Arthur drops a ball from a height of 81 feet above the ground. Its height, h, is given by the equation h = –16t2 + 81, where t i
2 answers:
Answer:
Step-by-step explanation:
We are given the position function and need to find the value of t when h<17.
Create an inequality that represents this situation:
The "less than" sign makes this very specifically a conjunction problem as opposed to a disjunction. That's important to the solution. But we'll get there.
The simplest way to solve this is to subtract 81 from both sides:
then divide both sides by -16:
Notice now that the sign is facing the other way since we had to divide by a negative number. Now it's a disjunction. The solution set to this inequality is that t>2 or t<-2. First and foremost, time will never be negative, so we can disregard the -2. Even if that was t<2, the more time that goes by, the greater the time interval is, not the lesser. It's the "<" that doesn't make sense, not only the -2. The solution to this inequality is
t > 2 sec. That means that after 2 seconds, the height of the ball is less than 17 feet.
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Answer:
We conclude that the mean wedding cost is less than $30,000 as advertised.
Step-by-step explanation:
We are given the following data set:(in thousands)
29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600
Formula:
where are data points,
is the mean and n is the number of observations.
Sum of squares of differences = 3408750
Population mean, μ = $30,000
Sample mean, = $29512.5
Sample size, n = 8
Alpha, α = 0.05
Sample standard deviation, s = $ 697.82
First, we design the null and the alternate hypothesis
We use one-tailed t test to perform this hypothesis.
Formula:
Putting all the values, we have
Now,
Since,
We fail to accept the null hypothesis and reject it.
We conclude that the mean wedding cost is less than $30,000 as advertised.
Answer:
The area of the shaded region is 0.9082.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean and standard deviation
, the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value, which is the area of the shaded region, is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
Area of the shaded region:
pvalue of Z
has a pvalue of 0.9082
So
The area of the shaded region is 0.9082.