The equation that represents the number of time a cricket chirp (y) given the temperature (x) in degree Fahrenheit is y = 0.23 x + 40
Steps to translate a word problem into an equation or a function:
- Assign the unknowns to variables
- Identify which one is independent variables, which one is dependent variables. The independent variable will become the input while the dependent variable will become the output.
In the given problem, there are two variables:
- temperature in the air (in Fahrenheit)
- number of time a cricket chirp
From the problem, we can conclude that the number of time a cricket chirp depends on the temperature of the air. Hence,
independent variable = temperature in the air (in Fahrenheit)
dependent variable = number of time a cricket chirp
Let:
y = number of time a cricket chirp
x = temperature in the air (in Fahrenheit)
It is said: The number of chirp per minute is equal to 0. 23 times the temperature of the air, in degree Fahrenheit, plus forty.
We can translate it into an equation:
y = 0.23 x + 40
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I need help I don’t know how to do this question on ixl
A statistics professor would like to build a model relating student scores on the first test to the scores on the second test. The test scores from a random sample of 21 students who have previously taken the course are given in the table.
Test Scores
Student First Test Grade Second Test Grade
1 50 70
2 91 58
3 55 74
4 58 65
5 79 60
6 70 60
7 97 48
8 51 73
9 51 73
10 59 66
11 69 67
12 56 70
13 56 73
14 41 76
15 49 72
16 58 68
17 58 73
18 99 53
19 87 58
20 95 50
21 97 55
Using statistical software, estimate the parameters of the model
Second Test Grade=β0+β1(First Test Grade)+εiSecond Test Grade=β0+β1(First Test Grade)+εi.
Enter a negative estimate as a negative number in the regression model. Round your answers to 4 decimal places, if necessary.
Sum of multiplied differences= -962.676 and β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619).
To estimate the parameters of the model, we can use the following steps:
Calculate the mean of the first test scores and the mean of the second test scores.
Calculate the difference between each student's first test score and the mean first test score, and the difference between each student's second test score and the mean second test score.
Multiply the differences from step 2 together for each student, and sum the results.
Divide the sum from step 3 by the sum of the squares of the differences from step 2. This will give us the value of β1.
Calculate β0 by substituting the values of β1 and the mean first and second test scores into the equation: Second Test Grade = β0 + β1(First Test Grade)
Using these steps, we can calculate the estimates of the parameters as follows:
Mean first test score = (50+91+55+58+79+70+97+51+51+59+69+56+56+41+49+58+58+99+87+95+97)/21 = 68.381
Mean second test score = (70+58+74+65+60+60+48+73+73+66+67+70+73+76+72+68+73+53+58+50+55)/21 = 64.762
Difference between student 1's first test score and mean first test score = 50 - 68.381 = -18.381
Difference between student 1's second test score and mean second test score = 70 - 64.762 = 5.238
Difference between student 2's first test score and mean first test score = 91 - 68.381 = 22.619
Difference between student 2's second test score and mean second test score = 58 - 64.762 = -6.762
Sum of multiplied differences = (-18.3815.238) + (22.619-6.762) + (-13.3818.238) + (-10.381-0.762) + (10.619*-6.238) + (2.619*-7.238) + (28.619*-16.762) + (-17.3819.238) + (-17.3819.238) + (-9.381*-0.762) + (0.619*-0.238) + (-2.3816.238) + (-2.3817.238) + (-27.38116.238) + (-18.3813.238) + (-10.381*-3.762) + (-10.3815.238) + (-10.3815.238) + (30.619*-11.762) + (18.619*-6.762) + (26.619*-14.762) + (28.619*-9.762) = -962.676
β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619)
Thus, Sum of multiplied differences= -962.676 and β1 = -962.676 / ((-18.381)^2 + (22.619)^2 + (-13.381)^2 + (-10.381)^2 + (10.619)^2 + (2.619)^2 + (28.619)^2 + (-17.381)^2 + (-17.381)^2 + (-9.381)^2 + (0.619).
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a quadrilateral must be a parallelogram if one pair of opposite sides is a. congruent, only b. parallel, only c. congruent and parallel d. parallel and the other pair of opposite sides is
a quadrilateral must be a parallelogram if one pair of opposite sides is congruent and parallel
A quadrilateral with two sets of opposing parallel sides is referred to as a parallelogram.To be a parallelogram, one pair of opposite sides must be congruent and parallel. Congruent means that two sides have the same measurements or length while parallel means that two lines never intersect. For example, if one pair of opposite sides is congruent and parallel, and the other pair of opposite sides is parallel, then the quadrilateral is a parallelogram. This is because the two pairs of opposite sides form parallel lines and the respective pairs have the same length. Therefore, the answer is c. congruent and parallel.
