Answer:
From $1600 to $3400.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 2500
Standard deviation = 300
What interval of dealer incentives would we expect approximately 99.7% of vehicles to fall within?
By the Empirical Rule, 99.7% fall within 3 standard deviations frow the mean. So
From 2500 - 3*300 = 1600 to 2500 + 3*300 = 3400.
Using the binomial distribution, the probabilities are given as follows:
- 0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.
- 0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.
- Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.
<h3>What is the binomial distribution formula?</h3>
The formula is:


The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
The values of the parameters for this problem are:
n = 10, p = 0.4.
The probability that more than 4 weigh more than 20 pounds is:

In which:

Then:






Hence:


0.3675 = 36.75% probability that more than 4 weigh more than 20 pounds.
The probability that fewer than 3 weigh more than 20 pounds is:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0061 + 0.0403 + 0.1209 = 0.1673
0.1673 = 16.73% probability that fewer than 3 weigh more than 20 pounds.
For more than 7, the probability is:





Since P(X > 7) < 0.05, it would be unusual if more than 7 of them weigh more than 20 pounds.
More can be learned about the binomial distribution at brainly.com/question/24863377
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An expression is defined as a set of numbers, variables, and mathematical operations. The second student is correct.
<h3>What is an Expression?</h3>
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given One student simplified x⁵ + x⁵ to x¹⁰. The second student simplified x⁵+x⁵ to 2x⁵. Since the simplification of (x⁵+x⁵) is equal to 2x⁵. Therefore, the second student is correct.
Learn more about Expression:
brainly.com/question/13947055
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Answer:
The length AD is greater than length BD.
Step-by-step explanation:
Hinge theorem states that if two triangles have two congruent sides then the triangle with the larger angle between those sides will have longer third side
In ΔACD and ΔBCD

So side opposite to greater angle is greater side
Therefore, length AD is greater than length BD.
We see that in these 3 terms, 6 is a common factor. So, let's factor out a 6:

We can set this equal to 0 and factor by using the quadratic formula which is:

So, let's do just that:

Note that the 6 goes away if you divide both sides by 6. In this case, a = 1, b = -1, and c = -2. Let's plug that into the quadratic equation:


So, we can write this as:

Notice that the 6 comes back because it was only temporarily mad. And that the roots have opposite signs in the parentheses because to find the roots, you need to set each parentheses equal to 0 and solve for n. With that in mind, your final answer is 6(n-1)(n+2). Hope I could help you!