The dimensions of the enclosure that can be erected at minimum cost are 21.25 feet by 42.50 feet
How to determine the dimensions of the enclosure that guarantees the minimum costFrom the question, the given parameters are
Area = 903 square feet
Shape = rectangle
From the question, we understand that:
One side of the area would be enclosed by the external wall of the store
If the dimensions of the area are Length (L) and Width (W), then we have
Area = LW
Perimeter = 2L + W
Rewrite as
A = LW
P = 2L + W
Substitute 903 for A in A = LW
LW = 903
Make W the subject
W = 903/L
Substitute W = 903/L in P = 2L + W
P = 2L + 903/L
Differentiate the equation
So, we have
P' = 2 - 903/L²
Set to 0
2 - 903/L² = 0
So, we have
903/L² = 2
This gives
L² = 903/2
Divide
L² = 451.5
Take the square roots
L = 21.25
Substitute L = 21.25 in W = 903/L
W = 903/21.25
Evaluate
W = 42.50
Hence, the dimensions of the enclosure are 21.25 feet by 42.50 feet
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You are catering at a ceremony and have a budget of R1 200 to spend on meat. You
want to serve chicken and steak. Chicken costs R30 per kilogram and steak costs R120
per kilogram.
3.1.1 In the problem description in 3.1 above, state what changes and what remains
the same. In other words, mention the variables for the problem.
Answer:
Step-by-step explanation:
The length of a rectangle is 5 in. longer than its width and the rectangle has an area of
50in².
What are the dimensions of the rectangle
The dimensions of the rectangle are L=10in, B=5in
What is rectangle?A rectangle includes everything listed below:
A plane figureA closed formA quadrilateralThe parallelogramYour polygon's four sides must be two congruent pairings in order to have two pairs of parallel sides. The length of the left and right sides, as well as the base and top, will be equal.
let width of rectangle be x, then length will be
B=5+x
given area of rectangle
A=50in²
area = length×width
A=L×B
50 = x×(5+x)
50=5x+x²
x²+5x-50=0
x²+10x-5x-50=0
x(x+10)-5(x+10)=0
x=-10 or x=5
since x=-10 is not possible
therefore, x=5
Length(L)=5+5=10in
Width(B) = 5in
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Bro help pls I need this done by tmr or else they take point if I turn it late
Answer:
180
Step-by-step explanation:
So, in the first 4 games, they score 10 points. If this continues to happen in the remaining 18 games, it would be 180.
10 x 18 = 180.
Let h(x) = (fog)(x) = (x - 2)^4. Find f(x) given g(x) = x - 2.
f(x) =
Answer:
f(x) = x^4
Step-by-step explanation:
h(x) = f(g(x)) = (x - 2)^4
g(x) = x - 2
h(x) = f(g(x)) = (g(x))^4
f(x) = x^4
The population of a certain city has been increasing exponentially accordingto the functionP (t) = 800, 000e0.051where t is the time in years (with t = 0 corresponding to 2014).a.) What was the population in the year 2014?b.) In what year will the population reach 1,200,000?c. what was the rate of change of the population in the year 2019?
