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ella [17]
3 years ago
13

Morgan is playing a board game that requires three standard dice to be thrown at one time. Each die has six sides, with one of t

he numbers 1 through 6 on each side. She has one throw of the dice left, and she needs a 17 to win the game. What is the probability that Morgan wins the game (order matters)?
Mathematics
1 answer:
PIT_PIT [208]3 years ago
8 0
The probability of having a 17 is the number of ways of having 17 divided by the number of different possible outcomes.

Ways of having 17:

Die 1     Die 2     Die 3    sum
6            6            5          6+6+5 = 17
6            5            6          6+5+6 = 17
5            6            6          5+6+6 = 17

Those are the only 3 possibilities of having 17 (you can only loose 1 point).

The total number of outcomes are 6*6*6 = 216

So the chances (probability) to win is 3 / 216 = 1/72 = 0.0139 
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You purchase a stereo system for $830. The value of the stereo system decreases 13% each year. a. Write an exponential decay mod
lorasvet [3.4K]

Answer:

a. y=830*(0.87)^x

b. The value of stereo system after 2 years will be $628.23.

c. After approximately 4.98 years the stereo will be worth half the original value.

Step-by-step explanation:

Let x be the number of years.

We have been given that you purchased a stereo system for $830. The value of the stereo system decreases 13% each year.

a. Since we know that an exponential function is in form: y=a*b^x, where,

a = Initial value,

b = For decay b is in form (1-r), where r is rate in decimal form.

Let us convert our given rate in decimal form.

13\%=\frac{13}{100}=0.13

Upon substituting our given values in exponential decay function we will get

y=830*(1-0.13)^x

y=830*(0.87)^x

Therefore, the exponential model y=830*(0.87)^x represents the value of the stereo system in terms of the number of years since the purchase.

b. To find the value of stereo system after 2 years we will substitute x=2 in our model.

y=830*(0.87)^2

y=830*0.7569

y=628.227\approx 628.23

Therefore, the value of stereo system after 2 years will be $628.23.

c. The half of the original price will be \frac{830}{2}=415.

Let us substitute y=415 in our model to find the time it will take the stereo to be worth half the original value.

415=830*(0.87)^x

Upon dividing both sides of our equation by 830 we will get,

\frac{415}{830}=\frac{830*(0.87)^x}{830}

0.5=0.87^x

Let us take natural log of both sides of our equation.

ln(0.5)=ln(0.87^x)

Using natural log property ln(a^b)=b*ln(a) we will get,

ln(0.5)=x*ln(0.87)

\frac{ln(0.5)}{ln(0.87)}=\frac{x*ln(0.87)}{ln(0.87)}

\frac{ln(0.5)}{ln(0.87)}=x

\frac{-0.6931471805599}{-0.139262067}=x

x=4.977286\approx 4.98

Therefore, after approximately 4.98 years the stereo will be worth half the original value.

5 0
3 years ago
Help!! (You will get 100 points! & Brainliest if you are correct)
Dafna1 [17]

Answer: The first number that appears in both sequences is 28.

Step-by-step explanation:

Let's write down numbers from each of the sequences

Sequence 1) We need to start from 7 and multiply 4

7x4=28, 28x4=112

The sequence is 7,28,112...

Sequence 2) We need to start from 8 and add 5

5+8=13, 13+5=18, 18+5=23, 23+5=28

The sequence is 8,13,18,23,28...

They both have 28

5 0
2 years ago
Read 2 more answers
Write the equation for the function graphed attached <br><br> f(x)=
Anna007 [38]

Answer:

here

Step-by-step explanation:

7 0
2 years ago
Determine where to place the decimal point in the dividend and divisor so that the quotient is between 23 and 25
timama [110]

Answer:

Place the decimal before the last digit in both number i.e. 1602.3 and 65.4

Step-by-step explanation:

We are given the numerical expression 16023÷654.

Here, we have,

Dividend = 16023

Divisor = 654

it is required that the quotient of the division to be between 23 and 25.

If we take the numbers,

1602.3 and 65.4

This gives us,

\frac{1602.3}{65.4}=24.5.

Hence, placing the decimal before the last digit in both number will give the desired result.

7 0
3 years ago
1. question in attachment
skelet666 [1.2K]
Was there a chart with this?
4 0
3 years ago
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