Answer:
After 5 half-lives, the remaining mass of the radioactive isotope will be 155 * (1/2)^5 = 4.84375 grams. Rounded to the nearest gram, the answer is 5 grams.
Step-by-step explanation:
What is the the slope-intercept form of (-5,-2)
Answer:
Step-by-step explanation:
we can't say because we don't have a couple of coordinates
Which equation best represents the relationship between X and Y in the graph?
A- y = 3x + 3
B- y = 3x - 1
C- y = 1/3x + 3
D- y = 1/3x - 1
Find ordered pairs y=-7x+8
The ordered pairs for the equation y = -7x + 8 are (0, 8), (1, 1), and (-1, 15).
What are the ordered pairs for the equation y?To find ordered pairs for the equation y = -7x + 8, we can substitute different values of x and solve for y.
Let's choose three values of x:
When x = 0, y = -7(0) + 8 = 8. So one ordered pair is (0, 8).
When x = 1, y = -7(1) + 8 = 1. So another ordered pair is (1, 1).
When x = -1, y = -7(-1) + 8 = 15. So another ordered pair is (-1, 15).
Therefore, the ordered pairs are (0, 8), (1, 1), and (-1, 15).
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In the figure shown, triangle RST is similar to triangle UVW. Write an expression in terms of m and p that represents tan (R).
The value of tan(R) is 2/3
What is the trigonometric ratio?
The trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.
using tan (θ) = opposite/Adjacent
Here, tan (R) = opposite/Adjacent
Where: opposite side = 14
Adjacent Side = 21
tan (R) = 14/21 = 2/3
tan (R) = 2/3
Hence, the value of tan(R) is 2/3
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The complete question is in the attached figure:
What is tan(R) =?
someone help me plss
The fraction of the panel, that is left after cutting out the hole is [tex]\frac{11}{12}[/tex]
What are the areas of some common plane figuresThe area of a rectangle equals the product of its 2 sides. The area of a triangle is equal to half of the product of the base and height.. If we choose one of the sides as the base, then for area calculation, for height we have to use the height of the opposite vertex from this base. To find it, we have to drop a perpendicular from the opposite vertex onto the base. The area of a parallelogram is the product of the length of the base and the perpendicular distance between the two parallel sides of the parallelogram. Area of a trapezium = half of the product of the distance between the parallel sides and the sum of the length of the parallel sides. Area of a circle is [tex]\pi r^2[/tex], in which r is the radius of the given circle. Sometimes the plane figure maynot be a standard shape. In that case we have to divide the figure into suitably many parts such that, each part is a standard figure whose area we can calculate. Also sometimes we can represent an area as the difference of the area of two standard figures. In that case to find the area we have to take the difference of the areas of the two standard figures.
In our question. Initial area of the panel is (3)(2) = 6 square ft.
Area of the cutout = (1)([tex]\frac{1}{2}[/tex]) = [tex]\frac{1}{2}[/tex] square ft.
Using the formula, fraction left = [tex]\frac{6 - \frac{1}{2}}{6} = 1 - \frac{1}{12} = \frac{11}{12}[/tex]
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Required fraction left is 11/12 square feet.
What is area of rectangle?
A rectangle is a geometric shape that has four sides and four right angles. It is a type of quadrilateral and is characterized by its two pairs of parallel sides. The opposite sides of a rectangle are congruent, which means they have the same length, and the adjacent sides are perpendicular to each other.
The area of a rectangle is the total amount of space inside the rectangle and is calculated by multiplying the length of the rectangle by its width. The formula for the area of a rectangle is Area = length x width
For example, if a rectangle has a length of 6 units and a width of 4 units, the area can be calculated as:
Area = 6 units x 4 units = 24 square units
The area of the panel is 3 feet x 2 feet = 6 square feet
The area of the hole is 1 foot x 1/2 foot = 1/2 square feet
Therefore, the area left is 6 square feet - 1/2 square feet = 11/2 square feet
The fraction left is (11/2 square feet) / (6 square feet) = 11/12
Therefore, the required correct option is C.
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Find the value of x please.
choices are..
16
19
18
15
Answer:
We have supplementary angles.
