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3 years ago

[25 POINTS] determine whether each relation is a function. If so, provide the domain and range.

Mathematics

1 answer:

ZanzabumX [31]3 years ago

7 0

Answer:

The first table is a function.

Domain for the first graph: {1, 5, 10, 11, 14}

Range for the first graph: {6, 50, 150, 176, 266}

The second table is a function

Domain for the second graph: {0, 10, 20, 30, 40}

Range for the second graph: {0, 300, 600, 900, 1200}

Step-by-step explanation:

To tell whether if a relation is a function is to determine if the x values repeat itself. If the x value repeats itself, it is not a function. If it doesn't repeat itself, it is therefore a function. You can also tell if a relation is a function by doing the vertical line test. Draw a vertical line on a graph and if it hits more than one point, the relation is not a function. The domain are the x values while the range are the y values. When you're plotting the domain/range, make sure to put the numbers in order from least to greatest, use curly brackets instead of parentheses, and don't repeat the same numbers. So yeah a brainliest would be great but you don't have too.

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Thirty percent (30%) of the bulbs in a large box are defective. If 12 bulbs are selected randomly from the box, calculate the pr

AleksandrR [38]

The probability that exactly 6 are defective is 0.0792.

Given:

30% of the bulbs in a large box are defective.

If 12 bulbs are selected randomly from the box.

To find:

The probability that exactly 6 are defective.

Solution:

Probability of defective bulbs is:

$p=30\%$

$p=\dfrac{30}{100}$

$p=0.3$

Probability of non-defective bulbs is:

$q=1-p$

$q=1-0.3$

$q=0.7$

The probability that exactly 6 are defective is:

$P(x=r)=^nC_rp^rq^{n-r}$

$P(x=6)=^{12}C_6(0.3)^6(0.7)^{12-6}$

$P(x=6)=924(0.3)^6(0.7)^{6}$

$P(x=6)=0.0792478958$

$P(x=6)\approx 0.0792$

Therefore, the probability that exactly 6 are defective is 0.0792.

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3 years ago

Factor out the common terms<br> 2x+4y

seraphim [82]

Answer:

Step-by-step explanation:

2x = 2*x

4y = 2*2*y

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Umnica [9.8K]

You can solve this with next proportion =>

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The correct answer is x= 6 (2/3)

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3 years ago

a plumber charges $55 for a service call plus $35 per hour. if the plumber’s bill was $160, how many hours was he there?

Allushta [10]

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3 years ago

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The owner of Mattâ€™s Gas Station wants to study gasoline purchases of customers at his station. In 2017, the mean amount of gas

gulaghasi [49]

Answer:

Step-by-step explanation:

a) We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 9

For the alternative hypothesis,

µ ≠ 9

This is a 2 tailed test

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 9

x = 9.9

σ = 2.5

n = 50

z = (9.9 - 9)/(2.5/√50) = 2.55

Looking at the normal distribution table, the probability corresponding to the area above the z score is 1 - 0.99461 = 0.00539

Recall, population mean is 9

The difference between sample sample mean and population mean is 9.9 - 9 = 0.9

Since the curve is symmetrical and it is a two tailed test, the x value for the left tail is 9 - 0.9 = 8.1

the x value for the right tail is 9 + 0.9 = 9.9

These means are higher and lower than the null mean. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area. We already got the area above the z score as z = 0.00539

We would double this area to include the area in the left tail of z = - 2.55. Thus

p = 0.00539 × 2 = 0.01078

Since alpha, 0.01 < 0.01078, we would reject the null hypothesis

But we are told to use the critical value approach, then

Since α = 0.01, the critical value is determined from the normal distribution table.

For the left, α/2 = 0.01/2 = 0.005

The z score for an area to the left of 0.005 is - 2.575

For the right, α/2 = 1 - 0.005 = 0.995

The z score for an area to the right of 0.995 is 2.575

In order to reject the null hypothesis, the test statistic must be smaller than - 2.575 or greater than 2.575

Since - 2.55 > - 2.575 and 2.55 < 2.575, we would reject the null hypothesis. This corresponds to our previous decision.

b) we would assume normal distribution because the sample size is sufficiently large and the population standard deviation is known.

c) Confidence interval is written in the form,

(Sample mean ± margin of error)

Since the sample size is large and the population standard deviation is known, we would use the following formula and determine the z score from the normal distribution table.

Margin of error = z × σ/√n

The z score for confidence level of 99% is 2.58

Margin of error = 2.58 × 2.5/√50 = 0.91

Confidence interval = 9.9 ± 0.91

The lower end of the confidence interval is

9.9 - 0.91 = 8.99

Therefore, p = 9 will be contained in the interval.

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3 years ago

[25 POINTS] determine whether each relation is a function. If so, provide the domain and range.​

[25 POINTS] determine whether each relation is a function. If so, provide the domain and range.