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1 year ago

Let ƒ(x) = x + 1 and g(x) = 5x. Evaluate the composition (ƒ ∘ g)(–1).

Mathematics

1 answer:

Lubov Fominskaja [6]1 year ago

3 0

The value of the composite function is option (D) (f ∘ g)( - 1) = - 4.

The functions are given as:

f(x) = x + 1 and g(x) = 5x.

We need to find the composite function:

(f ∘ g)( - 1).

= f (g ( - 1)

Substitute value of g(x):

= f ( 5 ( - 1))

= f ( - 5)

Substitute value of f(x):

= ( - 5 ) + 1

= - 5 + 1

= - 4

Therefore, the value of the composite function is option (D) (f ∘ g)( - 1) = - 4.

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Step-by-step explanation:

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2 years ago

The population of a town is increasing at a rate of 6.2% per year. The city council believes they will have to add another eleme

kow [346]

Answer:

The correct solution is "4.6".

Step-by-step explanation:

Given:

Interest rate,

r = 6.2%

or,

= 0.062

Amount,

A = 100000

Principle,

P = 76000

As we know,

⇒ $A=P(1+\frac{r}{100} )^n$

On substituting the values, we get

⇒ $100000=76000(1+\frac{6.2}{100} )^n$

⇒ $(1+0.062)^n=\frac{100}{76}$

On taking log both sides, we get

⇒ $n \ log_e(1.062)=log_e(\frac{100}{76} )$

⇒ $n=\frac{ln(\frac{100}{76} )}{ln(1.062)}$

By putting the values of log, we get

⇒ $=4.5622$

or,

⇒ $=4.6$

5 0

2 years ago

How to find the area of each face of a prism

tatiyna

If the face is a square, then (l*l)

If the face is a triangle, then (b*h)(1/2)

If the face is a rectangle, then (l*w)

If the face is a circle, then (r²)(3.14)

You can then add all these faces up to get the total surface area of the prism.

3 0

3 years ago

Write an equation for the nth term of the arithmetic sequence. Then find a50.<br> 8, 2, -4, - 10,

AlexFokin [52]

Answer: See below

Explanation:

Write an equation for nth term:

a + d(n - 1)

a = 8 (first term)
d = -6 (common difference)

8 - 6(n - 1)
= 8 - 6n + 6
= -6n + 14

Find a 50:

-6(50) + 14
= -300 + 14
= -286

6 0

3 years ago

A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an incr

ss7ja [257]

Answer:

a) There is a 12.11% probability that exactly 1 man has the marker.

b) There is a 85.07% probability that more than 1 has the marker.

Step-by-step explanation:

There are only two possible outcomes: Either the men has the chromosome, or he hasn't. So we use the binomial probability distribution.

Binomial probability

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

In which $C_{n,x}$ is the number of different combinatios of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And $\pi$ is the probability of X happening.

In this problem, we have that:

30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure, so $\pi = 0.30$

(a) If 10 men are selected randomly and tested for the marker, what is the probability that exactly 1 man has the marker?

10 men, so $n = 10$

We want to find P(X = 1). So:

$P(X = x) = C_{n,x}.\pi^{x}.(1-\pi)^{n-x}$

$P(X = 1) = C_{10,1}.(0.30)^{1}.(0.7)^{9} = 0.1211$

There is a 12.11% probability that exactly 1 man has the marker.

(b) If 10 men are selected randomly and tested for the marker, what is the probability that more than 1 has the marker?

That is $P(X > 1)$

We have that:

$P(X \leq 1) + P(X > 1) = 1$

$P(X > 1) = 1 - P(X \leq 1)$

We also have that:

$P(X \leq 1) = P(X = 0) + P(X = 1)$

$P(X = 0) = C_{10,0}.(0.30)^{0}.(0.7)^{10} = 0.0282$

$P(X \leq 1) = P(X = 0) + P(X = 1) = 0.0282 + 0.1211 = 0.1493$

Finally

$P(X > 1) = 1 - P(X \leq 1) = 1 - 0.1493 = 0.8507$

There is a 85.07% probability that more than 1 has the marker.

3 0

2 years ago