Three friends have been working in a garden. One has worked for 11 hours and the other 2 worked for 7 hours. The garden owner paid $500 for the work that was done. How should this money be divided fairly between the three friends?

Answer:

6/5

Step-by-step explanation:

8/15 - (-2/3)

8/15 + 2/3

24 + 30/45

54/45 = 6/5

Thus, the difference between 8/15 and -2/3 is 6/5

Start by changing the minus a negative to plus a positive.

So we have 8/15 + 2/3.

To add these two fractions together, we need a common denominator.

The common denominator is simply the

least common multiple for the two denominators.

You should find that the least common multiple is 15.

Since 8/15 already has 15 as its denominator, leave it.

To get a denominator of 15 in 2/3, we multiply top

and bottom of 2/3 by 5 to get 10/15.

So we have 8/15 + 10/5.

This simplifies to 18/15.

Now reduce to get 6/5.

Answer:

Well, we can write a really simple quadratic polynomial as:

P(x) = a*(x - c1)*(x - c2)

Where a is a constat, and c1 and c2 are the roots, here we have:

c1 = 5 and c2 = -3

P(x) = a*(x -5)(x + 3) = a*x^2 + a*x*3 - a*5*x - a*15

then the quadratic polynomial can be:

P(x) = a*x^2 + a*(3 - 5)*x - a*15

P(x) = a*x^2 - 2*a*x - a*15

Where a can be any real number.

Answer:

Reflection only and rotation then translation.

Step-by-step explanation:

im not sure

Answer:

look at the picture below

Step-by-step explanation:

Answer:

d-2  and d cannot = 8

Step-by-step explanation:

d^2 -10d+16

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

d-8

Factor the numerator

( d-8)(d-2)

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

d-8

The undefined values occur when the denominator is equal to zero

d-8 = 0  

  d= 8

This means d cannot equal 8

Now cancel like terms in the equation ( d-8)

This yields d-2

Answer: d - 2 and d cannot equal 8

Step-by-step explanation: To simplify this rational expression, start by factoring both the numerator and the denominator.

So factoring the numerator in this problem, we have a

trinomial that factors as the product of two binomials.

So we are looking for factors of +16 that add to -10 which are -8 and -2.

So we have (d - 8)(d - 2) in the numerator.

The denominator doesn't factor however.

So we have [tex]\frac{(d - 8)(d - 2)}{(d - 8)}[/tex] and the d - 8's cancel leaving us with d - 2.

The values d cannot be happen when the denominator is set equal to 0.

So we have d - 8 = 0 which means d = 8.

This means d = 8 wouldn't work!

Find the circumference of the wheel:

Circumference = PI x Diameter = 3.14 x 15 = 47.1 inches.

Every revolution the tire travels 47.1 inches.

1 mile = 5,280 feet, so 2 miles = 5280 x 2 = 10,560 feet.

1 foot = 12 inches.

2 miles = 10,560 feet x 12 = 126,720 inches.

Revolutions = total distance /  distance per revolution:

Revolutions = 126,720 / 47.1 = 2,690.45 revolutions ( round answer as needed.)

Answer:

6.71cm

Step-by-step explanation:

a²+b²=c²

6²+3²=x²

sqrt(6²+3²)=6.71

Answer:

[tex]\Large \boxed{\sf 6.71 \ cm}[/tex]

Step-by-step explanation:

The triangle is a right triangle. We can use Pythagorean theorem to solve for the hypotenuse.

a² + b² = c²

a and b are the lengths of the legs. c is the length of the hypotenuse.

6² + 3² = x²

Evaluate.

36 + 9 = x²

45 = x²

Take the square root of both sides.

√(45) = √(x²)

6.7082039325... = x

Answer: second choice

Explanation:

all the answers are prime factorized, meaning that everything under the sign should multiply up to 180. the second answer, 2*2*3*3*5=180 works

Answer:

(6x + 9y)(6x - 9y)

Step-by-step explanation:

We can use the difference of squares which states that a² - b² = (a + b)(a - b), in this case, a = 6x and b = 9y so the answer is (6x + 9y)(6x - 9y).

Answer:

Q10ii: x axis horizontal, y axis vertical, a straight line through the origin and point (5,20)

Q11i: z = 8y

Q11ii: y axis horizontal, z axis vertical, a straight line through the origin and (6,48)

Step-by-step explanation:

Linear proportions will always produce straight lines when graphed. Also, they will have to go through the origin when there is not some kind of offset.

Answer:

1/2 is the fractional part of cookie which was eaten by Dan.

Step-by-step explanation:

Dan has 2 1/2 cookies and ate 1/2, so we can just subtract the 2 1/2-1/2

which cancels out the 1/2, which is the fractional part.

He has 2 cookies left.

The fractional part that he ate will be 5/4.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of numerator and denominator.

Dan had 2 1/2 cookies and ate 1/2 of a cookie.

Of the original number of cookies.

Then the mixed fraction is converted into fraction.

2 1/2 = 5/2

The fractional part that he ate will be

⇒ (5/2) / 2

⇒ (5/2) x (1/2)

⇒ 5/4

The fractional part that he ate will be 5/4.