123 + 3x = 180
3x = 57
x = 19
Answer:
x = 19
Step-by-step explanation:
Angle on a straight line add up to 180
123 + 3x = 180
3x = 180 - 123
3x = 57
3x/3 = 57/3
x = 19
In 2014, Michelle's annual base salary was $87,000. She also earned 3% commission of her annual sales of $500,000. What was Michelle's income during 2014?
Answer: Michelle's income during 2014 was her base salary plus her commission.
Her commission was 3% of $500,000, which is 0.03 x $500,000 = $15,000.
So her total income for 2014 was $87,000 + $15,000 = $102,000.
Step-by-step explanation:
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Solve the system of equations algebraically. Show all of your steps.
y=x2+2x
y=3x+20
There are two solutions for given system of equations: (5, 35) and (-4, 8).
What does "system of equations" and its solution means ?A system of equations is a grouping of two or more equations with numerous variables that are treated as a whole. The solution to a system of equations is the set of variable values that satisfies all of the equations in the system at the same time.
Typical approaches for resolving equation systems include:
Substitution MethodElimination MethodMatrix MethodGraphical MethodGiven system of equations is,
[tex]y=x^2+2x[/tex]..................(1)
[tex]y=3x+20[/tex]..................(2)
Solving equations algebraically,
Equating the formulas for 'y' in both equations:
[tex]x^2 + 2x = 3x + 20[/tex]
Rearranging the equation :
[tex]x^2 - x - 20 = 0[/tex]
Here, we got a quadratic equation,Solving for values of x,
[tex](x - 5)(x + 4) = 0[/tex]
[tex]x - 5 = 0 \\x=5\\or\\x + 4 = 0\\x=(-4)[/tex]
For values of 'y', putting values of x in equation (1),
for x = 5,
[tex]y = 5^2 + 2(5)=25 + 10 = 35[/tex]
Thus, (5, 35) is one of the solution.
for x= -4,
[tex]y = (-4)^2 + 2(-4)=16 - 8 = 8[/tex]
Thus, (-4, 8) is other solution.
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Explain what the constant of proportionality means in the equation y = 5/2 x
Answer:
[tex]y = \frac{5}{2} x[/tex]
[tex] \frac{y}{x} = \frac{5}{2} [/tex]
The constant of proportionality is the ratio of y to x. Here, the ratio of y to x is 5 to 2. We see that y is directly proportional to x.
Determine the domain of the graph above
The domain of the graph in this problem is given as follows:
C) -3 ≤ x ≤ 4.
How to obtain the domain of the graph?To determine the domain of a graph, you need to identify the set of all possible input values (also known as the independent variable) that produce a valid output (also known as the dependent variable) on the graph.
On a graph, the input values are represented by the values of x of the graph.
On the graph in this problem, we have that it assumes values of x between -3 and 4, with closed intervals, hence the domain is given as follows:
-3 ≤ x ≤ 4.
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Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 2.7, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 1.6, 1.4
Determine the scale factor used.
2
3
one third
one half
The scale factor is 1/3.
What is the scale factor?
The difference in scale between an original object's scale and a new object that is its representation but is larger or smaller is known as a scale factor. For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Here, we have
Given: Triangle D has been dilated to create triangle D′.
To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:
4.8 / 1.6 = 3
4.2 / 1.4 = 3
2.7 / x = 3
Knowing that the scaling for each edge is 3, we can solve for x.
2.7 / 3 = x
0.9 = x
The edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.
So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.
Hence, the scale factor is 1/3.
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C. The table below shows the ages in years of 42 children at a birthday party. AGE(YEARS) NO OF CHIDREN 7 2x 8 3x 9 4x-1 10 X 11 X-2 (i). Find the value of x. (ii). Calculate, correct to the nearest whole number the mean age. (iii). Find the probability of selecting at random a child whose age is less than 9 years. 12 x-3 CURT
(1) The value of X is equal to 4 (2) The mean age is 3. (3) The probability of randomly selecting a child under the age of 9 is approximately 0.83.
How to calculate the average?
The formula for calculating the average of given numbers is equal to the sum of all values divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.
