Use a calculator to evaluate the expression. (Do not round until the final answer. Then round to three decimal places as needed.)
Answers
2.303
1) For the following expression:
[tex]\frac{\ln30+\ln15}{\log_{10}30+\log_{10}15}[/tex]We can simplify that and then round it off to the nearest thousandth:
2) Let's rewrite them simplifying using the logarithm property of multiplication:
[tex]\begin{gathered} \frac{\ln30+\ln15}{\log_{10}30+\log_{10}15}= \\ \frac{\ln(30\cdot15)}{\log_{10}30+\log_{10}15}= \\ \frac{\ln(30\cdot15)}{\log_{10}(30\cdot15)}= \\ \frac{\ln(450)}{\log_{10}(450)}= \end{gathered}[/tex]Note that the base of the Natural Log is the Euler's number "e" so let's move on now using the calculator, finally:
[tex]\frac{\ln(450)}{\log_{10}(450)}=\frac{6.10924}{2.65321}=2.30258\ldots\approx2.303[/tex]Note that only at the last step we have rounded it off. And that's the
answer
Related Questions
which of the following would be an acceptable first step in simplifying the expression?
Answers
Solution:
Given:
[tex]\frac{cos\text{ }x}{1-sin\text{ }x}[/tex]The only acceptable first step in simplifying the expression from the options that would not change or alter the values of the expression is by multiplying (1 + sin x) to both the numerator and the denominator.
Therefore, the correct answer is OPTION B.
You are researching the speed of sound waves in dry air
at 86°F. The linear function d = 0.217t represents the distances d (in miles) sound waves
travel in t seconds.
A. Represent the situation using a table and a graph.
B. Which of the three representations would you use to find how long it takes sound waves to travel 0.1 mile in dry air at 86°F? Explain.
Answers
By observing the pace at which this compressed region moves through the medium, we may determine the sound speed.The speed of sound is roughly 343 meters per second or 767 miles per hour in dry air at 20 degrees Celsius.
Calculate speed of sound wave?
The formula for the airborne sound speedThe equation for the speed of sound in air as a function of absolute temperature is given by the simplification of v=RTM:v=√γRTM=√γRTM(273K273K)=√(273K)γRM√T273K≈331m 2) Time required for 1620m to be traveled at that speed: t = d / v 0.217m / 0.1 m/s) = 2.17m/ s from the beginning of the sound wave.Since you were watching the lightning, you might have wanted to know the time.Then, using the speed of light, you can determine how long it was between the lights being generated o.217 meters distant from you and Light travels at a speed of3*108 m/s, hence t = 0.217m / (3*108 m/s) = 0.000669 s.
The answer is o.000669 s, as determined in step 2, even though this time is entirely negligible.
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The graph of F(x), shown below, resembles the graph of G(X) = x2, but it hasbeen changed somewhat. Which of the following could be the equation ofF(x)?600 = x2FUO = ?O. A. F(x) = 0.272 - 3B. F(x) = -x2 - 3C. F(x) = 2x2 - 3D. F(X) = 32 - 3
Answers
You have G(x) = x².
take into account that G(x) can be considered as an streched of the F(X), moreover, F(x) is a translation of G(x) downward 3 units. If G(x) is an strech of F(x), then, G(x) is multipled by a constant lower than 1.
Then, based on the previous considerations, you have that the form of F(x) is:
F(x) = 0.2x² - 3
A car drove 300 miles in four hours. How fast was the car traveling in miles per hour?
Answers
Given that,
A car drove 300 miles in four hours.
We can simply put it in this way.
In 4 hours, a total distance covered by the car = 300 miles
In 1 hour, a total distance covered by the car = 300/4 miles = 75 miles.
Hence, the car was traveling at a speed of 75 miles per hour.
what is the final cost of the purchase at discount heaven?
Answers
First, let's sum the single costs of each item.
[tex]32+32+20=84[/tex]Because they are buying 1 jacket, 2 pairs of jeans, and 1 vest. So, the subtotal of these items is $84. (At Discount Heaven)
Then, we apply a 7% sales tax.
[tex]84+0.07\cdot84=84+5.88=89.88[/tex]As you can observe, the sales tax is $5.88 for all the items purchased, and the total cost they have to pay is $89.88.
