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2 years ago

Four friends were born in consecutive years. The sum of their ages is 62. What is the age of the oldest friend?

1 answer:

3 0

Since our sum is 62, and we have consecutive numbers being added, our range is most likely going to be from 10-20.
To further solve this problem easily, try finding 4 consecutive numbers with the ones place adding up to 12, 22, 32, 42, or any number that sums up to the 2 in the ones place.
Let's try 14, 15, 16, 17, since 4, 5, 6, and 7 sum up to a number with a 2 in the ones place.
14 + 15 = 29,
16 + 17 = 33.
33 + 29 is 62.
We have found the age of the friends, but we're looking for the oldest.
Our largest number is 17.
Your answer is 17 years old.
I hope this helps!

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Jake came in second place in the long jump at his track meet. The winner jumped a distance of 29.18 feet and the person in third

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Answer: 29
Any number between 28.83 and 29.18 would work

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2 years ago

Translate and solve: 344% of what number is 34,400 ?

weqwewe [10]

1000

1000(344%) = 34400

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When a water tank is $30\%$ full, it contains 27 gallons less than when it is $20\%$ empty. How many gallons of water does the t

aksik [14]

Answer:

54 gallons

Step-by-step explanation:

Let x represent the volume of the full tank.

When the water tank is 30% full;

= 30% of x = 0.30x

when it is 20% empty:

= x - 20% of x = x - 0.20x = 0.80x

The difference is given as 27.

So, we can represent the question on an equation as;

0.80x - 0.30x = 27

Solving the equation, we have;

0.50x = 27

x = 27/0.50

x = 54 gallons

The tank can hold 54 gallons when it is full.

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2 years ago

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A 0.8-liter bottle of Mexican wine costs 101 pesos. At thatprice, how much would a half-gallon jug of the same wine cost ind

monitta

Answer:

$12.18

Step-by-step explanation:

Given:

Cost of 0.8 liter bottle of Mexican wine = 101 pesos

cost of 1 liter bottle of Mexican wine = $\frac{\textup{101}}{\textup{0.8}}$ pesos

Now,

1 Mexican pesos = 0.051 dollars

thus,

cost of 1 liter bottle of Mexican wine = $\frac{\textup{101}}{\textup{0.8}}\times0.051$ dollars

also,

1 gallon = 3.78541 Liter

Thus,

half gallon = $\frac{\textup{3.78541}}{\textup{2}}$ = 1.892705 Liters

therefore,

cost of half gallon jug = $\frac{\textup{101}}{\textup{0.8}}\times0.051\times1.892705$ dollars

cost of half gallon jug of wine = $12.18

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2 years ago

A student club holds a meeting. The predicate M(x) denotes whether person x came to the meeting on time. The predicate O(x) refe

Novay_Z [31]

Answer:

a) $\exists \, x \in C : O(x) = 0$

b) $\{ x \in C : O(x) = 1 \} \subseteq \{ x \in C : M(x) = 1 \}$

c) $\{ x \in C: M(x) = 1 \} = C$

d) $\{ x \in C : D(x) = 1 \} \, \cup \, \{x \in C : M(x) = 1 \} = C$

e) $\exists \, x \in C : M(x) = 1 \, \wedge D(x) = 1$

f) $\exists \, x \in C : O(x) = 1 \, \wedge M(x) = 0$

Step-by-step explanation:

M(x) = 1 if the person x came to the meeting, and 0 otherwise.

O(x) = 1 if the person is an officer of the club and 0 otherwise.

D(x) = 1 if the person has paid hid/her club dues and 0 otherwise.

Lets also call C the set given by the members of the club. C is the domain of the functions M, O and D.

a) If someone is not an officer, the there should be at least one value x such that O(x) = 0. This can be expressed by logic expressions this way

$\exists \, x \in C : O(x) = 0$

b) If all the officers came on time to the meeting, then for a value x such that O(x) = 1, we also have that M(x) = 1. Thus, the set of officers of the Club is contained on the set of persons which came to the meeting on time, this can be written mathematically this way:

$\{ x \in C : O(x) = 1 \} \subseteq \{ x \in C : M(x) = 1 \}$

c) If everyone was in time for the meeting, then C is equal to the set of persons who came to the meeting on time, or, equivalently, the values x such that M(x) = 1. We can write that this way:

$\{ x \in C: M(x) = 1 \} = C$

d) If everyone paid their dues or came on time to the meeting, then if we take the set of persons who came to the meeting on time and the set of the persons who paid their dues, then the union of the two sets should be the entire domain C, because otherwise there should be a person that didnt pay nor was it on time. This can be expressed logically this way:

$\{ x \in C : D(x) = 1 \} \, \cup \, \{x \in C : M(x) = 1 \} = C$

e) If at least one person paid their dues on time and came on time to the meeting, then there should be a value x on C such that M(x) and D(x) are both equal to 1. Therefore

$\exists \, x \in C : M(x) = 1 \, \wedge D(x) = 1$

f) If there is an officer who did not come on time for the meeting, then there should be a value x in C such that O(x) = 1 (x is an officer), and M(x) = 0. As a result, we have

$\exists \, x \in C : O(x) = 1 \, \wedge M(x) = 0$

I hope that works for you!

7 0

2 years ago