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3 years ago

Two number cubes are rolled in a board game. What is the probability that both number cubes land on the same number?

Mathematics

1 answer:

allsm [11]3 years ago

5 0

50% chance they will land on the same number and there’s also a 50% chance they won’t.

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Solve the Anti derivative.

Alex Ar [27]

Answer:

$\displaystyle \int {\frac{1}{9x^2+4}} \, dx = \frac{1}{6}arctan(\frac{3x}{2}) + C$

General Formulas and Concepts:

Algebra I

Factoring

Calculus

Antiderivatives - integrals/Integration

Integration Constant C

U-Substitution

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Trig Integration: $\displaystyle \int {\frac{du}{a^2 + u^2}} = \frac{1}{a}arctan(\frac{u}{a}) + C$

Step-by-step explanation:

Step 1: Define

$\displaystyle \int {\frac{1}{9x^2 + 4}} \, dx$

Step 2: Integrate Pt. 1

[Integral] Factor fraction denominator: $\displaystyle \int {\frac{1}{9(x^2 + \frac{4}{9})}} \, dx$
[Integral] Integration Property - Multiplied Constant: $\displaystyle \frac{1}{9} \int {\frac{1}{x^2 + \frac{4}{9}}} \, dx$

Step 3: Identify Variables

Set up u-substitution for the arctan trig integration.

$\displaystyle u = x \\ a = \frac{2}{3} \\ du = dx$

Step 4: Integrate Pt. 2

[Integral] Substitute u-du: $\displaystyle \frac{1}{9} \int {\frac{1}{u^2 + (\frac{2}{3})^2} \, du$
[Integral] Trig Integration: $\displaystyle \frac{1}{9}[\frac{1}{\frac{2}{3}}arctan(\frac{u}{\frac{2}{3}})] + C$
[Integral] Simplify: $\displaystyle \frac{1}{9}[\frac{3}{2}arctan(\frac{3u}{2})] + C$
[integral] Multiply: $\displaystyle \frac{1}{6}arctan(\frac{3u}{2}) + C$
[Integral] Back-Substitute: $\displaystyle \frac{1}{6}arctan(\frac{3x}{2}) + C$

Topic: AP Calculus AB

Unit: Integrals - Arctrig

Book: College Calculus 10e

7 0

2 years ago

Kyle`s phone bill is $45 per month. how much does he have to pay for half a year of phone service

ArbitrLikvidat [17]

Answer:

$270

Step-by-step explanation:

Its simply 45 times 6 months

4 0

3 years ago

An architect in Brussels measures something to be 2.5 feet (using the Brussels measurement). How many feet is this in Aalst (usi

borishaifa [10]

Answer:

$2.487F$

Step-by-step explanation:

From the question we are told that

Architect Measures 2.5 feet (using the Brussels measurement)

Generally in Brussels $1F=275.75mm$

Therefore

$2.5F=689.375mm$

Generally in Aalst $1F=277.2mm$

Therefore Mathematically converting to feet in Aalst measurement we get

$689.375mm*\frac{1}{277.2} =2.487F$

6 0

3 years ago

Please answer, i will give 20 points!!!

Lapatulllka [165]

Answer:

Step-by-step explanation:

Pentagon has 5 sides

The formula for finding the sum of the measure of the interior angles is (n - 2) * 180

(5-2)×180= 3×180=540

To get each interior angles

540/5 = 108

180 -108 = 72

To get x

72+72+x= 180 (sum if angles in a triangle)

144+x= 180

x = 180 -144 = 36

2. x is part of the interior angles = 108

4 0

3 years ago

Read 2 more answers

Lucy is estimating the income levels of households in a specific zip code. She randomly calls 100 households and collects

Lorico [155]

The average income for the household that is surveyed should represent the sample data is not relevant.

The information that should be considered as follows:

The level of the income of the household represents the parameter of the population.
The total income for the household that is surveyed represents the statistics of the sample.
The household i.e. surveyed is relevant for the sample of the total population that lives in the zip code.

Therefore we can conclude that the average income for the household that is surveyed should represent the sample data is not relevant.

Learn more about the income here: brainly.com/question/14732695

7 0

2 years ago