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Alja [10]
3 years ago
14

John is making baked goods for a party. He can either make muffins or bread, and he can use blueberries, bananas, apples, or cho

colate chips. Which table shows all of his possible options?.
Mathematics
1 answer:
Margarita [4]3 years ago
8 0

The total number of possible choices that John had for making baked goods for the party is 8.

<h3>What is Combination?</h3>

The combination helps us to know the number of ways an object can be arranged without a particular manner. A combination is denoted by 'C'.

^nC_r = \dfrac{n!}{r!(n-r)!}

where,

n is the number of choices available,

r is the choices to be made.

We know that the number of choices with John for his baked goods is only two which are muffins or bread, therefore, the choices of the baked good can be written as ^2C_1.

Also, the number of choices with John for flavors is four which are blueberries, bananas, apples, or chocolate chips, therefore, the choices of the flavor can be written as ^4C_1.

Now, the total possible choices that John had

= The choices of the baked good x The choices of the flavor

=\ ^2C_1 \times ^4C_1\\\\=\ 8

Hence, the total number of possible choices that John had for making baked goods for the party is 8.

Learn more about Combination:

brainly.com/question/11732255

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Answer:

The probability that the student is going to pass the test is 0.0545

Step-by-step explanation:

The variable that says the number of correct questions follows a Binomial distribution, because there are n identical and independent events with a probability p of success and a probability 1-p of fail. So, the probability of get x questions correct is:

P(x)=\frac{n!}{x!(n-x)!} *p^{x} *(1-p)^{n-x}

Where n is equal to 10 questions and p is the probability of get a correct answers, so p is equal to 1/2

Then, if the student pass the test with at least 8 questions correct, the probability P of that is:

P = P(8) + P(9) + P(10)

P=(\frac{10!}{8!(10-8)!}*0.5^{8}*(0.5)^{10-8})+(\frac{10!}{9!(10-9)!} *0.5^{9} *(0.5)^{10-9})+(\frac{10!}{10!(10-10)!} *0.5^{10} *(0.5)^{10-10})

P = 0.0439 + 0.0097 + 0.0009

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Step-by-step explanation:

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Answer:

1. P(X>69)=P(Z>-1.136)=1-P(Z

2. P(X

3. P(52.6 \leq X \leq 105.4)=P(-3

Step-by-step explanation:

Assuming the value for the mean 79 and the deviation 8.8

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

2) Part a

Let X the random variable that represent the amount of collagen of a population, and for this case we know the distribution for X is given by:

X \sim N(79,8.8)  

Where \mu=79 and \sigma=8.8

We are interested on this probability

P(X>69)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X>69)=P(\frac{X-\mu}{\sigma}>\frac{69-\mu}{\sigma})=P(Z-1.136)

And we can find this probability on this way:

P(Z>-1.136)=1-P(Z

3) Part b

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(X

And we can find this probability on this way:

P(Z

4) Part c

We need to find first the limits for 3 deviations within the mean

\mu -3 \sigma = 79-3(8.8)=52.6

\mu +3 \sigma = 79+3(8.8)=105.4

P(52.6

And we can find this probability on this way:

P(-3

And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.  

P(-3

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