In order for F to be conservative, there must be a scalar function f such that the gradient of f is equal to F. This means
[tex]\dfrac{\partial f}{\partial x}=3x^2-2y^2[/tex]
[tex]\dfrac{\partial f}{\partial y}=4xy+4[/tex]
Integrate both sides of the first equation with respect to x :
[tex]f(x,y)=x^3-2xy^2+g(y)[/tex]
Differentiate both sides with respect to y :
[tex]\dfrac{\partial f}{\partial y}=-4xy+\dfrac{\mathrm dg}{\mathrm dy}=4xy+4\implies\dfrac{\mathrm dg}{\mathrm dy}=8xy+4[/tex]
But we assume g is a function of y, which means its derivative can't possibly contain x, so there is no scalar function f whose gradient is F. Therefore F is not conservative.
In this problem, since the condition of equal derivatives does not apply, the vector field is not conservative.
A vector field can be described as:
[tex]F = <P,Q>[/tex]
It is conservative if:
[tex]\frac{\partial P}{\partial y} = \frac{\partial Q}{\partial x}[/tex]
In this problem, the field is:
[tex]F = <3x^2 - 2y^2, 4xy + 4>[/tex]
Then:
[tex]P(x,y) = 3x^2 - 2y^2[/tex]
[tex]\frac{\partial P}{\partial y} = -4y[/tex]
[tex]Q(x,y) = 4xy + 4[/tex]
[tex]\frac{\partial Q}{\partial x} = 4y[/tex]
Since [tex]\frac{\partial P}{\partial y} \neq \frac{\partial Q}{\partial x}[/tex], the field is not conservative.
A similar problem is given at https://brainly.com/question/15236009
(2²)³+(2³)²/4
Simplificar
━━━━━━━☆☆━━━━━━━
▹ Answer
80
▹ Step-by-Step Explanation
(2²)³ + (2³)² ÷ 4
Rewrite:
2⁶ + 2⁶ ÷ 2²
Divide:
2⁶ + 2⁴
Factor:
(2² + 1) * 2⁴
Evaluate:
(4 + 1) * 2⁴
Calculate:
5 * 16
= 80
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
The population of Jacksonville is 836,507. What is the population rounded to the
nearest hundred thousand?
A. 900,000
O
B. 850,000
C. 840,000
o D. 800,000
Answer:
D. 800,000
Step-by-step explanation:
It is D because you find the hundred thousand place which is the 8, the you go to the number next door which is 3, if the 3 is 5 or greater the 8 will become a 9 or if it is not then it will stay the same. And everything to the left stays the same, everything to the right turns into zeros.
Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 16 of 42 at one school and 18 of 34 at the other have ear infections. At the 0.05 level of significance, is there sufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools? Group of answer choices
Answer:
Step-by-step explanation:
The summary of the given data includes;
sample size for the first school [tex]n_1[/tex] = 42
sample size for the second school [tex]n_2[/tex] = 34
so 16 out of 42 i.e [tex]x_1[/tex] = 16 and 18 out of 34 i.e [tex]x_2[/tex] = 18 have ear infection.
the proportion of students with ear infection Is as follows:
[tex]\hat p_1 = \dfrac{16}{42}[/tex] = 0.38095
[tex]\hat p_2 = \dfrac{18}{34}[/tex] = 0.5294
Since this is a two tailed test , the null and the alternative hypothesis can be computed as :
[tex]H_0 :p_1 -p_2 = 0 \\ \\ H_1 : p_1 - p_2 \neq 0[/tex]
level of significance ∝ = 0.05,
Using the table of standard normal distribution, the value of z that corresponds to the two-tailed probability 0.05 is 1.96. Thus, we will reject the null hypothesis if the value of the test statistics is less than -1.96 or more than 1.96.
The test statistics for the difference in proportion can be achieved by using a pooled sample proportion.
