The function is given as,
[tex]h(x)=7x^2-4x-15[/tex]The objective is to determine the value h(20).
This can be obtained by substituting 20 for 'x' in the given expression,
[tex]\begin{gathered} h(20)=7(20)^2-4(20)-15 \\ h(20)=7(400)-80-15 \\ h(20)=2800-95 \\ h(20)=2705 \end{gathered}[/tex]Thus, the value of the given function h(20) is 2705.
Find the equation of the line described. Write your answer in standard form. Vertical and containing (10,14)
We have here a special case where the line is vertical. In this case, the line has an "infinite" slope (or it is not defined). Therefore, since the line is vertical and contains the point (10, 14), the line is given by the equation:
[tex]x=10[/tex]The standard form of the line is given by the general equation:
[tex]Ax+By=C[/tex]Then, we can rewrite the equation as follows:
[tex]x+0y=10[/tex]We can see that this line contains the point (10,14):
We can see that the vertical line, x + 0y = 10 passes through the point (10, 14).
In summary, the line is given by x + 0y = 10 (A = 1, B = 0, C = 10).
I need help with this practice Having trouble solving it The subject is trigonometry
To solve the problem, we will make use of the identity:
[tex]\cos (\alpha-\beta)=\cos (\alpha)\cos (\beta)+\sin (\alpha)\sin (\beta)_{}[/tex]ANGLE α
The angle lies in the second quadrant. The only positive ratio is the sine.
If we have that:
[tex]\tan \alpha=-\frac{12}{5}[/tex]Displaying this on a triangle for ease of working, we have:
Therefore, the length of the hypotenuse will be:
[tex]\begin{gathered} x=\sqrt[]{12^2+5^2}=\sqrt[]{144+25}=\sqrt[]{169} \\ x=13 \end{gathered}[/tex]Therefore, we have that:
[tex]\begin{gathered} \sin \alpha=\frac{12}{13} \\ \cos \alpha=-\frac{5}{13} \end{gathered}[/tex]ANGLE β
This angle lies in the fourth quadrant. Only the cosine ratio is positive in this quadrant.
We are given in the question:
[tex]\cos \beta=\frac{3}{5}[/tex]Displaying this on a triangle for ease of working, we have:
Therefore, using the Pythagorean Triplets, we have that:
[tex]y=4[/tex]Therefore, we have that:
[tex]\sin \beta=-\frac{4}{5}[/tex]SOLVING THE IDENTITY
Applying the identity quoted earlier, we have:
[tex]\begin{gathered} \cos (\alpha-\beta)=\cos (\alpha)\cos (\beta)+\sin (\alpha)\sin (\beta)_{} \\ \cos (\alpha-\beta)=(-\frac{5}{13})(\frac{3}{5})+(\frac{12}{13})(-\frac{4}{5}) \\ \cos (\alpha-\beta)=-\frac{63}{65} \end{gathered}[/tex]When finding the height of a triangle, you need to find the equation of the lineperpendicular to the base of the triangle that passes through the vertex opposite thebase and then find the point of the intersection of the base and the perpendicular line. True Or False?
EXPLANATION:
Given;
We are given the step by step procedure to find the height of a triangle.
Required;
We are required to determine if the step by step solution is true or false.
Solution/Explanation;
When finding the height of a triangle, we may use the Pythagoras theorem or we may use trigonometric ratios for right angled triangles.
Note that the Pythagoras' theorem is also used only for right angled triangles and one of the three sides will be the height of the triangle.
When required to calculate the the height of a triangle given a line perpendicular to the base (that is, at a 90 degree angle with the base), and passing through the vertex opposite the base, the triangle can be effectively split into two parts along the perpendicular and the perpendicular line will then become the height. Also depending on the amount of information available, we may use the Pythagoras' theorem (if the other two sides are given). Alternatively we may use the trigonometric ratios if one other side and one of the angles is given.
Therefore,
ANSWER:
FALSE
A line's slope is -5. The line passes through the point (5, 30). Find an equation for this line in both point-slope and slope-intercept form A) An equation for this line in point-slope form is:B) An equation for this line in slope-intercept form is.
