A projectile is fired straight up from ground level with an initial velocity of 112 ft/s. Its height, h, above the ground after
1 answer:
Answer:
Step-by-step explanation:
We can do this the easy way and just set up an inequality and let the factoring do the work for us. The inequality will look like this:
We will move the constant over and get
and when you factor this you get that
3 < t < 4
Between 3 and 4 seconds is where the projectile reaches a height higher than 192 feet. With a little more work and some calculus you can find the max height to be 196 feet.
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Answer:
Height of the building = 115.4 ft.
Step-by-step explanation:
Height of building = AB + 46.4 + CD + 30.5
By applying Pythagoras theorem in ΔABP,
(26)² = (10)²+ (AB)²
676 - 100 = AB²
AB² = 576
AB = 24 ft
By applying sine rule in ΔCDE,
cos(60°) =
CD = CE ×
CD =
CD = 14.5 ft
Total Height = 24 + 46.4 + 14.5 + 30.5
= 115.4 ft
Answer:
95.44% probability the resulting sample proportion is within .04 of the true proportion.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are 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 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.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For the sampling distribution of the sample proportion in sample of size n, the mean is and the standard deviation is
In this question:
So
How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?
This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16.
X = 0.24
By the Central Limit Theorem
has a pvalue of 0.9772.
X = 0.16
has a pvalue of 0.0228.
0.9772 - 0.0228 = 0.9544
95.44% probability the resulting sample proportion is within .04 of the true proportion.
Answer:
Step-by-step explanation:
Given
Required
Find the measure of a
Since there is no diagram to support the question, we'll assume that:
This gives:
Subtract 22 from both sides