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3 years ago

Find the solution to the system of equations represented by the matrix using an inverse matrix

1 answer:

8 0

To find the inverse of a 2x2 matrix: swap the positions of A and D, put negatives in front of B and C, and divide everything by the determinant.

You might be interested in

Complete the statement. Round to the nearest hundredth if necessary. 15 cm ≈ in.

Katarina [22]

Answer:

5.91 in

Step-by-step explanation:

1 cm = 0.393701 in

15 cm * 0.393701 in = 5.90551 in

Round to hundredth: 5.91 in

8 0

4 years ago

Determine the solution set of (x - 4)2 = 12

Travka [436]

Answer:

Step-by-step explanation:

(x - 4) × 2 = 12

x - 4 = 12 ÷ 2

x - 4 = 6

x = 10

4 0

3 years ago

Rebecca needs 10 1/2 yards of fabric to make a quilt. She has one piece of fabric that is 2 1/2 yards and another piece of fabri

yan [13]

Answer:

she needs 3 3/4 yards more to make a quilt

Step-by-step explanation:

Total cloth needed = 10 1/2 yards

she has a total of = 2 1/2 + 4 1/4

= 2+4 + 1/2 +1/4

=6 + 2+1/4

=6 3/4 yards

she needs more = 10 1/2- 6 3/4

= 21/2- 27/4

= 42-27/4

=15/4= 3 3/4 yards

4 0

3 years ago

A.The Murray family has produced 8 children.

Vlad [161]

Answer:

A. 0.2734 = 27.34% probability that there are an equal number of boys and girls

B. 0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly

Step-by-step explanation:

In each of these questions, the binomial probability distribution is used.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

A.The Murray family has produced 8 children.

What is the probability that there are an equal number of boys and girls?

8 children means that $n = 8$

Each children is equally as likely to be a boy or a girl, which means that $p = 0.5$

This probability is P(X = 4). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 4) = C_{8,4}.(0.5)^{4}.(0.5)^{4} = 0.2734$

0.2734 = 27.34% probability that there are an equal number of boys and girls

B.Margie has the uncanny ability of being able to guess the correct answer to TRUE/FALSE questions with an 80% accuracy rate. Tomorrow’s test has 7 questions on it and she needs to answer 5 questions correctly in order to make the Honor Roll. If she guesses on every question, what is the probability that she’ll answer exactly 5 questions correctly?

80% accurracy rate means that $p = 0.8$

7 questions means that $n = 7$

The probability is P(X = 5). So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{7,5}.(0.8)^{5}.(0.2)^{2} = 0.2753$

0.2753 = 27.53% probability that she’ll answer exactly 5 questions correctly

7 0

3 years ago

In a college parking lot, the number of ordinary cars is larger than the number of sport utility vehicles by 42.9%. the differen

fenix001 [56]

Let
x = number of common cars
y = number of suvs
we can write the following system of equations
x-y = 12
x = 1.429y
Solving the system we have
x-y = 12
1.429y-y = 12
and (1,429-1) = 12
y = (12) / (1,429-1) = 27.97202797
then,
x = 1429 * (27.97202797)
x = 39.97202797
answer
The number of suvs in the parking lot is 28

6 0

3 years ago