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3 years ago

Katie creates a game in which 3 dimes are flipped at the same time.

Mathematics

1 answer:

Vikentia [17]3 years ago

5 0

<em>*100% Correct answers</em>

Question 1

A surgical technique is performed on 10 patients. You are told there is an 80% chance of success. Find the probability that the surgery is successful for exactly 6 patients.

0.088

Question 2

Sam creates a game in which the player rolls 4 dice. What is the probability in this game of having at least 2 of the dice land on 5.

0.13101963141

Question 3

Katie creates a game in which 3 dimes are flipped at the same time.

5 points are awarded if all 3 dimes land on tails, but no points are awarded for anything else. What is the probability of not getting any points? (Hint: Find the complement).

0.875

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3 0

3 years ago

Read 2 more answers

2. Which ratio is equivalent to 4:9?

cestrela7 [59]

Answer:

4 : 9 is an equivalent ratio of 8 : 18.

Step-by-step explanation:

hope this helps

5 0

2 years ago

Read 2 more answers

let m represent the number of children playing soccer. those children are separated into four equal groups. write an expression

Mkey [24]

Answer:

m/4

Step-by-step explanation:

m is how many children are playing.

They are separated into 4 groups. Making it m(how many people are playing), out of 4.

For example, if m=12, then it would be 12/4, so 3 children will be in each group.

Hope this helps, you can change this to you own desire.

4 0

3 years ago

A polynomial function has roots of -5,2 and 7

sveta [45]

Answer:

P(x) =x³-4x²-31x+70

Step-by-step explanation:

The function is expressed as:

P(x) = (x+5)(x-2)(x-7)

P(x) =(x²-2x+5x-10)(x-7)

P(x) = (x²+3x-10)(x-7)

P(x) = x³-7x²+3x²-21x-10x+70

P(x) =x³-4x²-31x+70

Hence the polynomial is P(x) =x³-4x²-31x+70

3 0

3 years ago

A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial,

Tresset [83]

Answer:

The probability that it will choose food #2 on the second trial after the initial trial = 0.3125

Step-by-step explanation:

Given - A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%.

To find - If the animal chooses food #1 on an initial trial, what is the probability that it will choose food #2 on the second trial after the initial trial?

Proof -

By the given information, we get the stohastic matrix

$H = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]$

As we know that,

The matrix is a Markov chain $x_{k+1} = Hx_{k}$

Let

The initial state vector be

$x_{0} = \left[\begin{array}{ccc}1\\0\\0\end{array}\right]$

we choose this initial vector because given that If the animal chooses food #1 on an initial trial.

Now,

$x_{1} = Hx_{0} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}1\\0\\0\end{array}\right] \\= \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]$

∴ we get

$x_{1} = \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]$

Now,

$x_{2} = Hx_{1} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right] \\= \left[\begin{array}{ccc}0.25+0.0625+0.0625\\0.125+0.125+0.0625\\0.125+0.0625+0.125\end{array}\right]\\= \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]$

∴ we get

$x_{2} = \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]$

∴ we get

The probability that it will choose food #2 on the second trial after the initial trial = 0.3125

4 0

3 years ago