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6. The solid line is the parent function, f(x). Which of the following dotted line graphs shows the translation f(x) = f(x)
The function that is gotten after transformation is; f(x - 1) = -2x - 4
How to Interpret the Graph Transformation?We are told that the parent function is f(x).
Now, after transformation, the function becomes;
f(x) = f(x - 1)
Now, the solid line graph has;
y-intercept = -2
x intercept = 1
Slope = -2/1 = -2
Thus, equation is;
f(x) = -2x - 2
Thus, for f(x - 1), what it means is that we will plug in (x - 1) for x in the parent function to get;
f'(x - 1) = -2(x - 1) - 2
= -2x -2 - 2
= -2x - 4
The graph that represents the function after transformation is as attached.
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Complete question is;
The solid line is the parent function, f(x). Which of the following dotted line graphs shows the translation f(x) = f(x - 1)?
Use £1 = 9.60 francs and £1 = 240 pesetas to work out how much 1 franc is in
pesetas.
Answer:
1 franc = 25 pesetas---------------------------------
Given:
£1 = 9.60 francs and £1 = 240 pesetasIt gives us:
9.60 francs = 240 pesetasDivide both sides by 9.60 to find the rate:
1 franc = 240/9.60 pesetas1 franc = 25 pesetas. The flashlight shown below has no batteries. Instead, it is operated by squeezing and letting go of the handle
Inside the body of the flashlight are gears.
A Kinetic → electrical → light
8 Kinetic chemical → light
C. Chemical -kinetic light
D chemical- electrical → light
The sequence of the energy conversion is; Kinetic → electrical → light Option A
What is energy conversion?From the first law of thermodynamics, we know that energy can neither be created nor destroyed but it can be converted from one form to the other. We have been told that in this case, the flashlight shown below has no batteries. Instead, it is operated by squeezing and letting go of the handle.
The letting go of the handle is kinetic energy which would lead to electrical energy that is then converted into the visible light energy.
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Let P(t) denote the population of bacteria in a
Petri disht hours after bacteria are introduced to the environment
of the Petri dish. Suppose that the initial population of bacteria
is known to be 5000, and that the bacteria population doubles
every 6 hours. Assume that the population can grow indefinitely.
Give a formula for P(t).
well, if the population is doubling from whatever they happen to be, so that means the growth rate is 100%, so if they're hmmm "g", then later they become "2g", or doubled, and the later becomes "4g" and so on, so the rate is simply 100%, because "g" plus "g" is just 2g, and "2g" plus "2g" is just 4g and so on, anyhow
[tex]\textit{Periodic/Cyclical Exponential Growth} \\\\ A=P(1 + r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &5000\\ r=rate\to 100\%\to \frac{100}{100}\dotfill &1\\ t=hours\\ c=period\to &6 \end{cases} \\\\\\ A=5000(1 + 1)^{\frac{t}{6}}\implies A=5000(2)^{\frac{t}{6}}\implies {\Large \begin{array}{llll} P(t)=5000(2)^{\frac{t}{6}} \end{array}}[/tex]
determine the probability of drawing either a queen or a heart? write your answer as a reduced fraction.
The probability that the card drawn is either a queen or a heart is 4/13
According to the given information
Consider the random experiment of picking one card from a deck of 52 cards that has been expertly shuffled, as well as the subsequent occurrences.
A queen is the card that was drawn.
H: the heart card was shown.
The chance that "the card drawn is a queen" is P(Q) = 4/52 = 1/13 because there are four queens.
The probability that the card selected will be a heart is P(H) = 13/52, or 1/4, because there are 13 hearts in the deck. Because the queen of hearts is one of the deck's cards, events Q and H are inclusive events. P(Q and H) = 1/52 is the likelihood that "the card picked is a queen and a heart (the queen of hearts)".
Four queens and thirteen hearts are included in the chance that "the card picked is a queen or a heart," but we do not want to count the queen of hearts twice. There are so 16 different methods to depict a queen.
The probability that the card drawn is either a queen or a heart
P(Q or H) = P(Q) + P(H) - P(Q and H)
= [tex]\frac{4}{52} + \frac{13}{52} - \frac{1}{52}[/tex]
= [tex]\frac{16}{52}[/tex]
= [tex]\frac{4}{13}[/tex]
The probability that the card drawn is either a queen or a heart is 4/13
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20. Keith is offered an interest rate of 8.27% for a
loan with continuous compounding. Calculate
his equivalent rate with simple compounding.
