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3 years ago

¾ is considered a real and rational number. true or false?

Mathematics

2 answers:

allsm [11]3 years ago

8 0

True. 3/4 is both a real and rational number

allochka39001 [22]3 years ago

3 0

IT is True.
¾ is considered a real number

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Pls help me do absolute VALUE EQUATION 3/4I8t-12I=6(t-1)

mrs_skeptik [129]

There is no solution
Distributive property
3/4 x 8t - 12 x 3/4=6 x t - 1 x 6
6t - 9=6t - 6
The 6t being on both sides makes the answer. No solution.

4 0

3 years ago

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

The difference between the prediction interval and the confidence interval is that A. the prediction interval is narrower than t

Kitty [74]

Answer:

The prediction interval provides an interval estimation for a particular value of y while the confidence interval does it for the expected value of y.

Step-by-step explanation:

A. the prediction interval is narrower than the confidence interval.

the prediction interval is always wider than the confidence interval.

B. the prediction interval provides an interval estimation for the expected value of y while the confidence interval does it for a particular value of y.

False

C. the prediction interval provides an interval estimation for a particular value of y while the confidence interval does it for the expected value of y.

True

D. the confidence interval is wider than the prediction interval.

the prediction interval is wider

8 0

3 years ago

A certain organization recommends the use of passwords with the following format: vowel commavowel, consonant comma consonant c

zimovet [89]

The password format is = inpray93

vowel , consonant, consonant, consonant, vowel, consonant, number, number.

There are 21 consonants, 5 vowels and 10 number choices (0-9)

Since, there are 21 consonants and repetition is allowed so for 2nd, 3rd, 4th, and 6th positions 21 choices are available. For 1st and 5th positions, 5 choices are available and for 7th and 8th position there are 10 choices (0 to 9).

Passwords are not case sensitive which means upper case and lower case letters are same.

So, the number of passwords can be =

$5\times21\times21\times21\times5\times21\times10\times10$

= 486202500

Part (b) question is not given. But it can be opposite to the first part i.e when the password letters are case sensitive.

This means all the letters are different.

So, number of passwords will be =

$10\times42\times42\times42\times10\times42\times10\times10$

= 31116960000

4 0

3 years ago

Find the sum of (4x^3+2x) + (8x^3+4)

Savatey [412]

The answer would be 12x^3+ 2x + 4

5 0

3 years ago