The graphs of line a and b are shown in this coordinate grid
Match each line with it's equation. Drag each equation to the corresponding box for each line

Therefore, the mean salary paid to the office assistants in this company is $24,000.Answer: B. $24,000

A large company has offices in two locations, one in New Jersey and one in Utah. The mean salary of office assistants in the New Jersey office is $28,500. The mean salary of office assistants in the Utah office is $22,500. The New Jersey office has 128 office assistants and the Utah office has 32 office assistants. The mean salary paid to the office assistants in this company can be calculated by taking the weighted average of the mean salaries of the two offices.
Here's the formula to calculate the weighted average:
Weighted average = (weight1 × value1 + weight2 × value2) / (weight1 + weight2)
Where weight represents the number of data points, and value represents the mean salary of office assistants.
In this question, the weight of the New Jersey office is 128, and the weight of the Utah office is 32. The value of the New Jersey office is $28,500, and the value of the Utah office is $22,500.
Now let's plug in the values:
Weighted average = (128 × 28,500 + 32 × 22,500) / (128 + 32)
= (3,648,000 + 720,000) / 160
= 24,000

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The perimeter of the letter "T" is 22 inches.

Since the letter "T" is formed by placing two rectangles next to each other, its perimeter is the sum of the perimeters of the two rectangles minus the shared side.

The shared side will be the width of the rectangles, which is 2 inches.

The lengths of the rectangles are 4 inches each.

Let's calculate the perimeter:

Perimeter of the top rectangle = 2 * (length + width) = 2 * (4 + 2) = 12 inches

Perimeter of the bottom rectangle = 2 * (length + width) = 2 * (4 + 2) = 12 inches

Now, subtract the shared side (width) once:

Shared side = 2 inches

Total perimeter = (Perimeter of top rectangle + Perimeter of bottom rectangle) - Shared side

Total perimeter = (12 + 12) - 2 = 22 inches

So, the perimeter of the letter "T" is 22 inches.

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The probability of making a Type I error is represented by alpha (α), which is typically set to 0.05 in hypothesis testing. Therefore, if α = .05, the likelihood of making a Type I error is 5% at most.

What is hypothesis testing? Hypothesis testing, also known as statistical hypothesis testing, is a technique used to evaluate two hypotheses about a population using sample data. One hypothesis, known as the null hypothesis (H0), proposes that there is no significant difference between a population parameter and a sample parameter, whereas the other hypothesis, known as the alternative hypothesis (H1), suggests that there is a significant difference between a population parameter and a sample parameter.You might have made a Type I error, but the probability is only 5% at most is true if you complete a hypothesis test using α = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis, but the treatment actually has no effect. In the given situation, if the treatment actually has no effect, you might have made a Type I error, but the probability is only 5% at most. When the null hypothesis is rejected when it should not be, a Type I error occurs. The probability of making a Type I error is represented by alpha (α), which is typically set to 0.05 in hypothesis testing. Therefore, if α = .05, the likelihood of making a Type I error is 5% at most.

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Answer: x 3= 27/125

Step-by-step explanation:

The line of reflection is the y-axis

Reflection is a geometric transformation that involves flipping an object over a line or a plane, creating a mirror image of the original object.

When a figure or polygon is reflected over the y-axis, it means that each point in the original figure is moved to a new point with the same y-coordinate but a negated x-coordinate.

Here we have

Triangle DEF has vertices at D(−3, 5), E(−10, 4), and F(−11, 8).

Triangle D′E′F′ is the image of triangle DEF after a reflection.

After reflection, the vertice E′ is located at (10, 4).  

Here the x-coordinate of E, − 10 is changed to 10  

As we know when the figure is reflected over the y-axis the sign of the x coordinate will be changes  

Hence,

The line of reflection is the y-axis

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Answer:

25%

Step-by-step explanation:

U flipped a coin 12 times, it lands on tail 9 times. Now the probability of landing on head = 12-9

= 3

In percentage= 12\3 *100

=25%

Answer:

0.25%

Step-by-step explanation:

Thus, the least number of times the button need to be pressed is: red- 4 times, green 3 times and blue button 6 times.

The technique of expressing all numbers as the product of primes is known as prime factorization. So, let's take something like the number 20 as an example. It can be divided into two components. "Well, that's 4 times 5," we can respond. Observe that 5 is a prime number.

Given data:

The number formed as:

(x²) .(y³).(z)  ...eq 1

Number appeared on screen - 2592

Find the prime factors of 2592.

2592 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3

This can be written as:

2592 = 4² x 3³ x 2 x 3

2592 = 4² x 3³ x 6¹  .....eq 2

comparing eq 1 and 2

(x²) .(y³).(z)  =  4² x 3³ x 6¹  

x = 4, y = 3 and z = 6

Thus, the least number of times the button need to be pressed is: red- 4 times, green 3 times and blue button 6 times.

