One system of quadratic equations that has solutions of (-3, -3) and (3, -3) is:
x^2 + y^2 = 18
x + y = 0
You can check that for x = -3 and y = -3, the left-hand side of both equations is equal to the right-hand side, and the same is true for x = 3 and y = -3.
Select the figure with an angle of 300°
on a circle in standard position.
(a)
An angle in standard position with terminal side at five-sixths of a full revolution counterclockwise.
(b)
An angle in standard position with terminal side at one-twelfth of a full revolution counterclockwise.
(c)
An angle in standard position with terminal side at one-third of a full revolution counterclockwise.
(d)
An angle in standard position with terminal side at two-thirds of a full revolution counterclockwise.
Note that the figure with an angle of 300° on a circle in standard position is: "An angle in standard position with the terminal side at two-thirds of a full revolution counterclockwise." (Option D)
What is an Angle in Standard Position?A standard position angle is one measured counterclockwise from the positive x-axis in a coordinate plane.
This signifies that the angle's starting side is on the positive x-axis, while the angle's terminal side is in the first or fourth quadrant. The angle's vertex is placed at the origin.
Angles are commonly measured in degrees or radians, with a full rotation being comparable to 360 degrees or 2 radians. Angles may now be readily graphed and compared to one another in a coordinate plane.
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There is a mistake in each of these problems. Please help
Answer:
ii) Reduce :
[tex]$\begin{aligned} 5 \ln x-2 \ln (x y) & =\ln x^5-\ln (x y)^2 \\ & =\ln \left(\frac{x^5}{(x y)^2}\right) \\ & =\ln \left(\frac{x^5}{x^2 y^2}\right) \\ & =\ln \left(\frac{x^3}{y^2}\right)\end{aligned}$[/tex]
iii ) Expand :
[tex]\begin{aligned}\log _3\left(\frac{x^5}{y}\right)^4 & =4 \log _3\left(\frac{x^5}{y}\right) \\& =4 \log _3 x^5-4 \log _3 y \\& =20 \log _3 x-4 \log _3 y\end{aligned}[/tex]
Answer:
[tex]\textsf{ii)} \quad \ln \left(\dfrac{x^3}{y^2}\right)[/tex]
[tex]\textsf{iii)} \quad 20 \log_3 x-4 \log_3y[/tex]
Step-by-step explanation:
Question iiGiven expression:
[tex]5 \ln x-2 \ln (xy)[/tex]
[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]
[tex]\implies \ln (x^5) - \ln ((xy)^2)[/tex]
[tex]\textsf{Apply the quotient law}: \quad \ln x - \ln y=\ln \left(\dfrac{x}{y}\right)[/tex]
[tex]\implies \ln \left(\dfrac{x^5}{(xy)^2}\right)[/tex]
This is where the error occurred in the original calculation as the log quotient law was applied incorrectly.
[tex]\textsf{Apply exponent rule} \quad (ab)^c=a^{c}b^c\quad \textsf{to the denominator}:[/tex]
[tex]\implies \ln \left(\dfrac{x^5}{x^2y^2}\right)[/tex]
Simplify the fraction:
[tex]\implies \ln \left(\dfrac{x^3}{y^2}\right)[/tex]
Question iiiGiven expression:
[tex]\log_3\left(\dfrac{x^5}{y}\right)^4[/tex]
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies 4\log_3\left(\dfrac{x^5}{y}\right)[/tex]
[tex]\textsf{Apply the log quotient law}: \quad n\log_a \left(\dfrac{x}{y}\right)=n\log_ax - n\log_ay[/tex]
[tex]\implies 4 \log_3 x^5-4 \log_3y[/tex]
This is where the error occurred in the original calculation as the coefficient 4 was not applied to the both logarithms when applying the log quotient law.
[tex]\textsf{Apply the log power law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies 5 \cdot 4 \log_3 x-4 \log_3y[/tex]
[tex]\implies 20 \log_3 x-4 \log_3y[/tex]
Label The Missing angle measures for this triangle.
The measure of the missing angles are 100° and 30°
What is a triangle?A polygon with three vertices, angles and sides.
