Which if the following relations represent functions?

MatroZZZ [7]

Answer:

x = 115 - p

Step-by-step explanation:

generally in algebra you will use the letter "x" to represent a value you do not know, so it wants an algebraic expression for "p subtracted from 115", this can be rewritten as 115 - p. So the unknown value "x" is equal to 115 - p.

6 0

3 years ago

There is a boardwalk game at Point Pleasant where you are blindfolded to throw darts at a board full of balloons. Each time a da

arlik [135]

The given number of balloons, green = 10, purple = 4, red = 5, tie-dye = 2, black = 3, gives;

a. 5/138

b. 25/276

c. 5/1012

d. 35/46

<h3>How can the different probabilities be calculated mathematically?</h3>

Given parameters;

Number of balls;

Green = 10

Purple = 4

Red = 5

Tie-dye = 2

Black = 3

Mode of selection = Without replacement

Number of balloons = 10+4+5+2+3 = 24

a. Probability of popping a red balloon = 5/24

Probability of popping a second red balloon = 4/23

Therefore;

Probability of popping two reds consecutively = 5/24 × 4/23 = 5/138

b. Probability of popping a red balloon = 5/24

Probability of popping a green balloon next = 10/23

Therefore;

Probability of popping a red and then a green balloon = 5/24 × 10/23 = 25/276

c. Probability that the first balloon that pops is a red = 5/24

Next balloon is a black = 3/23

Third balloon is red = 4/22

The probability, P, is therefore;

P = 5/24 × 3/23 × 4/22 = 5/1012

d. The probability that the first balloon is a tie-dye = 2/24 = 1/12

Therefore;

Probability that the first balloon is not a tie-dye = 1 - 1/12 = 11/12

Probability that the second balloon is not a tie-dye = 21/23

Similarly;

Probability that the third balloon is not a tie-dye = 20/22 = 10/11

Which gives;

The probability, P, of popping anything but a tie-dye on three consecutive throws is therefore;

P = 11/12 × 21/23 × 10/11 = 35/46

Learn more about probability theory in mathematics?

brainly.com/question/13604758

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7 0

1 year ago

From measurements in a microscope, you determine that a certain bacterium covers an area of 1.50 μm2. Convert the area into squa

NemiM [27]

So the problem ask to find and convert the area into square meters. So to convert is you must do the cross multiplication process that could cancel out unit and made the answer into a square meter, so the answer would be 1. x10^-12m^2. I hope you are satisfied with my answer and feel free to ask for more

4 0

2 years ago

Suppose the probability that a softball player gets a hit in any single at-bat is 0.300. Assuming that her chance of getting a h

Ksivusya [100]

Answer:

$P(X=4)=(1-0.3)^{4-1} 0.3 = 0.103$

The probability that she will not get a hit until her fourth time at bat in a game is 0.103

Step-by-step explanation:

Previous concepts

The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"

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

Let X the random variable that measures the number os trials until the first success, we know that X follows this distribution:

$X\sim Geo (1-p)$

Solution to the problem

For this case we want this probability

$P(X=4)$

And using the probability mass function we got:

$P(X=4)=(1-0.3)^{4-1} 0.3 = 0.103$

The probability that she will not get a hit until her fourth time at bat in a game is 0.103

4 0

3 years ago

If 1200 cm^2 of material is available to make a box with a square base and an open top find the largest possible volume of the b

strojnjashka [21]

Surface area of box=1200 cm²
Volume of box=s²h 
s = side of square base 
h = height of box 
S.A. = s² + 4sh 
S.A. = surface area or 1200 cm², s²
= the square base, and 4sh = the four 'walls' of the box. 
1200 = s² + 4sh 
1200 - s² = 4sh 
(1200 - s²)/(4s) = h 

v(s) = s²((1200 - s²)/(4s)) 
v(s) = s(1200 - s²)/4 . 
v(s) = 300s - (1/4)s^3

by derivating
v'(s) = 300 - (3/4)s² 
0 = 300 - (3/4)s² 
-300 = (-3/4)s² 
400 = s² 
s = -20 and 20. 
again derivating
v"(s) = -(3/2)s 
v"(-20) = -(3/2)(-20) 
v"(-20) = 30 
v"(20) = -(3/2)(20) 
v"(20) = -30 

v(s) = 300s - (1/4)s^3 
v(s) = 300(20) - (1/4)(20)^3 
v(s) = 6000 - (1/4)(8000) 
v = 6000 - 2000
v=4000

4 0

2 years ago