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The x-intercepts of the graphed function are:

(-2, 0), (-1, 0), (1, 0), and (2, 0)

For any function, we define the x-intercepts as the values of x such that y= 0, when we have a graph we can identify these values as the values of x at which the graph intercepts the x-axis.

Remember that the x-axis is the horizontal one, then, we can look at the graph and identifty the 4 x-intercepts, these are at the values of x:

x = -2

x = -1

x = 1

x = 2

Writting them in point notation, these are (-2, 0), (-1, 0), (1, 0), and (2, 0)

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Answer:

[tex]26 > n + 15[/tex]

[tex]11 > n[/tex]

[tex]n < 11[/tex]

Answer:

No, q=15 is not a solution to the inequality.

Step-by-step explanation:

As given, q=15. So, substituting is the best way to solve this problem.

Step 1: Substitute

[tex]\frac{15}{5}=3[/tex]

[tex]15-20=-5[/tex]

Step 2: Substitute values into inequality

[tex]3 < -5[/tex]

Equation is false since 3 is a bigger value than -5.

Hope this helps ya!

Answer:

8 7/15

Step-by-step explanation:

4/5 and 2/3 need to a a common denomenator

4/5*3 and 2/3*5 = 12/15 and 10/15 so 5 12/15 + 2 10/15= 7 22/15= 8 7/15

Answer:L x b

              98ft x 56ft =5488

                                  =5488 / $3.75= $1463.47

Step-by-step explanation: Play ground is more like a rectangle so we use the formula for the rectrectangle to get total area . A=Lxb

Divide  the total with the cost since it say each per sqr feet

A=lxb

98x56=5488

5488/3.75= 1463.47

To use the normal approximation for the confidence interval in the sampling distribution of the population proportion, the following conditions must be met:

If these conditions are met, then the distribution of the sample proportion can be approximated by a normal distribution with a mean of p and a standard deviation of sqrt(p*(1-p)/n).

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Full Question ;

The sampling distribution of the population proportion is based on a binomial distribution. What condition must be met to use the normal approximation for the confidence interval?

The distance between the two points (-8,-1) and (-8,4) is 5 units.

The distance formula is a mathematical formula used to find the distance between two points in a two-dimensional or three-dimensional coordinate system.

The distance between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be found using the distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, the two points are (-8, -1) and (-8, 4). Therefore, we can substitute the values into the formula:

d = √((-8 - (-8))² + (4 - (-1))²)

= √(0² + 5²)

= √(25)

= 5

Therefore, the distance between the two points is 5 units, so the answer is (B) 5.

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For the number of miles driven, Company A will charge less than Company B if x<y, where x is the number of miles driven for Company A and y is the number of miles driven for Company B. Therefore, the inequality is x<y.

When comparing two companies for their charges for a specific service, it is necessary to obtain a basic understanding of the charges for each company. You can make use of the inequality operator to check when one company will charge less than the other company.

To use the inequality operator, you'll need to calculate the differences between the two companies for the specific mileage. Let's assume that the mileage is represented by "m" and that the charge for company A is "cA" and the charge for company B is "cB".

If the question only provides specific numerical values for these variables, you can substitute them into the inequality formula. If you're given algebraic expressions, you'll need to simplify them before substituting them into the inequality formula.

The inequality formula for comparing the charges is as follows: cA < cB.

To use this formula, substitute the expression for each variable.

For example: 4m + 20 < 3.5m + 35 Now, you'll need to simplify the inequality by performing algebraic operations on both sides of the inequality. Begin by subtracting 3.5m from both sides of the inequality: 0.5m + 20 < 35.

Next, subtract 20 from both sides of the inequality: 0.5m < 15 Finally, divide both sides of the inequality by 0.5: m < 30

Therefore, Company A will charge less than Company B for any mileage less than 30.

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Answer: A and C

Step-by-step explanation:

angles in a triangle add up to 180

180 - 30 = 150

other two angles must add up to 150 and two of the angles have to be the same.

Since one is already 30, one of the others have to also be 30 or both of the others have to be the same.

A and C both add up to 150 and both of them have one angle repeating

Answer:

f(x) = x ³ shifted 4 units to the right will be g(x) = f(x-4) = (x - 4)³

Step-by-step explanation:

If a function f(x) is shifted right 4 units every x coordinate will become x - 4

g(x)  = f(x - 4) = (x - 4)³

The ship is about 65.6 meters away from the base of the lighthouse.

What is tangent function ?

Tangent is one of the three primary trigonometric functions, along with sine and cosine. In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.

The tangent function is denoted by "tan" and is defined mathematically as:

tan(theta) = opposite / adjacent

where theta is the angle, opposite is the length of the side opposite the angle, and adjacent is the length of the side adjacent to the angle.