[tex]\bar p = \dfrac{x_1 +x_2}{n_1 +n_2}[/tex]
[tex]\bar p = \dfrac{16 +18}{42 +34}[/tex]
[tex]\bar p = \dfrac{34}{76}[/tex]
[tex]\bar p = 0.447368[/tex]
[tex]\bar p + \bar q = 1 \\ \\ \bar q = 1 -\bar p \\ \\\bar q = 1 - 0.447368 \\ \\\bar q = 0.552632[/tex]
The pooled standard error can be computed by using the formula:
[tex]S.E = \sqrt{ \dfrac{ \bar p \bar q}{ n_1} + \dfrac{\bar p \bar p}{n_2} }[/tex]
[tex]S.E = \sqrt{ \dfrac{ 0.447368 * 0.552632}{ 42} + \dfrac{ 0.447368 * 0.447368}{34} }[/tex]
[tex]S.E = \sqrt{ \dfrac{ 0.2472298726}{ 42} + \dfrac{ 0.2001381274}{34} }[/tex]
[tex]S.E = \sqrt{ 0.01177284105}[/tex]
[tex]S.E = 0.1085[/tex]
The test statistics is ;
[tex]z = \dfrac{\hat p_1 - \hat p_2}{S.E}[/tex]
[tex]z = \dfrac{0.38095- 0.5294}{0.1085}[/tex]
[tex]z = \dfrac{-0.14845}{0.1085}[/tex]
z = - 1.368
Decision Rule: Since the test statistics is greater than the rejection region - 1.96 , we fail to reject the null hypothesis.
Conclusion: There is insufficient evidence to support the claim that a difference exists between the proportions of students who have ear infections at the two schools
Suppose a vine maple grows in height linearly. Four weeks after it is planted it stands 10.67 inches, and after seven weeks it is 15.67 inches tall. Write an equation that models the growth, in inches, of the vine maple as a function of time, in weeks. 1. What is the slope of the function? 2. How tall was the tree when it was first planted? 3. Write the function 4. How tall will the vine maple be after 16 weeks?
Answer:
Height (z)= 4+(5/3)(z)
Where z is the number of weeks
1). Slope = 4
2). Height= 5.67 inches
3).Height (z)= 4+(5/3)(z)
4).Height= 30.67 inches
Step-by-step explanation:
At week four
10.67= x+4y
Week 7
15.67= x+7y
Solving both equation simultaneously
3y= 5
Y= 5/3
15.67= x+7y
15.67= x+7(5/3)
15.67-35/3= x
15.67-11.67= x
4= x
The modeled equation is
Height (z)= 4+5/3(z)
Where z is the number of weeks
Slope of the function as compared to y= mx+c is 4
The first week of it's plantation
Height (z)= 4+5/3(z)
Height (1)= 4+5/3(1)
Height= 5.67 inches
After 16 weeks
Height (z)= 4+(5/3)(z)
Height (16)= 4+(5/3)(16)
Height= 30.67 inches
What is 2 cm converted to feet?
Answer:
0.065617 ft
Step-by-step explanation:
Answer:
0.0656168 feet.
Step-by-step explanation:
Which of the following points IS a solution to the system: y > - 3x + 4 / y > 2x / - y < 7 Selected answer is not correct.
Answer:
Solution : Third Option
Step-by-step explanation:
The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.
[tex]\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}[/tex]
Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.
Therefore, the third option is a solution to the system.
What is the probability that a randomly selected individual on this campus weighs more than 166 pounds? (express in decimal form and round final answer to 4 decimal places)
Answer:
hello attached is the missing part of your question and the answer of the question asked
answer : 0.2951
Step-by-step explanation:
Given data:
number of persons allowed in the elevator = 15
weight limit of elevator = 2500 pounds
average weight of individuals = 152 pounds
standard deviation = 26 pounds
probability that an individual selected weighs more than 166 pounds
std = 26 , number of persons(x) = 15, average weight of individuals(u) = 152 pounds
p( x > 166 ) = p( x-u / std, 166 - u/ std )
= p ( z > [tex]\frac{166-152}{26}[/tex] )
= 1 - p( z < 0.5385 )
p( x > 166 ) = 1 - 0.70488 = 0.2951
2 lines intersect a horizontal line to form 8 angles. Labeled clockwise, starting at the top left, the angles are: A, B, C, D, E, F, G, D. Which of the pairs of angles are vertical angles and thus congruent? ∠A and ∠G ∠A and ∠B ∠C and ∠F ∠D and ∠H
Answer:
∠A and ∠G is the pair of vertical angles.