In a certain chemical, the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. How many grams of zinc does it contain.
Answers
If the ratio of zinc to copper is 4 to 11. A jar of the chemical contains 528 grams of copper. Then 192 grams of zinc does it contain
What is Ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.
Given that,
In a certain chemical, the ratio of zinc to copper is 4 to 11.
i.e 4:11 or 4 /11
If A jar of the chemical contains 528 grams of copper
We need to find how many grams of zinc does it contain.
Let us consider it as x.
Form a equation,
4/11=x/528
4×528=11x
2112=11x
Divide both sides by 11
192=x
Hence 192 grams of zinc does it contain.
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Find the trigonometric ratio using the diagram. Write the fraction in itssimplest form.
Answers
Answer
KM = 30 units
Tan M = (8/15)
Explanation
The Pythagoras Theorem is used for right angled triangle, that is, triangles that have one of their angles equal to 90 degrees.
The side of the triangle that is directly opposite the right angle or 90 degrees is called the hypotenuse. It is normally the longest side of the right angle triangle.
The Pythagoras theorem thus states that the sum of the squares of each of the respective other sides of a right angled triangle is equal to the square of the hypotenuse. In mathematical terms, if the two other sides are a and b respectively,
a² + b² = (hyp)²
For this question,
a = KM = ?
b = KL = 16
hyp = LM = 34
a² + b² = (hyp)²
KM² + 16² = 34²
KM² + 256 = 1,156
KM² = 1,156 - 256
KM² = 900
Take the square root of both sides
√(KM²) = √(900)
KM = 30 units
In a right-angle triangle, the side opposite the right angle is the Hypotenuse, the side opposite the given angle that is non-right angle is the Opposite and the remaining side is the Adjacent.
Using M as the given non-right angle,
Hypotenuse = LM = 34
Opposite = KL = 16
Adjacent = KM = 30
Using trignometric identities, we know that TOA means
Tan M = (Opp/Adj)
Tan M = (16/30)
Divide numerator and denominator by 2
Tan M = (16/30) = (8/15)
Hope this Helps!!!
For the function f(x)5x – 2, what does the x represent?
Answers
The given function is
f(x) = 5x - 2
If we are given a function f(x), the x is called argument of the function.
You just have to pass argument x to get the value of f(x).
Write the equation for a circle with the following informationcenter: (5,-3) radius: 7
Answers
Step 1: Problem
To determine the equation of a circle with centre (5, -3) and radius 7
Step 2: Substitute the centre value and radius to the equation
[tex]\begin{gathered} \text{Equation of a circle} \\ (x-a)^2+(y-b)^2=r^2 \\ \text{centre (5,-3) , radius =7} \\ a=5,\text{ b=-3, r=7} \\ (x-5)^2+(y-(-3))^2=7^2 \end{gathered}[/tex]Step 3: Simplify the above equation
[tex]\begin{gathered} (x-5)(x-5)\text{ + (y+3)(y+3) = 49} \\ x^2-5x-5x+25+y^2+3y+3y+9=49 \\ x^2-10x+25+y^2+6y+9=49 \\ x^2+y^2-10x+6y=49-25-9 \\ x^2+y^2-10x+6y=15 \\ x^2+y^2-10x+6y-15=0 \end{gathered}[/tex]Hence the equation of the circle is
[tex]x^2+y^2-10x+6y-15=0[/tex]according to recent study 7 out of every 500 Americans aged 13-17, years are vegetarian.in a group of 350 13 to 17- years old about how many would you expect to he vegetarian
Answers
7 out of every 500 Americans aged 13 -17 years are vegetarians
This implies that in a group of 500 Americans , 7 Americans that are within the age range of 13 - 17 years are vegetarians
7 ======== 500
x ======== 350
Introduce cross multiplication
7 x 350 = x * 500
2450 = 500x
Divide both sides by 500
2450/500 = 500x/ 500
x = 4.9
Approximately, 5
5 vegetarians aged 13 - 17 years will be present is in a group of 350 Americans
The answer is 5
Jacob is constructing a pentagonal tent for his school carnival. The tent has a side length of 5.13 meters. What is the area of the tent? What is the perimeter of the tent? What is the sum of three of the interior angles in the tent once Jacob obtains the value of its area and perimeter?
