You and your best friend Janine decide to play a game. You are in a land of make believe where you are a function, f(t), and she
is a function, g(t). The two of you move together throughout this land with you (that is, f(t) ) controlling your East/West movement and Janine (that is, g(t) ) controlling your North/South movement. If your identity, f(t), is given by
f(t)=(t2+44)323
and Janine's identity, g(t), is given by
g(t)=26t
How many units of distance do the two of you cover between the Most Holy Point o' Beginnings (t=0), and The Buck Stops Here (t=28)?
f(t)=(t2+44)323
and Janine's identity, g(t), is given by
g(t)=26t
How many units of distance do the two of you cover between the Most Holy Point o' Beginnings (t=0), and The Buck Stops Here (t=28)?
1 answer:
Answer:
8045 1/3
Step-by-step explanation:
Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
Check out attachment for the step by step solution of the given problem.
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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.