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GaryK [48]
2 years ago
15

One coin is flipped and then one die is rolled. What is the probability of getting a head on the coin and an odd number on the d

ie? {?} Give your answer as a percentage.
Mathematics
1 answer:
Margarita [4]2 years ago
7 0
Sample Space for coin=H,T
n(S)=2
n(head)=1
P(of getting a head)=1/2

Sample Space for die=1,2,3,4,5,6
n(S)=6
n(odd numbers)=3
P(of getting an odd number)=3/6=1/2

P(of getting a head on the coin and an odd number on the die)=1/2 + 1/2 =1
Probability expressed as a percentage=1*100%=100
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In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm
tangare [24]

Answer:

AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm

AL is angle A bisector, then angle A is 60°. Use the angle's bisector property:

\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD

Consider right triangle CAH.By the Pythagorean theorem,

CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8

The length cannot be negative, so CD=8 cm and

CA=\sqrt{3}CD=8\sqrt{3}\ cm

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

AB=2CA=16\sqrt{3}\ cm

By the Pythagorean theorem,

BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm

3 0
2 years ago
Zack is purchasing a bag of apples. The cost of apples is proportional to the weight of the apples in pounds as shown on the gra
White raven [17]
Hello,

The graph below is the graph you may have forgotten to upload. This will help me understand the question better and to give you a great answer.

  A:  " 1 lb of apples will cost Zack $2.50. "  
___________________________________________  C:  " 4 lb of apples will cost Zack $10. "
Hope this helps


-Jurgen :D

7 0
3 years ago
A car travels 45km in an hour. In each of the next two hours, it travels 78km. What is the average speed of the car.
romanna [79]

Answer:

The average speed of car is 67 kilometers per hour.

Step-by-step explanation:

Given that:

Distance travelled in one hour = 45 km

Distance travelled in next 2 hours = 78*2 = 156 km

Total distance = 45+156 = 201

Total time = 1+2 =  3 hours

Average speed of the car = \frac{Total\ distance}{Total\ time}

Average speed of the car = \frac{201}{3}

Average speed of the car = 67 km/hr

Hence,

The average speed of car is 67 kilometers per hour.

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3 years ago
Find 5x9 and 1x9, and add the answers.
kipiarov [429]
5*9=45
1*9=9
Then add both numbers together
45+9=54
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The answer is the first one in the options
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3 years ago
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