4. How many twelve-member committees are formed by selecting from 50 employees? What counting technique are you applying (M, P, S, or C)? 5. How many twelve-member committees consisting of five females and seven males are formed when selecting from 30 females and 20 males? What counting technique are you applying (M, M,S, or C) ? 6. How many twelve-member committees consisting of three females and nine males or five females and seven males are formed when selecting from 30 females and 20 males? What counting technique are you applying (M,P,S, or C) ?

Answer:

the answer would be 3/40

Answer:

3/40

Step-by-step explanation:

Scale factor = 9/10*12 = 3/40

Answer:

The correct option is;

A. Randomized block design

Step-by-step explanation:

A randomized block design is one where the sample or subjects of the experiment are split into groups called blocks of experimental units where the variation in each block is lower than the variation among or between blocks, such that variation is controlled. In a random order, the treatments are performed on each experimental of the blocks.

In the question, the experimental units are grouped by gender and the treatment (consumption of chocolate or placebo) is randomly administered to the experimental units.

The expression that can be used to find the area of triangle RST is (8 ∙ 4) - (5 6 8).

This is because the formula to find the area of a triangle is

A = 1/2 bh, where b is the base of the triangle and h is the height of the triangle.

In this case, the base is 8 and the height is 4, so the area is 1/2 (8)(4) = 16.

Therefore, the expression (8 ∙ 4) - (5 6 8) can be used to find the area of triangle RST.

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Correct question Which expression can be used to find the area of triangle RST?

1) (8 ∙ 4) - 1/2 (10 + 12 + 16)

2) (8 ∙ 4) - (10 + 12 + 16)

3) (8 ∙ 4) - 1/2 (5 + 6 + 8)

4) (8 ∙ 4) - (5 - 6 - 8)

Answer:

12 guests

Step-by-step explanation:

Given data

We are told that the cost per guest is $8

let the number of expected quest be x

Hence the inequality is

\(100\leq 8x\)

divide both sides by 8

x=100/8

x=12.5

Hence the number of guests should not be more than 12

Answer:

Median: 17

Mean: 16

Step-by-step explanation:

Median is the "middle number" or the average of the 2 middle numbers if the set has an even number of entries

(11+23)/2=34/2=17 which is the median

The mean is all the entries added up divided by the number of entries

(5+23+11+15)/2=64/4=16 which is the mean

Answer:

step two

explanation:

the first 17.8 (-17.8) he was supposed to use was negative but the 17.8 (17.8) he used was not

Answer:

-4x(x-3)^2

Step-by-step explanation:

Answer:

Step-by-step explanation:

Pull out -4x

So -4x(x^2 - 6x + 9)

Then find the factors of 9 which are 1,3,9 use those to solve

-4x ( X -3) (x-3)

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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The common factor of the equation is x+2 and the HCF is x+2 of the equation x²-4, x² +4x+ 4 and x²+3x + 2​.

Given that,

The equations are  x²-4, x² +4x+ 4 and x²+3x + 2​.

We have to find the HCF of the equation.

We know that,

The greatest possible number that evenly divides both numbers is known as the Highest Common Factor (HCF) of two numbers. The Greatest Common Divisor (GCD) and Highest Common Factor (HCF) (GCD).

Take the equation.

x²-4= (x+2)(x-2)

x² +4x+ 4= (x+2)(x+2)

x²+3x + 2​= (x+2)(x+1)

Therefore, The common factor of the equation is x+2 and the HCF is x+2 of the equation x²-4, x² +4x+ 4 and x²+3x + 2​.

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Answer:

it depends

Step-by-step explanation:

if you mean

\(6x\) and \(x^{6}\)

the difference is that 6x is the same as

\(x+x+x+x+x+x\)

and that \(x^{6}\) is

\(x*x*x*x*x*x\)

if you mean

\(6x\) and \(x*6\)

it's the same by the communatitive property of multiplication

The difference between two given expressions are 6x is six times x and x⁶ is x multiplied six times itself.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

The two given expressions are 6x and x⁶.

6x is six times x

x⁶ is x multiplied six times itself, that is

x×x×x×x×x×x=x⁶

Therefore, the difference between two given expressions are 6x is six times x and x⁶ is x multiplied six times itself.

