Answer:
43, 57, 71, 85, 99..
a(n)=a(n-1)+14
Step-by-step explanation:
Arithmetic sequence, ratio 14
Answer:
Height of the 12 cases will be =
inches.
Step-by-step explanation:
Thickness of each DVD storage case =
inches
Let number of DVD storage cases sold = x
Therefore, the height of cases sold will be represented by the expression 
If the number of cases sold x = 12
So the height of the cases sold will be =
inches
=
inches
Therefore, the answer is
inches.
Answer:
C. A dilation
Step-by-step explanation:
Dilations create entirely new shapes; however, other types of transformations maintain congruence to the original shape.
Using the <em>normal distribution and the central limit theorem</em>, it is found that the probability the mean cost of the weddings is more than the mean cost of the showers is of 0.9665.
<h3>Normal Probability Distribution</h3>
In a normal distribution with mean
and standard deviation
, the z-score of a measure X is given by:

- It 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, which is the percentile of X.
- By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation
.
- When two variables are subtracted, the mean is the subtraction of the means, while the standard error is the square root of the sum of the variances.
<h3>What is the mean and the standard error of the distribution of differences?</h3>
For each sample, they are given by:


For the distribution of differences, we have that:


The probability the mean cost of the weddings is more than the mean cost of the showers is P(X > 0), that is, <u>one subtracted by the p-value of Z when X = 0</u>, hence:

By the Central Limit Theorem



has a p-value of 0.0335.
1 - 0.0335 = 0.9665.
More can be learned about the <em>normal distribution and the central limit theorem</em> at brainly.com/question/24663213
Answer:
Step-by-step explanation:
Given the equation y=-2x+1 and given another equation y=mx+b in order for us to have no solution we must guarantee that both lines do not intersect. Recall that m is the slope of the second equation and b the y-intercept. To guarantee that both lines don't intersect, they must be parallel. To have this result, we must have that they have the same slope but different y intercept. That is take m = -2 and b any value different to +1. For example, the b = 6. So
y = -2x+6 = -2(x-3) is another equation that gives no solution to the system.