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3 years ago

A laptop battery has 80% power after 1 hour of use and 20% after 4 hours of use . What is the slope ?

Mathematics

1 answer:

Kruka [31]3 years ago

8 0

Answer: 5/1

Step-by-step explanation:

After 5 hours, it would be at zero. And 100 divided by 4, is 20. Meaning that the slope is 5/1, or 5.

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A Copy of machine produces 80 copies in 5 minutes. How many copies would be produced in 40 minutes?

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Consider the differential equation

Gennadij [26K]

The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.

The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.

This leaves us with the second choice. Recall that

1 + tan²(x) = sec²(x)

and the derivative of tangent,

(tan(x))' = sec²(x)

Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then

y' = sec²(x³/3 + 2) • x²

and substituting y and y' into the ODE gives

sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))

x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)

which is an identity.

So the solution is y = tan(x³/3 + 2).

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2 years ago

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A study of the US clinical population found that 24.1% are diagnosed with a mental disorder, 14.9% are diagnosed with an alcohol

jeka57 [31]

Answer:

a) 0.336

b) 0.207

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

We solve this problem building the Venn's diagram of these probabilities.

I am going to say that:

A is the probability that a person from the clinical population is diagnosed with mental disorder.

B is the probability that a person from the clinical population is diagnosed with alcohol related disorder.

We have that:

$A = a + (A \cap B)$

In which a is the probability that a person is diagnosed with mental disorder but not alcohol related disorder and $A \cap B$ is the probability that a person is diagnosed with both of these disorders.

By the same logic, we have that:

$B = b + (A \cap B)$

We find the values of a,b and the intersection, starting from the intersection.

5% are diagnosed with both disorders.

This means that $A \cap B = 0.05$

14.9% are diagnosed with an alcohol-related disorder

This means that $B = 0.149$

$B = b + (A \cap B)$

$0.149 = b + 0.05$

$b = 0.099$

24.1% are diagnosed with a mental disorder

This means that $A = 0.241$

$A = a + (A \cap B)$

$0.241 = a + 0.05$

$a = 0.203$

(a) What is the probability that someone from the clinical population is diagnosed with a mental disorder, knowing that the person is diagnosed with an alcohol-related disorder?

Desired outcomes:

Mental and alcohol-related disorders, which $A \cap B$ . So $D = 0.05$

Total outcomes:

Alcohol-related disorder, which is B. So $T = 0.149$

Probability:

$P = \frac{0.05}{0.149} = 0.336$

(b) What is the probability that someone from the clinical population is diagnosed with an alcohol-related disorder, knowing that the person is diagnosed with a mental disorder?

Desired outcomes:

Mental and alcohol-related disorders, which $A \cap B$ . So $D = 0.05$

Total outcomes:

Mental disorder, which is B. So $T = 0.241$

Probability:

$P = \frac{0.05}{0.241} = 0.207$

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3 years ago