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malfutka [58]
1 year ago
7

On a 8.5 x 11 inches (or larger) paper, create a carnival game (for example it could be: throwing a dart at a target, ball throu

gh a hoop, ball in cup, etc).
Provide a written description of your game.
Your game must use at least two different geometric shapes.
Label the dimensions of the shapes with the measurements in real life. Draw on the paper using a scale factor.
For example, if the game has a 3 feet diameter, label 3 feet on the image, but draw it to scale, so that the model game is similar to the actual dimensions. If the scale is 1 foot = 2 inches, then 3 feet = 6 inches.
Find the probability of winning your game. Include the calculations to show the probability.
Determine the type of prize a winner would deserve and the cost of playing your game.
Mathematics
1 answer:
Keith_Richards [23]1 year ago
7 0

The probability of winning the game is 0.065

<h3>The description of the game</h3>

The game involves throwing two darts at two targets.

To win the game, the darts must hit anywhere in the following shapes

  • Rectangle: 5 by 4 inches
  • Circle: Radius, r = 3 inches

<h3>The probability of winning</h3>

The area of the paper is:

Area = 8.5 inches * 11 inches

Area = 93.5 square inches

The area of the rectangle on the paper is:

Area = 5 inches * 4 inches

Area = 20 square inches

The area of the circle on the paper is:

Area = π * (3 inches)²

Area = 28.3 square inches

The probability of landing on both shapes is

P(Both) = 20/93.5 * 28.3/93.5

Evaluate

P(Both) = 0.065

Hence, the probability of winning the game is 0.065

Read more about probability at:

brainly.com/question/24756209

#SPJ1

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An insurance policy on an electrical device pays a benefit of 4000 if the device fails during the first year. The amount of the
lora16 [44]

Answer:

Expected benefit under this policy = $ 2694

Step-by-step explanation:

Given - An insurance policy on an electrical device pays a benefit of

            4000 if the device fails during the first year. The amount of the

            benefit decreases by 1000 each successive year until it reaches 0.

            If the device has not failed by the beginning of any given year, the

            probability of failure during that year is 0.4.

To find - What is the expected benefit under this policy ?

Proof -

Let us suppose that,

The benefit = y

Given that, the probability of failure during that year is 0.4

⇒Probability of non-failure = 1 - 0.4 = 0.6

Now,

If the device fail in second year , then

Probability = 0.6×0.4

If the device fail in third year, then

Probability = 0.6×0.6×0.4 = 0.6² × 0.4

Going on like this , we get

If the device is failed in n year, then

Probability = 0.6ⁿ⁻¹ × 0.4

Now,

The probability distribution is-

Benefit , x       4000       3000             2000            1000              0

P(x)                 0.4         0.6×0.4         0.6² × 0.4     0.6³ × 0.4     1 - 0.8704

                      (0.4)       (0.24)            (0.144)         (0.0864)       (0.1296)

At last year, the probability = 1 - (0.4+ 0.24+ 0.144+ 0.0864) = 1 - 0.8704

Now,

We know that,

Expected value ,

E(x) = ∑x p(x)

       = 4000(0.4) + 3000(0.24) + 2000(0.144) + 1000(0.0864) + 0(0.1296)

       = 1600 + 720 + 288 + 86.4 + 0

       = 2694.4

⇒E(x) = 2694.4 ≈ 2694

∴ we get

Expected benefit under this policy = $ 2694

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\frac{n(3n - 1)}{n(n) + n(1) - 1(n) - 1(1)} \div \frac{n^{2}}{n + 1}
\frac{n(3n - 1)}{n(n + 1) - 1(n + 1)} \div \frac{n^{2}}{n + 1}
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Figure a is dilated by a scale factor of 1/2 to form figure b. What is the length of x?
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Answer:

The correct option is 3. The value of x is 8 inches.

Step-by-step explanation:

It is given that Figure A is dilated by a scale factor of 1/2 to form Figure B. It means both figure are similar and corresponding sides of similar figures are proportional.

\text{scale factor}=\frac{\text{Side of image}}{\text{Side of preimage}}

\frac{1}{2}=\frac{x}{16}

Multiply both sides by 16.

\frac{16}{2}=x

8=x

Since scale factor is 1/2, so we can directly say that the side length of image is half of the corresponding side of preimage.

The length of x is 8 inches. Therefore the correct option is 3.

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Answer:

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Step-by-step explanation:

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