Identify the parent function.
A. Square root B. Cube root C. Absolute value D. Reciprocals

Answer: \(AB=4.7, BC=8.8, \angle C=28^{\circ}\)

Step-by-step explanation:

As angles in a triangle add to 180 degrees,

\(\angle C=180^{\circ}-90^{\circ}-62^{\circ}=\boxed{28^{\circ}}\)

We know that:

\(\sin 62^{\circ}=\frac{BC}{10}\\\\BC=10\sin 62^{\circ} \approx \boxed{8.8}\)

Similarly,

\(\cos 62^{\circ}=\frac{AB}{10}\\\\AB=10\cos 62^{\circ} \approx \boxed{4.7}\)

Answer: the last option is correct

Step-by-step explanation:Using the formulas for converting Cartesian coordinates to polar coordinates:

r = √(x^2 + y^2)

θ = atan2(y, x)

where x and y are the Cartesian coordinates, r is the distance from the origin to the point, and θ is the angle between the positive x-axis and the line connecting the origin to the point.

Given the Cartesian coordinates (x, y) = (-7√3/2, 7/2), we can substitute these values into the formulas:

r = √((-7√3/2)^2 + (7/2)^2)

θ = atan2(7/2, -7√3/2)

Simplifying the expressions:

r = √(147/4 + 49/4) = √(196/4) = √49 = 7

θ = atan2(7/2, -7√3/2)

Using a calculator or reference table to find the arctangent of 7/2 divided by -7√3/2, we get:

θ ≈ 5π/6

So the correct answer is: (7, 5π/6), which is option (6).

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

What is banquet?

A banquet is a large formal meal that usually involves multiple courses and is served to a group of people on special occasions such as weddings, awards ceremonies, or fundraising events. Banquets often include speeches, presentations, and entertainment, and are typically held in a large venue such as a hotel ballroom, banquet hall, or conference center. Banquets can be hosted for a variety of purposes, such as to honor a special guest, celebrate an achievement, or raise money for a charitable cause.

To create a graph showing the solution region of the system of inequalities representing the constraints of the situation, we can use custom relationships to define the variables and constraints.

Let's define the variables:

Let x be the number of adult guests.

Let y be the number of student guests.

Now, let's write the system of inequalities representing the constraints of the situation:

The total number of guests cannot exceed 125: x + y ≤ 125

The cost of hosting the banquet cannot exceed $3375: 45x + 15y ≤ 3375

To graph this system of inequalities, we can plot the boundary lines of each inequality and shade the region that satisfies all the constraints.

The boundary lines of each inequality are:

x + y = 125 (the line that connects the points (0, 125) and (125, 0))

45x + 15y = 3375 (the line that connects the points (0, 225) and (75, 0))

To find the viable combinations of guests that satisfy all the constraints, we need to shade the region that is below the line x + y = 125 and to the left of the line 45x + 15y = 3375.

The resulting graph should look like this:

The point where the two lines intersect, (75, 50), represents the maximum number of adult guests (75) and the maximum number of student guests (50) that can be invited to the banquet while staying within the budget and venue capacity. Any point within the shaded region represents a viable combination of guests.

We can label the point (75, 50) as the optimal solution for the banquet, as it represents the maximum number of guests that can be invited while staying within the constraints.

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Answer:

because 200 + 200 12 times is equal to 200 x 12Step-by-step explanation:

Answer:

Multiplication is a short way to write repeated addition. So 200 •12 means the same as 200 + 200 + . . . + 200.

Step-by-step explanation:

\(x7 - 2 \: or \: x \leqslant - 3\)

Answer:

Step-by-step explanation:

The vertex is the lowest point of the parabola.  The coordinates are:

(-3, -7)

Answer:

a) false, median is 1 for each store

b) false, median at store 2 is 1  

c) true

Step-by-step explanation:

To accurately determine the amount they would have to buy, we would need the specific measurements of the pool, the desired fence height and any other requirements they have.

To determine how much Gwen and Lisa would have to buy to replace the fence on their pool, we would need more specific information about the pool's dimensions, the type of fence they want, and any other relevant details.

Let's consider some factors that could affect the amount they would need to purchase:

Perimeter of the pool:

The length of the fence required would depend on the perimeter of the pool.

If we know the dimensions of the pool, we can calculate its perimeter by adding up the lengths of all sides.

Fence height:

The height of the fence is another important factor. Depending on local regulations or personal preferences, Gwen and Lisa might need a specific height for their pool fence.

This would determine the length of fencing material they need to purchase.

Fence type and style:

Different types of fences, such as chain-link, wood, vinyl, or wrought iron, have varying costs and installation requirements.

The choice of fence material and style will impact the amount they would have to buy.

Gates and openings:

If Gwen and Lisa require gates or openings in the fence, they would need to account for these as well.

The number and size of gates would affect the total amount of fencing material needed.

With these details, we can calculate the perimeter, account for gates and openings and factor in the material type and style to provide an estimate of the amount of fencing they need to purchase.

