Let x represent the number of quarts of Tuscan sauce and
y represent the number of quarts of marinara sauce Tiffany makes.
A quart of Tuscan sauce requires 6 tomatoes and 1 cup of oil
x quarts requires 6x tomatoes and 1x cups of oil
A quart of her marinara sauce requires 5 tomatoes and 1.25 cups of oil
y quarts requires 5y tomatoes and 1.25 y cups of oil
She has 45 tomatoes and 10 cups of oil on hand.
So the constraints are
x>=0 and y>=0
Answer:
The p value for this case would be given by:
For this case since the p value is higher than the significance level given we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.32 or 32 %
Step-by-step explanation:
Information given
n=750 represent the random sample taken
estimated proportion of people who thought the economy is getting worse
is the value that we want to verify
represent the significance level
z would represent the statistic
represent the p value
Hypothesis to test
We want to check if the true proportion of interest is equal to 0.32 or not.:
Null hypothesis:
Alternative hypothesis:
The statistic would be given by:
(1)
Replacing we got:
The p value for this case would be given by:
For this case since the p value is higher than the significance level given we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true proportion is not significantly different from 0.32 or 32 %
Answer:
387.06
Step-by-step explanation:
(0 to 5) = round down
(5 to 9) = round up
Answer:
Step-by-step explanation:
The general formula for exponential decay given a half-life 
is
where N(t) is the amount at time t, 
is the initial amount (at time t=0), and is the half life of the substance.
The half life of carbon-14, is approximately 5,730 years.
= 5730 years
= 6 milligrams
Therefore:
Amount of carbon-14 remaining in the bone fragment after t years is:
We can start solving this problem by first identifying what the elements of the sets really are.
R is composed of real numbers. This means that all numbers, whether rational or not, are included in this set.
Z is composed of integers. Integers include all negative and positive numbers as well as zero (it is essentially a set of whole numbers as well as their negated values).
W on the other hand has 0,1,2, and onward as its elements. These numbers are known as whole numbers.
W ⊂ Z: TRUE. As mentioned earlier, Z includes all whole numbers thus W is a subset of it.
R ⊂ W: FALSE. Not all real numbers are whole numbers. Whole numbers must be rational and expressed without fractions. Some real numbers do not meet this criteria.
0 ∈ Z: TRUE. Zero is indeed an integer thus it is an element of Z.
∅ ⊂ R: TRUE. A null set is a subset of R, and in fact every set in general. There are no elements in a null set thus making it automatically a subset of any non-empty set by definition (since NONE of its elements are not an element of R).
{0,1,2,...} ⊆ W: TRUE. The set on the left is exactly what is defined on the problem statement for W. (The bar below the subset symbol just means that the subset is not strict, therefore the set on the left can be equal to the set on the right. Without it, the statement would be false since a strict subset requires that the two sets should not be equal).
-2 ∈ W: FALSE. W is just composed of whole numbers and not of its negated counterparts.
