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3 years ago

5

A city has the population of 210,000 people. Suppose that each year the population grows by 7.5%. What will the population be af

ter 13 years?

1 answer:

Nady [450]3 years ago

8 0

Answer:

6 5

Step-by-step explanation:

4 5 6 7

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What is the coefficient of x2y3 in the expansion of (2x + y)5?

Zigmanuir [339]

Option C:

The coefficient of $x^{2} y^{3}$ is 40.

Solution:

Given expression:

$(2 x+y)^{5}$

Using binomial theorem:

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here $a=2 x, b=y$

Substitute in the binomial formula, we get

$(2x+y)^5=\sum_{i=0}^{5}\left(\begin{array}{l}5 \\i\end{array}\right)(2 x)^{(5-i)} y^{i}$

Now to expand the summation, substitute i = 0, 1, 2, 3, 4 and 5.

$$=\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}+\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1}+\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}+\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}$

$$+\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}+\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}$

Let us solve the term one by one.

$$\frac{5 !}{0 !(5-0) !}(2 x)^{5} y^{0}=32 x^{5}$

$$\frac{5 !}{1 !(5-1) !}(2 x)^{4} y^{1} = 80 x^{4} y$

$$\frac{5 !}{2 !(5-2) !}(2 x)^{3} y^{2}= 80 x^{3} y^{2}$

$$\frac{5 !}{3 !(5-3) !}(2 x)^{2} y^{3}= 40 x^{2} y^{3}$

$$\frac{5 !}{4 !(5-4) !}(2 x)^{1} y^{4}= 10 x y^{4}$

$$\frac{5 !}{5 !(5-5) !}(2 x)^{0} y^{5}=y^{5}$

Substitute these into the above expansion.

$(2x+y)^5=32 x^{5}+80 x^{4} y+80 x^{3} y^{2}+40 x^{2} y^{3}+10 x y^{4}+y^{5}$

The coefficient of $x^{2} y^{3}$ is 40.

Option C is the correct answer.

5 0

2 years ago

Is the graph increasing or decreasing?<br> A:increasing <br> B:decreasing <br> C:constant

Ann [662]

Looks like the graph is decreasing to me

3 0

3 years ago

Does anyone know this?

Anni [7]

7,8, and 9
8 * 9 = 72

5 0

3 years ago

I need help with this pls

Alexxx [7]

Hello!

<u>What is an x-intercept</u>:

⇒ <em>value of x</em> when the <em>value of y</em> equals '0'

$8x + 5y=25\\8x+5(0)=25\\8x=25\\\\x=\dfrac{25}{8}$

x-intercept is <u>25/8</u>

<u></u>

<u></u>

<u>What is a y-intercept:</u>

⇒ <em>value of y</em> when the <em>value of x</em> equals '0'

$8x+5y=25\\8(0)+5y=25\\5y=25\\y=5$

y-intercept is <u>5</u>

<u></u>

Hope that helps!

<u />

5 0

1 year ago

THIS IS MY 6TH TIME POSTING THIS HELP

Alenkasestr [34]

Answer:

14 yards

Step-by-step explanation:

length of basketball court=

7 inches

(times by 2.8) 2.5 inches-5 yards( times by 2.8)

7 inches=14

i hope i helped:)

3 0

3 years ago