The price per unit that yields maximum revenue is $400.
We can start by finding the demand function for the product. Since the demand is assumed to be linear, we can use two data points to find the equation of the line:
(40, 300) and (45, 275)
Using the point-slope form of a line, we get:
(275 - 300) / (45 - 40) = -5/25 = -1/5
y - 300 = (-1/5)(x - 40)
y = (-1/5)x + 320
where y is the number of units sold per week and x is the price per unit.
The revenue function is simply the product of the price and the number of units sold:
R = xy
Substituting the demand function, we get:
R = x(-1/5)x + 320x
Simplifying, we get:
R = -1/5x^2 + 320x
To find the price per unit that yields maximum revenue, we need to take the derivative of the revenue function with respect to x and set it equal to zero:
dR/dx = -2/5x + 320 = 0
Solving for x, we get:
x = 800/2 = $400
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pressure=Force/area A brake pad has an area of 0.35m² and has a force of 140 N applied to it. Calculate the pressure on the brake pad in N/m². If you answer is a decimal, give it to 1 d.p.
Answer:
Step-by-step explanation:
140/0.35squared
=1142.857142
to 1 d,p=1142.9
What is the relationship between the two quantities in the table?
The relationship between the quantities is “+ 90.”
The relationship between the quantities is “Minus 90.”
The relationship between the quantities is “+ 30.”
The relationship between the quantities is “Times 30.”
Answer: Your answer is C
Step-by-step explanation:
Have a nice day
Marisol burned 670 calories while exercising on Monday. If Ling burned x fewer calories while exercising than Marisol did, which of the following represents the number of calories Ling burned while exercising?
Choose 1 answer:
The answer is option C. (670 - x)
What is an expression?An expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, and division, among others. It is a mathematical phrase that represents a value or a set of values when evaluated. It can be simple or complex.
The number of calories Ling burned while exercising can be represented as:
Ling's calories burned = Marisol's calories burned - x
Since Marisol burned 670 calories, we can substitute this value:
Ling's calories burned = 670 - x
Therefore, the answer is 670 - x.
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Complete question-
Suppose that 1000 customers are surveyed and 850 are satisfied or very satisfied with a corporation's products and services. Test the hypothesis Upper H Subscript 0 Baseline colon p equals 0. 9 against Upper H Subscript 1 Baseline colon p not-equals 0. 9at. Find the P-value
The p-value is 0.1138 for the given hypothesis.
What exactly is a p-value?
A p-value, or probability value, is a statistical measure that helps to determine the strength of evidence against a null hypothesis in a hypothesis test. In hypothesis testing, a null hypothesis is a statement or assumption about a population parameter that we want to test using sample data. The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed test statistic, assuming the null hypothesis is true.
Now,
To test the hypothesis,
we need to perform a hypothesis test using a significance level (α) to determine whether the sample proportion of satisfied customers is significantly different from 0.9.
The null hypothesis (H0) is that the true proportion of satisfied customers is equal to 0.9. The alternative hypothesis (H1) is that the true proportion is not equal to 0.9.
We can use the normal approximation to the binomial distribution to test this hypothesis, since the sample size is large (n = 1000) and both np and n(1-p) are greater than or equal to 10, where p is the true proportion of satisfied customers.
The test statistic is given by:
z = (P - p0) / √(p0(1 - p0) / n)
where p0 is the proportion (0.9), P is the sample proportion (850/1000 = 0.85), and n is the sample size.
Plugging in the values, we get:
z = (0.85 - 0.9) / √(0.9 * 0.1 / 1000) = -1.5811
The P-value is the probability of getting a test statistic as extreme as -1.5811 or more extreme, assuming the null hypothesis is true. Since this is a two-tailed test (H1: p ≠ 0.9), we need to find the area in both tails of the standard normal distribution.
Using a standard normal distribution table, we find that the area to the left of -1.5811 is 0.0569, and the area to the right of 1.5811 is also 0.0569. Therefore, the total area in both tails is:
p-value = 0.0569 + 0.0569 = 0.1138
So,
the p-value is 0.1138.
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Which function has the given properties below?
The domain is the set of all real numbers.
One x-intercept is (2 pi, 0).
The amplitude is 4.