Step-by-step explanation:
From the figure attached,
Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.
Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."
Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.
From the given options,
∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.
Answer:
a
Step-by-step explanation:
distance between 2,-5 and 3,-7
Answer:
√5
Step-by-step explanation:
[tex](2 ,-5) = (x_1,y_1)\\(3,-7)=(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \\d = \sqrt{(3-2)^2 +(-7-(-5))^2}\\ \\d = \sqrt{(1)^2+(-7+5)^2}\\ \\d = \sqrt{(1)^2 + (-2)^2}\\ \\d = \sqrt{1 +4}\\ \\d = \sqrt{5}[/tex]
[tex]\sqrt{x+1+5=x}[/tex] Please help [tex]\sqrt{5x-x=0}[/tex] I actually can't do this, also thirty points
Answer:
It is undefined.
Step-by-step explanation:
Let's take a look at the first equation- if we simplify and move the terms, it becomes sqrt of 6 = 0, which results in an undefined value of x. The second equation works with x=0 but not the first so the value of x is undefined.
Kevin's total payroll deductions are 30% of his earnings. If his deductions add up to $369 for a two week period, how much were his earnings for the period?
Answer:
His earnings for the period= $123
Step-by-step explanation:
Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.
If 30% of his earnings = $369
His earnings = x
30/100 * x= 369
X= 369*100/30
X= 123*10
X=$ 1230
His earnings for the period= $123
1.
The ratio of the numbers of sides of two regular polygons is 1:2 .If each interior angle of the first
polygon is 1200 then the measure of each interior angle of the second polygon
is
(1)1400
(2)1350
(3)1500
(4)1600
first polygon
ext. angle=180°-120°
=60°
[tex]ext \: ang = \frac{360}{n} [/tex]
n=360°/60°
n=6
second polygon
n=2(6)=12
ext. ang= 360°/n = 360°/12° = 30°
int. ang = 180°-30°= 150°
answer is C
If the ratio of the numbers of sides of two regular polygons is 1:2 and each interior angle of first angle is 120° then the measure of each interior angle of the second polygon is 150° which is option 3).
What is regular polygon?A regular polygon is a polygon whose all sides are equal to each other.
How to find interior angle?We have been given ratio of sides of two polygon that is 1:2 and the interior angle of first polygon that is 120 degrees.
Exterior angle will be 180-120=60°
We know that exterior angle =360/n where n is the sides of the polygon.
60=360/n
n=360/60
n=6
Number of sides of other polygon=2*6=12
Exterior angle=360/n
=360/12
=30
Interior angle=180-30=150°
Hence the interior angle of the second polygon is 150 degrees.
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Determina el valor absoluto de 13 – 11|
Responder:
2
Explicación paso a paso:
El valor absoluto de una expresión es el también conocido como valor positivo devuelto por la expresión. Una expresión en un signo de módulo se conoce como valor absoluto de la expresión y dicha expresión siempre toma dos valores (tanto el valor positivo como el negativo).
Por ejemplo, el valor absoluto de x se escribe como | x | y esto puede devolver tanto + x como -x debido al signo del módulo.
Pasando a la pregunta, debemos determinar el valor absoluto de | 13-11 |. Esto significa que debemos determinar el valor positivo de la expresión como se muestra;
= | 13-11 |
= | 2 |
Este módulo de 2 puede devolver tanto +2 como -2, pero el valor absoluto solo devolverá el valor positivo, es decir, 2.
