Elena went to the store where you can scoop your own popcorn and buy as much as you want.she brought 10 ounces of spicy popcorn
for $2.50.How much popcorn can you buy per dollar?
1 answer:
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No, (2,2) is not solution of y < 4x - 6
Step-by-step explanation:
To solve above linear problem, we use standard method of Back- Substitution.
First of all, A point (2,2) only becomes solution of equation, if it satisfies equation .
Here, the seems to be like a linear equation.
In this Equation, using Back- Substitution method,
Point (2,2) : first digit 2 corresponds to x- coordinate and second digit 2 corresponds to y-coordinate.
By putting value of x and y in equation (1),
Equation becomes,
.... not true mathematically.
Finally, the result came is not true. Therefore, (2,2) is not solution for equation
Answer:
a) A sample of 256 was used in this survey.
b) 45.14% probability that the point estimate was within ±15 of the population mean
Step-by-step explanation:
This question is solved using the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
a. How large was the sample used in this survey?
We have that . We want to find n, so:
A sample of 256 was used in this survey.
b. What is the probability that the point estimate was within ±15 of the population mean?
15 is the bounds with want, 25 is the standard error. So
Z = 15/25 = 0.6 has a pvalue of 0.7257
Z = -15/25 = -0.6 has a pvalue of 0.2743
0.7257 - 0.2743 = 0.4514
45.14% probability that the point estimate was within ±15 of the population mean
Step-by-step explanation:
Use the method of TOA CAH SOH.
Perimeter of triangle = Sum of all sides =