A charity organization is collecting change to raise money. They have collected three times as many dimes as quarters, 11 more nickels than dimes, and 2 times as many pennies as nickels. Let x represent the number of quarters. Write an expression to represent the number of dimes. Write an expression to represent the number of nickels. Write an expression to represent the number of pennies. If they have collected a total of 4,453 coins, how many of each coin have they collected? Show your work.

The workers can be distributed in \(\frac{(2nk)!}{2^{kn}(k!)^{n} }\) ways.

What is distribution?

An expression that yields an accurate result with a little quantity of data is known as a closed-form solution. A definite integral, which determines the area under a curve, is one example.

Given total no. of workers: 2nk

No. of Floors: n

No. of offices per floor: k

Given:

To find: the number of ways there are to assign offices.

Here distribution occurs in 2 steps:

Step 1: Distribute 2nk people in n floors such that each floor has 2k people.

Since the floors are distinct, the order between the group of 2k workers matters.

This can be done as:

\(\left(\begin{array}{ccc}2nk\\2k\\\end{array}\right)\)\(\left(\begin{array}{ccc}2nk-2k\\2k\\\end{array}\right)\).............\(\left(\begin{array}{ccc}2k\\2k\\\end{array}\right)\)

[∵ The 2k workers in the \(1^{st}\) first floor can be distributed in \(\left(\begin{array}{ccc}2k\\2k\\\end{array}\right)\) ways. Then 2k workers can be distributed in \(2^{nd}\) floor in \(\left(\begin{array}{ccc}2nk-2k\\2k\\\end{array}\right)\)]

=\(\frac{(2nk)!}{(2k)! (2nk-2k)!} \frac{(2nk-2k)!}{(2k)!(2nk-2k)!} ....... \frac{(2k)!}{(2k)!}\)

\(=\frac{(2nk)!}{[(2k)!]^{n} }\)

Let it be (i)

Step 2:

For each floor, we distribute the 2k workers into k offices.

but the offices are identical hence the order between the pairs do not matter.

This can be done in:

\(\left(\begin{array}{ccc}2k\\2\\\end{array}\right)\left(\begin{array}{ccc}2k-2\\2\\\end{array}\right)\)................................ \(\left(\begin{array}{ccc}2\\2\\\end{array}\right).\frac{1}{k!}\)

[∵ for the first office we can choose the pair in \(\left(\begin{array}{ccc}2k\\2\\\end{array}\right)\) ways, for the 2nd office we can choose in \(\left(\begin{array}{ccc}2k-2\\2\\\end{array}\right)\) ways and so on. We divide the answer by (k!) because the order between the pairs do not matter.]

\(= \frac{(2k)!}{2!(2k-2)!} \frac{(2k-2)!}{2!(2k-1)!} ......... \frac{2!}{2!} . \frac{1}{k!}\)

\(= \frac{(2k)!}{2^{k} (k!)}\)                    [∵ 2! = 2]

∴ For every floor the workers can be distributed in \(\frac{(2k)!}{2^{k}(k!) }\) ways.

∴ For all the floors, the distribution can be done in \(\left[\begin{array}{ccc}\frac{(2k)!}{2^{k} (k!) } \\\\\end{array}\right] ^{n}\)ways

Therefore, the steps 1 and 2 can be together:

\(=\frac{(2nk)!}{[(2k)!]^{n} } * \frac{[(2k)!]^{n} }{2^{kn}(k!)^{n} }\)

\(= \frac{(2nk!)}{2^{kn}(k!)^{n} }\)

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The suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.

So, the flat rate is $7 and we're charged $0.65 per mile:

Then the suitable expression will be:

Cost if we traveled 15 miles:

So, 0.65x = y where x = 15.

It would cost $9.75 for 15 miles.

Therefore, the suitable expression will be (0.65x = 7) and the cost of traveling 15 miles would be $9.75.

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Answer:

5

Step-by-step explanation:

5/30 = 1/6

The slope and y-intercept will be the negative 5/2 and 4.

The complete question is attached below.

The equation of line is given as

y = mx + c

Where m is the slope and c is the y-intercept.

The equation is given below.

y > -(5/2)x + 4

The slope and y-intercept will be the negative 5/2 and 4.

The graph is also attached below.

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Answer:

48 1/8s

Step-by-step explanation:

a whole is 8/8 so u multiply 8 by 16 to get 48

hope this helps

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have an amazing day!!!

Answer:

393 + 39√6

Step-by-step explanation:

√639 + (393)

Simplify

393 + 39√6 (Answer)

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Answer:

Since the discovery of the tiger gar population in Lake Richmond, the population of bluegill fish has also shown significant change.​

the discovery of the tiger gar population in Lake Richmond, the population of bluegill fish has shown significant change. The number of bluegill fish has decreased from 2,465 in 2016 to 1,094 in 2021.

The equation of linear system in the form of inequality will be x + y ≥ 2 or y ≥ 2 – x.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The graph is given below.

