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3 years ago

Complete the inequality statement. 8 5/12 8 3/8

Mathematics

1 answer:

Gnoma [55]3 years ago

7 0

Answer:

8 5/12 > 8 3/8

Step-by-step explanation:

The integer parts of the numbers are the same, so we can find the desired result by comparing the fractions. To do that, we can subtract one from the other, or we can simply write them both with a common denominator.

Subtracting:

5/12 -3/8 = (5·8 -12·3)/(12·8) = 4/(12·8) = 1/24 > 0

so we have ...

5/12 > 3/8

8 5/12 > 8 3/8

Common Denominator:

The denominators of the fractions are 12 and 8. The least common multiple of these numbers is 12·2 = 8·3 = 24. Then the numbers can be written as ...

8 5/12 = 8 10/24

8 3/8 = 8 9/24 . . . . . . this is less than 8 10/24

Then the appropriate relation between the numbers is ...

8 5/12 > 8 3/8

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3. Consider the linear equation 2y - 3x = 5.

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Answer:

Step-by-step explanation:

2y - 3x = 5

2(-2) - 3x = 5

-4 - 3x = 5

-3x = 9

x = -3

(-3,-2) is another solution

(-1,1)

2y - 3x = 5

2(1) - 3(-1) = 5

2 + 3 = 5

5 = 5

true, the point is a solution to the equation because the equation is true after substituting x and y with the point (-1,1)

(4,1)

2y - 3x = 5

2(1) - 3(4) = 5

2 - 12 = 5

-10 = 5

not true, the point is not a solution to the equation because the equation is not true after substituting x and y with the point (4,1)

c. You can use the points from the given (-1,1) and (-3,-2) to form a line. You then shade whichever half solves the solution using points on the graph.

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3 years ago

What is the probability that a random person who tests positive for a certain blood disease actually has the disease, if we know

xeze [42]

Answer:

Step-by-step explanation:

Hello!

Any medical test used to detect certain sicknesses have several probabilities associated with their results.

Positive (test is +) ⇒ P(+)

True positive (test is + and the patient is sick) ⇒ P(+ ∩ S)

False-positive (test is + but the patient is healthy) ⇒P(+ ∩ H)

Negative (test is -) ⇒ P(-)

True negative (test is - and the patient is healthy) ⇒ P(- ∩ H)

False-negative (test is - but the patient is sick) ⇒ P(- ∩ S)

The sensibility of the test is defined as the capacity of the test to detect the sickness in sick patients (true positive rate).

⇒ P(+/S) = P(+ ∩ S)

P(S)

The specificity of the test is the capacity of the test to have a negative result when the patients are truly healthy (true negative rate)

⇒ P(-/H) = P(- ∩ H)

P(H)

For this particular blood disease the following probabilities are known:

1% of the population has the disease: P(S)= 0.01

95% of those who are sick, test positive for it: P(+/S)= 0.95 (sensibility of the test)

2% of those who don't have the disease, test positive for it: P(+/H)= 0.02

The probability of a person having the blood sickness given that the test was positive is:

P(S/+)= P(+ ∩ S)

P(+)

The first step you need to calculate the intersection between both events + and S, for that you will use the information about the sickness prevalence in the population and the sensibility of the test:

P(+/S) = P(+ ∩ S)

P(S)

P(+/S)* P(S) = P(+ ∩ S)

P(+ ∩ S) = 0.95*0.01= 0.0095

The second step is to calculate the probability of the test being positive:

P(+)= P(+ ∩ S) + P(+ ∩ H)

Now we know that 1% of the population has the blood sickness, wich means that 99% of the population doesn't have it, symbolically: P(H)= 0.99

Then you can clear the value of P(+ ∩ H):

P(+/H) = P(+ ∩ H)

P(H)

P(+/H)*P(H) = P(+ ∩ H)

P(+ ∩ H) = 0.02*0.99= 0.0198

Next you can calculate P(+):

P(+)= P(+ ∩ S) + P(+ ∩ H)= 0.0095 + 0.0198= 0.0293

Now you can calculate the asked probability:

P(S/+)= P(+ ∩ S) = 0.0095 = 0.32

P(+) 0.0293

I hope it helps!

6 0

3 years ago

Question 1

zhannawk [14.2K]

Answer:

Step-by-step explanation:

Since a die has six faces, 6 outcomes are possible

Since a coin has two faces, 2 outcomes are possible

Multiply the chances together and you get 12

6 0

3 years ago

Help me and you get 40 points

victus00 [196]

Answer:

The angle 6 measures 54 degrees

Step-by-step explanation:

Angle 6 is congruent to angle 7 ("-2x+34") as it is an opposite angle in straight line intersection. But angle 6 is congruent to angle 2 (-9x-36) due to the two horizontal lines being parallel. So we can write the following equality to determine the value of x:

-2x + 34 = -9x -36

7x = -70

==> x = -10

Now we can answer the question: the angle 6 is

-2x + 34 = -2(-10)+34 = 54 degrees

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