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Exam 7: Multivariable Calculus

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Question 41

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Use a Venn Diagram and the given information to determine the number of elements in the indicated region. -In a marketing survey involving 1,000 randomly chosen people, it is found that 660 use brand P, 440 use brand Q, and 220 use both brands. How many people in the survey use brand P and not brand

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Question 42

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Let A = {1, 3, 5, 7}; B = {5, 6, 7, 8}; C = {5, 8}; D = {2, 5, 8}; and U = {1, 2, 3, 4, 5, 6, 7, 8}. Determine whether the given statement is true or false. -

A) True
B) False

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Question 43

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Determine whether the given set is finite or infinite. Consider the set N of positive integers to be the universal set, and let -

Determine whether the given set is disjoint or not disjoint. Consider the set N of positive integers to be the universal set, and let -

Determine whether the selection is a permutation, a combination, or neither. -Mary baked 3 pies: 1 for her father, 1 for her friend Joe, and 1 for her coworkers.

Provide an appropriate response. -License plates are made using 3 letters followed by 3 digits. How many plates can be made if repetition of letters and digits is allowed?

Solve the problem. -How many ways can a committee of 3 be selected from a club with 12 members?

Provide an appropriate response. -How many different five-letter code words are possible from the first ten letters of the alphabet if the first letter cannot be a vowel and adjacent letters must be different.

Tell whether the statement is true or false. -

Use the Venn diagram below to find the number of elements in the region. -

Solve the problem. -A software company employs 9 sales representatives and 8 technical representatives. How many ways can the company select 5 of these employees to send to a computer convention if at least 4 technical representatives Must attend the convention?

Provide an appropriate response. -A restaurant offered pizza with 3 types of crusts and 7 different toppings. How many different types of pizzas could be offered?

Provide an appropriate response. -A Super Duper Jean company has 3 designs that can be made with short or long length. There are 5 color patterns available. How many different types of jeans are available from this company?

Provide an appropriate response. -Mrs. Bollo's second grade class of thirty students conducted a pet ownership survey. Results of the survey indicate that 8 students own a cat, 15 students own a dog, and 5 students own both a cat and a dog. How many Of the students surveyed own only a dog?

Use the Venn diagram to find the requested set. -Find B.

Use the Venn diagram below to find the number of elements in the region. -

Provide an appropriate response. -State the converse and contrapositive of the position, "If n is an integer that is a multiple of 15, then n is an integer that is a multiple of 3 and a multiple of 5."

Provide an appropriate response. -Construct a truth table for the proposition and determine whether it is a contingency, a tautology, or a contradiction: (q p ) ) ~q.

Provide an appropriate response. -How many nine-digit ZIP code numbers are possible if the first digit cannot be a four and adjacent digits cannot be the same?

Tell whether the statement is true or false. -{all odd integers greater than -3 and less than 5} = {-1, 1, 3}