The point (StartFraction pi over 2 EndFraction, negative 4 EndFraction) is on the graph.
The y-intercept is (0, 0).
y = –4sin(x)
y = –4cos(x)
y = 4sin(x)
y = 4cos(x)
The given data are:
A function that:
The domain is the set of all real numbers
One x-intercept
The amplitude is 4
The y-intercept is (0,0)
From the choices, the functions containing "cosine" can be eliminated since the described function passes through (0,0). So, we are left with two choices:
[tex]y = -4sin(x)[/tex] and [tex]y = 4sin (x)[/tex]
Given the amplitude of 4, the answer must be [tex]y = 4 sin(x)[/tex]
Emmy watson is buying a new oven for 915. 0. She made a down payment of 20% and financed the remainder. How much did she finance
Answer: Emmy Watson made a down payment of 20%, which means she paid 20% of the total cost of the oven upfront.
20% of 915.0 = 0.20 x 915.0 = 183.0
So, Emmy Watson paid $183.0 as a down payment.
To find out how much she financed, we need to subtract the down payment from the total cost of the oven:
Financed amount = Total cost - Down payment
Financed amount = $915.0 - $183.0
Financed amount = $732.0
Therefore, Emmy Watson financed $732.0.
Step-by-step explanation:
In December, The Corner Coffee Spot had an average inventory of $123, 456 and retail sales of $196, 450. Find the stock
turnover at retail. Round to the nearest tenth.
2.1
1.9
1.6
1.3
Answer:
1.6
Step-by-step explanation:
The stock turnover at retail is a measure of how many times a business sells its average inventory during a period of time. We can calculate the stock turnover by dividing the retail sales by the average inventory.
Stock turnover = Retail Sales / Average Inventory
Given the values :
Average Inventory = $123,456Retail Sales = $196,450Substituting these values
Stock turnover at retail = 196,450 / 123,456 = 1.6 (rounded to the nearest tenth)
The surface area of this rectangular prism is 94 square feet. What is the volume
The volume of the rectangular prism is 60 cubic feet.
What is a rectangular prism?
A rectangular prism is a three-dimensional geometric shape with six faces, where each face is a rectangle. It is also known as a rectangular cuboid. A rectangular prism has 8 vertices, 12 edges, and 6 rectangular faces. The opposite faces of a rectangular prism are congruent and parallel to each other. The length (l), width (w), and height (h) of a rectangular prism are the three dimensions that determine its size and shape.
The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism, respectively.
In this case, we have l = r, b = 5ft, h = 3ft, and SA = 94 sq ft. Substituting these values into the formula, we get:
94 = 2(r)(5) + 2(r)(3) + 2(5)(3)
94 = 10r + 6r + 30
94 = 16r + 30
64 = 16r
r = 4
So, the length of the rectangular prism is 4 feet.
Now, we can use the formula for the volume of a rectangular prism:
V = lwh
Substituting the values for l, w, and h, we get:
V = (4)(5)(3) = 60 cubic feet
Therefore, the volume of the rectangular prism is 60 cubic feet.
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A basketball team has II players, 5 of whom are in the starting line up. How many different starting line ups are possible if the star be in the time line up?
After answering the presented question, we can conclude that If the star equation player is in the starting lineup, there are 210 distinct starting lineups imaginable.
What is equation?In mathematics, an equation is a proposition that states the equivalence of two expressions. An equation consists of two sides separated by a system of equations (=). For instance, the statement "2x + 3 = 9" states that the word "2x Plus 3" equals the integer "9". The goal of solving equations is to find the value or amounts of the variable in the model) that will permit the calculation to be accurate. Mathematics can be simple or complex, linear or nonlinear, and contain one or more parts. For example, in the equation "x2 + 2x - 3 = 0," the variable x is raised to the power of 2. Lines are used in many areas of mathematics, including algebra, arithmetic, and geometry.
If the starting lineup includes the star player, there are only four spaces left to fill with the remaining ten players. The number of possible starting lineups is the number of ways to select four players from the remaining ten, which may be calculated using the combination formula:
C(10,4) = 10! / (4! * 6!) = 210
If the star player is in the starting lineup, there are 210 distinct starting lineups imaginable.
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b) Which number is smaller: -15 067 or -51 706 ?
