Let Z be the variable for the Standard normal distribution. Given that P(0 < Z < a) = 0.4793. Find a.
a. -0.52
b. 2.04
c. -2.04
d. 0.84

A. The number of hours of training that you can purchase with a $3,000 training budget at $40 per employee per hour and a one-time $200 fee is 70-employee-training-hours.

B. Each employee will get 7 hours of training, assuming your organization has 10 employees.

The training cost of employees varies from one organization to another.

The training cost also depends on the training provider and the number of hours of training being offered.

Training budget = $3,000

One-time fee = $200

Remainder after the one-time fee = $2,800 ($3,000 - $200)

Training costs per employer per hour = $40

Hours of training to purchase = 70 ($2,800/$40)

Thus, an organization with 10 employees can obtain 70 hours of training with the training budget.

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Answer:

2 \(\frac{1}{2}\) , 2 \(\frac{3}{4}\) , 3

Step-by-step explanation:

there is a common difference between consecutive terms , that is

2 - 1 \(\frac{3}{4}\) = 2 \(\frac{1}{4}\) - 2 = \(\frac{1}{4}\)

to find the next term in the sequence add \(\frac{1}{4}\) to the previous term

a₄ = 2 \(\frac{1}{4}\) + \(\frac{1}{4}\) = 2 \(\frac{1}{2}\)

a₅ = 2 \(\frac{1}{2}\) + \(\frac{1}{4}\) = 2 \(\frac{3}{4}\)

a₆ = 2 \(\frac{3}{4}\) + \(\frac{1}{4}\) = 3

To solve this equation, use the distributive property to rewrite it as 4x - 2y = 12. Then, solve the equation using either addition or subtraction.

To solve the equation 4x 2y = -12, the first step is to use the distributive property to rewrite the equation as 4x - 2y = 12. This allows us to solve the equation using either addition or subtraction. If we choose to use addition, we can add 2y to both sides of the equation to get 4x + 2y = 12. We can then subtract 2y from both sides to get 4x = 12 - 2y. Dividing both sides of the equation by 4 gives us the solution x = (12 - 2y)/4. If we choose to use subtraction, we can subtract 2y from both sides of the equation to get 4x - 2y = 12. We can then add 2y to both sides to get 4x = 12 + 2y. Dividing both sides of the equation by 4 gives us the solution x = (12 + 2y)/4. In either case, the solution is x = (12 ± 2y)/4.

Addition:

4x + 2y = 12

4x = 12 - 2y

x = (12 - 2y)/4

Subtraction:

4x - 2y = 12

4x = 12 + 2y

x = (12 + 2y)/4

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The mean will be the middle number or 12.1.

According to our question-

The median is the middle number  in the data set when the data set is written from least to greatest.

least to greatest 4.8, 6.9, 12.1, 14.8, 16.2

Hence, The mean will be the middle number or 12.1.

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Given :-

To Find :-

Solution :-

As we know that the angles opposite to the equal sides are equal . Hence the measure of two base angles will be 8x - 23° . Also we know that the angle sum property of a triangle is 180° . So ,

\(\sf\longrightarrow\) 8x - 23° + 8x -23° +34°=180°

\(\sf\longrightarrow\) 16x -12° = 180°

\(\sf\longrightarrow\) 16x = 180° + 12°

\(\sf\longrightarrow\) 16x = 192°

\(\sf\longrightarrow\) x = 12°

Hence the required answer is 12° .

Given:

The equation is,

Explanation:

Simplify the equation for y.

So answer is, -2w + 10

Answer:

C) g(x) = f(x) + 4

Step-by-step explanation:

A vertical shift is where you shift, slide or translate the whole graph up or down (on a graph) The way this shows up in the equation is just a number tacked on to the end of the equation. A +anumber (like the +4 in the answer) slides the function UP four units. A

-anumber would slide the function DOWN instead.

As for the other answers:

A) the 3multiplied in front is a vertical STRETCH.

