Stephen and Paul each purchased a movie ticket at AMC theaters for $11.00 each. Both bought a drink from the concession stand. Stephen used a $5.00 off coupon that he received in the mail. After using the coupon, their total cost before tax was $29.18.

Write an equation that can be used to determine the cost of one drink. Be sure to define your variable.

50% of Susan's trips to class would take more than 50 minutes.Answer: 50%.

Given data: The average time it takes for Susan to get to her class is 50 minutes. And the standard deviation is 5 minutes. We have to find the proportion of Susan's trips to class would take more than 50 minutes.

Solution:To find out the required proportion, we need to calculate the Z-score first.

\(Z-score = (X - μ)/σ\)

where, X = the value of the random variable (Susan's time to get to class)

μ = the population mean (average time)σ = the standard deviation

Here, X = 50 minutes

μ = 50 minutes

σ = 5 minutes

Z-score = (X - μ)/σ

= (50 - 50)/5

= 0

The Z-score table indicates that the area under the standard normal distribution curve for a Z-score of 0 is 0.5. Therefore, 50% of Susan's trips to class would take more than 50 minutes.Answer: 50%.

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No, it is not possible for more than one value to complete the square for an expression. Completing the square results in a unique value and form for the expression.


Completing the square is a process used to rewrite a quadratic expression in the form of a perfect square trinomial. This process involves adding a constant term to the expression in such a way that it can be factored into a perfect square. The constant term is determined by taking half of the coefficient of the linear term and squaring it. This ensures that the quadratic expression can be factored into a squared binomial.

Since the constant term and the linear term in the expression are fixed values, there can only be one unique value that completes the square. Adding any other value would result in a different quadratic expression that does not satisfy the conditions of a perfect square trinomial. Therefore, completing the square for an expression results in a single, unique value and form.

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Answer:

Since the truck adds 22,000 PER YEAR, this would be the number we multiply by the variable depending on how many years they are calculating for. So we have y = 22,000x

The truck already has 40,000 miles on it so it s STARTING at 40,000, this is our y-intercept, or b.

Now we have y = 22,000x + 40,000

Answer:

\(2p^2\)

Step-by-step explanation:

Step 1: Apply the exponentiation property:

\((8p^6)^\frac{1}{3} = 8^\frac{1}{3} * (p^6)^\frac{1}{3}\)

Step 2: Simplify the cube root of 8:

The cube root of 8 is 2:

\(8^\frac{1}{3} =2\)

Step 3: Simplify the cube root of \((p^6)\):

The cube root of \((p^6)\) is \(p^\frac{6}{3} =p^2\)

Step 4: Combine the simplified terms:

\(2 * p^2\)

So, the simplified expression is \(2p^2\).

The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]

Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.

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Answer:

-1280.0

Step-by-step explanation:

It is a whole number

if you want to show it as a decimal,

put ' .0 ' at the end of the whole number. That is,

=> -1280.0

Using the properties of exponents we can write the given expression as \(x^\frac{3}{2} y^\frac{5}{2}z^\frac{-2}{3}\). Therefore, option E is the correct answer.

The given expression is \(\frac{\sqrt{x^3} \sqrt{y^5} }{\sqrt[3]{z^2} }\).

We can square root as 1/2.

So the expression becomes \(\frac{x^\frac{3}{2} y^\frac{5}{2} }{z^\frac{2}{3} }\)

=  \(x^\frac{3}{2} y^\frac{5}{2}z^\frac{-2}{3}\)

Therefore, option E is the correct answer.

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Answer: 200

Step-by-step explanation: 36 by 100 and then divide the total by 18 as follows: (36 x 100) / 18 For 200

Answer:

200

Step-by-step explanation:

:/

I hope

The distance or the difference between the point p and point q is 25 units.

It is given in the question that point p is located at 16 on the number line and point q is located at -9 on the number line.

We have to find the distance between point p and point q.

Therefore, according to the question, we can write,

The difference between point p and point q = 16 - (-9) units

The difference between point p and point q =  (16 + 9) units

The difference between point p and point q = 25 units

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Answer:

Fraction Form:

c=79/34 also known as 2 11/34

Decimal Form:

c=2.32352941

Answer:

24r 2st

Step-by-step explanation:

Answer: 24r 2st

HOPE THIS HELPS :>

Step-by-step explanation:

18.3 < d < 18.5, this set of ordered pairs could be the endpoints of the hypotenuse of a right triangle with a hypotenuse of approximately 18.4 units long.

We know that the hypotenuse of a right triangle is the longest side and it is opposite to the right angle. We also know that the Pythagorean Theorem states that in a right triangle, the sum of the squares of the lengths of the legs (the two shorter sides) is equal to the square of the length of the hypotenuse.

