All categories

3 years ago

For which values of K with the product of K / 3 12 be greater than 12

Mathematics

1 answer:

soldier1979 [14.2K]3 years ago

7 0

Answer:

The values of k are all real numbers greater than 3

Step-by-step explanation:

we have

$(\frac{k}{3})12 > 12$

Solve for k

Divide 12 by 3

$4k > 12$

Divide by 4 both sides

$4k/4 > 12/4$

$k > 3$

The solution is the interval ------> (3,∞)

All real numbers greater than 3

You might be interested in

A light bulb has a lifetime X that is exponentially distributed with a mean 340 hours. Find the probability that the bulb lifeti

LUCKY_DIMON [66]

Answer:

0.7026

Step-by-step explanation:

Let X denote the lifetime of light bulb. Given $X \sim Exp(\lambda)$ where the mean is $E(X) = 340 =\frac{1}{\lambda} \implies \lambda = \frac{1}{340} = 0.00294$ .

Recall that,

$\displaystyle P(X>x) = 1 - \int_0^x e^{-\lambda x} = 1 - (1 - e^{-\lambda x} = e^{-\lambda x}$

$\displaystyle P(X>220 | X>100) = \frac{P(X>220,X>100)}{P(X>100)} = \frac{e^{-\lambda \times 220}}{e^{-\lambda \times 100}} = \frac{0.5236}{0.7452} = 0.7026$

7 0

3 years ago

Can anybody help me with this ?

frutty [35]

f(x) = (3/4)ˣ - 4

As x gets really negative (3/4)ˣ grows positively without bound (because it's (4/3)⁻ˣ and 4/3 > 1).

As x gets really positive (3/4)ˣ tends to zero but never quite gets there.

So (3/4)ˣ > 0 for all x

So f(x) > 0 - 4 for all x

Answer: { y | y > -4 }, first choice

7 0

3 years ago

. Laura and Alicia both exercise 5 days a week. Laura exercises for 30 minutes each day. Alicia exercises for 45 minutes each da

statuscvo [17]

Answer: 1 hour 15 minutes

Step-by-step explanation:

From the question, we are informed that Laura and Alicia both exercise 5 days a week and that Laura exercises for 30 minutes each day. For the 5 days, she'll exercise for:

= 5 × 30 minutes

= 150 minutes

= 2 hours 30 minutes

Alicia exercises for 45 minutes each day. Fir the 5 days, she'll exercise for:

= 5 × 45 minutes

= 225 minutes

= 3 hours 45 minutes

We then calculate the difference in their exercise per week which will be:

= 3 hours 45 minutes - 2 hours 30 minutes

= 1 hour 15 minutes

6 0

3 years ago

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

ddd [48]

Answer:

$f'(x) = 4x^2 - 3$ for $x \le -3$

Step-by-step explanation:

See attachment for proper question

Given

$f(x) = -\frac{1}{2}\sqrt{x + 3}$

For

$x \ge -3$

Required

Determine the inverse function

$f(x) = -\frac{1}{2}\sqrt{x + 3}$

Replace f(x) with y

$y = -\frac{1}{2}\sqrt{x + 3}$

Swap the positions of x and y

$x = -\frac{1}{2}\sqrt{y + 3}$

Multiply both sides by -2

$-2 * x =-2 * -\frac{1}{2}\sqrt{y + 3}$

$-2x =\sqrt{y + 3}$

Square both sides

$(-2x)^2 =(\sqrt{y + 3})^2$

$4x^2 =y + 3$

Make y the subject

$y = 4x^2 - 3$

The inverse has been solved. So, we need to replace y with f'(x)

$f'(x) = 4x^2 - 3$

Next, is to determine the interval

$x \ge -3$

Change inequality to $\le$

$x \le -3$

Hence, the inverse function is:

$f'(x) = 4x^2 - 3$ for $x \le -3$

7 0

3 years ago

If your net worth is 50,000 and you pay off your student loan from your savings account how will your net worth statement be aff

Zinaida [17]

You net worth will decrease because you’re paying a loan from the money that you have. While your net worth decreases your liabilities will decrease because you will no longer have a loan to pay for.

5 0

3 years ago