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Calculate the rate of change. ​

Answer:

Divide 6 miles by 0.5 hour:  6/0.5 = 12 miles per hour.

Step-by-step explanation:

The average speed must she rides her bike to get there on time will be 12 miles per hour.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

In a half-hour, Sarah is meeting her friends at the lake, 6 miles from her house.

The average speed must she rides her bike to get there on time will be

S = 6 / (1/2)

S = 6 x 2

S = 12 miles per hour

The average speed must she rides her bike to get there on time will be 12 miles per hour.

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(a) The average cost of the promotion per tire sold by Grear can be calculated by simulating the refund amounts for a large number of trials. (b) To determine the probability that Grear will refund more than $25 for a tire, we again simulate a large number of trials.

(a) The average cost of the promotion per tire sold by Grear can be calculated by simulating the refund amounts for a large number of trials. Assuming each trial represents a tire sold, we can calculate the refund amount for each trial based on the difference between the tire's lifetime and 30,000 miles. By averaging the refund amounts over the trials, we can determine the average cost of the promotion. Let's simulate at least 1,000 trials to obtain a reliable estimate.

(b) To determine the probability that Grear will refund more than $25 for a tire, we again simulate a large number of trials. For each trial, we calculate the refund amount as we did in part (a). Then, we count the number of trials where the refund amount exceeds $25 and divide it by the total number of trials. This will give us the probability of refunding more than $25. By simulating at least 1,000 trials, we can obtain a reasonably accurate estimation of the probability.

Due to the constraints of the current text-based interface, I'm unable to perform the simulations and calculations required to provide you with the specific numerical answers. However, you can apply the described methodology to conduct the simulations using programming or spreadsheet software to obtain the desired results.

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The probability that it will take more than 6 minutes for all the customers currently in line to check out is 0.15 Х s.

The probability distribution of the number of customers in line at a supermarket express checkout counter is given as below: х 0 1 2 3 4 5

P(x) 0.10 0.20 0.30 0.20 0.15 0.05

Here, we have to find the probability that it will take more than 6 minutes for all the customers currently in line to check out if each customer takes 3 minutes to check out.

We know that time taken for one customer to check out is 3 minutes.

So, time taken for n customers to check out is 3n minutes.

The probability of more than 6 minutes is P(x>6) = P(x=4) + P(x=5)

On substituting the given probability distribution, we have: P(x>6) = 0.15 Х s

Therefore, the probability that it will take more than 6 minutes for all the customers currently in line to check out is 0.15 Х s.

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The elasticity of expenditure is given by;e = δY/δX * X/Ywhere δY/δX is the slope of the demand curve and can be obtained by taking the derivative of the demand curve. X/Y is the expenditure share of X.In the given equation:

Y = 7.6182 + 0.08145X, we can rearrange to give X in terms of Y; X = (Y - 7.6182) / 0.08145Hence, expenditure share of X (X/Y) = (262.5 - 7.6182) / 29 = 8.9743.

Now we need to find δY/δX, by taking the derivative of the demand equation above, we get;δY/δX = 0.08145*Hence, the elasticity of expenditure is;e = δY/δX * X/Y = 0.08145*(262.5/29) = 0.731Conclusion:The value of elasticity of expenditure obtained above is less than one (0.731 < 1). This implies that the demand for X is inelastic. Hence, a 1% increase in the price of X will cause less than 1% decrease in the quantity demanded. Conversely, a 1% decrease in the price of X will cause less than 1% increase in the quantity demanded.

The elasticity of expenditure (E) is a metric used to measure the sensitivity of the quantity demanded of a good or service to a change in the price of that good or service. If E > 1, then the good or service is considered elastic. This means that a small change in price can cause a significant change in the quantity demanded of the good or service.

If E = 1, then the good or service is considered to have unit elasticity. This means that a change in price will cause a proportional change in the quantity demanded. If E < 1, then the good or service is considered inelastic. This means that a change in price will cause a relatively small change in the quantity demanded. In the given model above, the elasticity of expenditure was computed as 0.731. Since this value is less than one, it implies that the demand for the good is inelastic. A 1% increase in the price of the good will cause a less than 1% decrease in the quantity demanded. Conversely, a 1% decrease in the price of the good will cause less than a 1% increase in the quantity demanded.

