(3x - 2)<br> (10x - 11)<br> (3x + 1)<br> Find the value of X

Suppose x is a real number and epsilon > 0. Prove that (x - epsilon, x epsilon) is a neighborhood of each of its members; in

kaheart [24]

Answer:

See proof below

Step-by-step explanation:

We will use properties of inequalities during the proof.

Let $y\in (x-\epsilon,x+\epsilon)$ . then we have that $x-\epsilon$ . Hence, it makes sense to define the positive number delta as $\delta=\min\{x+\epsilon-y,y-(x-\epsilon)\}$ (the inequality guarantees that these numbers are positive).

Intuitively, delta is the shortest distance from y to the endpoints of the interval. Now, we claim that $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ , and if we prove this, we are done. To prove it, let $z\in (y-\delta,y+\delta)$ , then $y-\delta$ . First, $\delta \leq y-(x-\epsilon)$ then $-\delta \geq -y+x-\epsilon$ hence $z>y-\delta \geq x-\epsilon$

On the other hand, $\delta \leq x+\epsilon-y$ then $z$ hence $z$ . Combining the inequalities, we have that $x-\epsilon$ , therefore $(y-\delta,y+\delta)\subseteq (x-\epsilon,x+\epsilon)$ as required.

3 0

3 years ago

A digital camcorder repair service has set a goal not to exceed an average of 5 working days from the time the unit is brought i

garri49 [273]

Answer:

The degrees of freedom first given by:

$df=n-1=12-1=11$

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

$t_{\alpha}= 1.796$

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

Step-by-step explanation:

Information given

5, 7, 4, 6, 7, 5, 5, 6, 4, 4, 7, 5.

System of hypothesis

We want to test if the true mean is higher than 5, the system of hypothesis are :

Null hypothesis: $\mu \leq 5$

Alternative hypothesis: $\mu > 5$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

The degrees of freedom first given by:

$df=n-1=12-1=11$

Then we can find the critical value taking in count the degrees of freedom and the alternative hypothesis and then we need to find a critical value who accumulates 0.05 of the area in the right tail and we got:

$t_{\alpha}= 1.796$

And for this case the rejection region would be:

b) Reject H0 if tcalc >1.7960

6 0

3 years ago

Thirty-five sophomores, 69 juniors and 24 seniors are randomly selected from 461 sophomores, 328 juniors and 558 seniors at a ce

LekaFEV [45]

Answer:

Stratified sampling technique(A)

Step-by-step explanation:

From the question, the population of an high school from which selection was made equals 461 sophomores, 328 juniors and 558 seniors.

35 sophomores, 69 juniors and 24 seniors are randomly selected. The technique used in selecting is Stratified sampling technique. This is because stratified sampling involves dividing the entire population into stratas and then selects a final sample randomly from the different strata. This means that a smaller part of the entire population is used as a sample in drawing conclusions for the entire population.

7 0

2 years ago

Find the solution for the following equation using the algebraic method: 3x^2+10x=8

likoan [24]

The answer should be 0.875.

6 0

2 years ago

Find the surface area of the right triangle prism(above) using the net (below)

kifflom [539]

Answer:

144

Step-by-step explanation:

2( 1/2 × 3 × 4 ) + ( 11 × 5) + ( 11 × 4 ) + ( 11 × 3)

= 12 + 55 + 44 + 33

= 144

7 0

1 year ago

(3x - 2) (10x - 11) (3x + 1) Find the value of X