(b) To determine the year the population will reach 1,200,000, substitute p(t) = 1,200,000 into p(t) above and calculate the value of t
[tex]\begin{gathered} \text{ p(t) = 1,200,000} \\ 1,200,000=800,000e^{0.05t} \\ \text{divide both sides by 800,000} \\ \frac{1200000}{800000}\text{ =}\frac{\text{ 800000}e^{0.05t}}{800000} \\ \\ 1.5=e^{0.05t} \\ \text{take }\ln \text{ of both sides} \\ \ln 1.5\text{ = }\ln e^{0.05t} \\ \ln 1.5=0.05t\ln e \\ \ln 1.5=0.05t(1) \\ \ln 1.5\text{ = 0.05t} \\ \text{divide both sides by 0.05} \\ \frac{\ln 1.5}{0.05}\text{ = t} \\ t=8 \end{gathered}[/tex]The year when t= 8, given that t=0 in 2014 is the year 2022
(c) the rate of change of the population in the year 2019
Firstly, differentiate p(t) with respect to t
[tex]\begin{gathered} p(t)\text{ = }800,000e^{0.05t} \\ \frac{\text{ dp}}{\text{ dt}}\text{ = 0.05(800,000)}e^{0.05t} \\ \frac{dp}{\mathrm{d}t}\text{ = 40,000}e^{0.05t} \\ \text{ This means that the rate of change of the function at any time t is 40,000}e^{0.05t} \\ \end{gathered}[/tex]In the year 2019, t = 5
Substitute t=5 into the rate of change above
[tex]\begin{gathered} \text{ at t= 5, } \\ \text{rate of change = 40,000}e^{0.05(5)} \\ =\text{ 40,000}e^{0.25} \\ =40,000(1.284025) \\ =51361 \end{gathered}[/tex]PLEASE HELP I HAVE BEEN STUCK FOR 2 DAYS
A bag contains 42 red, 45 green, 20 yellow, and 32 purple candies, you pick one candy at random, find the probability that it is green or yellow
Answer: i believe its 0.46 im not for sure though
Step-by-step explanation:
Find the volume of the following right rectangular prism. Round answers to the hundredth.3.6 m21 m1.5 mthe height is 3.6m the base side is 2.1m and the base is 1.5m
Answer:
11.34 m³
Explanation:
The volume of a right rectangular prism can be calculated as:
[tex]\text{Volume}=\text{Height}\times\text{ Length}\times\text{ Width}[/tex]So, replacing the height by 3.6 m, the length by 2.1 m, and the width by 1.5m, we get:
[tex]\begin{gathered} \text{Volume}=3.6\text{ m }\times2.1\text{ m }\times1.5\text{ m } \\ \text{Volume = 11.34 m}^3 \end{gathered}[/tex]Therefore, the volume of the prism is 11.34 m³
Choose all the correct answers using the diagram below.
What is the length of the diagonal?
2
√2
1
√3
No answer text provided.
We want to find the diagonal length of the square given in the question.
[tex]x=?[/tex]Since this shape is a square, all four sides are of equal length. Therefore, each side of the square must be [tex]1[/tex] unit.
Next, we will use the Pythagorean Theorem to find the length of the hypotenuse of a right triangle. This value is also equal to the length of our diagonal. We can find the length of the diagonal using the formula below;
[tex]a^2+b^2=c^2[/tex]Therefore, the correct answer to our question is the following equality;
[tex]x^2=1^2+1^2[/tex][tex]x^2=2[/tex][tex]\sqrt{x^2} =\sqrt{2}[/tex][tex]x=\sqrt{2}[/tex]Second option should be the answer.
Solve negative a minus eight ninths equals one third for a. a equals 5 over 9 a equals negative 5 over 9 a equals 11 over 9 a equals negative 11 over 9
8/9 - 1/3
To subtract these two fractions, first find a common denominator.
The common denominator will be the
least common multiple for the two denominators.
In this case, the least common multiple of 9 and 3 is 9.
So to subtract, a denominator of 9 is needed in each fraction.
8/9 already has 9 in the denominator so it stays the same.
To get a 9 in the denominator of 1/3, multiply top and bottom by 3.
This gives us 3/9.
So we have 8/9 - 3/9 which is 5/9.
#7777
The full-time year-round median salary for U.S. men in 2010 was $42,600, and the full-time year-round salary for U.S. women in 2010 was $35,600.
If the full-time year-round median salary for U.S. men in 2010 was $42,600. The full-time year-round median salary for U.S. men in 2010 was 121% of the full-time year-round median salary for U.S. women in 2010.
Median salary percentageUsing this formula
Median salary percentage = 2010 Median salary in US men / 2010 Median salary in US women
Let plug in the formula
Median salary percentage = $42,500 / $35,000
Median salary percentage = 1.2143 × 100
Median salary percentage = 121.43%
Median salary percentage = 121% (Approximately)
Therefore median salary for men in 2010 was 121% of median salary for women in 2010.
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Put the numbers in order from smallest to largest.
PLEASE HELPP!!!
