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3 years ago

14

Alyssa flips a fair,two-sided coin four times.What is the probability that the coin lands with heads facing up exactly three tim

es?

1 answer:

NARA [144]3 years ago

5 0

Fair coin means P(heads) = 1/2 for each flip.
The three flips are independent, so multiplication rule applies.
P(head,head,head)=(1/2)(1/2)(1/2)=1/8

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A street light is mounted at the top of a 15-ft-tall pole. A man 6 ft tall walks away from the pole with a speed of 4 ft/s along

mina [271]

Answer:

The tip of the man shadow moves at the rate of $\frac{20}{3} ft.sec$

Step-by-step explanation:

Let's draw a figure that describes the given situation.

Let "x" be the distance between the man and the pole and "y" be distance between the pole and man's shadows tip point.

Here it forms two similar triangles.

Let's find the distance "y" using proportion.

From the figure, we can form a proportion.

$\frac{y - x}{y} = \frac{6}{15}$

Cross multiplying, we get

15(y -x) = 6y

15y - 15x = 6y

15y - 6y = 15x

9y = 15x

y = $\frac{15x}{9\\} y = \frac{5x}{3}$

We need to find rate of change of the shadow. So we need to differentiate y with respect to the time (t).

$\frac{dy}{t} = \frac{5}{3} \frac{dx}{dt}$ ----(1)

We are given $\frac{dx}{dt} = 4 ft/sec$ . Plug in the equation (1), we get

$\frac{dy}{dt} = \frac{5}{3} *4 ft/sect\\= \frac{20}{3} ft/sec$

Here the distance between the man and the pole 45 ft does not need because we asked to find the how fast the shadow of the man moves.

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3 years ago

Shirley picked out a kite for $3.50. If she gave the family a ten dollar bill, what is the fewest number of bills and coins that

Aleonysh [2.5K]

Answer:

6.50

Step-by-step explanation:

$10.00-$3.50=$6.50

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Good morning temperature is -15° but the afternoon the temperature raises by 20° right in addition expressions for the afternoon

stealth61 [152]

Answer:

+ 5°

Step-by-step explanation:

Given,

Good morning temperature = -15°

Raise in temperature = 20°

Afternoon temperature = -15° + 20°

= + 5°

Hence, temperature in after noon is equal to + 5°.

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3 years ago