Answer:
-51706
Step-by-step explanation:
when working with negative numbers, the number of greater size will be smaller.
FLOORING miguel is putting hardwood flooring in a hallway that measures 5 feet by 18 feet. The wood he has chosen is $5.48 per square foot. What is the range of the actual cost of putting the flooring in the hallway
Answer:
The cost of putting in the flooring is $493.20
Step-by-step explanation:
First you have to find the area
area = length times width
area = 5 x 18
a = 90 feet
The cost will be 90 x 5.48 = 493.20
Helping in the name of Jesus.
Una empresa procesadora de cafe produce 4000 kilogramos diarios de cafe tradicional obteniendo una ganancia diaria de 13500 dolares y una ganancia marginal de 4 dolares por kilo 1. Un administrador propone cambiar la produccion de cafe tradicional a cafe excelso, el administrador afirma que la funcion de ganancia diaria asociada a la produccion de cafe excelso es:
G(x) = Zx+1
1
t
2 + 1
t
dt
The function representing the daily profit based on production of premium coffee is given by ,
T = [tex]\int_{1}^{x}[/tex] [(t² + 1 ) / t² ] dt + (13,500 + (1/x) - x)
Function for daily profit associated with the production of excel so coffee is equal to,
G(x) =[tex]\int_{1}^{x}[/tex] [(t² + 1 ) / t² ] dt
Let's assume that the profit per kilogram of premium coffee is p dollars.
And total production of premium coffee is y kilograms per day.
Total profit from premium coffee is P = p × y
Company produces a total of 4000 kilograms of coffee per day.
⇒ y = 4000 - x
x = production of traditional coffee in kilograms per day.
Total profit for the company is,
T = G(x) + P
Substituting the expressions for P and y,
T = G(x) + p × (4000 - x)
Company's daily profit from producing traditional coffee = $13,500
⇒ 13,500 = G(x) + 4 × x
Substituted the marginal profit of $4 per kilogram for traditional coffee.
Profit per kilogram of premium coffee, p, in terms of x is equal to,
⇒ T = G(x) + p × (4000 - x)
⇒ 13,500 = G(x) + p×(4000 - x)
⇒ 13,500 = [tex]\int_{1}^{x}[/tex][(t² + 1 ) / t² ] dt + p×(4000 - x)
⇒ 13,500 = [x - (1/x)] + p× (4000 - x)
⇒13,500 = x - (1/x) + 4000p - px
⇒ 13,500 = (1-p)x - (1/x) + 4000p
p = (13,500 + (1/x) - x)/(4000 - x)
Function for daily profit associated with the production of premium coffee is,
T = G(x) + (13,500 + (1/x) - x)/(4000 - x) × (4000 - x )
Simplifying we get,
⇒ T = G(x) + (13,500 + (1/x) - x)
Therefore, the function for daily profit associated with the production of premium coffee is equal to
T = [tex]\int_{1}^{x}[/tex] [(t² + 1 ) / t² ] dt + (13,500 + (1/x) - x)
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The above question is incomplete , the complete question is:
A coffee processing company produces 4,000 kilograms of traditional coffee per day, obtaining a daily profit of 13,500 dollars and a marginal profit of 4 dollars per kilo 1. An administrator proposes to change the production of traditional coffee to premium coffee, the administrator affirms that the function of daily profit associated with the production of excel so coffee is:
G(x) = [tex]\int_{1}^{x}[/tex] [(t² + 1 ) / t² ] dt
Four more than half of the students in Bryan's homeroom have rickets to attend the school's musical. 20 students have tickets. Select all the equations that can be used to find the number of students in Bryan's homeroom.
Please
The equations that can be used to find the number of students in the homeroom are:
4 = 20 - 1/2m
1/2m + 4 = 20
What are the equations?An equation is a statement that expresses the equality of two expressions in mathematics. It is two expressions that are connected by an equals to sign.
