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3 years ago

In how many different ways can you answer a multiple choice test that has 5 questions and 3 choices for each answer?

Mathematics

2 answers:

Sladkaya [172]3 years ago

6 0

It would be 243 waysssssssssssssssssssss

algol133 years ago

5 0

3*3*3*3*3 = 243 ways

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Marla started her school work at 8:48am. If she has to do 4 hours of school, what time will she be off?

grigory [225]

Answer:

See below.

Step-by-step explanation:

Q) 8:48 a.m. + 4 hours

= 12:48 p.m.

Bonus Q) 8:56 a.m. + 4 hours

= 12:56 p.m.

They will both be off by 12:56 p.m.

8 0

2 years ago

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Kelly bought a new car for $20,000. The car depreciates at a rate of 10% per year.

Vlad1618 [11]

Answer:

Use the formula.

P=P'(1-R/100)^T

where,

P=final rate

P'=initial rate

R=Rate of Depreciation

T=Time.

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3 years ago

Find the percent of this number: 32% of 25 pages Would it be 8% or 32%?

GuDViN [60]

32% * 25 =
(32*25)/100
800/100=8
8%

5 0

3 years ago

Can someone help me with this?

Natalija [7]

use the Pythagoras theorem method

a squared plus b squared equals c square

8 0

3 years ago

PLEASE HELP 100 POINTS!!!!!!

horrorfan [7]

Answer:

A) See attached for graph.

B) (-3, 0) (0, 0) (18, 0)

C) (-3, 0) ∪ [3, 18)

Step-by-step explanation:

Piecewise functions have multiple pieces of curves/lines where each piece corresponds to its definition over an interval.

Given piecewise function:

$g(x)=\begin{cases}x^3-9x \quad \quad \quad \quad \quad \textsf{if }x < 3\\-\log_4(x-2)+2 \quad \textsf{if }x\geq 3\end{cases}$

Therefore, the function has two definitions:

$g(x)=x^3-9x \quad \textsf{when x is less than 3}$

$g(x)=-\log_4(x-2)+2 \quad \textsf{when x is more than or equal to 3}$

When graphing piecewise functions:

Use an open circle where the value of x is not included in the interval.
Use a closed circle where the value of x is included in the interval.
Use an arrow to show that the function continues indefinitely.

First piece of function

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=(3)^3-9(3)=0 \implies (3,0)$

Place an open circle at point (3, 0).

Graph the cubic curve, adding an arrow at the other endpoint to show it continues indefinitely as x → -∞.

Second piece of function

Substitute the endpoint of the interval into the corresponding function:

$\implies g(3)=-\log_4(3-2)+2=2 \implies (3,2)$

Place an closed circle at point (3, 2).

Graph the curve, adding an arrow at the other endpoint to show it continues indefinitely as x → ∞.

See attached for graph.

The x-intercepts are where the curve crosses the x-axis, so when y = 0.

Set the first piece of the function to zero and solve for x:

$\begin{aligned}g(x) & = 0\\\implies x^3-9x & = 0\\x(x^2-9) & = 0\\\\\implies x^2-9 & = 0 \quad \quad \quad \implies x=0\\x^2 & = 9\\\ x & = \pm 3\end{aligned}$

Therefore, as x < 3, the x-intercepts are (-3, 0) and (0, 0) for the first piece.

Set the second piece to zero and solve for x:

$\begin{aligned}\implies g(x) & =0\\-\log_4(x-2)+2 & =0\\\log_4(x-2) & =2\end{aligned}$

$\textsf{Apply log law}: \quad \log_ab=c \iff a^c=b$

$\begin{aligned}\implies 4^2&=x-2\\x & = 16+2\\x & = 18 \end{aligned}$

Therefore, the x-intercept for the second piece is (18, 0).

So the x-intercepts for the piecewise function are (-3, 0), (0, 0) and (18, 0).

From the graph from part A, and the calculated x-intercepts from part B, the function g(x) is positive between the intervals -3 < x < 0 and 3 ≤ x < 18.

Interval notation: (-3, 0) ∪ [3, 18)

Learn more about piecewise functions here:

brainly.com/question/11562909

3 0

2 years ago