Directions: State all the possible rational zeros for each function.
f(x) = 3x² + 2x - 1
The possible rational zeros are x = -1 and x = 1/3 for the given function f(x) = 3x² + 2x - 1.
What is a quadratic function?The quadratic function is defined as a function containing the highest power of a variable is two.
The function is given in the question as:
f(x) = 3x² + 2x - 1
To determine possible rational zeros for the given function.
f(x) = 3x² + 2x - 1
For finding rational zeros, f(x) = 0
3x² + 2x - 1 = 0
3x² + 3x - x - 1 = 0
3x(x +1) - 1(x +1) = 0
(x +1)(3x - 1) = 0
(x +1) = 0 and (3x - 1) = 0
x = -1 and 3x = 1
x = -1 and x = 1/3
Thus, the possible rational zeros are x = -1 and x = 1/3 for the given function f(x) = 3x² + 2x - 1.
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A school is arranging a field trip to the zoo. The school spends 526.26 dollars on passes for 47 students and 2 teachers. The school also spends 401.38 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student
The total amount of money spent on pass and lunch for each student is $19.28.
How much is spent on lunch and a pass?The first step is to determine the amount that was spent on a pass for each student. The cost of one pass can be determined by dividing the total amount spent on passes by the total number of teachers and students.
Cost of one pass = total amount spent on one pass / total number of people
Cost of one pass = 526.26 / (47 + 2)
Cost of one pass = 526.26 / 49
Cost of one pass = $10.74
The second step is to determine the amount spent on lunch for one student. This can be determined by dividing the total amount spent on lunch by the total number of students.
Cost of one lunch = total cost of lunch / total number of students
401.38 / 47 = $8.54
Total amount spent on pass and lunch for each student = cost of lunch for one student + cost of a pass for one student
$8.54 + $10.74 = $19.28
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Jose is wrapping a stack of 100 coins in a paper holder. Each coin is 18 inch thick and has a diameter of
1 inch. How many square inches of paper will Jose need to cover the stack of coins? Use 3.14 for π.
Jose will need 40.82 in² of paper to cover the stack of coins
How to determine the square inches of paper Jose will need to cover the stack of coins?The area in this scenario will be:
A = 2πr² + 2πrh
Where r and h represent the radius of the coins and the height of the coin stack respectively
Given: diameter of coin = 1 inch and thickness = 1/8 inch
radius(r) = diameter/2 = 1/2 inch
Substituting values gives:
A = 2×3.14 × (1/2)² + 2×3.14 ×(1/2)×(100 ×(1/8))
A = 40.82 in²
Note: the correct thickness of the coins should be 1/8 in
Therefore, the area of paper Jose will need to cover the stack of coins is 40.82 in²
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-4n+7+2n=1
ANSWER WITH EXPLAINATION
Answer:
n = 3
Step-by-step explanation:
-4n + 7 + 2n = 1
Collect like terms
-2n + 7 = 1
Subtract 7 from both sides
-2n = 1 - 7
Do the math on the right side
-2n = -6
Divide both sides by -2
n = 3
make r the subject of formula in V= pie h square(r-h/3)
When r is made the subject of the formula we have; V + πh^3/3πh^2
What is the subject of a formula?The term subject of a formula has to do with the variable that we are trying to obtain in the equation. Hence the subject of the formula must be written on the left hand side of the mathematical equation.
We have;
V = πh^2(r - h/3)
We open the bracket;
V = πrh^2 - πh^3/3
Adding πh^3/3 to both sides, we have;
V + πh^3/3 = πrh^2
Then we divide both sides by πh^2
r = V + πh^3/3/πh^2
r = V + πh^3/3πh^2
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4) Draw a Venn diagram to show these sets:
• The universal set U = {x | - 10 ≤ x ≤ 10, x El}
• N = {x|-10 ≤x≤-1, x El}
• P= {x|1 ≤ x ≤ 10, x El}
●
• E = {x | x = 2a, 1 ≤ a ≤ 5, a El}
I really need help, and I need it ASAP please!!!
