The circumference of a circle is 12pi feet. What is the diameter?

k0ka [10]

To divide by decimals, put the decimal right where it is above it, and you just do regular dividing

6 0

3 years ago

Solve the system by elimination.. x+5y-4z=-10. 2x-y+5z=-9. 2x-10y-5z=0. . a.) (5, –1, 0). b.) (–5, 1, 0). c.) (–5, –1, 0). d.) (

Troyanec [42]

Answer:

Your answer is option C … (-5, -1, 0)

Step-by-step explanation:

3 0

3 years ago

Rectangle ABCD is congruent to rectangle. Which sequence of transformations could have been used to transform rectangle ABCD to

il63 [147K]

Rectangle ABCD was rotated 90° counterclockwise around the origin and then translated 8 units down.

7 0

3 years ago

The sum of a two digit number and the number obtained by interchanging the digits is 132. If the two digits differ by 2, find th

damaskus [11]

Answer:

A two-digit number can be written as:

a*10 + b*1

Where a and b are single-digit numbers, and a ≠ 0.

We know that:

"The sum of a two-digit number and the number obtained by interchanging the digits is 132."

then:

a*10 + b*1 + (b*10 + a*1) = 132

And we also know that the digits differ by 2.

then:

a = b + 2

or

a = b - 2

So let's solve this:

We start with the equation:

a*10 + b*1 + (b*10 + a*1) = 132

(a*10 + a) + (b*10 + b) = 132

a*11 + b*11 = 132

(a + b)*11 = 132

(a + b) = 132/11 = 12

Then:

a + b = 12

And remember that:

a = b + 2

or

a = b - 2

Then if we select the first one, we get:

a + b = 12

(b + 2) + b = 12

2*b + 2 = 12

2*b = 12 -2 = 10

b = 10/2 = 5

b = 5

then a = b + 2= 5 + 2 = 7

The number is 75.

And if we selected:

a = b - 2, we would get the number 57.

Both are valid solutions because we are changing the order of the digits, so is the same:

75 + 57

than

57 + 75.

6 0

3 years ago

In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacem

Damm [24]

Answer:

a) P(A) = 0,4607 or P(A) = 46,07 %

b) P(B) = 0,7120 or 71,2 %

c) P(C) = 0,2055 or P(C) = 20,55 %

Step-by-step explanation:

We will use two concepts in solving this problem.

1.- The probability of an event (A) is for definition:

P(A) = Number of favorable events/ Total number of events FE/TE

2.- If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

a) The total number of events is:

C ( 24,4) = 24! / 4! ( 24 - 4 )! ⇒ C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!

C ( 24,4) = 24*23*22*21/4*3*2

C ( 24,4) = 24*23*22*21/4*3*2 ⇒ C ( 24,4) = 10626

TE = 10626

Splitting the group of tanks in two 6 with h-v and 24-6 (18) without h-v

we get that total number of favorable events is the product of:

FE = 6* C ( 18, 3) = 6 * 18! / 3!*15! = 18*17*16*15!/15!

FE = 4896

Then P(A) ( 1 tank in the sample contains h-v material is:

P(A) = 4896/10626

P(A) = 0,4607 or P(A) = 46,07 %

b) P(B) will be the probability of at least 1 tank contains h-v

P(B) = 1 - P ( no one tank with h-v)

Again Total number of events is 10626

The total number of favorable events for the ocurrence of P is C (18,4)

FE = C (18,4) = 18! / 14!*4! = 18*17*16*15*14!/14!*4!

FE = 18*17*16*15/4*3*2 = 3060

Then P = 3060/10626

P = 0,2879

And the probability we are looking for is

P(B) = 1 - 0,2879

P(B) = 0,7120 or 71,2 %

c) We call P(C) the probability of finding exactly 1 tank with h-v and t-i

having 4 with t-i tanks is:

reasoning the same way but now having 4 with t-i (impurities) number of favorable events is:

FE = 6*4* C(14,2) = 24 * 14!/12!*2!

FE = 24* 14*13*12! / 12!*2

FE = 24*14*13/2 ⇒ FE = 2184

And again as the TE = 10626

P(C) = 2184/ 10626

P(C) = 0,2055 or P(C) = 20,55 %

5 0

3 years ago