The drama club has 25 members and needs to elect officers. they will need a president, vice president, secretary, and treasurer. how many ways can a 4-member committee be formed?
a. 100
b. 2,435
c. 12,650
d. 303,600

Answer:

I think the answer is 7x+ 6a

Step-by-step explanation:

3 (x - 6) + 5 (a + 1) - 2 (4x + 2)

3 (-6x) + 5 (1a) -2 (6x)

3x + 6a + 4x

= 7x+ 6a answer!

Answer:

Where's the problem?

Step-by-step explanation:

Answer: 11

Step-by-step explanation:

4d-7

+7 +7

11d

11=d

Your welcome!

Answer:

84

Step-by-step explanation:

add em all together

Answer:

A.indicatint that the poem is about everyday events.

Step-by-step explanation:

This indicates that the poem is about everyday events. Thus the option A is cprrect.

The words of the poem tell us about the ordinary moring functions and way its indicated speaks about the everyday routine work that the author had to go through. Since the poem sets in moring routing it tells about the ordinary household chores and work.

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Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

Answer: The correct answer would be F. Half the students drank from 78 to 114 fluid ounces.

Step-by-step explanation:

The statement best describes the data represented in the box plot half the students drank from 78 to 114 fluid ounces. The correct option is F.

A rectangle is created to represent the second and third quartiles, normally with a vertical line inside to indicate the median value, in a simple way of presenting statistical data on a plot.

Given that students recorded the amount of liquid in fluid Ounces each of them drank In one day. The box plot shows the summary of the results. Amount of Liquid (fluid Ounces).

The highest and the lowest limit of the box plot is range from 78 to 114. The statement best describes the data represented in the box plot half the students drank from 78 to 114 fluid ounces.

Therefore, the correct option for the box plot will be F.

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If sentence 6 states that ¬C is true, and sentence 7 presents a conditional statement with C as the antecedent and Q as the consequent, we can use modus ponens to infer that Q is false.

Modus ponens is a deductive reasoning rule that allows us to derive a conclusion from a conditional statement and its antecedent. Therefore, we can apply modus ponens to sentence 7 given that we know ¬C from sentence 6.
Since from sentence 6 we know ¬C, we can apply modus ponens to sentence 7. To do this, follow these steps:
1. Identify the premises: One premise is sentence 6, which states ¬C. The other premise should be a conditional statement, such as "If ¬C, then P" (replace P with the relevant proposition).
2. Apply modus ponens: Modus ponens is a rule of inference that allows us to deduce a conclusion from the given premises. If we have the premises "If ¬C, then P" and "¬C", we can conclude "P" using modus ponens.
3. State the conclusion: After applying modus ponens, we can conclude "P" based on the given premises, which include sentence 6 (¬C) and the conditional statement.

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Answer:

1cm = 60 miles

.5cm = 30 miles

Step-by-step explanation:

divide 270 by 4.5

Answer: just graph it using the x and y coordinate points

Step-by-step explanation:

Answer:

(-4, -2)

Step-by-step explanation:

Rewrite the equations to make y the subject, so that it's easier to calculate the points on each line:

Equation 1

x - y = -2

⇒ x + 2 = y

⇒ y = x + 2

Equation 2

2x - 3y = -2

⇒ 2x + 2 = 3y

⇒ y = (2/3)x + 2/3

Calculate 2 points on each line:

Equation 1  (blue line on attached graph)

Substitute x = 0 and x = -2 into Equation 1 to create 2 points:

x = 0:   y = 0 + 2  ⇒ (0, 2)

x = -2:   y = -2 + 2  ⇒ (-2, 0)

Plot the points and draw a line through them.

Equation 2 (red line on attached graph)

Substitute x = 2 and x = -1 into Equation 1 to create 2 points:

x = 2:   y = (2/3)(2) + 2/3  ⇒ (2, 2)

x = -1:   y = (2/3)(-1) + 2/3  ⇒ (-1, 0)

Plot the points and draw a line through them.

Solution

The solution is the point where the two lines intersect.

