MATHEMATICS COLLEGE

Explain how to identify if the graph of a relation is a function or not

Answers

Answer 1

Answer:

Answer:

[see below]

Step-by-step explanation:

A function is a relation where one domain value is assigned to exactly one range.

An x-value in a function must not repeat.

One way to see if a graph is a function is to use a vertical line test. If the line passes trough the line twice, then it is not a function.
On a table, check the x-value column or row. If any of the numbers repeat, then it is not a function.
On a mathematical map, check to see if the arrows from a domain number points to one range value on the other side. If it points to two range numbers, then it is not a function.

Hope this helps.

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The sum of two consecutive integers is -39. List the two numbers from smallest to greatest

Answers

Answer:

-20, -19

Step-by-step explanation:

The average of the two numbers is -39/2 = -19.5. The smaller number is 0.5 less than this, -20, and the larger number is 0.5 more than -19.5, so is -19.

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Comment on the problem and solution

I find that working consecutive integer problems is often simplified by working with the average value of those integers:

the average of two consecutive odd integers is the even integer between them
the average of two consecutive even integers is the odd integer between them
the average of an odd number of integers of the same type (consecutive, consecutive odd, consecutive even) is the middle one
The average of an even number of consecutive integers is the "half" number between the middle two (as in this problem).

josh packed one layer of a rectangular prism with 15 unit cubes. The prism holds 4 layers of unit cubes. What is the volume of the rectangular prism?

Answers

The required volume of the rectangular prism is 60 cubic units,

Given that,
josh packed one layer of a rectangular prism with 15 unit cubes. The prism holds 4 layers of unit cubes.
To determine the volume of the rectangular prism.

What is volume?

Volume is defined as the ratio of the mass of an object to its density.

Here,
Dimension of the rectangular prism,
Each layer consists of 15 unit cubes,
Length of the rectangular prism = 15 units,
and consist of 4 layers,
Width = 4 * 1 = 4 units
height = 1

The volume of the rectangular prism = length * width * height
= 15 * 4 * 1
= 60 cubic units

Thus, the required volume of the rectangular prism is 60 cubic units,

Learn more about Volume here:
brainly.com/question/1578538

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Answer:60

Step-by-step explanation:

Consider a colony of E.Coli bacteria that is growing exponentially. A microbiologist finds that, initially, 1,000 bacteria are present and 50 minutes later there are 10,000 bacteria. a) Find expression for the number of bacteria Q(t) after t minutes. b) When will there be 1,000,000 bacteria?

Answers

Answer:

a) $Q(t)=Q_(0)e^((ln10/50)t)$

b) 150min

Step-by-step explanation:

a) Using the formula for colony growth $Q(t)=Q_(0)e^(kt)$ we need to find the specific value of k, to do this you'll use the time, initial and final number of colonies provided in your problem.

$Q(t)=Q_(0)e^(kt)\n\n10000=1000e^(k(50)) \n\n(10000)/(1000)=e^(50k) \n\n10=e^(50k)\n ln(10=e^(50k))\n\nln10=50k\n\nk=ln10/50\n\nQ(t)=Q_(0)e^((ln10/50)t)\n\n$

b) Once we have our expression we only have to use our final and initial number of bacteria to find t.

$Q(t)=Q_(0)e^((ln10/50)t)\n\n\n1000000=1000e^(0.046t)\n 1000=e^(0.046t)\nln( 1000=e^(0.046t))\nln1000=0.046t\nt=ln1000/0.046\nt=150 minutes$

I hope you find this information useful! good luck!

Line l passes through the points (- 4, 3) and (2, 1) What is the slope of a line that is perpendicular l

Answers

Answer:

m=1

Step-by-step explanation:

The plots (-4,3) and (2,1) have a slope of -1. Perpendicular lines would mirror that, making it a positive 1

Assume that the standard deviation of daily returns for Marcus, Inc. stock in a recent period is 1.5 percent. Furthermore, a 95 percent confidence interval is desired for the maximum loss. Daily returns are normally distributed, and the expected daily return is 0.05 percent. What is the lower boundary of the maximum expected loss

Answers

Answer:

= - 2.43%

Step-by-step explanation:

From the information given:

Since the variable (daily returns) is normally distributed, Then, using empirical rule at 95% confidence interval level, we have:

$( \mu - 1.96 \sigma \ , \ \mu + 1.96 \sigma)$

where;

The expected mean daily return $\mu = 0.05 \%$

The standard deviation $\sigma = 1.5\%$

Given that the 95% confidence interval is expected to be a maximum loss, then the probability is left-tailed which is 1.65 $\sigma$ away from the average.

Thus the distribution of the lower boundary can be computed as:

= $(0.05 - 1.65 * 1.5)\%$

= $(0.05 - 2.475)\%$

= $( - 2.425)\%$

= - 2.43%

In the past, 44% of those taking a public accounting qualifying exam have passed the exam on their first try. Latterly, the availability of exam preparation books and tutoring sessions may have improved the likelihood of an individual’s passing on his first try. In a sample of 250 recent applicants, 130 passed on their first attempt. At the 0.05 level of significance, what is the calculated value of test statistic? (Specify your answer to the 2nd decimal.)

Answers

Answer:

The calculated value of test statistic is z=2.48.

This has a P-value of P=0.00657.

If we state the null hypothesis $H_0: \pi\leq0.44$ at a significance level of $\alpha=0.05$ , we would reject this null hypothesis as $P-value<\alpha$ .

Step-by-step explanation:

We have in this problem, a hypothesis test of proportions.

The test statistic for this is the z-value, and is calculated like that:

$z=(p-\pi-0.5/N)/(\sigma)$

Where the term 0.5/N is the correction for continuity and is negative in the cases that p>π.

p: proportion of the sample; π: proportion of the population; σ: standard deviation of the population.

The standard deviation of the population has to be calculated as:

$\sigma=\sqrt{(\pi(1-\pi))/(N) } =\sqrt{(0.44(1-0.44))/(250) }=√(0.0009856)=0.0314$

The proportion of the sample (p) is $p=130/250=0.52$ .

Then, the test statistic z is

$z=(p-\pi-0.5/N)/(\sigma)=(0.52-0.44-0.5/250)/(0.0314) =(0.078)/(0.0314) =2.48$

The P-value of this statistic is P(z>2.48)=0.00657

If we state the null hypothesis $H_0: \pi\leq0.44$ at a significance level of $\alpha=0.05$ , we would reject this null hypothesis as $P-value<\alpha$ .

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