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1. 4 boys and 3 girls are to be seated in a row of 7 chairs. How many ways can it be done under the following conditions:
a. boys stay together?
b. girls stay together?
c. boys and girls are seated alternately?
2. Permute the letters of the word SAINT. How many permutations
a. begin with vowels?
b. end with consonants?
c. begin with a vowel and end with a consonant?
d. begin with a consonant and end with a vowel?
3. In how many ways can 4 people sit a round table if
a. two people insist in sitting beside each other?
b. two refuse to sit beside each other?
c. one has a reserved seat?
Find
lim tan x sec^2 x- x/x^3
x→0
Consider the following premises:
1. A "\\to" (B "\\to" A) is a Theorem of Propositional Calculus/Logic (i.e. it’s logically valid),
for all statement forms A and B.
Suppose then that the following are the temporary axioms (assumptions):
a) W (axiom 1)
b) Y (axiom 2)
c) Y "\\to" Z (axiom 3)
Using the logical rules of inference, Modus Ponens (MP) and/or Hypothetical Syllogism
(HS), show that X "\\to" Z is deducible (i.e. it is a logical/valid conclusion) from the given
premises (i.e. 1 and 2).
Consider the following premises:
1. A "\\to" (B "\\to" A) is a Theorem of Propositional Calculus/Logic (i.e. it’s logically valid),
for all statement forms A and B.
Suppose then that the following are the temporary axioms (assumptions):
a) W (axiom 1)
b) Y (axiom 2)
c) Y "\\to" Z (axiom 3)
Using the logical rules of inference, Modus Ponens (MP) and/or Hypothetical Syllogism
(HS), show that X "\\to" Z is deducible (i.e. it is a logical/valid conclusion) from the given
premises (i.e. 1 and 2).
a)
i) Give an inductive formula for the sum of the first n odd numbers:
1 + 3 + 5 + ... + 2n -1
Show your induction process.
ii) Use the proof by mathematical induction to prove the correctness of your
inductive formula in i) above.
A study was conducted to determine the average salary of a teacher. With this, 81 teachers were invited as samples. It was known that the mean salary of these sample teachers is Php 24,000.00 with a standard deviation of Php 1,000.00. Construct a 90% confidence interval estimate for the average salary of all teachers.
Mrs. Balao is randomly choosing 3 students for a team who will compete in a math quiz bee, and there are 5 girls and 8 boys to choose from. What is the probability of having a team made up 2 girls and a boy?
Tshepo wants to buy a big screen tv. She has five interest rates to choose from if she borrows money from the bank. The cheapest option for her is
1) 29% per year, compounded daily
2) 30% per year, compounded semi-annually
3) 28.5% per year, compounded weekly or
4) 29.5% per year, compounded every two months
Given the data: 123, 126, 129, 132, and (a) construct a sampling of
the mean (b) draw a histgyfor the sample means
b. Show on the real line and indicate in symbols each of the following:
S₁= {x: -7 < x < ∞ } ∩ {x: -∞ < x < 3}
S₂= (x:x ≥ ∞ } ∩ (x: x+ 3 < 6}
S3 = y: y²-2 y-3 < 0} U {y: -2 ≤ y ≤ 1}
#340153 on Dec 2023