Given is a triangle XYW, whose side WZ is extended to the point z,
We know that,
The sum of two opposite interior angles of a triangle is equal to the measure of exterior angle,
∠ 1 + 50° = 150°
∠ 1 = 100°
We know that, sum of the interior angles of a triangle is 180°
∠ 1 + ∠ 2 + 50° = 180°
150°-180° = ∠ 2
∠ 2 = 30°
Hence, the measure of the missing angles are 100° and 30°
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which has the lowest price per unit.
$23.35 per 6.5 lbs.
$31.60 per 8 lbs.
PLEASE HELP ME IT’S URGENT
The images of the points after the transformation are (6, 1), (3, 6), (5, 2) and (-8, -4)
How to determine the coordinates of the point?r(x-axis) o T(2, -3) (4, 2)
This implies that we reflect the point (4, 2) across the x-axis and then translate it by (x + 2, y - 3)
Mathematically, this is represented as
Image = (x + 2, 3 - y)
Substitute the known values in the above equation, so, we have the following representation
Image = (4 + 2, 3 - 2)
Evaluate
Image = (6, 1)
T(2, -5) o R 90 CCW (4, 2)
This implies that we translate the point (4, 2) by (x + 2, y - 5) and then rotate it by 90 degrees counterclockwise
Mathematically, this is represented as
Image = (5 - y, x + 2)
Substitute the known values in the above equation, so, we have the following representation
Image = (5 - 2, 4 + 2)
Evaluate
Image = (3, 6)
T(1, 4) o r(y-axis) (4, 2)
This implies that we translate the point (4, 2) by (x + 1, y + 4) and then reflect it across the y-axis
Mathematically, this is represented as
Image = (x + 1, 4 - y)
Substitute the known values in the above equation, so, we have the following representation
Image = (4 + 1, 4 - 2)
Evaluate
Image = (5, 2)
r(y-axis) o T(1, 4) (4, 2)
This implies that we reflect the point (4, 2) across the y-axis and then translate it by (x + 4, y + 2)
Mathematically, this is represented as
Image = (-x - 4, y + 2)
Substitute the known values in the above equation, so, we have the following representation
Image = (- 4 - 4, 2 + 2)
Evaluate
Image = (-8, 4)
Hence, the image is (-8, -4)
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What is the solution to this equation: 42 +82=²? (Round answer to the nearest tenth.)
O c= 8.9
O e = 12
Oc=6.3
O c=3.5
The solution to this equation: 42 +82=x² is x = 12.
What is square number?A square number, also known as a perfect square, is an integer that is the square of another integer; in other words, it is the result of multiplying another integer by itself. For instance, 9 is a square number because it equals 32 and can be written as 3 3.
Instead of the product n n, the equivalent exponentiation n2, which is typically pronounced "n squared," is used to represent a number's square. The name of the shape is where the term "square number" originated. The area of a unit square (1 × 1) is the unit of area.
The solution to this equation: 42 +82=x²
x = √(42 +82)
x = √(144)
x = 12
Thus, The solution to this equation: 42 +82=x² is x = 12.
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scenario 3-6 a researcher wishes to study how the average weight y (in kilograms) of children changes during the first year of life. he plots these averages versus the age x (in months) and decides to fit a least-squares regression line to the data with x as the explanatory variable and y as the response variable. he computes the following quantities. r
The slope of the least-squares line is: 0.30
The correct answer is an option (A)
We have following information:
correlation between X and Y (r) = 0.9
mean of the values of X ([tex]\bar{X}[/tex]) = 6.5
mean of the values of Y ([tex]\bar{Y}[/tex]) = 6.6
the standard deviation of the values of X ([tex]S_{X}[/tex]) = 3.6
the standard deviation of the values of Y ([tex]S_{Y}[/tex]) = 1.2
We know that the slope of a least squares regression can be calculated by the formula,
slope m = r [tex]\frac{S_\bar{Y}}{S_\bar{X}}[/tex],
where, r is the correlation coefficient
Let us assume that for given scenario, m represents the slope of of the least-squares line.