Por tanto, el valor absoluto de la expresión es 2
Express the function F in the form f∘g. (Enter your answers as a comma-separated list. Use non-identity functions for f(x) and g(x).)
F(x) = (x − 1)4
Answer:
[tex]f(x) = x^{4}[/tex], [tex]g(x) = x-1[/tex]
Step-by-step explanation:
Let be [tex]F(x) = f\circ g (x) = (x-1)^{4}[/tex], then expression for [tex]f(x)[/tex] and [tex]g(x)[/tex] are, respectively:
[tex]f(x) = x^{4}[/tex] and [tex]g(x) = x-1[/tex]
A girl has 98 beads, and all but 14 were lost. how many beads did she loose?
Answer:
84 beads
Step-by-step explanation:
She had 98 beads and lost all but fourteen. So it would be 98 - 14 which would get you 84 beads that the girl has lost
a theater has (2x+1) rows of seats, with (x-3) seats in each row. how many seats are in the theater?
A. 2x^2- 5x- 3
B. 2x^2+ 5x- 3
C. 2x^2- 7x+ 3
D. 2x^2- 7x- 3
(2x+1)(x-3)
y(x-3) .... let y = 2x+1
y*x+y(-3) .... distribute
xy - 3y
x( y ) - 3( y )
x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1
2x^2 + x - 6x - 3 ..... distribute
2x^2 - 5x - 3
Answer is choice A
22/25of a number is what percentage of that number?
Answer:
88%.
Step-by-step explanation:
Multiply the fraction by 100:
(22/25) * 100
= 22 * 4
= 88%.
Question: 2. Musah Stands At The Centre Of A Rectangular Field. He First Takes 50 Steps North, Then 25 Steps West And Finally 50 Steps On A Bearing Of 3150 Sketch Musah's Movement Mark 41 Ii. How Far West Is Musah's Final Point From The Centre? [Mark 41 Iv. How Far North Is Musah's Final Point From The Centre? Mark 41 Describe How You Would Guide A JHS Student
Answer:
60.36 steps West from centre
85.36 steps North from centre
Step-by-step explanation:
Refer to attached
Musah start point and movement is captured in the picture.
1. He moves 50 steps to North, 2. Then 25 steps to West, 3. Then 50 steps on a bearing of 315°. We now North is measured 0°or 360°, so bearing of 315° is same as North-West 45°.
Note. According to Pythagorean theorem, 45° right triangle with hypotenuse of a has legs equal to a/√2.
How far West Is Musah's final point from the centre?
25 + 50/√2 ≈ 60.36 stepsHow far North Is Musah's final point from the centre?
50 + 50/√2 ≈ 85.36 stepsHospitals typically require backup generators to provide electricity in the event of a power outage. Assume that emergency backup generators fail 18% of the times when they are needed. A hospital has two backup generators so that power is available if one of them fails during a power outage. Required:a. Find the probability that both generators fail during a power outage.b. Find the probability of having a working generator in the event of a power outage. Is that probability high enough for the hospital?c. Is that probability high enough for the hospital?
Answer:
a. 0.36
b. 0.1296
c. No.
Step-by-step explanation:
1. Note the probability of emergency backup generators to fail when they are needed = 18% or 0.18. Thus,
a. Probability of both emergency backup generators failing = P (G1 and G2 fails) where G represents the generators.
= P (G1 falls) x P ( G2 fails)
= 0.18 x 0.18
= 0.36
b. The probability of having a working generator in the event of a power outage = G1 fails x G2 works + G2 works x G2 fails
= 0.36 x 0.18 + 0.18 x 0.36
= 0.1296
c. Looking at the probability of any of the generators working, it is not meeting safety standards as lives could be lost if the backup generators needed to perform an emergency surgery operation fails.
15P! NEED TODAY! WILL MARK BRAINLIEST! HELP! 15P! NEED TODAY! WILL MARK BRAINLIEST! HELP! You need to solve a system of equations. You decide to use the elimination method. Which of these is not allowed? Equation 1: 2x - 3y = 12 Equation 2: -2x + y = 8 A. Add the left side of equation 2 to the left side of equation 1. B. Multiply equation 2 by 3. Then substract the result from equation 1. C. Add equation 2 to equation 1.
