MATHEMATICS COLLEGE

Use the binomial theorem to expand the expression :(3x + y)^5 and simplify.
(b) find the middle term in the expansion of
(1/x+√x)^4 and simplify your unswer.
(c) determine the coefficient of x^11 in the expansion of (x^2 +1/x)^10, simplify your answer.

Answers

Answer 1
Answer:

Answer:

a) (3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5.

b) The middle term in the expansion is (6)/(x).

c) The coefficient of x^(11) is 120.

Step-by-step explanation:

Remember that the binomial theorem say that (x+y)^n=\sum_(k=0)^(n) \binom{n}{k}x^(n-k)y^(k)

a) (3x+y)^5=\sum_(k=0)^5\binom{5}{k}3^(n-k)x^(n-k)y^k

Expanding we have that

\binom{5}{0}3^5x^5+\binom{5}{1}3^4x^4y+\binom{5}{2}3^3x^3y^2+\binom{5}{3}3^2x^2y^3+\binom{5}{4}3xy^4+\binom{5}{5}y^5

symplifying,

(3x+y)^5=243x^5+405x^4y+270x^3y^2+90x^2y^3+15xy^4+y^5.

b) The middle term in the expansion of ((1)/(x) +√(x))^4=\sum_(k=0)^(4)\binom{4}{k}(1)/(x^(4-k))x^{(k)/(2)} correspond to k=2. Then \binom{4}{2}(1)/(x^2)x^{(2)/(2)}=(6)/(x).

c) (x^2+(1)/(x))^(10)=\sum_(k=0)^(10)\binom{10}{k}x^(2(10-k))(1)/(x^k)=\sum_(k=0)^(10)\binom{10}{k}x^(20-2k)(1)/(x^k)=\sum_(k=0)^(10)\binom{10}{k}x^(20-3k)

Since we need that 11=20-3k, then k=3.

Then the coefficient of x^(11) is \binom{10}{3}=120

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Answers

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Which statement must be true according to the dot plot?The number of text messages that Reza sent each day so
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Answers

*see attachment for the dot plot being referred to

Answer:

The data is symmetric and shows that he typically sent about 6 to 8 text messages per day

Step-by-step explanation:

The distribution of the data set on a dot plot can be said to be symmetric when most of the data points in the data are located or are concentrated at the center of the dot plot.

As we can observe from the given dot plot in the attachment, it shows that 6 to 8 text messages per day have more frequencies and are just right at the center of the dot plot. This shows the data is symmetric.

This also shows that Reza dents averagely 6 - 8 text messages per day. Reza can be said to have typically sent 6 - 8 text messages per day.

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A fair coin is tossed 25 times. what is the probability that at most 24 heads occur?

Answers

The probability that at most 24 heads occur is; 24/25.

What do we mean by probability?

Probability is the branch of mathematics that deals with numerical descriptions of how likely an event is to occur or how likely it is that a proposition is true. The probability of all the events occurring need to be 1.

We have been given that a fair coin is tossed 25 times.

So, We need to find the probability:

Favourable outcomes = 24

Total outcomes = 25

The formula of probability = Favourable outcomes/Total outcomes

⇒ 24 /25

Therefore, the probability that at most 24 heads occur is; 24/25.

Know more about probability here:

brainly.com/question/24756209

#SPJ2
Very rare. Because 25 is a high chance of it always being heads.

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Answers

Answer:

c

Step-by-step explanation:

3.66+.72+1.77+2.17=8.32×6%=8.8192 =8.82

Answer:

C Yes, the total of her purchase after sales tax is $8.82.

Step-by-step explanation:

3.66+0.72+1.77+2.17= $8.32

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0.4992+8.32= $8.82

Hope this helps!

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Answers

Answer:

A:100°

Step-by-step explanation:

BECAUSE IS THE SAME
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Answers

Answer:

18

Step-by-step explanation:

2x-10=x+8

2x-x=8+10

x=18
Answer is 18 hoped this help
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