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2 years ago

Use the roster method to write each of the given sets. (Enter EMPTY for the empty set.)

Mathematics

1 answer:

Kitty [74]2 years ago

6 0

Answer:

a) Empty set

b) $\{x : x \in N \text{ and } x < 13\}$

Step-by-step explanation:

Roster form is a comma separated list form of set.

a) The set of natural numbers x that satisfy x + 4 = 1.

$x + 4 = 1\\x = -3 \notin N$

Thus, x is an empty set.

b) set-builder notation for the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}.

We use x to represent this set. Now x belongs to natural number and is less than equal to 12.

Thus, it can be written as:

$\{x : x \in N \text{ and } x < 13\}$

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From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that ag

Jlenok [28]

Answer:

If we compare the p value and the significance level given for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we to reject the null hypothesis, and the the actual mean starting age of smokers is significantly lower than 19.

Step-by-step explanation:

1) Data given and notation

$\bar X=18.1$ represent the mean age when smokers first start to smoke varies

$s=1.3$ represent the standard deviation for the sample

$\sigma=2.1$ represent the population standard deviation

$n=37$ sample size

$\mu_o =5.7$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to determine if the mean starting age is at least 19, the system of hypothesis would be:

Null hypothesis: $\mu\geq 19$

Alternative hypothesis: $\mu < 19$

We know the population deviation, so for this case is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{18.1-19}{\frac{2.1}{\sqrt{37}}}=-2.607$

Calculate the P-value

Since is a one-side lower test the p value would be:

$p_v =P(z$

Conclusion

4 0

2 years ago

A cell phone tower at point A receives a cell phone signal from the southeast. A cell phone tower at point B receives a signal f

never [62]

Answer: Postulate 1: -4,-4

Postulate 2: D. The postulates guarantee that unique lines can be draw that they will meet at a unique point.

Step-by-step explanation:

7 0

2 years ago

A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the given angular veloci

Gemiola [76]

Answer:

t = 1.57 sec

distance, d = 98.65 mm

Step-by-step explanation:

Given an angle of 540°

At 6 revolutions per second, which is the angular velocity.

Radius, r = 10 mm

We are asked to find the time and the distance.

To find the time, let's use the formula:

$\theta = a*t$

Where $\theta$ = angle in radians.

Converting 540° to radians, we have:

$\theta = 540 * \frac{\pi}{180} = 9.42 rad$

Therefore, from the formula, let's find t.

$\theta = a*t$

$9.42 = 6 * t$

$t = \frac{9.42}{6} = 1.57$

time = 1.57

To find the distance, we have:

$\frac{1.57 * 360}{360} = \frac{d}{2 \pi r}$

$\frac{1.57 * 360}{360} = \frac{d}{2\pi 10}$

$1.57 = \frac{d}{20\pi}$

$d = 20 \pi *1.57$

d = 98.65 mm

Therefore, the time is 1.57 seconds and the distance is 98.65 mm

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2 years ago

Angle A and B are supplementary. Angle a has a measure of 80. What is the measure of angle B? The measure of angle B is

ololo11 [35]

Well when two angles are supplementary they equal 180.
So if angle A is 80 degrees then that would mean that angle B equals 100 degrees.

Hope This Helped :)

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2 years ago

Kevin buys a leather jacket listed for $190. He receives a 15% discount at the register. What is the new price of the leather ja

QveST [7]

Take $190 and multiply it by 0.15 (28.5) and subtract that from $190= $161.50

3 0

2 years ago

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