A civil patrol unit of 15 members includes 4 officers. In how many ways can 3 members be selected for a search and rescue mission such that at least 1 officer is included?

Answer:

Mean-27

Step-by-step explanation:

Add all of the numbers and it equals 162

Then divide 162 by the amount of numbers presented.

Since there are 6 numbers listed we divide by 6

162/6=27

The area of triangle LMN is 49.61 square units.

We have,

To find the area of triangle LMN.

Area = (1/2) x base x height

where the base and height are the sides of the triangle perpendicular to each other.

First, we need to find the length of side L.

We can use the Law of Cosines.

L² = M² + N² - 2MNcos(132°)

L² = 6² + 8.3² - 268.3cos(132°)

L² = 36 + 68.89 + 99.36

L² = 204.25

L = √204.25

L = 14.28

Now that we know the length of the base of the triangle, we can find the height by dropping a perpendicular from vertex M to side LN.

Since triangle LMN is obtuse, the perpendicular will fall outside of the triangle.

Let's call the foot of the perpendicular point P.

Since M∠M is 132°, we can find the measure of the acute angle ∠LMP:

M∠LMP = 180° - M∠M

M∠LMP = 180° - 132°

M∠LMP = 48°

We can use trigonometry to find the length of MP:

tan(48°) = h/6

h = 6 x tan(48°)

h = 6.93

The area of triangle LMN is:

Area = (1/2) x base x height

Area = (1/2) x 14.28 x 6.93

Area ≈ 49.61

Thus,

The area of triangle LMN is 49.61 square units.

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Answer:d

Step-by-step explanation:

Taxes and transfers are used by the government to more equitably share revenue. A Medicaid participant typically receives $1500 in benefits.

We know that,

Medicare is a health insurance program for seniors, disabled individuals under 65, and dialysis patients. Medicaid is a program that provides financial aid for low-income patients' medical costs.

The federal government and the states share funding for the Medicaid program. The amount that the federal government reimburses states for program costs is known as the Federal Medical Assistance Percentage, or FMAP (FMAP).

Spending on Medicaid is mostly targeted at the elderly and those with disabilities. Despite accounting for over two-thirds of Medicaid spending, seniors and individuals with disabilities make up one in four beneficiaries, which reflects the high per-enrollee expenses for both acute and long-term care.

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The equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.

Let x be the number of credits the student had before starting college, and let y be the number of credits the student takes each semester. We can use this information to write an equation that represents the number of credits the student has earned after t semesters.

After 2 semesters, the student had 39 credits, which means the student earned 2y + x credits in those two semesters. Similarly, after 5 semesters, the student had 75 credits, which means the student earned 5y + x credits in those five semesters.

Using this information, we can write the following equation:

C(t) = yt + x

where C(t) represents the number of credits the student has earned after t semesters.

We know that C(2) = 2y + x = 39 and C(5) = 5y + x = 75. We can use these two equations to solve for x and y:

2y + x = 39

5y + x = 75

Subtracting the first equation from the second equation gives:

3y = 36

Therefore, y = 12, which means the student takes 12 credits each semester. Substituting y = 12 into either of the two equations above gives x = 15, which means the student had 15 credits before starting college.

Thus, the equation that represents the number of credits the student has earned after t semesters is C(t) = 12t + 15.

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The formula for the nth term of the geometric sequence is given as follows:

[tex]a_n = 7(-3)^{n - 1}[/tex]

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio q.

The formula for the nth term of the sequence is given as follows:

[tex]a_n = a_1q^{n-1}[/tex]

The first term of the sequence is given as follows:

[tex]a_1 = 7[/tex]

Each term is the previous term multiplied by -3, hence the common ratio is given as follows:

q = -3.

Thus the formula for the sequence is given as follows:

[tex]a_n = 7(-3)^{n - 1}[/tex]

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Answer: The region of the graph that contains the solution set of the system of linear equalities y ≤ 1/2x+3 y≥ 2x-2 is the area bounded by the two lines and the x-axis.

Step-by-step explanation:

Answer:

33

Step-by-step explanation:

To solve for the range, simply subtract the largest-value term from the smallest-value term. First, set all numbers from least to greatest:

14 , 23 , 28 , 36 , 40 , 42 , 47

The smallest term is 14.

The largest term is 47.

Subtract 47 with 14:

[tex]47 - 14 = 33[/tex]

The given range value will be 33.

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Krell's equity cost of capital, or expected total return, is 5.57%.

