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3 years ago

The diagram represents an enlargement of a rectangle by a scale factor of 4,

Mathematics

1 answer:

Lapatulllka [165]3 years ago

3 0

Answer:D 16inches by 8 inches

Step-by-step explanation:

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There are 20 pirates living on the Flightless Folly Ship. 25% of them are responsible for keeping the decks clean. How many pira

makkiz [27]

Answer:

5 pirates

Step-by-step explanation:

0.25 × 20 = 5

Hope that helps.

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3 years ago

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How many solutions are there to the equation, 220=2x-12x

galben [10]

Hi,

For the equation: 220=2x-12x there is only one solution, x=−22.

Have a great day!

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3 years ago

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A man starts walking north at 2 ft/s from a point P. Five minutes later a woman starts walking south at 3 ft/s from a point 500

Vedmedyk [2.9K]

Answer:

The rate at which both of them are moving apart is 4.9761 ft/sec.

Step-by-step explanation:

Given:

Rate at which the woman is walking, $\frac{d(w)}{dt}$ = 3 ft/sec

Rate at which the man is walking, $\frac{d(m)}{dt}$ = 2 ft/sec

Collective rate of both, $\frac{d(m+w)}{dt}$ = 5 ft/sec

Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min

Now,

Distance traveled by man and woman are $m$ and $w$ ft respectively.

⇒ $m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft$

⇒ $w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft$

As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate $\frac{dh}{dt}$ .

Lets calculate h.

Applying Pythagoras formula.

⇒ $h^2=(m+w)^2+500^2$

⇒ $h=\sqrt{(2400+2700)^2+500^2} = 5124.45$

Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.

Differentiating with respect to time.

⇒ $h^2=(m+w)^2+500^2$

⇒ $2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt} + \frac{d(500)}{dt}$

⇒ $\frac{d(h)}{dt} =\frac{2(m+w)\frac{d(m+w)}{dt} }{2h}$ ...as $\frac{d(500)}{dt}= 0$

⇒ Plugging the values.

⇒ $\frac{d(h)}{dt} =\frac{2(2400+2700)(5)}{2\times 5124.45}$ ...as $\frac{d(m+w)}{dt} = 5$ ft/sec

⇒ $\frac{d(h)}{dt} =4.9761$ ft/sec

So the rate from which man and woman moving apart is 4.9761 ft/sec.

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3 years ago

The ratio of boys to girls in Mr. Trent's

goldenfox [79]

Answer:

Step-by-step explanation:

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3 years ago

A candy store grab bag contains 10 pieces of sour candy, 12 pieces of chocolate candy, and 6 pieces of sweet candy. If you selec

harkovskaia [24]

Step-by-step explanation:

so we're making two draws *with* replacement (this is important)

step 1: for the first draw, it wants the probability of getting a sour candy. to calculate this:

(# of sour candy) / (total # of candy)

step 2: for the second draw, it wants the probability of *not* getting a sour candy. to calculate this, you can calculate 1 - (the probability form part 1).

step 3: to find the probability of both events happening together, simply multiply the probabilities from part 1 and 2 together

side note: for step 2, you can only do this because the candy is being replaced. if there were no replacement, you'd have to re-calculate (# of non-sour candies) / (total after the first candy is drawn)

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3 years ago

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