A number "z" when rounded to the nearest whole, is equal to

Find the upper and lower bound of "z"

Answer:

Step-by-step explanation:

Anatomical planes are created by imaginary lines that intersect the body into parts

Answer:

33/3  

55/5

77/7

When these are simplified, they are equal to 11/1

The normal distribution that best approximates X is N(42, 21).

In an accounting college class, 50% of students receive a B or above on the final exam. 84 students are randomly selected from an accounting class at a local college. Let X be the number of students who received a B or above on the final exam. The normal distribution that best approximates X is a normal distribution with mean µ = np and variance σ^2 = np(1 - p).

In this case, n = 84 and p = 0.5 since 50% of the students receive a B or above on the final exam, and we want to find the distribution of the number of students who receive a B or above on the final exam.X ~ N(µ, σ^2) = N(np, np(1 - p)) = N(84(0.5), 84(0.5)(0.5)) = N(42, 21)

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A consumer's optimal consumption bundle represents the best possible combination of goods and services that a consumer can purchase given their budget constraint and the prices of those goods. In this scenario, the utility function given is a(f, g) = 2√f + g

The price of good f is 2 and the price of good g is 1.

The consumer's income is 3/4 and 1/4 respectively. Using these, we can solve for the optimal consumption bundle for the consumer using the utility function.

a) To calculate the optimal consumption bundle when the income is 3/4, we can use the following method:

Let the optimal consumption bundle be represented as (x, y).

Here, x represents the quantity of good f consumed, and y represents the quantity of good g consumed.

The consumer's budget constraint can be given as follows:

2x + y = 3/4

The consumer's goal is to maximize their utility, which can be represented as:

a(f, g) = 2√f + g = 2√x + y

The consumer's optimization problem can be represented as follows:

Maximize 2√x + y subject to 2x + y = 3/4

To solve this optimization problem, we can use the Lagrangian function:

L(x, y, λ) = 2√x + y - λ(2x + y - 3/4)

To find the optimal consumption bundle, we must solve for the following set of equations:

∂L/∂x = 0,

∂L/∂y = 0, and

∂L/∂λ = 0

Solving for the first two equations yields the following:

x/√x = λ2y - λ

= 1

The third equation can be used to solve for λ:

2x + y - 3/4 = 0

Solving for x and y using the first two equations and the value of λ yields:

x = 1/2 and y = 1/4

Therefore, the optimal consumption bundle is (1/2, 1/4)

b) To calculate the optimal consumption bundle when the income is 1/4, we can use a similar method to the one used in part a.

Using the same budget constraint of 2x + y = 1/4 and the same utility function of 2√x + y, we can solve for the optimal consumption bundle by using the Lagrangian function L(x, y, λ) = 2√x + y - λ(2x + y - 1/4).

Solving for the same set of equations, we get:

x = 1/8 and y = 0

Therefore, the optimal consumption bundle is (1/8, 0)

Utility functions are mathematical representations of the satisfaction a consumer derives from consuming goods and services. A consumer's optimal consumption bundle represents the best possible combination of goods and services that a consumer can purchase given their budget constraint and the prices of those goods.In this question, we were given a specific utility function and the prices of two goods. We used this information to solve for the optimal consumption bundle when the consumer's income was 3/4 and 1/4 respectively.To solve for the optimal consumption bundle, we used the Lagrangian method to optimize the consumer's utility function subject to their budget constraint. The Lagrangian method involves creating a Lagrangian function that includes the consumer's utility function and their budget constraint. We then solve for the first-order conditions of the Lagrangian function, which are a set of equations that yield the optimal values of the goods consumed.This method is useful for solving for optimal consumption bundles because it takes into account both the consumer's preferences and their budget constraint. By solving for the optimal consumption bundle, we can determine how much of each good the consumer should consume to maximize their satisfaction given their budget constraint

Utility functions and optimal consumption bundles are important concepts in microeconomics. They allow us to understand how consumers make choices and how they allocate their resources. By solving for the optimal consumption bundle, we can determine the best combination of goods and services that a consumer can purchase given their budget constraint and the prices of those goods.

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The hypothenuse in the triangle when the sides that are given are ✓39 and 6 is 8.6.

