bubba's gym charges a $100 membership fee and $10 per visit.
write an expression that represents the cost of "x" visits: C=_______

Answer:

5/13

Step-by-step explanation:

Cos = opp/hyp

5 is opposite of angle R and 13 is the hypotenuse.

The correct answer is C) the mean is not subject to sampling variation.

The mean is actually subject to sampling variation. When calculating the mean from a sample, it is an estimate of the population mean, and different samples may yield slightly different means. This sampling variability is an inherent property of the mean. Therefore, option C is the property that does not apply to the mean.

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The average cost per item over the interval (1,000,1,010] is (C(1010) - C(1000)) / (1010 - 1000) = (10,000 + 5(1010) - 10,000 - 5(1000)) / 10 = $5.50.

The average cost per item over the interval [999.5, 1000] is (C(1000) - C(999.5)) / (1000 - 999.5) = (10,000 + 5(1000) - 10,000 - 5(999.5)) / 0.5 = $5.00.

The given function C(x) represents the cost in dollars to manufacture x items. To find the average cost per item over a given interval, we use the formula: (C(b) - C(a)) / (b - a), where a and b are the endpoints of the interval.

For the interval (1,000,1,010], we substitute a = 1000 and b = 1010 into the formula to obtain (C(1010) - C(1000)) / (1010 - 1000). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1010) - $10,000 - $5(1000)) / 10 = $5.50 per item.

For the interval [999.5, 1000], we substitute a = 999.5 and b = 1000 into the formula to obtain (C(1000) - C(999.5)) / (1000 - 999.5). Simplifying the expression using the given function C(x) yields ($10,000 + $5(1000) - $10,000 - $5(999.5)) / 0.5 = $5.00 per item.

To find C'(1000), we differentiate the function C(x) with respect to x, which gives C'(x) = 5. The value of C'(1000) is therefore 5, rounded to 1 decimal place.

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Answer:

Step-by-step explanation:

Step one:

give data

time= 8hours

distance=385mile

speed=?

Step two:

let us solve for the speed

Speed= distance/time

Speed=385/8

speed=48.125miles per hour

Step three:

let's find the time taken to cover 1000mile at the speed of 48.125 mi per hour

speed=distance/time

time=distance/speed

time=1000/48.125

time=20.779hours

approximately 21 hours

The volume of the hemisphere is 301.44mm²

Any circle drawn around the Earth that divides it into two equal halves is called a hemisphere. Examples is a ball cut into two part. Each part will be an hemisphere.

The volume of an hemisphere is expressed as;

V = 2/3πr³

where v is the volume and r is the radius

Here, r = 12mm

Therefore;

V = 2/3 × ×3.14 × 12²

V = 904.32/3

V = 301.44mm²

therefore the volume of the hemisphere is 301.44mm²

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a) The probability of being infected with the disease if a person is selected at random from the population is 0.2015, and

b) The probability of being vaccinated given that the person has the disease is 0.0445.

Probability is a mathematical concept that deals with the likelihood of an event occurring. It is a number between 0 and 1, where 0 means that an event is impossible and 1 means that an event is certain to occur.

A. Probability of being infected with the disease:

To find the probability of being infected with the disease if a person is selected at random from the population, we need to consider the proportion of vaccinated and unvaccinated people. Given that 45% of the population is properly vaccinated, 55% is unvaccinated.

The probability of being infected with the disease for vaccinated people is 0.02 and for unvaccinated people is 0.35.

Therefore, the overall probability of being infected with the disease is calculated as follows:

P(infected) = (0.45 * 0.02) + (0.55 * 0.35) = 0.009 + 0.1925 = 0.2015

So, the probability of being infected with the disease if a person is selected at random from the population is 0.2015.

B. Probability of being vaccinated given that the person has the disease:

To find the probability of being vaccinated given that the person has the disease, we need to calculate the conditional probability.

The conditional probability of being vaccinated given that the person has the disease is calculated as follows:

P(vaccinated | infected) = P(vaccinated and infected) / P(infected)

=>  (0.45 * 0.02) / 0.2015 = 0.009 / 0.2015 = 0.0445

So, the probability of being vaccinated given that the person has the disease is 0.0445.

Complete question:

3. if a person is vaccinated properly, the probability of his/her getting a certain disease is 0.02. without vaccination, the probability of getting the disease is 0.35. assume that 45% of the population is properly vaccinated.

sick     vaccination not sick             no vaccination       total

0.02         0.43                                         0.37

0.35         0.20                                         0.63

a. if a person is selected at random from the population, what is the probability of that person being infected with the disease?

b. given that the person has the disease, what is the probability that the person was vaccinated?

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By using the degree of freedom of chi square distribution, standard deviation is 7.0711

What is standard deviation?

At first it is important to know about variance.