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Answer:

400 minutes

Step-by-step explanation:

The speed for car 1 is 92 km/h and the speed for car two is 68 km/h. The time is unknown but we know it has to be converted into minutes so the time for both cars will be x/60. Now we multiply speed by time and get distance. The first car is 92 x/60 and the second car is 68 x/60. Cross multiply and you get 92x/60 and 68 x/60 now we can make an equation. 92x/60 - 68 x/60 = 80, x = 200. We multiply x by 2 to get the second time which is 400 minutes.

Answer:

2nd, 3rd and 5 th

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = [tex]\frac{2}{3}[/tex] and (a, b) = (1, 2) , thus

y - 2 = [tex]\frac{2}{3}[/tex] (x - 1) ← 2 nd option

Using (a, b) = (4, 4), then

y - 4 = [tex]\frac{2}{3}[/tex] (x - 4) ← 3 rd option

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = [tex]\frac{2}{3}[/tex] , thus

y = [tex]\frac{2}{3}[/tex] x + c ← is the partial equation

To find c substitute (4, 4) into the partial equation

4 = [tex]\frac{8}{3}[/tex] + c ⇒ c = 4 - [tex]\frac{8}{3}[/tex] = [tex]\frac{4}{3}[/tex]

f(x) = [tex]\frac{2}{3}[/tex] x + [tex]\frac{4}{3}[/tex] ← 5 th option

Answer:

B, look at the size compared to the others, it's DEFINITLY not d or c

Answer:

-4 is the y intercept. You know this because it is the only one without a variable.

The slope is -1.

Step-by-step explanation:

Answer:

  x = 23

Step-by-step explanation:

The marked angles are "corresponding," hence congruent:

  8x -27 = 7x -4

  x = 23 . . . . . . . . . add 27-7x to both sides

Answer: x=no solution

Step-by-step explanation:

Answer:

here

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

The equation for the red graph is,

⇒ 2y = f (x)

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

We have to given that;

The black graph is the graph of,

⇒ y = f (x)

Now,

The red graph is spread out the function of blk graph.

Hence, We get;

The equation for the red graph is,

⇒ y = f (x) / 2

⇒ 2y = f (x)

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Answer:

Three possible amounts are: 35+73+77

Step-by-step explanation:

The total amount of money the brother withdrew is 185 because 185 is 20 more than 165 the total of money Julie withdrew. Any three numbers that add up to 185 are possible answers.

The speed of the second runner is x = 40/9 miles per hour. The speed of the first runner is (4/5)x = (4/5)*(40/9) = 16/9 miles per hour.

Let the second runner's speed be x. Then the first runner's speed is 4/5 * x = (4/5)x.Therefore, the speed of the first runner is (4/5)x and the speed of the second runner is x.After running for 30 minutes, the first runner would have covered a distance of (4/5)x * 1/2 = (2/5)x miles.

The second runner would have covered a distance of x * 1/2 = (1/2)x miles. Since the runners are 2 miles apart, we can write an equation:(2/5)x + (1/2)x = 2. Multiplying both sides of the equation by 10 to eliminate fractions, we get: 4x + 5x = 40.

Simplifying the equation, we get: 9x = 40. Dividing both sides of the equation by 9, we get: x = 40/9. Therefore, the speed of the second runner is x = 40/9 miles per hour. The speed of the first runner is (4/5)x = (4/5)*(40/9) = 16/9 miles per hour.

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(a) We can use the exponential probability density function to calculate the probabilities:

(i) The probability that a bulb fails within the first 300 hours can be found by integrating the density function from 0 to 300:

P(failure within 300 hours) = ∫[0 to 300] (1/1000) * e^(-t/1000) dt

This integral can be solved to get the probability.