It should be noted that a triangle has three sides and the longest side is the hypothenuse. Based on the information given, it can be seen that we have two sides that we given in the question already.

In this case, the sides that are given are ✓39 and 6 and we wat to find the hypothenuse. This will go thus;

Hypothenuse ² = (✓39)² + 6²

Hypothenuse ² = 39 + 36

Hypothenuse ² = 75

Hypothenuse = ✓75

Hypothenuse = 8.6

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A correlation of .9 indicates that 81% of the variance between two variables has been explained.

Correlation measures the strength of the relationship between two variables. A perfect positive correlation is 1.0, indicating that the two variables move in the same direction together. A perfect negative correlation is -1.0, indicating that the two variables move in opposite directions. A correlation of 0 indicates no relationship between the two variables.

To determine the proportion of variance explained by a correlation, you need to square the correlation coefficient (in this case, 0.9). This is called the coefficient of determination (R^2). So, you calculate:

R^2 = (0.9)^2 = 0.81

Thus, a correlation of 0.9 explains 81% of the variance between the two variables.

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Answer: A

Step-by-step explanation:

If you look only at the ranges provided for x A is the only one that fits the graph. The domain of the first function (\(x^3-3\)) is everything equal to or less than 2. The equal to is represented by the closed circle at point (2,5) which represents that this value is included for that function. The other function continues on with values greater than 2, but does not include the x value 2 as it has an open circle at point (2,10).

The points on the surface at which the tangent plane is parallel to the given plane are (1/√21, -1/√21, -3/√21) and (-1/√21, 1/√21, 3/√21).

To find the points on the surface 3x^2 + 5y^2 + 2z^ 2=1 at which the tangent plane is parallel to the plane 1x -1y−3z=−3, we need to use the gradient of the surface and compare it to the normal vector of the given plane.

The gradient of the surface is given by ∇f = <6x, 10y, 4z>. The normal vector of the given plane is <1, -1, -3>.

Since the tangent plane is parallel to the given plane, their normal vectors must be parallel as well. This means that the gradient of the surface must be a scalar multiple of the normal vector of the given plane.

So, we have:

6x = k(1)

10y = k(-1)

4z = k(-3)

Solving for x, y, and z in terms of k gives us:

x = k/6

y = -k/10

z = -3k/4

Substituting these values back into the equation of the surface gives us:

3(k/6)^2 + 5(-k/10)^2 + 2(-3k/4)^2 = 1

3(k^2/36) + 5(k^2/100) + 2(9k^2/16) = 1

(k^2/12) + (k^2/20) + (9k^2/8) = 1

(10k^2/120) + (6k^2/120) + (135k^2/120) = 1

151k^2 = 120

k^2 = 120/151

k = ±2/√21.

Solving for k gives us k = ±2/√21.

Plugging these values of k back into the equations for x, y, and z gives us the points:

(1/√21, -1/√21, -3/√21) and (-1/√21, 1/√21, 3/√21).

Hence, the tangent plane is parallel to the given plane are at points (1/√21, -1/√21, -3/√21) and (-1/√21, 1/√21, 3/√21).

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The employer must pay $1,125. 25 per month, and the total recruitment fees that Flor pays is $3,849.99.

The given problem states that Flor got a job with a salary of $55K per annum, and the agency fee is 28% of her monthly salary for three months. We need to find how much the employer has to pay each month and the total recruitment fees that Flor has to pay. Flor got a job through the Valley Recruiting Service, which pays $55K per year. The agency fee is equivalent to 28% of her monthly salary for three months. Thus, the recruitment fee is $55,000/12 = $4,583.33 per month.Flor will be charged a 28% agency fee for each of the first three months she is employed, which is equivalent to 0.28*4,583.33 = $1,283.33. After that, Flor will not be charged any additional fees.Therefore, for the first three months, the employer must pay Flor a salary of $4,583.33 + $1,283.33 = $5,866.67. Therefore, the monthly payment that the employer must make is $5,866.67/3 = $1,955.56.Calculation:For the employer to pay each month, it can be calculated as follows:Employer must pay Flor a salary of $4,583.33 + $1,283.33 = $5,866.67.The monthly payment that the employer must make is $5,866.67/3 = $1,955.56.Thus, the answer is $1,125. 25.To calculate the total recruitment fees that Flor pays, we need to multiply the monthly salary by the agency fee per month. For the first three months, Flor will be charged $1,283.33 per month, so the total cost to her will be $1,283.33*3 = $3,849.99.Thus, the answer is $3,849.99.