The Venn diagram is attached below.
We have four sets. The sets are represented by the alphabets "U", "N", "P", and "E". The universal set is represented by U. The sets are defined as given below.
U = {x | - 10 ≤ x ≤ 10, x ∈ l}
N = {x | -10 ≤x≤-1, x ∈ l}
P = {x | 1 ≤ x ≤ 10, x ∈ l}
E = {x | x = 2a, 1 ≤ a ≤ 5, a ∈ l}
The elements in the universal set "U" are -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
The elements in the set "N" are -10, -9, -8, -7, -6, -5, -4, -3, -2, and -1.
The elements in the set "P" are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
The elements in the set "E" are 2, 4, 6, 8, and 10.
We need to draw the Venn diagram. A Venn diagram is a graphic representation of the contrasts and similarities between two concepts. Venn diagrams are sometimes known as logic diagrams or set diagrams.
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Select all the expressions that are equivalent to 8^3/2^3
Transform y=-2x + 5 into an equivalent equation that is in standard form
Answer: The standard form of a linear equation is Ax+By=C. To change an equation written in slope-intercept form (y=mx+b) to standard form, you must get the x and y on the same side of the equal sign and the constant on the other side. Use inverse operations to move terms.
Step-by-step explanation:
How to graph p(x)=-3x-1
The graph of the equation p(x) = -3x- 1 has been plotted
The equation is given that
p(x) = -3x - 1
We know the slope intercept form of the line
y = mx + b
Where m is the slope of the line
b is the y intercept
Compare both equation
The slope of the line m = -3
The y intercept b = -1
At x = 1
The value of p(1) = -3(1) -1
= -3 - 1
= -4
At x = 2
The value of P(2) = -3(2) -1
= -6 - 1
= -7
Substitute the value for x and find the value of y.
Draw the graph using the points
Hence, the graph of the equation p(x) = -3x- 1 has been plotted
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please help asap my mom and dad will kill me if i don't have this practice exam done. Liz wanted to buy a new book. When she checked the price last week, it was $16. This week, the same book was listed for $20. Write and solve an equation to show how much the book increased in price.
20 = p − 16; p = $36
20 = p + 16; p = $4
16 + p = 36; p = $20
2p = 20; p = $10
Answer:
Step-by-step explanation:
1. Since the price goes up by whatever number it eventually become 20$ from 16$. SO subtract to get number. 20-16= 4 $
So fitting best...: 20$=p+16;p=4$= TRUE
Answer:20$=p+16;p=4$ or Choice C
PS.Hope you find it helpful!!
Please help!!
5x -10y = 10
x + 2y = -18
(Enter the solution like this: ( , ) )
The value to the system of equations is (-10, -4)
How to determine the solution to the system of equations?In this case, the system of equations is given as
5x -10y = 10
x + 2y = -18
Make x the subject in the second equation
So, we have the following representation
x = -2y - 18
Substitute x = -2y - 18 in the equation 5x -10y = 10
So, we have
5(-2y - 18) -10y = 10
Open the brackets
This gives
-10y - 90 - 10y = 10
Evaluate the like terms
-20y = 80
Divide by -20
y = -4
Recall that x = -2y - 18
So, we have
x = -2 * -4 - 18
Evaluate
x = -10
Hence, the solution is (x, y) = (-10, -4)
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PLEASE HELP ASAP WILL GIVE ANYTHING
Spin a spinner with three equal sections colored red, white, and blue. What is P(green)?
0%
100%
33%
66%
Answer:
Step-by-step explanation:
Ok:
Since percent can only add up to 100%, the sum must be no longer over 100%
There is no green on the spinner only red, white, and blue!
This means that 0 out of 100 percent is available for green!
Answer: 0%
The solution is Option C.
