The volume of the rectangular prism is 13.125 cubic yards.
Calculating the number of cubes and the volumeTo find the number of cubes that fit along the length, width, and height of the rectangular prism, we need to divide the length, width, and height by the edge length of each cube, which is 1/2yd.
Along the length: (2 1/2 yd) / (1/2 yd) = 5 cubes
Along the width: (3 1/2 yd) / (1/2 yd) = 7 cubes
Along the height: (1 1/2 yd) / (1/2 yd) = 3 cubes
Therefore, there are 5 cubes along the length, 7 cubes along the width, and 3 cubes along the height of the rectangular prism.
To find the volume of the rectangular prism, we can multiply the length, width, and height:
Volume = (2 1/2 yd) x (3 1/2 yd) x (1 1/2 yd)
Volume = (5/2 yd) x (7/2 yd) x (3/2 yd)
Volume = (13.125 yd^3)
Therefore, the volume of the rectangular prism is 13.125 cubic yards.
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Please what is the answer?
Answer:
When we have a set of points, we can find the distance between them using the formula:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex], where d is the distance, x1 and x2 are one point and y1 and y2 are another point.
OB:
Thus, for OB, we can allow O(6, 6) to be our x1 and x2 point and we can allow B(9, 6) to be our y1 and y2 point:
[tex]d=\sqrt{(6-9)^2+(6-6)^2} \\d=\sqrt{(-3)^2+(0)^2} \\d=\sqrt{(-9)} \\d=3[/tex]
Thus, the first part/step in the equation is your subtraction expression to find the length of OB.
AB:
For AB, we can allow A(9, 10) to be our x1 and x2 point and we can allow B (9, 6) to be our y1 and y2 point:
[tex]d=\sqrt{(9-9)^2+(10-6)^2}\\ d=\sqrt{(0)^2+(4)^2}\\ d=\sqrt{16}\\ d=4[/tex]
The first part/step is your subtraction expression for the length of AB.
What is the slope of the line
Answer:
- 2/1
Step-by-step explanation:
if u look at the graph/line it's going up by 2 then across 1
The probability that the friend is at least 22 minutes late is
The probability that the friend is at least 22 minutes late is 0.266
Uniform density function for a friend = x minutes late
The Friend is at least 21 minutes late
Based on the above information, the probability that the friend is at least 21 minutes late is
= (Total minutes - minimum minutes)/Total minutes
=30-22/30
=8/30
=0.266
Based on the above formula we can easily find out the probability for the friend who is at least 22 minutes late
Hence, the probability that the friend is at least 22 minutes late is 0.266
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Use w for the unknown.
"A number split into 3 equal parts"
Answer:
[tex] \frac{w}{3} [/tex]
Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 18sin^2(x)cos^2(x)
An equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
How did we get the value?The power-reducing formulas state that:
sin^2(x) = (1 - cos(2x))/2
cos^2(x) = (1 + cos(2x))/2
Using these formulas, we can rewrite the expression 18sin^2(x)cos^2(x) as:
18sin^2(x)cos^2(x) = 18[(1 - cos(2x))/2][(1 + cos(2x))/2]
Expanding the right-hand side of the equation, we get:
18[(1 - cos^2(2x))/4]
Using the identity cos^2(2x) = (1 + cos(4x))/2, we can simplify further:
18[(1 - (1 + cos(4x))/2)/4] = 9 - 9cos(4x)/8
Therefore, an equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
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ASAPPP PLEAse 25 pointss
Show work it's already solved but show work\
`its 2 questions
Volume First Cylinder: 50.24 in³
Volume Second Cylinder: 127.5625 inch³
Volume Third Cylinder: 904.32 inch³
Volume First Cylinder:
= πr²h
= 3.14(2)² (4)
= 3.14 x 16
= 50.24 in³
Volume Second Cylinder:
= πr²h
= 3.14(2.5)² (6.5)
=3.14 (6.25)(6.5)
= 127.5625 inch³
Volume Third Cylinder:
= πr²h
= 3.14(6)² (8)
=3.14 (36)(8)
= 904.32 inch³
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cylinder radius2 cm height7 cm
13. What is the shape of the bases?
Answer:
88
Step-by-step explanation:
y=2cm h=7cm
CSA=22/7×4×7
the sevens get crossed out and then 22/1 ×4=88.
The committee spends $462 on costumes for 24 people. Each costume costs the same amount of money.
How much did each costume cost, in dollars?
Answer:
Step-by-step explanation: 462 Divided by 24 = 19.25$
Proof: 19.25 x 24 = 462
Answer: 19.25$
I need help please!!!
