The equation h = -16t 2+ 53x + 8 gives the height h, in feet, of a football as a function of time t, in seconds, after it is kic
1 answer:
Answer: The maximum height the football reaches = 51.89 feet.
Step-by-step explanation:
Given: The equation gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked.
Differentiate the given equation, we get
(i)
Put
Differentiate (i) w.r.t. t, we get
< 0 i.e. h is maximum at t= 1.65625
The value of h at t= 1.65625 will be
Hence, the maximum height the football reaches = 51.89 feet.
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Answer:
97.72% probability that their mean body temperature is greater than 98.4degrees° F.
Step-by-step explanation:
To solve this question, we have to understand the normal probability distribution and the central limit theorem.
Normal probability distribution:
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 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 random variable X, with mean and standard deviation
, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
If 36 adults are randomly selected, find the probability that their mean body temperature is greater than 98.4degrees° F.
This is 1 subtracted by the pvalue of Z when X = 98.4. So
By the Central Limit Theorem
has a pvalue of 0.0228
1 - 0.0228 = 0.9772
97.72% probability that their mean body temperature is greater than 98.4degrees° F.
Answer:
c.
Step-by-step explanation:
2x² - 4x - 3 = 0
Let's start by tidying up that equation and put it into slope-intercept form (y = mx + b); from there, we can plug in coordinates.
Let's use the distributive property on the right side:
Now add 4 to both sides
Which simplifies to:
Since that's the equation of our line, now we can plug in coordinates and see what it churns out.
We know that the x-coordinate of P = 4 so let's substitute 4 in for x and calculate the y-coordinate:
So the y-coordinate for point P = 10
Let's use the distributive property on the right side:
Now add 4 to both sides
Which simplifies to:
Since that's the equation of our line, now we can plug in coordinates and see what it churns out.
We know that the x-coordinate of P = 4 so let's substitute 4 in for x and calculate the y-coordinate:
So the y-coordinate for point P = 10