The order of the numbers from lowest to highest is 4.68 × 10⁻⁶, 8.34 × 10⁻², 1.2 × 10⁷, 3.24 × 10⁹ and 5.48 × 10⁹
What is the order of the numbers from lowest to highest?The given numbers are expressed in standard form. Standard form is a way of writing numbers as a power 10 e.g 100 = 1 × 10² and 0.01 = 1 × 10⁻².
So converting the numbers back to ordinary numbers will be useful.
To do this, we will multiply or divide the powers of 10 with the decimal numbers.
We will multiply if the power is positive e.g 2.4 x 10² = 2.4 x 100 = 240 and divide if the power is negative 2.4 x 10⁻² = 2.4/100 = 0.024
3.24 × 10⁹ = 3.24 x 1000,000,000 = 3240000000
4.68 × 10⁻⁶ = 4.68 / 1000000 = 0.00000468
5.48 × 10⁹ = 5480000000
8.34 × 10⁻² = 8.34/100 = 0.0834
1.2 × 10⁷ = 12000000
Therefore, arranging from lowest to highest. We have:
4.68 × 10⁻⁶, 8.34 × 10⁻², 1.2 × 10⁷, 3.24 × 10⁹ and 5.48 × 10⁹
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1. When a number is divided by 5, the result is 50 less than if the number had been divided by 6. What is the number?
2. I have two turtles. Today, the older turtle's age is 11 times that of the younger turtle. In 24 years, the older turtle's age will only be 7 times that of the younger turtle. If both turtles survive until then, how many years from today will the older turtle's age be 3 times that of the younger turtle?
1) A number that is divided by 5, with the result as 50 less than if the number had been divided by 6 is; -1500
2) If both turtles survive until then, the number of years from today that the older turtle's age would be 3 times that of the younger turtle is; 146 years
How to solve Algebra Word Problems?1) Let the number be x. We are told that it is divided by 5, and the result is 50 less than if the number had been divided by 6. Thus, we have;
(x/6) - (x/5) = 50
Multiply through by 30 to get;
5x - 6x = 1500
-x = 1500
x = -1500
2) Let the older turtle be x and the younger one be y.
Today, the older turtle's age is 11 times that of the younger turtle. Thus;
Todays age;
Older turtle = 11y years
Younger turtle = y years
In 24 years, the older turtle's age will only be 7 times that of the younger turtle. Thus;
11y + 24 = 7(y + 24)
11y + 24 = 7y + 168
11y - 7y = 168 - 24
4y = 144
y = 144/4
y = 36
Thus;
Age of older turtle today = 11 * 36 = 396 years
Age of younger turtle today = 36 years
Thus, for older turtle to be thrice the age of younger turtle, then;
3(36 + t) = 396 + t
108 + 3t = 396 + t
2t = 292
t = 292/2
t = 146 years
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Mei and Dennis compare the numbers graphed on the number line below. Mei writes theinequality -9 <-3. Dennis writes the inequality -3 <-9. Which statement is true?FILE-10 -9 -8 -7 -6 -5 -4 -3 -2 -10A)Mei is correct because -9 is greater than 3.B)Mei is correct because -9 is to the left of -3 onthe number line.C)Dennis is correct because 3 is less than 9.D)Dennis is correct because -3 is to the right of--9 on the number line.
The correct answer is:
Mei statement that the inequality is -9 < -3 is True.
Mei is correct because -9 is to the left of -3 on the number line. ( first option in the picture).
Greta offers to buy a team photo for 15 of her teammates, but 6 of them don't want one. If a team photo costs $2, how much will Greta spend on her teammates? Choose the correct expression and solution to this problem. O A. The expression is 2(15 + 6). Greta will spend $42. OB. The expression is 2(15 - 6). Greta will spend $18. C. The expression is 15(6 - 2). PREVIOUS
The teammates are 15 but 6 of them do not want the photo, so the number of the teammates who wants the photo is 15 - 6.
Now, each photo cost $2 adn the number of photo is equal to the number of teammates who wants the photo which is (15-6), so the expression for the total cost is:
[tex]2\cdot(15-6)_{}[/tex]We have to multiply the cost of each photo for the number of photo Greta will buy.
Identify the zeros of the funtion using a graphing calculator.
