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Paladinen [302]
2 years ago
9

Alice and Bob both go to a party which starts at $5:00$. Each of them arrives at a random time between $5:00$ and $6:00$. What i

s the probability that the number of minutes Alice is late for the party plus the number of minutes Bob is late for the party is less than $45$
Mathematics
1 answer:
faltersainse [42]2 years ago
3 0

The probability comes out to be 9/32.

Deducing Arrival Time Possibility

All the possible arrival times by Alice and Bob, in minutes after 5 PM, is constrained by the values of given values of x and y,

x = 0, y = 0, x = 60, y = 60.

Here, let the values of x represent how many minutes after 5 PM Alice arrives at the party.

Let the y values represent the time in minutes that Bob arrives at the party after 5 PM.

Calculating the Required Probability

The times that concern us, however, are obtained by the following probability function,

x + y ≤ 45.

And x = 0, y = 0, and x + y ≤ 45 define the constraints of this probability function. Thus the perimeter of such a graph will be given as,

(45² / 2) = 1012.5 square units

Since the total area of the various arrival times is 60 x 60, or 3600 square units, the probability that Alice and Bob will arrive together after 5 o'clock in the evening in less than 45 minutes is therefore = 1012.5 / 3600 = 9/32

Learn more about probability here:

brainly.com/question/11234923

#SPJ4

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Mary has a collection of nickels and quarters for a total value of 4.90.if she has 42 coins total how many of each kind are ther
Ray Of Light [21]

Let x be the number of nickels and y be the number of quarters.

Then, x + y = 42 --- (1)

It is given that total value = 4.90.

Therefore, 0.05x + 0.25y = 4.9 --- (2)

Multiply (1) by 0.25

0.25x + 0.25y = 10.5 --- (3)

Now, subtract (2) from (3), we get,

0.2x = 5.6

Divide both sides by 0.2.

x = 28

x + y = 42

y = 42 - x

= 42 - 28

= 14

Hence, Mary has 28 nickels and 14 quarters in total.

7 0
3 years ago
What is the Standard Deviation of the following set of data?
Whitepunk [10]

Answer:

34

Step-by-step explanation:

34 because i beleive so

5 0
3 years ago
Dalia owns a gravel pit. She took a random sample of rocks and counted 585858 sedimentary rocks, 213213213 metamorphic rocks, an
goblinko [34]

step One

Find the total number of rocks in the gravel pit

<em>58 + 213 + 522 = 793</em>

Step Two 

<em>Set up the probabilities.</em>

<em>P(Sedimentary) = 58 / 793 = 0.0731</em>

<em>P(metamorphic) = 213/ 793 =0.2686</em>

<em>P(igneous) =        522 / 793 = 0.6583</em>

Check

<em>When these are added together the answer should be one.</em>

<em>0.0731 + 0.2686 + 0.6583 = 1 just as it should.</em>

3 0
3 years ago
Donna de paul is raising money for the homeless. She discovers that each church group requires 2 hours of let her writing and 1
Salsk061 [2.6K]

Answer:

x  =  7

y  =  3

z (max)  =  4950/3  =  1650

Step-by-step explanation:

Let call  

x numbers of church goup and

y numbers of Union Local

Then  

First contraint

2*x + 2*y ≤ 20

Second one

1*x + 3*y ≤ 16

Objective Function

z = 150*x + 200*y

Then the system is

z = 150*x + 200*y To maximize

Subject to:

2*x + 2*y ≤ 20

1*x + 3*y ≤ 16

x ≥ 0 y ≥ 0

We will solve by using the Simplex method

z - 150 *x - 200*y = 0

2*x + 2*y + s₁ = 20  

1*x + 3*y + 0s₁ + s₂ = 16

First Table

z           x          y          s₁           s₂          Cte

1        -150    -200       0            0     =      0

0          2         2           1            0     =    20

0          1          3          0            1      =     16

First iteration:

Column pivot   ( y column ) row pivot (third row) pivot 3

Second table

z           x                y          s₁           s₂                Cte

1       -250/3           0          0         200/3    =    3200/3

0      - 4/3               0          -1           2/3       =    -20/3

0         1/3               1            0           1/3       =    -20/3

Second iteration:

Column pivot  ( x column ) row pivot  (second row)  pivot  -4/3

Third table

z           x                y          s₁           s₂                Cte

1            0               0      750/12    700/6    =   4950/3

0            1                0        3/4          -1/2     =    7

0            0                1         -1/4          1/2     =  9/3

5 0
3 years ago
Nine times the sum of a number and 2 is 3
ivolga24 [154]
More specific please?
3 0
3 years ago
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