Answer:
y - 30 = 5(x - 5) (point slope form)
slope intercept form is y = 5x+5
Explanation:
Given the following
Slope m = -5
Point = (5, 30)
x0 = 5 and y= = 30
The equation of the line in point slope form is expressed as y-y0 = m(x-x0)
Substitute
y - 30 = -5(x - 5) (point slope form)
Express in slope intercept form (y = mx+c)
y - 30 = -5x + 25
y = -5x + 25 + 30
y = -5x + 55
Hence the equation of the line in slope intercept form is y = -5x+55
Write an equation for a rational function with:
Vertical asymptotes at x = -5 and x =
-6
x intercepts at x = -3 and x = -4
y intercept at 4
Equation for a rational function is 10(x2 + 7x + 12) / (x2 + 11x + 30) = 0.
What is Rational Function?
Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers; they can be found in any field K.
So this will be a rational function with the vertical asymptotes given by the denominators:
(x + 5) and (x + 6).
The x-intercepts will be provided by the numerator,
which will be:
a(x + 3)(x + 4)
The letter an is a constant.
Given that (0,4) is the y intercept, we have:
4 = a(0+3)(0+4) / (0+5)(0+6)
4= 12a / 30
12a = 120
now,
a = 120/12,
a = 10,
and a = 1.
Now,
a(x+3)(x+4) / (x+5)(x+6) = 0
10 (x^2 + 7x + 12) / (x^2 + 11x + 30) = 0
Hence, We have the following equation for a rational function:
10 (x2 + 7x + 12) / (x2 + 11x + 30) = 0.
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1. Write the equation of the line with a slope of -3 that passes through the point (1,9).y=3x + 12y=3x + 6y=-32 +6y=-3x+12
Answer:
y = -3x + 12
Explanation:
The equation of a line with slope m that passes through the point (x1, y1) can be calculated as:
[tex]y-y_1=m(x-x_1)[/tex]So, replacing m by -3, and (x1, y1) by (1, 9), we get:
[tex]y-9=-3(x-1)[/tex]Finally, solving for y, we get:
[tex]\begin{gathered} y-9=-3x-3(-1) \\ y-9=-3x+3 \\ y-9+9=-3x+3+9 \\ y=-3x+12 \end{gathered}[/tex]Therefore, the answer is:
y = -3x + 12
The angle of elevation to the top of a Building in New York is found to be 11 degrees from the ground at a distance of 1 mile from the base of the building. Using this information, find the height of the building. Round to the tenths. Hint: 1 mile = 5280 feet
Your answer is __________ feet.
The height of the building is given as 1026.43 feet
What is angle of elevation?This is the term that is used to refer to the angle that is usually formed from the horizontal line to the angle of sight of a person.
We have to make use of the trig function that tells us that
tan(∅) = opposite length /adjacent length.
where ∅ = 11 degrees
adjacent length = 1
opposite length = x
When we put these values in the formula we would have
tan 11 = x / 1
0.1944 = x /1
we have to cross multiply to get x
x = 0.1944 x 1
= 0.1944
Then the height of the building would be 0.1944 x 5280 feet
= 1026.43 feet
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Find the annual fixed expense for car insurance if John makes
six payments in a year at $174.45 each?
The annual fixed expense for car insurance is $ 1,046.70.
It is given in the question that John makes six payments in a year at $174.45 each.
We have to find the annual fixed expense for car insurance.
We know that,
The annual fixed expense for the car insurance will be 6 times the individual payment given in the question.
Hence, by simple multiplication, we can write,
Annual fixed expense for the car insurance = 6*174.45 = $ 1,046.70
Car insurance
Car insurance is a type of financial protection that covers the cost of another driver’s medical bills and repairs if you cause an accident with your car, or in case your car is stolen or damaged some other way.
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Help meeeee4) Consider the equation z(x)=(x-5,x s101-x+8, x > 10Note that for this problem, you do not actually have to evaluate the results. Just make sure that youexplain your choices.a. If you are trying to evaluate Z(3), which equation would you choose, and why?b. If you are trying to evaluate Z(11), which equation would you choose, and why?c. If you are trying to evaluate Z(10), which equation would you choose, and why?