More about the Algebra link is given below.

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Answer:

The correct option is;

B. I only

Step-by-step explanation:

The central limit theorem states that when adequately large random samples are taken from a population that has a mean, μ, and standard deviation, σ, the distributions of the sample means of individual samples taken will be more or less (approximately) normally distributed

The central limit theorem is correct for both normal and skewed populations such that estimates can be made about the population mean based on available sample mean information.

Answer:

II only

Step-by-step explanation:

I got the answer from Chegg, took the test, and got it right! :)

Answer:

1

Step-by-step explanation:

(-2)(1/4)=-1/2

(-2)(-1/2)

=1

the third term of the geometric sequence with first term = 1/4 and common ratio r = -2 is 1

We have a geometric sequence in which the first term is [tex]\frac{1}{4}[/tex] and the common ratio is -2.

We have to find the third term of this geometric sequence.

The formula to find the [tex]n^{th}[/tex] term of a geometric sequence with first term [tex]a_{1}[/tex] and common ratio r is -

[tex]a_{n} =a_{1} r^{n-1}[/tex]

In our question, [tex]a_{1}[/tex] = [tex]\frac{1}{4}[/tex]  and r = -2 and n =3.

Substituting the values, we get -

[tex]a_{3} =\frac{1}{4}(-2)^{3-1} = \frac{1}{4} (-2)^{2} =\frac{1}{4}\times4=1[/tex]

Hence, the third term of the geometric sequence with first term = 1/4 and common ratio r = -2 is 1.

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Answer:

(7, 5)

Step-by-step explanation:

(x+5)/2, ( y-3)/2)=(6,1)

(x+5)/2=6, x= 7

( y-3)/2=1, y=5

Answer:

[tex] = ( \frac{ - b}{a} )( \frac{c}{a} )[/tex]

[tex] = ( \frac{ 1}{3} )( \frac{ - 5}{3} )[/tex]

[tex] = \frac{ - 5}{9} [/tex]

Answer:

- [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Given

P(x) = 3x² - x - 4

with a = 3, b = - 1 and c = - 4

If α and β are the roots of the quadratic then

α + β = - [tex]\frac{b}{a}[/tex] and αβ = [tex]\frac{c}{a}[/tex] , thus

α + β = - [tex]\frac{-1}{3}[/tex] = [tex]\frac{1}{3}[/tex] and αβ = - [tex]\frac{4}{3}[/tex]

Thus

α + β by αβ

= [tex]\frac{\frac{1}{3} }{-\frac{4}{3} }[/tex] = [tex]\frac{1}{3}[/tex] × - [tex]\frac{3}{4}[/tex] = - [tex]\frac{1}{4}[/tex]

Answer:

1.34%

Step-by-step explanation:

First of all subtract the 2 values

9.84−9.71=0.13

use this value and find the percentage from the original price which was 9.71

0.13

-------  ⋅100

9.71

percentage increase is

1.34%

Answer:

A = 15

B = -3

Step-by-step explanation:

3 ,7,11..... You add 4 each time so 11+4 is 15

12,7,2.... You take 5 each time so 2-5 is -3

-5+6=1 because if it's not a normal equation it has a negative

Answer:

1

Step-by-step explanation:

When adding a negative and a positive number, subtract the biggest number from the smallest (ignore the signs), so :

[tex]6-5=1[/tex]

After you have your answer, keep the symbol of the bigger number (pay attention to the signs now). Since positive 6 is greater than negative 5, keep the positive. Add this symbol to the answer, making the answer positive.

[tex]-5+6=1[/tex]

Answer:

3

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

5

Answer:

A. <

Step-by-step explanation:

-9.5 is greater than -11.5

Answer:

A) <

less than

Step-by-step explanation:

-11.5 < -9.5

Answer:

Step-by-step explanation: 2 raised to 2 or 2^2 is the same as saying 2*2 so 2 raised to 2 or 2^2 is 4

Answer:

Step-by-step explanation: 2 raised to 2 or 2^2  

is the same as saying 2*2 so 2 raised to 2 or 2^2 is 4

Answer:

75 of the adult ones and 150 of the children ones.

Answer:

0.15(5,-1)

Step-by-step explanation:

[tex]\frac{v_{1} * v_{2} }{|v_{2}|^{2} }*v_{2}[/tex]  ⇒ [tex]\frac{(2)(5)+(6)(-1)}{\sqrt{5^2+(-1)^2} }(5,-1)[/tex] ⇒  [tex]\frac{4}{26} (5,-1)[/tex]  ⇒  [tex]0.15(5,-1)[/tex]

The best approximation of the projection  IS ( 5,-1).

Vector A ,

                 (2,6) in terms of vectors is represented by = 2 i +6 j

Vector B,

                 (5,-1) in terms of vectors is represented by =5 i - 1 j

Projection of Vector A on Vector B

       [tex]\frac{(A . B)(B)}{IBI^{2} } \\[/tex] =  [tex]\frac{[(2i + 6j).(5i - j)]( 5i - j)}{\sqrt{5^{2} }+ (-1)^{2} }[/tex]

[tex]= \frac{(2)(5) +(6)(-1)}{\sqrt{5^{2} }+(-1)^{2} }[/tex]

= ( 5 ,-1 ) ⇒ 0.15 (5,-1)

Therefore, The best approximation of the projection  IS ( 5,-1) .

