A relation is a set of numbers that have a relationship through the use of a domain and a range, while a function is a relation that has a specific set of numbers that causes there to be only be one range of numbers for each domain of numbers. All functions are relations, but all relations are not functions.
Given two sets [tex] A [/tex] and [tex] B [/tex], the "starting" set is called the domain, while the "landing" set is called the codomain.
With that being said, a relation is any way you can associate any number of elements in the domain with every number of elements in the codomain.
A function has more restriction: you can associate one and only one output for every input.
If you visualize this with arrows linking domain and codomain, in order for a relation to be a function, only one arrow can start from each point in the domain.
The domain is thus the set of elements from whence an arrow starts. The range is the subset of the codomain, given by the elements that are reached by at least one arrow.
How many combinations exist of the letters w, x, y, z, taking two at a time?
The binomial coefficient
[tex] \displaystyle \binom{4}{2} = \dfrac{4!}{2!(4-2)!} = \dfrac{4\cdot 3}{2} = 2\cdot 3 = 6 [/tex]
Tells you that there are 6 ways of choosing a subset of two letters from the four given letters.
For each of these subsets there are two combinations (you can interchange the two letters: say that you choose the subset wz, you have the two combinations wz and zw)
So, there is a total of 12 combinations of the letters w, x, y, z, taking two at a time.
There are 6 ways of choosing a subset of two letters from the four given letters.
What is a combination?The arrangement of the different things or numbers in a number of ways is called the combination.
For each of these subsets there are two combinations (you can interchange the two letters: say that you choose the subset wz, you have the two combinations wz and zw)
So, there is a total of 6 combinations of the letters w, x, y, z, taking two at a time.
The combination will be calculated as:-
[tex]^4C_2=\dfrac{4!}{2!(4-2)!}[/tex]
[tex]^4C_2=\dfrac{4\times 3}{2}[/tex]
[tex]^4C_2=6[/tex]
Therefore there are 6 ways of choosing a subset of two letters from the four given letters.
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What is the next term in the pattern shown below? 4.5, 9, 13.5, 18
22.5
note that the difference (d ) between each term is
d = 9 - 4.5 = 13.5 - 9 = 18 - 13.5 = 4.5
to obtain the next term add 4.5
next term = 18 + 4.5 = 22.5
The next term in the pattern is 22.5.
To find the next term in the pattern, it's essential to identify the underlying rule or mathematical operation that governs the progression of the given numbers.
In this case, we can observe that the sequence is increasing by a consistent difference of 4.5 between each consecutive term.
Starting from 4.5 and adding 4.5 successively, we get:
4.5 + 4.5 = 9
9 + 4.5 = 13.5
13.5 + 4.5 = 18
The next term would be:
18 + 4.5 = 22.5
So, the next term in the pattern is 22.5.
In this sequence, each term is obtained by adding 4.5 to the previous term, resulting in an arithmetic progression.
If you continue this pattern, you will keep adding 4.5 to each subsequent term to find the following numbers in the sequence.
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On the moon, the time, in seconds, it takes for an object to fall a distance, d, in feet, is given by the function f(d) = 1.11√d. Part a: determine f(2) and explain what it represents.
Answer:
The value of f(2)≈1.57
The time it takes an object to fall 2 feet is 1.57 seconds.
Step-by-step explanation:
Consider the provided function.
[tex]f(d) = 1.11\sqrt{d}[/tex]
It takes for an object to fall a distance, d, in feet,
We need to determine f(2).
Substitute the value d = 2 in the above function.
[tex]f(2) = 1.11\sqrt{2}[/tex]
[tex]f(2)\approx 1.57[/tex]
The value of f(2)≈1.57
The time it takes an object to fall 2 feet is 1.57 seconds.
Please help .!!!!!!!!!!!!!!!!!!!
((V/π)(3/4))1/3 = R so I would say possibly the second one
Circumference of a circle with diameter of 12.5 feet??
What are the domain and range of the function f(x) = -3 (x-5)^2 + 4?
Domain=all real numbers
Range is x≤4
Hope this helps :)
31 points for the right answer if you DON'T KNOW Skip pass this
Substitute x = 2 into each of the expressions
left: 6* 8 - 2(2) = 48 - 4 = 44
right: 6(5 +2) = 6(7) = 42
44 > 42
Answer
>
Four times a number increased by six is the same as seven times the number.
Call that number x.
Then rewrite as equation:
4x+6=7x
solve for x
6=3x
2=x
So the number is 2.