Answers
The tent is pentagonal , this means it has 5 sides. The tent have a side length of 5.13 meters.
The area of the pentagon can be calculated below
[tex]\begin{gathered} \text{area of the tent=}\frac{perimeter\times apothem}{2} \\ \tan \text{ 36=}\frac{2.565}{a} \\ a=\frac{2.565}{\tan \text{ 36}} \\ a=\frac{2.565}{0.726542528} \\ a=3.53041962601 \\ \text{perimeter}=\text{ 5.13}\times5=25.65\text{ meters} \\ \text{area =}\frac{25.65\times3.53041962601}{2} \\ \text{area}=\frac{90.5445}{2} \\ \text{area}=45.27225 \\ \text{area}\approx45.27meter^2 \end{gathered}[/tex]Each interior angle of a pentagon is
[tex]\begin{gathered} \text{ interior angle=}\frac{180\times3}{5}=\frac{540}{5}=108^{\circ} \\ \text{ Sum of thr}ee\text{ interior angles = 108}\times3=\text{ }324\text{ degre}e \end{gathered}[/tex]Rewrite the polynomial expression using the GCF: 4x^2+8x+24 ?What is the new polynomial expression
Answers
GCF of 4,8 and 24
is. = 4
Then new expression is
y = 4• (x^2 + 2x + 6)
Find the volume of the cone. Round to the nearest tenth.27 m-45°O 10,306,0 m320,612.0 m341,224.0 m3763.4 m3
Answers
The volume of a cone is given by the formula:
[tex]\begin{gathered} V=\frac{1}{3}\times\pi\times r^2\times h \\ r\text{ is the radius} \\ h\text{ is the height} \end{gathered}[/tex]From the question, we are provided with following:
[tex]\begin{gathered} h=27m \\ \theta=45^0 \end{gathered}[/tex]We have to use the given parameters to obtain the radius of the cone.
Thus, we have:
[tex]\begin{gathered} \text{Tan 45}^0=\frac{opposite}{\text{adjacent}} \\ 1=\frac{27}{\text{radius}} \\ \text{Therefore, radius=27m} \end{gathered}[/tex]Therefore, the volume of the cone is:
[tex]\begin{gathered} V=\frac{1}{3}\times\frac{22}{7}\times27^2\times27 \\ V=20,611.98m^3 \end{gathered}[/tex]Hence, the correct option is option BH
Calculate the five-number summary and the IQR from the following values given: {17, 20, 21, 25, 25, 29, 40}
Answers
Answer:
• 17, 20, 25, 29 and 40
,• IQR=9
Explanation:
(a)Given the set of values:
{17, 20, 21, 25, 25, 29, 40}
• The minimum value = 17
The first quartile
The first quartile is the median of the lower half of the data set.
The lower half of the data set = 17, 20, 21
• Therefore, the first quartile =20
The Median
The median is the number in the middle of the set of values.
The number in the middle is 25, therefore:
• Median = 25
The third quartile
The third quartile is the median of the upper half of the data set.
The upper half of the data set = 25, 29, 40
• Therefore, the third quartile =29
Finally, Maximum Value = 40.
The five-number summary of the set of values is: 17, 20, 25, 29 and 40
(b)Interquartile Range
Interquartile Range = Third Quartile - First Quartile
=29 - 20
IQR=9
A 39 -ft ladder leans against a building so that the angle between the ground and the ladder is 85∘
How high does the ladder reach the building? __________ ft
Answers
The height of the building is 38.85 ft.
Given;
length of the ladder, x = 39 ft
the angle between the ground and the ladder, θ = 85°
let the height of the building be h.
Construct this triangle, the ladder forms the hypotenuse side of the right angle triangle, the height of the triangle is the opposite side of the triangle while the base of the triangle is the adjacent side of the triangle.
Apply the following trig ratio to determine the height of the triangle;
sin(θ) = opposite/hypotenuse
sin(85°) = h/39
h = 39sin(85°)
h = 38.85 ft
Therefore, the height of the building is 38.85 ft (approx.).