Using above formula,
⇒ m = r [tex]\frac{S_\bar{Y}}{S_\bar{X}}[/tex]
⇒ m = 0.9 × [tex]\frac{1.2}{3.6}[/tex]
⇒ m = 0.9 × 0.333
⇒ m = 0.2997
⇒ m ≈ 0.3
Thus, the slope is 0.30
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The complete question is:
A researcher wishes to study how the average weight Y (in kilograms) of children changes during the first year of life. He plots these averages versus the age X (in months) and decides to fit a least- squares regression line to the data with X as the explanatory variable and Y as the response variable. He computes the following quantities.
r = correlation between X and Y = 0.9
X = mean of the values of X = 6.5
Y = mean of the values of Y = 6.6
S_(X) = standard deviation of the values of X = 3.6
S_(Y) = standard deviation of the values of Y = 1.2
The slope of the least-squares line is: ?
A. 0.30 B. 0.88 C. 1.01 D. 2.70 E. 3.00
#20 i need help with this question
Answer:
Step-by-step explanation:
tha answer is 69
Sophie is a dog that loves to play catch. Unfortunately, she isn't very good, and the probability that she catches a ball is only 0.2. Let x be the number of tosses required until Sophie catches a ball. (a) Does x have a binomial or a geometric distribution? (b) What is the probability that it will take exactly two tosses for Sophie to catch a ball? P(exactly two tosses) (c) What is the probability that more than three tosses will be required? P(more than three tosses)
X has a geometric distribution because it is the number of trials (tosses) required until a success (catching the ball) occurs.
b) The probability that it will take exactly two tosses for Sophie to catch a ball is P(x=2) = (0.2)(0.8)^1 = 0.16. This is calculated by multiplying the probability of success (0.2) by the probability of failure (0.8) raised to the power of the number of trials (2-1=1)
c) To find the probability that more than three tosses will be required, we need to find the probability that Sophie does not catch the ball on the first three tosses and then catch it on the fourth toss.
This can be found by summing the probabilities of Sophie not catching the ball on the first three tosses (0.8^3 = 0.512) and Sophie catching the ball on the fourth toss (0.8^3*0.2 = 0.1024). The probability that more than three tosses will be required is P(x>3) = 1 - P(x≤3) = 1 - (0.512 + 0.1024) = 0.3856.
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A liter of petrol cost 93 for an equation to find the cost in pound of any number of liter of petrol
The equation for finding cost y for x liters of petrol is y = 93x
What is an equation?An equation is a mathematical statement that shows that two mathematical expressions are equal.
Given that, A liter of petrol cost £93,
Since, the unit rate of the petrol is £93 per liter
If we say let x be the number of liters we need, the total cost will have to pay will be = 93x
And, if total cost is y, then,
y = 93x
Hence, the equation for finding cost y for x liters of petrol is y = 93x
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for each limit in exercise 55-64 use graphs and algebra to approximate the largest delta or the smallest magnitude n taht corresponds to the given value of epsilon or m, according to the appropriate formal limit definition
The largest δ value of the given limit [tex]\lim_{x \to 1^+} \frac{1}{x^2-1}=\infty[/tex] and M=1000 is calculated. The required δ value is [tex]\delta=\sqrt{1+10^{-3}}-1[/tex].
When no values are defined, a limit is used to assign values to certain functions. It is possible to assess the limits using algebraic techniques. A collection of guidelines for manipulating limits when using other operators is known as the algebra of limits. Given the expression [tex]\lim_{x \to 1^+} \frac{1}{x^2-1}=\infty[/tex] and M=1000. When x>1, we write this expression as,
[tex]\begin{aligned} \frac{1}{x^2-1}& > 1000\\x^2-1& < 1000^{-1}=10^{-3}\\x^2& < 10^{-3}+1\\x& < \sqrt{1+10^{-3}}\end{aligned}[/tex]
Now, choosing, [tex]\delta=\sqrt{1+10^{-3}}-1[/tex] when we have δ > 0. Therefore, [tex]\sqrt{1+10^{-3}} > 1[/tex]. Then, [tex]x\in(1, 1+\delta)[/tex]. This is given by,
[tex]\begin{array}{ccc}1& < x& < 1+\delta\\1& < x& < \sqrt{1+10^{-3}}\end{array}[/tex]
This implies, [tex]\frac{1}{x^2-1} > 1000=M[/tex].