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The statement that "an estimated regression coefficient is statistically significant if it is statistically different from 1" is false.

When we say that an estimated regression coefficient is statistically significant, we mean that it is statistically different from zero, not from 1.

The reason for this is that the null hypothesis in a hypothesis test for a regression coefficient is typically that the true value of the coefficient is zero. Therefore, if we reject the null hypothesis and find that the estimated coefficient is statistically significant, we conclude that there is evidence to suggest that the coefficient is not equal to zero and therefore has a non-zero effect on the response variable.

In some cases, we may be interested in testing whether a regression coefficient is equal to a specific value, such as 1. However, this would be a different hypothesis test with a different null hypothesis, and the result of this test would not necessarily be related to whether the coefficient is statistically significant or not.

Therefore, the statement that "an estimated regression coefficient is statistically significant if it is statistically different from 1" is not accurate.

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The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Using the tangent ratio, the height of the lighthouse from the top of the cliff ≈ 161.2 meters.

For solving a right triangle, the tangent ratio that can be applied is: tan ∅ = opposite length / adjacent length.

Find the height of the light house and the cliff using the tangent ratio:

tan 51.3 = height/980

Height of lighthouse + cliff = (tan 51.3)(980)

Find the height of the cliff only using the tangent ratio:

tan 47.3 = height/980

Height of cliff = (tan 47.3)(980)

Height of the lighthouse from the top of the cliff = (tan 51.3)(980) - (tan 47.3)(980)

Height of the lighthouse from the top of the cliff ≈ 161.2 meters.

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Answer:

they are the same line

Step-by-step explanation:

if you divide the first line by 2 you'll get:

2(3x)+2y=2(23)===> 3x+y=23

Answer:

66

Step-by-step explanation:

CD means to multiply C*D

6*11

66

So the answer is 66

Answer:

0.7 pound per dollar

Step-by-step explanation:

To find the pounds per dollar, divide the number of pounds by the number of dollars:

560/800

= 0.7

So, the unit rate is 0.7 pounds per dollar

Answer:

y=(-1/4)x -6

Step-by-step explanation:

you have to use the equation y=mx+b where

m is the slope =rise /run and is negative because the line goes down from left to right m= -1/4 (take two points on the graph to see the change in y and x)

b is the y-intercept and from graph we see is -6

so the equation is y=(-1/4)x -6

The number of strides the runner will make during 1 hour run will be =

10,800.

To calculate the distance or number of strides made by the runner in an

hour, the graph given above is considered as follows;

The y-axis which represents the number of strides is plotted against the x-axis which is the number of hours.

From the graph

20 minutes= 3600 strides

60 minutes = X strides

make X the subject of formula;

x= 3600×60/20

= 216000/20

= 10,800

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Answer:

y = 1/2x + 2.5

Step-by-step explanation:

First we want to plug it into the \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\). This gets us 6-2/7-(-1) which solves to 4/8 which simplifies to 1/2. This gives us the slope. Now, when using slope intercept form y = mx + b, we can plug our newly found slope in for m and get y = 1/2x + b. To find b plug in any point on the line into the equation, I chose (7,6) because we are given that, and both numbers are positive. Now plug those in for x and y. 6 = 1/2(7). Solve, and get 2.5. are final equation is

y = 1/2x + 2.5

Answer:

A. 12 ft², 16 ft², and 20 ft²

Step-by-step explanation:

Answer:

y-intercept: -4, slope: -3/2 or -1.5

Step-by-step explanation:

The point where the line goes through the y axis has y coordinate of -4 so that is the y-intercept.

The line goes down 3 units every 2 units to the right. The slope is rise over run, so that makes the slope -3/2.

If we divide 300 into parts using the ratio 2:3:5, we get:

2 parts = 2/10 of the total ratio = 2/10 x 300 = 60

3 parts = 3/10 of the total ratio = 3/10 x 300 = 90

5 parts = 5/10 of the total ratio = 5/10 x 300 = 150

Therefore, 300 divided in the ratio 2:3:5 would result in three parts of 60, 90, and 150.

