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If A={1,2,3} , find the relation R={(a, b) ∈ A²|a>b}
A shelf has 4 books, of which 2 are of science and 2 are of social studies. In how many ways can we select 3 books from the shelf such that we have atleast one science book and atleast one social studies book?
A bottler of drinking water fills plastic bottles with a mean volume of 999 milliliters (mL) and standard deviation 5 mL. The fill volumes are normally distributed. What proportion of bottles have volumes between 992 mL and 998 mL?
The calorie count of a serving of food can be computed based on its composition of carbohydrate, fat, and protein. The calorie count C for a serving of food can be computed using the formula C=4h+9f+4p, where h is the number of grams of carbohydrate contained in the serving, f is the number of grams of fat contained in the serving, and p is the number of grams of protein contained in the serving.
A serving of raisins contains 114 calories and 25 grams of carbohydrate. If raisins are a fat-free food, how much protein is provided by this serving of raisins?
Assume that 4 years from now you need 1000. Your bank compounds interest at an 8% annual rate.
a. how much must you deposit now to have a balance of 1000 at year 4?
b. if you want to make equal payments at the end of years 1 through 4 to accumulate the 1000, how large must each of the 4 payments be?
c. if your father were to offer either to make payments calculated in part b above or to give you a lump sum of 750 one year from now, which option would you choose and why?
d. if you have 750 at the end of year 1, what interest rate, compounded annually, would you have to earn to have necessary 1000 at year 4?
e. suppose you can deposit only 186.29 each at the end of year 1 through 4, but you still need 1000 at the end of year 4, what interest rate, with annual compounding, is required to achieve your goal?
f(x)=x^2+x-4 for a<=x<=a+3. if the range of the function f is -2<=f(x)<=16, find the possible values of a
Draw the Venn diagrams for each of these combinations of the sets A, B, and C.
A ∩ (B − C)
(A ∩ B) ∪ (A ∩ C)
(A ∩ ) ∪ (A ∩ )
Show that if A, B, and C are sets, then A ∩ B ∩ C = A ∪ B ∪ C
by showing each side is a subset of the other side.
using a membership table.
Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6}, and C = {4, 5, 6, 7, 8, 9, 10}. Find
A ∩ B ∩ C.
A ∪ B ∪ C.
(A ∪ B) ∩ C.
(A ∩ B) ∪ C.
f(x)=x^2-2x-3 for x>=0, -a<=x<=a. if the range of the function f is -4<=f(x)<=5, find the value of a.
