Which of the relations given by the following sets of ordered pairs is a function? { ( 1 , 2 ) , ( - 4 , 8 ) , ( - 3 , 5 ) , ( 1 , - 2 ) , ( 7 , 12 ) } { ( 5 , 4 ) , ( 5 , 6 ) , ( 5 , 8 ) , ( 5 , 10 ) , ( 5 , 12 ) } { ( 5 , 4 ) , ( 4 , 3 ) , ( 3 , 2 ) , ( 4 , 5 ) , ( 2 , 1 ) } { ( 6 , 1 ) , ( - 3 , 1 ) , ( 3 , 5 ) , ( 2 , 4 ) , ( - 1 , 2 ) }
Answers
The relation that represents a function is:
{ ( 6 , 1 ) , ( - 3 , 1 ) , ( 3 , 5 ) , ( 2 , 4 ) , ( - 1 , 2 ) }
Which of the given relations is a function?Remember that a relation maps elements from one set into elements from another set.
If the relation is defined by a set of ordered pairs like:
{(x₁, y₁), (x₂, y₂), (x₃, y₃)}
It means that the mappings are:
x₁⇒ y₁
x₂ ⇒ y₂
x₃ ⇒ y₃
A relation is a function if each of the inputs (values of x) is mapped into only one value of y.
Then we can see that:
{ ( 1 , 2 ) , ( - 4 , 8 ) , ( - 3 , 5 ) , ( 1 , - 2 ) , ( 7 , 12 ) }
Is not a function, because the input x = 1 is mapped into two different values, y = 2 and y = -2
The one that is a function is:
{ ( 6 , 1 ) , ( - 3 , 1 ) , ( 3 , 5 ) , ( 2 , 4 ) , ( - 1 , 2 ) }
Where each input appears once.
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Related Questions
Find the measure of angle AEB
Answers
Answer:
∠ AEB = 114°
Step-by-step explanation:
the chord- chord angle AEB is half the sum of the measures of the arcs intercepted by the angle and its vertical angle , that is
∠ AEB = \(\frac{1}{2}\) (AB + CD) = \(\frac{1}{2}\) (140 + 88)° = \(\frac{1}{2}\) × 228° = 114°
30. When the polynomial f(x) = (p-1)x³ + px² + qx +r, where p, q and r are constants, is divided by (x + 2) and (x - 1), the remainders are - 5 and 4 respectively. If (x + 1) is a factor of f(x), find the values of p, q and r. Hence, factorize f(x) completely.
Answers
Answer:
Step-by-step explanation:
Using the remainder theorem we get:
\(f(-2)=-5\), \(f(1)=4\), and \(f(-1)=0\)
So we get
\(f(-2)=(-8)(p-1)+4p-2q+r=-5\)
\(-8p+8+4p-2q+r=-5\)
\(-4p-2q+r=-13\) \((a)\)
\(f(1)=(p-1)+p+q+r=4\)
\(2p+q+r=5\) \((b)\)
\(f(-1)=-(p-1)+p-q+r=0\)
\(-q+r=-1\) \((c)\)
We need to solve (a), (b) and (c) simultaneously to find p,q, and r.
from \((c)\) \(r=q-1\). Sub this into (a) and (b):
\(-4p-2q+(q-1)=-13 \rightarrow -4p-q=-12\) \((d)\)
\(2p+q+(q-1)=5 \rightarrow q=3-p\) \((e)\)
Sub (e) into (d) we get
\(-4p-(3-p)=-12 \rightarrow p=3\)
Sub \(p=3\) into \((e) \rightarrow q=0\)
Sub \(p=3,q=0\) into \((c) \rightarrow r=-1\)
SOLUTION: \(p=3,q=0,r=-1\)
So \(f(x)=2x^3+3x^2-1\)
by dividing (x+1) into f(x) we get (I am not showing working for this division)
\(f(x)=(x+1)(2x^2+x-1)\)
\(\rightarrow f(x)=(x+1)(2x-1)(x+1)\)
Students at two high schools were asked about their plans after graduation. The table displays the results for 300 students at Henderson High School. The bar graph displays the results for 300 students at Johnson High School. Which Statement about the results from Henderson High School and johnson high school must be true?
