Marcy has $1.51 in quarters and pennies. She has 7 coins altogether. How many coins of each kind does she have?

a) The number of number plates that can be made with each letter and each digit used once is 120.

b)  There are 46,656 possible number plates if the letters and digits can be repeated.

a) Each letter and each digit can only be used once.

There are 3 letters and 3 digits, so we can use the permutation formula:

P(6,6) =65! / (6-6)! = 6!

This gives us a number of ways to arrange the 5 characters without repetition.

P(6,6) = 6! = 720

b) The letters and digits can be repeated:

The number of permutations of n things taken r at a time is \(n^r\).

Here, n = 6 and r = 6

So, 6⁶ = 46,656 ways

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The complete question is as follows:

A number plate can be made by using the letters A, B, and C and the digits 1, 2, and 3. If all the digits are used and all the letters are used, find the number of plates that can be made if used once are:

a) Each letter and each digit

b) The letters and digits. can be repeated.

The calculated expectation of X is 0.1

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

P{X = -1}=0.2, P{X = 0} = 0.5, P{X = 1}=0.3

The expectation of X is calculated as

E(x) = ∑xp(x)

So, we have

E(x) = -1 * 0.2 + 0 * 0.5 + 1 * 0.3

Evaluate

E(x) = 0.1

Hence, the expectation of X is 0.1

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If the customer source has an arrival rate of 10 customers per hour , then

(a) the number of customers arrivals follows a Poisson Distribution .

(b) The probability formula is P(n) = \(e^{-\lambda t} \times \frac{(\lambda t)^{n} }{n!}\) .

(c) 80 customers are expected .

(d) Probability of at least 3 customers is 0.9972 .

(e) The probability function follows exponential distribution .

(f) The probability density function is f(x) = λ\(e^{\lambda x}\) .

(g) The 8th customer will be welcomed in 48th minute .

(h) probability of 8th customer arriving is 0.113 .

(i) probability distribution follows exponential distribution .

(j) expected inter arrival time in 1/6 .

Part (a) : If the customer source has an arrival rate of 10 customers per hour , then the number of customers arrivals follows a Poisson Distribution .

Part(b) : Probability of n customers arrivals at time t, can be calculated by the formula : P(n) = \(e^{-\lambda t} \times \frac{(\lambda t)^{n} }{n!}\)

Part (c) : substituting the value of lambda = 10 and t = 8 ,

We get , Number of customers expected during 8 hr day =10×8=80 .

Part (d) : Probability of having at least 3 customers within one hour

⇒ P(n≥3) = 1 - P(n≤2)

= 1 - e⁻¹⁰ × {(10⁰/0!) + (10¹/1!) + (10²/2!)}

= 1 - e⁻¹⁰ × {1 + 10 + 50}

= 1 - 0.0028

= 0.9972

Part (e) : The probability function that the nth customer follows is the exponential function.

Part (f) : The Probability density function (pdf) of this exponential function is as follow:

f(x) = λ\(e^{\lambda x}\) ,

Part (g) : The time at which we expect the 8th customer to arrive is :

⇒ 10 customers arrive in One hour, which means 1st customer arrive at 1/10th of an hour.

So,  by unitary method, we say that 8th customer arrives at 8/10th of an hour which is  48th minute.

Part (h) : The probability of 8th customer arriving in one hour is calculated by the formula :

⇒ P(X=x) = {λˣ \(e^{-\lambda}\)}/x! ,

⇒ P(X=8) = (10)⁸ e⁻¹⁰/8! = 0.113 .

Part (i) : The probability distribution for the inter-arrival time follows an exponential distribution.

Part (j) : The expected inter arrival time between the nth and (n + 1)th customer is calculated as :

⇒ (no. of customers per hour)/(no. of mins in 1hour ) = 10/60 =1/6 .

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The given question is incomplete , the complete question is

Suppose that we have a Poisson customer source, which has an arrival rate of 10 customers per hour.

(a) What probability distribution does the number of customer arrivals follow at time t?

(b) Write out the probability when we have n customer arrivals at time t.

(c) How many customers are expected during an 8-hour day?

(d) What is the probability of having at least 3 customers within one hour?

(e) What probability distribution does the nth customer arrival time follow?

(f) Write out is probability density function.

(g) What time do you expect to welcome the 8th customer?

(h) What is the probability you have 8 customers in one hour?

(i) What probability distribution does the inter-arrival time follow?

(j) What is the expected inter-arrival time between nth and (n+1)th customer?

Answer:

Step-by-step explanation:

Remark

That word about is a killer. It's a good thing they tell you they want the answer rounded to the nearest tenth, otherwise you'd be stuck.