(i). Given that there are a total of 42 children on the birthday, finding the value of x:
2x + 3x (4x-1) + x + (x-2) + (x-3) = 42
11x - 6 = 42
11x = 48
x = 4
Therefore, the value of x is equal to 4.
(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:
Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42
= (14 + 24 + 27 + 40 + 22 +12) / 42
= 139/42
= 3.31
Rounded to the nearest whole number, the average age is 3.
(iii). The probability of randomly selecting a child under 9 is obtained by adding the number of children aged 7, 8 or 9 (because we want children under 9) and dividing by the total number of children:
Number of children under 9 years = 2x + 3x + (4x-1)
Number of children under 9 years = 9x - 1
Number of children under 9 = 9(4)–1
Number of children under 9 years = 35
Probability of choosing a child under 9 = number of children under 9 / total number of children
Probability of choosing a child under 9 = 35/42
The probability of choosing a child under 9 years old is ≈ 0.83
Thus, the probability of randomly selecting a child under the age of 9 is approximately 0.83.
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Each tile is 3/4 of inch by 3/4 of an inch what is the area of each tile
Answer:
9/16 of a square inch
Step-by-step explanation:
[tex] \frac{3}{4} \times \frac{3}{4} = \frac{9}{16} [/tex]
Answer:
9 /16 inches^2
Step-by-step explanation:
To find the area of the tile, multiply the length by the width
A = 3/4 * 3/4
A = 9 /16 inches^2
Solve the inequality for x.
−8+ x/3>-7
Simplify your answer as much as possible.
Answer:
x > 3
Step-by-step explanation:
−8 + x/3 > -7
x/3 > 1
x > 3
We can't simplify anymore, so the answer is x > 3
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Therefore , the solution of the given problem of angles comes out to be the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6.
An angle's meaning is what?The point of intersection of the paths joining a skew ends yields the skew's greatest and smallest walls. A crossroads may be where two paths converge. Angle is another outcome of two things interacting. They approach dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various configurations between their endpoints.
Here,
Regarding the illustrated diagram, the appropriate statements are:
=> m∠3 + m∠4 + m∠5 = 180°
This is accurate since every triangle's internal angles add up to 180°.
=> m∠5 + m∠6 = 180°
This is true because a triangle's internal angle and outside angle are always equal to 180 degrees.
=> m∠2 + m∠3 = m∠6
This is accurate because, based on the information provided,
the exterior angle at angle 2 (m2) of the triangle is equal to the corresponding interior angle at angle 6 (m6) of the triangle.
Therefore, the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. are always true in relation to the given figure.
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What does a residual value of –0.8 mean in reference to the line of best fit?
The given point is 0.8 units above the line of best fit.
The given point is 0.8 units below the line of best fit.
The line of best fit is not appropriate to the data.
The line of best fit has a slope of 0.8.
Which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page?
y = –55x + 407
y = –41x + 814
y = –38x + 922
y = –26x + 723
Answer: A residual value of –0.8 means that the given point is 0.8 units above the line of best fit.
The equation that represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page is:
y = –38x + 922.
Therefore, the answer is y = –38x + 922.
Step-by-step explanation:
radical form of a^2/5
help please
Answer:
The answer is ⁵√a²
Step-by-step explanation:
a⅖=⁵√a²
If y = x and y = 4, then what is (x + y)² ? A. 0 B. 16 C. 25 D. 64
Step-by-step explanation:
y = x and y = 4
(x + y)²
(4 + 4)² = (8)² = 64
A recliner is discounted by $190. If the original price is $800, estimate the sale price by first rounding each number to the nearest hundreds
all u got to do is subtract
For #1 - 6, use the information given to write the equation of the line in slope intercept form.
1. Line where slope is -32 and y-intercept is 7
1. Line where slope is 5 and x -intercept is 2
1. Line going through the points (-1, -5) and (4, -2)
1. Line going through the points (0, 1) and (2, -2)
1. Line where m = 4 and and b = -76
1. Line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0
An equation of a line where slope is -32 and y-intercept is 7 is y = -32x + 7.