Answer:
a. Plot the points on the graphing calculator, then generate a logarithmic regression equation.
y = 34.17860108 - 5.682632245ln(x)
b. Setting this equation equal to 10, we have x = 70.44 mph
c. If x = 75 mph, then y = 9.64.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
g°f = -9 So, the correct answer is (B) -9.To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.
what is function ?
In mathematics, a function is a relation between two sets, called the domain and the range, that assigns to each element of the domain exactly one element of the range.
In the given question,
To find g°f, we need to first apply the function f to -3, and then apply the function g to the result.
Step 1: Apply f to -3
f(x) = 3x + 7
f(-3) = 3(-3) + 7 = -2
Step 2: Apply g to the result of f(-3)
g(x) = 2x - 5
g(-2) = 2(-2) - 5 = -9
Therefore, g°f = -9.
So, the correct answer is (B) -9.
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Enter the value for x that makes the equation 3(2x+5)=x-10 true.
Answer:
Step-by-step explanation:
6x + 15 = x - 10
5x + 15 = -10
5x = -25
x = -5
The population of a city increases by 3.5% per year. If this year's population is
p, which expression does NOT represent next year's population?
3.5p
O (1+0.035)p
1.035p
O 1p+ 0.035p
The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]
What is an expression ?Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an operator. Mathematical operations include addition, subtraction, multiplication, and division.
An example is the expression x + y, which combines the terms x and y with an addition operator.
In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers.
A number is [tex]6[/tex] more than half of the other number, which is x. This statement is represented by the mathematical equation [tex]\frac{x}{2} +6[/tex]. Mathematical expressions are used to solve complicated puzzles.
According to the problem,
The expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]
This is because it incorrectly adds [tex]1p to 0.035p[/tex], which would result in an overestimation of the population growth.
The correct way to calculate next year's population with a growth rate of [tex]3.5[/tex]% is to multiply the current population (p) by [tex]1[/tex] + [tex]0.035[/tex], as shown in the other three expressions: [tex]3.5p, 1.035p, (1+0.035)p[/tex].
Therefore,the expression that does NOT represent next year's population is: [tex]O(1p +0.035)p[/tex]
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Use the functions [tex]f(x)[/tex] and [tex]g(x)[/tex] to find the domain of the indicated functions, and simplify the expressions for the domain in question.
FUNCTIONS:
[tex]f(x) = x^4[/tex]
[tex]g(x)=\sqrt{x+7}[/tex]
1) [tex](f+g)(x)[/tex] = [tex]f(x)+g(x)[/tex]
2) [tex](f-g)(x)[/tex] = [tex]f(x)-g(x)[/tex]
3) [tex](fg)(x)[/tex] -> [tex](f(g(x))[/tex]
POSSIBLE ANSWERS:
A) The domain of all three pairs is -∞ ≤ [tex]x[/tex] ≤ ∞.
B) The domain for #1 and #2 is [tex]x[/tex] ≥ -7 and the domain for #3 is -∞ ≤ [tex]x[/tex] ≤ ∞.
C) The domain of every pair is [tex]x[/tex] ≥ -7.
D) A through C are partially true.
E) None of the above OR the domain is undefined.
B) The domain for #1 and #2 is ≥ -7 and the domain for #3 is -∞ ≤ ≤ ∞.
Explanation:1. [tex](f + g)(x) = f(x) + g(x)[/tex]
The domain of [tex](f + g)(x)[/tex] is the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for [tex]x > = -7[/tex] (since we can't take the square root of a negative number), the domain of [tex](f + g)(x)[/tex] is [tex]x > = -7[/tex].
2. [tex](f - g)(x) = f(x) - g(x)[/tex]
The domain of [tex](f - g)(x)[/tex] is also the intersection of the domains of [tex]f(x)[/tex] and [tex]g(x)[/tex]. Since [tex]f(x) = x^4[/tex] is defined for all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for[tex]x > = -7[/tex], the domain of [tex](f - g)(x)[/tex] is also [tex]x > = -7[/tex].
3. [tex](fg)(x) - > (f(g(x))[/tex]
The domain of [tex]f(g(x))[/tex] is the set of all values of [tex]x[/tex] such that [tex]g(x)[/tex] is in the domain of [tex]f[/tex]. Since the domain of [tex]f[/tex] is all real numbers [tex]\mathbb {R}[/tex], and [tex]g(x) = (x + 7)^(1/2)[/tex] is defined only for [tex]x > = -7[/tex], the domain of [tex]f(g(x))[/tex] is [tex]x > = -7[/tex].
