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bagirrra123 [75]
2 years ago
7

Ally's tricycle has two different wheel sizes: one larger wheel and two smaller wheels. As Ally travels the distance between her

house and her neighbor's house on the tricycle, the larger wheel revolves 10 times and each of the smaller wheels revolve 25 times. If half the circumference of the larger wheel is 5 inches more than the circumference of one of the smaller wheels, what is the distance, in inches, traveled by the tricycle between Ally's house and her neighbor's house?
Mathematics
1 answer:
vazorg [7]2 years ago
8 0

Answer:

500 inches

Step-by-step explanation:

Let C₁ and n₁ be the circumference and the number of rotations of the larger wheel. Also, let C₂ and n₂ be the circumference and the number of rotations of the smaller wheel. Since the distance moved by both wheels from Ally's house to her neighbor's house is the same, n₁C₁ = n₂C₂. (1)

Also it is given that half the circumference of the larger wheel is 5 inches more than the circumference of one of the smaller wheels.

So, C₁/2 = C₂ + 5

C₁ = 2(C₂ + 5)  (2)

Substituting C₁ into (1), we have

n₁C₁ = n₂C₂.

n₁[2(C₂ + 5)] = n₂C₂.

Since n₁ = 10 and n₂ = 25, we have

10[2(C₂ + 5)] = 25C₂

20(C₂ + 5) = 25C₂

expanding the bracket,

20C₂ + 100 = 25C₂

collecting like terms, we have

25C₂ - 20C₂ = 100

5C₂ = 100

dividing both sides by 5, we have

C₂ = 100/5

= 20 inches

So, the distance between Ally's house and her neighbor's house is d = n₂C₂ = 25(20)

= 500 inches

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Answer:

B would be a *dependent* event, and A would be an *independent* event.

Step-by-step explanation:

Independent events are separate events where the outcome in either event does not affect the other's probability. The opposite, where the outcome of the one event affects the other's probably, is dependent.

For Option A, taking a tile out and then replacing it does not affect the probability that the same tile will be picked for the 2nd picking.

For Option B, taking a tile out of the bag and then picking another tile are 2 separate events and both have different probabilities for picking identical tiles.

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Answer:

A

Step-by-step explanation:

Given

a = \frac{1}{x} - \frac{1}{y} = \frac{y-x}{xy} ← as a single fraction

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\frac{1}{a} = \frac{1}{\frac{y-x}{xy} } = \frac{xy}{y-x} → A

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3 years ago
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7 0
3 years ago
Read 2 more answers
Solve for X: 1/2(4+X)+2=16
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Which of the following uses parallel construction? Select one: a. Jim likes to hunt, bike, and throwing darts. b. Mimie has to s
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Answer:

The correct answer is:

c. Joe will go running, biking and hunting

Step-by-step explanation:

Parallel construction or parallelism or parallel structure is a style used in writing a sentence, where there is a balance in phrases or clauses within one or more sentences by them having the same grammatical structure. parallelism adds elegance, clarity and symmetry to sentences. It essentially has to so with a repetition of a chosen grammatical form within a sentence.

In our example:

a.  Jim likes to hunt, bike, and throwing darts. (not parallel)

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The verbs, hunt, bike and throw must be in the same form (present continuous) to be parallel

b. Mimie has to study, drive her sister to the store, and enjoy herself in the garden. (not parallel).

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the sentence is not parallel because there is an inconsistency in the pattern of the construct. a parallel version is:

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d. Joe will go running, biking, and hunting. (parallel)

all the verbs are in the present continuous form.

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