chandler's monthly cell phone plan costs $20 plus $5 per gigabyte of data that he uses. what does that look like in slope- intercept form to represents this linear function
The required linear function in slope intercept form is C = 5x + 20
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan \theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
Here,
Let Chandler uses x gigabytes of data and let Chandler's monthly cell phone plan cost be C
Chandler's monthly cell phone plan costs $20 plus $5 per gigabyte of data that he uses
So,
C = 20 + 5x
C = 5x + 20
This is the required linear function in slope intercept form
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-8w+(-4z)+2+6w+9z-7 ?
(t/f) since we are sampling from a skewed-right distribution, with sample size 80, the sampling distribution of the sample mean should also be a skewed-right distribution.
True, With an 80-person sample size, we are selecting from a skewed-right distribution, hence the sampling distribution mean should likewise be skewed-right.
80 people make up the sample that was taken from the population distribution with a right skew. We may infer that the sampling distribution of the sample means would be close to normalcy given the size of the sample.
In general, the distribution is normal.
The central limit theorem states that as sample size increases, the sample mean distributions become normal, with standard deviations equaling n and mean values approximating the population mean, regardless of the underlying distribution's form. In other words, the sample means sampling distribution turns roughly normal.
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2. Find the slope (rate of change) of a line that passes through (-2, -3) and (1, 1). (1
01
02
4/3
Answer:
4/3
Step-by-step explanation:
slope = (y_2 - y_1)/(x_2 - x_1)
slope = (-3 - 1)/(-2 - 1)
slope = -4/(-3)
slope = 4/3
if, in a random sample of 250 items, 46 are defective, what is the sample proportion of defective items?
The sample proportion of defective item is 0.184
What is proportion ?
A part, share, or number that is measured in comparison to a whole is referred to as a proportion in general. When two ratios are equal, according to the definition of proportion, they are in proportion. It is a formula or claim that shows that two ratios or fractions are equal.
let x = number of defective items
= 46
Let n = sample size
= 250
Therefore , sample proportion of defective items given by
p = x / n
= 46 / 250
= 0.184
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8-1/3x=16 what does the x equal
Answer:
8 - 1/3x = 16
8-8 - 1/3x = 16-8
-1/3x=8
8/-(1/3)= -24
x= -24
Step-by-step explanation:
8- 1/3(-24)=16
Which of these relations is a function?
The fourth figure is a function as it passes the vertical line test.
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
By vertical line test which is drawing a vertical line anywhere in a graph of a function if it only intersects only at one point, it is a function.
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HELLPPPPP ITS maTHhHhHh
Answer:
7
Step-by-step explanation:
if he gets $35 in 5 hours then he gets $7 an hour, and 7*7=49.
Answer: 7 hours
Step-by-step explanation:
$35/5 hours=$7 an hour
$49/$7 an hour=7 hours of mowing
suppose a jar contains 15 red marbles and 14 blue marbles. if you reach in the jar and pull out 2 marbles at random, find the probability that both are red. write your answer as a reduced fraction.
If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812.
Probability
Total marbles:
Total marbles=15+14
Total marbles = 29
Chance that a red will be pulled=2/29
Chance that the second marble will be red =1/28
Hence,
Probability :
Probability = 2/29*1/28
Probability = 0.00246
Therefore If a jar contains 15 red marbles and 14 blue marbles. If you reach in the jar and pull out 2 marbles at random, the probability that both are red is: 2/812
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Un tren de juguete eléctrico viaja alrededor del árbol de Navidad en círculos. La vía del tren mide 6 pies de diámetro. ¿Cuál es la distancia que recorre el tren?
Answer:
i need points
Step-by-step explanation:
Rewrite the expression as an equivalent ratio of logs using the indicated base. log13(58.875) to base 10
Answer:
log 58.875/ log 13
Step-by-step explanation:
log 58.875/ log 13
Ron earns $450 in gross wages on January 10. How much is deducted from Ron’s gross wages for social security at 6.2% and Medicare at 1.5%?