Therefore, the correct answer is option:
B) The domain for 1) and 2) is [tex]> = -7[/tex] and the domain for 3) is -∞ ≤ [tex]x[/tex] ≤ ∞.
Consider the following random sample of diameter measurements (in inches) of 14 softballs.
4.75, 4.71, 4.78, 4.81, 4.69, 4.89, 4.68, 4.86, 4.84, 4.86, 4.75, 4.72, 4.71, 4.69
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If we assume that the diameter measurements are normally distributed, find a 99% confidence interval for
the mean diameter of a softball. Give the lower limit and upper limit of the 99% confidence interval.
Step-by-step explanation:
sadly, we have only 14 data points. that is a very small sample to find a more or less reliable standard deviation for the production of softballs.
because to create the desired answer we need to calculate the mean value and the standard deviation. and we need to mix that with the Z- value of the standard normal distribution table representing the 99% confidence (= coverage of 99% of the area under the normal distribution curve, meaning therefore from 99.5% to 0.5%).
the confidence interval limits are
mean ± Z×sd/sqrt(n)
mean = mean value of the sample.
sd = standard deviation (either of - preferred - the entire population or of the sample)
n = number of data points (here 14).
Z = Z value of the standard normal distributing table for 99% (2.576).
here a little table for different confidence intervals :
Confidence Interval Z
80% 1.282
85% 1.440
90% 1.645
95% 1.960
99% 2.576
99.5% 2.807
99.9% 3.291
mean value = sum of all data points divided by the number of data points :
mean = 66.74/14 = 4.767142857...
sd = sqrt(sum((data point difference to mean)²)/n)
let's use some calculation tool like Excel (after all, the mean value is not a simple number, and to write this all up here takes a lot of space).
sd = 0.069941667...
the confidence interval limits are then
4.767142857... ± 2.576×0.069941667.../sqrt(14) =
= 4.767142857... ± 0.048152387...
upper limit = 4.815295244 ... ≈ 4.82
lower limit = 4.71899047 ... ≈ 4.72
that means, we are 99% sure that the true mean value across all produced softballs is between these 2 limits.
in other words, for 99% of such samples we can pick, their mean values will be between these 2 limits. and 1 % of such samples we expect to have a mean value outside of these 2 limits.
Find the maximize z = 4x + y. Subject to the constraints x + y ≤ 50, 3x + y ≤ 90, x,y ≥ 0
The maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.
How to deal with inequality?To find the maximum value of z = 4x + y subject to the given constraints, we can use linear programming.
Graph the constraints:
First, we will graph the constraints to visualize the feasible region.
The constraint x + y ≤ 50 represents the region below the line x + y = 50:
The constraint 3x + y ≤ 90 represents the region below the line 3x + y = 90:
The feasible region is the shaded region that satisfies both constraints:
Identify the corner points of the feasible region:
The feasible region has four corner points: (0, 0), (0, 50), (30, 20), and (45, 0).
Evaluate z at each corner point:
z(0, 0) = 4(0) + 0 = 0
z(0, 50) = 4(0) + 50 = 50
z(30, 20) = 4(30) + 20 = 140
z(45, 0) = 4(45) + 0 = 180
Compare the values of z at the corner points:
The largest value of z is 180, which occurs at the corner point (45, 0).
Therefore, the maximum value of z = 4x + y subject to the given constraints is 180, which occurs at x = 45 and y = 0.
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A dance instructor ears $75 for teaching 3 classes. The instructor receives a 10% raise. Enter how much the instructor earns, in dollars, per class after the raise.
. According to the National Highway Traffic Safety Administration, seat belt using among American
drivers and front-seat passengers passed 90% for the first time in 2016. At that time, 90.1% of
people used seat belts. If four people are selected at random, find the probability that all four
regularly use seat belts.
The probability that all four people regularly use seat belts is approximately 0.656 or 65.6%.
To find the probability that all four people regularly use seat belts, we need to use the multiplication rule of probability which states that the probability of two or more independent events occurring together is the product of their individual probabilities.
The probability that the first person uses a seat belt is 0.901, and assuming that the events of seat belt use by different people are independent, the probability that the second person also uses a seat belt is 0.901.
The probability that the third person uses a seat belt is also 0.901, and the probability that the fourth person uses a seat belt is also 0.901.
Therefore, the probability that all four people regularly use seat belts is:
P(all four use seat belts) = P(person 1 uses seat belt) x P(person 2 uses seat belt) x P(person 3 uses seat belt) x P(person 4 uses seat belt)
P(all four use seat belts) = 0.901 x 0.901 x 0.901 x 0.901
P(all four use seat belts) = 0.656
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The area of this rhombus is 20 square miles. One of its diagonals is 10 miles. What is the length of the missing diagonal?
