Mary has 4 gallons of water. She wants to put 2/3 gallon in each bottle. How many bottles can she fill?

For the pair of supply-and-demand equations, where x represents the quantity demanded in units of 1000 and p is the unit price i

Liono4ka [1.6K]

Answer:

7 and 6 respectively

Step-by-step explanation:

Firstly, we have to solve the equations simultaneously.

2x + 7p = 56

3x - 11p = -45

Multiply equation I by 3 and ii by 2

6x +21p = 168

6x - 22p = -90

Subtract the second from first to yield:

43p = 258

p = 6

Insert this in equation 1 where we have 2x + 7p = 56

2x + 7(6) =56

2x + 42 = 56

2x = 14 and x = 7

The equilibrium price is 6 and the equilibrium quantity is 7

8 0

3 years ago

The arithmetic mean (average) of four numbers is 85. If the largest of these numbers is 97, find the mean of the remaining three

Margaret [11]

Answer:

81

Step-by-step explanation:

Let's do this systematically:

Four numbers: a, b, c, d

Whose mean is 85: $\frac{a + b + c + d}{4} = 85$

Whose largest number is 97: $\frac{a + b + c + 97}{4} = 85$

Lets solve for the other numbers:

a+b+c+97 = 85*4 = 340

340 - 97 = 243

a+b+c = 243

at this point it doesn't matter what the numbers are, they just need to add up to 243.

We can do 243÷3=81, which is our answer

3 0

3 years ago

The area of a circle is 47.39cm2. find the length of the radius rounded to 2 dp.

Tpy6a [65]

The length of the radius rounded to 2 decimal points is 3.88cm.

In geometry, the area enclosed by a circle of radius r is pie π $r^2$ .

How to round decimals?

Rounding decimals consists of rounding a decimal number to a certain number of decimal places, to save time and help us express really long numbers in shorter terms. There are certain rules to follow when rounding a decimal number. Put simply, if the last digit is less than 5, round the previous digit down. However, if it’s 5 or more than you should round the previous digit up. So, if the number you are about to round is followed by 5, 6, 7, 8, 9 round the number up. And if it is followed by 0, 1, 2, 3, 4 round the number down.

The area of circle is $47.39cm^2$ .

Putting it in the formula we get

$47.39cm^2$ = π $r^2$

$r^2$ = 47.39 / π

r^2 = 15.0847

r = 3.88 cm

Hence the length of the radius rounded to 2 decimal points is 3.88cm.

Learn more about circles here :

brainly.com/question/22275589

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5 0

2 years ago

Let U = {q, r, s, t, u, v, w, x, y, z}

Sliva [168]

The Set A’∪ B = { r, t, v, x, z, q, s, y, z }

We have the following sets -

U = {q, r, s, t, u, v, w, x, y, z}

A = {q, s, u, w, y}

B = {q, s, y, z}

C = {v, w, x, y, z}

We have to determine the set represented by - A' ∪ B.

A set is a collection of elements or numbers or objects, represented within the curly brackets { }. For example: {1,2,3,4} is a set of numbers.

According to question, we have -

U = {q, r, s, t, u, v, w, x, y, z} (Universal Set)

A = {q, s, u, w, y}

B = {q, s, y, z}

C = {v, w, x, y, z}

Consider Set A = {q, s, u, w, y}

A' = U - A = {q, r, s, t, u, v, w, x, y, z} - {q, s, u, w, y} = { r, t, v, x, z }

and Set B = {q, s, y, z}

Now -

A' ∪ B = { r, t, v, x, z } ∪ {q, s, y, z} = { r, t, v, x, z, q, s, y, z }

Hence, the Set A’∪ B = { r, t, v, x, z, q, s, y, z }

To solve more questions on Set theory, visit the link below -

brainly.com/question/13042571

#SPJ1

6 0

1 year ago

A person ate 2400 calories in a day. Of these, 36% came from fat. How many calories came from fat. Edit this was already answere

mamaluj [8]

36/100 = 0.36

0.36 * 2400 = 864

864 calories came from fat.

7 0

3 years ago