What is the solution set for this linear-quadratic system of equations?

"There are 15 questions on an exam. In how many ways can the exam be answered with exactly 8 answers correct?"

erastovalidia [21]

Answer:

The exam can be answered with exactly 8 answers correct in 6435 ways.

Step-by-step explanation:

The order is not important.

For example, answering correctly the questions 1,2,3,4,5,6,7,8 is the same outcome as answering 2,1,3,4,5,6,7,8. So we use the combinations formula to solve this problem.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

"There are 15 questions on an exam. In how many ways can the exam be answered with exactly 8 answers correct?"

Combinations of 8 questions from a set of 15. So

$C_{15,8} = \frac{15!}{8!(15-8)!} = 6435$

The exam can be answered with exactly 8 answers correct in 6435 ways.

5 0

3 years ago

Virtual Nerd™: How Do You Use a Tree Diagram to Count the Number of Outcomes in a Sample Space?

kipiarov [429]

Answer:

We use tree diagram by connecting relevant samples

Step-by-step explanation:

thats all

8 0

3 years ago

A factory makes light fixtures with right regular hexagonal prisms where the edge of a hexagonal base measures 4 cm and the leng

chubhunter [2.5K]

The maximum length of the prism is highest length of the hexagonal prism

The maximum length of each prism is 8.0 cm

<h3>How to determine the maximum length of each prism?</h3>

The surface area of the hexagonal prism is calculated using:

A = 6al + 3 $\sqrt$ 3 a^2

Where:

a represents the edge length; a = 4 cm

l represents the length (or height) of the prism

The surface area costs $0.04 per square centimeter.

So, we have:

C = 0.04 * [6al + 3 $\sqrt$ 3 a^2]

The maximum cost is $11.

So, the equation becomes

11 = 0.04 * [6al + 3 $\sqrt$ 3 a^2]

Substitute 4 for a

11 = 0.04 * [6 * 4l + 3 $\sqrt$ 3 * 4^2]

Evaluate the products and exponents

11 = 0.04 * [24l + 48 $\sqrt$ 3]

Divide both sides by 0.04

275 = 24l + 48 $\sqrt$ 3

Subtract 48 $\sqrt$ 3 from both sides

24l = 275 - 48 $\sqrt$ 3

Evaluate the difference

24l = 191.9

Divide both sides by 24

l = 8.0

Hence, the maximum length of each prism is 8.0 cm

Read more about surface areas at:

brainly.com/question/6613758

6 0

2 years ago

A student solving for the acceleration of an object has applied appropriate physics principles and obtained the expression a=a1+

egoroff_w [7]

Answer:

$a=\frac{3\times 7}{7}+\frac{12}{7}$ (First step for obtaining a common denominator for the two fraction)

$a=\frac{33}{7}\text{ m/s}^2$

Step-by-step explanation:

$\text{Given Expression: }a=a_1+\frac{F}{m}$

where,

a is acceleration of an object.(Need to calculate)

$a_1=3.00\text{ m/s}^2$

$F=12.0\text{ Kg.m/s}^2$

$m=7.00\text{ kg}$

$\text{Substitute }a_1, \text{ F, and m into expression and we get}$

$a=3+\frac{12}{7}$

Now we will simplify above expression for a

First we make common denominator.

Common denominator is 7. So, we make both denominator 7. We multiply by 7 at top and bottom with 3. We get

$a=\frac{3\times 7}{7}+\frac{12}{7}$ (First step for obtaining a common denominator for the two fraction)

Now we combine the numerator

$a=\frac{21+12}{7}$

$a=\frac{33}{7}\text{ m/s}^2$

3 0

4 years ago

Read 2 more answers

A number to the 10th power divided by the same number to the 7th power equals 125. What is the number?

Viefleur [7K]

Answer:

the number is 5

Step-by-step explanation:

x^10 ÷ x^7 = 125

x^3 = 125

x = 5

6 0

3 years ago