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aleksandr82 [10.1K]
2 years ago
6

Which of the following points would be on the graph of the equation: y=-4x+6

Mathematics
1 answer:
lawyer [7]2 years ago
7 0

Answer:

Option 2: (10, -34)

Step-by-step explanation:

Given the linear equation in slope-intercept form, y = -4x + 6, where the <u>slope</u>, <em>m</em> = -4, and the <u>y-intercept</u>, <em>b</em> = 6:

An easier way of finding out which of the given options is a solution is to substitute their values into the equation to see whether they will provide a true statement.

<h3>Option 1: (-10, 34)</h3>

Substitute x = -10, and y = 34 into the equation.

y = -4x + 6

34 = -4(-10) + 6

34 = 40 + 6

34 = 46 (False statement). Hence, Option 1 is not a solution to the given equation.

<h3>Option 2: (10, -34)</h3>

Substitute x = 10, and y = -34 into the equation.

y = -4x + 6

-34 = -4(10) + 6

-34 = -40 + 6

-34 = -34  (True statement). Hence, Option 2 is a solution to the given equation.

<h3>Option 3: (5, 10)</h3>

Substitute x = 5, and y = 10 into the equation.

y = -4x + 6

10 = -4(5) + 6

10 = -20 + 6

10 = -14  (False statement). Hence, Option 3 is not a solution to the given equation.

<h3>Option 4: (-5, 10)</h3>

Substitute x = -5, and y = 10 into the equation.

y = -4x + 6

10 = -4(-5) + 6

10 = 20 + 6

10 = 26  (False statement). Hence, Option 4 is not a solution to the given equation.

Therefore, the correct answer is Option 2: (10, -34).

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A diagnostic test for a disease is such that it (correctly) detects the disease in 90% of the individuals who actually have the
Ne4ueva [31]

Answer:

0.2177 = 21.77% conditional probability that she does, in fact, have the disease

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probability of event B happening, given that A happened.

P(A \cap B) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Test positive

Event B: Has the disease

Probability of a positive test:

90% of 3%(has the disease).

1 - 0.9 = 0.1 = 10% of 97%(does not have the disease). So

P(A) = 0.90*0.03 + 0.1*0.97 = 0.124

Intersection of A and B:

Positive test and has the disease, so 90% of 3%

P(A \cap B) = 0.9*0.03 = 0.027

What is the conditional probability that she does, in fact, have the disease

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.027}{0.124} = 0.2177

0.2177 = 21.77% conditional probability that she does, in fact, have the disease

3 0
3 years ago
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