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Answer:the answer is A

Step-by-step explanation:

The step is

Real number - rational(irrational)_ - integer - whole - then natural

The true statement regarding number sets are b. all irrational numbers are real numbers.

Irrational numbers are those numbers which have a non-repeating, non-terminating pattern after decimal place.

According to the given statements we have to determine which is true.

a. all integers are not whole numbers as 0 contains in the set of whole numbers but not in the set of integers.

b. all irrational numbers are real numbers this is a true statement because all the real numbers consist of rational and irrational numbers.

We don't need to check other options because we have been asked which of the following is true not which of the following is/are true.

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Answer:

52 / 5424 = 0.00958..

198 / 8549 = 0.0231 ..

Step-by-step explanation:

52 / 5424

First of all, you need to add 0 plus a coma → 0.

52 becomes 520, but this value is smaller than 5424, so we need to add another 0

5200 → another 0 → 52000

So now, we have 52000 / 5424.

We start,  5424 . 10 = 54240, we are higher than 52000, so let's try 9

5424 . 9 = 48816, great!

52000 - 48816 = 3184

This is smaller than 5424, so we need a zero, again. But we do not add 0 to the result, because we are in the decimal side

31840 → 31840 / 5424. We would try 6,

5424 . 6 = 32544. It's bigger!, We use 5

5424 . 5 = 27120!

31840 - 27120 = 4720. We get another 0

47200, and we try 8.

5424 . 8 = 43392

47200 - 43392 = 3808.

So we are going to add 0, until we have four digits that can be divided by 5424 and decimals are infinte.

52 / 5424 = 0.00958..

198 / 8549 → Need to add, the first 0 to convert 198 to 1980

1980 = 0. → Another zero

19800 = 0.0 → 19800 / 8549

We try 2 → 8549 . 2 = 17098

19800 - 17098 = 2702 → we add 0

27020 / 8549 → We try 3

8549 . 3 = 25647 → 27020 - 25647 = 1373 → we add 0

13730 / 8549 → We use 1 → 13730 - 8549 = 5181

As decimal are infinite, we can express the result as:

198 / 8549 = 0.0231 ..

Answer:

D) 7 meters

Step-by-step explanation:

So I would start this off by plugging in the variables into side B. So if we were to plug 7 into B there would be 22 meters left of the perimeter. Therefore meaning 22 between A and C. Now A is 3 meters shorter than TWICE of B. So 7 times 2 is 14 and 14 minus 3 is 11. now we have 11 and 7 which equals 18. 29 minus 18 giving us 11 left. 11 is C. Now it says c is 4 meters longer than B so it 7 plus 4 is 11. And everything adds up. HOPE THIS HELPS.

Answer:

Side b=7 meters

Step-by-step explanation:

Given:

Perimeter of triangle=29m

Side a=2b-3

Side b=b

Side c=4+b

To find:

Side b

Solution:

P of triangle=a+b+c

29=2b-3+b+4+b

29=2b+b+b+4-3

29=4b+1

29-1=4b

b=28/4

b=7m

I hope my answer is right.

Answer:

549 ft

Step-by-step explanation:

take 670ft away from 1,220 ft ( not all the way sure of I'm right)

Answer:

550

Step-by-step explanation:

1,220+(-670)= 550

Thank you! :)

Answer:

27.89 hours.

Step-by-step explanation:

I hope this helps! If you would like an explanation, let me know!

Answer:

First question, 28 hours

Second question, 20 minutes

Step-by-step explanation:

$9.50 for each hour + $75 for showing up on time

Let's say the employee showed up on time

(340 - 75) ÷ 9.5 = 28 hours approximately

120 ÷ 6 = 20 minutes

Answer:

Friday & Sunday

Step-by-step explanation:

Thursday: 287

Friday: 618

Saturday: 973

Sunday: 532

973 < 287 + 618 = 973 < 905

We now know this isn't true.

973 < 287 + 532 = 973 < 819

This isn't true either.

973 < 532 + 618 = 973 < 1150

This is true.  The two days with the time are Friday and Sunday.

I really hope this helps you!  Tell me if it's right or not! :D

Answer:

D; b = -20.75

Step-by-step explanation:

Here in this question, we want to find solution to the given linear equation.

The linear equation is;

-83 = b4

Now, to find the value of b, we will need to divide both sides by its coefficient.

Looking at the question, the coefficient of b is 4

Mathematically, that would be :

-83/4 = b4/4

b = -83/4

b = -20.75

Answer:

b = -20.75

Step-by-step explanation:

Given:

-83 = b4

It can also be written as

-83 = 4b

divide both sides by the coefficient of b which is 4

-83 / 4 = 4b / 4

-20.75 = b

Therefore,

b = -20.75

Check:

-83 = b4

-83 = -20.75(4)

-83 = -83