Answers
Armed force and other for Henderson high school is greater than
Johnson High School.
The mode for each school is college.
Options F and G are the correct answer.
We have,
The number of students in Henderson High School.
Work = 96
College = 114
Armed forced = 48
Other = 42
The number of students in Johnson High School.
Work = 30
College = 40
Armed forced = 15
Other = 15
From the information,
The number of students in Work for Henderson High School is greater than Johnson High School.
Now,
Henderson High School:
Armed force and other = 48 + 42 = 90
Mode = college
Johnson High School.
Armed force and other = 15 + 15 = 30
Mode = college
Thus,
Armed force and other for Henderson high school is greater than
Johnson High School.
The mode for each school is college.
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evaluate in the following expression when x = 4 and y = 5
Answers
3.8
14.83
19.58
23.5
Sally has 2 cats and each cat eats of a tin of cat food each day.
Sally buys 7 tins of cat food.
For how many days will the cat food feed her 2 cats?
You must show your working.
days=?
Answers
Answer:
Step-by-step explanation:
9 tins of cat food feed her 2 cats for 18 days
Step-by-step explanation:
Sally has 2 cats
food eaten by 1 cat each day =
food eaten by 2 cat each day= tins
sally buys 9 tins of cat food
then
tins required in = 1 day
1 tin required in
i.e 1 tin required in 2 days
9 tin required for = 9×2 = 18 days
hence , 9 tins of cat food feed her 2 cats for 18 days
#Learn more :
Sue has 2 cats. Each cat eats 1/4 tin of food each day. Sue buys 8 tine of cat food. Has sue got enough cat food to feed her 2 cats for 14 days?
7 tins of cat food = 3 1/2 days
12
a + 5
18
Find the value of a.
A. 3
B. 5
C. 8
D. 11
Answers
What's the question asking? 12a+15(18)?
Answer:
the answer is 3
Step-by-step explanation:
can someone please help me
50 points
Answers
Answer:.
Step-by-step explanation im not sure
Answer:
Step-by-step explanation:
47.) sin20 = 6/b
b = 6(sin20) = 17.5
c = √6²+17.5² = 18.5
48.) tan61 = y/18
y = 18(tan61) = 32.5
z = √18²+32.5² = 37.1
49.) r = √25²+23² = 34
50). d = √30²+7² = 30.8
51.) sin71 = j/19
j = 19(sin71) = 18
k = √19²-18² = 6.2
52.) y = √4²-1² = √7 = 2.6
53.) sin49 = f/26
f = 26(sin49) = 19.6
h = √26²-19.6² = 17
54.) t = √7²+4² = 8.1
g a study based on the association primate ebmarah looked at the average age a baby gorilla leaves it's mother versus the average age a human baby leaves it's mother. naturally they are different, so we don't want a hypothesis test. instead, find an 86% confidence interval for the difference in age to leave mother.
Answers
An 86% confidence interval for the difference in age to leave mother is -3.10091
What is confidence Interval?
The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
Given, Gorilla Baby sample
x means x bar here so, \(x_{1}\) = 3.21
\(s_{1}\) = 0.81
\(n_{1}\) = 64
Human Baby sample
x means x bar here so, \(x_{2}\) = 19.1
\(s_{2}\) = 2.16
\(n_{2}\) = 200
Confidence interval needs t score
t score = 1.18
86% confidence interval = \(x_{1}\) - \(x_{2}\) ± tc \(\sqrt{s^{2} {1} / n_{2} + s^{2} {2} / n_{2}\)
= 3.21 - 19.1 ± 1.18 √0.81²/64 +2.16²/200
= 3.21 - 19.1 ± 1.18 √0.033
= -3.10091
An 86% confidence interval for the difference in age to leave mother is -3.10091
The detail question is here,
A study based on the Association primate Ebmarah looked at the average age a baby gorilla leaves it’s mother versus the average age the human baby leaves it’s mother . Naturally they are different , so we don’t want a hypothesis test. Instead, find an 86% confidence interval for the difference in age to leave mother.
