The expected number of heads in 500 tosses of an unbiased coin is:

Answers

Answer 1

Answer:

Using the binomial distribution, it is found that the expected number of heads in 500 tosses of an unbiased coin is 250.

For each coin, there are two possible outcomes, either it is heads, or it is tails. The probability of a coin being head/tails is independent of any other coin, hence the binomial distribution is used.

Binomial distribution:

Probability of x successes on n trials, with p probability.

The expected number of successes is:

$E(X) = np$

In this problem:

500 tosses, hence $n = 500$ .
Unbiased, that is, equally as likely to be heads or tails, hence $p = 0.5$ .

The expected number of heads is:

$E(X) = np = 500(0.5) = 250$

A similar problem is given at brainly.com/question/24261244

Answer 2

Answer: There is a 50%, or 1/2, chance of getting heads on each flip. Each of the 500 trials is independent. Because there is a 1/2 chance of getting heads, you would expect half of them to land on heads. 500/2 = 250. You would theoretically expect 250 heads if you tossed an unbiased coin 500 times.

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Emily ran her first lap in 75 seconds she ran her second lap in 69 seconds using percentages how much better was her second lap when comapared to her first lap

Answers

Answer:

Her second lap was 8% better when compared to her first lap.

Step-by-step explanation:

Given:

Emily ran her first lap in 75 seconds she ran her second lap in 69 seconds.

Now, to find how much better was her second lap when compared to her first lap.

Emily ran her first lap in 75 seconds.

Emily ran her second lap in 69 seconds.

So, we get the difference in seconds:

$75-69=6\ seconds.$

Thus, in her second lap she was 6 seconds better than first.

Now, to get the percentage of her first lap better than second:

$(6)/(75)* 100$

$=0.08* 100$

$=8\%.$

Therefore, her second lap was 8% better when compared to her first lap.

A bicycle wheel has a radius of 28 cm. what is the circumference of the wheel?

Answers

Answer:

176 cm

Step-by-step explanation:

You want the circumference of a wheel with a radius of 28 cm.

Circumference

The circumference of a circle is given by ...

C = 2πr

For r = 28 cm, this is ...

C = 2π(28 cm) = 56π cm ≈ 176 cm

The circumference of the wheel is 56π cm, about 176 cm.

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In sunlight, a vertical stick 6 ft tall casts a shadow 2 ft long. At the same time a nearby tree casts a shadow 14 ft long. How tall is the tree? Round to the nearest tenth A) 42.0 ft 
B) 85.7 ft 
C) 18.0 ft 
D) 52.5 ft<br /

Answers

The nearby tree's height is 42.0 ft, which is A

Alrighty friend, let me explain you a math.
We're gonna want to start by setting up a fraction. We'll set up the fraction as height/shadow. The stick's height is 6 feet and the shadow is 2 feet, making the fraction 6/2. The second fraction only gives us the shadow, so the fraction is x/14.
Now, we're gonna do some cross multiplication m8. 6/2 x x/14. Multiply 6x14= 84 and 2x(x)= 2x ---> 2x = 84
Do you some basic algebra here, and divide both sides by 2.
Your final answer is 42, so the tree is 42 feet tall.

The volume of a cube is 1728 cubic units. what is the length of one side?

Answers

12 is the length of one side of cube.

What is cube?

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices

According to question, the volume of a cube is 1728 cubic units.

We have to find the length of the cube.

Volume= $1728$ cubic units

⇒ $lenght^(3) =12^(3)$

⇒ $length =12$ $units$

Hence, $12$ is the length of one side of cube.

Learn more about cube here:

brainly.com/question/21270685?referrer=searchResults

#SPJ2

L × W × H = 1728
L = W = H
I got 12 because 12 x 12 x 12 = 1728 I'm absolutely sure :)

The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new function?A.(x – 11)2 + 58
B.(x + 22)2 – 121
C.(x + 7)2 – 47
D.(x – 15)2 + 94

Answers

The right answer for the question that is being asked and shown above is that: "D.(x – 15)2 + 94." The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. the vertex form of the new function is that D.(x – 15)2 + 94

The answer is C i just did it on e2020 :)

Evaluate b^2c^1 for b=-4 and c= 2.