The probability of getting a green colored section on the spinner is given by the equation P ( green ) = 33 %
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the probability of getting a green colored section on the spinner be represented as P ( green )
Now , the equation will be
The number of sections on the spinner = 3 sections
The 3 sections are = { red , white , green }
So , probability of getting a green colored section P ( green ) = 1 / number of sections on the spinner
Probability of getting a green colored section P ( green ) = 1/3
Probability of getting a green colored section P ( green ) = 0.33
Probability of getting a green colored section P ( green ) = 33 %
Therefore , the value of P ( green ) is 33 %
Hence , the probability is 33 %
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PLEASE HELPP!!! MORE POINTS AND BRAINIEST MARK!
Mr. Gonzales would like to create a playground in his
backyard. He has 20 ft of fencing to enclose the play
area. Use this information for Items 10-13. S
10, Write a quadratic function in standard form that
models f(x), the total area of the playground in
square feet in terms of its width x in feet. Then
graph f(x).
11. Write the x- and y-intercepts of f(x) and interpret
them in terms of the problem.
12. Give the reasonable domain and range of f(x) as
inequalities, in interval notation, and in set
notation. Explain how you determined the
reasonable domain and range..
13. What is the maximum area for the playground?
What are the dimensions of the playground with
the maximum area?
Please, I need this tmr!
The quadratic equation is −x²+10x. Domain for the given equation is (0,10) and the Range is (0,25]. The x-intercept is (0,10) and the area is 10.
What is equation?Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.
Here,
quadratic function in standard form that models f(x), the total area of the playground in square feet in terms of its width x in feet,
f(x)=−x²+10x
The graph is given below,
Domain=(0,10)
range=(0,25]
To determine the domain that must exist between them, we used the xx-intercepts. We excluded them from the domain because the area at the x-intercepts is 0.
Since an area must be greater than 0, y>0y>0 follows. Remembering that the vertex of the graph of f(x) has the maximum point of (5,25) the maximum value for y is 25.
−x²+10x is the quadratic equation. The domain and range of the given equation are (0,10) and (0,25), respectively. (0, 10) is the x-intercept, and 10 is the area.
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Which equations have the same value of x as Three-fifths (30 x minus 15) = 72? Select three options.
18 x minus 15 = 72
50 x minus 25 = 72
18 x minus 9 = 72
3 (6 x minus 3) = 72
x = 4.5
Answer:
Option 3 ) 18x - 9 = 72
Step-by-step explanation:
Algebraic equations:
[tex]\sf \dfrac{3}{5}(30x - 15) = 72\\\\\\[/tex]
Multiply each term of (30x - 15) by 3/5,
[tex]\sf \dfrac{3}{5}*30x - \dfrac{3}{5}*15=72\\\\\\3*6x - 3*3 = 72\\\\18x - 9 = 72[/tex]
The given equation is same as 18x - 9 = 72
On Friday, a local hamburger shop sold a combined total of 303 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Friday?
Answer:
101
Step-by-step explanation:
Since the total number of cheeseburgers was twice the number of hamburgers, let the number of sold hamburgers be h
Twice of h = 2(h)
Hence,
2(h) + h = 303
2h + h = 303
3h = 303
Divide both sides by the coefficient of h
h = 101
Therefore, the total number of hamburgers sold was 101
Here are two closed containers and four balls just fit in each container. Container A Container B Curved surface area of a cylinder is 2лrh Each ball has a diameter of 60 mm. Which container has the smaller surface area? You must show your working (using mm). Your final line should say either, 'A is smaller' or 'B is smaller'.
There are two closed containers and four balls can just fit in each of the containers, then container A has a smaller surface area.
What is volume?A three-dimensional solid shape's capacity is referred to as its volume. It is difficult to visualize in any shape, yet this can be evaluated among forms.
As per the data in the question,
Radius, r = 30 mm
Height, h = 60 × 4 = 240 mm
Use the equation of the surface area of the cylinder, SA = 2πr² + 2πrh
SA = 2π(30)² + 2π (30)(240)
SA = 50,868.
