All categories

3 years ago

Solve |z| > (1/2)

Mathematics

1 answer:

Anestetic [448]3 years ago

8 0

Answer:

{ $z|z$ }U{ $z|z>\frac{1}{2}$ }

Step-by-step explanation:

Given the inequality $|z| > \frac{1}{2}$ you need to set up two posibilities:

FIRST POSIBILITY : $z>\frac{1}{2}$

SECOND POSIBILTY: $z$

Therefore, you got that:

$z\frac{1}{2}$

Knowing this, you can write the solution obtained in Set notation. This is:

Solution: { $z|z$ }U{ $z|z>\frac{1}{2}$ }

You might be interested in

Amoeba dapat membelah diri menjadi 2 setiap 20 menit . Jika mula mula terdapat 15 amoeba maka setelah dua jam banyaknya amoeba a

leva [86]

<span>Amoeba splits 3 times an hour. If Amoeba can split into two every 20 mins then if you divide 60 mins (which would be an hour) by 20 mins (the time they split) you would find that Amoeba can split 3 times in an hour. The question asks how many times it can split in two hours. To find this you have to multiply the 3 times 2. This means that a single Amoeba can split 6 times in two hours. There are 15 Amoeba which means if you take 15 Amoeba time 6 in two hours and 90 would be your answer. There will be 90 Amoeba after the two hours.</span>

7 0

3 years ago

The measures of angle 1 and angle 2 are 30% and 45% of the sum of the angle measures of the triangle. Find the value of x. ASAP

s344n2d4d5 [400]

Answer: x = 25%

Step-by-step explanation: 45% + 30% = 75%

75% + 25% = 100%

7 0

3 years ago

Read 2 more answers

Suppose A and B represent mutually exclusive events.

mart [117]

Answer:

14/15

Step-by-step explanation:

simple

3/5 + 1/3= 14/15

4 0

2 years ago

Many high school students take the AP tests in different subject areas. In 2007, of the 144,796 students who took the biology ex

Nataly [62]

Answer:

$(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942$

$(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978$

And the 90% confidence interval would be given (0.0942;0.09978).

We are confident at 90% that the difference between the two proportions is between $0.0942 \leq p_A -p_B \leq 0.09978$

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p_A$ represent the real population proportion female for Biology

$\hat p_A =\frac{84199}{144796}=0.582$ represent the estimated proportion female for biology

$n_A=144796$ is the sample size for A

$p_B$ represent the real population proportion female for calculus AB

$\hat p_B =\frac{102598}{211693}=0.485$ represent the estimated proportion female for Calculus AB

$n_B=211693$ is the sample size required for B

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

The confidence interval for the difference of two proportions would be given by this formula

$(\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}$

For the 90% confidence interval the value of $\alpha=1-0.90=0.1$ and $\alpha/2=0.05$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.64$

And replacing into the confidence interval formula we got:

$(0.582-0.485) - 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.0942$

$(0.582-0.485) + 1.64 \sqrt{\frac{0.582(1-0.582)}{144796} +\frac{0.485(1-0.485)}{211693}}=0.09978$

And the 90% confidence interval would be given (0.0942;0.09978).

We are confident at 90% that the difference between the two proportions is between $0.0942 \leq p_A -p_B \leq 0.09978$

5 0

3 years ago

Tickets to a play cost $14 each by mail, plus a $2 processing fee for each order or one or more tickets. Write a rule to describ

Aneli [31]

The equation would be 14x+2=t......

Breakdown: 14 times X (the number of tickets purchased) plus the one time processing fee of 2 dollars will equal T (the total)

6 0

3 years ago