If all entries of A and A^−1 are integers, prove that detA = 1 or −1.

Given :

A group of men decided to do a job in 8 days.

10 men dropped out every day, the job  got completed at the end of the 12th day.

To Find :

How  many men were at the beginning ?

Solution :

Let, total number of men initially are n.

It none of them leave, total work :

W = 8n    ...1)

It is given that 10 men are dropped each day it takes them 12 day to complete the work :

W = ( n ) + ( n - 10 ) + ( n - 20 ) +  ....   + ( n - 110 )

W = 12n - ( 0 + 10 + 20 + ...... + 110 )

W = 12n - 660    ...2)

Since, total work is same in both the cases, so equating both equation, we get :

12n - 660 = 8n

4n = 660

n = 165

Therefore, their are 165 men in the beginning.

Answer:

1352 cm

Step-by-step explanation:

Length (l) = 13 cm

Width (w) = 52 cm

Perimeter of the rectangle = 2(l + w) units

P = 2(13 + 8)

P = 2 (21)

P = 42

Thus, the perimeter of the rectangle is 42 cm.

Example 2: If a rectangle's length is 2x + 1 and its width is 2x – 1. If its area is 15 cm2, what are the rectangle's dimensions and what is its perimeter?

Solution:

We know that the dimensions of the rectangle in terms of x:

l = 2x + 1

w = 2x – 1

Since the area of a rectangle is given by:

A = l * w

We can substitute the expressions for length and width into the equation for area in order to determine the value of x.

A = l * w

15 = (2x + 1) (2x -1)

15 = 4x2 – 1

16 = 4x2

x = ±2

Note that the value of x must be positive and therefore in our case, the value of x is 2. And now we have:

l = 11 cm

w = 52 cm

Therefore, the dimensions are 5cm and 3cm.

Now, substituting these values in the formula for perimeter, we will get

P = 2l + 2w

P = 2(5)+2(3)

P = 10+6

P = 16 cm

Answer:

0.82

step-by-step explanation:

Answer:

red

Step-by-step explanation:

1/2 is larger than 1/4, 1/6, and 1/12 meaning the chance of pulling red is greater than getting blue, green, or yellow.

hope i helped you!

Answer:

D)

Step-by-step explanation:

Answer:

n<4

It goes to the left

Step-by-step explanation:

Let's solve your inequality step-by-step.

6n+7<31

Step 1: Subtract 7 from both sides.

6n+7−7<31−7

6n<24

Step 2: Divide both sides by 6.

6n/6<24/6

n<4

Answer I think its 6 and -3

Step-by-step explanation:

Answer:

The answer would be 0,0754716981

Answer:

j

Step-by-step explanation:

Answer:

12 inches

Step-by-step explanation:

1. The diagonal is the hypotenuse of the right triangle.  so since we know one side length, we can figure out the other side length

Answer:

True

Step-by-step explanation:

1.45 the 5 is equal/above it so it is true

Answer:

[tex]P(B') = 0.77[/tex]

Step-by-step explanation:

Given

[tex]P(A) = 0.23[/tex]

[tex]P(A\ n\ B) = 0.12[/tex]

[tex]P(A\ u\ B) = 0.34[/tex]

Required

Find P(B')

First, we calculate P(B).

We have:

[tex]P(A\ n\ B) = P(A) + P(B) - P(A\ u\ B)[/tex]

Substitute values

[tex]0.12 = 0.23 + P(B) - 0.34[/tex]

[tex]0.12 = 0.23 - 0.34 + P(B)[/tex]

Collect like terms

[tex]P(B) = 0.12 - 0.23 + 0.34[/tex]

[tex]P(B) = 0.23[/tex]

P(B') is then calculated as:

[tex]P(B') = 1 - P(B)[/tex]

[tex]P(B') = 1 -0.23[/tex]

[tex]P(B') = 0.77[/tex]

Answer:

the answer is 39

Step-by-step explanation:

you take 300 - 271 and you get 39

Answer:

29? or I'm just gullible.

Step-by-step explanation:

It seems like 29 so hopefully it is

Answer:37.5

Step-by-step explanation:

Answer:

37.5

Step-by-step explanation:

Answer: all i can read is number 2 and the answer is 5ft

Step-by-step explanation:

Answer:

Step-by-step explanation:

To solve question 1, you use the Pythagorean Theorem to solve. Option B uses this correctly.

Question 2 also uses the Pythagorean Theorem to solve. The answer is a decimal, but rounded to the nearest whole number, the answer is 5.

Question 3 uses the Pythagorean Theorem to see which triangles have the correct measurements of a right triangle. The triangle D is the only incorrect one.

Number 4 uses the Pythagorean Theorem to find the distance it would take to walk in a straight line. The answer to this is 51. Then subtract (24 + 45) - 51 to get 18 yards.

Hope it helps!

Answer:

y = 8

Step-by-step explanation:

3y = 24

3y ÷ 3 = 24 ÷ 3

y = 8

Step-by-step explanation:

whatever amount her bank account balance is at the same time frame when paying off her loan as only her bank knows

Answer:

It will take 28 minutes to complete a 7-kilometer race

Step-by-step explanation:

If you can job 3 kilometers in 12 minutes, that means you can jog 1 kilometer in 4 minutes. so if you multiply 7 times 4, you would get 28. So your answer is 28 minutes.

Answer:

X=55

Step-by-step explanation:

(2x+10)+(x+5)=180

Combine like terms.

3x+15=180

Subtract 15.

3x=165

Divide by 3.

x=55

Answer:

see attached

Step-by-step explanation:

angles on a straight line

Answer:

15 meters per second

Step-by-step explanation:

60/4 = 15

Answer:

15 meters per second

Answer:

x_<2

Step-by-step explanation:

its shaded in so you have to flip it

Answer:

The answer is

x_<2

The circle is shaded and the arrow is going to the left hand side

Answer: Your answer is (C) 6/14

Step-by-step explanation: Have a brilliant day mate - Lily ^-^

Answer:

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

In this question, we have that:

The time between arrivals of customers at an automatic teller machine is an exponential random variable with a mean of 4 minutes, and we have three customers, which means that [tex]m = 3*4 = 12, \mu = \frac{1}{12} = 0.0833[/tex]

(a) What is the probability that more than three customers arrive in 10 minutes

This is P(X > 3). So

[tex]P(X > 3) = e^{-0.0833*3} = 0.7788[/tex]

0.7788 = 77.88% probability that more than three customers arrive in 10 minutes

9514 1404 393

Answer:

  60°

Step-by-step explanation:

  60 × 1° = 60°

The angle measure is 60°.

Answer:

C. 82.84

Step-by-step explanation:

Answer:

73

Step-by-step explanation:

Probably