4 + 1/2m = 20
Where m is the number of students in Bryan's home room
In order to determine the value of m, take the following steps:
Combine similar terms:
1/2m = 20 - 4
Add similar terms
1/2m = 16
Multiply both sides of the equation by 2
m = 16 x 2
m = 32
Substitute for m in the above equation:
4 + 1/2(32) = 20
4 + 16 =20
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Work out the size of angle x give reasons for your answer
Answer:
x° = 80
Step-by-step explanation:
Remember a line is 180°
Because B is = 100°
B and x are interior angles meaning B + x = 180°
100° + x = 180°
x = 80°
Answer:
80 °
Step-by-step explanation:
[tex]\frac{360-2*100}{2} = 80[/tex]
I need this asap please help
Answer:
Step-by-step explanation:
the answer would be 5/4 i belive
A 3-pack of baseball caps costs $4.93. What is the unit price, rounded to the nearest cent?
Answer:
$1.64
Step-by-step explanation:
To find the unit price, we need to divide the total cost by the number of units. In this case, we have 3 caps in a pack, so the unit price is:
$4.93 / 3 = $1.64333333...
Rounding to the nearest cent, the unit price is $1.64.
*see image* The number of wolves in a forest
increases by 25% each year.
This year, there are 400 wolves in the
forest.
Calculate the number of wolves that there
will be in the forest
a) after 1 year.
b) after 2 years.
Answer:
Below
Step-by-step explanation:
After 1 year there will be 25 % more than 400 or 1.25 * 400 = 500 wolves after two years there will be 25 % more than 500 wolves
= 1.25 * 500 = 625 wolves
Please help (Look at image) QUICKLY
Answer:
See below.
Step-by-step explanation:
We are asked to identify the Proof for Statement 7.
To start, we already have 2 sides and 1 angle proven, meaning that we can prove ΔABX ≅ ΔABY by the Side-Angle-Side Triangle Congruency Theorem. (SAS).
Because both Triangles are congruent, every side, and angle of the triangles are congruent. ASA, and SAS are incorrect choices, they're only used to prove that 2 triangles are congruent. HL is incorrect as well, the HL (Hypotenuse - Leg Theorem) is only used to prove that 2 triangles are congruent also. Our only option is CPCTC (Corresponding parts of congruent triangles are congruent); Meaning that every angle and every side of the 2 triangles are congruent.
For Statement 7, AX ≅ AY proved by CPCTC.
A contractor needs to buy nails to build a house. The nails come in small boxes and large boxes. Each small box has 100 nails and each large box has 450 nails. The contractor bought 3 more small boxes than large boxes, which all together had 2500 nails. Determine the number of small boxes purchased and the number of large boxes purchased. PLEASE HELP!!
Answer: Let's call the number of large boxes purchased "L" and the number of small boxes purchased "S".
From the problem, we know that:
Each small box has 100 nails, so the total number of nails from the small boxes is 100S.
Each large box has 450 nails, so the total number of nails from the large boxes is 450L.
The contractor bought 3 more small boxes than large boxes, so S = L + 3.
The total number of nails purchased is 2500, so 100S + 450L = 2500.
We can use the second equation to solve for one of the variables in terms of the other. For example, we can solve for L:
100S + 450L = 2500
Substituting S = L + 3:
100(L + 3) + 450L = 2500
Expanding the parentheses:
100L + 300 + 450L = 2500
Combining like terms:
550L + 300 = 2500
Subtracting 300 from both sides:
550L = 2200
Dividing both sides by 550:
L = 4
So the contractor purchased 4 large boxes of nails.
We can use the equation S = L + 3 to find the number of small boxes purchased:
S = L + 3 = 4 + 3 = 7
So the contractor purchased 7 small boxes of nails.
Therefore, the contractor purchased 4 large boxes and 7 small boxes of nails.
Step-by-step explanation:
A cylinder has a diameter of 10 inches and a height of 18 inches. What is the
volume of the cylinder?
OA. 8107
OB. 450TT
O C. 1800T
O D. 1807
After answering the presented question, we can conclude that As a cylinder result, option C. 1800 is the correct answer.
what is cylinder?A cylinder is a three-dimensional geometric shape made up of two parallel congruent circular bases and a curving surface connecting the two bases. The bases of a cylinder are always perpendicular to its axis, which is an imaginary straight line passing through the centre of both bases. The volume of a cylinder is equal to the product of its base area and height. A cylinder's volume is computed as V = r2h, where "V" represents the volume, "r" represents the radius of the base, and "h" represents the height of the cylinder.
volume of the cylinder is:
[tex]V = \pi r^2h\\V = \pi (5^2)(18)\\V = \pi (25)(18)\\V = 450\pi cubic inches\\V =450 x 3.14\\V =1413.00 cubic inches\\[/tex]
As a result, option C. 1800 is the correct answer.
