1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
nevsk [136]
3 years ago
10

Let D = {x| x is a student} be the domain, and let ƒ(x) = “date of birth” be the possible function. Determine if the relation is

an example of a function. Yes, ƒ is a function. No, ƒ is not a function.
Mathematics
1 answer:
Ugo [173]3 years ago
3 0
Remember that a function is a special type of relation in which each element of the domain is paired with only one element in the range; in other words for each D value, there is only a f(x) value.

Since D = {x| x is a student}, the domain of the relation is the set of all students; on the other hand, <span>ƒ(x) = “date of birth”, so the range of the relation is the set of the birth dates of the students. Since in a room of 23 people there is a 50% chance of two people sharing the same date of birth, it is inevitable that in the set of all the students there is at least two students that share the same date of bird; therefore two elements in the domain will be paired with the same element in the range. Given that, We can conclude that the relation is not a function.
</span>
You might be interested in
Which theorem can you use to prove that AAEB is congruent to ACED?
sleet_krkn [62]
I don’t no sorry bye
6 0
3 years ago
Read 2 more answers
Antoine and Adriane are each at the top of a Ferris wheelAfter one revolution each will again be at the topWhich sinusoid (sine
Valentin [98]

Answer(s):

\displaystyle y = 100sin\:(\frac{\pi}{50}x + \frac{\pi}{2}) + 100 \\ y = 100cos\:\frac{\pi}{50}x + 100

Step-by-step explanation:

\displaystyle y = Asin(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 100 \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \hookrightarrow \boxed{-25} \hookrightarrow \frac{-\frac{\pi}{2}}{\frac{\pi}{50}} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{100} \hookrightarrow \frac{2}{\frac{\pi}{50}}\pi \\ Amplitude \hookrightarrow 100

<em>OR</em>

\displaystyle y = Acos(Bx - C) + D \\ \\ Vertical\:Shift \hookrightarrow D \\ Horisontal\:[Phase]\:Shift \hookrightarrow \frac{C}{B} \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \\ Amplitude \hookrightarrow |A| \\ \\ Vertical\:Shift \hookrightarrow 100 \\ Horisontal\:[Phase]\:Shift \hookrightarrow 0 \\ Wavelength\:[Period] \hookrightarrow \frac{2}{B}\pi \hookrightarrow \boxed{100} \hookrightarrow \frac{2}{\frac{\pi}{50}}\pi \\ Amplitude \hookrightarrow 100

You will need the above information to help you interpret the graph. First off, keep in mind that although this looks EXACTLY like the cosine graph, if you plan on writing your equation as a function of <em>sine</em>, then by all means, go for it, but be careful and follow what is explained here. Now, as you can see, the photograph on the right displays the trigonometric graph of \displaystyle y = 100sin\:\frac{\pi}{50}x + 100, in which you need to replase "cosine" with "sine", then figure out the appropriate C-term that will make the graph horisontally shift and map onto the <em>co</em><em>sine</em> graph [photograph on the left], accourding to the <u>horisontal shift formula above</u>. Also keep in mind that the −C gives you the OPPOCITE TERMS OF WHAT THEY <em>REALLY</em> ARE, so you must be careful with your calculations. So, between the two photographs, we can tell that the <em>sine</em> graph [photograph on the right] is shifted \displaystyle 25\:unitsto the right, which means that in order to match the <em>cosine</em> graph [photograph on the left], we need to shift the graph BACKWARD \displaystyle 25\:units,which means the C-term will be negative, and by perfourming your calculations, you will arrive at \displaystyle \boxed{-25} = \frac{-\frac{\pi}{2}}{\frac{\pi}{50}}.So, the sine graph of the cosine graph, accourding to the horisontal shift, is \displaystyle y = 100sin\:(\frac{\pi}{50}x + \frac{\pi}{2}) + 100.Now, with all that being said, in this case, sinse you ONLY have a graph to wourk with, you MUST figure the period out by using wavelengths. So, looking at where the graph hits \displaystyle [220, 100],from there to \displaystyle [120, 100],they are obviously \displaystyle 100\:unitsapart, telling you that the period of the graph is \displaystyle 100.Now, the amplitude is obvious to figure out because it is the A-term, but of cource, if you want to be certain it is the amplitude, look at the graph to see how low and high each crest extends beyond the <em>midline</em>. The midline is the centre of your graph, also known as the vertical shift, which in this case the centre is at \displaystyle y = 100,in which each crest is extended <em>one hundred units</em> beyond the midline, hence, your amplitude. So, no matter how far the graph shifts vertically, the midline will ALWAYS follow.

**I knew exactly what you were talking about the moment you posted this, so here was what you were looking for. It really does not matter which sinusoid and person you select because you will get the same information either way.

