Answer:
Option C.
Step-by-step explanation:
If the graph of a function f(x) lies above the x-axis, then f(x) > 0.
If the graph of a function f(x) lies below the x-axis, then f(x) < 0.
From the given graph it is clear that the graph of f(x) intersect the x-axis at x=3.
Before x=3 the graph lies below the x-axis. So,
over the interval
.
After x=3 the graph lies above the x-axis. So,
over the interval
.
Therefore, the correct option is C.
The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.
<h3>What is the approximation about?</h3>From the question:
Mars: F(x) = 2/3
Therefore, If x = 15
Then:
f (15) = 2/3
= 16/3
= 20.7ft/s
Hence, The nearest tenth of how fast a rover will hit Mars' surface after a bounce of 15 ft in height is 20.7ft/s.
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Answer:
15.15% probability that the sample mean will be $192,000 or more.
Step-by-step explanation:
To solve this problem, 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 random variable X, with mean and standard deviation
, a large sample size can be approximated to a normal distribution with mean
and standard deviation
In this problem, we have that:
The probability that the sample mean will be $192,000 or more is
This is 1 subtracted by the pvalue of z when X = 192000. So
By the Central Limit Theorem
has a pvalue of 0.8485.
1-0.8485 = 0.1515
15.15% probability that the sample mean will be $192,000 or more.
Answer: 16384
Step-by-step explanation:
Given, Total jars = 4
Total marbles = 7
Since we need to put marbles in 4 different jars, we need to choose a jar each time.
Possible choices for jars =4
Number of time we need to choose = number of marbles
So, by fundamental counting principle, we have
Total ways to put 7 marbles in 4 jars =
Hence, the required number of ways =16384