Suppose there is a data set

Variance of the data set  is the sum of the square of difference of every number of the data from the mean.

On taking the square root of variance, we get standard deviation.

Degree of freedom of chi square distribution is 25

Standard deviation = \(\sqrt{2 \times 25}\) = \(\sqrt{50} = 7.0711\)

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Answer:

d :4h

Step-by-step explanation:

hope this helps (;

Answer:

The brother is 11 years and the sister 14 years

Step-by-step explanation:

Let x represent the age of the brother and let y represent the age of the sister. Since the sum of their ages is 25 years, the sum can be represented by the equation:

x + y = 25           (1)

The sister age is 8 years less than twice the brother’s age, this can be represented by the equation:

y = 2x -8

2x - y = 8           (2)

Solve equation 1 and equation 2 simultaneously. Add equation 1 and equation 2, this gives:

3x = 33

x = 33/3

x = 11 years

Put x = 11 in equation 1:

11 + y = 25

y = 25 - 11

y = 14 years

Warranty data cannot be viewed as a random sample of failure because the warranty claim data only represents failures that are covered by the warranty and does not account for failures that may have occurred outside of the warranty period.

Not all customers may choose to make a warranty claim for a failure, so the data may not be representative of the entire population of failures. Therefore, the warranty data should be viewed as a biased sample of failure rather than a random sample.

The analysis of warranty claim data is an example of an observational study because the data is collected from the company's dealer network without any manipulation or intervention by the company. The study is simply observing the data that is being reported and analyzing it for potential design problems. It is not an experimental study where the company would manipulate the design of the vehicles to see the effect on failure rates.

In summary, warranty data cannot be viewed as a random sample of failure due to biases in the data collection process, and the analysis of warranty claim data is an example of an observational study because the data is collected without manipulation or intervention by the company.

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Answer:

The surface charge density is \(7.8\times10^{-8} C/m^2\).

Step-by-step explanation:

separation, d = 85 mm

Work, W = 6 x 10^-3 J

charge , Q = 8µC

The potential difference is given by

W = q V

\(V=\frac{6\times 10^{-3}}{8\times 10^{-6}}=750 V\)

Let the charge on he capacitor is q.

\(q = CV\\\\q = \frac{\varepsilon oA}{d}\times V\\\\\frac{q}{A} = \frac{8.85\times 10^{-12}\times750}{0.085} =7.8\times10^{-8} C/m^2\)

Answer: 40 inches

Step-by-step explanation:

You do

30 / 12 = 2.5

So

16 x 2.5 = 40

The correct answer is "decrease by 20 units."Because if the price is increased by 2 units, the demand for the product is expected to decrease by 20 units.

Based on the estimated regression equation Cap Y = 120 - 10X, we can determine the effect of a 2-unit increase in price (X) on the demand for the product (Y).

The coefficient of X in the regression equation (-10) represents the change in demand for the product for each unit change in price. In this case, since the price is increased by 2 units, the change in demand can be calculated by multiplying the coefficient (-10) by the price change (2).

Change in demand = Coefficient of X × Change in price

Change in demand = -10 × 2

Change in demand = -20

Therefore, if the price is increased by 2 units, the demand for the product is expected to decrease by 20 units.

Hence, the correct answer is "decrease by 20 units."

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Answer:

b ≥ 8

Step-by-step explanation:

b + 4 + 2(-2b + 4) ≤ -12

b + 4 - 4b + 8 ≤ -12

-3b + 12 ≤ -12

-3b ≤ -24

b ≥ 8

Answer:

78

Step-by-step explanation:

9x7 equal 63 plus 15 is 78

Answer:

Step-by-step explanation:

$9 = x

$15 = y

x times 7 + y = $78

Hope this helped!

Answer:

Or

Step-by-step explanation:

\(\bf 18a=56\)

Divide both sides by 18:-

\(\bf \cfrac{18a}{18}=\cfrac{56}{18}\)

Simplify:-

\(\bf a=\cfrac{28}{9}\)

Or

\(\bf a=3.111....\)

________________________

Hope this helps!

The mathematical expression y(x,t) = Asin(kx)sin(wt) provides a way to describe the behavior of a standing wave in terms of its amplitude, frequency, and location along the string.

At time t=0,

the standing wave can be mathematically expressed as

y(x,0) = Asin(kx)sin(w*0) = Asin(kx)sin(0) = 0.

This means that the displacement of the string is zero at time t=0.

However, it is important to note that this does not mean that the string is not moving at all. Rather, it means that the string is in a state of equilibrium at time t=0, with the maximum transverse displacement being A.

As time progresses, the standing wave will oscillate between the maximum positive and negative transverse displacement values, creating a pattern of nodes (points of zero displacements) and antinodes (points of maximum displacement).

The wave number k and angular frequency w are both constants that are dependent on the physical properties of the string and the conditions under which the wave is being produced.

