1)A bookshelf holds 4 mysteries, 3 biograpghies, 1 book of poetry, and 2 reference books. If a book is selected at random from the shelf, find the probability that the book selected is a biography or reference book.
A)1/2
B)1/6
C)5/6
D)3/50
I chose A
5 bio/reference/10 total books
1/2
2)Find the standard deviation of the data set to the nearest tenth. (21,13,18,16,13,35,12,8,15)
A)16.8
B)7.8
C)7.3
D)5.7
I chose C
mean = 21+13+18+16+13+35+12+8+15/9
16.8
variance = (21-16.8)^2 = 17.64...did that with the rest and added them to get sqrt 53.7
standard deviation = sqrt 53.7
= 7.3
3)Find the exact value of sin165
A)(sqrt6) - (sqrt2)/4
B)(sqrt6) + (sqrt2)/4
C)(sqrt2) - (sqrt6)/4
D)(sqrt of sqrt6 - sqrt2)/4
I chose A
(in D, there is a sqrt over both the sqrt6 and sqrt2
If I have it wrong can you explain how to do these types of problems b/c what I do is just take the sqrt of 6, subtract that from the sqrt of 2 and then divide by 4. I always end up with the same answer when I get the value of sin165 when I type it in my calculator
For question one use:
P( A or B) = P(A) + P(B) - P(A and B)
The rule for OR takes into account those values that may get counted more than once when the probability is determined.
Let P = probability
Let A = biographies
Let B = reference book
Can you finish?
No. why would I not just take the number of bio and ref. and divide by the total number of books?
since P(A and B) from blueridge's formula is zero, you are right, total is 5
so prob. = 5/10 = 1/2
1) To find the probability that the book selected is a biography or reference book, you need to determine the total number of books in the shelf and the number of biographies and reference books.
Total number of books = 4 (mysteries) + 3 (biographies) + 1 (book of poetry) + 2 (reference books) = 10
Number of biographies and reference books = 3 (biographies) + 2 (reference books) = 5
The probability is calculated by dividing the number of biographies and reference books by the total number of books:
Probability = Number of biographies and reference books / Total number of books = 5 / 10 = 1/2
So, the correct answer is A) 1/2.
2) To find the standard deviation of the given data set, you need to follow these steps:
1. Find the mean (average) of the data set:
Mean = (21 + 13 + 18 + 16 + 13 + 35 + 12 + 8 + 15) / 9 = 16.8
2. Find the deviation of each data point from the mean:
Deviation for each data point = Data point - Mean
3. Square each deviation:
Squared deviation for each data point = (Deviation)^2
4. Find the variance by taking the average of the squared deviations:
Variance = (sum of squared deviations) / (total number of data points)
5. Finally, find the standard deviation by taking the square root of the variance.
Calculating the variance:
Variance = [(21-16.8)^2 + (13-16.8)^2 + (18-16.8)^2 + (16-16.8)^2 + (13-16.8)^2 + (35-16.8)^2 + (12-16.8)^2 + (8-16.8)^2 + (15-16.8)^2] / 9
Variance = 53.7
Calculating the standard deviation:
Standard deviation = sqrt(53.7) ≈ 7.3
So, the correct answer is C) 7.3.
3) To find the exact value of sin165, you can use the trigonometric identity:
sin(180 - θ) = sin(θ)
Since 165 is less than 180, we can use this identity to simplify the problem.
sin(165) = sin(180 - 15)
Now, we know that sin(15) can be written as sin(45 - 30) using another trigonometric identity:
sin(45 - θ) = (sqrt(2) / 2) * sin(θ) - (sqrt(2) / 2) * cos(θ)
sin(30) = (sqrt(2) / 2) * sin(15) - (sqrt(2) / 2) * cos(15)
Substituting sin(30) = 1/2 and cos(30) = sqrt(3)/2, we get:
sin(165) = (sqrt(2) / 2) * (1/2) - (sqrt(2) / 2) * (sqrt(3) / 2)
Doing the calculations, we simplify to:
sin(165) = (sqrt(6) - sqrt(2)) / 4
So, the correct answer is A) (sqrt(6) - sqrt(2)) / 4.
You did a great job in calculating the values correctly! To solve these types of problems, remember to use trigonometric identities, formulas, and calculator functions to simplify and find exact values.