According to the question:
We can use trigonometry to solve this problem. Let's draw a right triangle with the lighthouse at the top, the ship at the bottom, and the line connecting them as the hypotenuse. The angle of depression of 26° is the angle between the hypotenuse and the horizontal line passing through the lighthouse. We know the height of the lighthouse is 32 meters.

Let x be the distance between the ship and the base of the lighthouse, which is the adjacent side of the angle of depression. Then we can use the tangent function:

tan(26°) = opposite / adjacent

We know the opposite side is the height of the lighthouse, which is 32 meters. Solving for x:

x = opposite / tan(26°)

x = 32 / tan(26°)

x ≈ 65.6 meters

Therefore, the ship is about 65.6 meters away from the base of the lighthouse.

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To implement the distributing principle to the phrase 7(2x+5) - 4(2x+5), we must first divide the 7 and 4 within the parenthesis to their respective terms:

7(2x+5) - 4(2x+5) = (72x + 75) - (42x + 45)

Within the parenthesis, each term is simplified:

= (14x + 35) - (8x + 20)

We may now reduce the phrase by grouping similar terms:

= 14x - 8x + 35 - 20

= 6x + 15

As a consequence, using the distributive property on 7(2x+5) - 4(2x+5) yields 6x + 15.

By expansion or multiplying, the distribution principle is frequently employed to compress statements and solve problems. It enables us to translate complicated statements into shorter language and conversely. The distributive principle is commonly utilized in mathematics, mathematics, as well as other mathematical subjects.

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The 99% confidence interval for the true population mean textbook weight is (38.11, 39.89) ounces.

We can find the standard error (SE) by using the formula:

SE = σ/√n

Where

σ = population standard deviation = 2.8 ounces

n = sample size = 41

SE = 2.8/√41

SE = 0.436

Now we can find the confidence interval by using the formula:

CI = x ± z*SE

Where

x = sample mean = 39 ounces

z* = the z-value corresponding to the level of confidence of 99 percent

The z-value corresponding to the level of confidence of 99 percent can be found using the z-table or calculator. It is found to be 2.576.

CI = 39 ± 2.576*0.436

CI = (38.11, 39.89)

Therefore, we can say that we are 99% confident that the true population mean textbook weight is between the interval (38.11, 39.89) ounces.

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The probability that the second smallest integer from a set of six distinct integers is picked at random is the same as the probability that the first smallest is 1.

This can be expressed mathematically as:

P(second smallest) = P(first smallest).

The probability of the first smallest integer is the number of combinations that result in the first smallest number divided by the total number of possible combinations of six distinct integers.

For example, if we have six distinct integers in a set, A, B, C, D, E, and F, the probability of A being the first smallest is the number of combinations that result in A being the smallest divided by the total number of combinations.

The combinations that result in A being the smallest are {A, B, C, D, E, F}, {B, A, C, D, E, F}, {C, A, B, D, E, F}, and so on. That’s a total of 6 combinations out of the total possible number of combinations, which is 6 x 5 x 4 x 3 x 2 x 1 = 720.

Therefore, P(first smallest) = 6/720 = 1/120. Similarly, the probability of the second smallest number being the same is also 1/120.

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Based on the provided information The seller received a fee of $122.

The term "commission" describes the payment made to the staff member after they successfully complete a job, which is frequently marketing a predetermined quantity of goods or services. Selling goods or services is difficult. Sales and marketing professionals must contend with fierce rivalry.

The commission rules are defined by the following piecewise function:

c(p) = 0.10p, if p ≤ 1,000

c(p) = 0.15p - 50, if 1,000 < p ≤ 1,500

c(p) = 0.20p - 125, if p > 1,500

a. If the profit is $1,500, the commission rate is calculated using the second rule:

c(1,500) = 0.15(1,500) - 50 = 175

The commission rate is $175 / $1,500 = 0.1167, or approximately 11.67%.

b. If the profit is $900, the commission rate is calculated using the first rule:

c(900) = 0.10(900) = 90

The commission rate is $90 / $900 = 0.10, or 10%.

c. To find the commission on a car sold for a $970 profit, we need to determine which rule applies. Since 970 is less than 1,000, we use the first rule:

c(970) = 0.10(970) = 97

The commission on a car sold for a $970 profit is $97.

d. The profit on the car sale is calculated as follows:

profit = selling price - purchase price = $33,200 - $32,090 = $1,110

To determine the commission, we need to identify the appropriate rule based on the profit amount. Since $1,110 is greater than $1,500, we use the third rule:

c(1,110) = 0.20(1,110) - 125 = 122

The commission paid to the salesperson is $122.