Now, calculate the area of a rectangular prism,
Area of top and bottom,
= (60 + 60) × (60 + 60) × 2
= 120 × 120 × 2 = 28,800
Area of 2 sides,
= 2 × (60 × 120) = 14,400
Area of front and back,
= 2 × (60 × 120) = 14,400
Total Surface Area = 28,800 + 14,400 + 14,400 = 57,600
Therefore, A has a smaller surface area.
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If the perimeter of the window is 28 feet, find the exact value of x (in ft) so that the greatest possible amount of light is admitted.
the exact value of x, so that the greatest possible amount of light is admitted is 3.92 ft.
let x represents the radius of a semicircle, thus the width of the rectangle = 2x, length be y.
perimeter of the rectangular window = πx + 2y + 2x = x(π +2) + 2y
it is given that the perimeter is 28 ft.,
28 = x(π +2) + 2y
y = 28 - x(π +2) / 2
the area of the window A = 1/2 πx² = 2yx ( area of semicircle + area of rectangle)
A = 1/2 πx² + 2x [(28 - x(π +2) / 2] (Substituting the value of y)
A = 1/2 πx² + 28x - πx² - 2x²
A = 28x - x² ( 2 + π/2 )
The maximum value of x is when dA/dx = 0
A' = 28- 2x ( 2 + π/2 )
2x ( 2 + π/2 ) = 28
x ( 2 + π/2 ) = 14
x = 3.92 ft
hence the value of x so that the greatest possible amount of light is admitted is 3.92 ft.
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(complete question)
A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle. See the figure below.) If the perimeter of the window is 28 ft, find the value of x so that the greatest possible amount of light is admitted.
14. A baker needs to make 3 batches of
3 cups of
cupcakes. If each recipe uses
sugar, how much sugar will the baker need?
(Example 5)
The baker needs [tex]\frac{25}{12}[/tex] cups of sugar.
Number of batches of cupcakes a baker needs to make = [tex]3 \frac{1}{8}[/tex]
Number of cups of sugar each recipe uses = [tex]\\\frac{2}{3}[/tex]
Quantity of sugar required to make [tex]3 \frac{1}{8}[/tex] batches of cupcakes = [tex]3 \frac{1}{8}[/tex] × [tex]\\\frac{2}{3}[/tex]
= [tex]\frac{25}{8}[/tex] × [tex]\frac{2}{3}[/tex]
= [tex]\frac{25}{12}[/tex]
Therefore, the quantity of sugar required to make [tex]3\frac{1}{8}[/tex] batches of cupcakes is [tex]\frac{25}{12}[/tex] cups.
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A jungle has 594 monkeys.
It also has 62 birds.
How many more monkeys than birds are there?
Answer:
532
Step-by-step explanation:
594 [monkeys] - 62 [birds] = 532
You can buy 3 apples at the quick market for $1.26 you can buy 5 of the same apples at the stop and save for $2.55 witch place is better buy
Answer:
quick market
Step-by-step explanation:
because it more cheaper
Find two positive numbers for which the product is 196 and the sum of the first plus four times the second is a minimum. ONE of these numbers is B) 14 C) 12 D) 8 E) 7
Minimum number is 33+4*6= 57
Give us two positive numbers, x and y.
196 is the result: x*y = 19
The minimum is the product of the first plus four times the second: x + 4y.
The first equation results in y = 196/x. Put that into the second equation as a replacement:
x + 4y = x + 4(196/x) = x + 784/x
Taking the first derivative now, we can solve for x by setting it to zero.
d(x + 784/x)/dx = 1 - 784/[tex]x^{2}[/tex]
0 = 1 - 784/[tex]x^{2}[/tex]
0 = [tex]x^{2}[/tex]- 784 [[tex]x^{2}[/tex] multiplied on both sides]
784 = [tex]x^{2}[/tex]
[tex]\sqrt{784}[/tex] = [tex]\sqrt{x^{2} }[/tex]
Y = 196/x = 7 since we want a positive integer, hence x = 28
The factors of 196 are 196*1, 99*2, 66*3, 6*33,22*19, and 11*18 as a check.