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Brody spent $260 on 4 chairs. To find out how much he spent on each chair, he did the following work in long division. 65 4) 260 -24 20 -20 0 Did he do the problem correctly? Why or why not? O A. No, because there is a remainder of o. B. No, because the first digit in the quotient should be 4, not 6. O C. No, because the problem should be 260 14. O D. Yes, he worked the problem correctly.
Answers
He spend $260 on 4 chairs:
To know how much he spent on each chair he must:
Divide 260 into 4You first pick the firt digit of the dividend (260) and look if you can divide that digit into the divider (4) as in this case the firt digit 2 cannot be divided into 4 you take the first and secon digit (26) and divide it into 4 (how many times fix 4 in 26), this is equal to 6 times (this is the first digit of the quotient), then you multiply the 6 by 4 (6*4=24)and put the result under the 26 to substract it:
Now you lower the zero (of the 260) next to the result of the previous subtraction:
And divide 20 into 4 (how many times fix 4 in 20) this is equal to 5 times (this is the second digit of the quotient ) then you multiply the 5 by 4 (5/4 =20) and put the result under the 20 to substract it:
The remainder of 0 means the division has not decimal result, the result of 260 into 4 is an interger number (65)
The firt digit of the quotient is 6 because 26 into 4 is 6.
So the division he did is the correct form to find how much cost each chair ($65)Add these fractions using fraction bars after choosing a common denominator Use the fraction bar inactivate to find the difference
Answers
The fractions you have to add are 1/3 and -5/6
[tex]\frac{1}{3}+(-\frac{5}{6})[/tex]The denominators are "3" and "6"
The common denominator between both numbers is 6.
6*1=6
3*2=6
Multiply 1/3 by factor 2 so that both fractions will have the same denominator
[tex]\frac{1}{3}\cdot2=\frac{1\cdot2}{3\cdot2}=\frac{2}{6}[/tex]Now you can add both fractions
[tex]\frac{2}{6}+(-\frac{5}{6})=\frac{2}{6}-\frac{5}{6}=\frac{2-5}{6}=-\frac{3}{6}[/tex]The result is not in its most reduced form, to siplify the fraction divide both the numerator and denominator by 3
[tex]-\frac{3}{6}\div3=-\frac{1}{2}[/tex]The result is -1/2, in the number line:
given that the measure of arc AD=(17×+2), measure of arc AC=(7×-10),and measure of angle ABC=(4×+15) find the measure of angle ABC
Answers
In the given figure, angle ABC is formed by a tangent and a secant.
The angle formed by tangent and secant is given by
[tex]m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC})[/tex]Where mAD and mAC are the intercepted arcs.
For the given case,
[tex]\begin{gathered} m\angle ABC=(4x+15)\degree \\ m\bar{AD}=(17x+2)\degree \\ m\bar{AC}=(7x-10)\degree \end{gathered}[/tex]Let us substitute the given values into the above formula and solve for x
[tex]\begin{gathered} m\angle ABC=\frac{1}{2}(m\bar{AD}-m\bar{AC}) \\ (4x+15)\degree=\frac{1}{2}\lbrack(17x+2)\degree-(7x-10)\degree\rbrack \\ 2\cdot(4x+15)\degree=(17x+2)\degree-(7x-10)\degree \\ 8x+30=17x+2-7x+10 \\ 8x-17x+7x=2+10-30 \\ -2x=-18 \\ x=\frac{-18}{-2} \\ x=9 \end{gathered}[/tex]The value of x is 9
So, the measure of angle ABC is
[tex]\begin{gathered} m\angle ABC=4x+15 \\ m\angle ABC=4(9)+15 \\ m\angle ABC=36+15 \\ m\angle ABC=51\degree \end{gathered}[/tex]Therefore, the measure of angle ABC is 51°
The science class is taking a trip to the science center. there are 20 students and an unknown number of adult chaperones going. the bus holds at most 35 people.what is the greatest number of adults who can chaperone? I know the answer is 15. however, what they want us to do is create an equation using inequalities (<, >, etc..) That's what I don't know how to do with this problem. I'm trying to explain it to my daughter but I don't know how to do it myself.
Answers
We are given that there are 20 students and an unknown number of adult chaperones.