Givens

pi = 3.14

r = 3

Formula

V = (4/3) pi r^3

V =  (4/3) * 3.14 * 3^3

V =  (4/3) * 3.14 * 27

V =  (4/3) * 84.78

Answer: V = 113.0 in^3

The value of the car five years after Alex purchased it for $28,000, with a depreciation rate of 7.25% each year, will be approximately $18,239.

To calculate the value of the car after five years, we will use the formula for exponential depreciation: V = P * (1 - r)^t, where V is the final value of the car, P is the initial purchase price, r is the annual depreciation rate as a decimal, and t is the number of years.

Step 1: Convert the annual depreciation rate from percentage to decimal.
7.25% = 0.0725

Step 2: Subtract the depreciation rate from 1.
1 - 0.0725 = 0.9275

Step 3: Raise the result from Step 2 to the power of the number of years (5 years).
0.9275^5 ≈ 0.649672

Step 4: Multiply the initial purchase price ($28,000) by the result from Step 3.
$28,000 * 0.649672 ≈ $18,239.216

Step 5: Round the final value to the nearest dollar.
$18,239.216 ≈ $18,239

So, the value of the car five years after it was purchased will be approximately $18,239.

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Answe

Step-by-step explanation:

Answer: \(\frac{33}{65}\)

Step-by-step explanation:

cosine of ∠T = \(\frac{adjacent}{hypotenuse}\)

For ∠T,

cosine of ∠T = \(\frac{33}{65}\)

The value of the trigonometric relation cos ∠T = 0.507

Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles

The six trigonometric functions are sin , cos , tan , cosec , sec and cot

Let the angle be θ , such that

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

Given data ,

Let the triangle be represented as ΔTUV

where the measure of ∠UVT = 90°

And , the measure of side UT = 65 units

The measure of VU = 56 units

And , the measure of TV = 33 units

From the trigonometric relations ,

cos θ = adjacent / hypotenuse

On simplifying , we get

cos ∠T = TV / UT

cos ∠T = 33 / 65

cos ∠T = 0.50769

Hence , the trigonometric relation is solved

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The interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.

The answer to this question is option D, which is μ - σ to Q3. To understand why this is the correct answer, we need to first understand what each of the intervals represents. Q1 and Q3 are the first and third quartiles of the data set, respectively. μ is the mean of the data set, and σ is the standard deviation.

When we look at the interval μ - σ to Q3, we can see that it includes the upper quartile and some of the data points to the left of it. This means that the area under the normal curve within this interval will be relatively small compared to the other options.

On the other hand, option B includes the mean and a larger range of data points, which would result in a larger area under the curve. Option C includes Q1 and a larger range of data points, which would also result in a larger area. Option A includes both Q1 and Q3, which cover the majority of the data set and would therefore have the largest area under the curve.

In summary, the interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.
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In 0.75lb (340g) of 85% lean ground beef, there are approximately 72 grams of fat.

To calculate the grams of fat in 0.75lb of 85% lean ground beef, we need to determine the fat content based on the percentage given. The term "85% lean" indicates that 85% of the weight of the ground beef is lean meat, while the remaining 15% is fat.

First, we convert 0.75lb to grams. Since 1lb is equal to 454g, multiplying 0.75lb by 454g/lb gives us 340g.

Next, we calculate the fat content by multiplying the weight of the ground beef (340g) by the percentage of fat (15%).

340g * 0.15 = 51g

Therefore, in 0.75lb (340g) of 85% lean ground beef, there are approximately 51 grams of fat.

However, the question asks for the fat content, so we subtract this value from the total weight to find the grams of fat:

340g - 51g = 289g

Therefore, there are approximately 72 grams of fat in 0.75lb (340g) of 85% lean ground beef.

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the dilemma of using a sample mean is that it is not likely to be the population mean, and it can never be used with 100% certainty.

The dilemma of using a sample mean is that it is not likely to be the exact population mean. This means that when we calculate the mean of a sample, it may not perfectly represent the true average of the entire population from which the sample was drawn.

Using a sample mean introduces uncertainty because we are working with a subset of the population rather than the entire population. There can be variations and differences between the sample and the population in terms of characteristics, distribution, or other factors. Therefore, the sample mean may provide an estimate, but it may not be an accurate reflection of the population mean.

Additionally, it is important to note that no statistical measure can be used with 100% certainty. Sampling is inherently probabilistic, and there is always a margin of error or uncertainty associated with any statistical estimate, including the sample mean.

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Answer:

It should.

Step-by-step explanation:

If a nearby city is losing people then the large city should try to help.  

To find the work done in pumping the entire contents of the fuel tank into the tractor, we need to calculate the potential energy difference between the initial position of the gasoline in the truck's tank and its final position in the tractor's tank.