196 + 4*1 = 200
99 + 4*2 = 107
66 + 4*3 = 78
33+4*6= 57
22 + 4*19 = 98
11 + 4*18=82
In fact, 33+4*6= 57 is minimum.
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what number "x" makes the equation 8^x=2 correct?
Answer:
x = (1/3)
Step-by-step explanation:
8ˣ = 2
8 = 2³
2³ˣ = 2¹
3x = 1
÷3 ÷3
------------
1
x = ------
3
I hope this helps!
I need to find the slope and the y-intercept please help
Answer: 30
Step-by-step explanation:
1. You find the slope by picking 2 points and dividing the change in the y-axis by the change in the x-axis. (Time is ALWAYS x)
(50-40)/40-20
(10)/20)
1/2
SLOPE=1/2
2. You find the y-intercept by picking a point, and plugging them into your equation, and solving for b.
(I will be using the point (20,40) )
40=1/2(20)+b
40=10+b
b=30
Y-INTERCEPT=30
Anna is working two summer jobs, making $9 per hour washing cars and $12 per
hour landscaping. Last week Anna worked a total of 7 hours and earned a total of
$78. Determine the number of hours Anna worked washing cars last week and the
number of hours she worked landscaping last week.
By solving a system of equations we will see that Anna works 2 hours washing cars and 5 hours landscaping.
How to determine the number of hours in each job?
First, we need to define the variables that we will be using, these are:
x = number of hours washing cars.y = number of hours landscaping.We know that she works 7 hours in total and earns $78 in total, so we can write the system of equations:
x + y = 7
x*$9 + y*$12 = $78
Isolating x on the first equation we get:
x = 7 - y
Replacing this on the other equation we get:
(7 - y)*$9 + y*$12 = $78
$63 - $9*y + $12*y = $78
$63 + $3*y = $78
$3*y = $78 - $63
$3*y = $15
y = $15/$3 = 5
Then the value of x is:
x = 7 - y = 7 - 5 = 2
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Identify the solution of the inequality |9m| + 40 > 4 and the graph that represents it.
Answer:
B) All real numbers===========================
GivenInequality |9m| + 40 > 4Solution|9m| + 40 > 4|9m| > - 40 + 4|9m| > - 36|m| > - 4Since absolute value is never negative, this inequality is correct for any value of m.
Correct answer choice is B.
Answer:
All real numbers.
Step-by-step explanation:
The bars either side of an expression or a value are the absolute value symbol. "Absolute value" means how far a value is from zero. Therefore, the absolute value of a number is its positive numerical value.
Given inequality:
[tex]|9m|+40 > 4[/tex]
Subtract 40 from both sides to isolate the absolute value on one side of the equation:
[tex]\implies |9m|+40-40 > 4-40[/tex]
[tex]\implies |9m| > -36[/tex]
As the absolute value of a number or expression is its positive numerical value:
[tex]\implies |9m| \geq 0[/tex]
Therefore, as 9m is always greater than or equal to zero, it will always be greater than -36, regardless of the value of m.
Therefore, the solution of the given inequality is all real numbers.
Ue Greatet Common Factor (GCF) and the Ditributive Property to write 3550 a a product
By using GCF and distributive Property, it is obtained that
3550 = 5 [tex]\times[/tex] 710 as a product
What is Greatest Common Factor and distributive property?
Greatest Common factor (GCF) of two numbers a and b is the greatest number that divides both a and b.
Distributive property is the property over both addition and multiplication.