Therefore, the largest δ value will be [tex]\sqrt{1+10^{-3}}-1[/tex].
The complete question is -
For each limit, use graphs and algebra to approximate the largest δ or the smallest magnitude N that corresponds to the given value of ∈ or M, according to the appropriate formal limit definition.
[tex]\lim_{x\to 1^+} \frac{1}{x^2-1}=\infty[/tex], M=1000, find largest δ > 0.
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The corner store sells pencils for $0.05, $0.10, and $0.15. List all the ways Kay can spend exactly $0.45 on pencils.
Nine pencils at $0.05 each, 2. Five pencils at $0.10 each and three pencils at $0.05 each 3.Six pencils costing $0.05 apiece and three pencils costing $0.15 each. Pencils: four for $0.15 each, and five for $0.05 each.
What is combination theory?This question uses the combination theory, which states that the total number of combinations of a set of items is equal to the number of variations in one item multiplied by the number of variations in the second item, and so on.
in this question
1. Nine pencils at $0.05 each: Kay can buy nine pencils for $0.45. Nine pencils times $0.05 each equal $0.45.
2. Five pencils at $0.10 each and three pencils at $0.05 each: Kay can buy five pencils for $0.50 and three pencils for $0.15.
Five pencils times $0.10 each equal $0.50 and three pencils times $0.05 each equal $0.15.
Adding the two totals together equals $0.45.
3. Three pencils at $0.15 each and six pencils at $0.05 each: Kay can buy three pencils for $0.45 and six pencils for $0.30.
Three pencils times $0.15 each equals $0.45 and six pencils times $0.05 each equal $0.30.
Adding the two totals together equals $0.45.
4. Four pencils at $0.15 each and five pencils at $0.05 each:
Kay can buy four pencils for $0.60 and five pencils for $0.25.
Therefore, Four pencils times $0.15 each equals $0.60 and five pencils times $0.05 each equal $0.25. Subtracting the two totals together equals $0.45.
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Tim+is+attempting+to+bike+a+12+mike+race+he+knows+at+every+third+of+the+race+he+will+need+to+take+a+break+to+stretch+his+leg+how+many+miles+wo
Answer:
he takes a stretch every 4 miles
Step-by-step explanation: 12/3 = 4
Claire is 5 feet tall and casts a 96 inch shadow. How tall is her friend Steve if his shadow is 1.5 inches shorter than hers?
Answer:
4.725 ft
Step-by-step explanation:
well if i see this right the shadow for claire is 1.60x the person's hight
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Review the Monthly Principal & Interest Factor chart to answer the question:
APR 30-Year Term 20-Year Term 15-Year Term
5.5 $5.68 $6.88 $8.17
6.0 $6.00 $7.16 $8.44
6.5 $6.32 $7.46 $8.71
7.0 $6.65 $7.75 $8.99
7.5 $6.99 $8.06 $9.27
The Apolaro household will be financing a principal balance of $115,200.00 for their property. They are trying to decide whether to take a 30-year or 15-year term mortgage. Based on their credit score, they qualify for an APR of 7.0%. Calculate the difference in total interest they would pay between the two terms. (2 points)
$81,012.83
$84,353.72
$89,372.16
$92,416.64
Answer: c
Step-by-step explanation:
Answer:
Step-by-step explanation:
its $89,372 i did the math took the test
–35 –
–20 = N please need k to
Answer: - 15 = N
Step-by-step explanation:
2 negatives make a positive so it would be -35 + 20 = -15 Have a nice day ;)
9b² – 100
Factor it
Please help me on this
Here we are interested in finding the slope of the line. From the given graph we can see that that the line passes through points (6,0) and (0,-8) . We know that slope can be calculated by ,
[tex]\longrightarrow slope \ (m)=\dfrac{y_2-y_1}{x_2-x_1} =\tan\theta [/tex]
[tex]\longrightarrow m =\dfrac{y_2-y_1}{x_2-x_1}\\[/tex]
[tex]\longrightarrow m =\dfrac{0-(-8)}{6-0}\\[/tex]
[tex]\longrightarrow m =\dfrac{8}{6}\\ [/tex]
[tex]\longrightarrow m =\dfrac{4}{3}\\ [/tex]
[tex]\longrightarrow \underline{\underline{ m = 1.\bar{3}}}[/tex]
And we are done!