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Please help on Math Problem
40 Points!!
Answer:
murray= 58÷2= 29
kris=78÷3=26
Logan=84÷3=28
Taylor=92÷4=23
answer=logan
Answer:
C
Step-by-step explanation:
84÷3 = 28
which means that logan was able to solve 28 problems per minute
Elliot a mangé les 2 tiers de la pizza , et sa soeur Eve a mangé 1 cinquième de la pizza .
En reste t'il pour leur frère Tom ?
The top of a ladder rests at a height of 12 feet against the side of a house. If the base of the ladder is 9 feet from the house, what is the length of the ladder? Round to the nearest foot.
3 ft
11 ft
15 ft
21 ft
We can say that after answering the offered question The ladder is Pythagorean theorem therefore 15 feet long, rounded up to the next foot. Thus, 15 feet is the solution.
what is Pythagorean theorem?The Pythagorean Theorem is the foundational Euclidean geometry connection that exists between the three sides of the right triangle. According to this rule, the area of either a cube with the length x side is equal to the total of the regions of triangles shared by its other two sides. According to the Pythagorean Theorem, the square that spans the hypotenuse of a right triangle opposite the perfect angle is the combined squares that spanned its sides. It is sometimes expressed as a2 + b2 = c2 in general algebraic notation.
The ladder serves as the hypotenuse in this basic example of a right triangle, which also includes the distance from the house as one of its legs and the ladder's height as its second leg. The Pythagorean theorem can be used to find the ladder's length.
[tex]c^2 = a^2 + b^2[/tex]
In this instance, we know that the distance from the house (a) is 9 feet, and the height of the ladder (b) is 12 feet. Hence, we can enter these values into the formula as follows:
[tex]c^2 = 9^2 + 12^2 c^2 = 81 + 144\sc^2 = 225\sc = √225\sc = 15[/tex]
The ladder is therefore 15 feet long, rounded up to the next foot. Thus, 15 feet is the solution.
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Solve the compound inequality
-2<-x ≤3
Answer:2>x[tex]\geq[/tex]-3
Step-by-step explanation:
when we divide each side with a negative number "<" turns into ">",">" turns into "<" and so on.
we can divide each side with -1, the we get,
2>x[tex]\geq[/tex]-3
[tex]-2 < -x \leq 3 \iff 2 > x \geq -3[/tex]
[tex]-3 \leq x < 2 \implies x \in [-3;2)[/tex]
Please help I really struggle with these !!!
[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ r=4\\ \theta =312 \end{cases}\implies s=\cfrac{(312)\pi (4)}{180}\implies s=\cfrac{104\pi }{15}\implies s\approx 21.8[/tex]
An auditorium has 288
seats distributed evenly in
6 rows. Find the unit rate of seats per row.
Answer: To find the unit rate of seats per row, we can divide the total number of seats by the number of rows:
288 seats ÷ 6 rows = 48 seats per row
Therefore, the unit rate of seats per row is 48.
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The sides of a triangle are 54, 31, and 69. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
The triangle is acute since a² + b² < c² ( 2916 + 961 < 4761.
Is the triangle is right, acute, or obtuse?To determine whether the triangle is right, acute, or obtuse, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.
We can start by finding the longest side of the triangle, which is the hypotenuse.
hypotenuse = 69
Now we can use the Pythagorean Theorem to check whether the triangle is right:
a² + b² = c²
where a and b are the lengths of the other two sides of the triangle.
Plugging in the values we know, we get:
54² + 31² = 69²
Simplifying, we get:
2916 + 961 = 4761
3877 = 4761
Since this equation is not true, we know that the triangle is not a right triangle.
To determine whether the triangle is acute or obtuse, we need to compare the sum of the squares of the lengths of the shorter sides to the square of the length of the longest side:
a² + b² < c² => the triangle is acute
a² + b² > c² => the triangle is obtuse
c² = 69² = 4761
Plugging in the values we know, we get:
54² + 31² = 2916 + 961 = 3877
Since 3877 < 4761, we can conclude that the triangle is acute.
