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Allushta [10]
3 years ago
10

Bobby's Christmas list had 3 more than twice as many items on it than Johnny's list. Jhonny asked for 8 fewer items than bobby.

How many items were on Johnny's (x) and Bobby's (y) Christmas lists
Mathematics
2 answers:
miskamm [114]3 years ago
4 0
Because jonny asked for 8 fewer items than bobby and bobby's list had 3 more than twice that of johny, the "twice" is 5. Two possible answers for this problem could be 13 and 5 since they both satisfy the requirement. if you can't logically deduct a function for it, look at the problem closely, then test and guess! Have fun with math!
Delvig [45]3 years ago
4 0

Answer:

<h2>Bobby made the Christmas list with 13 items, and Johnny with only 5 items.</h2>

Step-by-step explanation:

"Bobby's Christmas list hat 3 more than twice as many items than Johnny's". This statement is represented by:

B=2J+3; where B is Bobby, and J is Johnny.

Then, the problem states, "Johnny asked for 8 fewer items than bobby", it's represented by:

J=B-8

Now, to find the value of each variable, we solve this system of equations by substitution:

B=2J+3\\B=2(B-8)+3\\B=2B-16+3\\13=2B-B\\B=13

Then, we replace this into second equation to find J:

J=B-8=13-8=5

Therefore, Bobby made the Christmas list with 13 items, and Johnny with only 5 items.

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A pan of warm water (46∘ Celsius) was put in a refrigerator. After 15 minutes, the water's temperature was 27∘ C; 15 minutes aft
Cloud [144]

Answer:

The refrigerator was at around 13 ∘C

Step-by-step explanation:

Newton's Law of Cooling:

The rate of change of a body temperature  (amount of heat loss/time of loss) is directly proportional to the difference between its own temperature and the surroundings.

\frac{T(t2)-T(t1)}{t2-t1} = -h (T(t2) - Tenv)

T ⇒ temperature

t ⇒ time

Tenv ⇒refrigerator temperature

\frac{T(t2)-T(t1)}{t2-t1} ⇒ rate of change of he temperature

-h ⇒ constant of proportionality (negative because the temperature is decreasing inside the refrigerator)

We have 3 points:

time (minutes) - Temperature (∘ C)

0 (when the pan was put in the refrigerator) - 46

15 (after 15 minutes) - 27

30 (15 minutes after the first 15 minutes) - 19

\frac{27 - 46}{15 - 0} = -h (27 - Tenv)

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)

Now we have a system of two equations and two variables

\frac{-19}{15} = -h (27 - Tenv)\\ \frac{19}{15} = h (27 - Tenv)\\ \frac{19}{15(27 - Tenv)} = h

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)\\\frac{-8}{15} = -h (19 - Tenv)\\\frac{8}{15} = h (19 - Tenv)\\\frac{8}{15} = \frac{19}{15(27 - Tenv)} (19 - Tenv)\\8(27 - Tenv) = 19 (19 - Tenv)\\216 - 8 Tenv = 361 - 19 Tenv\\19 Tenv - 8 Tenv = 361 - 216\\11 Tenv = 145 \\Tenv = 145/ 11\\Tenv = 13. 18

The refrigerator was at around 13 ∘C

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