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 52 minutes of calls is $14.06 and the monthly cost for 78 minutes is $17.18. What is the monthly cost for 73 minutes of calls?
Answer:
16.58
Step-by-step explanation:
as you can see from the graph, there's a monthly fixed cost on Y axis. so you need to figure out 1: how much per minute. and 2. the monthly fixed fee. you've got 2 scenarios = 2 equations, for 2 variables. so you can solve both.
assume: x=per min rate; m = monthly fixed cost.
1. 14.06 =52x+m
2. 17.18 =78x+m
use equation 2 minus equation 1 & you get
3.12 = 26 x. so x = 0.12
plug this into equation 1: 14.06 =52*0.12 +m so m=7.82
now for 73 mins the cost = 73*0.12 +7.82 =16.58
4. For a process quality characteristics, the specification limits are 0.4037 +/- 0.0013 (that is from 0.4024 to 0.4050). The following data gives the data for 14 measurement data sets, each data set is a subgroup of 5 measurement. The value is recorded in the units of 0.0001 (that is, the specification limit will be considered 24 to 50) Based on the following data, compute Cp,Cpk,Pp and Ppk.(Use MINITAB is ok) and determine if the capability of the process. Subgroup Subgroup # 1 2 3 4 5 # 1 2 3 4 5 . 1 36 35 34 33 32 34 28 35 34 38 . 2 31 31 34 32 30 36 35 37 34 33 . 3 30 30 32 30 32 30 37 33 34 35 . 4 32 33 33 32 35 38 31 33 33 33 . 5 32 34 37 37 35 33 30 34 33 35
If the calculated Cp and Cpk values are greater than 1, the process is considered capable. If Pp and Ppk are greater than 1, the process is considered capable.
To calculate Cp, Cpk, Pp, and Ppk using MINITAB, you would need to input the data into the software and run the appropriate statistical analysis.
Cp and Cpk are measures of a process's capability, they are calculated as follows:
Cp = (USL - LSL) / (6*σ)Cpk = min(Cpu, Cpl)Where,
USL and LSL are the upper and lower specification limitsσ is the standard deviation of the process.Pp and Ppk are similar to Cp and Cpk, but they are calculated using the range of the data instead of the standard deviation.
Pp = (USL - LSL) / (4*R)Ppk = min(Ppu, Ppl)Where R is the range of the data.
If the calculated Cp and Cpk values are greater than 1, the process is considered capable. If Pp and Ppk are greater than 1, the process is considered capable.
It is worth noting that Capability analysis can only be performed on stable and in-control processes. If the process is not in control, analyzing process capability is not meaningful.
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Mrs. Lopez needs 40 ounces of sweetened milk to make flans. She has 24 ounces. Which equation shows how many more ounces of sweetened milk Mrs. Lopez needs to make flans?
Answer: As Mrs Lopez required 40 ounce
Step-by-step explanation:
A company is expanding its team at a rate of 10% per year. 17 a) Calculate how many members of staff there will be after 1 year if there are initially 200 members of staff.
Step-by-step explanation:
If a company is expanding its team at a rate of 10% per year, and it currently has 200 members of staff, we can calculate the number of staff after 1 year using the formula:
number of staff after 1 year = 200 + (10/100) * 200
number of staff after 1 year = 200 + 20
number of staff after 1 year = 220
So, there will be 220 members of staff after 1 year if there are initially 200 members of staff.
4 2/3 - 3/4 answer? Please help me anwser this
Answer: 3 11/12
Step-by-step explanation:
Rewrite the equation with the parts seperated:
4 + 2/3 − 3/4
Find the LCD of 2/3 and 3/4
(Which is 12)
Keep going
8/12−9/12= −1/12
Finally, subtract 4 − 1/12 to get 3 11/12
Hope this helps!
