Is two ratios are formed at random from the four numbers 1,2,4, and 8 what is the probability that the rations are equal? Show works please?

Answers

Answer 1

Answer: 4/8 because you could make the ratios 1/2 and 4/8 and 1/4 and 2/8 8/2 and 4/1

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Prove that: (a2 - b2)3 + (b2-c2)3+ (c2-a2)3 = 3 (a+b) (b+c) (c+a) (a-b) (b-c) (c-a).

Answers

$L=(a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3=(*)\n\n(a^2-b^2)^3=a^6-3a^4b^2+3a^2b^4-b^6\n\n(b^2-c^2)^3=b^6-3b^4c^2+3b^3c^4-c^6\n\n(c^2-a^2)^3=c^6-3c^4a^2+3c^2a^4-a^6\n\n(*)=a^6-3a^4b^2+3a^2b^4-b^6+b^6-3b^4c^2+3b^2c^4-c^6+c^6-\dots\n\dots-3c^4a^2+3c^2a^4-a^6\n\n=-3a^4b^2+3a^2b^4-3b^4c^2+3b^2c^4-3c^4a^2+3c^2a^4\n\n=3(-a^4b^2+a^2b^4-b^4c^2+b^2c^4-a^2c^4+a^4c^2)$

$R=3(a+b)(a-b)(b+c)(b-c)(c+a)(c-a)\n\n=3(a^2-b^2)(b^2-c^2)(c^2-a^2)\n\n=3(a^2b^2-a^2c^2-b^4+b^2c^2)(c^2-a^2)\n\n=3(a^2b^2c^2-a^4b^2-a^2c^4+a^4c^2-b^4c^2+a^2b^4+b^2c^4-a^2b^2c^2)\n\n=3(-a^4b^2+a^2b^4-b^4c^2+b^2c^4-a^2c^4+a^4c^2)\n\nL=R$

$(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a + b)(b +c)(c + a)(a - b)(b - c)(c - a)$
$(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a + b)(a - b)(b + c)(b - c)(c + a)(c - a)$
$(a^2 - b^2)^3 + (b^2 - c^2)3 + (c^2 - a^2)^3 = 3(a^2 - b^2)(b^2 - c^2)(c^2 - a^2)$

$(a^2 - b^2)^3 = (a^2 - b2)(a^2 - b^2)(a^2-b^2) = a^6 - 3a^4b^2 + 3a^2b^4 - b^6$
$(b^2 - c^2)^3 = (b^2 - c^2)(b^2 - c^2)(b^2 - c^2) = b^6 - 3^4c^2 + 3b^2c^4 - c^6)$
$(c^2 - a^2)^3 = (c^2 - a^2)(c^2 - a^2)(c^2 - a^2) = c^6 - 3a^2c^4 + 3a^4c^2 - a^6$

$a^6 - 3a^4b^2 + 3a^2b^4 - b^6 + b^6 - 3b^4c^2 + 3b^2c^4 - c^6 + c^6 - 3a^2c^4 + 3a^4c^2 - a^6$
$-3a^4b^2 + 3a^2b^4 - 3b^4c^2 + 3b^2c^4 - 3a^2c^4 + 3a^4c^2$
$3(-a^4b^2 + a^2b^4 - b^4c^2 + b2^c^4 - a^2c^4 + a^4c^2)$

$3(a^2 - b^2)(b^2 - c^2)(c^2 - a^2) = 3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2)$

$3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2) = 3(-a^4b^2 + a^2b^4 - b^4c^2 + b^2c^4 - a^2c^4 + a^4c^2$

Lane is 10 times Mels age. If the difference in their age is 27, how old is Mel?

Answers

The answer is 3!

explanation; 3x10 equals 30. the difference is 27 years and 30-3=27!

L = 10M
27 = L - M

27 = 10M - M

27 = 9M

M = 3

L = 10M = 10(3) = 30

Lane is 30 years old
Mel is 3 years old

The graph represents f(x) = x + 3On a coordinate plane, a step graph has horizontal segments that are each 1 unit long. The left end of each segment is an open circle. The right end of each segment is a closed circle. The left-most segment goes from (negative 5, negative 1) to (negative 4, negative 1). Each segment is 1 unit higher and 1 unit farther to the right than the previous segment. The right-most segment goes from (1, 5) to (2, 5).

What is f(−2.2)?

-2
0
1
2

Answers

Answer:

The answer is C, 1.

Step-by-step explanation:

The answer is simple. You round up to the nearest whole number (cant be a negative,) and it can't be a 0. Therefore, you get 1.

The answer to this question is (-2,0)

Which is greater: -999 + (-1)?

Answers

Step-by-step explanation:

To determine which is greater between -999 and -1 when added together, we can simply perform the addition:

-999 + (-1) = -1000

Therefore, -1000 is the result of adding -999 and -1.

the simple interest I (in dollars) for a savings account is jointly proportional to the product of time (in years) and the principal P (in dollars). After 11 months the interest on a principal of $3970 is $86. What is the constant of the variation

Answers

Simple interest I is jointly proportional to the product of time in years and the principal, therefore; mathematically;
I α Pt
introducing a constant;
I = kPt; but I = $ 86, P = $ 3970, while t = 11/12 years
Thus; k = I/Pt
= 86/ 3970(11/12)
= 0.0236
Therefore, the constant of the variation is ≈ 0.024

Find the range for f(x) = x^2 1, for x < 0.y ≥ 1
y > 1
y < 1
y ≤ 1

Answers

For x < 0, range is y ≤ 1.

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