========================================================
Work Shown:
[tex]d_1 = \text{ one of the diagonals} = 10\\\\d_2 = \text{ the other diagonal}= \text{x}\\\\A = \text{ area of the rhombus} = 20\\\\A = \frac{d_1*d_2}{2}\\\\20 = \frac{10\text{x}}{2}\\\\20*2 = 10\text{x}\\\\40 = 10\text{x}\\\\\text{x} = 40/10\\\\\text{x} = 4[/tex]
The other diagonal is 4 miles long.
Breck has 22 dimes and nickels. The total value of the coins is $1.45.
How many dimes and how many nickels does Breck have?
Answer:
11 dimes and nickels.
Step-by-step explanation:
22 total coins divided by 2 equals 11 for each.
the number 2 represents the dimes and nickels, 22 for the total amount of coins, and 11 for the answer.
Answer:15 nickels and 7 dimes.
Step-by-step explanation:
help please quick i need these
ANSWER:
368
EXPLANATION:
youre given:
l=14
w=5
h=5
just plug those into the given formula,
2×(14×5)+2×(14×6)+2×(5×6)
(you should do it yourself to check my math...)
for your land line phone service monthly bill, you pay 3¢ for each minute you use plus a $10 monthly charge. you budget yourself to spend no more than $40 on your phone bill. what is the range of minutes you can use this month?
Answer:
100 Minutes
Step-by-step explanation:
Step 1: Break it down-
3¢ can be expressed as 0.3
Step 2: Add monthly charge-
Since there is a 10$ monthly charge: 40-10=30
Step 3: Subtract-
Now divide: 30 ÷ 0.3
Step 4: Final Answer-
Hence the amount of minutes per month= 100
Chanasia buys a plastic bucket. The bucket weighs 460 g. The label on the bucket says made with 20% recycled plastic. How many grams of recycled plastic are used to make Chanasia’s bucket?
please help and please show work
92 grams of recycled plastic were used to make Chanasia's bucket
How to calculate the amount of recycled plastic that was used to make Chanasia's bucket?Chanasia buys a plastic bucket
The bucket weighs 460 grams
The label on the bucket says it was made with 20% recycled plastic
The number of grams of recycled plastic that was used to make the bucket can be calculated as follows
= 460/100
= 4.6
= 4.6 × 20
= 92
Hence 92 grams of recycled plastic was used to make the bucket
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Please help studying for next grade:
192-84÷(71+16)x3
Answer:
189.1034.
Step-by-step explanation:
The result of the expression is approximately 189.1035.
To calculate the expression 192 - 84 ÷ (71 + 16) x 3, follow the order of operations, which is commonly remembered by the acronym PEMDAS:
Parentheses: Perform the operation within the parentheses first.
71 + 16 = 87
Division: Perform the division.
84 ÷ 87 ≈ 0.9655 (rounded to four decimal places)
Multiplication: Perform the multiplication.
0.9655 * 3 ≈ 2.8965 (rounded to four decimal places)
Subtraction: Finally, perform the subtraction.
192 - 2.8965 ≈ 189.1035 (rounded to four decimal places)
The result of the expression is approximately 189.1035.
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Consider the following.
f(x) = x^5 − x^3 + 4, −1 ≤ x ≤ 1
(a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
The function has a local maximum at x = 1 and a local minimum at x = 1/5, as shown in the graph, and the absolute maximum and minimum occur at x = 0 and x = (3/5), respectively.
what is function?Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.
A function is an association between inputs and outputs that yields one unique outcome for each input. Every function has a domain and a codomain, often known as a scope. Functions are commonly represented with the letter f. (x). As input, an x is used. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four fundamental types of functions available.
To obtain the absolute maximum and lowest values of the function over the interval −1 ≤ x ≤ 1, we must examine the critical points and the interval endpoints.
We first take the derivative of f(x) and set it to zero to determine the critical points:
The function is then assessed at these pivotal points and the interval's endpoints:
As we can see from the information above, f(x) has a maximum value of 4 and occurs at the values x = 0 and x = 1. The absolute minimum value of f(x) is approximately 2.65 for x = (3/5).
We can corroborate these findings by charting the graph of f(x) across the 1 x 1 interval: graph of f(x) = x5 x3 + 4
According to the graph, the function has a local maximum at x = 1 and a local minimum at x = 1/5, but the absolute maximum and lowest are, respectively, x = 0 and x = (3/5).