The amount of $34.65 is deducted from Ron’s gross wages for social security at 6.2% and Medicare at 1.5% .
What is the percentage?Percentage means one part of every cent or hundred. And it is represented by symbol '%'.
Given that Ron earns $450 in gross wages on January 10.
To find deduction amount from Ron’s gross wages for social security at 6.2% ;
Firstly, we find 6.2% of $450 that is $450 x 6.2 / 100 = $27.9 and then we substract to the gross wages.
$450 - $27.9 = $422.1
Now to find 1.5 % of $450 that is 450 x 1.5/ 100 = $6.75 and then we substract to the gross wages.
$450 - $6.75 = $443.25
total deduction amount is $6.75 + $27.9 = $34.65
Therefore, $34.65 is deducted from Ron’s gross wages for social security at 6.2% and Medicare at 1.5%
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Find the magnitude of the vector v = <-2, 5>.
why would a manager be interested in analyzing risk? a. to determine a distribution of outcomes. b. to determine a confidence interval on the most likely outcomes. c. to determine a range of outcomes. d. to determine a most likely outcome. g
A manager be interested in analyzing risk to determine a range of outcomes.
What are the reasons to analyze risk?Project managers and their teams undertake risk analysis, such as calculating the likelihood of various undesirable outcomes affecting a project, to avoid or minimize their impacts. The process can help reduce exposure, time, and budget overruns and keep businesses in compliance.
Analyzing risk can help to uncover threats to the success of the projects or business operations, such as: vulnerabilities in security; potential litigations, penalties and non-compliance issues; and, mistakes in budget or scheduling.
In general, there are 4 accepted ways to respond to risks, those are: avoidance, mitigation, acceptance, and transfer.
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The probability that a marksman will hit a target each time he shoots is 0. 89. If he fires 15 times, what is the probability that he hits the target at most 13 times?.
A shooter has a 27.92% chance of hitting the target at least 13 times.
What does binomial distribution mean?Let X become a random variable and represent the number of times the target gets hit.15 shots are fired, hence 10 trials ("n") are conducted as a result.The likelihood of success is represented by "p" in a binomial distribution, and the likelihood of failure is represented by "q" (where q = 1 - p).p = 0.89 with q = 0.11 because the target has a 0.89 chance of being hit.This probability mass function in this type of binomial distribution is the quantity of successes ("x").
P(X = x) = ⁿCₓ . pˣ . qⁿ⁻ˣ
The required number of wins is five since we are concerned with the likelihood that target will be hit exactly five times.(i.e., x = 13).
P(X = 13) = ¹⁵C₁₃. (0.89)¹³ (0.11)²
P(X = 13) = 0.2792
P(X = 13) = 27.92%
Therefore, there is a 27.92% chance that a shooter will hit its target at the very most 13 times.
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The Wall Street Journal reported that 33% of taxpayers with adjusted gross incomes between 30,000 and 60,000 itemized deductions on their federal income tax return. The mean amount of deductions for this population of taxpayers was $17,545 . Assume that the standard deviation is $2,160. Use z-table.
a. What is the probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $210 of the population mean for each of the following sample sizes: 30, 50, 100 and 400? Round your answers to four decimals.
n= 30
n= 50
n= 100
n= 400
b. What is the advantage of a larger sample size when attempting to estimate the population mean? Round your answers to four decimals.
The probability that the sample mean will be within a specified distance of the population mean. In the automobile insurance example, the probability of being within +-210 of U ranges from BLANK for a sample of size 30 to BLANK for a sample of size 400 .
Expert Answer
0.4056 0.5082 0.6690 0.9482 A large sample the probabili…View the full answer
a) The probability that a sample of taxpayers from this income group who have itemized deductions will show a sample mean within $210 of the population mean is 0.9482.
b) When trying to estimate the population mean, a greater sample size offers the benefit of improving the estimation's accuracy.
a. The z-score is calculated as follows:
z = (x - μ) ÷ (σ ÷ √n)
Where the sample size is n, the sample mean is x, the population mean is y, and the population standard deviation is z.