4). a. If you are trying to evaluate Z(3) in order to know which equation would you choose we would have to make the following calcuations:
So, if Z(3), then:
substitute the x with the number 3
[tex]z\left(3\right)=3-5=-2,3\leq10,\text{ 1-3=-2, 3}>10[/tex]Therefore, the equation to choose if Z(3) would be x>10, because by substitute the x with the number 3 would be the largest function with a positive number and sign.
express the quadratic function f(x)=3x^2 + 6x - 2 in the form a(x + h)^2 + k where a,h and k are constants
Answer:
Explanation:
Given:
[tex]f(x)=3x^2+6x-2[/tex]First, we do completing the square on the given function to express it into vertex form. So,
We write it in the form:
[tex]\begin{gathered} x^2+2ax+a^2 \\ \end{gathered}[/tex]And, factor out 3: So,
[tex]\begin{gathered} 3(x^2+2x-\frac{2}{3}) \\ \text{where:} \\ 2a=2\text{ or a=1} \\ \text{Hence} \\ 3(x^2-2x-\frac{2}{3}+1^2-1^2) \end{gathered}[/tex]Since:
[tex]\begin{gathered} x^2+2ax+a^2=(x+a)^2 \\ So, \\ x^2+2x+1^2=(x+1)^2 \end{gathered}[/tex]Then,
[tex]\begin{gathered} 3(x^2-2x-\frac{2}{3}+1^2-1^2) \\ =3((x+1)^2-\frac{2}{3}-1^2) \\ \text{Simplify} \\ f(x)=3(x+1)^2-2-3 \\ f(x)=3(x+1)^2-5 \end{gathered}[/tex]Therefore, the answer is:
[tex]f(x)=3(x+1)^2-5[/tex]Find the surface area of the cylinderA). 188.4 ft^2B). 226.08 ft^2C). 244.92 ft^2D). 282.6 ft^2
To solve this problem, we will use the following formula for the surface area of a cylinder:
[tex]A=2\pi rh+2\pi r^2,[/tex]where r is the radius of the base, and h is the height of the cylinder.
Substituting h= 10 ft, and r = 3 ft in the above formula, we get:
[tex]A=2\pi(3ft)(10ft)+2\pi(3ft)^2.[/tex]Simplifying, we get:
[tex]A=244.92ft^2.[/tex]Answer: Option C.
The coordinates of three vertices of a rectangle are (3,7), (-3,5), and (0,-4). What are the coordinates of the fourth vertex?A. (6,-2)B. (-2,6)C. (6,2)D. (-2,-6)
ANSWER
A. (6, -2)
EXPLANATION
Let's graph these three vertices,
The fourth vertex must be at the same distance from (0, -4) as vertex (3, 7) is from (-3, 5),
Note that the horizontal distance between these two points is 6 units and the vertical distance is 2 units. The fourth vertex is,
[tex](0+6,-4+2)=(6,-2)[/tex]Hence, the fourth vertex is (6, -2)
what is the value of x in the solutions to the system of equations below3x-8y=112y+x=13
Given system of equations
3x - 8y = 11 ______________________1
2y + x = 13 ______________________ 2
Use the substution method
How to use the substitution method
1. pick one of the equation
2. make one of the variable subject of relation
3. substitute
From equation (1)
2y + x = 13
x = 13 - 2y
substitute x from equation 1 to 2.
3(13 - 2y) - 8y = 11
39 - 6y - 8y = 11
39 - 11 = 6y + 8y
28 = 14y
y = 28/14
y = 2
Next, substitute y in equation 2 to find x.
x = 13 - 2y
x = 13 - 2(2)
x = 13 - 4
x = 9
Final answer x = 9
Which calculation and answer show how to convert 13 to a decimal?
when evalueatong the expression 13/15,
13 serves as the dividend and
15 is the divisor
Divisor is always placed outside the division sign and the dividend inside.
According to the option, you can see that 15 which is the divisor is placed outside and 13 is placed inside.
check the diagram below:
Option A is the correct answer in this case
The perimeter of a quarter circle is 3.57 kilometers. What is the quarter circle's radius? Use 3.14 for . kilometers Siubmit explain
Given:
It is given that the perimeter of a quarter circle is 3.57 km.
To find :
The radius of the quarter circle.