D) the 1/2 multiplied in front is a vertical shrink (smash)

B) The -3 in close tight with the x is a horizontal shift(slide, translate) It is a RIGHT shift. A +anumber would be a LEFT shift. Horizontal shift seem kind of backwards. + goes LEFT and - goes RIGHT.

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

From the question, we have the following parameters that can be used in our computation:

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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Answer:

Its D :p

Step-by-step explanation:

Answer:

a reflection across the x axis

Step-by-step explanation:

Based on the given information and performing a one-sample t-test, the conclusion is that if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis.

Given:

Sample mean (x') = 30 km per litre

Sample standard deviation (s) = 3.5 km per litre

Sample size (n) = 50

Significance level (α) = 0.05 (5%)

Null hypothesis \((H_0)\): The mean petrol consumption of the new car is equal to or higher than that of the existing car.

Alternative hypothesis \((H_1)\): The mean petrol consumption of the new car is lower than that of the existing car.

We'll calculate the test statistic (t-value) and compare it with the critical t-value.

The formula for the t-value is:

t = (x' - μ) / (s / √n)

where μ is the population mean (mean petrol consumption of the existing car).

First, we need to calculate the critical t-value from the t-distribution table. Since we have a significance level of 0.05 and (50 - 1) degrees of freedom, the critical t-value for a one-tailed test is approximately -1.677.

Now, let's calculate the t-value:

t = (30 - μ) / (3.5 / √50)

To reject the null hypothesis, the t-value should be less than the critical t-value.

Simplifying the equation:

t = (30 - μ) / (0.495)

To find the critical value, we compare it with the calculated t-value:

-1.677 > (30 - μ) / (0.495)

Multiplying both sides of the inequality by 0.495:

-0.8294 > 30 - μ

Rearranging the inequality:

μ > 30 + 0.8294

μ > 30.8294

Therefore, if the population mean (μ) is greater than 30.8294 km per litre, we reject the null hypothesis in favor of the alternative hypothesis, concluding that the mean petrol consumption of the new car is lower than that of the existing car.

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at the point (24,8), we can find t = 2 and the slope of the tangent is 2.

How to solve the quadrant?

To find the slope of the tangent to the parametric curve, we need to first find the derivative of the y-coordinate with respect to the x-coordinate. This can be done using the chain rule of differentiation:

dy/dx = (dy/dt) / (dx/dt)

= (2t - 2) / (2t + 2)

At the point (48,16), we can find the value of t by solving the equations:

x = t² + 2t = 48

y = t² - 2t = 16

Solving these equations, we get t = 4 or -6. At t = 4, the point on the curve is (48,16), and at t = -6, the point is (-32,68). However, since the curve is going down and left at (48,16), we need to consider the slope of the tangent at the point where t = -6.

Substituting t = -6 into the derivative expression, we get:

dy/dx = (2(-6) - 2) / (2(-6) + 2) = -5/7

Therefore, the slope of the tangent to the parametric curve at the point (48,16) is -5/7.

Using similar methods, we can find the slopes of the tangents at the other key points on the curve. At the point (0,4.3), we can find t = -0.75 and the slope of the tangent is 0.2. At the point (-1,2.5), we can find t = -0.5 and the slope of the tangent is -1. At the point (0,1), we can find t = 0.5 and the slope of the tangent is -0.6. At the point (3,0), we can find t = -1 and the slope of the tangent is -1/3. At the point (5.2,-0.2), we can find t = 0.2 and the slope of the tangent is 3. At the point (7.9,0), we can find t = 1.3 and the slope of the tangent is 15/17. Finally, at the point (24,8), we can find t = 2 and the slope of the tangent is 2.

Therefore, the curve starts out with a steep negative slope, then levels off to a shallow negative slope, changes direction and becomes steep in the positive direction, levels off to a shallow positive slope, and then becomes steep in the positive direction again. The slope of the tangent at the point (24,8) is positive, indicating that the curve is still going up and to the right at that point.