The graph is a linear equation.

Then the equation of linear system in the form of inequality will be

The two point are given as (0, 2) and (1, 1). Then the equation of linear system will be

y – 2 ≥ [(2 – 1) / (0 – 1)] (x – 0)

y – 2 ≥ – x

x + y ≥ 2

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Answer:

\(\huge\boxed{y= \frac{r-p}{t-q}}\)

Step-by-step explanation:

In order to solve for y in this equation, we can algebraically manipulate it to isolate y one one side of the equation.

Step 1: Subtract \(p\) from both sides of the equation.

Step 2: Factor out the common term \(y\) from the left side

Step 3: Divide both sides by \(t-q\)

Hope this helped!

Answer:

The answer is C: 11 and 12.

Step-by-step explanation:

the correct option is B. At x = 0.20, f has a relative maximum value. To find the relative maximum value of the function f, we need to identify the critical points where the derivative f'(x) changes from positive to negative. In other words, we need to find the values of x for which f'(x) = 0 and the second derivative f''(x) is negative.

Given that f'(x) = e^x - 3x^2, we can set it equal to zero and solve for x:

e^x - 3x^2 = 0

To find the critical points, we need to solve this equation. Unfortunately, it doesn't have an algebraic solution that can be expressed in terms of elementary functions. We can, however, use numerical methods or approximation techniques to estimate the values of x.

By plugging in the values of x given in the options, we can determine which one yields a relative maximum. Let's evaluate f'(x) at each option:

A. f'(-0.46) ≈ e^(-0.46) - 3(-0.46)^2 ≈ -0.244

B. f'(0.20) ≈ e^(0.20) - 3(0.20)^2 ≈ 0.121

C. f'(0.91) ≈ e^(0.91) - 3(0.91)^2 ≈ -0.525

D. f'(0.95) ≈ e^(0.95) - 3(0.95)^2 ≈ -0.400

E. f'(3.73) ≈ e^(3.73) - 3(3.73)^2 ≈ 17.540

From the values above, we can observe that f' changes from positive to negative around option B (0.20). This indicates a relative maximum at x = 0.20.

Therefore, the correct option is B. At x = 0.20, f has a relative maximum value.

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Answer:

f(3) = g (3)

Step-by-step explanation:

graphically, we notice that the graphs of f and g intersect

at the point of coordinates (3 , 0)

Then

f(3) = 6 = g(3)

Then

f(3) = g (3)

Pilot program means  is a small scale, short term experiment that helps an organization or company to learn how a large scale project might work in practice.

Pilot program:

The best  pilot program provides a platform for the organization to test logistics, prove value before spending a significant amount of time, energy or money on a large scale project.

The pilot program is also called as feasibility study or experimental trial.

Steps for pilot program:

1.

set clear goals

2.

Decide on a length of time

3.

Choose your testing group

4.

Develop a plan for on-boarding

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Answer:

d

Step-by-step explanation:

Answer:

D

because the least popular thing that was sell at the bake sale is the corn muffins

hope this helps!!!

Since the limit is less than 1, by the ratio test, the series converges absolutely.

To determine the convergence or divergence of the series, the ratio test is applied. The ratio test involves taking the limit of the absolute value of the ratio of the (k+1)-th term and the k-th term as k approaches infinity. If this limit is less than 1, then the series converges. If the limit is greater than 1 or does not exist, then the series diverges.

In this case, the ratio test is applied to the series ∑(k=1 to infinity) ke^(-5k). After applying the ratio test and simplifying, the limit is found to be 0, which is less than 1. Therefore, the series converges. This means that the sum of the series exists and is a finite value.

Applying the ratio test:

lim k→∞ (k+1)e−5(k+1) / ke−5k

= lim k→∞ (k+1) / e5 * k

As k approaches infinity, the denominator (e5k) grows much faster than the numerator (k+1), so the limit is 0.

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The amplitude of motion is approximately 0.6096 meters and the period of motion is approximately 1.1604 seconds.

To determine the amplitude and period of motion for a mass weighing 64 pounds that stretches a spring 2 feet, we follow these steps:

Step 1: Convert the weight of the mass from pounds to Newtons.

64 pounds ≈ 284.50608 Newtons.

Step 2: Convert the displacement of the spring from feet to meters.

2 feet ≈ 0.6096 meters.

Step 3: Apply Hooke's Law:

F = kx, where F is the force, k is the spring constant, and x is the displacement.

Step 4: Determine the spring constant (k) using the equation

k = F / x. In this case,

k ≈ 466.6156 N/m.

Step 5: Calculate the angular frequency (ω) using

ω = sqrt(k / m), where m is the mass. In this case,

m ≈ 29.03 kg and

ω ≈ 5.4194 rad/s.

Step 6: Determine the period (T) using

T = 2π / ω. In this case,

T ≈ 1.1604 s.

