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DanielleElmas [232]

3 years ago

13

You need to know the number of different arrangements possible for five distinct letters. You decide to use the permutations rul

e, but your friends tells you to use 5!. Who is correct? Explain.
Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.

Your friend is correct because applying the permutations rule in this setting would be inappropriate.

Neither method is correct. The combinations rule should be applied in this setting.

Your method is correct because you are applying the permutations rule in the appropriate setting.

2 answers:

Mice21 [21]3 years ago

8 0

Answer:

Option A

Step-by-step explanation:

Whenever we want to arrange a number of objects or letters or numbers n then we must check whether

i) repitition is allowed

If repitition is allowed then total number of ways = n!

ii) repitition not allowed.

In this case again we have to check whether order matters or not.

If order matters then no of ways nPn.

Here n =5

We find that nPn = 5!

Thus both are correct.

Hence option A

svlad2 [7]3 years ago

3 0

<span>First option is correct

Both methods are correct, since you are counting all possible arrangements of 5 items taken 5 at a time.</span>

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Step-by-step explanation: 20%= 20/100= 0.2

Which means = d-0.2

Hope this helped.

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3 years ago

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The varsity basketball team started selling T-shirts online in 1994. The number of T-shirts sold online, s, is modeled by the gr

-Dominant- [34]

(PART-A): s-intercept in this case represents the y-intercept of the graph, whereas the t-intercept in this case represents the x-intercept of the graph.

Always remember that y-intercept represents the value of y where the curve (or line) crosses the y-axis, and x-intercept represents the value of x where the curve (or line) crosses the x-axis.

In the graph attached with the question, at point (0,6) the curve crosses the y-axis. Therefore, the <em>y-intercept (s-intercept) in this case is 6</em>. It means that in year 2000 (t=0), 6 hundred shirts were sold.

However, there is no point on the graph where the curve crosses the x-axis, meaning there is <em>no x-intercept (t-intercept)</em>. It means that there is <em>not</em> a single year when the number of shirts sold is 0.

(PART B): As you can see in the graph (attached with the question) that the <em>f(t)</em> is increasing (exponentially) with the increase in <em>t. </em>Therefore, we can safely say that as t increases without bound, the f(t) increases (also). In this context, it means that the sale of shirts increases as the years go by. Hence, the correct blank is "increases."

(PART C): The average rate of change is actually the slope. To find the slope, we can use the following formula:

slope = $\frac{y_2 - y_1}{x_2 - x_1}$ --- (X)

Given points: (5, 12.5) and (7, 22). Plug the values in equation (X),

slope = $\frac{22-12.5}{7-5} = 4.75$

Hence, the average rate of change for the function between t=5 and t=7 is 4.75 (answer).

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You can see in the graph that number of Shirts sold is in <em>hundreds. </em>It means that 1 unit (of y-axis in a graph) represents 100 shirts. Therefore, as in the question it is mentioned that there are 1000 T-shirts sold, it will become 10 units (since 10*100 = 1000). So, the function g(t) will become the following:

$g(t) = f(t) + 10$ --- (Y)

Why did I add f(t)? Because in the question, the word "<em>and</em>" is underlined. It means that g(t) represents not only 1000 T-shirts (10*100 = 1000) sold at the basketball games each year, but it also has the number of T-shirts sold ONLINE, which is f(t).

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2 years ago

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VikaD [51]

Name all the angles that have v as a vertex

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3 years ago

Determine whether is a right triangle for the given vertices. Explain. Q(7, –10), R(–3, 0), S(9, –8)

andriy [413]

Answer:

Yes, It is a right triangle for the given vertices.

Step-by-step explanation:

Given:

Q(7, –10),

R(–3, 0),

S(9, –8)

To Find:

determine whether is a rig ht triangle for the given vertices = ?

Solution:

QR= $\sqrt{(-3-7)^2+(0-(-10))^2}$

QR= $\sqrt{(-10)^2+(10)^2}$

QR= $\sqrt{100+100}$

QR= $\sqrt{200}$ --------------------------(1)

QR=14.142136

RS= $\sqrt{(9-(-3))^2+(-8-0)^2}$

RS= $\sqrt{(12)^2+(-8)^2}$

RS= $\sqrt{144+64}$

RS= $\sqrt{208}$ ---------------------------(2)

RS=14.422205

QS= $\sqrt{(7-9)^2+(-10-(-8))^2}$

QS= $\sqrt{(-2)^2+(-2)^2}$

QS= $\sqrt{4+4}$

QS= $\sqrt{8}$ -------------------------------------(3)

QS=2.828427

According to Pythagorean Theorem,

$RS^2 = QR^ +QS^2$

Substituting the values,

$(\sqrt{208})^2 = (\sqrt{200})^2 +(\sqrt{8})^2$

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