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Answer:

B: Corresponding angles are congruent, so x = 43

Answer:

B: Corresponding angles are congruent, so x = 43

Step-by-step explanation:

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently.

Yes, when dealing with a multi-value attribute with a variable number of values that need to be processed independently, it is recommended to consider creating a new dependent entity to represent the values. This can help to simplify the design and make it easier to manage and maintain. The new entity can be linked to the original entity through a relationship, allowing each value to be processed independently while still maintaining the integrity of the data. Overall, this approach can improve the efficiency and effectiveness of the system, making it easier to work with and providing better results for the end user.

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The Annual Percentage Yield is approximately 3.04%.

Given that Garrett deposits $8000, there is an APR of 3 % compounded daily.

We need to calculate Annual Percentage Yield.

To determine the APY (Annual Percentage Yield) with an APR (Annual Percentage Rate) of 3% compounded daily, we can use the formula:

APY = (1 + (APR / n))ⁿ⁻¹

where "n" represents the number of compounding periods per year. In this case, since it is compounded daily, there are 365 compounding periods per year.

Let's calculate the APY:

APY = (1 + (0.03 / 365))³⁶⁵⁻¹

Simplifying,

APY ≈ 0.030416

To round the APY to the nearest hundredth of a percent, we multiply by 100 and round to two decimal places:

APY ≈ 3.04%

Therefore, the Annual Percentage Yield is approximately 3.04%.

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Answer:

Janice and Karen could do in 1 day:

Step-by-step explanation:

To identify how much of the job could janice and caren do in 1 day, first, we must find how much of the job make just 1 person at the same rate:

If three persons make a job in 3 1/3 days, 1 person make the job in x:

Then:

Just a person would need 10 days to complete a job, now, we're gonna divide this value in 2 to obtain the time that need two persons to complete a job:

How two persons need 5 days to complete a job (in this case, the two persons are Janice and Karen), we can make a simple rule of three to obtain the percentage made in 1 day:

Then:

As you can see, Janice and Karen just in a day could do 20% of the job.

The profit-maximizing price and quantity for the monopolist are $350 and 150 units, respectively ,The expected return is greater than the initial investment And the producer surplus is $33,750, consumer surplus is $31,875, and firm profit is $37,500.

Ignoring the time value of money and discounting, the expected value of the lottery winnings each year is 2% × $1 million = $20,000, and this goes on for 10 years.

Thus, the expected value of the investment is 10 × $20,000 = $200,000.

Hence, the expected return is greater than the initial investment, and there is a condition under which the investment can be made.

The monopolist’s total cost can be represented as:

TC = 300 + 200Q + 3Q².

The demand function for the monopolist is given as:

Q = 500 - P,

which can be rearranged to derive the price function as:

P = 500 - Q.

From the total cost function, we can obtain the marginal cost (MC) as the derivative of TC with respect to Q, and it can be represented as follows:

MC = dTC/dQ = 200 + 6Q.

From the marginal cost, we can set the marginal revenue (MR) equal to MC to get the profit-maximising quantity as follows:

MR = dTR/dQ = P + Q(500 - P) = 500 - Q + 500Q - Q² = 1000Q - Q² - 500 = MC = 200 + 6Q.

Substituting P = 500 - Q in the above expression and rearranging yields the following:

Q = 150, and hence, P = $350.

Therefore, the profit-maximising price is $350, and the quantity is 150. We can verify that the solution is a maximum by computing the second-order condition, which is negative.

To calculate the producer surplus, we first need to obtain the area above the marginal cost and below the price.

Thus, we have:

PS = ∫ MC to QdQ

= ∫ (200 + 6Q) dQ from 0 to 150

= [200Q + 3Q²] from 0 to 150

= $33,750.