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Help with all please
A scatter plot of the data is shown below.
An equation of a reasonable trend line is y = x - 0.1.
The arm span of someone who is 1.6 m tall is 1.5 meter.
The arm span of someone who is 2.2 m tall is 2.1 meters.
How to write an equation of the line of best fit for the data?In order to write a linear equation for the line of best fit (trend line) that models the data points contained in the table, we would have to use a graphing calculator (scatter plot).
In this scenario, the heights would be plotted on the x-axis of the scatter plot while the arm span would be plotted on the y-axis of the scatter plot.
At point (2.0, 1.9), an equation of this line can be calculated by using the point-slope form:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 1.9 = (2.0 - 1.9)/(2.1 - 2.0)(x - 2.0)
y - 1.9 = (x - 2.0)
y = x - 0.1.
For someone who is 1.6 m tall, their arm span is given by;
y = x - 0.1
y = 1.6 - 0.1.
x = 1.5 meter.
For someone who is 2.2 m tall, their arm span is given by;
y = x - 0.1
y = 2.2 - 0.1.
x = 2.1 meters.
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Ruben and Estelle just had business cards made. Ruben's printing company charged a one-time setup fee of $8 and then $18 per box of cards. Estelle, meanwhile, ordered hers online. They cost $6 per box. There was no setup fee, but she had to pay $20 to have her order shipped to her house. By coincidence, Ruben and Estelle ended up spending the same amount on their business cards. How much did each spend? How many boxes did each buy?
Ruben ordered 0 boxes of cards and Estelle ordered 2 boxes of cards. Ruben spent $8 and Estelle spent $20 + $6(2) = $32.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
Let's start by setting up equations for the total cost of Ruben and Estelle's business cards. Let R be the number of boxes of cards Ruben ordered and E be the number of boxes Estelle ordered. Then we have:
Ruben's cost = 8 + 18R
Estelle's cost = 6E + 20
We know that Ruben and Estelle spent the same amount, so we can set their costs equal to each other and solve for R and E:
8 + 18R = 6E + 20
18R - 6E = 12
3R - E = 2
This equation tells us that Ruben ordered two more boxes of cards than Estelle. We can use trial and error to find the values of R and E that satisfy this equation and give us the same cost:
If R = 4 and E = 2, then Ruben's cost = 8 + 18(4) = 80 and Estelle's cost = 6(2) + 20 = 32, which are not equal.
If R = 3 and E = 1, then Ruben's cost = 8 + 18(3) = 62 and Estelle's cost = 6(1) + 20 = 26, which are not equal.
If R = 2 and E = 0, then Ruben's cost = 8 + 18(2) = 44 and Estelle's cost = 6(0) + 20 = 20, which are not equal.
If R = 1 and E = -1, then Ruben's cost = 8 + 18(1) = 26 and Estelle's cost = 6(-1) + 20 = 14, which are not equal.
If R = 0 and E = -2, then Ruben's cost = 8 + 18(0) = 8 and Estelle's cost = 6(-2) + 20 = 8, which are equal.
Therefore, Ruben ordered 0 boxes of cards and Estelle ordered 2 boxes of cards. Ruben spent $8 and Estelle spent $20 + $6(2) = $32.
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a bowl of fruit is on the kitchen table it contains 5 apples 2 oranges and 2 bananas christian and Aaron come home from school and randomly grab one fruit each what is the probability that both grab oranges
Answer:
The probability that both grab oranges would be = 1/30
Step-by-step explanation:
bc 1/8 * 2/9 = 1/30
hope this helps
Answer: The probability that both grab oranges would be =1/36
Step-by-step explanation:
Given,
A bowl contains,
Apples = a = 5
Oranges = o = 2
bananas = b = 2
Total fruits in bowl = x = a + o + b = 5 + 2 + 2 = 9
Now, Christian and Aaron come home from school and randomly grab one fruit each.
The probability of first selecting orange would be = o/b =2/9
Now, the oranges left would be 2 - 1 = 1
and total fruits would be = 9 - 1 = 8
Hence, the probability of selecting second orange would be = 1/8
Therefore, the probability that both grab oranges would be = 1/8 2/9 =1/36