Therefore, the employer must pay $1,125. 25 per month, and the total recruitment fees that Flor pays is $3,849.99.

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Answer:

I just got this correct on the Edge practice

B.) -13.86, 13.86

Answer:

4(2)(5)+2(2)=40+4=44

Answer:

Hey Dude...

Step-by-step explanation:

This is ur answer...

Hope it helps!

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Follow me! :)

Answer:

(2, -3)

Step-by-step explanation:

the intersection point is the solution.

Answer:

2,-3

Step-by-step explanation:

Because the other guy said so

plot the frequency distribution with frequency 11, 8, 7, 5, 2, 2,2 and box numbers on X axis

It will show a graph which is Positively skewed.

The vertex and range are (-2, -3) and y >= -3 respectively

The equation is given as:

y = |x +2| - 3

The above equation is an absolute value equation

An absolute value equation is represented as:

y = a|x - h| + k

Where

Vertex = (h, k)

So, we have

Vertex = (-2, -3)

Also, we have

a = 1

Since a is positive, then the vertex is a minimum

Hence, the vertex and range are (-2, -3) and y >= -3 respectively

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CenterWare's direct labor rate variance is $2,100 unfavorable, indicating that the actual rate paid for labor was higher than the standard rate. The direct labor efficiency variance is $2,500 favorable, suggesting that the company achieved higher productivity than expected. The total variance for direct labor is $400 favorable.

To compute the direct labor rate variance, we need to calculate the difference between the actual rate and the standard rate, and then multiply it by the actual hours worked. The formula for the rate variance is (Actual Rate - Standard Rate) × Actual Hours. In this case, the standard rate is $21.00 per hour, and the actual rate is $18.00 per hour. The actual hours worked are 2,500 DLH. Plugging in these values, we find the direct labor rate variance to be ($18.00 - $21.00) × 2,500 = -$7,500, indicating an unfavourable variance.

To calculate the direct labor efficiency variance, we need to find the difference between the actual hours worked and the standard hours allowed, and then multiply it by the standard rate. The formula for the efficiency variance is (Actual Hours - Standard Hours) × Standard Rate. The standard hours allowed are 2,000 DLH (1,000 pots × 2.0 hours per pot). Substituting the values, we get (2,500 - 2,000) × $21.00 = $10,500, indicating a favorable variance.

The total variance for direct labor is the sum of the rate variance and the efficiency variance. In this case, the total variance is -$7,500 + $10,500 = $3,000, which is favorable, indicating that the company performed better than expected in terms of labor cost and efficiency.

The responsibility for the rate variance generally lies with the purchasing department, as they are responsible for negotiating labor rates and purchasing materials at the standard price. The efficiency variance is typically the responsibility of the production department, as they are accountable for achieving the standard labor hours and maximizing productivity.

The rate variance reflects the difference between the actual rate paid for labor and the standard rate. An unfavorable rate variance suggests that the company paid more for labor than anticipated, which could be due to factors like higher wages or inefficient labor management. Conversely, a favorable rate variance would indicate cost savings in labor.

The efficiency variance measures the productivity of labor and represents the difference between the actual hours worked and the standard hours allowed. A favorable efficiency variance implies that the company achieved higher productivity or used fewer labor hours than expected. It could result from factors such as skilled and efficient labor, improved production processes, or effective workforce management.

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Considering the definition of a line and zero of a linear function, the zero of the linear function that passes through the point (3, 2) and has a slope of 2 is 2.

A linear equation o line can be expressed in the form y = mx + b

where

The points where a linear function crosses the axis of the independent term (x) represent the so-called zeros of the function.

That is, zeros of the function are those values ​​of x for which the expression is equal to 0.

In this case, you know:

Substituting the value of the slope m, you get:

y= 2x +b

Replacing the value of the point in the  previous expression, the value of the ordinate to the origin b can be obtained:

2= 2×3 + b

2= 6 + b

2-6= b

-4= b

The equation of the line that passes through the point (3, 2) and has a slope of 2 is y= 2x -4.