Similarly, the consumer surplus can be computed as the difference between the market value of the product and what the consumers paid for it. The area below the price line and above the demand curve yields the consumer surplus.

Thus, we have:

CS = ∫ P to QdQ

= ∫ (500 - Q) dQ from 0 to 150

= [(500 × Q) - (Q²/2)] from 0 to 150

= $31,875.

Finally, the firm profit can be obtained by multiplying the profit-maximizing quantity by the profit-maximizing price and subtracting the total cost.

Thus, we have:

Profit = TR - TC = Q × P - TC = (150 × $350) - (300 + 200 × 150 + 3 × 150²) = $37,500.

Hence, the producer surplus, consumer surplus, and firm profit are $33,750, $31,875, and $37,500, respectively.

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Answer:710.4

Step-by-step explanation:

If the coordinates of the point a is (2,1) and midpoint is (0.-3), then the coordinates of b is (-2,-7).

Midpoint:

Midpoint is the middle point of a line segment. It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

The formula for midpoint is,

\((x_{m},y_{m})= (\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2} )\)

Where

(x₁,y₁) is the coordinates of the first point and

(x₂,y₂) is the coordinates of the second point

and

\((x_m,y_m)\) is the mid point of the first and second points.

Given,

Mid point = (0,-3)

Point a = (2,1)

Here we need to find the point b.

Let (x,y) be the point of b.

Now,

Apply the values on the formula,

Then we get,

\((0,-3)=(\frac{2+x}{2},\frac{1+y}{2})\)

Compare the values in order to solve it,

=> 0 = (2 +x)/ 2

=> 0 = 2 + x

=> x = -2

Similarly,

=> -3 = (1 + y)/2

=> -3 x 2 = 1 + y

=> -6 = 1 + y

=> y = -6 - 1

=> y = -7

Therefore, the coordinates of b is (-2,-7).

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Option B "Perpendicular Lines"  is correct.

"Perpendicular Lines" are two lines that intersect at a right angle, forming 90-degree angles between them. Thus, Option B holds the truth.

Perpendicular lines are a fundamental concept in geometry and they are defined as two lines that meet at a right angle; forming four 90-degree angles. This means that the slopes of the two lines are negative reciprocals of each other. Perpendicular lines are important in many areas of mathematics and physics because they allow us to calculate angles, distances and other geometric properties.

Perpendicular lines are useful in many practical applications such as: architecture, engineering and construction. By understanding the properties of perpendicular lines, one can better understand the geometry of our world and solve real-world problems.

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Answer:

60 seconds

Step-by-step explanation:

Two factories.  Let's calculate a rate for each:

Factory 1:  (1 case/20 sec) or (20 cases/case)

Factory 2:  (1 case/30 secs) or (30 sec/case)

Cases Produced will be the time (in seconds) times each rate.  Let T be the time of production, in seconds:

  Cases Produced = T*(1 case/20 sec)+ T*(1 case/30 sec)

  Cases Produced = T*[(1 case/20 sec)+ (1 case/30 sec)]

  Cases Produced = T*[(1 case/20 sec)*(3/3)+ (1 case/30 sec)*(2/2)]  [covert the fractios to the same denominator]

  Cases Produced = T*[(3 case/60 sec)+ (2 case/60 sec)]

  Cases Produced = T*[(5 case/60 sec)]

 To produce 5 cases:

      5 Cases  = T*[(1 case/20 sec)]

     T = (5 cases)/(5 cases/60 sec)

     T  = 60 seconds

In 60 seconds,

Factory 1 produces:  

 (60 sec)(1 case/20 sec) = 3 cases

Factory 2 produces:

  (60 sec)(1 case/30 sec) = 2 cases

A total of 5 cases will be obtained if both factories manufacture for 60 seconds each.

=====

Factory 1:  (1 case/20 sec) or (20 cases/case)

Factory 2:  (1 case/30 secs) or (30 sec/case)

Answer: I’m assuming 160.