[A] 0.0795 or 7.95%
[B] 0.0998 or 9.98%
[C] 0.0106 or 1.06%
[D] 0.0863 or 8.63%
[E] 0.1108 or 11.08%
Keith's equivalent rate with simple compounding is 0.0998 or 9.98%.
The Correct option is (B).
What is Compound Interest?The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors. The resulting value is subsequently deducted from the loan's entire original amount.
Given:
Keith is offered an interest rate of 8.27% for a loan.
Now, using the following formula:
r = ([tex]e^{(i/n)[/tex] - 1) x n
where r is the equivalent rate with simple compounding, i is the interest rate with continuous compounding, and n is the number of compounding periods per year.
We have, i = 8.27%
Also assume that the number of compounding periods per year is 12, since many loans are compounded monthly.
Then,
r = ([tex]e^{(0.0827/12[/tex]) - 1) x 12
= (1.0082 - 1) x 12
= 0.0082 x 12
= 0.0984 or 9.84%
Hence, The equivalent rate is 0.0984 or 9.84%.
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find f. f ''(x) = x−2, x > 0, f(1) = 0, f(3) = 0
Answer:
Step-by-step explanation:
Here we have the second derivative of a function and we need to go back to the original function. This situation is inverse of taking derivative which is called antiderivative or integral. But because we have the second derivative, we have to integrate twice because the first integral will give me the first derivative then the second integral will give me the function itself.
1. Let's start taking the 1st integral of x-2 which is x²/2-2x+C1
2. Take the 2nd integral which is the integral of the 1st one
x³/6-2x²/2+C1x+C2
remember: the integral is the inverse of derivative, that means we have to add 1 to the power of x and divide by that power. I did that in steps 1 and 2.
3. After simplifying the second term, f(x)=x³/6-x²+C1x+C2 this is the function, but I have to find C1 and C2 the constants. We can use the two conditions given. the 1st one means that when x=1 , y=0
0=1/6-1+C1+C2 now combine like terms and move them to the left side of the equation C1+C2=5/6
the 2nd condition means that when x=3 , y=0
0=27/6-9+3C1+C2 after simplifying 3C1+C2=9/2
4. We got 2 equations with 2 variables C1 and C2, we can solve these system of equations. You can eliminate C2 and find C1 which is 11/6 then plug in C1 in any of the two equations to find C2, which is -1
5. Last step substitute C1 and C2 in the function from step 3 and you will get f(x)=x³/6-x²+11x/6-1
A hotel ha food proviioned for 30 day to erve 80
people. If 40 more men join the hotel, the ame proviion
would have lat for how many day?
By using the formula, days = (original number of people / new number of people) * original number of days, the same food would last for 20 days.
What is number?A number is a mathematical concept that refers to a quantity or value that can be represented by a symbol. Numbers can be used to represent quantities in various contexts, such as counting, measuring, and quantifying.
What is irrational numbers?Irrational numbers are numbers that cannot be expressed as the ratio of two integers (e.g. pi, the square root of 2).
days = (original number of people / new number of people) * original number of days
In this case, we can plug in the values as follows:
days = (80 / (80 + 40)) * 30
days = (80 / 120) * 30
days = 2/3 * 30
days = 20
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5c=13
what does equal?
help please
The equal gives the solution for the variable 'c' in the given equation. I.e., c = 2.6.
What is a solution for an equation?A solution is the only value that satisfies the equation. It is also said to be the root of the equation.
Calculation:The given equation is
5c = 13
To solve the equation, divide both sides of the equation by 5.
So, we get
5c/5 = 13/5
⇒ c = 13/5
On converting the fraction into a decimal, we get c = 2.6.
To find whether the solution is correct or wrong, just substitute the value into the equation. If we get L.H.S = R.H.S, then that solution is the valid or correct one.
Substituting the value in L.H.S of the given equation, we get
5c = 5(2.6)
On multiplying,
5c = 13.0 ≈ 13
⇒ L.H.S = R.H.S
Hence, the solution is valid. The value of c is 2.6.
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What’s the surface area of this prism ?
The surface area of the triangular prism is 191 cm².
What is a triangular prism?A triangular prism is a polyhedron made up of two triangular bases and three rectangular sides. It is a three-dimensional shape that has three side faces and two base faces, connected to each other through the edges.
We know the surface area of a triangular prism is (S₁ + S₂ + S₃)/l + bh.
The given triangular prism has a surface area from the given diagram we determine, 3(D×A) + 2(B×C) [area of rectangles and triangles],
= 3(8×4) + 2(10×6).
= 3(24) + 2(60).
= 71 + 120.
= 191 cm².