The zero of the function is calculated as:

0= 2x -4

Solving:

0 + 4= 2x

4= 2x

4÷2= x

2=x

Finally, the zero of the linear function is 2.

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We can say that the cartesian product is not commutative for r and s because r × s ≠ s × r.

What is meant by cartesian product?

The set of all ordered pairs of the sets is the cartesian product of two or more sets. Set theory is where it is used the most frequently. A pair of items that are an ordered pair have one element assigned first and the other element assigned second. The set of all ordered pairs (a, b) with the first element from C and the second element from D is the cartesian product C × D,  if C and D are two non-empty sets. We denote the cartesian product between two sets using the same multiplication sign as we do for the other product operations, which is ×.

Given:

r = {1,2,3}

s = {3,4}

We first find the cartesian product r×s

In this, the resulting ordered pair will have x values from r.

The cartesian product = {(1,3) , (1,4) , (2,3), (2,4), (3,3), (3,4)}

Now we find the cartesian product  s×r

The cartesian product = {(3,1) , (3,2) , (3,3), (4,1), (4,2), (4,3)}

We can see that both r×s and s×r do not have the same ordered pairs.

Therefore we can say that the cartesian product is not commutative for r and s because r × s ≠ s × r.

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Answer: The measure of a central angle is twice as big as the measure of an inscribed angle IF they intercept the same arc on a circle

Step-by-step explanation: See photo. A central angle’s vertex is at the center of the circle. The measure of a central angle is equal to the measure of the included arc. An inscribed angle’s vertex lies on the circle. The measure of an inscribed angle is equal to half the measure of the included arc. Therefore the measure of the central angle is double the measure of the inscribed angle that intercept the same arc on a circle

The measure of a central angle is twice the measure of an inscribed angle, they intercept the same arc on a circle.

A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.

A central angle’s vertex is at the center of the circle. The measure of a central angle is equal to the measure of the included arc.

An inscribed angle’s vertex lies on the circle. The measure of an inscribed angle is equal to half the measure of the included arc.

Therefore, the measure of the central angle is double the measure of the inscribed angle that intercept the same arc on a circle.

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It is going to be 10 times 36 and that is how you will get your number

Answer:

the 2nd option

Step-by-step explanation:

the second option is in standard form (y = ax^2 + bx + c), c gives us the y intercept

The σx (standard deviation) for this sample with n = 6 scores and a mean (m) of 24 cannot be determined without the individual scores or variance.

To calculate the standard deviation (σx) for a sample, we need the individual scores or at least the variance of the sample. The given information only provides the sample size (n = 6) and the mean (m = 24), which is insufficient to determine σx.

If we have the individual scores, we can follow these steps:

1. Calculate the mean (m) of the sample.
2. Subtract the mean from each score and square the result.
3. Find the average of these squared differences.
4. Take the square root of this average to get the standard deviation (σx).

Alternatively, if we have the variance (s²), we can simply take the square root of the variance to obtain the standard deviation (σx). In this case, without the necessary information, we cannot calculate the standard deviation.

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The required equation of line is: \((y - 4)= \frac{3}{5}(x+6)\)

Given:

To find: Equation of new line

Finding:

=> y = \(\frac{5}{3} (1-x) = \frac{-5}{3}(x-1)\)

We get: m = -5/3 and \((x_0,y_0)\) = (1,0) for the given line.

Slope of the new line = m' = \(\frac{-1}{m} = \frac{3}{5}\)

Hence, On substituting the values for \((x_0,y_0)\) and m', we get the equation of the new line as:

\((y - 4)= \frac{3}{5}(x+6)\)

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Answer: the measure of angle 1 is 55 degrees

Step-by-step explanation:

so you see the outside of 5 is 125 degrees on the right side? So that 125 is equal to the 5 on the other side. So to find measure 1 you need to figure out the measure of the rest of the outside which is the outer angle of measure 1.

So you do

125+125=250

and then,

360-250=110

and since measure of angle 1 starts at the edge of the angle and not the center, you do 110/2 which is 55.

IF THE ANGLE OF MEASURE 1 WAS FROM THE CENTER POINT TO THE END DO NOT DIVIDE BY TWO.

Value of r is different for every series

let

a , b , c , d ..... be geometric series then

r = b/a or d/c and so on

where r is common ratio