We have,

The dividend yield is the annual dividend divided by the current share price:

Dividend yield

= Annual dividend / Share price

= $0.98 / $22.08 = 0.0444 = 4.44%

The equity cost of capital is the expected total return on the stock, which includes both the dividend yield and the expected capital appreciation:

Equity cost of capital = Dividend yield + Capital Appreciation

= 4.44% + [(24.98 - 22.08) / 22.08]

= 4.44% + 0.1314

= 5.57%

Therefore,

Krell's equity cost of capital, or expected total return, is 5.57%.

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Answer:

True

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Every number has multiple qualities beyond its distance from zero. Some of the qualities of a number include its sign (positive or negative), its magnitude (Absolute Value), its parity (whether it is even or odd), and its relationship to other numbers (greater than, less than, or equal to). Additionally, numbers can have properties such as being prime or composite, rational or irrational, and real or complex. Therefore, a number is characterized by more than just its distance from zero.

The resultant of the two vectors or the sum of the two vector is equal to the diagonal of parallelogram.

Parallelogram law of vector addition states that if two vectors are represented in magnitude and direction by the adjacent sides of a parallelogram, the diagonal of the parallelogram drawn from the point of intersection of the vectors represents the resultant vector in magnitude and direction.

For the given vector a, and vector, the resultant of the two vector is calculated as;

-----------> a  and --------------->b = a + b

The diagram represents the addition of the two vectors, a and b;

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Where the information relating to the circle and its diameter are given, the equation of the circle would be: "(x  5)²  + y2 = 81" (Option B)

The above is determined by the standard form equation of a circle which is:

(x- h) ² + (y - k)² = r²

Here,

(h, k)  is the center of the circle and r   is the radius

In this case, the center is (-5 , 0) and the diameter is 18, so the radius is half the diameter, whic is 18/ 2 = 9

So making the required substitutions, the expression becomes:

(x-(-5))² + (y-(0))² = 9²

Which becomes

(x  5)²  + y2 = 81

Thus, it is correct to state that Option B is the equation of the circle.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

The center of a circle is at (-5, 0), and the diameter of the circle is 18. Which of the following is the equation of the circle?

A. (x  5)²  + y = 9

B. (x  5)²  + y2 = 81

C. (x  5)²  + y2 = 9

D. (x  5)²  + y2  81

The angle measures for the triangles are given as follows:

Similar triangles are triangles that share these two features listed as follows:

The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of angle Z is given as follows:

m < Z + 20 + 105 = 180

m < Z + 125 = 180

m < Z = 55º.

Hence the measures are given as follows:

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The area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.

Given that, the dimensions of rectangular flower bed are length= 6 feet and  width = 4 feet.

Dimensions of large rectangle are Length = 6+2x and width = 4+2x

Now, area of large rectangle = (6+2x)×(4+2x)

= 24+8x+12x+4x²

Area of a rectangular flower bed = 6×4

= 24 square feet

Tulips and Daisy have same area to plant

So, the equation is 24+20x+4x²=24

4x²+20x=0

Therefore, the area of a flower bed is 24 square feet and the equation to represent the equal area is 24+20x+4x²=24.

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Reflecting the triangle Q over the line y = 1 would map it onto triangle T

Reflection over line x = 1

This means that we draw a vertical line that passes through x = 1

And then we create a triangle that is a mirror of the triangle P across the reflection line

The reflection of the triangle is attached

Reflection over line y = 2

This means that we draw a vertical line that passes through y = 2

As done in part (a), we then create a triangle that is a mirror of the triangle P across the reflection line

The reflection of the triangle is also attached

Using the same transformation rule above;

A reflection over the line y = 1 would map the triangle Q onto triangle T

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The x-intercept will be (5/3, 0) and the y-intercept will be (0, -5/2).

The x-intercept of an equation is the point at which the graph of the equation intersects the x-axis, which means that the y-coordinate of that point is 0. To find a x-intercept, we can set y = 0 in equation and solve for x.

Given the equation: 3x - 2y = 5

Setting y = 0, we get;

3x - 2(0) = 5

3x = 5

x = 5/3

So, the x-intercept is (5/3, 0).

The y-intercept of an equation is the point at which the graph of the equation intersects the y-axis, which means that the x-coordinate of that point is 0. To find y-intercept, we can set x = 0 in equation and solve for y.

Setting x = 0, we get;

3(0) - 2y = 5

-2y = 5

y = -5/2

So, the y-intercept is (0, -5/2).

