Ask question

Ask question

All categories

3 years ago

6

What are three integers that do not all have the same sign that have a sum of -20. Write three integers that do not all have the

same sign that have a sum of 10

1 answer:

Ratling [72]3 years ago

8 0

There isn't an unique solution to these equations. For example, for the first one, you may pick two arbitrary positive number, and fix the third so that the sum is -20.

Say that you choose 4 and 26. Their sum is 30. To reach -20, the third number must be -50.

So, 4, 26 and -50 are three numbers that sum to -20 and don't have all the same sign.

Similarly, for the second requirement, pick two negative numbers, and adjust the third.

If you choose -3 and -2, their sum is -5. So, the third must be 15. In fact, -3, -2 and 15 are three numbers that sum to 10 and don't have all the same sign.

You might be interested in

The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 99% confidence interval ab

Dmitry_Shevchenko [17]

Answer:

The minimum sample size needed is 125.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

$\pi = 0.25$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?

This minimum sample size is n.

n is found when $M = 0.1$

So

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.1 = 2.575\sqrt{\frac{0.25*0.75}{n}}$

$0.1\sqrt{n} = 2.575{0.25*0.75}$

$\sqrt{n} = \frac{2.575{0.25*0.75}}{0.1}$

$(\sqrt{n})^{2} = (\frac{2.575{0.25*0.75}}{0.1})^{2}$

$n = 124.32$

Rounding up

The minimum sample size needed is 125.

5 0

3 years ago

Jessica is asked to write a quadratic equation to represent a function that goes through the point (8, –11) and has a vertex at

vesna_86 [32]

the answer is c. I just did the review

5 0

3 years ago

Read 2 more answers

Laura rents a movie for a flat fee of $2.00 plus an additional $0.50 for each night she keeps the movie. Choose the cost functio

Oksana_A [137]

Hi.

The answer is:

<em />b. c(x) = 2.00 + 0.50<em>x</em>

Cheers~

8 0

3 years ago

Read 2 more answers

Solve the following recurrence relation: <br> <img src="https://tex.z-dn.net/?f=A_%7Bn%7D%3Da_%7Bn-1%7D%2Bn%3B%20a_%7B1%7D%20%3D

-Dominant- [34]

By iteratively substituting, we have

$a_n = a_{n-1} + n$

$a_{n-1} = a_{n-2} + (n - 1) \implies a_n = a_{n-2} + n + (n - 1)$

$a_{n-2} = a_{n-3} + (n - 2) \implies a_n = a_{n-3} + n + (n - 1) + (n - 2)$

and the pattern continues down to the first term $a_1=0$ ,

$a_n = a_{n - (n - 1)} + n + (n - 1) + (n - 2) + \cdots + (n - (n - 2))$

$\implies a_n = a_1 + \displaystyle \sum_{k=0}^{n-2} (n - k)$

$\implies a_n = \displaystyle n \sum_{k=0}^{n-2} 1 - \sum_{k=0}^{n-2} k$

Recall the formulas

$\displaystyle \sum_{n=1}^N 1 = N$

$\displaystyle \sum_{n=1}^N n = \frac{N(N+1)}2$

It follows that

$a_n = n (n - 2) - \dfrac{(n-2)(n-1)}2$

$\implies a_n = \dfrac12 n^2 + \dfrac12 n - 1$

$\implies \boxed{a_n = \dfrac{(n+2)(n-1)}2}$

4 0

2 years ago

A square with side x is changing with time where x(t)=3t+1. What is rate of change of the area of the square when t=2 seconds.

GuDViN [60]

Answer:

Rate of change of the area of the square is 42 units at t = 2.

Step-by-step explanation:

We note that the area of the square is given by: $A(x) = x^2$ but we aim to find $\frac{dA}{dt}$ . But we can use the chain rule to pull out that dA/dt. Doing so gives us:

$\frac{dA}{dt} = \frac{dA}{dx} \times \frac{dx}{dt}.$

Now, $\frac{dA}{dx} = 2x$ (by the power rule and $\frac{dx}{dt} = 3.$

But since we have "x" and not "t", we want to find what x is when t = 2. Substituting t = 2 gives us x(2) = 3(2) + 1 = 7.

So, finally, we see that:

$\frac{dA}{dt} = 2(7) \times 3 = 14 \times 3 = 42.$

7 0

3 years ago