Check that 2 is the number by following the original wording, mentally.
Hey there!!
Let's take the number as 'x'
4 times the number is 4x
This is increased by 6
We will have to add 6.
... 4x + 6
7 times a number is 7x
... 7x
Both these values are equal.
Hence,
... 4x + 6 = 7x
... 6 = 3x
... x = 2
Hence, the number is 2.
HELP ASAP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!
chose the pieces with no symmetry
The answer would be the bottom left. You can't fold it in half and have it match up with the other side.
PLEASE HELP WILL GIVE BRAINLIEST, THANKS, AND RATE 5 STARS!!!
First answer, this is because if you were to substitute the x and y variables which are the height and days the plant grew, then the 1st answer would be the answer
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Simplify: 12 + 10i +14i
Simplify: 12 + 10i +14i = 12 +24i
answer
B) 12 +24i
24i+12 thats pretty basic though
Leticia Cox is a biochemist. She is testing two different types of drugs that induce cell growth. She has selected two cultures of 1000 cells each. To culture A, she administers a drug that raises the number of cells by 200 each day and every day thereafter. Culture B gets a drug that increases cell growth by 8% each day and every day thereafter. Assuming no cells die, how many cells will have grown in each culture by the end of the seventh day? a. Culture A: 1400 cells Culture B: 713 cells c. Culture A: 713 cells Culture B: 1400 cells b. Culture A: 800 cells Culture B: 517 cells d. Culture A: 517 cells Culture B: 800 cells
1. Culture A.
Since the number of cells increases by 200 each day and every day thereafter, then after seven days the number of cells will increase by
[tex]200\cdot 7=1,400.[/tex]
2. Culture B.
The initial number of cells was 1,000. Since the number of cells increases 8% each day and every day thereafter, then after seven days the number of cells will be
[tex]1,000\cdot (1.08)^7\approx 1,713.[/tex]
The number of cells that have grown by the end of the seventh day is
1,713-1,000=713.
Answer: option A -- Culture A: 1400 cells Culture B: 713 cells
Answer:
A is correct: Culture A: 1400 cells
Culture B: 713 cells
Step-by-step explanation:
Correct on Edge 2020 Quiz
To determine when the coin will be worth $150, you can substitute 150 for y and solve for t. What value do you get for t when you do that?
Answer:
5.23 years, the time at which the coin has increased in value to $150.
Step-by-step explanation:
Use the exponential function f(t) = 4*2^t.
Substitute $150 for f(t): $150 = 4*2^t.
Simplify this by dividing both sides by 4: $150/4 = 2^t, or $37.50 = 2^t.
Next, solve for the value of t. To do this, take the common log of both sides, obtaining:
log 37.50 = t*log 2. Thus, t = [log 37.50] / [log 2]. Evaluate this using a calculator:
t = 1.57403 / 0.30103 = 5.23 time units. For example, this could be 5.23 years.
Answer:
It will take about 17.7 years, or almost 18 years, for the coin to be worth $150.
Because the initial year was 2016, the coin is predicted to be worth $150 in 2034.
Step-by-step explanation:
What is the function rule for the line?
Choices are in the screenshot! I'd appreciate the help! :)
Answer:its correct got a 100
Step-by-step explanation:
Paulo took out a $900 loan using an 12% simple interest rate for a period of 9 months. What the effective annual interest rate for the loan? Give your answer as a percentage to the nearest tenth of a percent.
Answer:
12.68%
Step-by-step explanation:
To calculate effective annual interest rate we need to use the following formula:
[tex]i=(1+\frac{r}{m})^m-1[/tex]
Where, 'i' is the effective annual interest rate
'r' is the annual rate of interest
'm' is the frequency of compounding.
When there is continuous compounding the effective annual rate uses the following formula:
[tex]i=e^r-1[/tex]
In our case we would are assume that there is continuous compounding since no information regarding the frequency of compounding is given:
Plugging r=12%=0.12, we get:
[tex]i=e^{0.12}-1[/tex]
[tex]i=1.1274-1=0.1274[/tex]
[tex]i=0.1274[/tex]
[tex]i=12.74\%[/tex]
Therefore, the effective annual interest rate is 12.74%.
Answer:
13.2
Step-by-step explanation:
The graph represents a person’s heart rate in beats per minute during 30 minutes of exercise. Which statement best describes the relationship between heart rate and time during exercise? The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes. The heart rate decreases for 6 minutes, remains constant for 19 minutes, and then gradually increases for 5 minutes. The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes. The heart rate remains constant for 6 minutes, increases for 19 minutes, and then gradually decreases for 5 minutes.