(ii) The probability that a bulb burns for more than 600 hours can be found by subtracting the probability of failure within 600 hours from 1:

P(burns for more than 600 hours) = 1 - P(failure within 600 hours)

Again, this probability can be calculated by integrating the density function from 600 to infinity.

(b) The median lifetime of the lightbulbs is the value of t for which the cumulative distribution function (CDF) equals 0.5. In other words, we need to find the value of t such that ∫[0 to t] (1/1000) * e^(-x/1000) dx = 0.5.

Solving this equation will give us the median lifetime of the lightbulbs.

Note: To provide specific numerical answers for parts (i), (ii), and (b), the exact values and calculations need to be performed using the given exponential probability density function.

(a) P(t > 600) = 1 - P(t < 600) = 1 - 0.00368 = 0.99632

(b) t = 1000 ln(2) = 693.14 hours

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Answer:

y = 1/3x + 10/3  

I hope this helped

Step-by-step explanation:

Answer:y = 1/3x + 10/3

Step-by-step explanation: got it right on edge

Answer:

5l² + 25ln

Step-by-step explanation:

Step 1: Write expression

4l(10n - 3m + 2l) - 3l(l - 4m + 5n)

Step 2: Distribute

40ln - 12lm + 8l² - 3l² + 12lm - 15ln

Step 3: Combine like terms

5l² + 25ln

Answer:

4⁶

Step-by-step explanation:

Exponent Rule: [tex]\frac{b^m}{b^n} =b^{m-n}[/tex]

4⁹/4³ = 4⁹⁻³ = 4⁶

Answer:

Step-by-step explanation:

You have 2 equations and 3 unknowns (A, x, y). You could use any value for A and it would be correct because then you could solve for the other unknowns. See picture for many exampleS.

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The socially optimal level of output in the Troubled Waters region is 7.5 units, and the corresponding price is $5. The consumer surplus at this level of output is $37.5.

To calculate the socially optimal level of output, we need to find the point where marginal cost (MC) equals the inverse demand curve (P). In this case, MC(Q) = 5 and P(Q) = 10 - Q. Setting these equal to each other, we have:

5 = 10 - Q

Solving for Q, we find Q = 5. The socially optimal level of output is thus 5 units.

To find the corresponding price, we substitute the value of Q into the inverse demand curve:

P = 10 - 5 = 5

So the socially optimal price is $5.

Consumer surplus is the difference between what consumers are willing to pay for a good and what they actually pay. To calculate consumer surplus, we need to integrate the area under the demand curve from 0 to the socially optimal quantity (Q = 5). Using the formula for the area under the curve, we find:

Consumer Surplus = ∫[0,5] (10 - Q) dQ

= [10Q - (Q^2/2)] [0,5]

= [(10*5) - (5^2/2)] - [(10*0) - (0^2/2)]

= (50 - 12.5) - (0 - 0)

= 37.5

Therefore, the consumer surplus at the socially optimal level of output is $37.5.

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Answer:

N must a negitve number.

Step-by-step explanation:

They opposite would be positive. Anything positive is bigger than a negitve

Answer:

The integer must be negative (less than 0)

Step-by-step explanation:

The opposite of a number is the same number but but with the opposite sign (+/-). E. G. The opposite of (+)2 is -2.

If N is less than its opposite, than it means that it is negative as its opposite will be positive (greater than 0). E.g. If N=-2, its opposite would be 2.

2>-2

Hope this helped!

Answer:

D'(-14,1), F'(4,1) and E'(4,7)

Step-by-step explanation:

Let's take each point and dilate about the point (1,1) using rule (x,y)--->(kx,ky). Where 'k' is dilation factor

Answer:

35.8 I just used a calculator to find the answer

Answer:

3x+12=20 is the equation

Step-by-step explanation:

Answer:

x= 2.666

Step-by-step explanation:

3x+12=20 is the equation

Answer:

Step-by-step explanation:

x = 7

y = 13

[tex]y - x[/tex]

Substitute values into the given equation

[tex]13 - 7 = 6[/tex]

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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