2
f(x)=x(squared) - 9
enter your answer in {brackets} from least to greatest
The zeros of the function are x = 3 and x = -3
How to determine the zeros of the function?The equation of the function is given as
f(x) = x(squared) - 9
Rewrite the equation properly
So, we have the following equation
f(x) = x^2 - 9
Express the equation as a difference of two squares
So, we have the following equation
f(x) = (x - 3)(x + 3)
Set the equation to 0
(x - 3)(x + 3) = 0
Split
x - 3 = 0 and x + 3 = 0
Solve for x
x = 3 and x = -3
Hence, the solutions are -3 and 3
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1. -35=5b2. x-6=-263. 130=13b4. 19=16+m5. a+15=116. p-8= -87. -17+x= -248. 4+n=139. -3x=010. 0.6=m-0.811. x-5.3=1.27
In any equation in math, the most basic thing is the the fact that both expressions on either side of the equality sign are of the same value. This means -35 and 5b (in number 1) are of the same value. Therefore, whatever you do to the one on the left, you must likewise do to the one on the right. That is, if you have to add 10 to the one on the left, you must simultaneously add 10 to the one on the right. Hence, number 1 is solved as follows;
(1) -35 = 5b
To eliminate the 5 and isolate the b variable, divide both sides by 5
-35/5 = 5b/5
- 7 = b
(2) x - 6 = - 26
Add 6 to both sides of the equation;
x - 6 + 6 = - 26 + 6
x = - 20
(3) 130 = 13b
Divide both sides of the equation by 13
130/13 = 13b/13
10 = b
(4) 19 = 16 + m
Subtract 16 from both sides of the equation
19 - 16 = 16 - 16 + m
3 = m
(5) a + 15 = 11
Subtract 15 from both sides of the equation
a + 15 - 15 = 11 - 15
a = - 4
(6) p - 8 = - 8
Add 8 to both sides of the equation
p - 8 + 8 = - 8 + 8
p = 0
(7) - 17 + x = - 24
Add 17 to both sides of the equation
- 17 + 17 + x = - 24 + 17
x = - 7
(8) 4 + n = 13
Subtract 4 from both sides of the equation
4 - 4 + n = 13 - 4
n = 9
(9) - 3x = 0
Divide both sides of the equation by - 3
- 3x/-3 = 0/-3
x = 0
(10) 0.6 = m - 0.8
Add 0.8 to both sides of the equation
0.6 + 0.8 = m - 0.8 + 0.8
1.4 = m
(11) x - 5.3 = 1.27
Add 5.3 to both sides of the equation
x - 5.3 + 5.3 = 1.27 + 5.3
x = 6.57
Jim, Eduardo, Larry, Simone, Ian, Dawn, Tyrone, and Kim have all been invited to a dinner party. They arrive randomly and each person arrives at a different time.
a. In how many ways can they arrive?
b. In how many ways can Jim arrive first and Kim Last?
c. Find the probability that Jim will arrive first and Kim last.
Part a: The people can arrive in 5040 ways
Part b: In 120 ways, Jim can arrive first and Kim last
Part c: The probability that Jim will arrive first and Kim last is 1/42
People invited to the party: Jim, Eduardo, Larry, Simone, Ian, Dawn, Tyrone, and Kim
Part a:
Since there are 7 people, the number of ways they can arrive is 7*6*5*4*3*2*1 =.5040 ways
Part b:
For Jim to arrive first and Kim last:
The remaining 5 people can arrive in any order so, the number of ways in which they can arrive is 5*4*3*2*1 = 120 ways
Part c:
The probability that Jim will arrive first and Kim last is given by:
Number of ways Jim can arrive first and Kim last/ Total number of ways in which all the people can arrive at the party
= 120/5040 = 1/42
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There were 18,652 geese on a lake. What is this number rounded to the tenthousands place?A20,000B19.600C19.000D18.600car mechanic rounds a car's weight to the nearest thousand. He says theweight is 4,000 pounds. What is the least and the greatest amounts the carcould actually weigh? Explain.
Step 1
There are 18,652 geese on a lake
Required: To round this off to the ten thousand place
Step 2
Hence, we will approximate the thousands and add its value to the ten thousand.