We know that
when we start exercise our hear beats starts increasing gradually
because blood flowing rate becomes higher
and it keeps increasing upto a certain limit
because for normal human beings maximum heart rate is 135 beats per minute
and it remains constant there for few minutes
and as we slow down slowly
It will start decreasing gradually and then becomes normal
we can see the graph
so,
The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes..........Answer
Answer:The heart rate increases for 6 minutes, remains constant for 19 minutes, and then gradually decreases for 5 minutes. Positive
Step-by-step explanation:
F (x) = -7x^2 g(x)=-35x^2+5
What transformations change the graph of f(x) to the graph of g(x)?
A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/5 and translated down 5 units.
B. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 5
and translated down 5 units.
C.The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/5
and translated up 5 units.
D. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 5
and translated up 5 units.
Answer:
D
Step-by-step explanation:
hello!!! the correct answer for this problem is D
Answer:
D. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 5
and translated up 5 units.
Step-by-step explanation:
Why do you think the AA Similarity Postulate is introduced as a postulate and not a theorem?
What would be the correct answer for my question, 25 divided by 715. I need an answer as soon as possible
What shows the correct substitution of the values a,b, and c from the equation 0=-3x^2-2x+6
When dealing with a quadratic equation, you usually assign the following name to the coefficients of the variables:
[tex] ax^2+bx+c=0 [/tex]
So, [tex] a [/tex] is the coefficient of [tex] x^2 [/tex], [tex] b [/tex] is the coefficient of [tex] x [/tex] and [tex] c [/tex] is the constant term.
In your case, the coefficient of [tex] x^2 [/tex] is -3, so [tex] a=-3 [/tex]
The coefficient of [tex] x [/tex] is -2, so [tex] b = -2 [/tex]
The constant term is 6, so [tex] c = 6 [/tex]
A group of hikers walks 2 miles east and then 1 mile north. After taking a break, they then hike 4 miles east to their final destination. What vector describes their hike from their starting position to their final destination? Let 1 unit represent 1 mile.
Answer:
Intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction
Step-by-step explanation:
Required vector is consists of the two components
vx= 2+4=6 units and vy= 1 unit and vx ⊥ vy
We will use Pythagorian theorem to find intensity of the vector v
v∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 units
The angle ∡α between vector and east direction we wil find with tanα
tanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°
Good luck!!!
Answer:
The vector that describes their hike from their starting position to their final destination is < 6, 1 >
Please help!!! Important!!!! Sister needs help!!!!
Answer,
14Explanation,
All you need to do is simplify,
15 - (-3) -4 = ?
15 - (-3) = 18
18 - 4 = 14
Hope this helps :-)
Drag a statement or reason to each box to complete this proof.
Answer:
The required answer is shown below:
Step-by-step explanation:
Consider the provided equation.
Statement Reason
1. [tex]5(x+6)=x+38[/tex] Given
2. [tex]\bold{5x+30=x+38}[/tex] Distributive property
3. [tex]5x+30-30=x+38-30[/tex] Subtraction property of equality
4. [tex]\bold{5x=x+8}[/tex] Simplifying
5. [tex]\bold{5x-x=x+8-x}[/tex] Subtraction property of equality
6. [tex]\bold{4x=8}[/tex] Simplifying
7. [tex]\frac{4x}{4}=\frac{8}{4}[/tex] Division property of equality
8. [tex]x=2[/tex] Simplifying
Hence the required answer is shown above.
Dr. Jimenez found that after applying an antibiotic to bacteria, he observed only 90% of the bacteria left in the culture dish each hour. If the initial bacteria count was 100, what was the bacteria count after 5 hours? Round to the nearest whole number.
There were ___ bacteria after 5 hours.
The complete statement is:
There were 59 bacteria after 5 hours
The initial population of the bacteria is given as:
[tex]a =100[/tex]
The proportion left after each hour is given as:
[tex]b = 90\%[/tex]
An exponential function is represented as:
[tex]f(x) = ab^x[/tex]
Substitute values for (a) and (b)
[tex]f(x) = 100 \times (90\%)^x[/tex]
Express percentage as decimal
[tex]f(x) = 100 \times (0.9)^x[/tex]
After 5 hours, the value of x is 5
i.e. x = 5
So, we have:
[tex]f(x) = 100 \times (0.9)^5[/tex]
Evaluate the exponent
[tex]f(x) = 100 \times 0.59049[/tex]
Multiply
[tex]f(x) = 59.049[/tex]
Approximate
[tex]f(x) = 59[/tex]
Hence, there were 59 bacteria after 5 hours
Read more about exponential population function at:
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below is the graph of f(x)= ln (x) how would you describe the graph of g (x) = 1/3 ln (x)
Graph of f(x)=ln(x) is missing but we can still answer this problem.
