All categories

4 years ago

7. which set of ordered pairs represents y as a function of x? explain.

Mathematics

1 answer:

Gennadij [26K]4 years ago

4 0

A function is a rule that tells you how to associate inputs and outputs.

In other words, expressing y as a function of x means: "tell me the value for x, and I will use a formula to compute the value for y".

This implies that, when a certain input x is chosen, there can only be a unique y value as output.

So, the only feasible option is C. All other options assign two different outputs to the same input. For example, in option A, you have the couples (-1, 3) and (-1, 6), which can't happen in a function: you would be claiming that, when you choose -1 as input, the output would be 3, but also 6, which is impossible. The output must be unique.

The same goes with option B (you assign two outputs to the same input 0) and option D (the input 2 has two outputs)

You might be interested in

A player of a video game is confronted with a series of opponents and has an 80% probability of defeating each one. Success with

Vikentia [17]

Answer:

(a) The PMF of X is: $P(X=k)=(1-0.20)^{k-1}0.20;\ k=0, 1, 2, 3....$

(b) The probability that a player defeats at least two opponents in a game is 0.64.

(d) The probability that a player contests four or more opponents in a game is 0.512.

(e) The expected number of game plays until a player contests four or more opponents is 2.

Step-by-step explanation:

Let X = number of games played.

It is provided that the player continues to contest opponents until defeated.

(a)

The random variable X follows a Geometric distribution.

The probability mass function of X is:

$P(X=k)=(1-p)^{k-1}p;\ p>0, k=0, 1, 2, 3....$

It is provided that the player has a probability of 0.80 to defeat each opponent. This implies that there is 0.20 probability that the player will be defeated by each opponent.

Then the PMF of X is:

$P(X=k)=(1-0.20)^{k-1}0.20;\ k=0, 1, 2, 3....$

(b)

Compute the probability that a player defeats at least two opponents in a game as follows:

P (X ≥ 2) = 1 - P (X ≤ 2)

= 1 - P (X = 1) - P (X = 2)

$=1-(1-0.20)^{1-1}0.20-(1-0.20)^{2-1}0.20\\=1-0.20-0.16\\=0.64$

Thus, the probability that a player defeats at least two opponents in a game is 0.64.

(c)

The expected value of a Geometric distribution is given by,

$E(X)=\frac{1}{p}$

Compute the expected number of opponents contested in a game as follows:

$E(X)=\frac{1}{p}=\frac{1}{0.20}=5$

Thus, the expected number of opponents contested in a game is 5.

(d)

Compute the probability that a player contests four or more opponents in a game as follows:

P (X ≥ 4) = 1 - P (X ≤ 3)

= 1 - P (X = 1) - P (X = 2) - P (X = 3)

$=1-(1-0.20)^{1-1}0.20-(1-0.20)^{2-1}0.20-(1-0.20)^{3-1}0.20\\=1-0.20-0.16-0.128\\=0.512$

Thus, the probability that a player contests four or more opponents in a game is 0.512.

(e)

Compute the expected number of game plays until a player contests four or more opponents as follows:

$E(X\geq 4)=\frac{1}{P(X\geq 4)}=\frac{1}{0.512}=1.953125\approx 2$

Thus, the expected number of game plays until a player contests four or more opponents is 2.

4 0

3 years ago

What value for f makes the equations, 5f - 12 = 23, true? f = 7 f = 2.1 f = 35

Salsk061 [2.6K]

The answer to this question is f=7

5 0

3 years ago

Matthew paid $5 for 8 toothbrushes. Jon paid $18 for 25 toothbrushes. Find the unit cost to determine how much each person paid

garik1379 [7]

Answer:

Matthew payed .63 (rounded .625) cents for each toothbrush while Jon payed .72 cents per toothbrush

Step-by-step explanation:

$5 = 8 toothbrushes

$18 = 25 toothbrushes

5 / 8 = .625

18/25 = .72

6 0

3 years ago

Read 2 more answers

1-5 PLEASE SHOW WORK!! I will mark brainliest and a lot of points!!

madreJ [45]

Answer:

Step-by-step explanation:

2. -x+4+3x+2=2x+6

3. -x-2-4x-3=-5x-5

4.-36-24=-60

5. 9+10-6-6=7

5 0

3 years ago

OPRobert made a design on his wall with the similar pentagon tiles shownR9 cm9 cmKMQs15 cm10 cm10 cm15 cmUT10 cmP15 cmNnot drawn

kakasveta [241]

Since they are simmilar we will then have the following relationships.

$\frac{15}{10}=\frac{9}{x}$

Now, we solve for x, as follows:

$x=\frac{9\cdot10}{15}\Rightarrow x=6$

The expression goes along the lines of. 15 is to 10 what 9 is to x, with this as was done we solve for x and determine it's value, that since they keep proportionality.

7 0

1 year ago

7. which set of ordered pairs represents y as a function of x? explain.​

7. which set of ordered pairs represents y as a function of x? explain.