[tex]=\text{ 20,000}[/tex]Step 3
The mechanic rounds the weight of the car to the nearest thousand and gets 4000 lb.
Using the rule below;
[tex]\begin{gathered} (4000\text{ - 500)lb - least} \\ or \\ (4000\text{ + 49}9)lb-\text{ greatest} \\ \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{If we subtract 500 from 4000 we get 3500lb} \\ 3500lb\text{ is the least weight of the car} \\ \text{Notice that 3500 rounded off to the nearest thousand = 4000} \\ \text{Any number less than that say 3499 rounded off to the nearest thousand}=3000 \end{gathered}[/tex][tex]\begin{gathered} \text{If we add 499 to 4000, we get 4499 pounds} \\ 4499\text{ pounds is the greatest weight of the car} \\ \text{Notice if you round off 4499 to the nearest thousand = 4000} \\ \text{Any number more than this say 4500 rounded to the nearest thousand=5}000lb \\ \text{Hence the greatest weight of the car= 4499} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} \text{Least weight of the car = 3500}lb \\ \text{Greatest weight of the car = }4499lb \end{gathered}[/tex]K increased by the product of 5 and 3 what is the expression
K (5 * 3)
K * 15
15K
The answer is 15K based on the information available. I asked the student twice if he has more details about this exercise but he become unresponsive.
Hope that this is the answer to the actual exercise.
Closing the session.
b.This interval includes one endpoint but not the other; do you see why?We can express this range of values in inequality notation and in interval notation:• Inequality notation: -4 << 4 (alternatively: z>-4 AND 2 ≤4)• Interval notation: (-4,4)Rewrite each of the following inequalities in interval notation:a.-8 -7-6-8 -7-6 -5 -4-8 -7 -6 -5 -4 -3-8 -7 -6-5 -4-B -7 -6-5C.d.0.-5 -4 -3 -2 -10123as an inequality: -7<< -5in interval notation:-1 0 12 3as an inequality: -6 ≤ ≤6in interval notation:-2 -1 0 1 2 3as an inequality: -7 < x < -1in interval notation:-2 -1 0 12 3as an inequality: 5 ≤ ≤7in interval notation:-3-2 -1 0 1 2 3as an inequality: -2 << -1.in interiell-4-34444455555
Given
To find the interval.
Explanation:
It is given that,
That implies,
a) The interval notation is, (-7,-5).
b) The interval notation is, [-6,6].
c) The interval notation is, (-7,-1).
d) The interval notation is, [5,7].
e) The interval notation is, [-2,-1).
Geometry help for A and B. Answer B approximate volume?
The volume of the silo with given height and diameter is 4374π ft or 13734.36 ft. (approximately).
What is volume?
Volume is a measurement of 3-D space that is occupied. Numerous imperial units or SI-derived units, such as the cubic meter and liter, are frequently used to quantify it numerically (such as the gallon, quart, cubic inch). Volume and length (cubed) have a symbiotic relationship. The volume of a container is typically thought of as its capacity, not as the amount of space it takes up.
Given in the question,
The diameter of the cylindrical silo is 18 ft,
and its height is 54 ft.
Volume of a cylinder can be calculated using the formula:
[tex]V = \pi r^2 h[/tex]
Here, V = volume, r = radius, h = height,
We know that, radius is half of diameter. So, radius = 18/2 = 9 ft
Putting the given value in the formula:
[tex]V = \pi 9^2 \times 54[/tex]
[tex]V = \pi \times 81 \times 54[/tex]
V = 4374π ft.
Putting the value of π as 3.14 (approximately)
So, volume of the silo becomes 13734.36 ft.
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look at step by step solution shown below and fill in the missing stepthe solution is the missing step
Solving an Equation
We are given the equation:
[tex]3(2x+5)=4(5-x)[/tex]The first step is to multiply the constants by the binomials in parentheses:
[tex]6x+15=20-4x[/tex]This step was correctly done by Jose.
The second step is to 'pass' the 4x from the right side of the equation to the left by adding 4x on both sides:
[tex]10x+15=20[/tex]This step was also correct.
Now we must 'pass' 15 to the right by subtracting 15:
[tex]10x=5[/tex]And here we find the first error. Jose subtracted 15-20 instead of 20-15 and erroneously got -5.
