1 Find the slope of the line y = 1/4 X+9.

Which of the following accurately lists all discontinuities of the function below?

jeka94

Checking the discontinuity at point -4
from the left f(-4) = 4
from the right f(-4) = (-4+2)² = (-2)² = 4
∴ The function is continues at -4

Checking the discontinuity at point -2
from the left f(-2) = (-2+2)² = 0
from the right f(-2) = -(1/2)*(-2)+1 = 2
∴ The function is jump discontinues at -2

Checking the discontinuity at point 4
from the left f(4) = -(1/2)*4+1 = -1
from the right f(4) = -1
but there no equality in the equation so,
∴ The function is discontinues at 4

The correct choice is the second
point discontinuity at x = 4 and jump discontinuity at x = -2

5 0

3 years ago

Read 2 more answers

In triangle MNO shown below, segment NP is an altitude:

Effectus [21]

Answer: C. Definition of an Altitude

Step-by-step explanation:

Given: In triangle MNO shown below, segment NP is an altitude from the right angle.

Let ∠MNP=x

Then ∠PNO=90°-x

Therefore in triangle MNO,

∠MPN=∠NPO =90° [by definition of Altitude]

[Definition of altitude : A line which passes through a vertex of a triangle, and joins the opposite side forming right angles. ]

Now using angle sum property in ΔMNP

∠MNP+∠MPN+∠PMN=180°

⇒x+90°+∠PMN=180°

⇒∠PMN=180°-90°-x

⇒∠PMN=90°-x

Now, in ΔMNO and ΔPNO

∠PMN=∠PNO=90°-x

and ∠MPN=∠NPO =90° [by definition of altitude]

Therefore by AA similarity postulate, we have

ΔMNO ≈ ΔPNO

5 0

3 years ago

Meridith runs at a rate of 190 meters per minute. use the formula d= r times t to find how far she runs in 6 minutes.

Mariulka [41]

D= r×t
D= 190×6
D= 1140 meters

6 0

3 years ago

Assume that the probability that a baseball player will get a hit in any one at bat is 0.250. What is the probability that he wi

Yanka [14]

Answer: 0.0791

Step-by-step explanation:

Given : The probability that a baseball player will get a hit in any one at bat is 0.250.

Let x be the first hit.

According to the geometric probability , the probability that x (th) trial is the first success = $P(X=x)=(1-p)^{x-1}p$ , where p is the probability of getting success in each trial.

As per given p= 0.250

Then, the probability that he will get his first hit on his 5th at bat will be :

$P(X=x)=(1-0.25)^{5-1}(0.25)\\\\=(0.75)^4(0.25)\\\\=0.0791015625\approx0.0791$

Hence, the probability that he will get his first hit on his 5th at bat is 0.0791 .

7 0

3 years ago

A player of a video game is confronted with a series of four opponents and an 80% probability of defeating each opponent. Assume

mixer [17]

Answer:

(a) 0.4096

(b) 0.64

(c) 0.7942

Step-by-step explanation:

The probability that the player wins is,

$P(W)=0.80$

Then the probability that the player losses is,

$P(L)=1-P(W)=1-0.80=0.20$

The player is playing the video game with 4 different opponents.

It is provided that when the player is defeated by an opponent the game ends.

All the possible ways the player can win is: {L, WL, WWL, WWWL and WWWW)

(a)

The results from all the 4 opponents are independent, i.e. the result of a game played with one opponent is unaffected by the result of the game played with another opponent.

The probability that the player defeats all four opponents in a game is,

P (Player defeats all 4 opponents) = $P(W)\times P(W)\times P(W)\times P(W)=[P(W)]^{4} =(0.80)^{4}=0.4096$

Thus, the probability that the player defeats all four opponents in a game is 0.4096.

(b)

The probability that the player defeats at least two opponents in a game is,

P (Player defeats at least 2) = 1 - P (Player losses the 1st game) - P (Player losses the 2nd game) = $1-P(L)-P(WL)$

$=1-(0.20)-(0.80\times0.20)\\=1-0.20-0.16\\=0.64$

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

(c)

Let X = number of times the player defeats all 4 opponents.

The probability that the player defeats all four opponents in a game is,

P(WWWW) = 0.4096.

Then the random variable $X\sim Bin(n=3, p=0.4096)$

The probability distribution of binomial is:

$P(X=x)={n\choose x}p^{x} (1-p)^{n-x}$

The probability that the player defeats all the 4 opponents at least once is,

P (X ≥ 1) = 1 - P (X < 1)

= 1 - P (X = 0)

$=1-[{3\choose 0}(0.4096)^{0} (1-0.4096)^{3-0}]\\=1-[1\times1\times (0.5904)^{3}\\=1-0.2058\\=0.7942$

Thus, the probability that the player defeats all the 4 opponents at least once is 0.7942.

3 0

3 years ago