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sorry i chose the wrong image
Show calculations
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i just got some free money off of you kid
need help struggling!
Answer:
Step-by-step explanation:
This is the same as before, two sides are the same length, so we know the angles are also the same. That is, D and C are equal
180= 106+2a
now algebra again
(180-106)/2 = a
74/2 = a
37 = a
Estimation Gabe goes to the mall. If k is the number of items he bought, the
expression 12.92k + 27 gives the amount he spent in dollars at one store. Then he
spent 20 dollars at another store. Find the expression which represents the amount
Gabe spent at the mall. Then estimate how much Gabe spent if he bought 2 items.
The total spent at the mall by Gabe is $72.84 and the expression which represents the amount is 12.92 k + 27 + 20 or 12.92 k + 47.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
12.92 k + 27, where k is the number of items bought,
Calculate the expression which represents the amount Gabe spent at the mall as shown below,
Total amount = Amount spent in one store + Amount spent in the second store
Total amount = 12.92 k + 27 + 20
Calculate the estimate of Gabe spent by putting k = 2,
Total spent in mall = 12.92 × 2 + 27 + 20
Total spent in mall = 25.84 + 47
Total spent in mall = $72.84
Therefore, the total spent at the mall by Gabe is $72.84, and the expression which represents the amount is 12.92 k + 27 + 20 or 12.92 k + 47.
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what is the angle of rotation that maps point P to point Q?
Answer:225 degrees
Step-by-step explanation:
Find equivalent expressions of 3 2x−9−4x 11 5x−x. choose three expressions.
Answer:
[tex]-(220x^2-5x+9)[/tex]
Step-by-step explanation:
[tex]3*2x-9-4x*11*5x-x\\\\-4*11*5xx+3*2x-x-9\\\\-4*11*5xx+6x-x-9\\\\-220x^2 +6x-x-9\\\\-44 5x^2 +6x-x-9\\\\-220x^2+6x-x-9\\\\-220x^2 +(6x-x)-9\\\\-220x^2+5x-9\\\\(-(220x^2-5x+9))[/tex]
Factor -1 out of -220x^2 +5x-9
Tanisha has 51 m of fencing to build a
three-sided fence around a rectangular
plot of land that sits on a riverbank. (The
fourth side of the enclosure would be the
river.) The area of the land is 304 square
meters. List each set of possible
dimensions (length and width) of the
field.
Possible dimensions #1:
meters by
meters.
Possible dimensions #2:
meters by
meters.
Answer:
Two sets of dimensions are possible:
L(m) W(m) Area(m^2) Fence (m) Perimeter
Set 1 19 16 304 51
Set 2 32 9.5 304 51
Step-by-step explanation:
Let's set L and W for the Length and Width of the perimeter. We know that:
Area = L*W
Area = 304 m^2
Perimeter = 51 m
Let's say that the side bounded by the river is the length side. No fence is required for that portion, so the fencing for the perimeter is given by:
Perimeter, P = L + 2W
P = 51 m
We can write: L+2W=51 m
Rearrange to isolate one of the two variables. Lets pick L:
L+2W=51
L=51-2W
L = (51-2W)
Now use this in the area equation:
304 m^2 = L*W
304 m^2 = (51-2W)*W
304 m^2 = (51-2W)*W
304 m^2 = 51W-2W^2
Arrange this in the standard form of a quadratice equation and solve:
-2W^2+51W-304 m^2 = 0
W = 16 and 9.5 meters
W = 16 m
Since L=51-2W
L=51-2*(16)
L = 51-32
L = 19 m
Area = L*W
L*W = 304 m^2
(19m)W = 304 m^2
W = 16 m
Check:
Does a length (L) of 19 m and a width (W) of 16 m give an area of 304 m^2 and a fencing perimeter of 51 m if one of the L sides is the river?
Area = (19 m)*(16 m) = 304 m^2 YES
Per. = 2*(16)+ 19 = 51 m YES
W = 9.5 m
Ding the same calculation for a width of 9.5 m also satisfies all the equations, as per above.
Both values of W are valid, so the twos sets of possible dimensions are:
L(m) W(m) Area(m^2) Fence (m) Perimeter
Set 1 19 16 304 51
Set 2 32 9.5 304 51
Factorise this expression please help!!
Answer:
(a + 9)(a + 5)
Step-by-step explanation:
a² + 14a + 45
consider the factors of the constant term (+ 45) which sum to give the coefficient of the a- term (+ 14)
the factors are + 9 and + 5 , since
+ 9 × + 5 = = + 45 and + 9 + 5 = + 14 , then
a² + 14a + 45 = (a + 9)(a + 5)
Please help me solve this algebraic expression
Answer:
Step-by-step explanation:
4+5(7)
4+ 35
39
I got this answer by simply plugging in the number that was given because it said a =7 I plugged in 7 instead of using a. The same goes to b it said that b=4 so then i plugged in 4 instead of using b.