Step 7: Calculate the amplitude (A) using

A = x. In this case,

A = 0.6096 m.

Therefore, for a mass of 64 pounds stretching a spring 2 feet, the amplitude of motion is approximately 0.6096 meters, and the period of motion is approximately 1.1604 seconds.

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Answer:

10.5in

Step-by-step explanation:

first we make a ratio of sides PO:CD

this is to give us the general length ratio between the two shapes

the ratio is 12:16

upon simplifying we get 3:4

now that we got our general ratio we have to create the ratio between DA and MP , MP:14

now we compare it to the general formula

3:4

MP:14

next we cross multiply

4MP=42

then solve for MP

=42/4

=10.5

Answer:

A

Step-by-step explanation:

All triangles have 180 degrees, these set of measures do not add up to 180°. They add up to 181°, so it is the answer.

Answer:

a

Step-by-step explanation:

Multiplicative rule's probability is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

According to the statement

we have to explain about the those law which is used when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

So, For this purpose we know that the

According to multiplicative rule of probability ,

If A and B are two independent events in a probability experiment, then the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B) In case of dependent events , the probability that both events occur simultaneously is: P(A and B)=P(A)⋅P(B | A)

and we see that these conditions are fulfilled by the definition of the multiplicative rule.

So, Multiplicative rule is a rule which states that the when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities

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Answer:

-6 and 7

Step-by-step explanation:

I hope this helps!

Answer:

7 and -6

Step-by-step explanation:

7 x -6 = -42

7 - 6 = 1

The sampling shows that the conclusion by the teacher is done as D. The teacher conducted an observational study by comparing the performance on the test.

Sampling simply means a process on statistical analysis that's used to take observations about a population.

In this case, the teacher conducted an observational study by comparing the performance on the test of those who completed their review worksheets to those who did not complete their review worksheets.

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Answer:

5/8

Step-by-step explanation:

This means 0.625 as a fraction can be written as 5/8.

Answer: 5/8

Step-by-step explanation:

125 times 5 is 625

125 times 8 is 1000

625/1000 is equivalent to 5/8

Answer:

rip

Step-by-step explanation:

The 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

What is Confidence interval?

A confidence interval (CI) is a range of estimates for an unknown parameter in frequentist statistics. The 95% confidence level is the most popular, however other levels, such 90% or 99%, are occasionally used when computing confidence intervals.

As given,

n = 150 = drivers

x = 100 = wear seat belts.

We have to find 95% confidence interval for proportion P that do not wear seat belt.

From 150 we have 100 wear seat belts

Not wear seat belt = 150 - 100

Not wear seat belt = 50

P = 50/150

P = 0.33

95% confidence interval for P is

CI = (P - zα/2√(P(1 - P)/n), P + zα/2√(P(1 - P)/n))

For 95% CI, zα/2 = 1.96

Substitute values,

CI = (0.33 - 1.96√(0.33(1 - 0.33)/150), 0.33 + 1.96√(0.33(1 - 0.33)/150))

CI = (0.33 - 0.075, 0.33 + 0.075)

CI = (0.255, 0.405)

Therefore 95% CI for proportion of driver that do not wear seat belt is 0.255 < p < 0.405.

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Answer:

Hello!! answer: a = 45

Step-by-step explanation:

This is a complimentary angle so we will just do 90 - 45 and get 45 because 45 + 45 = 90 Hope that helps!

Answer:

a = 45

Step-by-step explanation:

The total angle of the shape is 90°

That means you should subtract 90° from 45°

90 - 45 = 45

That's your answer!

Hope this helped :)

Answer:

752 ft

Step-by-step explanation:

Assuming t represents time, and the time we are trying to find is how high the rockets go after 1.5 seconds, we must take the equation and put 1.5 in wherever t occurs, this looks like:

-16(1.5)²+64(1.5)+80

solving this, we get:

-24²+96+80

576+96+80

752

Answer:

a) A region below both lines

b) A region above both lines

c) No solution

d) A region between both lines

Step-by-step explanation:

a) The lines shadings overlap below both lines

b) The lines shadings overlap above both lines

c) The lines shadings don’t overlap

d) The lines shadings overlap between both lines

To provide Logical Proofs with line-by-line justifications for the following arguments,

Let's use the first 4 rules of inference.

Given below is the justification for each step of the proof with the applicable rule of Inference.

E > M1. A > (E > ~F) Premise2. H v (~F > M) Premise3. A Premise4. ~H  Premise5. A > E > ~F 1, Hypothetical syllogism6.

E > ~F 5,3 Modus Ponens 7 .

~F > M 2,3 Disjunctive Syllogism 8.

E > M 6,7 Hypothetical SyllogismIf

A is true, then E must be true because A > E > ~F.

Also, if ~H is true, then ~F must be true because H v (~F > M). And if ~F is true,

Then M must be true because ~F > M. Therefore, E > M is a valid  based on the given premises using the first four rules of inference.

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