Suppose that F(x) = x² and G(x) = -1/3 (x+4)^2. Which statement best compares the graph of G(x) with the graph of F(x)?
2 answers:
Answer: C
Step-by-step explanation:
The graph is shifted 4 units left as seen with (x+4) so x = -4.
The graph is reflected over the x axis as seen with -a
The graph is compressed vertically because the functions a value is less than f(x) =
Answer:
<u>D</u>
Step-by-step explanation:
Changes observed :
- Coefficient of x² becomes 1/3 of original, this means it is vertically compressed
- Also, the coefficient has become negative, meaning it is flipped over the x-axis
- x² is now (x + 4)², this means it has shifted 4 units to the left.
The correct option is <u>D</u>.
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The required two-digit number is 75.
<h3>What is arithmetic?</h3>In mathematics, it deals with numbers of operations according to the statements.
let the number in tenth place be x.
And has two fewer units than tens.
= x - 2
The two-digit number can be given as
= 10x + (x - 2)
= (11x - 2)
Reversing the digits
= (x - 2)10 + x
= 11x -20
The difference between twice the number and the number reversed is 93.
Now the required two-digit number is,
= 11x -2
= 11*7 - 2
= 77 -2
= 75
Thus the required two-digit number is 75.
Learn more about arithmetic here:
#SPJ1
Answer:
P(111.2-cm < ¯ x < 111.4-cm) = 0.4726
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.
In this problem, we have that:
Find the probability that the average length of a randomly selected bundle of steel rods is between 111.2-cm and 111.4-cm.
This is the pvalue of Z when X = 111.4 subtracted by the pvalue of Z when X = 111.2. So
X = 111.4
By the Central Limit Theorem
has a pvalue of 0.5.
X = 111.2
has a pvalue of 0.0274.
0.5 - 0.0274 = 0.4726
P(111.2-cm < ¯ x < 111.4-cm) = 0.4726