If a, b and c are three numbers, then distributive property is given by
[tex]a \times (b + c) = a \times b + a \times c[/tex]
3550 = 3000 + 550
Now,
[tex]3000 = 2\times 2 \times 2\times 3\times 5 \times 5 \times 5\\550 = 2 \times 5 \times 5 \times 11[/tex]
GCF of 3000 and 550 = 5
3550 = 5 [tex]\times[/tex] 600 + 5 [tex]\times[/tex] 110
3550 = 5 [tex]\times[/tex] (600 + 110) [Distributive Property]
3550 = 5 [tex]\times[/tex] 710
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Gus is buying juice drinks, x, and snack packs, y, for a school picnic. The system of inequalities models how many of each item Gus needs to buy and how much he can spend. Which of the following points represents a viable solution to the system?
I will give Brainliest to whoever answers
x + y ≥ 150
1.5x + 3.5y ≤ 600
A. (−10, 170)
B. (80, 90)
C. (250, −50)
D. All real whole numbers, with x ≥ 0 and y ≥ 0
The points that represents a viable solution to the system of inequalities include the following:
A. (−10, 170)
B. (80, 90)
C. (250, −50)
How to determine the points for a viable solution to the system?In order to determine which points are true and viable with respect to a solution of the given system of inequalities, we would have to test the each of the points by substituting their values into the inequalities as follows;
For points (-10, 170), we have:
x + y ≥ 150
-10 + 170 ≥ 150
160 ≥ 150 (Viable).
1.5x + 3.5y ≤ 600
1.5(-10) + 3.5(170) ≤ 600
-15 + 595 ≤ 600
580 ≤ 600 (Viable).
For points (80, 90), we have:
x + y ≥ 150
80 + 90 ≥ 150
170 ≥ 150 (Viable).
1.5x + 3.5y ≤ 600
1.5(80) + 3.5(90) ≤ 600
120 + 315 ≤ 600
435 ≤ 600 (Viable).
For points (250, -50), we have:
x + y ≥ 150
250 - 50 ≥ 150
200 ≥ 150 (Viable).
1.5x + 3.5y ≤ 600
1.5(250) + 3.5(-50) ≤ 600
375 - 175 ≤ 600
200 ≤ 600 (Viable).
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9. A contractor is pouring a rectangular concrete slab with dimensions of 16 feet by 30
feet. To ensure that the sides of the slab form 90° angles, how many feet should
each diagonal measure?
If each sides of the slab form 90° angles, The number of feet that
each diagonal measure is 34 feet.
How to find the diagonal feet?Using Pythagoreans theorem formula to find the diagonal feet
D² =L² + W²
Where:
D = Diagonal
L= Length = 16 feet
W = Width = 30
Let plug in the formula
D² = 16² + 30²
D² = 256 + 900
D=√1156
D= 34 feet
Therefore the diagonal measure 34feet
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Which of the following are solutions to the equation below?
Check all that apply.
(2x+3)² = 10
x= √2/2
A. x=
□ B. x-10-3
2
C. x= -√/10 +
5 + 2/1/2
☐ D. x =
-10-3
2
<= -√
2
☐ E. x = -
32
OF. x= √10 +
332
The solutions for the equation (2x+3)² = 10 is:
x=√10-3/2x=-√10-3/2Given:
the equation is:
(2x+3)² = 10
we need to solve the following equation.
⇒ (2x+3)² = 10
taking square roots on both sides.
⇒ √(2x+3)² = √10
⇒ 2x+3=±√10
Now solving:
2x+3=√10 and 2x+3=-√10
2x=√10-3 and 2x=-√10-3
x=√10-3/2 and x=-√10-3/2
Hence we get the solutions of the given equation.
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Which size bag of raisins has the lowest cost per gram?
A
100 g at $1.00
B
250 g at $2.00
C
500 g at $3.00
D
750 g at $6.00
Answer: A
Step-by-step explanation:
A for 1 gram it is $1.00
B for 1 gram it is $1.25
C for 1 gram it is $1.66
D for 1 gram it is $1.25