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The function is increasing in the intervals: (-∞, -3) and (2, 5)

The axis of symmetry is the one in option D, x = 2-

For a quadratic equation whose vertex is (h, k), the axis of symmetry is:

x = h

Here we have the quadratic equation:

y = −3(x − 2)² +1

We can see that the vertex is (2, 1) because the equation is in vertex form, and thus, we can conclude that the axis of symmetry of the equation is:

x = 2

So the correct option is D.

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Answer:

27

Step-by-step explanation:

whats the question. I just added both the numbers for free points. Thanks you S H M U C K.

Answer:

7 feet 6 inches

Step-by-step explanation:

5 yards = 15 feet

15 feet = 180 inches

180/2 = 90 inches

90 = 7.5 feet

Or 7 feet and 6 inches

This is an example of a reflection.

The maximum number of ccf Jake can use if he wants his bill to be no more than $62.00 is 14.417 ccf (approximately).

Given, Jake's water bill is $27.40 per month plus $2.40 per ccf of water.Let's say that the maximum number of ccf Jake can use if he wants his bill to be no more than $62.00 be x.Therefore, the expression that represents Jake's monthly bill can be represented as follows:f(x) = 27.40 + 2.40x (where x is the number of ccf used)Since Jake wants his monthly bill to be no more than $62.00, it means the following: f(x) ≤ 62.00.

Therefore, we can write the inequality as follows:27.40 + 2.40x ≤ 62.00Simplifying the above inequality we get,2.4x ≤ 34.6x ≤ 34.6/2.4x ≤ 14.417Therefore, the maximum number of ccf Jake can use if he wants his bill to be no more than $62.00 is 14.417 ccf (approximately).Therefore, the answer is: The maximum number of ccf Jake can use if he wants his bill to be no more than $62.00 is 14.417 ccf (approximately).

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A measurable part of a line that consists of two points, called endpoints, and all of the points between them are called Line sigments.

Geometry is a branch of mathematics that deals with how objects can be expressed as relationships of points, lines, planes, surfaces, and dimensions. When we draw lines in geometry, we use an arrow at each end to show that it expands infinitely. A line is a path between two points that can be measured. Since line segments have a defined length, they can form the sides of any polygon. The figure below shows the line AB, where the length of the line AB is related to the distance between its endpoints, A and B. The symbol for the line is named after its two endpoints, e.g.

\( \bar{AB}\)

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Answer:

46

Step-by-step explanation:

length x width x height

7 x 5 x 3

Answer: surface area = 142

Volume = 105

* make sure to add labels (units^2, etc.)

Step-by-step explanation:

Area = length x height

Volume = length x width x height

Answer:

C i think, i could be wrong.

Step-by-step explanation:

It is assumed here that rats always eat at the same rate, 3 rats eat 3 identical pieces of cheese in 3 hours.

6 rats eat 6 identical pieces of cheese in 6 hours.

Assuming rats eat at the same rate,

3 pieces of cheese last three rats?

It is assumed here that rats always eat at the same rate, 3 rats eat 3 identical pieces of cheese in 3 hours.

Therefore, six rats eat six identical pieces of cheese in six hours and 3 rats eat 3 identical pieces of cheese in 3 hours.

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Answer: D, 912

Step-by-step explanation:

g(21) = 24 (21 + 17)

g(21) = 24 x 38

g(21) = 912 (Use your calculator for this part)

Given sequence, a such that a1 = 3, a2 = 5 and for each n ≥ 3, an = an−1 + 2an−2 − 2. It is required to use strong induction to prove that for each n ∈ N, an = 2n + 1.Theorem: For each n ∈ N, an = 2n + 1.Proof: We will proceed by strong induction.

It is given that a1 = 3, a2 = 5, we will prove that an = 2n + 1 for n ≥ 1.Base Case: When n = 1, a1 = 3 = 2*1 + 1. Hence, the theorem holds true for the base case n = 1. When n = 2, a2 = 5 = 2*2 + 1. Hence, the theorem holds true for the base case n = 2.Assumption: Let's assume that the theorem holds for all values of k where 1 ≤ k ≤ n. That is, ak = 2k + 1 for 1 ≤ k ≤ n.Now, we have to prove that the theorem holds for n+1. i.e., we have to prove that a(n+1) = 2(n+1) + 1 = 2n + 3.Using the given sequence relation, an = an−1 + 2an−2 − 2, we get,an+1 = an + 2an-1 - 2 Substitute an-1 = a(n-1) = 2(n-1) + 1an+1 = 2n + 1 + 2(2n-1 + 1) - 2an+1 = 4n - 1 = 2(n+1) + 1Thus, by strong induction, we have proved that the given sequence is equal to 2n+1 for each n ∈ N.

