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3 years ago

Determine the solution, if any, to the system of equations below.

Mathematics

1 answer:

AleksandrR [38]3 years ago

3 0

Answer:

DNE.

Step-by-step explanation:

8x - 2y = 1 ---------------------(1)

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

Multiply (2) by 2

-8x +2y = 6 -----------------(3)

Add (1) to (3)

8x - 2y + (- 8x + 2y) = 1+6

8x - 2y - 8x +2y = 7

But all the terms in LHS cancel out, leaving 0.

So you get 0=7, which is not valid.

Therefore no solution exists. DNE

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Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are sel

serious [3.7K]

Complete Questions:

Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers.

a. 40

b. 48

c. 56

d. 64

Answer:

a. 0.35

b. 0.43

c. 0.49

d. 0.54

Step-by-step explanation:

(a)

The objective is to find the probability of selecting none of the correct six integers from the positive integers not exceeding 40.

Let s be the sample space of all integer not exceeding 40.

The total number of ways to select 6 numbers from 40 is $|S| = C(40,6)$ .

Let E be the event of selecting none of the correct six integers.

The total number of ways to select the 6 incorrect numbers from 34 numbers is:

$|E| = C(34,6)$

Thus, the probability of selecting none of the correct six integers, when the order in which they are selected does rot matter is

$P(E) = \frac{|E|}{|S|}$

$= \frac{C(34, 6)}{C(40, 6)}\\\\= \frac{1344904}{3838380}\\\\=0.35$

Therefore, the probability is 0.35

Check the attached files for additionals

8 0

3 years ago

QUICKLY PLEASE

KengaRu [80]

Answer:

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Step-by-step explanation:

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4 years ago

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LiRa [457]

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3 0

3 years ago

What is the value of x?

WINSTONCH [101]

Answer:

$\large\boxed{x=8\sqrt2}$

Step-by-step explanation:

$\bold{METHOD\ 1}\\\\\text{Use the Pythagorean theorem:}\\\\leg^2+leg^2=hypotenuse^2\\\\\text{We have}\ leg=8,\ leg=8,\ hypotenuse=x.\\\text{Substitute:}\\\\x^2=8^2+8^2\\\\x^2=2(8^2)\to x=\sqrt{2(8^2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\x=\sqrt2\cdot\sqrt{8^2}\qquad\text{use}\ \sqrt{a^2}=a\\\\x=8\sqrt2$