Gorilla:
Sampled 64 babies
Stayed with mother on average 3.21 years
Standard deviation: 0.81
Human:
Sampled 200 babies
Stayed with mother on average 19.1 years
Standard deviation: 2.16
Matched pairs standard deviation :0.23
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An electrical panel has five switches. How many ways can the switches be positioned up or down if three switches must be up and two must be down
Answers
Answer:
10
Step-by-step explanation:
use permutations with repetitions formula
An Internet company located in Southern California has season tickets to the Los Angeles Lakers basketball games. The company president always invites one of the seven vice presidents to attend games with him, and claims he selects the person to attend at random. One of the seven vice presidents has not been invited to attend any of the last four Lakers home games. What is the likelihood this could be due to chance
Answers
Answer:
0.5398
Step-by-step explanation:
Given that :
Total possible numbers vice presidents invited = 7
Required number of vice presidents invited = 1
Probability that a certain vice president is invited ;
P(a certain V. P is invited) = required outcome / Total possible outcomes
P(a certain V. P is invited) = 1/ 7
P(1 of the V. P's hasn't been invited to attend any of the last 4 games)
Then ; it means any of the remaining (7 - 1) = 6 has been invited ;
Hence,
P(1 of the V. P's hasn't been invited to attend any of the last 4 games) = ((7-1) / 7)^4
Likelihood that it could be due to chance :
(6/7)^4 = 0.5397750
= 0.5398
The point P=(1/2,y)lies on the unit circle shown below. What is the value of y in simplest form?
Answers
The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.
To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.
Plugging in the coordinates of the point P = (1/2, y), we get:
(1/2)^2 + y^2 = 1
1/4 + y^2 = 1
y^2 = 1 - 1/4
y^2 = 3/4.
To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).
Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.
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A population of rabbits is described by the function R(t) = 100(2t/5), where t is measured in months and R is measured in rabbits. Create a clear and properly labeled graph of R(t) on the domain 0 ≤ t ≤ 15 months.
Required:
a. Find ΔR on [1,2].
b. Find R(0).
c. Find R(10)
d. When will the population be 500 rabbits?
Answers
Answer and Step-by-step explanation: The graph is shown in the attachment.
a. ΔR on [1,2] is mathematically expressed as:
ΔR = R(2) - R(1)
which means difference of population of rabbits after 2 months and after 1 month.
\(R(1) = 100(\frac{2}{5}.1 )\)
\(R(1) = 100(\frac{2}{5} )\)
R(2) = \(100(\frac{2}{5}.2 )\)
\(R(2) = 100(\frac{4}{5} )\)
\(\Delta R = 100(\frac{4}{5} )-100(\frac{2}{5} )\)
\(\Delta R = 100[\frac{4}{5} - \frac{2}{5} ]\)
\(\Delta R=\) 40
Difference of rabbits between first and second months is 40.
b. R(0) = 100(\(\frac{2}{5} .0\))
R(0) = 0
Initially, there no rabbits in the population.
c. R(10) = \(100(\frac{2}{5}.10 )\)
R(10) = 400
In 10 months, there will be 400 rabbits.
d. R(t) = 500
\(500=100(\frac{2}{5}.t )\)
\(\frac{500}{100}=\frac{2}{5}.t\)
\(t = \frac{500.5}{100.2}\)
t = 12.5
In 12 and half months, population of rabbits will be 500.
ABC and △XYZ are similar. Find the missing side length. A B C X Y Z 4 8 ? 42 24 48 (The triangles are not drawn to scale.)
Answers
The missing side length of triangle XYZ is 7.
Given,
Triangle ABC and triangle XYZ are similar.
Triangle ABC;Length of AB = 4
Length of BC = 8
Length of AC = x
Triangle XYZ;Length of XY = 24
Length of YZ = 48
Length of XZ = 42
We have to find the missing length x.
