1. If quadrilateral ABCD is rotated 270° clockwise about the origin, find the coordinates of B'.

Mathematics

1 answer:

Zielflug [23.3K]3 years ago

4 0

Answer:

The coordinates of B' are (-3, 5).

Step-by-step explanation:

For every 90 degrees rotated, the coordinate numbers switch and one is multiplied by -1, when clockwise it's the 2nd one, and when counterclockwise, it's the 1st.

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A library has five copies of a certain textbook on reserve of which two copies (1 and 2) are hardcover books and the other three

Gre4nikov [31]

Answer and Step-by-step explanation:

(a) Since the student have to stop when he gets to w softcover book, then the sample space should always stop at either 3 or 4 or 5. If the students examines the books randomly and stops at a softcover book, here are the possible ways he could carry this out,

S = {3, 4, 5, 13, 14, 15, 23, 24, 25, 123, 124, 125, 213, 214, 215}

2. Since only one book is to be examined then the student must check only one softcover book and end the examining. To do this, either he examines just 3 or 4 or 5. Therefore,

A = {3, 4, 5}

3. We need to pick the possibilities from the sample space that shows that the examining ended at book 5. Therefore,

B = {5, 15, 25, 125, 215}

4. We need to pick possibilities from the sample space that shows that book 1 was not examined. Therefore,

C = {3, 4, 5, 23, 24, 25}

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3 years ago

9. A band director wants to form a committee of 4 parents from a list of 45 band parents.

Alex73 [517]

Answer:

Part (A): The number of ways to select 12 jurors are 86493225.

Part (B): The number of ways to select 2 alternates are 306.

Part (C): Part (a) is an example of combination and Part (a) is an example of permutation

Step-by-step explanation:

Consider the provided information.

A band director wants to form a committee of 4 parents from a list of 45 band parents.

Part (A): How many different groups of 4 parents can the band director select?

Since order doesn't matter so we will use combination.

Use the formula for combination $^{n}C_{r}=\frac{n!}{r!(n-r)!}$

Substitute n=45 and r=4 in above formula.

$^{45}C_{4}=\frac{45!}{4!(45-4)!}$

$^{45}C_{4}=\frac{45!}{4!41!}$

$^{45}C_{4}=148995$

Hence, the number of ways are 148995.

Part (B) How many different ways can the band director select 4 parents to serve in the band parents’ association as president, vice president, treasurer, and secretary?

Since the order matter so we will use permutation:

The formula for permutation is: $^{n}P_{r}=\frac{n!}{(n-r)!}$