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Mekhanik [1.2K]
3 years ago
13

Using the matrices below determine if the product of AB is defined. If defined, state the dimension (Picture provided)

Mathematics
1 answer:
il63 [147K]3 years ago
4 0

Answer:

option C. Defined, 3 x 3

Step-by-step explanation:

The order of matrix A is 3 x 2 i.e 3 rows and 2 columns

The order of matrix B is 2 x 3 i.e. 2 rows and 3 columns

Two matrices can be multiplied if and only if the number of columns of 1st matrix is equal to the number of rows of 2nd matrix. Since the number of columns in matrix A is equal to the number of rows in matrix B, the product AB is defined.

The product AB will have number of rows equal to the rows of 1st matrix i.e. matrix A and number of columns equal to the columns of 2nd matrix i.e. matrix B.

So the order of AB will be 3 x 3 .

Therefore, the correct answer is option C. Defined 3 x 3

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When Theresa got her puppy, it weighed 6 ponds less than 2/3 of its weight now. If the puppy weighed 4 pounds when she first rec
sesenic [268]

Answer:

15 lb

Step-by-step explanation:

let the current weight of the puppy be X, the  initial weight of the puppy is 4lb or \frac{2}{3}X-6\ lb, (6 lb less 2/3 X) .

#We equate the current weight to the initial weight to determine X:

4\ lb=\frac{2}{3}X-6\ lb\\\\10 \ lb=\frac{2}{3}X\\\\X=15

Hence, the current weight of the puppy is 15 lb

5 0
3 years ago
You roll a pair of honest dice. If you roll a total of 7, you win $18; if you roll a total of 11, you win $54; if you roll any o
amm1812
Answer: -1
The negative value indicates a loss

============================================================

Explanation:

Define the three events
A = rolling a 7
B = rolling an 11
C = roll any other total (don't roll 7, don't roll 11)

There are 6 ways to roll a 7. They are
1+6 = 7
2+5 = 7
3+4 = 7
4+3 = 7
5+2 = 7
6+1 = 7
Use this to compute the probability of rolling a 7
P(A) = (number of ways to roll 7)/(number total rolls) = 6/36 = 1/6
Note: the 36 comes from 6*6 = 36 since there are 6 sides per die

There are only 2 ways to roll an 11. Those 2 ways are:
5+6 = 11
6+5 = 11
The probability for event B is P(B) = 2/36 = 1/18

Since there are 6 ways to roll a "7" and 2 ways to roll "11", there are 6+2 = 8 ways to roll either event. 
This leaves 36-8 = 28 ways to roll anything else
P(C) = 28/36 = 7/9

-----------------------------

In summary so far,
P(A) = 1/6
P(B) = 1/18
P(C) = 7/9

The winnings for each event, let's call it W(X), represents the prize amounts.
Any losses are negative values
W(A) = amount of winnings if event A happens 
W(B) = amount of winnings if event B happens
W(C) = amount of winnings if event C happens
W(A) = 18
W(B) = 54
W(C) = -9

Multiply the probability P(X) values with the corresponding W(X) values
P(A)*W(A) = (1/6)*(18) = 3
P(B)*W(B) = (1/18)*(54) = 3
P(C)*W(C) = (7/9)*(-9) = -7

Add up those results
3+3+(-7) = -1

The expected value for this game is -1.
The player is expected to lose on average 1 dollar per game played.


Note: because the expected value is not 0, this is not a fair game.


7 0
3 years ago
Read 2 more answers
Only 4 please i need it by tomorrow
seraphim [82]
No she is not correct she needs to go back to school and learn math 
8 0
3 years ago
The population of a town gradually decreases by about 30
topjm [15]
It would be 3,600 - 30 = 3570
3 0
2 years ago
You employ 28 people making an average of $33,000 per year. You want to give every employee a 5% increase for next year. What wi
PilotLPTM [1.2K]
I think the average would increase by $1,650. 5% of 33000 is 1,650. So the the total amount would increase by that.
3 0
3 years ago
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