All categories

3 years ago

Can you think of a number k for which k^2 < k is true?

Mathematics

1 answer:

wariber [46]3 years ago

4 0

Answer:

Some k's that will work:

1/2

1/3

1/4

(There are infinitely many answers.)

Step-by-step explanation:

Obviously 5 won't work because 25<5 is not true.

What about a negative? -5?

25<-5 is not true.

How about 1/3? 1/9<1/3 is true so 1/3 works.

Note: Think of a number between 0 and 1.

1/4<1/2 is true and (1/2)^2=1/4.

1/16<1/4 is true and (1/4)^2=1/16.

You can solve k^2<k.

Subtract k on both sides.

k^2-k<0

Factor.

k(k-1)<0.

So k^2-k is a parabola with x-intercepts (k-intercepts) at k=0 and k=1.

The parabola is open up so any number between 0 and 1 will satisfy k^2<k since between 0 and 1 the parabola is less than y=0 ( the x-axis).

You might be interested in

How do I get an equation from 9x-y=45 but the equation has to equal y

Brilliant_brown [7]

First add y to both sides to get 9x=45+y than subtract 45 from both sides to get 9x-45=y or y=9x-45

6 0

3 years ago

Read 2 more answers

The vertices of triangle DEF are D(0,0), E(0,7), and F(6,3). find the coordiantes of the orthocenter of triangle DEF

const2013 [10]

Idk idk idk idk idk idk idk

Maybe 73

8 0

3 years ago

Suppose Z has a standard normal distribution with a mean of 0 and standard deviation of 1. 27% of the possible Z values are grea

inessss [21]

Answer:

27% of the possible Z values are greater than 0.613

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

$\mu = 0, \sigma = 1$

27% of the possible Z values are greater than

The 100 - 27 = 73rd percentile, which is X when Z has a pvalue of 0.73. So X when the z-score is 0.613.

$Z = \frac{X - \mu}{\sigma}$

$0.613 = \frac{X - 0}{1}$

$X = 0.613$

27% of the possible Z values are greater than 0.613

6 0

3 years ago

25 POINTS HELP PLEASE! Complete the table and pattern. Determine the common difference. Write the explicit rule.

Mumz [18]

Answer:

Look below for the answers.

Step-by-step explanation:

What I'm going to do is one of these very carefully and leave the other 2 to you. They follow exactly the same pattern and once you see one of them done, you should be able to do any of them.

Six

Step one

Find the common difference.

Two values on the second line are always together so subtract the higher number one from the lower numbered on.

n = 3 and n = 4 on this question are side by side. That is you have f(4) and f(3)

ALWAYS subrract the lower numbered one from the higher numbered one

d = f(4) - f(3) = 60 - 64 = - 4

Step Two

Find the first term.

The first term is ALWAYS f(1). Always. There is never any kind of exception. f(1) in this case is 72

Step Three

Write the general explicit term

The general formula for the explicit Formula is ALWAYS

tn = first term + (n -1)*d

first term = 72

d = - 4 from above.

Explicit formula = 72 + (n - 1)*(-4) So the fifth term is

Example

t5 = 72 + (5 - 1)*(-4)

t5 = 72 + 4*(-4)

t5 =72 - 16

t5 = 56

Step Four

Write the Recursive formula

It is always in the same formal

tn = t_(n - 1) + (common difference)

tn = t_(n - 1) - 4 in this case

Example

Find t2

t2 = t1 - 4

t2 = 72 - 4

t2 = 68

If you do the other two, you can leave them in my PM and I will mark them.

5 0

4 years ago

Math question answer A B C

Sergeu [11.5K]

1a.
you still have
k=C+273.15
k-C= 273.15 as related equations

b. at C=23
k=23+273.15 = 296.15

c. 25°C in kelvin = 25+273.15 = 298.15
so 300K is greater than 25°C

3 0

4 years ago

Can you think of a number k for which k^2 < k is true?​

Can you think of a number k for which k^2 < k is true?