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Given that, a1 = 3, a2 = 5.

For each n ≥ 3, an = an−1 + 2an−2 − 2.

We need to use strong induction to prove that for each n ∈ N, an = 2n + 1.

Define the sequence: 3, 5, 9, 17, 33, …

Let P(n) be the statement that an = 2n + 1 for n ∈ N.

To establish P(n) for all n ∈ N, we need to show that the following two things hold:

Base Case:

P(1) and P(2) are true, that is a1 = 2(1) + 1 and a2 = 2(2) + 1. Therefore, the base case is true.

Inductive Hypothesis: Let k be an arbitrary but fixed natural number. We assume that P(1), P(2), ..., P(k) are true, that is an = 2n + 1 holds for n = 1, 2, ..., k. This is called the inductive hypothesis.

We now need to establish that P(k + 1) is true, i.e., a(k+1) = 2(k+1) + 1.

To do this, we can use the recurrence relation given:

For each n ≥ 3, an = an−1 + 2an−2 − 2.

We can rearrange the recurrence relation above to get:an−1 = an−2 + 2an−3 − 2

Therefore, we can write an = an−2 + 2(an−2 + 2an−3 − 2) − 2= 3an−2 − 4an−3 + 2

We know that P(1), P(2), ..., P(k) are true from the inductive hypothesis.

So, we have:a(k−1) = 2(k−1) + 1a(k−2) = 2(k−2) + 1

Therefore, we can write a(k+1) = 3ak−2 − 4ak−3 + 2= 3(2k−1) − 4(2k−3) + 2= 6k − 3 − 8k + 12 + 2= 2k + 11

This proves that P(k+1) is true.

Therefore, by the principle of strong induction, P(n) is true for all n ∈ N. Hence, an = 2n + 1.

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Answer:

Either do 28+28+28, etc. 38 times, or follow the diagram I attached.

If you want to know more about what I did in the attachment, just ask <3

Answer:

Start by multiplying the ones: 6 times 28 is 168. Next, multiply the tens: 30 times 28 is 840. Add the products to get 1,008.

Step-by-step explanation:

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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The finance charge is $285

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

\(\dfrac{a}{100} \times b\)

Given;

An installment loan that has an APR of 16 percent

The motor scooter sells for $1,687

The store financing requires a 20 percent down payment

Monthly payments are for 30months

Now,

Downpayment= cost of scooter*20%

=1687*20%

=$337.4

Amount of finance = Cost of scooter - Down payment

=1687-337.4=1349.6

Interest rate=16%*1/12=1.3% per month

Monthly payment = Amount of finance*I/[1-(1+I)^-n]

=1349.6*1.3%/[1-(1+1.3%)^-30]

=1349.6*0.013(1-0.6780)

=17.5448/0.322

=54.486

Total amount paying for loan over a period = Monthly payment * Term

=54.486*30=1634.6

Amount of finance charge = Total amount paying for loan - Amount of loan

Amount of finance charge =1634.6-1349.6

=285

Therefore, the finance charge by given percent will be $285

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Answer:

product is a ⋅ c = 3 ⋅ − 6 = − 18 and whose sum is b = − 7 .

Step-by-step explanation:

Factor

− 7 out of − 7 x .

3 x 2 − 7 ( x ) − 6

Rewrite

−7 as 2 plus −9

3 x 2 + (2−9) x −6

Apply the distributive property.

3 x 2 + 2 x − 9 x − 6

Answer:

∠x = 67°

Step-by-step explanation:

∠x = 67° because they both are inscribed angles of the same arc

Answer:

x = 67

Step-by-step explanation:

Angles on the circle subtended by the same arc are congruent.

x and 67° are on the circle and subtended by the same arc, then

x = 67

Answer:

81.8 kg

Step-by-step explanation:

To find the total mass you have to add both of their mass

46.2 kg+35.6 kg= 81.8 kg

Their total mass is 81.8 kg #