Explanation :
The perimeter of the quarter circle is
[tex]P=\frac{2\pi r}{4}\text{ }+2r[/tex]Substitute the value of perimeter in the above formula
[tex]3.57=\frac{\pi r}{2}+2r[/tex][tex]3.57=(\frac{3.14}{2}+1)r[/tex][tex]3.57=2.57r[/tex][tex]r=1.39[/tex]Answer
Hence the radius of a quarter circle is 1.39 km.
J is the midpoint of CT if CJ=5x-3 and JT=2x+21 find CT
Since J is the midpoint of the CT segment, then:
[tex]\begin{gathered} CJ=JT \\ 5x-3=2x+21 \end{gathered}[/tex]Now, you can solve the equation for x:
[tex]\begin{gathered} 5x-3=2x+21 \\ \text{ Add 3 from both sides of the equation} \\ 5x-3+3=2x+21+3 \\ 5x=2x+24 \\ \text{ Subtract 2x from both sides of the equation} \\ 5x-2x=2x+24-2x \\ 3x=24 \\ \text{ Divide by 3 from both sides of the equation} \\ \frac{3x}{3}=\frac{24}{3} \\ x=8 \end{gathered}[/tex]Replace the value of x into the equation for segment CJ or segment JT to find out what its measure is. For example in the equation of the segment CJ:
[tex]\begin{gathered} CJ=5x-3 \\ x=8 \\ CJ=5(8)-3 \\ CJ=40-3 \\ CJ=37 \end{gathered}[/tex]Finally, you have
[tex]\begin{gathered} CJ=37 \\ CJ=JT \\ 37=JT \\ \text{ Then} \\ CT=CJ+JT \\ CT=37+37 \\ CT=74 \end{gathered}[/tex]Therefore, the measure of the segment CT is 74.
translate the following into an equation:6 less decreased by twice a number results in 8
Let the number be x.
Twice the number means 2 * x = 2x
Twice the number decreased by 6 means
2x - 6
Given that the result is 8, we have
2x - 6 = 8
A particular lawn requires 6 bags of fertilizer. A lawn next door requires 4 bags of fertilizer. How big is the lawn next door?A. 10 feet square feetB. 24 feet square feetC. 50 feet square feetD. Not enough information is given
Answer:
D. Not enough information is given
Explanation:
To know the size of the lawn next door, we would need a relation between the square feet and the number of bags of fertilizer.
Since all we know is the bags of fertilizer for the particular lawn and the lawn next door, we can say that we didn't have enough information to answer the question.
Therefore, the answer is:
D. Not enough information is given
the answer is red show me how to get to the answer
The given expression is:
[tex]\frac{5\sqrt{4}}{\sqrt{3}}[/tex]The first step is to find the square root of 4 in the numerator, that is:
[tex]\sqrt{4}\text{ = 2}[/tex]Substitute this into the given expression:
[tex]\frac{5(2)}{\sqrt{3}}[/tex][tex]\frac{10}{\sqrt{3}}[/tex]The next step is to rationalize, that is, multiply the numerator and the denominator by √3
[tex]\frac{10}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}[/tex][tex]\frac{10\sqrt{3}}{\sqrt{9}}[/tex]Since √9 = 3[tex]\frac{10\sqrt{3}}{3}[/tex]Given that 1 inch = 2.54 centimeters how many centimeters are in 6 feet?
Answer:
182.88 centimeters are in 6 feet!
Step-by-step explanation:
I hope this helped! c:
Answer:
182.88 centimetersStep-by-step explanation:
If
1 in. = 2.54 cm.
and
12 in. = 1 ft.
lets convert cm into feet
1 * 12 = 12 (how many inches are in a foot )
2.54 * 12 = 30.48 (how many centimeters are in a foot)
so now that we know how many centimeters are in a foot, we can find out how many centimeters are in 6 feet
30.48 * 6 = 182.88
182.88 centimeters are in 6 feetGiven the following linear function sketch the graph of the function and find the domain and range.
F(x)=2/7x-2
pls show how did u solve it
Linear function f(x) = 2/7x - 2
It has no domain or range restrictions, so both of them include all real numbers.