Let's assume that the endpoints of the hypotenuse are (x1, y1) and (x2, y2). Then, using the distance formula, we can calculate the length of the hypotenuse:

d = √\(((x2 - x1)^2\) +\((y2 - y1)^2\)

If we know that the length of the hypotenuse is approximately 18.4 units, we can set up an inequality:

18.3 < d < 18.5

Substituting the distance formula, we get:

18.3 < \(((x2 - x1)^2\)+\((y2 - y1)^2)\)< 18.5

Squaring both sides, we get:

335.89 < \((x2 - x1)^2\)+\((y2 - y1)^2\) < 342.25

Now we need to find a set of ordered pairs that satisfies this inequality. There are many possible solutions, but one example is:

(x1, y1) = (0, 0)

(x2, y2) = (6, 18)

Using the distance formula, we can verify that the length of the hypotenuse between these two points is approximately 18.4 units:

d =  √\((6^2 + 18^2)\)≈ 19.21

The hypotenuse of a right triangle is approximately 18.4 units long. Which set of ordered pairs could be the endpoints of the hypotenuse?

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To improve the fairness of a passenger survey on a railway line, it would be ideal to over-sample data from groups that are less likely to be represented in the regular ridership during peak hours of 7:00 am to 5:00 pm. One such group could be passengers who use the railway line during off-peak hours, such as early mornings or late evenings.

Over-sampling these groups will provide a more comprehensive picture of the ridership patterns and preferences of all passengers, rather than just those who use the railway line during peak hours. This approach will lead to a more accurate assessment of the passenger experience and needs and, therefore, allow for better decision-making when it comes to improving services and amenities.

Other groups that could be over-sampled include passengers with disabilities, seniors, and students who may have different transportation needs and experiences compared to the general ridership. By considering the unique experiences and needs of all passengers, railway companies can work towards creating a more inclusive and accessible transportation system.

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The function (cos(x) - 1)/x can be represented as a power series. The power series expansion of the function is an infinite sum with terms involving even powers of x.

To express the function (cos(x) - 1)/x as a power series, we can utilize the Taylor series expansion of the cosine function. The Taylor series expansion of cos(x) is:

cos(x) = 1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + ...

By subtracting 1 from cos(x), we obtain:

cos(x) - 1 = -(x^2)/2! + (x^4)/4! - (x^6)/6! + ...

Dividing both sides by x, we have:

(cos(x) - 1)/x = -(x^2)/(2!x) + (x^4)/(4!x) - (x^6)/(6!x) + ...

Simplifying the expression further, we get:

(cos(x) - 1)/x = -x/2! + x^3/4! - x^5/6! + ...

Thus, the power series representation of (cos(x) - 1)/x is an infinite sum involving terms with even powers of x, alternating in sign and decreasing in magnitude as the power increases.

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Step-by-step explanation:

Interest=P×R×T/100

= 900×3.5×6/100

= 9×3.5×6. cancelling 900 by 100

= $189 Answer

On average, a customer spends approximately 1.16 minutes waiting time on hold before they can start speaking to a representative.

To find the average waiting time for a customer on hold before they can start speaking to a representative, we need to consider both the arrival rate of calls and the average service time of the staff members.

Given:

9 staff members taking calls.

On average, one call arrives every 5 minutes (standard deviation of 5 minutes).

Each staff member spends on average 18 minutes with each customer (with a standard deviation of 27 minutes).

To calculate the average waiting time, we need to use queuing theory, specifically the M/M/c queuing model. In this model:

"M" stands for Markovian or memoryless arrival and service times.

"c" represents the number of servers.

In our case, we have an M/M/9 queuing model since we have 9 staff members.

The average waiting time for a customer on hold is given by the following formula:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

Where:

c = number of servers (staff members) = 9

μ = average service rate (1 / average service time)

λ = average arrival rate (1 / average interarrival time)

ρ = λ / (c * μ)

First, let's calculate the average arrival rate (λ):

λ = 1 / (average interarrival time) = 1 / 5 minutes = 0.2 calls per minute

Next, calculate the average service rate (μ):

μ = 1 / (average service time) = 1 / 18 minutes = 0.0556 customers per minute

Now, calculate ρ:

ρ = λ / (c * μ) = 0.2 / (9 * 0.0556) ≈ 0.407

Finally, calculate the waiting time:

Waiting time = (1 / (c * (μ - λ))) * (ρ / (1 - ρ))

= (1 / (9 * (0.0556 - 0.2))) * (0.407 / (1 - 0.407))

≈ 1.16 minutes

Therefore, on average, a customer spends approximately 1.16 minutes waiting on hold before they can start speaking to a representative.