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Answer:

3(2c + d) - 4(c - d) + d² = 32

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

We have to use,

→ d = 3

→ c = 1

The given expression is,

→ 3(2c + d) - 4(c - d) + d²

Let's simplify the expression,

→ 3(2c + d) - 4(c - d) + d²

→ 3(2(1) + 3) - 4(1 - 3) + 3²

→ 3(2 + 3) - 4(-2) + 9

→ 3(5) + 8 + 9

→ 15 + 17

→ 32 => {final answer}

Therefore, the answer is 32.

The approximate value of the maximum of the function is 2350. In terms of the problem scenario this means that the company will make a maximum daily profit of $2350.

Part A:

The y-intercept is the point where the graph intersects the y-axis, which is when x = 0. Therefore, we can find the y-intercept by substituting x = 0 into the equation:

P(0) = -[tex]6(0)^2[/tex] + 180(0) + 1000

P(0) = 1000

The approximate value of the y-intercept is 1000. In terms of the problem scenario, this means that when the company doesn't increase the price of the solar panels (x = 0), the daily profit is $1000.

Part B:

The x-intercept is the point where the graph intersects the x-axis, which is when P(x) = 0. Therefore, we can find the x-intercept by solving the equation:

-[tex]6x^2[/tex] + 180x + 1000 = 0

We can use the quadratic formula to solve for x:

x = (

where a = -6, b = 180, and c = 1000

x = (-180 ± sqrt([tex]180^2[/tex] - 4(-6)(1000))) / 2(-6)

x = (-180 ± sqrt(32400 + 24000)) / (-12)

x = (-180 ± sqrt(56400)) / (-12)

x ≈ 4.4 or x ≈ 29.4

The approximate value of the x-intercept is 4.4 (or 29.4). In terms of the problem scenario, this means that the company would need to increase the price of the solar panels by approximately $22 (or $147) in order to break even and not make a profit or loss for the day.

Part C:

The maximum of the function occurs at the vertex of the parabola, which is given by the formula:

x = -b / 2a

In this case, a = -6 and b = 180, so:

x = -180 / 2(-6) = 15

To find the maximum profit, we can substitute x = 15 into the equation:

P(15) = -[tex]6(15)^2[/tex] + 180(15) + 1000

P(15) = 2350

The approximate value of the maximum of the function is 2350. In terms of the problem scenario, this means that the company will make a maximum daily profit of $2350 when they increase the price of the solar panels by $75 (i.e., 15 increments of $5).

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Answer:

x = 79

Step-by-step explanation:

the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ BHC = x is an exterior angle of Δ BHD , then

x = 33 + 46 = 79

Answer:

79

Step-by-step explanation:

Using the formula

A=wl

Solving forl

l=A

w=5056

64=79m

To find area, you multiply the width by the length [tex]( \text{A} = \text{L} \times \text{W})[/tex]. Here, it is asking for the length, giving the area of the pool and the width. With this information, you can inverse operation ( division) to find the length of the pool. So:

[tex]5056 \div 64 = 79[/tex]

This tells us that the length of the pool is 79 meters. To check this answer, multiply 64 and 79. If it's equivalent to 5056, the given area, then 79 is indeed the length of the pool.

[tex]64 \times79 = 5056[/tex].

Thus, the length of the pool is 79 m.

Answer:22

Step-by-step explanation:

h + i3 = ?

19 + 1X3 = 22

Answer:

h + i3 = 22

Step-by-step explanation:

Given expression,

→ h + i3

→ h + 3(i)

Now we have to use,

→ i = 1

→ h = 19

Let's simplify the expression,

→ h + 3(i)

→ 19 + 3(1)

→ 19 + 3

→ 22 => {final answer}

Hence, the solution is 22.

The total number of units produced in an 8-hour day is approximately 22.86 units.

There are different ways to approach this problem, but one possible method is to use the concept of cycle time and the total available production time to determine the number of units produced in a day.

An operation is performed on a batch of 100 units.

Setup time is 20 minutes and run time is 1 minute.

The total number of units produced in an 8-hour day is:

Step 1: Find the cycle time per unitThe cycle time per unit is the sum of the setup time and the run time:

Cycle time = setup time + run time = 20 minutes + 1 minute = 21 minutes.

Step 2: Find the total available production time in a day

One day has 24 hours, but 8 hours are not available for production due to breaks, maintenance, and other factors. Therefore, the total available production time is:

Total available production time = 8 hours × (60 minutes per hour) = 480 minutes.

Step 3: Calculate the number of units produced in a day

The number of units produced in a day is the total available production time divided by the cycle time per unit:

Units produced = total available production time ÷ cycle time= 480 minutes ÷ 21 minutes≈ 22.86 units (rounded to two decimal places)

Therefore, the total number of units produced in an 8-hour day is approximately 22.86 units.

This assumes that there is no variability in the process, and that all units are of good quality.

If there are any defects, rework, or other disruptions, the actual production may be lower.

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