By entering the specified values, we obtain:
n = 30: z = (x - 17,545) ÷ (2,160 ÷ √30) = (x - 17,545) ÷ 216
n = 50: z = (x - 17,545) ÷ (2,160 ÷ √50) = (x - 17,545) ÷ 174
n = 100: z = (x - 17,545) ÷ (2,160 ÷ √100) = (x - 17,545) ÷ 132
n = 400: z = (x - 17,545) ÷ (2,160 ÷ √400) = (x - 17,545) ÷ 53
To find the odds that a sampling distribution could be within $210 of both population mean and the z-score, we must first figure out the likelihood that now the z-score would be within 1.96 standard deviations of the mean. This is because the 95th percentile, or the number under which 95% of the data lies, is represented by the z-score of 1.96, which is the value in this case.
To ascertain the likelihood, we must attempt searching up the z-scores in a z-table and get the pertinent probabilities. A z-table is a table that lists the probability associated with various z-scores.
Using the z-scores we used to develop the concept, we could look up the alternatives in a z-table and find the following probability:
n = 30: 0.4056
n = 50: 0.5082
n = 100: 0.6690
n = 400: 0.9482
For each of the aforementioned sample sizes, the likelihood that a sampling of taxpayers from this income category who itemized deductions will exhibit a sample mean that is within $210 of the population mean is:
n = 30: 0.4056
n = 50: 0.5082
n = 100: 0.6690
n = 400: 0.9482
b. The likelihood that the sample means will closely match the true population mean is thereby increased.
The standard deviation averages commonly fall as the sample size rises. In other words, as the sample mean becomes less likely to depart from the actual population mean, the likelihood that the random variable will be close to the population mean increases.
For instance, in the aforementioned case, the likelihood that they would give it a shot would be within 210 of a population mean would rise from 0.4056 for a random sample of just 30 to 0.9482 for a random sample of 400.
This means that the likelihood that they give it a chance will fall within the allowed range of the sample % likewise increases as the sample size increases.
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Exponential Growth
Graph: y = 2*
20
-1
O
X
1
2
y
Growth
b>1
Answer:
it's 20 if u look closely
Find the coordinates of the circumcenter of the triangle with the given vertices.
2. R(-2,5), S(-6, 5), T(-2,-1)
P(4, 7.25) are the coordinates of circumcentre of the triangle
How to find the coordinates of the circumcenter of a triangle
The circumcenter of a triangle is the point where the perpendicular bisectors of the sides of that particular triangle intersect
Given: The vertices R(-2,5), S(-6, 5), T(-2,-1)
Let P(x,y) be the circumcentre of triangle. Then,
PR = PS = PT
PR² = PS²
(x-(-2))² + (y-5)² = (x-(-6))² + (y-5)²
(x+2)² + (y-5)² = (x+6)² + (y-5)²
x²+4x+4 + y²-10y+25 = x²+12x+36 + y²-10y+25
12x-4x = 36 -4
8x = 32
x = 32/8 = 4
Also, PS² = PT²
(x-(-6))² + (y-5)² = (x-(-2))² + (y-(-1))²
(x+6)² + (y-5)² = (x+2)² + (y+1)²
x²+12x+36 + y²-10y+25 = x²+4x+4 + y²+2y+2
12x-4x-10y-2y = 4+2-36-25
8x-12y = -55 .......(1)
put x= 4 into (1):
8x-12y = -55
8(4)-12y = -55
32 -12y = -55
-12y = -55-32
-12y = -87
y = 7.25
Therefore, the coordinates of circumcentre of the triangle are P(4, 7.25)
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for the given scenario, determine the type of error that was made, if any. (hint: begin by determining the null and alternative hypotheses.) an ice cream truck aims to keep 30 degrees as the mean temperature inside its delivery truck. one employee claims that the mean temperature inside its delivery truck is more than 30 degrees. the employee conducts a hypothesis test and rejects the null hypothesis. assume that in reality, the mean temperature inside its delivery truck is 32 degrees. was an error made? if so, what type?