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The minimum sample size needed for 95% confidence that the sample variance is within 5% of the population variance is given by n = (1.96² * σ²) / (0.05²).

The minimum sample size needed to be 95% confident that the sample variance is within 5% of the population variance can be calculated using the formula:

n = (Z² * σ²) / (E²)

where:

n is the minimum sample size,

Z is the z-score corresponding to the desired confidence level (in this case, 95% confidence corresponds to a z-score of approximately 1.96),

σ² is the population variance, and

E is the maximum allowable difference between the sample variance and the population variance (expressed as a proportion of the population variance).

The formula ensures that the desired confidence level is achieved while limiting the difference between the sample and population variances within the specified threshold.

In summary, to determine the minimum sample size needed to be 95% confident that the sample variance is within 5% of the population variance, you can use the formula n = (1.96² * σ²) / (0.05²), where σ² represents the population variance.

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Answer: 769 bottles ≤ 12x + 205, or 564 bottles ≤ 12x

Step-by-step explanation:

➜ They need at least 769 bottles, so our inequality will use either ≤ or ≥ depending on how we set it up.

➜ They currently have 205 bottles, so we will use addition to show there are some glasses currently owned

➜ If each set contains 12 glasses, we will multiply x, the number of sets bought, by 12

     With these details, we will write an inequality.

769 bottles ≤ 12x + 205

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Answer:

the Slope: 11

the y-intercept: (0, - 8) x        y

                                     0       -8

                                     1         3

Step-by-step explanation:

Answer:

\(y=\frac{11}{8}x+\frac{1}{2}\)

The number of X values listed in the first column of the frequency distribution table will be d) 4.

In a frequency distribution table, the first column typically represents the range or interval of the scores. Since the given sample has a range from X = 7 to X = 4, the first column of the frequency distribution table will include the four distinct X values: X = 4, X = 5, X = 6, and X = 7.

hese are the possible values within the given range, and thus, there will be 4 X values listed in the first column. So the correct option is d in this question.

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= 816,480 arrangements.

To keep TH together we have do arrangements of : M, A, TH, E, M, A, T, I, C, S, so there are 10 objects to be arranged.We will make arrangements of these 10 and then substract cases where THE exists.Number of arrangements of above 10 objects = 10!/(2!*2!) = 907,200 ( We have divided by 2! twice because two copies of M and A are present). Number of arrangements where THE is together = 9!/((2!*2!) =  90,720.So Number of arrangements = 907,200 - 90,720 = 816,480

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The value of the infinite series as n tends to 0 is: 0

Infinite series is defined as the sum of infinitely many numbers related in a given way and listed in a given order. Infinite series are important in mathematics and in such disciplines as physics, chemistry, biology, and engineering.

From the infinite series, we want to find the value of the series as n tends to 0.

We are given the series as:

x/2ˣ

At x = 0, we have:

0/2⁰ = 0/1 = 0

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Answer:

Step-by-step explanation:

all values are true

The  solution of the given system of equations is (8, -1). of the given system of equations is (8, -1).

One method to solve the given system of equations is substitution:

- Solve one of the equations for one of the variables (e.g., x = 9 + y from the second equation).

- Substitute the expression for the variable into the other equation.

- Solve the resulting equation for the remaining variable.

- Substitute the value for the remaining variable back into one of the original equations to find the value of the other variable

Using this method with the given equations

- x - y = 9 -> x = 9 + y

- 3x + 2y = 22 -> 3(9 + y) + 2y = 22

- Simplifying and solving for y: 27 + 5y = 22 -> 5y = -5 -> y = -1

- Substituting y = -1 into x = 9 + y: x = 8

To check this solution, we can substitute these values back into both original equations and confirm that they are true statements.

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Based on the randomly sampled data, we would expect approximately 126 customers to prefer ham sandwiches out of a sample of 300 customers.

Based on the circle graph, we can see that the ham sandwich is the most popular with 42% of customers choosing it as their favorite sandwich. We can use this information to estimate the number of customers who would prefer ham sandwiches in a sample of 300 customers.

If 42% of customers prefer ham sandwiches, then we can estimate the number of customers who prefer ham sandwiches as follows:

Number of customers who prefer ham sandwiches = proportion who prefer ham sandwiches x total number of customers

= 0.42 x 300

= 126

Therefore, based on the randomly sampled data, we would expect approximately 126 customers to prefer ham sandwiches out of a sample of 300 customers.

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A sandwich shop took a randomly sampled survey of 300 customers that asked them to name their favorite sandwich. The results are presented in the circle graph.

Sandwiches

> T

> Er

> M

> Re

✓ Sc

salami 12%

roast beef 20%

ham 42%

chicken 26%

Based upon the randomly sampled data, if 80 customers preferred roast beef sandwiches, how many customers would you expect to prefer ham sandwiches?