Given:

- Diameter of the cylindrical gasoline tank: 4 feet

- Length of the cylindrical gasoline tank: 5 feet

- Opening on the tractor tank is 5 feet above the top of the tank in the truck

First, let's calculate the volume of the cylindrical gasoline tank using the formula for the volume of a cylinder:

Volume = π * (radius^2) * height

The radius of the tank is half the diameter, so the radius is 4 feet / 2 = 2 feet.

Volume = π * (2^2) * 5 = 20π cubic feet

Since the entire contents of the fuel tank need to be pumped, the volume of gasoline to be pumped is 20π cubic feet.

To calculate the work done in pumping the gasoline, we need to find the vertical height through which the gasoline is lifted. This height is the sum of the height of the tank and the distance between the top of the tank and the opening on the tractor tank.

Height = 5 feet + 5 feet = 10 feet

The work done in pumping the gasoline can be calculated using the formula:

Work = Force × Distance

In this case, the force is the weight of the gasoline, and the distance is the height through which it is lifted. To calculate the weight of the gasoline, we need to know the density of gasoline. The density of gasoline can vary, but an average value is around 6.3 pounds per gallon.

Let's convert the volume of gasoline from cubic feet to gallons:

1 cubic foot = 7.48052 gallons (approximately)

Volume in gallons = 20π * 7.48052 ≈ 149.61π gallons

Weight of gasoline = Volume in gallons * Density of gasoline

Assuming the density of gasoline as 6.3 pounds per gallon:

Weight of gasoline = 149.61π * 6.3 ≈ 940.06π pounds

Finally, we can calculate the work done:

Work = Weight of gasoline * Height

Work = 940.06π * 10 ≈ 9400.6π foot-pounds

Therefore, the work done in pumping the entire contents of the fuel tank into the tractor is approximately 9400.6π foot-pounds.

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Answer:

u + 15

Step-by-step explanation:

Since we don't know the value of u, we have to put the equation like this.

Hope I helped :)

Please consider Brainliest :)

Answer:

Step-by-step explanation:

yeah

Answer:

So 1) x²-2x-8

= x(x-2-8/x)

2) y²-13y+42

= y(y-13+42/y)

3) m²-6m-7

= m(m-6-7/m)

Hope it helps

Answer: 1891 mm^21

Step-by-step explanation:

The average time patients waited in 2014 was approximately 76 minutes, calculated by dividing the 2015 waiting time by 0.89 as patients waited 11% less time in 2015.

Let's call the average time patients waited in 2014 as per Wenford Hospital records "x" (in minutes). According to the problem statement, patients waited 11% less time in 2015 compared to 2014, so,

0.89x = 68

Solving for x,

x = 68 / 0.89

x ≈ 76.4

Therefore, the average time patients waited in 2014 was approximately 76 minutes (rounded to the nearest minute).

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Caloy needs to pay 140.00 in order to rent a bicycle for 4 hours.

Caloy rented a bicycle in the park for 4 hours.

He must pay a fixed amount of P20.00 and an additional P30.00 per hour.

The total amount he needs to pay:

Let us calculate,

Total amount = Fixed amount + (Per hour rate x Number of hours)

Fixed amount = P20.00

Per hour rate = P30.00

Number of hours = 4 hours

Total amount = 20 + (30 × 4)

Total amount = 20 + 120

Total amount = P 140.00

Therefore, Caloy needs to pay P 140.00 in order to rent a bicycle for 4 hours.

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The fraction of the 30 cakes does Simon have left with os 7/10

A fraction is a part of a whole number, and a way to split up a number into equal parts.

Given that, Simon makes 30 cakes, he gives 1/5 of the cakes to Sali, he gives 10% of the 30 cakes to Jane,

We need to find, what fraction of the 30 cakes does Simon have left,

Number of cakes given to Sali = 1/5 of 30

= 30 / 5 = 6

That mean, Sali got 6 cakes out of 30.

Number of cakes given to Jane = 10% of 30

= 30 × 10/100

= 300 / 100

= 3

That mean, Jane got 3 cakes, out of 30.

The remaining number of cake = 30 - (6+3)

= 30 - 9

= 21

Therefore, the fraction of cakes left = 21 / 30

= 7/10

Hence, the fraction of the 30 cakes does Simon have left with os 7/10

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Answer:

you can buy 9 poundssss

Suppose the detector will sound the alarm if more than 2 milligrams of the dye are in your system. It will take 56 minutes for the visit of the doctor

The amount of radioactive dye remaining in your system after t minutes can be modeled as:

A(t) = 11 * (1/2)^(t/20)

where A(t) is the amount of dye remaining after t minutes. We want to find the time t when A(t) = 2 milligrams.

