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3 years ago

Which situation requires the addition counting principle to determine the number of possible outcomes?

Mathematics

1 answer:

IgorLugansk [536]3 years ago

8 0

Answer:

Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available

Step-by-step explanation:

Creating a stuffed animal when there are 6 animals, 3 fur colors, and 12 clothing themes available

This condition requires multiplication or factorials to determine outcomes

Renting a vehicle when there are 5 cars, 3 vans, and 10 sports utility vehicles available

This situation requires the addition counting principle to determine the number of possible outcomes as there is only one car to be picked so all the numbers 10+5+3 = 18 will be added to get the possible outcomes ..

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Find the value of f(2)

sergiy2304 [10]

Answer:

We have, y=f(x)

From graph, when x = 2, y =f(x)=-5. So, functional value at x=2, f(2) = -5

3 0

3 years ago

Given the functions f(x) = x² – 8 and g(x) = 4-x, determine the equation for the combined function

ElenaW [278]

Answer:

$y=x^2+x-12$

Step-by-step explanation:

f(x) = x² – 8 and g(x) = 4-x

y=f(x) - g(x)

y=(x² – 8) - (4-x)

$y=x^2-8-4+x\\y=x^2+x-12$

6 0

2 years ago

Find the polynomial function

laiz [17]

Answer:

y = 2x³ +x² -3x +6

Step-by-step explanation:

The polynomial correlation function of a graphing calculator can work with the table of function values to give you the equation. (See attached)

_____

If you want to solve this by hand, you can write the equations for the unknown coefficients in the polynomial function, then solve those. First of all, notice that you are given the y-intercept, (0, 6), so you know one of the coefficients already. That leaves a system of 3 equations in 3 unknowns that need to be solved.

___

<em>Writing the equations</em>

... ax³ +bx² +cx +6 = y . . . . the generic linear equation in a, b, c that you're writing

For x = -1:

... -a +b -c +6 = 8

For x = 1

... a + b + c + 6 = 6

For x = 2

... 8a +4b +2c +6 = 20

In augmented matrix terms, this set of linear equations looks like ...

$\left[\begin{array}{ccc|c}-1&1&-1&2\\1&1&1&0\\8&4&2&14\end{array}\right]$

___

<em>Solving the equations</em>

There are a number of ways to solve these. Again, a graphing calculator often has solution functions, such as reducing a matrix to row-echelon form, that will solve this in a keystroke or two.

If you add the first two equations, you get ...

... 2b = 2 ⇒ b = 1

Substituting that into the first equation allows you to simplify it to ...

... -a -c = 1

Dividing the third equation by 2 (and substituting for b) makes it ...

... 4a +c = 5

Adding these equations gives ...

... 3a = 6 ⇒ a = 2

Then ...

... c = -a -1 = -2 -1 = -3

And our polynomial function is ...

... y = 2x³ +x² -3x +6

7 0

2 years ago

An open window is at the height of 15 ft above the ground. A ladder is placed 8 ft away from the side of the house. What will be

mestny [16]

It was a lot better then you got me in my life that way

7 0

2 years ago

Read 2 more answers

Select the correct answer. Sean and Colleen are raking leaves in their yard. Working together, they can clear the yard of leaves

Lera25 [3.4K]

Answer:

40 minutes

Step-by-step explanation:

Let c represent the number of minutes it would take colleen to finish the job when he is working alone. Hence, it can be represented by the equation:

$\frac{1}{c}+\frac{1}{c+20} =\frac{1}{24} \\\\Finding\ the\ L.C.M\ of\ the\ fraction\ to\ get\ 24c(c+20)\ as\ the\ L.C.M.\\Multiply\ the\ whole\ equation\ by\ 24c(c+20):\\\\\frac{1}{c}(24c(c+20))+\frac{1}{c+20}(24c(c+20)) =\frac{1}{24}(24c(c+20)) \\\\24c+480+24c=c^2+20c\\\\48c+480=c^2+20c\\\\c^2+20c-48c-480=0\\\\c^2-28c-480=0$

Solving the quadratic equation to get c gives:

c = -12 and c = 40

Since the time cannot be negative, hence c = 40 minutes.

It would take colleen 40 minutes to clear the yard of leaves alone

6 0

2 years ago