Answer:
(A)
Step-by-step explanation:
That rule isn't used in the elimination methods for systems of equations, but, rather, it is used in substitution methods. The other rules are used in elimination.
Please tell me if I got it wrong. I really hope it is correct.
A. Add the left side of equation 2 to the left side of equation 1.
B. Multiply equation 2 by 3. Then subtract the result from equation 1.
C. Add equation 2 to equation 1.
A random sample of 1003 adult Americans was asked, "Do you think televisions are a necessity or a luxury you could do without?" Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without. Construct and interpret a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a luxury they could do without out.
Answer:
The 95% confidence interval is [tex]0.503 < p < 0.535[/tex]
The interpretation is that there is 95% confidence that the true population proportion lie within the confidence interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 1003
The number that indicated television are a luxury is k = 521
Generally the sample mean is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
[tex]\r p = \frac{521}{1003}[/tex]
[tex]\r p = 0.519[/tex]
Given the confidence level is 95% then the level of significance is mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
The margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]
=> [tex]E = 1.96 * \sqrt{ \frac{ 0.519 (1- 0.519 )}{1003} }[/tex]
=> [tex]E = 0.016[/tex]
The 95% confidence interval is mathematically represented as
[tex]\r p -E < p < \r p +E[/tex]
=> [tex]0.519 - 0.016 < p < 0.519 + 0.016[/tex]
=> [tex]0.503 < p < 0.535[/tex]
What is the factorization of the polynomial below? 9x^2+12x+4
Answer:
(3x+2)^2
Step-by-step explanation:
a scientist used 2 gallons of liquid for every 7 hours he works. he used__of a gallon each hour he works
Answer: 2/7 of a gallon (in decimal it’s 0.286)
Step-by-step explanation: This one’s really easy.
2/7 of 1 gallon. Checking: so that if you multiply it by 7 it equals to 2
The gallon he used each hour he works is 2/7.
What is unit rate?
A rate is a ratio that is used for comparing two different kinds of quantities which have different units. On the other hand, the unit rate illustrates how many units of quantity correspond to the single unit of another quantity.
The common examples used are:
Distance per second
Kilometer per hour
Meter per second
Earning per month
Given,
he used 2 gallons liquid for every 7 hours he works.
gallons used for per hour = 2/7
Hence, He used 2/7 gallons per hour.
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What is the value of x?
Answer:
58
Step-by-step explanation:
By the property of intersecting secants outside of a circle, we have:
x° = 1/2( 141° - 25°) = 1/2 * 116° = 58°
Therefore, x = 58
Solve for x if 2(1+3x)=14
Answer:
x=2
Step-by-step explanation:
2(1+3x)=14
Divide each side by 2
2/2(1+3x)=14/2
1+3x = 7
Subtract 1 from each side
3x =7-1
3x = 6
Divide by 3
3x/3 = 6/3
x =2
Heights of men on a baseball team have a bell-shaped distribution with a mean of and a standard deviation of . Using the empirical rule, what is the approximate percentage of the men between the following values? a.166 cm and 202 cm b. 172cm and 196cm
Let assume that the mean is 184 and the standard deviation is 6
Heights of men on a baseball team have a bell-shaped distribution with a mean 184 of and a standard deviation of 6 . Using the empirical rule, what is the approximate percentage of the men between the following values? a.166 cm and 202 cm b. 172 cm and 196cm
Answer:
P(156<X<202) = 99.7%
P(172<X<196) = 95.5%
Step-by-step explanation:
Given that :
Heights of men on a baseball team have a bell-shaped distribution with a mean of and a standard deviation of . Using the empirical rule, what is the approximate percentage of the men between the following values? a.166 cm and 202 cm b. 172 cm and 196cm
For a.
