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rewona [7]
3 years ago
5

In how many ways can a 12-question true-false exam be answered? (Assume that no questions are omitted.)

Mathematics
1 answer:
ch4aika [34]3 years ago
5 0

Answer:

4,096 ways

Step-by-step explanation:

Assuming that all questions have to be answered, there are two ways to answer each of the 12 questions (True or False). The total number of possible answers is given by:

n=2^{12}\\n=4,096\ ways

A 12-question true-false exam can be answered in 4,096 different ways.

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PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!<br><br> What is the value of x?
MA_775_DIABLO [31]

Answer:   \bold{C)\ -\dfrac{1}{2}}

<u>Step-by-step explanation:</u>

.\qquad \dfrac{x+2}{15}=\dfrac{x+1}{5}\\\\\\\rightarrow (15)\dfrac{x+2}{15}=\dfrac{x+1}{5}(15)\\\\\\\rightarrow x+2=3(x+1)\\\\\rightarrow x+2=3x+3\\\\\rightarrow \qquad 2=2x+3\\\\\rightarrow \qquad -1=2x\\\\\rightarrow \qquad -\dfrac{1}{2}=x

8 0
3 years ago
Solve the following system of equations by substitution. Show all steps.
Alinara [238K]

Answer:

Given system of equations:

\begin{cases}f(x)=-x^2+2x+3\\g(x)=-2x+3\end{cases}

To solve by substitution, equate the equations and solve for x:

\begin{aligned}f(x) & = g(x)\\\implies -x^2+2x+3 & = -2x+3\\-x^2+4x & = 0\\x^2-4x & = 0\\x(x-4) & = 0\\\implies x & = 0\\\implies x-4 & = 0 \implies x=4\end{aligned}

Therefore, the x-values of the solution are x = 0 and x = 4.

To find the y-values of the solution, substitute the found values of x into the functions:

f(0)=-(0)^2+2(0)+3=3

g(0)=-2(0)+3=3

f(4)=-(4)^2+2(4)+3=-5

g(4)=-2(4)+3=-5

Therefore, the solutions to the given system of equations are:

(0, 3) and (4, -5)

4 0
2 years ago
Use the formula A=2πrh to find the area of the curved surface of each of the cylinders below. (Express your answers correct to 1
shusha [124]

Answer:

here,

A=2×22÷7×17/2×21

A=22×17×3

A=1122 sq.cm

3 0
3 years ago
A large college wishes to determine the average SAT scores for students who apply from New York. They surveyed 105 students from
sweet [91]

Answer:

Statements I and II

Step-by-step explanation:

In Statistics, parameter is any numerical value that characterizes a population while statistics are numerical values that characterizes a sample from a given population.

Statistics are most often used to estimate the population parameters

For example the sample mean is a statistic and the population mean is a paranmeter

The mean SAT score of all students from New York is the parameter.

The mean SAT score of 105 students from New York is called the statistic.

The correct choice is the third option.

5 0
3 years ago
The population of a town is 14,000 and is decreasing at a rate of 1.5% each year. Write an exponential decay equation to find th
sergejj [24]

Answer: the population after 10 years is 12036

Step-by-step explanation:

We would apply the formula for exponential growth which is expressed as

A = P(1 - r)^ t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 14000

r = 1.5% = 1.5/100 = 0.015

t = 10 years

Therefore, the exponential decay equation to find the population of the town after 10 years is

A = 14000(1 - 0.015)^10

A = 14000(0.985)^10

A = 12036

8 0
3 years ago
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