Here,
Triangle ABC and triangle XYZ are similar.
So,
AB : XY = BC : YZ = AC : XZ
Then,
Take AB : XY = AC : XZ
= 4 : 24 = x : 42
= 4 × 42 = 24x
x = 4 × 42 / 24
x = 42/6
x = 7
That is,
The missing side length of triangle XYZ is 7.
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Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.3 years with a standard deviation of 1.1 years.
Step 1 of 2: If a sampling distribution is created using samples of the ages at which 35 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.
Answers
Answer:
The mean of the sampling distribution of sample means is equal to the population mean, which is 5.3 years.
give thanks for more! your welcome!
Step-by-step explanation:
What does "things" refer to? Choose the word that completes the sentence.
The store was crammed with racks of used clothes. "How
pretty!" Mama said with a sigh as she stopped to examine
some silky scarves and beaded necklaces. "But we're here to
find things for you girls, not me."
"But we're here to find
for you girls, not me."
necklaces
clothes
racks
scarves
P
Answers
Answer: Clothes
Step-by-step explanation:
They are in a clothing store for the girls.
Hope this helped
Represent the following sentence as an algebraic expression, where "a number" is the letter x. The difference of 4 and a number
Answers
The algebraic expression "difference of 4 and a number" where the number is letter x is represented as 4 - x.
What is an algebraic expressionAlgebra is an elementary branch of mathematics that deals with the numbers and the basic mathematics operations of addition, subtraction, division and multiplication. Algebraic expression involves arithmetic where the use of unknown quantities along with numbers.
From the question, we have the mathematical statement "difference of 4 and a number" and the number is "a number" is represented with the letter x.
the word difference in mathematics implies Subtraction (-)
Therefore, the mathematical statement "difference of 4 and a number" is represented as 4 - x.
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Dividing fractions word problem,
I need your help, yes you!
Answers
Answer: 2
Step-by-step explanation:
Answer:
I think it's 2kg
Step-by-step explanation:
13/5 ÷ 13/10
Reciprocate
13/5 × 10/13
= 26/13
=2kg
Find the x-intercept and the y-intercept of the line below. Click on "None" if applicable.
Answers
Answer:
x-intercept: 4
y-intercept: -4
Step-by-step explanation:
Hope this helps. Plz give brainliest! Also, plz sub to kgirl633 on yt!
A sample of 100 cars driving on a freeway during a morning commute was drawn, and the number of occupants in each car was recorded. The results were as follows: NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Occupants 1 2 3 4 5 Number of Cars 64 19 12 3 2 Find the sample median number of occupants.
Answers
Answer:
The sample median number of occupants is 1.
Step-by-step explanation:
Median:
The measure that separates the lower half of the distribution from the upper half.
In this question:
Total of 100 cars.
64 have 1 occupant.
19 have 2 occupants
12 have 3 occupants
3 have 4 occupants
2 have 5 occupants.
Median:
In the cumulative distribution
100/2 = 50
While we count until 64, it has 1 occupant, so 50 is one occupant, which means that the sample median is 1.
The sample median number of occupants is 1.
The committee spends $462 on costumes for 24 people. Each costume costs the same amount of money.
How much did each costume cost, in dollars?
Answers
Answer:
Step-by-step explanation: 462 Divided by 24 = 19.25$
Proof: 19.25 x 24 = 462
Answer: 19.25$
Luigi cannot decide which store he should buy a TV from. The original price of the TV is $380. Best buy marked down the TV by 50%. Walmart marked down the TV by 30% with an additional 20% off. Which store should Luigi buy from and why?
Answers
Answer:
• Best Buy
,• Their selling price is lower
Explanation:
The original price of the TV = $380.
BestBuy
If Best buy marked down the TV by 50%
Then the selling price of the TV will be:
\(\begin{gathered} =380-\mleft(50\mright.\%\text{ of 380)} \\ =380(1-50\%)=380(1-\frac{50}{100}) \\ =380(1-0.5) \\ =0.5\times380 \\ =\$190 \end{gathered}\)The selling price at BestBuy will be $190.