Using the empirical rule, what is the approximate percentage of the men between the following values 166 cm and 202 cm.
the z score can be determined by using the formula:
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z(166) = \dfrac{166-184}{6}[/tex]
[tex]z(166) = \dfrac{-18}{6}[/tex]
z(166) = -3
[tex]z(202) = \dfrac{202-184}{6}[/tex]
[tex]z(202) = \dfrac{18}{6}[/tex]
z(202) = 3
P(156<X<202) = P( μ - 3σ < X < μ + 3σ )
P(156<X<202) = P( - 3 < Z < 3)
P(156<X<202) = P( Z < 3) - P(Z < -3)
P(156<X<202) = 0.99865- 0.001349
P(156<X<202) = 0.997301
P(156<X<202) = 99.7%
For b.
b. 172 cm and 196cm
[tex]z = \dfrac{X - \mu}{\sigma}[/tex]
[tex]z(172) = \dfrac{172-184}{6}[/tex]
[tex]z(172) = \dfrac{-12}{6}[/tex]
z(172) = -2
[tex]z(196) = \dfrac{196-184}{6}[/tex]
[tex]z(196) = \dfrac{12}{6}[/tex]
z(196) = 2
P(172<X<196) = P( μ - 2σ < X < μ + 2σ )
P(172<X<196) = P( - 2 < Z < 2)
P(172<X<196) = P( Z < 2) - P(Z < -2)
P(172<X<196) = 0.9772 - 0.02275
P(172<X<196) = 0.95445
P(172<X<196) = 95.5%
.... i repost bec brainly would not allow me to make it lager
that is all i can do
Answer:
Hey there!
Richard has 480 dollars.
Giving 1/4 of the money to his brother would mean giving 120 dollars to his brother.
Richard has 480-120, or 360 dollars left.
Giving 1/3 of the money left would be giving 120 dollars to his sister.
His sister and brother both got 120 dollars from Richard.
Hope this helps, and let me know if you need more help. :)
A player at a fair pays Rs. 100 to roll a dice. The player receives Rs. 50 if the number of dots facing up is equal to 5, Rs. 200 if the number is 6, but nothing otherwise. Find the expected value of the reward Y. What is the expected value of the gain? Find out the standard deviation of Y.
Answer:
The dice has 6 options:
if the outcome is 5, player wins 50
if the outcome is 6, player wins 200
if the outcome is another number, the player does not win anything.
Now, remember that the expected value can be written as:
E = ∑xₙpₙ
where xₙ is the event n, and pₙ is the probability of that event.
for a dice, the probabilty for each number is 1/6
The expected value is:
E = (1/6)*(0 + 0 + 0 + 0 + 50 + 200) = 41.66
The expected gain will be E - 100 (because the player pays 100 in order to play)
Then the expected gain is:
G = 41.66 - 100 = -58.33
The standard deviation can be written as:
s = √( ∑(x - x)^2/n)
where x is the mean, in this case the mean is:
(200 + 50 + 4*0)/6 = 41.66 and n = 6.
s = √( (1/6)*(4*(0 - 41.66)^2 + (50 - 41.66)^2 + (200 - 41.66)^2) ) = 73
So we have a lot of standard deviation on Y.
Is y = 8x -15 a function?
Answer:
Hey there!
A function only has one y value for every x value, so this is a function. Additionally, all linear equations (that are in the y=mx+b form) are functions.
Hope this helps :)
Use the graph showing Debra's account balance to answer the question that follows. ^
About how long will it take for Debra's account balance to equal $60?
A - 6 months
B - 6 years
C - 3 months
D - 3 years
Answer: 2 years
Step-by-step explanation:
In the given graph, we have
Account Balance ($) on y-axis
Time (years) on x-axis.
To know the time taken to get a balance of $60 , we check the point corresponding to 60 at y-axis and then join it to the line of the function and stop.
Then from there we drop a line to x-axis.
We get x=2.
That is it will take 2 years to get $60 balance in Debra's account.
So the correct answer is 2 years.