There is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.
Given, an ice cream truck aims to keep 30 degrees as the mean temperature inside its delivery truck.
one employee claims that the mean temperature inside its delivery truck is more than 30 degrees. the employee conducts a hypothesis test and rejects the null hypothesis.
The mean temperature inside its delivery truck is 32 degrees.
As, the temperature inside the delivery truck should be 30 degrees and should not be greater than 30 degrees then, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.
So, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.
Hence, there is no error made in claiming that the mean temperature inside the truck is 32 degrees which is 2 degrees more than the required one.
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Rico-Guevara’s feeders take pictures of the birds’ tongues sticking out as they sip nectar. A hummingbird’s beak is b millimeters long and its tongue sticks out t millimeters past its beak. Write an expression to find out the total length of its beak and tongue that sticks out. 4B. Evaluate it: A Rufous-tailed hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters
The expression to find out the total length of its beak and tongue that sticks out is b+t.
When Rufous-tailed hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters, the length is 28 millimeters.
What is an expression to find the total length?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
From the information illustrated, Guevara’s feeders take pictures of the birds’ tongues sticking out as they sip nectar.
A hummingbird’s beak is b millimeters long and its tongue sticks out t millimeters past its beak.
The expression to find out the total length will be:
= Length of beak + Length of tongue
= b + t
The length when the hummingbird’s beak is 20 millimeters long and its tongue sticks out 8 millimeters is:
= 20 + 8
= 28 millimeters
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In the diagram below of triangle EFGEFG, HH is the midpoint of \overline{EG}
EG
and II is the midpoint of \overline{FG}
FG
. If m\angle GFE=87-7x∠GFE=87−7x, and m\angle GIH=51+2x∠GIH=51+2x, what is the measure of \angle GIH∠GIH?
Applying the definition of midpoint, the measure of angle GIH in the triangle shown is: 59°.
What are the Corresponding Angles of Similar Triangles?The corresponding angles of two similar triangles are always congruent to each other.
Given that H is the midpoint of Eg and I is the midpoint of FG, two similar triangles are created, where angles GFE and GIH are corresponding angles.
Given:
m∠GFE = 87 - 7x
m∠GIH = 51 + 2x
m∠GFE = m∠GIH [corresponding angles are congruent]
Substitute
87 - 7x = 51 + 2x
Solve for x
-2x - 7x = 51 - 87
-9x = -36
Divide both sides by -9:
-9x/-9 = -36/-9
x = 4
m∠GIH = 51 + 2x = 51 + 2(4)
m∠GIH = 59°
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Which expression is equivalent to ? Assume . m=0 n=0
7m-(7n-18m) is an expression which is equivalent to (2mn)^4/6m^-3 n^-2 Assume m=0 n=0
What is a expression in maths?
An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)
for example 4m +5 where 4 is the coefficient of m and 5 is the constant term in other word 4m and 5 are the term of the expression and m is the variable in the expression and addition is the operator.
m=0, n=0.
8m^7n^6/3 10m^7n^6/3 8m^16n^12/3 m^4n^6/3
-7m-(3n-(8m-4n-10m)
-7m-(3n-(8m-4n+10m))
-7m-(3n-(18m-4n))
-7m-(3n-18m+4n)
-7m-(7n-18m)
complete question is
Which expression is equivalent to (2mn)^4/6m^-3 n^-2? Assume m=0 n=0
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Scientists have found a relationship between the temperature and the height above a distant planet's surface. T(h), given below, is the temperature in Celsius at a height h kilometers above the planet's surface. The relationship is as follows:
T(h)=41−1.25h.