Let x denotes the unknown number of adult chaperones.
The bus holds at most 35 people
We know that 20 students plus x number of adult chaperones should be at most 35
at most 35 means equal or less than 35
So we can write
[tex]20+x\le35[/tex]Now we can easily solve for x
[tex]\begin{gathered} 20+x\le35 \\ x\le35-20 \\ x\le15 \end{gathered}[/tex]A can contains 24 fluid ounces of fruit juice. How many pints of fruit juice does the can contain?A 12 ptB 3 pt C 1 1/2 ptD 1/3 pt
Answers
In order to convert from fluid ounce to pint, we need to know that 16 fluid ounces is equivalent to 1 pint.
Then, to find how many pints is 24 fluid ounces, we can use a rule of three:
[tex]\begin{gathered} 16\text{ fluid ounces}\to1\text{ pint} \\ 24\text{ fluid ounces}\to x\text{ pints} \\ \\ \frac{16}{24}=\frac{1}{x} \\ x=\frac{24}{16}=\frac{3}{2}=1\frac{1}{2} \end{gathered}[/tex]So 24 fluid ounces is equivalent to 1 1/2 pints, therefore the correct answer is C.
35% of the employees in a company receive an incentive in the month of April. What is theprobability that among 4 employees chosen at random, all 4 do not receive the incentive inApril?
Answers
ANSWER :
0.1785
EXPLANATION :
35% will receive an incentive and (100% - 35% = 65%) will NOT receive an incentive.
So an employee has 65% chance of NOT receiving an incentive.
The probability that among 4 employees do not receive the incentive is :
[tex](0.65)^4=0.1785[/tex]Miscavage Corporation has two divisions: the Beta Division and the Alpha Division.
The Beta Division has:
sales of $320,000,
variable expenses of $158,100,
and traceable fixed expenses of $72,300.
The Alpha Division has:
sales of $630,000,
variable expenses of $343,800,
and traceable fixed expenses of $135,100.
The total amount of common fixed expenses not traceable to the individual divisions is $137,200.
What is the total company's net operating income?
Answers
The total company's net operating income (NOI) is $103,500.
What is a Net operating income?In accounting, a Net operating income refers to the figure that equals to all revenue from the property minus all reasonably necessary operating expenses.
The computation of the Net operating income is as follows:
= Gross Income - Operating Expenses
= (Sales+Sales) - [(variable expenses + variable expenses) + (fixed expenses + fixed expenses) + 137,200]
= (320,000+630,000) - [(158,100 + 343,800) + (72,300 + 135,100) + 137,200]
= 950,000 - (5,01,900 + 2,07,400 + 137,200)
= 950,000 - 8,46,500
= $1,03,500
In conclusion, the total company's net operating income (NOI) is $103,500.
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Find the exact values of the six trigonometric functions of the real number t
Answers
In a unit circle, given the (x,y) coordinate, x corresponds to cosine, and y corresponds to sine.
Then use the trigonometric identity to solve for tangent.
We therefore have the following ratios for sin, cos, and tan.
[tex]\begin{gathered} \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=\frac{\sin t}{\cos t}=\frac{\frac{15}{17}}{-\frac{8}{17}}=-\frac{15}{8} \\ \\ \text{Therefore,} \\ \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=-\frac{15}{8} \end{gathered}[/tex]Solving for the reciprocal of sin, cos, and tan we have
[tex]\begin{gathered} \csc t=\Big(\sin t\Big)^{-1}=\Big(\frac{15}{17}\Big)^{-1}=\frac{17}{15} \\ \sec t=\Big(\cos t\Big)^{-1}=\Big(-\frac{8}{17}\Big)^{-1}=-\frac{17}{8} \\ \cot t=\Big(\tan t\Big)^{-1}=\Big(-\frac{15}{8}\Big)^{-1}=-\frac{8}{15} \\ \\ \text{Therefore,} \\ \csc t=\frac{17}{15} \\ \sec t=-\frac{17}{8} \\ \cot t=-\frac{8}{15} \end{gathered}[/tex]the water pressure on Mustafa as he dives is increasing at a rate of 0.992 atmospheres (atm) per meter
What is the rate of increase in water pressure in atm/km
Answers
The rate of increase in water pressure in atm/km = 992 atm/km
what is pressure?Pressure can be defined as the external or internal force that acts on an area of an object which can be measured in atmosphere per meter.