An equation of a line where slope is 5 and x-intercept is 2 is y = 5x - 10.
An equation of a line that is going through the points (-1, -5) and (4, -2) is y = 3x/5 - 22/5
An equation of a line that is going through the points (0, 1) and (2, -2) is y = -x/2 + 1
An equation of a line where m = 4 and and b = -76 is y = 4x - 76.
An equation of a line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0 is y = 3x + 0.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 + 5)/(4 + 1)
Slope (m) = 3/5
At data point (-1, -5) and a slope of 3/5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 5 = 3/5(x + 1)
y = 3x/5 + 3/5 - 5
y = 3x/5 - 22/5
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Expand the expressions and simplify 5(x + 4) + 3(x + 2) =
8x + 4
6x + 18
8x+ 26
7x - 18
Answer:
8x+26
Step-by-step explanation:
distribute the 5 into the numbers in the parentheses. you get (5x+20) then do the same with 3(x+2) which wll be (3x+6) now add like terms, which are 5x+3x=8x and 20+6=26. boom 8x+26.
8x + 26
multiply the outside number by the inside numbers and add them. remember, if the variable is singular example x, then it equals 1 :) I hope this helps you understand, I'm currently doing algebraic expressions.
Ejercicio 2.- La temperatura ambiente a las 8 am era de 61 grados Farenheit. Fue aumentando de forma lineal hasta la 1 pm en que el termómetro marcó 81 grados. a) Escriba una ecuación lineal que muestre la temperatura en función de la hora en ese intervalo. b) Calcule con esa ecuación la temperatura a las 11:15 am. Aproxime a la décima de grado Farenheit si fuera necesario. oprondamos a hacer ecuaciones y resolver
a)Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es T(h) = 4h + 29
b) Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
what is aproximadamente ?
"Aproximadamente" is a Spanish word that means "approximately" or "roughly" in English. It is often used to indicate that a value or measurement is not exact, but rather an estimation or approximation.
In the given question,
a) La ecuación lineal que relaciona la temperatura con la hora en ese intervalo es:
T(h) = m*h + b
donde T es la temperatura en grados Farenheit, h es la hora en formato de 24 horas, m es la pendiente de la recta y b es el término independiente.
Primero encontramos la pendiente m:
m = (81 - 61) / (13 - 8) = 4
Luego, encontramos el término independiente b utilizando uno de los puntos:
61 = 4*8 + b
b = 29
Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es:
T(h) = 4h + 29
b) Para encontrar la temperatura a las 11:15 am, primero convertimos el tiempo a horas decimales:
11:15 am = 11 + 15/60 = 11.25 horas
Luego, sustituimos este valor en la ecuación lineal:
T(11.25) = 4(11.25) + 29 = 75.25
Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
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Express answers in terms of pi.
The radius of a cylinder is 10; the length is 2. Find:
a. circumference of the base.
b. area of the base.
c. L.A.
d. T.A.
e. V
Answer:
a. The circumference of the base is 2πr, where r is the radius of the cylinder. Therefore, the circumference of the base is:
2π(10) = 20π
So the circumference of the base is 20π.
b. The area of the base is πr^2, where r is the radius of the cylinder. Therefore, the area of the base is:
π(10)^2 = 100π
So the area of the base is 100π.
c. The lateral area of the cylinder is given by the formula 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the lateral area of the cylinder is:
2π(10)(2) = 40π
So the lateral area of the cylinder is 40π.
d. The total surface area of the cylinder is the sum of the lateral area and the areas of the two bases. The area of each base is πr^2, which we already calculated to be 100π. Therefore, the total surface area of the cylinder is:
2(100π) + 40π = 240π
So the total surface area of the cylinder is 240π.
e. The volume of the cylinder is given by the formula πr^2h, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the volume of the cylinder is:
π(10)^2(2) = 200π
So the volume of the cylinder is 200π.
A bus traveled on a level road for 2 hours at an average speed 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 3 hours. Find the average speed on the level road if the entire trip was 225 miles.
