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2 years ago

The lines graphed below are perpendicular. The slope of the red line is -1/3. What is the slope of the green line?

Mathematics

1 answer:

Serggg [28]2 years ago

7 0

Answer:

The slope of the green line is 3.

Step-by-step explanation:

<em><u>Definition: </u></em>If the two lines are said to be perpendicular, than the multiplication of their slope is -1.

In other words, the slope of the perpendicular line is the negative reciprocal of the given slope of the line.

Here we are slope of the red line, which is -1/3

Let's take it as "m1"

Let's take "m2" the slope of the green line.

By the above definition,

$m_1 *m_2 = -1$

Given: $m_1 = -\frac{1}{3}$

Now plug m1 value in the above statement, we get

$-\frac{1}{3} *m_2 = -1$

Multiply both sides by reciprocal of -1/3. The reciprocal of -1/3 = -3

$-3*-\frac{1}{3} *m_2 = -3*-1$

$m_2 = 3$

Therefore, the slope of the green line is 3.

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2 years ago

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According to a study in a medical journal, 202 of a sample of 5,990 middle-aged men had developed diabetes. It also found that m

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Answer:

0.0588 = 5.88% probability that a middle-aged man with diabetes is very active

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: Has diabetes.

Event B: Is very active.

Probability of having diabetes:

To find this probability, we take in consideration that:

It also found that men who were very active (burning about 3,500 calories daily) were a fourth as likely to develop diabetes compared with men who were sedentary. Assume that one-fifth of all middle-aged men are very active, and the rest are classified as sedentary.

So the probability of developing diabetes is:

x of 4/5 = x of 0.8(not active)

x/4 = 0.25x of 1/5 = 0.2(very active). So

$P(A) = 0.8x + 0.25*0.2x = 0.85x$

Probability of developing diabetes while being very active:

0.25x of 0.2. So

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What is the probability that a middle-aged man with diabetes is very active?

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1 year ago

What is the sum of all positive integers smaller than $1000$ that can be written in the form $100\cdot 2^n$, where $n$ is an int

netineya [11]

Answer:

The sum is 1575.

Step-by-step explanation:

Consider the provided information.

It is given that positive integers smaller than 1000 and that can be written in the form $100\cdot 2^n$

Where n is integer that means the value of n can be a positive number or a negative number.

For n = 0

$100\cdot 2^{0}=100$

For n=-1

$100\cdot 2^{-1}=50$

For n=-2

$100\cdot 2^{-2}=25$

For n = -3 the obtained number is not an integer.

Now consider the positive value of n.

For n=1

$100\cdot2^1 = 200$

For n=2

$100\cdot2^2 = 400$

For n=3

$100\cdot2^3 = 800$

For n=4 the obtained number is greater than 1000.

Now add all the numbers.

$100+50+25+200+400+800=1575$

Hence, the sum is 1575.

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1 year ago

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Answer:

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