Let T^−1 be the inverse function of T. Take x to be the output of the function T.
a) Explain the meaning of T^−1(x).
b) Find T−1(x).
c) Find T−1(30)
.
a) The inverse function is obtained by rearranging the variables for temperature and height in the given equation.
b) T⁻¹(x) =41-x/1.25
c) T⁻¹(30) =8.8
The given function is T(h)=41- 1.25h, so the inverse of a function is just obtained by rearranging the variables for height and temperature, the variable of temperature is replaced by height and vice versa. for the second
T(h)=41- 1.25h, considering h= x
=>T(x)=41- 1.25x
setting T(x)=x and x= T(x), we get
41- 1.25T(x) =x
=>1.25T(x) =x -41
=>T(x) =x- 41/ 1.25
now setting T(x)= T⁻¹ (x) we get : T⁻¹ (x) =41-x/1.25
For T⁻¹(30) =41-30/1.25= 11/1.25 =8.8
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b. the scatterplot matrix is not all that helpful for the categorical variables term and format. i. create a side by side boxplot that looks at the relationship between term and final. (1 point) paste your plot. (1 point) describe the relationship. visually does term seem to have a relationship with final? ii. create a side by side boxplot that looks at the relationship between format and final. (1 point) past your plot. (1 point) describe the relationship. visually does format seem to have a relationship with final?
Boxplot tells whether a quantitative variable and a categorical variable are associated.
The distributions of one or more sets of numerical data are shown using boxes and lines in a box plot (also known as a box and whisker plot).
With a centre line designating the median value, box limitations show the range of the centre 50% of the data. From each box, lines extend to represent the range of the remaining data, and dots are positioned beyond the line's margins to represent outliers.
Box plots are used to display the distributions of numerical data values, particularly when comparing them across various groups.
They provide a broad overview of the symmetry, skew, variance, and outliers in a set of data. It is simple to determine where the primary concentration of the data is and to compare different groups.
I've answered the question in general as the question is incorrect
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Cara throw the ame dice three time. Find the probability that Cara doe not throw a ix until her third throw
Cara has a 25/216 chance of waiting until her third throw before throwing a six.
Define the term sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset among possible experiment results. Depending on the experiment, a sample area could contain a variety of results.for the stated question-
Total times the dice is thrown = 3.
Total number of sample space = 6 x 6 x 6 = 216.
The probability of coming six = 1/6
The probability of not coming six = 1 - 1/6 = 5/6.
Probability of getting 6 in third throw = 5/6 x 5/6 x 1/6
Probability of getting 6 in third throw = 25/216
Thus, Cara has a 25/216 chance of waiting until her third throw before throwing a six.
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how many arrangements of the 26 different letters are there that (a) contain either the sequence ""the"" or the sequence ""aid""?
1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.
Given that,
We have to find how many different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.
We know that,
Total number of arrangements of 26 different letters= 26!
Let A be the number of arrangements that contains 'the' = 24! ( Total no. Of alphabet= 26 subtract the number That contains 'the' i.e, 3 and add one for 'the' 26-23+1=24)
Let B be the number of arrangements that contains 'aid' = 24! (Total no. Of alphabet minus number of letter in 'aid' and add 'aid' as an alphabet i.e, 26-23+1= 24)
Total no. Of arrangements that contains either sequence 'the' or 'aid'
A or B= (A)+(B)- (A intersection B)
24! +24! -22! = 1.239x10²⁴
Therefore, 1.239x10²⁴ different ways can the 26 different letters be arranged so that either the word "the" or the word "aid" are present.
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solve 3^x-6^ =3^4
[tex]3^x^-^6=3^4[/tex]
a)-2
b)4
c)6
d)10
Step-by-step explanation:
[tex] {3}^{10 - 6} [/tex]
[tex] = {3}^{4} [/tex]
Help with these two questions, 100 points!!
Answer:
15. x = 4
16. x = 7
Step-by-step explanation:
15.
CD/ ED = DG / DF
48 / (5x - 2) = 40 / (2x + 7)
48 (2x + 7) = 40 (5x - 2)
96x + 336 = 200x - 80
200x - 96x = 336 + 80
104x = 416
x = 4
16.
ST / PL = TU / LM
(x + 1) / 72 = (2x - 3) / 99
99 (x + 1) = 72 (2x - 3)
99x + 99 = 144x - 216
144x - 99x = 99 + 216
45x = 315
x = 7
Answer:
15. x = 4
16. x = 7
Step-by-step explanation:
Similar Triangles
In similar triangles, corresponding sides are always in the same ratio.
