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3 years ago

PLEASE HELPPPPPPPPPPP

Mathematics

1 answer:

Shkiper50 [21]3 years ago

3 0

Answer:

P(S or T) = 3/4

Step-by-step explanation:

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If:

PSYCHO15rus [73]

Take some trinomial expansions to find some useful expressions and their values.

• 2nd degree expansion

$x + y + z = 7 \\\\ \implies (x+y+z)^2 = x^2+y^2+z^2+2(xy+xz+yz) = 7^2 \\\\ \implies xy+xz+yz = \dfrac{49-33}2 = 8$

• 3rd degree expansion

$x+y+z=7 \implies (x+y+z)^3 = 7^3 \\\\ \implies \\ 243 = x^3+y^3+z^3+3(x^2y+x^2z+xy^2+y^2z+xz^2+yz^2) + 6xyz \\\\ \implies \\ x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 + 2xyz = \dfrac{343 - 145}3 = 66$

• 4th degree expansion

$x+y+z=7 \implies (x+y+z)^4 = 7^4 \\\\ \implies \\ 2401 = x^4+y^4+z^4+4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~+ 6(x^2y^2+x^2z^2+y^2z^2) + 12(x^2yz+xy^2z+xyz^2) \\\\ \implies \\\\ x^4+y^4+z^4 = 2401 - 4(x^3y+x^3z+xy^3+y^3z+xz^3+yz^3) \\\\ ~~~~~~~~~~~~~~~~~~~~~~- 6(x^2y^2+x^2z^2+y^2z^2) - 12(x^2yz+xy^2z+xyz^2)$

Simplify:

$x^3y+x^3z+xy^3+y^3z+xz^3+yz^3 \\\\ ~~~~ = x^2 (xy+xz) + y^2 (xy+yz) + z^2 (xz + yz) \\\\ ~~~~ = x^2 (xy+xz+yz) + y^2 (xy+xz+yz) + z^2 (xy + xz + yz) - (x^2yz + xy^2z + xyz^2) \\\\ ~~~~ = (x^2+y^2+z^2) (xy+xz+yz) - xyz (x+y+z) \\\\ ~~~~ = 264 - 7xyz$

$x^2y^2+x^2z^2+y^2z^2 \\\\ ~~~~ = xy\cdot xy + xz \cdot xz + yz \cdot yz \\\\ ~~~~ = xy(xy+xz+yz) + xz(xy+xz+yz) + yz(xy+xz+yz) - 2(x^2yz+xy^2z+xyz^2) \\\\ ~~~~ = (xy+xz+yz)^2 - 2xyz(x+y+z) \\\\ ~~~~ = 64 - 14xyz$

$x^2yz+xy^2z+xyz^2 = xyz (x + y + z) = 7xyz$

Then the equation we got from the 4th degree expansion reduces to

$x^4+y^4+z^4 = 2401 - 4(264-7xyz) - 6(64-14xyz) - 12(7xyz) \\\\ ~~~~~~~~~~~~~~~~~= 961 + 28xyz$

and all we need now is the value of $xyz$ .

In the 3rd degree expansion, we have

$x^2y+x^2z+xy^2+y^2z+xz^2+yz^2 \\\\ ~~~~ = x(xy + xz) + y(xy + yz) + z(xz + yz) \\\\ ~~~~ = x(xy+xz+yz) + y(xy+xz+yz) + z(xy+xz+yz) - 3xyz \\\\ ~~~~ = (x+y+z)(xy+xz+yz) - 3xyz \\\\ ~~~~ = 56 - 3xyz \\\\ \implies (56 - 3xyz) + 2xyz = 66 \\\\ \implies xyz = -10$

So, we end up with

$x^4+y^4+z^4 = 961 - 280 = \boxed{681}$

4 0

1 year ago

8x3+70÷7-7 tell accordingly the correct answer will be marked as brainliest

trasher [3.6K]

Is 27

U have to solve it by order of operation ( u start solving from right to left)
Order of operation in this case:
- ➗or✖️
- ➕or➖
So we can see that 70 divided by 7 is first so we solve it and it will give us 10.
Then we solve 8x3 which is 24, so now we have 24 +70+10-7, so the FINAL ANSWER IS 27

8 0

2 years ago

Read 2 more answers

When solving negative one over five (x − 25) = 7, what is the correct sequence of operations? (5 points) a Multiply each side by

german

Answer:

Hello!!

When solving $-\frac{1}{5} (x-25)=7$ , the correct sequence of operations would be...

Multiply each side by −5, add 25 to each side

Step-by-step explanation:

When completing the order of operations use PEMDAS Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Hope this helps!!

7 0

3 years ago

Item 15 Your math class is collecting canned food for a local food drive. The goal is to collect at least 130 cans but no more t

Margarita [4]

For this case, the first thing we must do is define variables.

We have then:

n: number of cans that each student must bring

We know that:

The teacher will bring 5 cans

There are 20 students in the class

At least 105 cans must be brought, but no more than 205 cans

Therefore the inequation of the problem is given by:

Answer:

105 < 20n + 5 < 205

the possible numbers n of cans that each student should bring in is:

105 < 20n + 5 < 205

8 0

3 years ago

Bill earns an annual salary of $65 000. He receives a pay rise of 13.5%, how much does he earn after the increase?

photoshop1234 [79]

65000x.135=8775
65000+8775=73775
So Bill earns $73,775 after the increase
Hoped this helped

4 0

3 years ago

Read 2 more answers