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The range of the repairs to the cars is 241.

The sample variance is 11, 671.33

The sample standard deviation would be 108.03.

Range = Maximum repair cost - Minimum repair cost

= 456 - 215

= 241

Find mean :

= (422 + 456 + 401 + 215) / 4

= 373. 5

Sample variance :

= Sum of ( each repair cost - mean ) ² / (Number of cars - 1)

= ( 2, 340.25 + 6, 812.25 + 756.25 + 25, 105.25 ) / ( 4 - 1 )

= 11, 671. 33

Sample standard deviation:

= √sample variance

= √11, 671. 33

= 108. 03

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Answer:

I can explain how the relationship between the amount of money the painter earns and the number of rooms he paints can be represented in a graph.

The amount of money the painter earns depends on the number of rooms he paints. The painter charges $25 for each room he paints, so the amount of money he earns can be calculated by multiplying the number of rooms painted by $25. However, he also has to pay $100 for supplies regardless of the number of rooms painted.

Therefore, the relationship between the amount of money the painter earns and the number of rooms painted is a linear function, where the y-intercept (when no rooms are painted) is -$100 and the slope (how much he earns per room painted) is $25. This relationship can be represented in a graph as a straight line with a positive slope that intersects the y-axis at -$100.

I hope this helps

Option C is the correct graph for the given condition.

Graphs are a not unusual place technique to visually illustrate relationships withinside the statistics. The reason for a graph is to provide statistics that are too severe or complex to be defined appropriately withinside the textual content and in much less space.

Let's assume that the number of rooms painted is represented by the variable "x". The cost of painting x rooms can be calculated using the following equation:

Cost = 100 + 25x

The $100 is a fixed cost for the supplies, and the $25 is the cost per room painted. The variable "x" represents the number of rooms painted, which can vary.

We can draw a graph of this equation by plotting points for different values of "x" and connecting them with a straight line. For example:

We can continue this process to find additional points, and then plot them on a coordinate grid. Here's what the graph might look like:

The line passes through the point (0, 100), which is the y-intercept. As we move to the right along the x-axis (increasing the number of rooms painted), the cost increases at a constant rate of $25 per room. The slope of the line is therefore 25.

The equation for the line is in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. In this case, we have:

Cost = 25x + 100

This equation gives us the cost of painting x rooms, where x can be any non-negative integer.

The correct graph is option C

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Yes, The given graph is shows a function.

And, Range = {y | y ≥ - 2}

Domain = (- ∞ , ∞)

We have to given that;

the graph is shown in image.

Now, We can check the graph is a function or not by vertical line test.

Hence, By vertical line test it's shows the function as it cut at one point for each value of y.

Thus, The given graph is shows a function.

Since, The set of all inputs of the function is called Domain of set.

Hence, We get;

Domain = (- ∞ , ∞)

And, The set of all outputs of the function is called range of set.

Hence, We get;

Range = {y | y ≥ - 2}

Thus, Yes, The given graph is shows a function.

And, Range = {y | y ≥ - 2}

Domain = (- ∞ , ∞)

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Answer:

To find the area of the rectangle BCDE, we can use the formula:

Area = length x width

First, we need to find the length and width of the rectangle.

The length of the rectangle is the distance between points B and C, which can be calculated using the distance formula:

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

= sqrt((-6 - (-9))^2 + (-8 - (-4))^2)

= sqrt(3^2 + (-4)^2)

= sqrt(9 + 16)

= sqrt(25)

= 5

The width of the rectangle is the distance between points C and D:

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

= sqrt((10 - (-6))^2 + (4 - (-8))^2)

= sqrt(16^2 + 12^2)

= sqrt(256 + 144)

= sqrt(400)

= 20

Since BCDE is a rectangle, the length and width are perpendicular. Therefore, the area of the rectangle can be calculated by multiplying the length and width:

Area = length x width = 5 x 20 = 100

Therefore, the area of BCDE is 100 square units.

Step-by-step explanation:

Answer:

260

Step-by-step explanation:

The z score for a normal distribution is given by the formula
[tex]z = \dfrac{X-\mu}{\sigma}[/tex]

where
X is the data point, μ is the mean and  σ is the standard deviation

Given

Mean μ = 500
Standard deviation σ = 80
z-score = -3

and plugging in these values for z-score formula we get

[tex]-3 = \dfrac{X -500}{80}[/tex]

==>
-240 = X - 500
-240 + 500 = X

260 = X

or

X = 260

Answer:

The nearest tenth, Container A is about 46.3% full after the pumping is complete.