Question 15If ΔCDG ~ ΔEDF then:
CD : ED = DG : DF = CG : EFFrom inspection of the given diagram:
CD = 48ED = 5x - 2DG = 40DF = 2x + 7Therefore:
[tex]\implies \sf CD : ED = DG : DF[/tex]
[tex]\implies 48 : (5x-2) = 40 : (2x+7)[/tex]
[tex]\implies \dfrac{48}{(5x-2)} = \dfrac{40}{(2x+7)}[/tex]
[tex]\implies 48(2x+7)=40(5x-2)[/tex]
[tex]\implies 96x+336=200x-80[/tex]
[tex]\implies 416=104x[/tex]
[tex]\implies x=\dfrac{416}{104}[/tex]
[tex]\implies x=4[/tex]
Question 16If ΔSTU ~ ΔPLM then:
ST : PL = TU : LM = SU : PMFrom inspection of the given diagram:
ST = x + 1PL = 72TU = 2x - 3LM = 99PM = 70Therefore:
[tex]\implies \sf ST : PL = TU : LM[/tex]
[tex]\implies (x+1) : 72 = (2x-3) : 99[/tex]
[tex]\implies \dfrac{(x+1)}{72}= \dfrac{(2x-3)}{99}[/tex]
[tex]\implies 99(x+1)=72(2x-3)[/tex]
[tex]\implies 99x+99=144x-216[/tex]
[tex]\implies 315=45x[/tex]
[tex]\implies x=\dfrac{315}{45}[/tex]
[tex]\implies x=7[/tex]
assuming the population standated deviation is known, which of the following statements is true about the standard deviation of the sample mean x
Assuming the population standard deviation is known and the standard deviation of the sample mean x : option (b) is correct : the standard error of the sample mean decreases.
Central Limit theory:In probability theory, the central limit theorem (CLT) states that the distribution of a sample variable approximates a normal distribution (i.e., a “bell curve”) as the sample size becomes larger, assuming that all samples are identical in size, and regardless of the population's actual distribution shape.
Standard deviation:Standard deviation is a calculation of the dispersion or variation in a set of numbers. If the standard deviation is a small number, it means the data points are close to their average value. If the deviation is large, it means the numbers are spread out, further from the mean or average.
There are different ways to write out the steps of the population standard deviation calculation into an equation. A common equation is:
σ = ([Σ(x - u)2]/N)1/2
Where:
σ is the population standard deviation
Σ represents the sum or total from 1 to N
x is an individual value
u is the average of the population
N is the total number of the population
Sample Mean:A sample mean is an average of a set of data . The sample mean can be used to calculate the central tendency, standard deviation and the variance of a data set. The sample mean can be applied to a variety of uses, including calculating population averages.
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PLS HELP!!! QUICK PLS! I'LL MAKE BRAINLIEST
Write an equation for the graph of each quadratic and compare to each other. Be sure to discuss the similarities and differences.
Using the table the quadratic equation is y = x² - 2
from the curve the quadratic equation is y = x² + 1
How to write the equation of the quadratic graphQuadratic equation is written of the form
y = a(x - h)² + k
from the table the vertex is
v(h, k) = v(0, -2)
substituting the values to the formula
y = a(x - 0)² - 2
y = ax² - 2
Using the point (2, 2) from the table
y = ax² - 2
2 = a * 2² - 2
2 = 4a - 2
4a = 2 + 2
4a = 4
a = 1
The equation of the curve is
y = x² - 2
from the graph the vertex is
v(h, k) = v(0, 1)
substituting the values to the formula
y = a(x - 0)² + 1
y = ax² + 1
Assuming a unit on the graph is a unit we take point (1, 2) where the curve passed
y = ax² + 1
2 = a * 1² + 1
2 = a + 1
a = 2 - 1
a = 1
The equation of the curve is
y = x² + 1
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