Walmart
Walmart marked down the TV by 30%
\(\begin{gathered} =380-\mleft(30\mright.\%\text{ of 380)} \\ =380(1-30\%) \\ =380(1-0.3) \\ =0.7\times380 \\ =\$266 \end{gathered}\)There was also an additional 20% off.
\(\begin{gathered} =266-\mleft(20\mright.\%\text{ of 266)} \\ =266(1-20\%) \\ =266(1-0.2) \\ =0.8\times266 \\ =\$212.80 \end{gathered}\)The selling price at Walmart is $212.80
Therefore, Luigi should buy from BestBuy since they have a lower selling price of $190.
I think it’s 40%, am I correct?
Answers
my thought process is
There are 100 ticks (20 spaces with 5 marks)
the area it wants has 6 large spaces (6*5=30) and 3 marks
30+3 is 33
Five new dresses have been sewn. Chelsea did 1/7 of the total sewing. What fraction of each dress did Chelsea sew?
Answers
Answer:
1/35
Step-by-step explanation:
We can use proportion.
5 dresses --- 1/7
1 dress ---- x
x = 1*1/7: 5= 1/7 *1/5 = 1/35
Alan is making spaghetti for the picnic
at the end of a 40-mile bike ride. Each
batch requires 3. jars of pasta sauce.
He plans to make 42 batches of
spaghetti. How many jars of pasta
sauce does he need?
Answers
Answer:
126 jars
Step-by-step explanation:
Each batch requires 3 jars so the equation for 42 batches is:
42*3 = 126
Answer:
i think its 126 but i may be wrong which i think i am sorry
Step-by-step explanation:
What is the solution to this equation? (1/27)^2-x=9^3x
Answers
Answer:
= 1/532170
Step-by-step explanation:
an arithmetic sequence is as follows: 2, 24, 46... find the formula for the nth term.
Answers
The nth term of an arithmetic sequence is given as:
\(a_n=a_1+(n-1)d\)Where
a_1 is first term
d is common difference (diff between terms)
n is the term number
Now,
in the sequence, we see
First Term = 2
Common DIff = 24 - 2 = 22 and 46 - 24 = 22, so Common Difference = 22
So, the general formula is:
\(\begin{gathered} a_n=a_1+(n-1)d \\ a_n=2+(n-1)(22) \\ a_n=2+22n-22 \\ a_n=22n-20 \end{gathered}\)At Pizza Pi, 52% of the pizzas made last week had extra cheese. If 13 pizzas had extra cheese, how many pizzas in all were made last week?
There were _______ pizzas made last week.
Answers
Answer:
Im trying to find it too :(
Step-by-step explanation:
please i meed help!!! im stuck and cant concentrate
Answers
Answer:
A. 8h=m
Step-by-step explanation:
$8* h= total money m earned.
need help please with this problem
Answers
The surface area of the pyramid, in square feet is \(84.84\) \(ft^2\)
All the triangles are equilateral.
Here, the side of one triangle is perfectly in line with the side of the other triangle as seen in the net.
So, all the triangles are congruent and hence the area of all the triangles will also be equal.
Base of the triangle \(= 7\) ft.
Height of the triangle \(= 6.06\) ft
Area \(= \frac{1}{2} \times base \times height\)
Area \(= \frac{1}{2} \times 7 \times 6.06\)
Area \(= 21.21 ft^2\)
There are \(4\) triangles in the net.
So, total area \(= 4 \times 21.21\)
\(= 84.84 ft^2\)
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Please help me solve this fast!
Answers
Answer:
1) 7/8 8/7
2) 4.4
3) 3.7
4) 2.8
Step-by-step explanation:
Length of bottom side of Figure A: 8 cm
Length of bottom side of Figure B: 7 cm
From Figure A to Figure B, the scale factor is 7/8.
7/8
8/7
5 × 7/8 = 35/8 = 4.375
4.4
3.2 × 8/7 = 3.657...
3.7
3.2 × 7/8 = 2.8
2.8