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3 years ago

14

Is

ormula"> rational or irrational?

1 answer:

TEA [102]3 years ago

5 0

Answer:

Rational

Step-by-step explanation:

$2^{-3}$ simplifies to $\frac{1}{8}$ .

Therefore, it is rational.

$2^{-3}\\\\\text {Apply negative exponent rule: } a^{-n} = \frac{1}{a^n} \\2^{-3}= \frac{1}{2^3}\\ \rightarrow 2^3 = 2*2*2=8\\\boxed{2^{-3}=\frac{1}{8}}$

<em>Brainliest Appreciated. </em>

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What should the following rate be divided by to convert it to a unit rate?<br> 6 inches<br> 12 hours

iragen [17]

Answer:

0.5 Inches per hour

Step-by-step explanation:

Most normal people won't know exactly what unit rate is, or how to calculate it. So I'm here to help!

This is a fraction equal to

6 inches ÷ 12 hours

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 12

6 inches ÷ 12

12 hours ÷ 12

=

0.5 inches

1 hour

=

0.5 inches

hour

= 0.5 inches per hour

Glad I was able to help!

7 0

3 years ago

find 2 consecutive integers such that three times the square of the first is equal to seven more than five times the second

melamori03 [73]

Answer:

Step-by-step explanation:

We are looking for two numbers, $N$ and $N + 1$ . From the problem statement, we can setup the following equation:

$3N^{2} = 5(N + 1) + 7$

$3N^{2} = 5N + 5 + 7$

$3N^{2} - 5N - 12 = 0$

$(3N + 4)(N - 3)$

$N = \frac{-4}{3}, 3$

Because 3 is the only integer solution, the answer is 3 and 4.

5 0

3 years ago

Of all the soft drink consumers in a particular sales region, 30% prefer Brand A and 70% prefer Brand

victus00 [196]

Answer:

Option D -0.67

Step-by-step explanation:

Given : Preference of Brand A =30% ⇒ $P(A)=\frac{30}{100}=0.3$

Preference of Brand B =70% ⇒ $P(B)=\frac{70}{100}=0.7$

Prefer Brand A and are Female = 20% ⇒ $P(A/F)=\frac{20}{100}=0.2$

Prefer Brand B and are Female = 40% ⇒ $P(B/F)=\frac{40}{100}=0.4$

To find : Selected consumer is female, given that the person prefers Brand A $P(F/A)$

Solution : Using Bayes' theorem, which state that

$P(A/B)=\frac{P(B/A)P(A)}{P(B)}$

where, P(A) and P(B) are probabilities of observing A and B.

P(B/A)= is a conditional probability where event B occur and A is true

P(A/B)= also a conditional probability where event A occur and B is true.

Now, applying Bayes' theorem,

$P(F/A)=\frac{P(A/F)P(A)}{P(B)P(B/F)+P(A)P(A/F)}$

$P(F/A)=\frac{(0.2)(0.3)}{(0.7)(0.4)+(0.3)(0.2)}$

$P(F/A)=\frac{0.6}{0.28+0.6}$

$P(F/A)=\frac{0.6}{0.88}$

$P(F/A)=0.68$

Therefore, Option D is correct probability that a randomly selected consumer is female, given that the person prefers Brand A -0.67

3 0

3 years ago

Read 2 more answers

If the radius of a circle with center 0 is 15.5, and the measure of angle AOB is 90, what is the length of arc AB?

Zina [86]

The circumference of the circle is found using the formula C = 2 PI r

Circumference = 2 *PI * 15.5 = 31pi

The angle is 90 degrees, which is 1/4 of a complete circle ( 360 degrees).

The arc length would be 1/4 of the circumference:

Arc length = 31pi / 4 = 7.75PI

3 0

2 years ago

3/10 divided by -1/3

Snezhnost [94]

Answer:

-9/10

Step-by-step explanation:

Find the LCM of 10 and 3: 30
Alter the numerators to fit the denominators: 3 × 3 = 9, -1 × 10 = -10
Re-write the fractions: 9/30 ÷ -10/30
9/30 ÷ -10/30 = 9/30 × -30/10
9/30 × -30/10 = -270/300
$-\frac{270}{300} = -\frac{9}{10}$

I hope this helps!

8 0

3 years ago