A(t) = 11 * (1/2)^(t/20) = 2

Solving for t:

(1/2)^(t/20) = 2/11

Taking the natural logarithm of both sides:

(t/20) = ln(2/11) / ln(1/2)

Multiplying both sides by 20:

t = 20 * ln(2/11) / ln(1/2)

Using a calculator or logarithm tables, we can estimate t to be approximately 56 minutes. So, your visit to the doctor would take about 56 minutes.

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By using the concept of confidence interval, it can be concluded that-

To reduce confidence interval, it is needed to increase sample size.

Option c is correct

What is confidence interval?

Suppose there is an unknown parameter whose range of estimate is required. Confidence interval gives the range of estimate of this unknown parameter.

Formula for percentage confidence interval

\(\bar{x} \pm z_\frac{\alpha}{2} \times \frac{\sigma}{\sqrt{n}}\)

We have to reduce the size of the confidence interval

Confidence interval has no effect on  mean, directly proportional to  standard deviation and inversely proportional to sample size

So to reduce confidence interval, it is needed to increase sample size.

Option c is correct

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Complete Question

After constructing a confidence interval estimate for a population mean, you believe that the interval is useless because it is too wide. in order to correct this problem, you need to:

Select one:

a. increase the population standard deviation

b. increase the level of confidence

c. increase the sample size

d. increase the sample mean

e. none of these would help

The average acceleration during the time interval 0 seconds to 10 seconds is \(\frac{V_{1}-V_{2} }{10}\) unit per second per second.

As per the question statement, we are supposed to find out the average acceleration during the time interval 0 seconds to 10 seconds. But before solving this question we should be aware about what actually average acceleration is.

Average acceleration : \(\frac{change in velocity}{total time interval}\)

Here in the question, we are not given information about velocity of the object hence we assume the initial and final velocities of the object to be \(V_{1}\) and \(V_{2}\) respectively, hence

Change in velocity = \(V_{1}-V_{2}\)

Total time interval = \((10 - 0)sec=10sec\)

Therefore by definition of average acceleration we get

\(A_{avg}\)\(= \frac{V_{1}-V_{2} }{10}\) unit per sec per second

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The solution of the equation X/9 = 7/15 is (b) X = 21/5

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

X/9 = 7/15

Multiply both sides of the equation by 9

So, we have the following representation

9 * X/9 = 7/15 * 9

Evaluate the products

This gives

X = 7/15 * 9

Evaluate the products

This gives

X = 63/15

Simplify

X = 21/5

Hence, the solution is (b) X = 21/5

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The total number of game played are 108.

What is baseball?

In the bat-and-ball game of baseball, two teams of nine players each alternate between batting and fielding. When the umpire indicates to the pitcher that the ball is now in play, either verbally or physically, the game is in progress.

9 teams means each team will play 8 other teams 3 times (totaling 24). 24 games times 9 teams is 216.

However, when you count the first 24 games for team 1, you are counting the 3 games played against team 2.

When you add the games for team 2, you can’t also add the games played against team 1, or you’d be doubling the games counted.

This continues for each team. Team 3 can’t count it’s games against teams 1 or 2. Team 4 can’t count it’s games against teams 1, 2, or 3.

Continuing this and adding the total gets you 108.

Also, taking the first total of 216, you can simply divide by 2 and get the same number.

Hence, the total number of game played are 108.

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Answer:

a) rs 3000

b) rs 16800

a) rs 1600

b) rs 4000

A and B have the same elements, the measure of AUB will be equal to the measure of B.

To show that if m*(A) = 0, then m*(AUB) = m*(B), we need to prove the following:
1. If m*(A) = 0, then A is a null set.
2. If A is a null set, then AUB = B.
3. If AUB = B, then m*(AUB) = m*(B).
Let's break down each step:
1. If m*(A) = 0, then A is a null set:
  - By definition, a null set has a measure of 0.
  - Since m*(A) = 0, it implies that A has no elements or its measure is 0.
  - Therefore, A is a null set.
2. If A is a null set, then AUB = B:
  - Since A is a null set, it means that it has no elements or its measure is 0.
  - In set theory, the union of a null set (A) with any set (B) results in B.
  - Therefore, AUB = B.
3. If AUB = B, then m*(AUB) = m*(B):
  - Since AUB = B, it implies that both sets have the same elements.
  - The measure of a set is defined as the sum of the measures of its individual elements.
  - Since A and B have the same elements, the measure of AUB will be equal to the measure of B.
  - Therefore, m*(AUB) = m*(B).
By proving these three steps, we have shown that if m*(A) = 0, then m*(AUB) = m*(B).

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