I am delighted to assist you at any time.

6 0
2 years ago
The director of health services is concerned about a possible flu outbreak at her college.
Anna [14]
"Given that he is male" is an important phrase here. The "given" in any probability problem is often important. This tells us "only focus on the males" because we know 100% that whoever we picked, the person is a male. 

So we only focus on the "male" column. Use a highlighter to mark this column or cover up the other values if they are too distracting. There are 51 males total (bottom row) and 39 males had a flu shot (top row)

Divide the two values: 39/51 = (13*3)/(17*3) = 13/17

Answer: 13/17
5 0
3 years ago
Read 2 more answers
Evaluate the double integral.
Fynjy0 [20]

Answer:

\iint_D 8y^2 \ dA = \dfrac{88}{3}

Step-by-step explanation:

The equation of the line through the point (x_o,y_o) & (x_1,y_1) can be represented by:

y-y_o = m(x - x_o)

Making m the subject;

m = \dfrac{y_1 - y_0}{x_1-x_0}

∴

we need to carry out the equation of the line through (0,1) and (1,2)

i.e

y - 1 = m(x - 0)

y - 1 = mx

where;

m= \dfrac{2-1}{1-0}

m = 1

Thus;

y - 1 = (1)x

y - 1 = x ---- (1)

The equation of the line through (1,2) & (4,1) is:

y -2 = m (x - 1)

where;

m = \dfrac{1-2}{4-1}

m = \dfrac{-1}{3}

∴

y-2 = -\dfrac{1}{3}(x-1)

-3(y-2) = x - 1

-3y + 6 = x - 1

x = -3y + 7

Thus: for equation of two lines

x = y - 1

x = -3y + 7

i.e.

y - 1 = -3y + 7

y + 3y = 1 + 7

4y = 8

y = 2

Now, y ranges from 1 → 2 & x ranges from y - 1 to -3y + 7

∴

\iint_D 8y^2 \ dA = \int^2_1 \int ^{-3y+7}_{y-1} \ 8y^2 \ dxdy

\iint_D 8y^2 \ dA =8 \int^2_1 \int ^{-3y+7}_{y-1} \ y^2 \ dxdy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( \int^{-3y+7}_{y-1} \ dx \bigg)   dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( [xy^2]^{-3y+7}_{y-1} \bigg ) \ dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( [y^2(-3y+7-y+1)]\bigg ) \ dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ([y^2(-4y+8)] \bigg ) \ dy

\iint_D 8y^2 \ dA =8 \int^2_1  \bigg ( -4y^3+8y^2 \bigg ) \ dy

\iint_D 8y^2 \ dA =8 \bigg [\dfrac{ -4y^4}{4}+\dfrac{8y^3}{3} \bigg ]^2_1

\iint_D 8y^2 \ dA =8 \bigg [ -y^4+\dfrac{8y^3}{3} \bigg ]^2_1

\iint_D 8y^2 \ dA =8 \bigg [ -2^4+\dfrac{8(2)^3}{3} + 1^4- \dfrac{8\times (1)^3}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [ -16+\dfrac{64}{3} + 1- \dfrac{8}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{64-8}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [ -15+ \dfrac{56}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [  \dfrac{-45+56}{3}\bigg]

\iint_D 8y^2 \ dA =8 \bigg [  \dfrac{11}{3}\bigg]

\iint_D 8y^2 \ dA = \dfrac{88}{3}

4 0
2 years ago
A scuba diver descends 80 feet, rises 25 feet, descends 12 feet, and then
cluponka [151]

Answer: That would be 15ft

3 0
3 years ago
Other questions:
  • im too lazy to answer my sister questions (its easy but I got something else to do) do all multiplication all way to 12
    14·2 answers
  • Brianna took out a car loan for $12,250 that has a 0% APR for the first 20 months and will be paid off with monthly payments ove
    12·2 answers
  • Joe's taxable income is $67,825. Use this tax schedule to calculate the total amount he owes in taxes.1. $8,993.752. $13,380.003
    14·2 answers
  • Point A is located in which quadrant ?
    8·1 answer
  • If (x, 1/100) lies on the graph of y = 10, then x =<br> 2<br> -1/2<br> 0-2
    12·1 answer
  • Four and one sixth divided by five
    11·1 answer
  • Mrs. Adams buys 4 bananas and 6 apples. Tell which ratio statement is true
    15·2 answers
  • Identify the domain of the function shown in the graph.
    5·1 answer
  • What must be Subtracted from the product of 25 and 23 to equal 275
    9·1 answer
  • (a) Laura owns 6 shares of a certain stock. Yesterday the total value of her shares went down by
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!