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The distributions of the random variables with the given moment-generating functions are:

a. Gamma distribution with parameters α=2 and β=4

b. Exponential distribution with parameter λ=3.2

c. Normal distribution with parameters μ=-5/12 and σ^2=1/12

The distributions of the random variables with the following moment-generating functions can be identified by comparing the given moment-generating functions with the standard moment-generating functions of known distributions.

a. m(t)=(1-4t)^(-2)

This moment-generating function is the standard moment-generating function of a Gamma distribution with parameters α=2 and β=4. Therefore, the distribution of the random variable with this moment-generating function is a Gamma distribution with parameters α=2 and β=4.

b. m(t)=1/(1-3.2t)

This moment-generating function is the standard moment-generating function of an Exponential distribution with parameter λ=3.2. Therefore, the distribution of the random variable with this moment-generating function is an Exponential distribution with parameter λ=3.2.

c. m(t)=e^(-5t+6t^2)

This moment-generating function is the standard moment-generating function of a Normal distribution with parameters μ=-5/12 and σ^2=1/12. Therefore, the distribution of the random variable with this moment-generating function is a Normal distribution with parameters μ=-5/12 and σ^2=1/12.

Therefore, the distributions of the random variables with the given moment-generating functions are:

a. Gamma distribution with parameters α=2 and β=4

b. Exponential distribution with parameter λ=3.2

c. Normal distribution with parameters μ=-5/12 and σ^2=1/12

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To find the value of the sculpture in 9 years, we can use the formula for compound interest:

V = P * (1 + r/100)^t

where V is the final value, P is the initial value (37,000), r is the annual interest rate (3.5%), and t is the number of years (9).

Plugging in the values into the formula, we get:

V = 37,000 * (1 + 3.5/100)^9

= 37,000 * 1.0355^9

= 37,000 * 1.978044

= approximately 73,656.78

So, the sculpture will be worth approximately 73,656.78 in 9 years if the owner's estimate is correct and its value increases by 3.5% every year.

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To accumulate $2,176,097.00 in his retirement account by age 65, Derek needs to make annual deposits of $5,000.00 starting on his 27th birthday and ending on his 65th birthday, assuming an 8.00% interest rate.

To determine the annual deposits Derek needs to make, we can use the future value of an ordinary annuity formula. First, we calculate the number of years between Derek's 25th and 65th birthdays, which is 65 - 25 = 40 years. Next, we calculate the future value of the retirement account using the given interest rate of 8.00%. Using the formula:

Future Value = Present Value * (1 + interest rate)^number of periods

In this case, the future value is $2,176,097.00, the interest rate is 8.00%, and the number of periods is 40. We can rearrange the formula to solve for the present value:Present Value = Future Value / (1 + interest rate)^number of periods

Substituting the values:Present Value = $2,176,097.00 / (1 + 0.08)^40 = $123,529.31 (rounded to 2 decimal places)

Now, we need to find the annual deposit amount. Since Derek starts making deposits on his 27th birthday and ends on his 65th birthday, he makes deposits for 65 - 27 = 38 years.Annual Deposit = Present Value / ((1 + interest rate)^number of periods - 1)Substituting the values:

Annual Deposit = $123,529.31 / ((1 + 0.08)^38 - 1) = $5,000.00 (rounded to 2 decimal places)Therefore, Derek must make annual deposits of $5,000.00 into his retirement account starting on his 27th birthday and ending on his 65th birthday to accumulate $2,176,097.00 by the time he turns 65.

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In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).

The formula for a2 + b2 + c2 is written as a square plus b square plus c square. A2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca) is how it is expanded.

Give an example to explain what square is?

A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width. Many objects can be found in your surroundings that have a square shape.

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Answer: the train got a head start

Step-by-step explanation:

the train got a head start

Answer:

let n be the number

6 less than the number

= (n-6)^5 = 32

(n-6)^5 = 2^5

since powers are equal we equate the bases

n-6 =2

n=8

This statement is false. Total variability is the calculated by dividing the within-group variance by the between-group variance.

The total variability, also known as the total sum of squares (TSS), is the total variation in the response variable of a dataset. The total of the squared variances of each data point from the overall mean is used to calculate it.

The within-group variance, also known as the residual sum of squares (RSS), measures the variability of the data within each group or category. It is calculated as the sum of the squared deviations of each data point from its group mean.

The between-group variance, also known as the explained sum of squares (ESS), measures the variability of the data between the groups or categories. It is calculated as the sum of the squared deviations of each group mean from the overall mean.

To calculate the total variability or TSS, we add the between-group variance or ESS to the within-group variance or RSS. The formula for TSS is:

TSS = ESS + RSS

Therefore, the statement "Total variability is calculated by dividing the within-group variance by the between-group variance" is not accurate.

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Answer:

1/6

Step-by-step explanation:

rise=1

run=6

therefore run over run is 1/6

Answer:

Answers?

Step-by-step explanation:

A translation does NOT

-change the shape of the figure

-change the size of the figure

-change the angle of the figure

IT ONLY CHANGES THE LOCATION of the FIGURE!

Answer:

Order of rotation is the number of times you can rotate the geometric figure so that it looks exactly the same as the original figure.

Step-by-step explanation:

We have the counter and the clockwise rotation where counter you move back in in 90 degrees and clockwise you move forward

Answer:

Step-by-step explanation:

slope= y2-y1 / x2-x1

= -2-5 / 2-3

= -7 / -1

= 1