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3 years ago

1/2x - 3/4y=-2 Solve for Y

1 answer:

5 0

$\frac{1}{2}x-\frac{3}{4}y=-2\ \ \ |Add\ \frac{3}{4}y\\\\
\frac{1}{2}x=-2+\frac{3}{4}y\ \ \ |Add\ 2\\\\
\frac{1}{2}x+2=\frac{3}{4}y\ \ |*\frac{4}{3}\\\\
y=\frac{4}{3}(\frac{1}{2}x+2)\\\\
\boxed{y=\frac{2}{3}x+\frac{8}{3}}$

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You have two biased coins. Coin A comes up heads with probability 0.1. Coin B comes up heads with probability 0.6.However, you a

Andrews [41]

Answer:

The probability that our guess is correct = 0.857.

Step-by-step explanation:

The given question is based on A Conditional Probability with Biased Coins.

Given data:

P(Head | A) = 0.1

P(Head | B) = 0.6

By using Bayes' theorem:

$P(B|Head) = P(Head|B) \times \frac{P(B)}{P(Head)}$

We know that P(B) = 0.5 = P(A), because coins A and B are equally likely to be picked.

Now,

P(Head) = P(A) × P(head | A) + P(B) × P(Head | B)

By putting the value, we get

P(Head) = 0.5 × 0.1 + 0.5 × 0.6

P(Head) = 0.35

Now put this value in $P(B|Head) = P(Head|B) \times \frac{P(B)}{P(Head)}$ , we get

$P(B|Head) = P(Head|B) \times \frac{P(B)}{P(Head)}$

$P(B|Head) = 0.6 \times \frac{0.5}{0.35}$

$P(B|Head) = 0.857$

Similarly.

$P(A|Head) = 0.857$

Hence, the probability that our guess is correct = 0.857.

7 0

3 years ago

2. Tiangle ABC has vertices A(3, 3), B(2,-4), and c(0, 0). This triangle is rotated 90

Irina18 [472]

I pretty sure it (B) sorry if I’m wrong

5 0

3 years ago

What is the nth term rule of the quadratic sequence below?

Vladimir [108]

Answer:

3n² + 5n - 2

Step-by-step explanation:

Given sequence:

6, 20, 40, 66, 98, 136, ...

Calculate the first differences between the terms:

$6 \underset{+14}{\longrightarrow} 20 \underset{+20}{\longrightarrow} 40 \underset{+26}{\longrightarrow} 66 \underset{+32}{\longrightarrow} 98 \underset{+38}{\longrightarrow} 136$

As the first differences are not the same, calculate the second differences:

$14 \underset{+6}{\longrightarrow} 20 \underset{+6}{\longrightarrow} 26 \underset{+6}{\longrightarrow} 32 \underset{+6}{\longrightarrow} 38$

As the second differences are the same, the sequence is quadratic and will contain an n² term.

The coefficient of the n² term is half of the second difference.

Therefore, the n² term is: 3n²

Compare 3n² with the given sequence:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 & 3 & 12 & 27 & 48 \\\cline{1-5} \sf operation & +3&+8 & +13 & +18 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

The second operations are different, therefore calculate the differences between the second operations:

$3 \underset{+5}{\longrightarrow} 8 \underset{+5}{\longrightarrow} 13\underset{+5}{\longrightarrow} 18$

As the differences are the same, we need to add 5n as the second operation:

$\begin{array}{|c|c|c|c|c|}\cline{1-5} n & 1 & 2 & 3 & 4\\\cline{1-5} 3n^2 +5n & 8&22 & 42 & 68\\\cline{1-5}\sf operation & -2 &-2 &-2 & -2 \\\cline{1-5} \sf sequence & 6 & 20 & 40 & 66\\\cline{1-5}\end{array}$

Finally, we can clearly see that the operation to get from 3n² + 5n to the given sequence is to subtract 2.

Therefore, the nth term of the quadratic sequence is:

3n² + 5n - 2

6 0

1 year ago

If the measure of angle 1 is (3 x minus 4) degrees and the measure of angle 2 is (4 x + 10) degrees, what is the measure of angl

arlik [135]

Answer:

58 degrees

Step-by-step explanation:

If angle 1 + angle 2 = 90 degrees, then:

(3x - 4) + (4x+10) = 90

Combine like terms:

(3x+4x) + (10-4) = 90

7x + 6 = 90

Subtract 6 from both sides:

7x = 84

Divide both sides by 7:

x = 12

**Plug x back into angle 2 (This step is easy to forget!):

angle 2 = 4(12) + 10

angle 2 = 48 + 10

angle 2 = 58 degrees

4 0

3 years ago

Solve for x in the equation x squared + 4 x minus 4 = 8.

Goryan [66]

Step-by-step explanation:

x² + 4x − 4 = 8

x² + 4x − 12 = 0

(x + 6) (x − 2) = 0

x = -6 or x = 2

5 0

3 years ago

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