The rate at which Mustafa dives = 0.992atm/meter.
That is,
0.992 atm = 1 meter
X atm = 1 km
But 1000m = 1 km
make X atm the subject of formula;
x atm = 0.992 × 1000
X atm = 992 atm/km
Therefore, the rate in atm/ km would be = 992 atm/km
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write three things you used to do but don't do anymore
Answers
Answer:
Trusting peoples
Be happy
make friends
A runner has a track lap time of 3 minutes while at a run, 5 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog, and 1/10 at a walk, what is the total track lap time of the runner? Write the solution as a mixed number or a fraction in lowest terms.
Answers
The total track lap time of the runner is 4 11/15 and it has been written as a mixed number or a fraction in lowest terms.
Mixed fraction:
The fraction represented with its quotient and remainder is known as mixed fraction.
Given,
A runner has a track lap time of 3 minutes while at a run, 5 minutes while at a jog, and 7 minutes while at a walk. If 2/5 of the lap is paced at a run, 1/2 at a jog, and 1/10 at a walk.
Here we need to find the total track lap time of the runner.
Here we can compute the Total Lap Time by multiplying each fraction by its associated lap time, then we get,
Run Lap Time = (2/5)(3) = 6/5 minutes
Jog Lap Time = (1/3)(5) = 5/3 minutes
Walk Lap Time = (4/15)(7) = 28/15 minutes
So, the total lap time is, written as,
Total Lap Time = 6/5 + 5/3 + 28/15
Now, we have to make the fraction equal to each other,
=> (6x3)/(5x3) + (5x5)/(3x5) + (28 x 1)(15 x1)
=> 18/15 + 25/15 + 28/15
=> (18 + 25 + 28)/15 = 71/15
Now, we have to convert this into mixed fraction then we get,
=> 71/15 = 4 11/15
Therefore, the total Lap Time is 4 11/15 minutes.
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Point A is shown on the complex plane.What is the standard form of the complex number that point A represents?
Answers
Hello there. To solve this question, we have to remember some properties about the representation of a complex number in the complex or Argand-Gauss plane.
Given the complex plane with the point A representing a complex number:
We have to remember that in the complex plane, a complex number z:
[tex]z=a+ib[/tex]has coordinates
[tex](a,\,b)[/tex]And it is more commonly represented by a vector starting at the origin and with the tip on this point.
In this case, we find that the coordinates of the point A are:
[tex]A=(-5,\,3)[/tex]Which means that the complex number is
[tex]-5+3i[/tex]And this is the answer contained in the last option.
Karen is planning to drive 870 miles on a road trip. If she wants to complete the trip in 6 days, how many miles will she need to drive each day??
Answers
Answer:
145 miles
Step-by-step explanation:
870 ÷ 6 = 145
how do I find the correct answer? (answers in the dropbox below)
Answers
A rhombus have 4 sides and angles
it first must be proven to have 4 sides, or 4 angles
thats a definition for Quadrilateral
then correct option is D
Tom Blasting invested $4,500 in an investment paying 10% compounded quarterly for 3 years. Find the interest
Answers
Given that Tom invested $4500 in an investment paying 10% compounded quarterly for 3 years.
We have to find the interest for the given time period.
We know that the formula of amount on a principal P, rate r per annum, time t years where interest is compounding quarterly is:
[tex]A=P(1+\frac{r}{4})^{4t}[/tex]Here, P = 4500, r = 0.1 and t = 3. So,
[tex]\begin{gathered} A=4500(1+\frac{0.1}{4})^{4(3)} \\ =4500(1+0.025)^{12} \\ =4500(1.025)^{12} \\ =4500(1.3448) \\ =6051.6 \end{gathered}[/tex]So, the amount we get is $6051.6.
Now, it is known that the interest is the difference between the amount and the principal. So,
[tex]\begin{gathered} \text{ interest}=\text{ amount-principal} \\ =6051.6-4500 \\ =1551.6 \end{gathered}[/tex]Thus, the interest is $1551.6.