1)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
2)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)
3)Use the Binomial Theorem to find the sixth term in the expansion of (m+2p)^7.
A)21m^2p^5
B)672m^2p^5
C)32m^2p^5
D)448mp^6
I chose A
7/(7-k)!k!^m7-kpk
7/(7-5)!5!^m7-5p5
7*6*5*4*3/5*4*3*2*1^m2p5
2520/120
21m^2p^5
Discard this post
For the first question, the standard deviation of a data set measures how spread out the values are from the mean. To calculate the standard deviation, you can follow these steps:
1) Calculate the mean by adding up all the values and dividing by the total number of values:
mean = (21+13+18+16+13+35+12+8+15) / 9 = 16.8
2) Calculate the variance by finding the difference between each value and the mean, squaring it, and then taking the average of all the squared differences:
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 = (17.64 + 11.76 + 1.44 + 0.64 + 11.76 + 321.84 + 18.24 + 81.44 + 2.56) / 9 = 74.4
3) Calculate the standard deviation by taking the square root of the variance:
standard deviation = sqrt(74.4) ≈ 7.3
So the correct answer is C) 7.3.
For the second question, to find the value of sin165, you can use the following trigonometric identity:
sin(180 - x) = sin(x)
Since 165 degrees is 180 minus 15 degrees, we can rewrite sin165 as sin(180-15).
sin(180-15) can be further simplified using the angle addition formula:
sin(180-15) = sin(180)*cos(15) - cos(180)*sin(15)
Since sin(180) = 0 and cos(180) = -1, the equation becomes:
sin(165) = 0*cos(15) - (-1)*sin(15) = sin(15)
Now, to find sin(15), you would typically use a calculator or a trigonometric table.
Using a calculator, sin(15) is approximately 0.2588.
So the correct answer is A) (sqrt6) - (sqrt2)/4.
For the third question, to find the sixth term in the expansion of (m+2p)^7 using the Binomial Theorem, you can use the formula:
Term(k+1) = (nCk)*(a^(n-k))*(b^k)
Where:
- n is the exponent of the binomial (in this case, 7),
- k is the power that the first term is raised to,
- a is the coefficient of the first term,
- b is the coefficient of the second term in the binomial (in this case, m and 2p respectively).
To find the sixth term, k would be 5 since it starts from 0.
Plugging in the values into the formula, we get:
Term(6) = (7C5)*(m^(7-5))*(2p)^5
= (7C5)*(m^2)*(32p^5)
= (7*6/2)*(m^2)*(32p^5)
= 21m^2p^5
So the correct answer is A) 21m^2p^5.