand, is a method of predicting the relationship between two variables through a straight-line equation. Therefore, it is not considered to be a Time-Series method of forecasting.

A moving average is a common Time-Series method that calculates the average of a specific number of past observations to forecast future values. Exponential smoothing, another popular Time-Series method, assigns more weight to recent observations than to older ones. Seasonality analysis and multiplicative/additive decomposition are also Time-Series methods that are used to analyze trends and patterns in data over time.

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Answer: It is 6x+12

Step-by-step explanation: Distribute 2 to the parenthesis, then do the same at the second parenthesis, 10x+6-4x+6, combine like terms, 10x-4x and +6+6, so 6x+12 is the final result.