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3 years ago

If function g is the inverse of function f, then what does f(g(-5)) equal?

Mathematics

1 answer:

alekssr [168]3 years ago

5 0

Answer:

C). -5.

Step-by-step explanation:

If g is the inverse of f then f(g(x) = x.

So f(g(-5)) = -5.

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Determine the area and perimeter

frosja888 [35]

Answer:

Area is the total surface covered by the shape and perimeter is the total length of the shape.

4 0

3 years ago

A sphere with a radius of 5 cm fits inside a box. Every face of the box is tangent to the sphere. What is the ratio of the volum

BARSIC [14]

Volume of box with side length of 5 = 5^3 = 125

Volume of sphere = (4/3)*pi*5^3 = (4/3)pi * 125

Ratio = 125/(4pi/3)*125 = 1/(4pi/3) = 3/(4pi)

Answer: B

8 0

3 years ago

Read 2 more answers

Amy received a $80 gift card for a coffee store. She used it in buying some coffee that cost $8.24 per pound. After buying the c

SVEN [57.7K]

Answer:

5 pounds

Step-by-step explanation:

Given that:

Amount of gift card = $80

Cost of coffee per pound = $8.24

Amount left in the card = $38.80

To find:

Number of pounds of coffee bought = ?

Solution:

Let the number of pounds of the coffee bought = $x$ pounds

Cost of 1 pound = $8.24

Cost of $x$ pounds = $8.24 $\times x$

Writing the equation as per question statement:

$80 - 8.24x = 38.80\\\Rightarrow 80 - 38.80 = 8.24x\\\Rightarrow 8.24x = 41.2\\\Rightarrow x = \dfrac{41.2}{8.24}\\\Rightarrow \bold{x = 5\ pounds}$

Therefore, 5 pounds of coffee was bought.

3 0

3 years ago

The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated

statuscvo [17]

We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.

We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.

So we can define the proportion of coffee that Jeremiah has in his body as:

P(t) = 1*e^{k*t}

Such that:

P(4.8 h) = 0.5 = 1*e^{k*4.8}

Then, if we apply the natural logarithm we get:

Ln(0.5) = Ln(e^{k*4.8})

Ln(0.5) = k*4.8

Ln(0.5)/4.8 = k = -0.144

Then the equation is:

P(t) = 1*e^{-0.144*t}

Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:

P(t) = 0.6 = 1*e^{-0.144*t}

Again, we use the natural logarithm:

Ln(0.6) = Ln(e^{-0.144*t})

Ln(0.6) = -0.144*t

Ln(0.6)/-0.144 = t = 3.55

So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.

If you want to learn more, you can read:

brainly.com/question/19599469

7 0

2 years ago

A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 90% of the time when t

garik1379 [7]

Answer:

a) P[A/B] = 0,019 or P[A/B] = 1,9 %

b) P[A- /B-] = 0,9996 or P[A- /B-] = 99,96 %

Step-by-step explanation:

Bayes Theorem :

P[A/B] = P(A) * P[B/A] / P(B)

The branches of events are as follows

Condition 1 real infection 1/300 and not infection 299/300

Then

1.- 1/300 299/300

When the test is done (virus present) 0,9 (+) 0,15 (-)

2.- 299/300

When the test is done ( no virus ) 0,15 (+) 0,85 (-)

Then:

P(A) = event person infected P(B) = person test positive

a) P[A/B] = P(A) * P[B/A] / P(B)

where P(A) = 1/300 = 0,0033 P[B/A] = 0,9

Then P(A) * P[B/A] = 0,0033*0,9 = 0,00297

P(B) is ( 1/300 )*0,9 + (299/300)*0,15

P(B) = 0,0033*0,9 + 0,9966*0,15 ⇒ P(B) = 0,1524

Finally

P[A/B] = 0,00297 /0,1524

P[A/B] = 0,019 or P[A/B] = 1,9 %

b) Following sames steps:

P[A- /B-] = (299/300) * 0,85 / (299/300) * 0,85 + (1/300 * 0,1)

P[A- /B-] = 0,8471 /0,8474

P[A- /B-] = 0,9996 or P[A- /B-] = 99,96 %

6 0

3 years ago