Step-by-step explanation: If x = 2:

using PEMDAS

(4(2))(5(2^2)) =

(8)(5(4)) =

(8)(20) = 160

20x^3

20(2^3)=

20(8) = 160

hope this helps

The equation that represents the function shown on the graph is (d) y = 4x

The graph that completes the question is added as an attachment

On the graph, we have the following ordered pairs

Line starts at (0. 0) and through (2, 8), (4, 16), then end at (5, 20)

These ordered pairs are

(x, y) = (0. 0), (2, 8), (4, 16), (5, 20)

The ordered pair (0, 0) implies that the line passes through the origin

This means that the equation can be represented as

y = Y/X * x

Where

(X, Y) = any of (2, 8), (4, 16), (5, 20)

So, we have

y = 8/2 * x

Evaluate the quotient

y = 4 * x

This gives

y = 4x

Hence, the equation is (d) y = 4x

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Answer: d

Step-by-step explanation:

yw

Answer:

6.3294✖️10^7

Step-by-step explanation:

To find the statdard form, you place the decimal after the largest unit, int his case 6.

Then you write down all the numbers except for "0".

This becomes:

6.3294

Then, you add the multiplying sign, and count how many digits are there after 6, and in this case, there are 7, so you add the power "7" after 10.

6.3294✖️10^7

Hope this helped!

Have a nice day:)

To solve this problem, we need to find the x-values where the curve intersects the x-axis, which occurs when y=0.
0=x²-2kx ,We can factor out an x: 0=x(x-2k) .So the x-intercepts are at x=0 and x=2k.

To find the value of k, we need to follow these steps:

Step 1: Find the points of intersection between the curve y = x^2 - 2kx and the x-axis.
To do this, set y = 0:
0 = x^2 - 2kx
x(x - 2k) = 0

This means that the curve intersects the x-axis at x = 0 and x = 2k.

Step 2: Determine the limits of integration.
Since we are looking for the region in the fourth quadrant, we will have limits 0 and 2k for our integration.

Step 3: Calculate the area using integration.
Area = ∫[0 to 2k] (x^2 - 2kx) dx

Step 4: Solve the integral.
Area = [1/3x^3 - kx^2] evaluated from 0 to 2k
Area = (1/3(2k)^3 - k(2k)^2) - (1/3(0)^3 - k(0)^2)
Area = (8k^3/3 - 4k^3)

Step 5: Set the area equal to 36 and solve for k.
36 = 8k^3/3 - 4k^3
36 = (8k^3 - 12k^3)/3
36 = -4k^3/3

Now, multiply both sides by 3 and divide by -4:
-108/-4 = k^3
27 = k^3

Take the cube root of both sides:
k = 3

The value of k is 3 (Option b).

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Answer:

4 hours and 30 minutes.

Step-by-step explanation:

270÷60=4.5

Answer:

4 1/2 hours (((:

Step-by-step explanation:

It will take approximately 15.78 years for the city's population to reach 131,000 people.

To calculate how many years it will take for the city's population to reach 131,000 people, we can use the formula for compound interest. The formula is:

A = P(1 + r/n)^(nt)

Where:
A is the final amount (131,000)
P is the initial amount (93,000)
r is the annual growth rate (4% or 0.04)
n is the number of times the interest is compounded per year (assuming it is compounded annually, so n = 1)
t is the number of years

Let's plug in the values:

131,000 = 93,000(1 + 0.04/1)^(1t)

Next, we simplify the equation:

1.408 = (1.04)^t

To solve for t, we need to take the logarithm of both sides of the equation. Let's assume we are using the natural logarithm (ln):

ln(1.408) = ln(1.04)^t

Using the logarithm property, we can bring down the exponent:

ln(1.408) = t * ln(1.04)

Now we can solve for t by dividing both sides of the equation by ln(1.04):

t = ln(1.408) / ln(1.04)

Using a calculator, we find that t is approximately 15.78.

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