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1) You're traveling to Spain this
summer. You'll have $200 to spend on
memorabilia items. How much euros
do you have to spend on memorabilia
items? Note: $1=0.84 E
Using the conversion factor we know that we will spend 180.69€ on memorabilia items.
What is the conversion factor?A conversion factor is a number that is used to multiply or divide one set of units into another.
If a conversion is required, it must be done using the correct conversion factor to get an identical value.
A fraction that is equal to "1" is a conversion factor.
The numerator and denominator are the same amounts, but they are expressed in different units. It is used to change a number's unit of measurement.
By multiplying the initial number by the fraction that is equal to "1," you can change the units without changing the original number's value.
So, in the given situation:
$200 = euros?
We know that:
$1 = 0.90€
Then,
$200 = 180.69€
Therefore, using the conversion factor we know that we will spend 180.69€ on memorabilia items.
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A surge function is a function of the form
f (t) = Atne(−bt)
The values A, n, and b are the parameters of the function.
This function accurately represents the way a drug interacts in the bloodstream. Studying
this function is essential to doctors and pharmacists because it allows them to administer
dosages of medicine correctly.1
A drug dose is being designed for a 90kg male patient. The amount of the drug in the
patient’s bloodstream after t hours, measured in nanograms per milliliter (ng/ml) is given
by a surge function.
Any positive value of A can be achieved by increasing or decreasing the amount of
medicine given. However, depending on the type of delayed release mechanism selected
there are choices possible for the value of the pair (n,b): The achievable pairs are listed in
the table below.
Delay Type n value b value
Extended 2 0.3
Medium 3 0.5
Rapid 3 0.7
The medical requirements for the treatment are:
• The dose (in ng/ml) may not exceed 100 at any time.
• The dose must fall to be at or below 20 ng/ml by 24 hours.
Within these parameters, the treatment effect will be measured in ng/ml-hours. (1
ng/ml concentration for 1 hour is 1 ng/ml-hour of treatment). The objective is to obtain
the maximum possible treatment effect while ensuring the requirements are met.
1Tarko, Olta (2021) ”Surge Functions and Drug Interactions,” Undergraduate Journal of Mathematical
Modeling: One + Two: Vol. 12: Iss. 1, Article 7
How many times smaller is 1.2 × 106 than 1.47 × 107?
Answer: It is 1.24x smaller.
Step-by-step explanation:
1.2(106)= 127.2
1.47(107)= 157.3
157.3/127.2 = 1.24x smaller
NO LINKS!! URGENT HEL PLEASE!!!
Use tests for symmetry to determine which graphs from the lists below are symmetric with respect to the y-axis, the x-axis, and the origin. (Select all that apply)
a. symmetric with respect to the y-axis
Using the tests for symmetry, the following are symmetric with respect to y-axis:
y = - x + 7y = - 7x²x = - y² + 9How to determine symmetricity?A graph is symmetric with respect to the y-axis if replacing x with -x produces an equivalent equation.
A graph is symmetric with respect to the x-axis if replacing y with -y produces an equivalent equation.
A graph is symmetric with respect to the origin if replacing x with -x and y with -y produces an equivalent equation.
(a) symmetric with respect to the y-axis:
y = 7x - 4 (no)
y = - x + 7 (yes)
y = - 7x² (yes)
y = 6x² - 9 (no)
x = 1/4 × y² (no)
x = - y² + 9 (yes)
y = - 1/6 × x³ (no)
y = x³ - 1 (no)
y = √(x) (no)
y = √(x) - 6 (no)
Therefore, the graphs that are symmetric with respect to the y-axis are:
y = - x + 7
y = - 7x²
x = - y² + 9
None of the graphs are symmetric with respect to the x-axis or the origin.
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Sarah is borrowing money from a friend. She is paying 5% interest. after 18 months, she paid her friend the principal plus $45. what was the original amount she borrowed?
A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.
A 2-pound package of hamburger costs $7.00, and you pay $10.50 for a 3-pound package of hamburger.
To find the cost per pound of hamburger, we need to divide the total cost by the weight in pounds.
For the 2-pound package
Cost per pound = Total cost / Weight in pounds
Cost per pound = $7.00 / 2 lbs
Cost per pound = $3.50 per pound
For the 3-pound package
Cost per pound = Total cost / Weight in pounds
Cost per pound = $10.50 / 3 lbs
Cost per pound = $3.50 per pound
Therefore, the cost per pound of hamburger is the same for both packages, at $3.50 per pound.
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