I hope I helped!

~~~Harsha~~~

Answer:

2.5

Step-by-step explanation:

We Know

You buy 4 5/8 blue fabric and 2 1/8 green fabric .

4 5/8 = 37/8 = 4.625 blue fabric

2 1/8 = 17/8 = 2.125 green fabric

How much blue than green did you buy?

We Take

4.625 - 2.125 = 2.5

So, you buy 2.5 blue more than green.

The given slope of the graph is explaining about the swimmer's lap completion throughout the time of 10 minutes.

In the given graph on the x-axis, we can find the time (in minutes) of 10 minutes.

On the y-axis, the graph represents the number of laps the swimmer is completing.

When we observe closely, the slope is giving very important information. At initial time=0, the no. of laps remaining for swimmer is 30. We can show this data clearly as below:

Number of laps remaining----------Time (in minutes)

30 --- 0

27 --- 1

24 --- 2

21 --- 3

18 --- 4

15 --- 5

12 --- 6

9 --- 7

6 --- 8

3 --- 9

0 --- 10

From the above slope data, we can conclude that for every 1 minute of time elapsing, the swimmer is completing 3 laps.  

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Answer:

-32

Step-by-step explanation:

Let the number be x.

\(2(x+8)=-48 \\ \\ x+8=-24 \\ \\ x=-32\)

Answer:

39.9 rounded to 40 degrees

Step-by-step explanation:

Answer:

the probability assignments for the x distribution can be computed using the binomial probability formula, with p = 0.26 and n = 5, and the results are shown in the table above.

Step-by-step explanation:

If approximately 26% of adults in the United States live with a disability, then the probability of a randomly selected US adult living with a disability is 0.26. We can use this probability to determine the probability of getting a certain number of adults out of five that live with a disability.

To do this, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where n is the sample size (in this case, 5), x is the number of adults with a disability, p is the probability of an adult having a disability (0.26), and (n choose x) is the binomial coefficient, which can be calculated as:

(n choose x) = n! / (x! * (n-x)!)

where ! denotes the factorial function.

 = 10 * 0.0676 * 0.4052

 = 0.211

The solution is, 0.211 is the probability assignments for the x distribution.

Here, we have,

the probability assignments for the x distribution can be computed using the binomial probability formula, with p = 0.26 and n = 5, and the results are shown in the table above.

now, we have,

If approximately 26% of adults in the United States live with a disability, then the probability of a randomly selected US adult living with a disability is 0.26. We can use this probability to determine the probability of getting a certain number of adults out of five that live with a disability.

To do this, we can use the binomial probability formula:

P(x) = (n choose x) * p^x * (1-p)^(n-x)

where n is the sample size (in this case, 5), x is the number of adults with a disability, p is the probability of an adult having a disability (0.26), and (n choose x) is the binomial coefficient, which can be calculated as:

(n choose x) = n! / (x! * (n-x)!)

where ! denotes the factorial function.

= 10 * 0.0676 * 0.4052

= 0.211

So, 0.211 is the probability assignments for the x distribution.

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The following statements which must be true is \(\lim_{x \to \1} _1\) f ( x ) = ∞.

Given :

the values f ( x ) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1.

Function :

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and a co - domain.

x sufficiently close to 1 means x → 1

but x ≠ 1.

so function = \(\lim_{x \to \1} _1\) f ( x ) = ∞

Therefore the following statements which must be true is \(\lim_{x \to \1} _1\) f ( x ) = ∞.

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Answer:

Statement:

Reason: Alternate Interior Angles

Statement

The monthly Payment for the loan is approximately $271.24.

To calculate the monthly payment for the loan, we can use the formula for calculating the monthly payment on an intermediate-term loan. The formula is:

Monthly Payment = (Loan Amount * Monthly Interest Rate) / (1 - (1 + Monthly Interest Rate)^(-Number of Months))

Given:

Loan Amount = $50,000

Interest Rate = 6.5% per year

Number of Years = 5

First, we need to convert the annual interest rate to a monthly interest rate. Since there are 12 months in a year, the monthly interest rate is:

Monthly Interest Rate = (6.5% / 100) / 12 = 0.00541667

Plugging in the values into the formula, we get:

Monthly Payment = ($50,000 * 0.00541667) / (1 - (1 + 0.00541667)^(-5 * 12))

              = $271.24

Therefore, the monthly payment for the loan is approximately $271.24.

The owners of the restaurant want to use the loan to renovate the kitchen and expand the dining room, which they expect will generate additional monthly revenue between $2,000 and $5,000.

If we assume a conservative estimate of $2,000 per month in additional revenue, the loan payment of $271.24 represents approximately 13.56% of the additional revenue. This means that the owners would still have a significant portion of the additional revenue available for other expenses or profit.

On the other hand, if we consider the higher estimate of $5,000 per month in additional revenue, the loan payment would represent only about 5.42% of the additional revenue, leaving a substantial amount of money for other purposes.

Considering these calculations, it appears that taking this loan is a smart business decision. The monthly payment is manageable and leaves a significant portion of the additional revenue for the restaurant's operation and potential profit. However, it is essential for the owners to ensure that the projected additional revenue is realistic and sustainable to cover the loan payment and other business expenses.

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Answer:

We know that the x-coordinate of point A is -11, and that the distance between point A and point B is 15 units. Let's call the y-coordinate of point A "y". Then we can use the distance formula to find the two possible values of y:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1,y1) = (-11,y) is the coordinates of point A, and (x2,y2) = (1,2) is the coordinates of point B. Substituting the values, we get:

15 = sqrt((-11 - 1)^2 + (y - 2)^2)

15 = sqrt(144 + (y - 2)^2)

15^2 = 144 + (y - 2)^2

225 = 144 + (y - 2)^2

81 = (y - 2)^2

y - 2 = ±9

y = 2 ± 9

So the possible coordinates of point A are (-11,11) and (-11,-7).