What is -1/4(-8.6) written as a decimal to the nearest hundredth
Answer:
2.15
Step-by-step explanation:
Xavier makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?.
The correct option A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.
Explain the term even integer?Odd numbers cannot be divided by two exactly, whereas even numbers were integers that can be divided by two exactly. Even number examples include 2, 6, 10, 20, 50, etc.The statement made by Xavier that the product of two odd integers always results in an even integer should be noticed.
For the given case, conjecture that the sum of two odd integers is always an even integer is -
Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.To know more about the even integer, here
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The complete question is-
Xavier makes a conjecture that the sum of two odd integers is always an even integer. Which choice is the best proof of his conjecture?
Select option;
A: Let 2a + 1 be one odd number, and let 2b + 1 be the other odd number. (2a + 1) + (2b + 1) = 2a + 2b + 2 = 2(a + b + 1). Because 2(a + b + 1) is evenly divisible by 2, it is an even number.
B: Look at these different examples: 3 + 5 = 8, 13 + 5 = 18, 23 + 5 = 28. So the sum of two odd numbers must be even.
C: Let a and b both represent odd numbers, and let a + b be an even number. Therefore, a + b = b + a, which shows that the sum of two odd numbers is even.
D: Every time you add two odd numbers, the sum is an even number.
Pleaseeee helppppp meeeeee
Answer:
C
Step-by-step explanation:
You can do trial and error since it is a multiple ans question
Answer:
c
Step-by-step explanation:
do trial and error it's right the answer is c
Nadia typically type 32 word per minute, but her rate may vary by a much a 5 word per minute. Let x be the actual rate at which Nadia type. What i the range of rate, in word per minute, that Nadia could type?
The range of rate that Nadia can type is 27 to 37.
We will calculate the lower and upper limit stating the minimum and maximum number of words Nadia can type in a minute. It will depict the range of rate.
Minimum number of words = 32 - 5
Performing subtraction on Right Hand Side of the equation
Minimum number of words = 27
Maximum number of words = 32 + 5
Performing subtraction on Right Hand Side of the equation
Minimum number of words = 37
Hence, Nadia's range of word typing is 27 to 37 per minute.
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if f(x)=-2x+5, find x so f(x)=3
Answer:
f(x)=-2x+5
f(x)=3
then,
f(x)=-2x+5
or, 3=-2x+5
or, 2x=5-3
or,2x=2
or, x=2÷2
x=1
so, the value of x is 1
Answer:
x=1
Step-by-step explanation:
3= -2x+5
-5. -5
-2= -2x
/-2. /-2
1=x
hopes this helps
Name the x- and y - intercepts for the equation:
5x - 3y = 15
Answer:
Red=X-Int: (3,0) Y-int: (0,-5)
Step-by-step explanation:
To find the y and x intercepts you have to plug in the 0 for the variable. You'd get 5(0)-3y=15 you get this by plugging in the 0 for x and then you solve. 5 x 0 is 0 so you'd get -3y=15 divide -3 on both sides and get y=--5 meaning that is the y-intercept. You'd do the same when you look for the x-int. Just that you'd plug in a 0 for y instead of x. Which is 5x-3(0)=15. -3 x 0 is 0. So you'd have 5x=15 divide both sides by 5 and you'd get x=3 meaning that is the x intercept.
(Hopefully you were able to understand how I got the x and y intercepts for this equation)
A. 2.9 inches
B. 40 inches
C. 3.2 inches
D. 2.1 inches
The required measure of length of the box is 2.9 inches. Option A is correct.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
according to the question,
h = 3l - 2.5
w = 3/4l
The volume of the box,
40 = l × w × h
40 = l × 3/4l × [3l-2.5]
40 = 3/4l²[3l - 2.5]
40 = 9/4l³ - 7.5/4l²
9/4l³ - 7.5/4l² - 40 = 0
t = 2.91932
t ≈ 2.9 inches
Thus, the length of the box must be at least 2.9 inches. Option A is the right answer.
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solve please
A
B
c
d
Answer:
the answer is A
Hope this helps
Write the range for the relation.
((-1, 1), (-2, 5), (-3, 7). (5, 8))
The range of a relation is the set of all possible values of the second element of the ordered pairs in the relation. In this case, the range of the relation is the set {1, 5, 7, 8}. This can be found by looking at the second element of each ordered pair in the relation and listing all the different values that appear.