I need help with 3, 5, 8, and 10

For the binomial expansion of (x + y)^10, the value of k in the term 210x 6y k is a) 6 b) 4 c) 5 d) 7

Sloan [31]

Answer:

a) 6

Step-by-step explanation:

Expanding the polynomial using the formula:

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

Also

$\binom{n}{k}=\frac{n!}{(n-k)!k!}$

I think you mean $210x^6y^4$

We can deduce that this term will be located somewhere in the middle. So I will calculate $k= 5; k=6 \text{ and } k =7$ .

For $k=5$

$\binom{10}{5} (y)^{10-5} (x)^{5}=\frac{10!}{(10-5)! 5!}(y)^{5} (x)^{5}= \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5! }{5! \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } \\ =\frac{30240}{120} =252 x^{5} y^{5}$

Note that we actually don't need to do all this process. There's no necessity to calculate the binomial, just $x^{n-k} y^k$

For $k=6$

$\binom{10}{6} \left(y\right)^{10-6} \left(x\right)^{6}=\frac{10!}{(10-6)! 6!}\left(y\right)^{4} \left(x\right)^{6}=210 x^{6} y^{4}$

5 0

2 years ago

The distribution of annual profit at a chain of stores was approximately normal with mean \mu = \$66{,}000μ=$66,000mu, equals, d

Pepsi [2]

Answer:

The closest to the maximum profit is $x = \$ 83682$

Step-by-step explanation:

From the question we are told that

The mean is $\mu = \$66,000$

The standard deviation is $\sigma = \$ 21000$

The percentage of profit is 20%

Generally the closest to the maximum annual profit at a store where the executives conducted an audit is mathematically evaluated as follows

$P(X > x ) = 0.20$

=> $P(X > x ) = P(\frac{X -x}{\sigma } > \frac{x -66000}{21000} ) = 0.20$

From the z-table the z-score for 0.20 is

$z-score = 0.842$

So

$\frac{x -66000}{21000} = 0.842$

=> $x = \$ 83682$

4 0

2 years ago

Ernest is purchasing a $175,000 home and is making a 20% down payment toward the cost. He is also buying 2 points in order to lo

belka [17]

Your answer would be. $39,075.

5 0

2 years ago

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According to a nutrition coach, a 100 kg person should eat

alexira [117]

Answer:

0.07%

Step-by-step explanation:

This equation is solving for what percentage of 100 kg is 0.07 kg.

1. Set up the equation

$\frac{0.07}{100}$ = $\frac{x}{100}$

0.07 kg out of 100 kg is equal to x out of 100 because x represents the percentage and percentages are out of 100.

2. Solve by cross multiplying

100x = 7

3. Solve for x by dividing both sides by 100

x = 0.07

The answer is 0.07%

4 0

2 years ago

Which table shows a constant rate of change of –3? A 2-column table with 4 rows. Column 1 is labeled x with entries 3, 4, 5, 6.

Andrew [12]

Answer:

c

Step-by-step explanation:

6 0

2 years ago

Read 2 more answers