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Inessa [10]
3 years ago
6

My sister needs help... blahhh!!! please answer 8,9, and 10 please!!!! Thank you!

Mathematics
1 answer:
castortr0y [4]3 years ago
6 0
8:1 -4/15 9:6 1/2 10:can't figure it out!
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In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8;
Fiesta28 [93]

We have to find the expansion of (3a+4b)^{8}

We will use binomial expansion to expand the given expression, which states that the expression (a+b)^{n} is expanded as :

(a+b)^{n}=^{n}C_{0}a^{n}+^{n}C_{1}a^{n-1}b+^{n}C_{2}a^{n-2}b^{2}+........^{n}C_{n}b^{n}

Now expanding (3a+4b)^{8} we get,

(3a+4b)^{8}=^{8}C_{0}(3a)^{8}+^{8}C_{1}(3a)^{7}(4b)+^{8}C_{2}(3a)^{6}(4b)^{2}+^{8}C_{3}(3a)^{5}(4b)^{3}+^{8}C_{4}(3a)^{4}(4b)^{4}+^{8}C_{5}(3a)^{3}(4b)^{5}+^{8}C_{6}(3a)^{2}(4b)^{6}+^{8}C_{7}(3a)(4b)^{7}+^{8}C_{8}(4b)^{8}

(3a+4b)^{8}=^{8}C_{0}(3)^{8}a^{8}+^{8}C_{1}(3)^{7}(4)(a^{7}b)+^{8}C_{2}(3)^{6}(4)^{2}(a^{6}b^{2})+^{8}C_{3}(3)^{5}(4)^{3}(a^{5}b^{3})+^{8}C_{4}(3)^{4}(4)^{4}(a^{4}b^{4})+^{8}C_{5}(3)^{3}(4)^{5}(a^{3}b^{5})+^{8}C_{6}(3)^{2}(4)^{6}(a^{2}b^{6})+^{8}C_{7}(3)(4)^{7}(ab^{7})+^{8}C_{8}(4)^{8}(b^{8})

So, the variables are a^{5}b^{3} , b^{8} , a^{4}b^{4} , a^{8}  , [tex] ab^{7}

5 0
3 years ago
The Great Eagles of the Misty Mountains wish to estimate the mean number of orcs per raiding party. To do so, they measure the n
Anestetic [448]

Answer:

The Upper Bound of the 99% confidence interval about the mean number of orcs per raiding party is of 106.83 orcs per party.

Step-by-step explanation:

We have the standard deviation of the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 13 - 1 = 12

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 12 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.99}{2} = 0.995. So we have T = 3.0545

The margin of error is:

M = T*s = 3.0545*7.8 = 23.83

In which s is the standard deviation of the sample.

The upper end of the interval is the sample mean added to M. So it is 83 + 23.83 = 106.83 orcs per party.

The Upper Bound of the 99% confidence interval about the mean number of orcs per raiding party is of 106.83 orcs per party.

7 0
4 years ago
What is the radius of a circle whose equation is x2 + y2 + 8x - 6y + 21 = 0?<br> units
pickupchik [31]

Answer:r=2

Step-by-step explanation:

6 0
3 years ago
6_7/8 + 9_5/16 pls help
Paladinen [302]
16_3/16 is the answer! hope this helps!! :)
8 0
3 years ago
PLEASE HELP! IN DESPERATE NEED! Please SHOW YOUR WORK! Thx so much! :)
spayn [35]
1.

92+\frac{56}{14-x}=100\\\\\frac{56}{14-x}=8\\\\(\frac{56}{14-x})*(14-x)=8*(14-x)\\\\56=(8*14)+[8*(-x)]\\\\56=112-8x\\\\-56=-8x\\\\\\x=7


2.

\frac{410-x}{7}+70=120\\\\\frac{410-x}{7}=50\\\\(\frac{410-x}{7})*7=50*7\\\\410-x=350\\\\-x=-60\\\\\\x=60
4 0
3 years ago
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