Please help!! I have tried it on my own and I am stuck
1 answer:
Answer:
1. 23.59 feet
2. 32.9°
Step-by-step explanation:
1. See the diagram attached.
The man is 11 feet distance from the bottom of the tree.
And the angle of elevation from the man to the top of the tree is 65°.
Now, we need to approximate the height of the tree,
Using the trigonometry, we can write
⇒ h = 11 tan 65° = 23.59 feet (Approx.) (Answer)
2. See the diagram attached.
From the given right triangle the hypotenuse is 25 feet and the base is 21 feet.
And the angle between the hypotenuse and the base is the pitch of the ram of a NASCAR turn.
Using trigonometry, we can write
⇒ (Answer)
You might be interested in
Answer:
15.87% probability that a random sample of 16 people will exceed the weight limit
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 sums, the theorem can be applied, with mean and standard deviation
In this problem, we have that:
If a random sample of 16 persons from the campus is to be taken, what is the chance that a random sample of 16 people will exceed the weight limit
This is 1 subtracted by the pvalue of Z when X = 2508. So
By the Central Limit Theorem
has a pvalue of 0.8413
1 - 0.8413 = 0.1587
15.87% probability that a random sample of 16 people will exceed the weight limit
Notice the picture below
the directrix is above the focus point, meaning the parabola is vertical and is opening downwards
now, "p" is the distance from the vertex to the focus point or the directrix, so that means, the vertex is between those two fellows, over the axis of symmetry, x = -2, since "p" is 1 unit, that puts the vertex at -2,5
since the parabola is opening downwards, that means the "p" value is negative, so is -1
the directrix is above the focus point, meaning the parabola is vertical and is opening downwards
now, "p" is the distance from the vertex to the focus point or the directrix, so that means, the vertex is between those two fellows, over the axis of symmetry, x = -2, since "p" is 1 unit, that puts the vertex at -2,5
since the parabola is opening downwards, that means the "p" value is negative, so is -1