Step-by-step explanation:

To solve this problem, we need to find the volume of water in Container A and compare it to the volume of Container B.

The volume of water in Container A can be found using the formula for the volume of a cylinder:

V_A = πr^2h = π(6^2)(9) = 324π cubic feet

The volume of Container B can also be found using the same formula:

V_B = πr^2h = π(5^2)(12) = 300π cubic feet

After the water is pumped from Container A to Container B, Container B will be completely full, which means it will contain 300π cubic feet of water. To find the height of the water level in Container A, we need to find the height of the cylinder that would contain 300π cubic feet if it had a radius of 6 feet:

V_A' = πr^2h' = 300π

h' = 300/(36π) = 25/6 feet

So the height of the water level in Container A is 25/6 feet. Since the height of Container A is 9 feet, the percent of Container A that is full is:

(25/6) / 9 * 100% ≈ 46.3%

Therefore, to the nearest tenth, Container A is about 46.3% full after the pumping is complete.

Making x as a subject, we get equation as x=(y+2)/5.

The given equation is y=5x-2.

To make x as the subject

y+2=5x

x=(y+2)/5

Therefore, making x as a subject, we get equation as x=(y+2)/5.

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"Your question is incomplete, probably the complete question/missing part is:"

Rearrange the formula to make x the subject y=5x-2.

The data set that best describes the histogram is

(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)

We have,

The histogram shows that there are different intervals on the x-axis, and for each interval, there is a corresponding frequency on the y-axis.

From the given data, we can see that there are more passengers in the 11 to 20 interval than in the 1 to 10 interval, and so on.

Looking at the answer choices, we need to choose the data set that matches the histogram.

The first step is to check if the data set has the same range as the histogram.

The histogram has intervals from 1 to 10, 11 to 20, 21 to 30, 31 to 40, and 42 to 50.

Now,

The first answer choice has numbers less than 1 and greater than 50, so it cannot be the correct choice.

The second answer choice has a range from 4 to 42, which matches the histogram.

We can check if the frequencies in the data set match the heights of the bars in the histogram.

For example, the histogram has a bar for the 11 to 20 interval that stops at 4, which means there are 4 passengers in that interval.

The second data set has 4 passengers in the 11 to 20 interval, so it matches.

We can do the same for the other intervals and find that the second data set matches the histogram.

Therefore,

The data set that best describes the histogram is

(4, 7, 11, 13, 14, 19, 22, 24, 26, 27, 29, 31, 33, 35, 36, 38, 40, 42, 42, 42)

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The solution set for the given equation is 25.

In Mathematics and Geometry, a square root function is a type of function that typically has this form f(x) = √x, which basically represent the parent square root function i.e f(x) = √x.

Next, we would determine the solution set for the given equation by translating the word problem into an equation and then divide both sides of the square root function as follows;

-√x = 5

√x = -5

By taking the square of both both sides of the square root function, we have:

x = (-5)²

x = 25

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Determining if the proportion is true. If is not true and correcting the error v/x = x/v+w is: B. false, it should be  w/x = x/v+w.

In order for us to know whether the proportion v/x = x/v+w is true or not we need to cross multiply and simplify both sides:

v(x + v + w) = x^2

Expand the left-hand side:

vx + v^2 + vw = x^2

Subtract vx from both sides:

v^2 + vw = x^2 - vx

Factor out v on the left-hand side and x on the right-hand side:

v(v + w) = x(x - v)

Divide both sides by (v + w)x:

v/(v + w) = x/(x - v)

Therefore the correct option is B.

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Based on the rate of change, the total charge will be $ 12.60 in 4 days

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

Rate of change of investment = $3.15

Value of the investment = $12.60

Using the above as a guide, we have the following:

Number of days = Value of the investment/Rate of change of investment

Substitute the known values in the above equation, so, we have the following representation

Number of days = 12.60/3.15

Evaluate

Number of days = 4

Hence, the number of days is 4

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Answer: x < 5, see attached

Step-by-step explanation:

     To solve for x, we will isolate the given variable.

Given:

  [tex]\displaystyle 1 > \frac{x}{5}[/tex]

Multiply both sides of the equation by 5:

  [tex]\displaystyle5 > x[/tex]

Flip equation:

  [tex]\displaystyle x < 5[/tex]

     To graph, we will first plot a point on 5 with an open circle. Then, we will shade to the left since x is less than 5. See attached.