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4 years ago

A number added to itself is one

Mathematics

1 answer:

Ivenika [448]4 years ago

6 0

The number would be .5 I'm pretty sure

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Help me asap! I will give you marks

Law Incorporation [45]

Recall the binomial theorem.

$(a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k$

1. The binomial expansion of $\left(1+\frac x3\right)^7$ is

$\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}$

Observe that

$k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x$

$k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2$

When we multiply these by $8-9x$ ,

• $8$ and $\frac73 x^2$ combine to make $\frac{56}3 x^2$

• $-9x$ and $\frac73 x$ combine to make $-\frac{63}3 x^2 = -21x^2$

and the sum of these terms is

$\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}$

2. The binomial expansion is

$\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k$

We get the $a^6b^2$ term when $k=2$ :

$k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2$

6 0

1 year ago

There are 418 students at a school. Han estimates that they each drink about 5 glasses of water each day.

Sauron [17]

Answer:

Step-by-step explanation:

a) together, they all drink about 2,090 glasses of water in one day. (418 * 5 = 2,090).

b) 2,090 * 7 (7 days in 1 week) = They drink about 14,630 glasses of water in one week.

c) 14,630 * 4 (4 weeks in 1 month) = About 58,520 glasses of water in one month.

d) 1,000,000/58,520 ≈ 17. It would take all of the students about 17 months to drink 1,000,000 glasses of water.

Hope that helps!

6 0

3 years ago

PLS HELP ME

eimsori [14]

Answer:

5.5

Step-by-step explanation:

2,3,3,4,5,7,8,8,8,10,10,12

The mean of this data is 7.5. So what you are trying to figure out is the mean between 2 and 7. Since that is 3 and 4 it would be 3.5. So 3.5 is the Q1. Now you have to figure out the mean between 8 and 12. That is 9. This is Q3. You have to subtract 9-3.5 and that is the interquartile range. So 5.5 is the answer. I hope that made sense.

6 0

2 years ago

Suppose 10 people are chosen at random from a group of 1200. What is the probability that all 10 would rate their financial shap

Pachacha [2.7K]

1200/10= 120 and 120 is your answer

5 0

4 years ago

What is 2/3x+4=4/5x-2

Anuta_ua [19.1K]

Hey there!

Apply fraction cross multiply: if a/b = c/d , then a *d = b*c

2 ( 5x - 2 ) = ( 2x + 4 ) * 4

expand : 2 (5x-2 ) => 2*5x - 2*2 => 10x - 4

expand : ( 2x +4 ) * 4 => 2x * 4 + 4*4 => 8x + 16

10x - 4 = 8x+16

add 4 to both sides:

10x-4+4 = 8x+16+4

simplify :

10x = 8x + 20

subtract 8x from both sides:

10x -8x = 8x+20-8x

simplify:

2x = 20

Therefore:

x = 20 / 2

x = 10

Hope that helps!

8 0

3 years ago

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