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3 years ago

Help What is f(3)? -9 -1 1 9

Mathematics

2 answers:

nirvana33 [79]3 years ago

6 0

Answer:

D. 9

Step-by-step explanation:

f(3)=9

The table represents the function f(x) is 9.

Hope this helps!

Yanka [14]3 years ago

3 0

The answer is D. 9
f(3)=9

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(x-1/x ²-4) + (1/x-2)

kodGreya [7K]

Answer:

(2x+1)/(x^2 -4)

Step-by-step explanation:

When you add fractions (or rational expressions) you need to express each of them over a common denominator, so you can add the numerators. (Parentheses or other grouping symbols are required.)

$\dfrac{x-1}{x^2-4}+\dfrac{1}{x-2}=\dfrac{x-1}{(x-2)(x+2)}+\dfrac{(1)(x+2)}{(x-2)(x+2)} \qquad\text{now we have a common denominator}\\\\=\dfrac{(x-1)+(x+2)}{(x-2)(x+2)}=\dfrac{2x+1}{(x-2)(x+2)}=\dfrac{2x+1}{x^2-4}$

You factor the denominator on the left so you can see what factors are missing from the denominator on the right.

<em>Numerical example</em>

Suppose you want to add the fractions 4/15 and 3/5. You would factor the denominator 15 into 3·5, so you can see that the fraction 3/5 needs to be multiplied by (3/3) in order to give it a denominator of 15. Once the two fractions have a common denominator, you can add their numerators.

4/15 + 3/5 = 4/15 + (3/5)(3/3)

= 4/15 + 9/15

= (4+9)/15 = 13/15

_____

<em>Comment on grouping symbols</em>

When a rational expression is typeset, the division bar of the fraction identifies the numerator and the denominator:

$\dfrac{x-1}{x^2-4}$

When you write it in plain text as ...

x - 1/x^2 -4

this becomes a 3-term expression:

(x) -(1/x^2) -(4)

which is very different from what you may intend. In order to match the original typeset expression, parentheses must be added to show the group in the numerator and the group in the denominator:

(x -1)/(x^2 -4)

The same holds for exponents. The superscript position in a typeset expression tells you what the exponent is. When you write the same thing in plain text, parentheses are needed to show the exponent group.

$3^{x-1}$ = 3^(x -1) ≠ 3^x -1

7 0

4 years ago

Thirty Mercedes and Audi participated in a 30 mile race. The average driving speed of the Mercedes and Audi were recorded. A ran

vladimir1956 [14]

Answer:

Median for sample 1 = 142

Median for sample 2 = 134

Step-by-step explanation:

For Sample 1:

For finding median, the data is first arranged into ascending or descending order. We are arranging the data in ascending order.

120, 130, 132, 136, 139, 142, 142, 144, 156, 165, 167

The formula for calculating the term which will be median is:

Median= ((n+1)/2)

Here in sample 1, n=11

So, putting n=11 in the formula

= ((11+1)/2)

= (12/2)

=6th term

The sixth term is 142, so

Median of sample 1=142

For Sample 2:

For finding median, the data is first arranged into ascending or descending order. We are arranging the data in ascending order.

112, 112, 113, 114, 125, 134, 141, 145, 146, 163, 165

The formula for calculating the term which will be median is:

Median= ((n+1)/2)

Here in sample 2, n=11

So, putting n=11 in the formula

=((11+1)/2)

=(12/2)

=6th term

The sixth term is 134, so

Median of sample 2=134

7 0

4 years ago

Seventy-two percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of th

Anton [14]

Answer:

a) 0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) 0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) 0.064 = 6.4% probability that 7 of them are discovered.

Step-by-step explanation:

For itens a and b, we use conditional probability.

For item c, we use the binomial distribution along with the conditional probability.

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.

Binomial probability distribution

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

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

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

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

And p is the probability of X happening.

a) If it has an emergency locator, what is the probability that it will not be discovered?

Event A: Has an emergency locator

Event B: Not located.

Probability of having an emergency locator:

66% of 72%(Are discovered).

20% of 100 - 72 = 28%(not discovered). So

$P(A) = 0.66*0.72 + 0.2*0.28 = 0.5312$

Probability of having an emergency locator and not being discovered:

20% of 28%. So

$P(A cap B) = 0.2*0.28 = 0.056$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.056}{0.5312} = 0.105$

0.105 = 10.5% probability that it will not be discovered if it has an emergency locator.

b) If it does not have an emergency locator, what is the probability that it will be discovered?

Probability of not having an emergency locator:

0.5312 of having. So

$P(A) = 1 - 0.5312 = 0.4688$

Probability of not having an emergency locator and being discovered:

34% of 72%. So

$P(A \cap B) = 0.34*0.72 = 0.2448$

Probability:

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.2448}{0.4688} = 0.522$

0.522 = 52.2% probability that it will be discovered if it does not have an emergency locator.

c) If we consider 10 light aircraft that disappeared in flight with an emergency recorder, what is the probability that 7 of them are discovered?

p is the probability of being discovered with the emergency recorder:

0.5312 probability of having the emergency recorder.

Probability of having the emergency recorder and being located:

66% of 72%. So

$P(A \cap B) = 0.66*0.72 = 0.4752$

Probability of being discovered, given that it has the emergency recorder:

$p = P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.4752}{0.5312} = 0.8946$

This question asks for P(X = 7) when $n = 10$ . So

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

$P(X = 7) = C_{10,7}.(0.8946)^{7}.(0.1054)^{3} = 0.064$

0.064 = 6.4% probability that 7 of them are discovered.

8 0

3 years ago

Magalie brings 48 ounces of soda to her daughter's birthday party. She wants to divide allof her soda evenly among the 9 people

Talja [164]

Answer:

Each person will get 5.34 ounces of soda.

Step-by-step explanation:

In order to find out how many ounces of soda each person gets we need to take the total amount of soda Magalie brought to the party and divide it by the number of people that will drink the soda. In this case we have:

amount per person = 48/9 = 5.34 ounces

Each person will get 5.34 ounces of soda.

7 0

3 years ago

Prove that if b is a square matrix then b+b^t is symmetric

WARRIOR [948]

A matrix $\mathbf X$ is symmetric if $\mathbf X=\mathbf X^\top$ . We have

$(\mathbf B+\mathbf B^\top)^\top=\mathbf B^\top+(\mathbf B^\top)^\top=\mathbf B^\top+\mathbf B=\mathbf B+\mathbf B^\top$

and so $\mathbf B+\mathbf B^\top$ is indeed symmetric.

6 0

4 years ago