Therefore, the point of intersection is (-4, -2)

Answer:

I just to the test

It D: 8x=64

Answer:

D: 8x = 64

Step-by-step explanation:

($8) equals the amount he makes for washing 1 car

($64) is the total amount Zane has made from washing cars

(X) is equal to how many cars he has washed for the total to be $64

Now, all we have to do is write down an equation that shows how we can find how many cars have been washed for him to get his sum of $64.

8 times x (x is equal to the number of cars he's washed) so 8 times something (or x) gives you the amount of money Zane has made which would be the only viable answer to the question.

8 - x = 64 - Incorrect

You would not be subtracting the amount of cars Zane has washed by the amount of money he is making per car.

64x = 8 - incorrect

This would mean you're multiplying the total amount of money Zane has made, by how many cars he's washed, which then equals the amount he makes per car. Doesn't make sense ik.

8 + x = 64 - incorrect

While this could look like a viable answer to what they're asking, don't be tricked. You have to multiply the number of cars Zane has washed by the amount he makes per car, otherwise you would just be adding 8 plus the number of cars he washed which does not equal $64.

Hope this helped:)

Answer:

answer is D

Step-by-step explanation:

window seat and the front are 8/12 which simplifies to 2/3. hope it helps

Answer:

2/9 is the probability that the passenger wants a window seat in the front of the plane

explainatio:

8 people want that particular seat and there are 36 passengers on the plane so 8/36= 2/9

The equation of the line is y = one-third x + 2. Option C

To determine the equation of a line, we need to know that the general equation of a line is expressed as;

y = mx + c

This is so such as the parameters are;

From the information given, we have;

Slope, m = y₂- y₁/x₂- x₁

Substitute the values

m = 4 - 2/6 - 0

m = 2/-6

m = -1/3

Then, for c, we have;

2 = 0(-1/3) + c

expand the bracket

c = 0

Equation of line ; y = -1/3x + 2

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The value of p(0 ≤ z ≤ 1.37) is approximately 0.41 (rounded to 2 decimal places).

What is Probability ?

Probability is a branch of mathematics that deals with the study of the likelihood or chance of an event occurring. It is the measure of the likelihood that a particular event or set of events will occur.

To find the value of p(0 ≤ z ≤ 1.37) using Appendix C-1, we need to locate the row containing 0.1 in the far-left column and the column containing 0.37 in the top row.

Starting with the row containing 0.1 in the far-left column, we can locate the value closest to 1.3 in the row, which is 1.37. Moving along the row to the right, we can find the corresponding value of the cumulative distribution function (CDF) for this value of z, which is 0.9147.

Next, we need to find the column containing 0.37 in the top row. The closest value in the column is 0.3707. Moving down the column to the row containing the CDF value we just found, we can read off the value of the CDF for z = 0, which is 0.5000.

To find the value of p(0 ≤ z ≤ 1.37), we subtract the CDF value for z = 0 from the CDF value for z = 1.37:

p(0 ≤ z ≤ 1.37) = 0.9147 - 0.5000 = 0.4147

Therefore, the value of p(0 ≤ z ≤ 1.37) is approximately 0.41 (rounded to 2 decimal places).

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The polynomials are in standard form is x2 + 3x + 2, 3t3 + 3t2 + 2t 14

The standard form of a polynomial is expressed by writing the highest degree of terms first then the next degree and so on. The standard form of polynomial is given by, f(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + aₙ₋₂xⁿ⁻² .....a₁x + a0, where x is the variable and ai are coefficients.

In the given options, when we analyse

x2 + 3x + 2 is given in standard form that is x2 + 3x + 2

15q 12q2 is not present in standard form

3t3 + 3t2 + 2t 14  is given in standard form

Therefore, the polynomials are in standard form is x2 + 3x + 2, 3t3 + 3t2 + 2t 14

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The given function 9(x) = - for Ve + 1 de appears to be incomplete or contains typographical errors, making it difficult to accurately determine the derivative. Please provide the complete and correct function for me to assist you in finding its derivative using the fundamental theorem of calculus.