We just have to explain about what will happen if f(x)=ln(x) changes into g(x)=1/3 ln(x)
To find that compare both functions.
We see that ln(x) gets multiplied by 1/3 to produce graph of 1/3ln(x)
there multiplifaction factor 1/3 lies between 0 and 1.
Hence graph of f(x) will compress vertically by factor of 1/3 to produce graph of g(x).
So for the final answer we will write f(x) compress vertically by factor of 1/3 to produce graph of g(x)=1/3 ln(x)
You can check attached file for more related rules
Answer:
compress vertically by factor of 1/3 to produce graph of g(x)=1/3 ln(x)
Step-by-step explanation:
A mouse scurries across your kitchen floor at 2.0 feet per second. How many miles can the mouse travel in 1.5 hours (rounded to the nearest tenth)?
Answer: The mouse can travel 2.045 miles .
Step-by-step explanation:
Speed of mouse = 2.0 feet per second.
Time traveled by mouse = 1.5 hours = 1.5 × 3600 seconds [ as 1 hour = 3600 seconds]
Distance traveled by mouse in 1.5 hours = speed × time
= 2.0 × 1.5 × 3600 = 10800 feet.
We know that
1 mile = 5280 feet
then 1 foot = 1/5280 miles
Distance in miles = [tex]10800\times \frac{1}{5280} miles=2.045miles[/tex]
Given
A mouse scurries across your kitchen floor at 2.0 feet per second.
Find out the mouse travel in 1.5 hours.
To proof
FORMULA
Distance = speed × time
[tex]1foot = \frac{1}{5280} miles[/tex]
Convert feet per second into miles per second
[tex]= \frac{2.0}{5280}[/tex]
As given in the question
Time = 1.5 hours
1 hours = 3600 second
Time convert in the second
Time = 1.5 × 3600 second
= 5400 second
put all these value in the above formula
we get
[tex]Distance= \frac{2.0\times 1.5 \times 3600}{5280}[/tex]
[tex]Distance= \frac{10800}{5280}[/tex]
= 2.04 (approx) miles
= 2.0 miles
Hence proved
Which equation represents a direct linear variation?
direct linear variation is a straight line in which the y intercept is 0
a- wrong because it is quadratic, not linear.
b- correct, linear with a y intercept of 0
c- wrong because its exponential
d- wrong, its linear but the y intercept is 3, not 0
I'd appreciate it if anyone could help! :)
Which graph represents the function?
Answer: Upper right corner
=========================================================
How I got that answer:
The line y = x goes through (0,0) and (1,1). You would normally extend this line out as far as you can in both directions. However, the inequality x < -1 says you can only graph this if x is less than -1. We will not graph any part of the graph that is beyond x = -1 to the right. So we only have a small piece of it. The left piece of y = x. There is an open hole at the endpoint.
Similarly, y = -x is only graphed if x >= -1. We have a closed endpoint here. This graph goes through (0,0) and (1,-1). We erase the portion that is to the left of x = -1.
Doing all this leads to the upper right corner choice as our answer. The bottom right corner is close to the answer, but the open and closed endpoints are in the wrong spots.
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
An on-line electronics store must sell at least $5000 worth of computers and printers per day. Each printer costs $350 and each computer costs $750. The store can ship a maximum of 20 items per day. Which system of inequalities models correctly the number of computers, c, and number printers, p, the store could sell per day?
"An on-line electronics store must sell at least $5000 worth of computers and printers per day"
The bold faced words tell us greater than or equal to 5000
"The store can ship a maximum of 20 items per day"
The bold faced words tell us less than or equal to 20
We can automatically eliminate A and B since they don't have EQUAL sign in them. From C and D, we choose D because it correctly attaches the price of printers and computers to the respective variables (printers is p & computers is q). Choice C does this wrong!
ANSWER: D
Which statement is true?Which statement is true? The value of money that you save increases over time the value of money remains constant over time the present value of money is greater than its future value
The value of money that you save increases over time is the right answer