Which of the following sets of ordered pairs represents a function?

Lauren spent 3/5 of her money on a refrigerator. The refrigerator cost $756. How much money did she have left?

Lelechka [254]

Fractions are the part/whole. We can set this up to be...

3/5 = 756
756 x5/3 = 1260.

if she had 1260 to begin with and spent 756, she would have 504.00 left.

3 0

2 years ago

A right triangle has side lengths 4 units, 5 units, and x units. It is unknown if the missing length is the longest or shortest

mel-nik [20]

Possible values = 3.0 and 6.0

6 - 3 = 3

The difference is 3

4 0

2 years ago

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Suppose you roll a pair of honest dice. If you roll a total of 7 you win $22, if you roll a total of 11 you win $66, if you roll

JulijaS [17]

Answer:

The expected payoff for this game is -$1.22.

Step-by-step explanation:

It is given that a pair of honest dice is rolled.

Possible outcomes for a dice = 1,2,3,4,5,6

Two dices are rolled then the total number of outcomes = 6 × 6 = 36.

$\{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),\\(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}$

The possible ways of getting a total of 7,

{ (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) }

Number of favorable outcomes = 7

Formula for probability:

$Probability=\frac{\text{Favorable outcomes}}{\text{Total outcomes}}$

So, the possibility of getting a total of 7 = $\frac{6}{36}=\frac{1}{6}$

The possible ways of getting a total of 11,

{(5,6), (6,5)}

So, the probability of getting a total of 11 = $\frac{2}{36}$ = $\frac{1}{18}$

Now, other possible rolls = 36 - 6 - 2 = 36 - 8 = 28,

So, the probability of getting the sum of numbers other than 7 or 11 = $\frac{28}{36}$ = $\frac{7}{9}$

Since, for the sum of 7, $ 22 will earn, for the sum of 11, $ 66 will earn while for any other total loss is $11,

Hence, the expected value for this game is

$\frac{1}{6}\times 22+\frac{1}{18}\times 66-\frac{7}{9}\times 11$

$\frac{11}{3}+\frac{11}{3}-\frac{77}{9}$

$\frac{22}{3}-\frac{77}{9}$

$\frac{66-77}{9}$

$-\frac{11}{9}$

$-1.22$

Therefore the expected payoff for this game is -$1.22.

4 0

2 years ago

A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally. A piece of climbing equipment at a

Dahasolnce [82]

Answer: The comparison is mentioned below.

Step-by-step explanation:

A piece of climbing equipment at a playground is 6 feet high and extends 4 feet horizontally.

Therefore its slope = length of the equipment vertically / length of equipment horizontally

$m_1$ = 6/4 = 3/2 = 1.5

And, A piece of climbing equipment at a gym is 10 feet high and extends 6 feet horizontally.

Therefore slope, $m_2$ = 10/6 = 5/3=1.67 (approx)

Since, $m_1$ < $m_2$

Thus the slope of equipment first is less than slope of second equipment.

5 0

2 years ago

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For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations

Nookie1986 [14]

Option C

The expression 20(22 - x) represents the value of the $20 traveler's checks she has.

<u>Solution:</u>

Given, For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations travelers checks in all,

We have to find how many of each denomination does she have?

Let x represent the number of $10 traveler's checks she has,

Then, $10(x) + $20(number of $20 checks) = 300

10x + 20($20 checks) = 300

x + 2(number of $20 checks) = 30 ⇒ (1)

Now let us see the given options, for value of $20 checks,

It should be in format, that, $20 x number of $20 checks

⇒ 20(total checks - $10 checks) ⇒ 20(total checks – x), as we can see only C is in that format, it is correct and total number of checks = 22.

Then, (1) ⇒ x + 2(22 – x) = 30

⇒ x + 44 – 2x = 30

⇒2x – x = 44 – 30

⇒ x = 14

So, $10 checks count = 14, then, $20 checks count = 22 – 14 = 8.

Hence, there are 14 $10 checks and 8 $20 checks, and option c is correct.

7 0

2 years ago