In a group of 50 patrons, 12 patrons like lattes, 11 patrons like espressos, and 6 patrons like both coffee drinks. How many patrons don't like either of the coffee drinks?

Final answer:

To find a person's weight on earth when you know their weight on the moon, multiply the moon weight by 6 (since weight on the moon is 1/6 of weight on earth). Therefore, if a person weighs 16 pounds on the moon, they would weigh 96 pounds on earth.

Explanation:

The question asks how much a person weighs on earth if he weighs 16 pounds on the moon. The fact that a person weighs about 1/6 on the moon than on earth would indicate that weight on earth is larger. In this case, you can find the earth weight by multiplying the moon weight to 6 (since it is 1/6). So, using this formula, if a person weighs 16 pounds on the moon, he would weigh 16 * 6 = 96 pounds on earth.

To check if this is reasonable, if you have the earth weight, you can divide by 6 to see if you return to the original moon weight. In this case, 96 / 6 = 16, which is the given moon weight, so the answer seems reasonable.

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Answer:

The constant is 40

Step-by-step explanation:

According to the question we are given an equation that represents the given situation as d = 40t where;

d is the distance in km

t is the time in seconds.

The given function is a direct proportionality. For example if p is directly proportional to q, this is expressed as p ∝ q where ∝ is the proportionality sign. In order to remove the sign we will introduce a constant say "k". The equation will become;

p = kq (p and q are the variables)

A direct proportionality means that as a variable is increasing, the other is increasing and vice versa. Comparing p = kq with d = 40t, we can see that k is equal to 40 and d is directly proportional to t

Hence the constants of proportionality for the relationship between distance in kilometers and number of hours is 40 on comparing.

The system of equations that represents the given statements is

x + 1.5y = 12

x + y = 9

Where x is the number of pencils and y is the number of pens that Shawn bought.

How to write an equation for a statement?

To write an equation:

• Observe the variableterms from the given statement
• Add/subtract required terms according to the word's 'total or difference' given in the statements
• Multiply/divide required terms according to the words 'more or less given the statements
• Equate with the respective values related to the variable term.

Calculation:

Given that,

A pencil at a stationery store costs - $1

and A pen costs - $1.50

Shawn spent $12 at the store. He bought a total of 9 items.

So,

Consider number of pencil = x and number of pens = y

Since he bought a total of 9 items, we can add the number of pencils and pens and equate the sum with 9

I.e., x + y = 9 ...(i)

We have cost for a single pencil and a single pen

So, to get the cost for the total number of pencils and pens that he bought, multiply the cost of a single one by the number of pencils and pens. I.e.,

1 × x and 1.50 × y

Since it is given that he spent $12 for both pencils and pens, we can write

x + 1.5 y = 12  ...(ii)

Thus, from equations (i) and (ii), the system we can write

x + 1.5 y = 12

x + y = 9

So, option 2 is the correctset of equations for the given system.

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Answer:

x = 3  

Step-by-step explanation:

5x + 4 = 19

5x +4 -4 = 19 -4

5x = 15

5x / 5  = 15 / 5

x = 3  

We're told (5,-2) is on the line, that's x=5, y=-2

First one y-5 = -7, (x+2)/3=7/3, not equal

Second one y+5=3, (x-2)/3=1, not equal

Third one y+2=0, (x-5)/3=0, TRUE, equal

Fourth one, y-2=-4 (5+5)/3=10/3, not equal

Answer: third choice y+2 = (1/3)(x+5)