Doman x ∈ ( - ∞, + ∞),Range y ∈ ( - ∞, + ∞).The graph is attached
What is the value of the expression below when w = 3?3w² - 6w - 4
ANSWER:
5
STEP-BY-STEP EXPLANATION:
We have the following expression:
[tex]3w^2-6w-4\:[/tex]We substitute the value of w, when it is equal to 3, just like this:
[tex]\begin{gathered} 3\left(3\right)^2-6\left(3\right)-4\: \\ \\ 3\cdot \:9-6\left(3\right)-4 \\ \\ 27-18-4 \\ \\ 5 \end{gathered}[/tex]The value of the expression is equal to 5
Jerry takes out a 30-year mortgage for $170,000.00 to buy a condo. His monthly mortgage payment is $939.00. How much interest will he pay over the life of the loan? Round your answer to the nearest whole dollar.
Okay, here we have this:
Considering the provided information we obtain the following:
Mortgage capital=$170,000
Total payment = Monthly payment * 12 months of the year * number of years
Total payment = $939*12*30
Total payment = $338,040
Total payment = Mortgage capital + Interest
Replacing we obtain:
Total payment = Mortgage capital + Interest
$338,040=$170,000+interest
Interest= $338,040-$170,000
Total Interest=$168,040
Finally we obtain that the total interest is $168040.
7 1/3 × 2 2/11 3/5 × 6 2/34 1/5 × 1 1/14
It is easier to perform the operations if you convert the mixed fractions into improper fractions.
For point 1. Make the mixed fractions improper first
[tex]7\frac{1}{3}=\frac{3\cdot7+1}{3}=\frac{21+1}{3}=\frac{22}{3}[/tex][tex]2\frac{2}{11}=\frac{11\cdot2+2}{11}=\frac{22+2}{11}=\frac{24}{11}[/tex]Now, the multiplication of fractions is done like this
[tex]\frac{a}{b}\cdot\frac{c}{d}=\frac{a\cdot c}{b\cdot d}[/tex]Then, you have
[tex]7\frac{1}{3}\cdot2\frac{2}{11}=\frac{22}{3}\cdot\frac{24}{11}=\frac{528}{33}=16[/tex]For point 2.
[tex]6\frac{2}{3}=\frac{3\cdot6+2}{3}=\frac{18+2}{3}=\frac{20}{3}[/tex]Now multiplying the improper fractions you have
[tex]\frac{3}{5}\cdot6\frac{2}{3}=\frac{3}{5}\cdot\frac{20}{3}=\frac{60}{15}=4[/tex]Finally for point 3.
[tex]4\frac{1}{5}=\frac{5\cdot4+1}{5}=\frac{20+1}{5}=\frac{21}{5}[/tex][tex]1\frac{1}{14}=\frac{14\cdot1+1}{14}=\frac{14+1}{14}=\frac{15}{14}[/tex]Now multiplying the improper fractions you have
[tex]\begin{gathered} 4\frac{1}{5}\cdot1\frac{1}{14}=\frac{21}{5}\cdot\frac{15}{14}=\frac{315}{70}=\frac{35\cdot9}{35\cdot2}=\frac{9}{2} \\ 4\frac{1}{5}\cdot1\frac{1}{14}=\frac{9}{2} \end{gathered}[/tex]< BackSee SolutionShow ExampleRecord: 1/3 Score: 1 Penalty: 1 offComplete: 11% Grade: 0%Brianna AllenFinding the Slope from PointsJon 03, 7:15:08 PMWhat is the slope of the line that passes through the points (4, -9) and (8, -3)?Write your answer in simplest form.
To obtain the slope of the line that passes through the two given points, the following steps are recommended:
Step 1: Recall the formula for the slope of a line that passes through any two points (x1, y1) and (x2, y2), as follows:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Step 2: Apply the formula to find the slope of the line that passes through the points (4, -9) and (8, -3), as follows:
[tex]\begin{gathered} \text{Given that:} \\ (x_1,y_1_{})=(4,-9) \\ (x_2,y_2)=(8,-3) \\ \text{Thus:} \\ \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ \Rightarrow\text{slope}=\frac{-3_{}-(-9)_{}}{8_{}-4_{}}=\frac{-3+9}{4}=\frac{6}{4}=\frac{3}{2} \\ \Rightarrow\text{slope}=\frac{3}{2} \end{gathered}[/tex]Therefore, the slope of the line that passes through the points (4, -9) and (8, -3) is 3/2
Dante is arranging 11 cans of food in a row on a shelf. He has 7 cans of beans, 3 cans of peas, and 1 can of carrots. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical (not distinct)?