By answering the presented question, we may conclude that As a result, the average speed on the flat road is 57 miles per hour.
what is expression ?In mathematics, you can multiply, divide, add, or subtract. An expression is constructed as follows: Number, expression, and mathematical operator A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to contrast expressions and phrases. An expression or algebraic expression is any mathematical statement that has variables, integers, and an arithmetic operation between them. For example, the phrase 4m + 5 has the terms 4m and 5, as well as the provided expression's variable m, all separated by the arithmetic sign +.
Let's apply the formula:
distance = time speed
The bus went for 2 hours on the level road, hence the distance travelled is:
1 distance = x 2
The bus went for 3 hours on the twisting route, hence the distance travelled is:
3 distance2 = (x - 20)
Because the bus's total distance travelled is 225 miles, we may write:
distance1 plus distance2 equals 225
Substituting distance1 and distance2 expressions yields:
x × 2 + (x - 20) × 3 = 225
When we simplify this equation, we get:
2x + 3x - 60 = 225
5x = 285\sx = 57
As a result, the average speed on the flat road is 57 miles per hour.
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Which is the best estimate of the difference between 67/8 and 1/82
Answer:
8.36
Step-by-step explanation:
67 - 1
8. 82
= 2747 - 4
328
=2743
328
= 8.36
Name
Date
- Sarah received a coupon for 15% off the total purchase price at a shoe store. Let p be the
original price of the purchase. Use the expression p-0.15p for the new price of the purchase.
Write an equivalent expression by combining like terms.
Convert: 83.36m= cm
pls help
Answer: 8,336
Step-by-step explanation:
So 1 meter is equal to 100 centimeters. All you have to do is multiply 83.36 by 100.
83.36 * 100 = 8,336
Hope this helps!!! :)
6 = 1/2 × z what is the value of z
Answer:
To solve for the value of z in the equation 6 = 1/2 × z, we can use algebraic manipulation. First, we can multiply both sides of the equation by 2 to eliminate the fraction:
2 × 6 = 2 × (1/2 × z)
Simplifying the right side:
12 = z
Therefore, the value of z is 12.
Step-by-step explanation:
Find the probability of drawing a green, then yellow, with replacement.
A bag has 4 green blocks, 6 red blocks, 7 blue and 3 yellow.
P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%.
What is Probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of science, such as statistics, physics, and engineering, as well as in everyday life to make informed decisions based on the likelihood of various outcomes.
The probability of drawing a green block on the first draw is 4/20 (since there are 4 green blocks out of a total of 20 blocks in the bag).
Since the block is being replaced back into the bag after each draw, the probability of drawing a yellow block on the second draw is still 3/20.
Therefore, the probability of drawing a green block followed by a yellow block is:
P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%
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7.
Colin uses
cup of vegetable oil in each cake that he makes for his father's beker
If Colin made 8 cakes, how much oil did Colin use in all?
Mark only one oval.
I added 13:5
A. 51/3 cups
OB. 41/3 cups
OC. 51/2 cups
OD.41/2 cups
Spain
42°
The number of cups of vegetable oil used by Colin to make 8 cakes is given by A = 5 1/3 cups
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data,
Let the equation be represented as A
Now, the value of A is
Substituting the values in the equation, we get
Let the number of cups of vegetable oil used by Colin to make 8 cakes be represented as A
Now , the number of cups of vegetable oil used by Colin to make 1 cake is given by = ( 2/3 ) cups of oil
And , number of cups of vegetable oil used by Colin to make 8 cakes A =
A = 8 x number of cups of vegetable oil used by Colin to make 1 cake
On simplifying the equation, we get
[tex]\text{A} = 8 \times \huge \text{(} \dfrac{2}{3} \huge \text{)}= \dfrac{16}{3}[/tex]
[tex]\boxed{\bold{A = 5 \dfrac{1}{3} \ cups}}[/tex]
Therefore, the value of A is 5 1/3 cups
Hence, the number of cups of vegetable oil required is 5 1/3 cups
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Complete question is-
Colin uses 2/3 cup of vegetable oil in each cake that he makes for his father's bakery.
If Colin made 8 cakes, how much oil did Colin use in all?
A. 5 1/3 cups
B. 7 1/3 cups
C. 8 2/3 cups
D. 16 1/3 cups