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Vinvika [58]
3 years ago
8

Out of 10 students, 2 will be chosen to ride in a car instead of a van on an upcoming field trip. Which statement best describes

this situation?
A. There are 10P2 = 90 ways the students can be chosen to ride in the car because the order in which the students are chosen matters.

B. There are 10C2 = 45 ways the students can be chosen to ride in the car because the order in which the students are chosen matters.

C. There are 10P2 = 90 ways the students can be chosen to ride in the car because the order in which the students are chosen doesn’t matter.

D. There are 10C2 = 45 ways the students can be chosen to ride in the car because the order in which the students are chosen doesn’t matter.
Mathematics
1 answer:
Rudiy273 years ago
8 0

Answer:

D

Step-by-step explanation:

Firstly, since it is a selection question, we shall be using a combination approach.

So here we are trying to select the best answer that describes that 2 out of 10 students are selected.

Let’s consider the scenario below;

selecting r out of n can be resolved using the combination nCr

= n!/(n-r)!r!

Now in this case, our n = 10 and r = 2.

Thus, 10C2, we have ;

10!/(10-2)!2! = 10!/8!2! = (10 * 9 * 8!)/8!2! = (10 *9)/2! = 90/2 = 45

Thus, 10C2 = 45

Here, the order of selection does not matter as we can select in random fashion. This makes option D correct

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The answer is: From any point on the graph, he counts down 2 then right 3 to end up on the line again.

Step-by-step explanation:

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Each serving of fruit punch that Will makes has 2/3 cup of pineapple juice and 1/2 cup of cranberry juice. How many cups of frui
Sindrei [870]

Answer:

\frac{56}{3}cups

Step-by-step explanation:

There will be \frac{2}{3}*16= \frac{32}{3} cups of pineapple juice in 16 servings of punch

There will be \frac{1}{2}*16= 8 cups of cranberry juice in 16 servings of punch

In total there will be \frac{32}{3}+8= \frac{56}{3}cups of juice in 16 servings of punch

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3 years ago
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took these 100 customer
AlladinOne [14]

Answer:

4-2.326\frac{1}{\sqrt{100}}=3.767    

4+2.326\frac{1}{\sqrt{100}}=4.233    

So on this case the 98% confidence interval would be given by (3.767;4.233)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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".

\bar X=4 represent the sample mean

\mu population mean (variable of interest)

\sigma=1 represent the population standard deviation

n=100 represent the sample size  

Solution to the problem

The confidence interval for the mean is given by the following formula:

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.98 or 98%, the value of \alpha=0.02 and \alpha/2 =0.01, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.01,0,1)".And we see that z_{\alpha/2}=2.326

Now we have everything in order to replace into formula (1):

4-2.326\frac{1}{\sqrt{100}}=3.767    

4+2.326\frac{1}{\sqrt{100}}=4.233    

So on this case the 98% confidence interval would be given by (3.767;4.233)

   

4 0
3 years ago
Perform the multiplication, (7x2+a2)(x2–3a2)
aksik [14]

Answer:

The given multiplied expression is

(7x^2+a^2)(x^2-3a^2)=7x^4-20x^2a^2-3a^4

Step-by-step explanation:

Given expression is (7x^2+a^2)(x^2-3a^2)

To find the multiplication of the given expression :

(7x^2+a^2)(x^2-3a^2)

By using the distributive property to solve the given expression as below

(7x^2+a^2)(x^2-3a^2)=(7x^2)(x^2)+(7x^2)(-3a^2)+(a^2)(x^2)+(a^2)(-3a^2)

=7x^2.x^2-21x^2a^2+a^2x^2-3a^2.a^2

=7x^{2+2}-21x^2a^2+a^2x^2-3a^{2+2}  ( by using the property a^m.a^n=a^{m+n} )

=7x^4-21x^2a^2+a^2x^2-3a^4

Adding the like terms in the above expression we get

=7x^4-20x^2a^2-3a^4

Therefore (7x^2+a^2)(x^2-3a^2)=7x^4-20x^2a^2-3a^4

Therefore the given multiplied expression is

(7x^2+a^2)(x^2-3a^2)=7x^4-20x^2a^2-3a^4

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