Given:
The number of cans of food =11
The number of cans of beans=7
the number of cans of peas=3
the number of cans of carrots=1
Condition : two cans of the same food are considered identical.
To arrange the n objects in order,
[tex]\begin{gathered} \text{Number of ways= }\frac{n!}{r_1!r_2!r_3!} \\ =\frac{11!}{7!3!1!} \\ =\frac{39916800}{30240} \\ =1320 \end{gathered}[/tex]Answer: the number of ways are 1320.
Write a rule for the nth term of the geometric sequence given a_2 = 64, r = 1/4
The n-th term of a geometric sequence is given by the formula:
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ r=\text{ common ration} \\ a_1=\text{ first term} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} a_2=64 \\ r=\frac{1}{4} \\ n=2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} a_2=a_1(\frac{1}{4})^{2-1}=64 \\ a_1(\frac{1}{4})=64 \\ a_1=64\times4 \\ =256 \end{gathered}[/tex]Therefore, the rule for the nth term of the sequence is
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ U_n=256_{}(\frac{1}{4})^{n-1} \end{gathered}[/tex]A pool is filled to 3/4 of its capacity 1/9 of water in the pool, evaporates. If the pool can hold 24,000 gallons when it is full, how many gallons of water will have to be added in order to fill the pool?A. 6,000B. 8,000C.12,000D.16,000
First, the pool was filled to 3/4 of its capacity, which is equal to:
[tex]24000\cdot\frac{3}{4}gal=18000gal.[/tex]Then, 1/9 of the water evaporated remaining 8/9 of the 18000 gal:
[tex]18000\text{gal}\frac{8}{9}=16000gal.[/tex]Therefore, to fill the pool we need to add:
[tex]24000-16000[/tex]gallons of water.
Answer: B. 8000.
Consider an investment whose return is normally distributed with a mean of 10% and a standard deviation of 5%. (2.4)
Justify which statistics methodology needs to be used in the above context and
a) Determine the probability of losing money.
b) Find the probability of losing money when the standard deviation is equal to 10%.
a) The probability of losing money when standard deviation is 5% is 2.27%
b) The probability of losing money when standard deviation is 10% is 15.87%
Given,
There is an investment whose return is normally distributed.
The mean of the distribution = 10%
The standard deviation of the distribution = 5%
a) We have to determine the probability of losing money:
Lets take,
x = -0.005%
Now,
P(z ≤ (-10.005 / 5) ) = P(z ≤ - 2.001) = 0.02275
Now,
0.02275 × 100 = 2.27
That is,
The probability of losing money is 2.27%
b) We have to find the probability of losing money when the standard deviation is 10%
Let x be 0.01%
Now,
P(z ≤ (-10.01/10)) = P(z ≤ -1.001) = 0.15866
Now,
0.15866 × 100 = 15.87
That is,
The probability of losing money is 15.87%
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Karine invests $6,100 in an account with an annual interest rate of 4.5% compounded daily for 2 years.What is the return on investment for Karine's account?
The return on investment for Katerine's account = 9.4%
Explanation:Amount invested is the principal
Principal, P = $6,100
Annual Interest Rate, r = 4.5% = 0.045
The interest is compounded daily
Number of times the interest is compounded per year, n = 365
Number of years, t = 2 years
The amount after 2 years is calculated as:
[tex]\begin{gathered} A(t)=P(1+\frac{r}{n})^{nt} \\ A=6100(1+\frac{0.045}{365})^{365(2)} \\ A=6100(1.094) \\ A=6673.4 \end{gathered}[/tex]The amount after 2 years = $6673.4
The interest = Amount - Principal
The interest = $6673.4 - $6100
The interest = $573.4
The return on investment is calculated as:
[tex]\begin{gathered} \text{ROI = }\frac{Interest}{Pr\text{incipal}}\times100\text{ \%} \\ \text{ROI}=\frac{573.4}{6100}\times100\text{ \%} \\ \text{ROI = }9.4\text{ \%} \end{gathered}[/tex]The return on investment for Katerine's account = 9.4%