Answer: First error in step 3
I need help I’m not sure I did this right and need help on the graphing!! And table next to it please :( !
The solution for the given system of equations, y = [tex]\frac{-1}{2}[/tex]x + 5 and y = 3x - 2 is (2,4) and the graph is attached below
What is the system of equations?The system of equations is a set of equations consist the same variables. If the given equation are all linear then, it is the system of linear equation.
To solve such system, it is required to figure out the variable values that can solve all the equations involved in the system.
For the given system of equation the variable value is x.
So, [tex]\frac{-1}{2}[/tex]x + 5 = 3x - 2
2 + 5 = 3x + [tex]\frac{x}{2}[/tex]
7 = x ([tex]\frac{6+1}{2}[/tex]) = [tex]\frac{7x}{2}[/tex]
x = 2
Now apply the obtained value of x in either of the equations:
y = 3x - 2
y = 6 - 2
y = 4
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Solve quickly!3(x+10)=4(x-2)
ANSWER
x = 38
EXPLANATION
To solve this equation, first, we have to apply the distributive property of multiplication over addition to eliminate the parenthesis,
[tex]\begin{gathered} 3\cdot x+3\cdot10=4\cdot x-4\cdot2 \\ \\ 3x+30=4x-8 \end{gathered}[/tex]Subtract 3x from both sides of the equation,
[tex]\begin{gathered} 3x-3x+30=4x-3x-8 \\ \\ 30=x-8 \end{gathered}[/tex]And add 8 to both sides,
[tex]\begin{gathered} 30+8=x-8+8 \\ \\ 38=x \end{gathered}[/tex]Hence, the solution is x = 38.
The lines shown below are perpendicular. If the green line has a slope of 23/1,what is the slope of the red line?-510-9-1051015XOA. 3/4OB.4/3O C.-4/3O D. -3/4MIN
Solution
Step 1
Two lines are perpendicular if the product of their slope = -1
Step 2
[tex]m1\times m1=\text{ -1}[/tex]Step 2
[tex]\begin{gathered} m1\text{ = }\frac{3}{4} \\ \\ \frac{3}{4}m2\text{ = -1} \\ \\ 3m_2\text{ = -4} \\ \\ m_2\text{ = }\frac{-4}{3} \end{gathered}[/tex]whats 1 plus 1 in mathmaticals
Answer:
2
Step-by-step explanation:
If you have 1 cookie and someone gives you another cookie you now have 2.
Which statement is true of the graphed function? (PICTURE OF GRAPH BELOW)a) More information is needed to determine whether the graphed function is even, odd, or neither.b)The function is neither an even nor an odd function.c) The function is an even function.d) the function is an odd function
To determine if a function is even or odd, we start from its definition.
While for an EVEN FUNCTION we have: F(x) = F(-X), for an ODD FUNCTION we have F(-X) = -F(X)
Now, from this, we can check that all the values the function achiever for any X value, the -X has same height. The function presents a symmetry over the Y-axis, and this implies in a function to be an EVEN FUNCTION.
And from the solution developed above, the only statement that is true is the
C) The function is an even function.
Rewrite the following equation in slope-intercept format.x-11=-3y
Slope-intercept format is represented by the following expression:
[tex]y=mx+b[/tex]Then to rewrite it, we need to isolate the variable y, using inverse operations to solve equations:
[tex]\begin{gathered} 3y=-x+11 \\ y=-\frac{1}{3}x+\frac{11}{3} \end{gathered}[/tex]Let f(x)=(x−7)(x+6)(x−5). Find the y-intercept(s), the x-intercept(s), the values of x where f(x)>0, and the values of x where f(x)<0.
2. Find the x-intercept(s). List your answers as points in the form (a,b).
Answer:
ez
Step-by-step explanation:
ezz
Evaluate using order of operations: (8 + 7) + (3.5)
Answer:
Step-by-step explanation:
18.5
Answer:
18.5
Step-by-step explanation:
PEMDAS (parenthesis, exponents, multiplication, division, addition, subtraction)
(8+7)+(3.5)
(15)+(3.5)
18.5