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Zielflug [23.3K]

3 years ago

7

Each side of a sandbox is 6 feet long. It will cost $3.00 per square foot to replace the sand in the sandbox. What would be the

total cost to replace the sand?

1 answer:

omeli [17]3 years ago

3 0

Answer:

I don't know

Step-by-step explanation:

Unknown, but you could probably use Googl#

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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

3 years ago

Based on the table, what is Nick's rate?

Nookie1986 [14]

7 yrds/sec because in the course of two seconds, he runs 14 yrds divide that by 2 to get 7 yrds/sec. you can allo chech with the next time which is 3 seconds more and he goes 21 yards more.

5 0

3 years ago

Answer two questions about Systems A and B:System A x+3y=−9 2x+y=4 System B 3x+4y=−9 2x+y=4

Jet001 [13]

Answer:

A=(21/5,-22/5) B=(5,-6)

Step-by-step explanation:

6 0

3 years ago

Sarah says that 26 divided by 8 equals 14 divided 4 because both are "3 R2. show her mistake using decimal division

mezya [45]

26/8=3.25
14/4=3.5
You must show your work.

8 0

3 years ago

If the temperature dropped by 7.f each hour from 5:00 am to 9:00 am. What was the beginning temperature at 5:00 am if the temper

arlik [135]

If the temperature dropped by 7.f each hour from 5:00 am to 9:00 am. the beginning temperature at 5:00 am if the temperature at 9:00 am was -10.f is 18.f.

<h3>Beginning temperature</h3>

Dropped in temperature=7.t

Number of hours= 5:00 am to 9:00 am=4 hours

Temperature at 9:00 am=-10.f

Hence:

Beginning temperature can be calculated as:

Beginning temperature=(4× 7) + (-10)

Beginning temperature=28 + (-10)

Beginning temperature= 18.f

Check:

Since temperature dropped by 7.f each hour from 5:00 am to 9:00 am

which implies that temperature 7.f dropped for 4 hours.

Hence:

18-7-7-7-7=-10.f

Therefore If the temperature dropped by 7.f each hour from 5:00 am to 9:00 am. the beginning temperature at 5:00 am if the temperature at 9:00 am was -10.f is 18.f.

Learn more about Beginning temperature here:brainly.com/question/24746268

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4 0

2 years ago