What is the slope of the following linear graph 2/3 -2/3 3/2 -3/2
The slope of following points (3, 3) and (6,1) is -2/3 .
What is Linear equation ?
Linear equation can be defined as the equation in which the highest degree is one.
Given points are (3, 3) and (6,1)
we know that slope = y2-y1 / x2-x1
y2-y1 = 1-3
The difference of y -intercept is -2
= -2
x2-x1 = 6-(3)
= 6-3
The difference of x-intercept is 3
= 3
So, slope could be y2-y1 / x2-x1 that is -2/3.
Therefore, The slope of following points (3, 3) and (6,1) is -2/3 .
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graph these equations? y = 3x - 5, y = 1/2x + 5
The solution of the given system of equations is (4, 7).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The given system of equations are y=3x-5 -------(I) and y=1/2 x+5 -------(II)
Substitute equation (I) in (II), we get
3x-5=1/2 x+5
3x-1/2 x=5+5
2.5x=10
x=4
Substitute x=4 in equation (I), we get
y=3(4)-5
y=7
So, solution is (4, 7)
Therefore, the solution of the given system of equations is (4, 7).
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Francisco added a new sidewalk to his front yard. The
diagram represents Francisco's sidewalk. Determine
the area of the sidewalk to the nearest square foot.
A 10 ft²
B 16.28 ft²
C 3.14 ft²
D 13.14 ft²
Is this correct?
The required of the sidewalk to the nearest square foot is 13.14 ft².
What is area of rectangle?
The area a rectangle occupies is the space it takes up inside the limitations of its four sides. The dimensions of a rectangle determine its area. In essence, the area of a rectangle is equal to the sum of its length and breadth.
Explain are of circle.A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = r2, (Pi r-squared), where r is the circle's radius. The square unit, such as m2, cm2, etc., is the unit of area.
According to question:We have,
Length = 5 ft, width = 2 ft, Radius of circle = 2 ft
Now,
Area of sidewalk = area of rectangle + area quadrant
Area of sidewalk = (5×2) + π(2)^2/4
Area of sidewalk = 10 + 3.14
Area of sidewalk = 13.14 ft²
Thus, required area of the sidewalk is 13.14 ft².
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14. Calculate the x-intercepts of the equation by factoring:
8x²-16x = 0
carrie is flying on two different airlines with a heavy bag both airlines have the same weight limit by charge different fees the first airline charges $25 checked bag fee plus an additional four dollars for every pound that the bag is over the weight limit with the second airline and the price is three dollars per pound over the weight limit and addition to a $28 fee for checking the bag Carrie ended up paying the exact amount and baggage fees at the two airlines how many pounds over the limit was Carrie’s bag how much did she have to pay in fees for each airline
Answer: Let x be the weight of the bag over the limit in pounds.
We know that both airlines have the same weight limit and Carrie paid the same baggage fee at each airline, so we can set up the following equation:
25 + 4x = 28 + 3x
Solving for x:
x = 25
So, Carrie's bag was 25 pounds over the weight limit.
To find the fee for each airline, we can substitute x into the equations for the fees:
Fee for the first airline: 25 + 4(25) = $125
Fee for the second airline: 28 + 3(25) = $103
Therefore, Carrie paid $125 in fees for the first airline and $103 in fees for the second airline.
Step-by-step explanation:
Which of the following arrow diagrams represent a mapping? If that is the case give the domain and range.
The arrow diagram that represents a mapping include the following: arrow diagram C.
The domain of this arrow diagram is equal to {a, c, d}
The range of this arrow diagram is equal to {q, r, s}.
What is a domain?In Mathematics, a domain can be defined as the set of all real numbers for which a particular function is defined.
This ultimately implies that, a domain is the set of all possible input numerical values (x-values) to a function and the domain of a graph comprises all the input numerical values (real numbers) which are located on the x-coordinate.
In this scenario, we can reasonably infer and logically deduce that only the above mentioned relation (arrow diagram C) represents a function because each input variable (domain) has exactly an output variable (range) as illustrated in the diagram.
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A youth group and their leaders visited a museum
Answer:
What is the question please respond so I may give a complete response