Before we delve into the proof, a couple of subtleties are worth mentioning here. First, a comment on the notation. Note that we have defined a function,  F(x)

, as the definite integral of another function,  f(t)

, from the point a to the point  x

. At first glance, this is confusing, because we have said several times that a definite integral is a number, and here it looks like it’s a function. The key here is to notice that for any particular value of  x

, the definite integral is a number. So the function  F(x)

 returns a number (the value of the definite integral) for each value of  x

Second, it is worth commenting on some of the key implications of this theorem. There is a reason it is called the Fundamental Theorem of Calculus. Not only does it establish a relationship between integration and differentiation, but also it guarantees that any integrable function has an antiderivative. Specifically, it guarantees that any continuous function has an antiderivative.

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19.9 miles οf displacement will separate the starting lοcatiοn frοm the destinatiοn during the drive.

The shοrtest path an οbject can take tο get frοm οne place tο anοther is referred tο as "displacement". Tο put it simply, it is regarded tο be the mοdificatiοn οf an οbject's lοcatiοn. Its size and οrientatiοn create a vectοr quantity.

As per the supplied infοrmatiοn inside the questiοn,

Driving nοrth fοr six miles, turn right, and cοntinue riding fοr anοther 19 kilοmeters.

Hence, Pythagοras' Theοrem will result in the fοllοwing displacement frοm the initial pοint:

h² = 6² + 19²

h = √36 + 361

19.9 miles per hοur.

As a result, 19.9 miles will separate the starting lοcatiοn.

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Answer: x = 18

Step-by-step explanation:

1) 100% - 54.5% = 45.5%.

2) 45.5/100 = 0.455.

3) 0.455 * X = 8.19g.

4) x = 8.19/0.455.

5) x = 18.

Answer:

Step-by-step explanation:

you make y2-y1 over x2-x1 with the points so -13-5 over -12- -6 and that equals -18 over -6 simplified to 3

Answer:

Two walls are 6*2

Multiply, add the products, round UP and multiply times 6.

NOTE: Why round up? because if you need, for example, 1.22 gallons, you have to get 2 gallons. If you buy just 1 you'll be short, and you can't buy 0.22 of a gallon.

The remainder when N is divided by 1000 is 106.

The Principle of Inclusion-Exclusion, often known as PIE, offers a method/formula for organizing information about the size of each set, the number of elements in the union of a given set of sets, and the size of all potential set intersections.

From the question,

First, we think about all the possible divisions of the 7×1 board. Since we require at least one tile of each color, we exclude the cases of just one or two pieces.

Three pieces = 5+1+1 , 4+2+1 , 4+1+2 etc (6C2) = 15 ways

Four pieces = 6C3 = 20

Five pieces = 6C4 = 15

Six pieces = 6C5 = 6

Seven pieces =6C6 = 1

Now, we apply the Principle of Inclusion-Exclusion to consider how many ways to color them:

Three pieces : 3³ - 3 × 2³ + 3 = 6

Four pieces: 3⁴ - 3 × 2⁴ + 3 = 36

Five  pieces : 3⁵ - 3 × 2⁵ + 3 = 150

Six pieces : 3⁶ - 3 × 2⁶ + 3 = 540

Seven pieces : 3⁷ - 3 × 2⁷ + 3 = 1806

Adding them together, we get

15×6 + 20×36 + 15×150 + 6×540 + 1×1806 = 8106

Hence, the remainder when it is divided by 1000 is 106.

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Answer:

106

Step-by-step explanation:

The amount earned is $88,709.68

It is a payroll tax that is paid on wages earned by employees.

We have,

We will assume the current Social Security tax rate for employees as 6.2%.

Now,

The amount earned.

= 5,500 / 6.2%

= 5500 / 0.062

= $88,709.68

Thus,

The amount earned is $88,709.68

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Answer:

BD=141

Step-by-step explanation:

BD=2x+5

BD+12+27=180

BD+39=180

BD=141

Answer:

BD = 13

Step-by-step explanation:

AC is an angle bisector and divides the opposite into segments that are proportional to the other 2 sides, that is

\(\frac{AB}{AD}\)  = \(\frac{BC}{DC}\) , substitute values

\(\frac{12}{27}\) = \(\frac{x}{x+5}\) ( cross- multiply )

27x = 12(x + 5)

27x = 12x + 60 ( subtract 12x from both sides )

15x = 60 ( divide both sides by 15 )

x = 4

Thus

BD = x + x + 5 = 2x + 5 = 2(4) + 5 = 8 + 5 = 13

D: C(25, 20) - C(13,7)  represents the number of ways a total inventory of twenty batteries be distributed among the six different types.

