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2 years ago

State the domain and range and determine if it's a function?

Mathematics

1 answer:

pishuonlain [190]2 years ago

4 0

if we do a <u>vertical line test</u> on that graph, we'll find that a vertical line will pass by and hit the line only once on its way down, only once meaning the graph is the graph of a function.

<h2>Range</h2>

well, is really how high and low it goes or namely over the y-axis.

well, it goes up up up to 3 then U-turns and back down it goes, now the graph has arrowheads, meaning the graph keeps on going towards infinity, vertically as well as horizontally since it's a parabola, so the range will be

<h2>Domain</h2>

well, is simply how left and right it goes or namely over the x-axis.

judging from the arrowheads it moves from infinity to infinity, so

You might be interested in

Assume that females have pulse rates that are normally distributed with a mean of mu equals 72.0 beats per minute and a standard

larisa86 [58]

Answer:

a) 36.88% probability that her pulse rate is between 66 beats per minute and 78 beats per minute

b) 66.30% probability that they have pulse rates with a mean between 66 beats per minute and 78 beats per minute

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using 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.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 72, \sigma = 6.5$

a. If 1 adult female is randomly selected, find the probability that her pulse rate is between 66 beats per minute and 78 beats per minute.

The probability is?

This is the pvalue of Z when X = 78 subtracted by the pvalue of Z when X = 66. So

X = 78

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

$Z = \frac{78 - 72}{12.5}$

$Z = 0.48$

$Z = 0.48$ has a pvalue of 0.6844

X = 66

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

$Z = \frac{66 - 72}{12.5}$

$Z = -0.48$

$Z = -0.48$ has a pvalue of 0.3156

0.6844 - 0.3156 = 0.3688

36.88% probability that her pulse rate is between 66 beats per minute and 78 beats per minute

b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 66 beats per minute and 78 beats per minute

The probability is?

Now we have $n = 4, s = \frac{12.5}{\sqrt{4}} = 6.25$

X = 78

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

By the Central Limit Theorem

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

$Z = \frac{78 - 72}{6.25}$

$Z = 0.96$

$Z = 0.96$ has a pvalue of 0.8315

X = 66

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

$Z = \frac{66 - 72}{6.25}$

$Z = -0.96$

$Z = -0.96$ has a pvalue of 0.1685

0.8315 - 0.1685 = 0.6630

66.30% probability that they have pulse rates with a mean between 66 beats per minute and 78 beats per minute

c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?

The condition for the sample size exceeding 30 is when the population is skewed. If it is normally distributed, the size is not a condition.

So the correct answer is:

Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.

3 0

3 years ago

Read 2 more answers

Find Tan Θ given sin Θ = √3/2 and cos Θ = 1/2 a √3 b 3 c 2 d 4

densk [106]

We know:

$\tan\Theta=\dfrac{\sin\Theta}{\cos\Theta}$

We have:

$\sin\Theta=\dfrac{\sqrt3}{2},\ \cos\Theta=\dfrac{1}{2}$

Substitute:

$\tan\Theta=\dfrac{\frac{\sqrt3}{2}}{\frac{1}{2}}=\dfrac{\sqrt3}{2}:\dfrac{1}{2}=\dfrac{\sqrt3}{2}\cdot\dfrac{2}{1}=\sqrt3$

Answer: a. √3

4 0

3 years ago

Read 2 more answers

Suppose on a certain test, fifty students earn a perfect score and fifty students earn a zero. determine the mean grade and stan

kodGreya [7K]

Answer:

Mean=50.

standard deviation=50.

Step-by-step explanation:

Let the perfect score be 100.

The mean(average) of a data is given by: $Mean=\frac{sum of data points}{number of data points}$

Here the number of data points are 100. out of which 50 attains a value 100,and 50 attains value 0.

so, sum of data points=50×100+50×0=5000.

$Mean=\frac{5000}{100}$

Mean=50.

"Now the standard deviation of data points are calculated by firstly subtracting mean from every entry and then square the number and take it as new entry and calculate the mean of the new data entry and lastly taking the square root of this new mean".

Here if 50 is subtracted from each entry the new entry will have 50 entries as '50' and 50 entries as '-50'.

next on squaring we will have all the 100 entries as '2500'.

now the mean of these entries is: $\frac{2500\times100}{100}$

=2500

taking it's squareroot we have $\sqrt{2500}=50$

Hence, standard deviation=50.

5 0

4 years ago

Read 2 more answers

Help please! There are 3 items in an order. They cost $8.95, $11.49, and $12.75. The sales tax for this order is 6.5%.

vredina [299]

Answer: $35.35

Step-by-step explanation:

Facts

3 items

item 1: 8.95

item 2: 11.49

item 3: 12.75

6.5% sales tax

Step 1: Find the total cost of the items ,before tax

8.95+11.49+12.75= 33.19

Step 2: Apply the sales tax

6.5% of 33.19 = 2.15735 --> approximatley $2.16

Step 3: Add the sales tax amount to the total cost of the items to find the final total cost.

$33.19+$2.16= $35.35

Hence the answer is B

Hope this helps !! :)) And brainliest would be appreciated

3 0

2 years ago

Read 2 more answers

Help me please <3 ill give yall 20 points

lozanna [386]

Answer:

4. -1

5. +_ 2/5

6. 3.5

Step-by-step explanation:

8 0

2 years ago