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3 years ago

How do you know if a decimal is an irrational or rational number?

1 answer:

8 0

A decimal is rational if it:

either ends and doesn't go on forever; OR
it is a repeating decimal.
A decimal is irrational if it goes on forever and ever and never stops without repeating.

The number: 5.77777777 is rational because it goes on forever, REPEATING the same number (the digit 7).

It can also repeat a group of numbers, like the number: 8.789789789789789789

See how the "789" is REPEATING over and over again and never stops? That is a rational decimal!

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An account earns simple annual interest. You deposit $600 into an account at 5% interest rate for 2 years. (a) Find the interest

Ilia_Sergeevich [38]

Answer:

(a) $60 | (b) $660

Step-by-step explanation:

We can use the simple interest formula for this:

$I=Prt$

I = interest amount

P = principal amount

r = interest rate (decimal form)

t = time (years)

First, change 5% into its decimal form:

5% -> $\frac{5}{100}$ -> 0.05

Next, plug in the values into the equation:

$I=600(0.05)(2)$

$I=60$

The interest earned is $60. To find the total balance, just add the $600 back.

$600+60=660$

The total interest earned is $60 and the total is $660.

4 0

3 years ago

The temperature at sunrise was -3*F. By noon, the temperature climbed 18 degrees. By sundown the temperature was -14*F. How much

Nostrana [21]

Answer:

29*

Step-by-step explanation:

if th temperature was -3* and then climbed 18* it would end up being *15 because it was going up

but the it went down to -14* ,, which means that you have to get form 15* to -14*

you first go down 15* to get to 0 and go down *14 to get to -14*

when you add 15 and 14 it gets you to 29*

7 0

4 years ago

Read 2 more answers

The function f(x) = x2 is translated 7 units to the left and 3 units down to form the function g(x). Which represents g(x)? g(x)

Verdich [7]

Answer:

g(x)=(x+7)^2-3

Step-by-step explanation:

Given:

f(x)= x^2

Now we have to translate f(x) 7 units to the left and 3 units down to form the function g(x).

As per the rules of translation

when any parent function, in given case f(x)=x^2, is translated to 'a' units to the left then 'a' is added to the value of x. thus making f(x+a)

Also when the parent function is translated any 'a' units down then 'a' is subtracted from the value of function. thus making f(x)-a

Translating f(x), 7 units to the left

f(x+7)= (x+7)^2

Translating f(x+7), 3 units down

f(x+7)-3 = (x+7)^2-3

Hence new function g(x)=(x+7)^2-3!

7 0

3 years ago

How do you know that the decimal 2\11 repeats without end?

seropon [69]

It doesn't, it ends after 32 digits after 0.

5 0

3 years ago

The probability that a randomly selected teenager watched a rented video at least once during a week was 0.75. What is the proba

Whitepunk [10]

Answer:

There is a 75.65% probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week.

Step-by-step explanation:

For each teenager, there are only two possible outcomes. Either they watched a rented video at least once during a week, or they did not. This means that we can solve this problem using the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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

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

And p is the probability of X happening.

In this problem we have that:

The probability that a randomly selected teenager watched a rented video at least once during a week was 0.75. This means that $p = 0.75$ .

What is the probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week?

Group of 7, so $n = 7$ .

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7)$ .

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{7,5}.(0.75)^{5}.(0.25)^{2} = 0.3115$

$P(X = 6) = C_{7,6}.(0.75)^{6}.(0.25)^{1} = 0.3115$

$P(X = 7) = C_{7,7}.(0.75)^{7}.(0.25)^{0} = 0.1335$

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) = 0.3115 + 0.3115 + 0.1335 = 0.7565$ .

There is a 75.65% probability that at least 5 teenagers in a group of 7 watched a rented movie at least once last week.

3 0

3 years ago