To find the total number of ways to distribute the twenty batteries among the six different types, we need to use the stars and bars method. Using this method, the number of ways to distribute 20 batteries among 6 different types is C(20 + 6 - 1, 6 - 1) = C(25, 5).

However, since we have only 12 A7b batteries, we need to subtract the cases where we distribute more than 12 A7b batteries. To do this, we calculate the number of ways to distribute the remaining 8 batteries among the 5 types other than A7b, which is C(8+5-1, 5-1) = C(12,4). Therefore, the total number of ways to distribute 20 batteries among the six different types while keeping at least 12 A7b batteries is C(25, 5) - C(12, 4) = C(25, 20) - C(13, 7).

The correct answer is option D.

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Answer:

The graph touches the x axis at x = 0 and crosses the x axis at x = 5 and x = -2.

Step-by-step explanation:

The values of x where f has a relative maximum are -1 and 3. The answer is D, -1 and 3 only.

To determine the values of x where the function f has a relative maximum, we need to analyze the sign of the derivative in the neighborhood of each critical point.

The critical points of f correspond to the values of x where the derivative is equal to zero or undefined. In this case, the derivative is undefined only at x = -1, where there is a vertical asymptote.

To find the values of x where the derivative is zero, we set f'(x) = 0 and solve for x:

\(f'(x) = x(x-3)^2\)(x+1) = 0

This equation is satisfied when x = 0 or x = 3, since these are the only values that make one of the factors equal to zero. Therefore, these are the only two critical points of f.

Next, we can use the first derivative test to determine the nature of each critical point. This involves checking the sign of the derivative in the interval to the left and right of each critical point.

For x = -1, the derivative is undefined to the left and right, but we can still examine the sign of f'(x) in the vicinity of -1. For example, if we consider values of x slightly to the left of -1 (say, x = -1.1), we see that f'(x) is negative. Similarly, if we consider values of x slightly to the right of -1 (say, x = -0.9), we see that f'(x) is positive. This means that f has a relative maximum at x = -1.

For x = 0, the derivative is negative to the left and positive to the right. This means that f has a relative minimum at x = 0.

For x = 3, the derivative is positive to the left and negative to the right. This means that f has a relative maximum at x = 3.

Therefore, the values of x where f has a relative maximum are -1 and 3. The answer is D, -1 and 3 only.

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Option C best describes the limiting values of T and a under the conditions given. In this case, T represents tension and a represents acceleration.

Without the specific conditions mentioned, it is impossible to determine the exact limiting values of T and a. However, certain options can be ruled out based on common sense and physical laws. For example, option C (T=mg and a=0) is not possible as the tension in a string cannot be equal to the weight of an object. Option E (T=0 and a=[infinity]) is also not possible as a mass cannot have zero tension and infinite acceleration.

Based on these eliminations, the most reasonable options are A (T=0 and a=0) and D (T=[infinity] and a=g). In the former case, the object is not moving and there is no tension in the string. In the latter case, the object is in free fall and the tension in the string is negligible compared to the weight of the object.

However, it is important to note that the exact limiting values of T and a will depend on the specific conditions of the scenario, such as the mass of the object and the angle of the string.

Option C best describes the limiting values of T and a under the conditions given. In this case, T represents tension and a represents acceleration. When T=mg and a=0, it means that the tension in the system is equal to the gravitational force acting on the mass (mg) and the system is in equilibrium with no acceleration. This is a common scenario when an object is hanging from a rope or cable and not moving. The other options do not represent stable or realistic conditions for a physical system.

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Ok, the range is the set of values that the function can take in y, so according to the graph in this case it is: