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3 years ago

7

a carton can hold 1,000 unit cubes that measure 1 inch by 1 inch by 1 inch. Describe the dimensions of the carton using unit cub

es.

1 answer:

Ne4ueva [31]3 years ago

6 0

the cartons dimensions are 10x10x10

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Use induction to prove that 2? ?? for any integer n>0 . Indicate type of induction used.

Hoochie [10]

Answer with explanation:

The given statement is which we have to prove by the principal of Mathematical Induction

$2^{n}>n$

1.→For, n=1

L H S =2

R H S=1

2>1

L H S> R H S

So,the Statement is true for , n=1.

2.⇒Let the statement is true for, n=k.

$2^{k}>k$

---------------------------------------(1)

3⇒Now, we will prove that the mathematical statement is true for, n=k+1.

$\rightarrow 2^{k+1}>k+1\\\\L H S=\rightarrow 2^{k+1}=2^{k}\times 2\\\\\text{Using 1}\\\\2^{k}>k\\\\\text{Multiplying both sides by 2}\\\\2^{k+1}>2k\\\\As, 2 k=k+k,\text{Which will be always greater than }k+1.\\\\\rightarrow 2 k>k+1\\\\\rightarrow2^{k+1}>k+1$

Hence it is true for, n=k+1.

So,we have proved the statement with the help of mathematical Induction, which is

$2^{k}>k$

3 0

3 years ago

Simply the following radicals, showing ALL WORK

prisoha [69]

Had to do this since it’s kinda hard to type it out

3 0

3 years ago

An insurance company found that 9% of drivers were involved in a car accident last year. If seven drivers are randomly selected,

zzz [600]

Answer: 0.1061

Step-by-step explanation:

Given : An insurance company found that 9% of drivers were involved in a car accident last year.

Thus, the probability of drivers involved in car accident last year = 0.09

The formula of binomial distribution :-

$P(X=x)^nC_xp^x(1-p)^{n-x}$

If seven (n=7) drivers are randomly selected then , the probability that exactly two (x=2) of them were involved in a car accident last year is given by :-

$P(X=2)=^7C_2(0.09)^2(1-0.09)^{7-2}\\\\=\dfrac{7!}{2!5!}(0.09)^2(0.91)^{5}=0.106147867882\approx0.1061$

Hence, the required probability :-0.1061

3 0

3 years ago

Find the equation of the line parallel to 2y-3x= 4 and passing through the point (6,7)

frutty [35]

Answer:

We have equation of a line:

2y - 3x = 4 => y = (3/2)x + 4

The equation of the line that is parallel to above line and passes through the point (6, 7) would have form y = ax + b, and

a = 3/2

6a + b = 7

=> b = 7 - 6a = 7 - 6 x 3/2 = 7 - 9 = -2

=> The equation of that line: y = (3/2)x - 2

Hope this helps!

:)

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3 years ago

A rectangular prism is completely packed with 90 cubes of edge length fraction 1 over 2 inch, without any gap or overlap. Which

coldgirl [10]

Answer:

11 unit cubes and 2 smaller cubes of volume fraction 1 over 8 cubic inch each

6 0

3 years ago