Answer:
Since the prism is completely filled with 96 cubes that have an edge length of 1/2 cm, we can find the volume of the prism by multiplying the number of cubes by the volume of each cube.
The volume of each cube is (1/2 cm)^3 = 1/8 cm^3.
The number of cubes is 96.
Therefore, the volume of the prism is:
volume = (number of cubes) x (volume of each cube)
volume = 96 x (1/8 cm^3)
volume = 12 cm^3
So, the volume of the prism is 12 cubic centimeters.
please answer this question: the length of a rectangle is 6 centimeters less than its width. what are the dimensions of the rectangle if it's area is 160 square centimeters?
Which of the following sets of numbers could represent the three sides of a
triangle?
{7, 15, 20}
{7, 16, 23}
O {11, 22, 35}
O {5, 17, 22}
The following sets of numbers could represent the three sides of a
triangle is {7, 15, 20}.
How to determine the set that represent the three sides of a triangleThe set of numbers {7, 15, 20} could represent the three sides of a triangle, but the other sets of numbers do not satisfy the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side. Checking the sets of numbers:
For {7, 15, 20}, 7 + 15 > 20, 7 + 20 > 15, and 15 + 20 > 7, so they satisfy the triangle inequality theorem and could represent the sides of a triangle.
For {7, 16, 23}, 7 + 16 < 23, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.
For {11, 22, 35}, 11 + 22 < 35, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.
For {5, 17, 22}, 5 + 17 < 22, so they do not satisfy the triangle inequality theorem and cannot represent the sides of a triangle.
Therefore, the answer is {7, 15, 20}.
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3% of a sum of money is $60.What is the sum of money?
Answer:
2000
Step-by-step explanation:
Formula = Number x 100/Percent = 600 x 100/3 = 2,000
Following shows the steps on how to derive this formula and find out 3% of what number is 60.
Step 1: If 3% of a number is 60, then what is 100% of that number? Setup the equation.
60/3% = Y/100%
Step 2: Solve for Y
Using cross multiplication of two fractions, we get
3Y = 60 x 100
3Y = 6000
Y = 6000/100= 2000
Each of the lists below is in order from least to greatest
and has one number missing. List an example of a value
that could correctly complete the blank in each list.
I. -0.65,
2.
4.
/
3. 1.2%, 10%,
1
20'
12 13
4'5'2'2
,-0.6, -0.5, -0.4
6.2%,
/
1
16.7%, 40%
10.45
Answer:
-0.63
1/7
15%
10%
Step-by-step explanation:
hope this helps
Polly's sister-in-law is going to have a baby! For the baby shower, Polly decided to sew pillow to give as a gift. She is using a flower-printed rectangular piece of fabric that is 26 inches long and 22 inches wide.
Answer:
The answer is 96
Step-by-step explanation:
2*(26+22)
2*48
96
which is more 7,000 millimeters or 7 liters?
in square abcd, BE=13 find BC
Answer:
13sqrt{2}
Step-by-step explanation:
let's assume one side of square is a;
diognal which is BD=
[tex]a\sqrt{2}\\BE is BD/2=\frac{a\sqrt{2}}{2}=13\\a\sqrt{2}=26\\a=26/\sqrt{2}=13\sqrt{2}[/tex]
BC=CD=DA=AB=a=13sqrt{2}
13. The profit, in thousands of dollars, from the sale of x kilogram of coffee bean can be modelled by the function () = 5−400 +600 . a) State the asymptotes and the intercepts. Then, sketch a graph of this function using its key features. (5 pts) b) State the domain and range in this context. (2 points) c) Explain the significance of the horizontal asymptote. (1 point) d) Algebraically, find how much amount of tuna fish, in kg, should be sold to have a profit of exactly $4000? (4 points) SOLUTION
Answer: a) The profit function can be written as:
P(x) = 5x - 400x + 600
To find the asymptotes, we can look at the denominator of the second term, which is (x - 3). This means that there is a vertical asymptote at x = 3. To find the intercepts, we can set P(x) = 0:
5x - 400x + 600 = 0
Solving for x, we get:
x = 1.5 and x = 2.5
Therefore, there are x-intercepts at (1.5, 0) and (2.5, 0). To sketch the graph, we can also note that the coefficient of x^2 is negative, which means that the graph is a downward-facing parabola.
b) The domain of the function is the set of all possible values of x, which in this context represents the amount of coffee sold. Since we cannot sell a negative amount of coffee, the domain is x ≥ 0.
The range of the function is the set of all possible values of P(x), which represents the profit. Since the coefficient of x^2 is negative, the maximum profit occurs at the vertex of the parabola. The vertex has x-coordinate:
x = -b/(2a) = -(-400)/(2(-200)) = 1
Therefore, the maximum profit occurs when x = 1. The vertex has y-coordinate:
P(1) = 5(1) - 400(1) + 600 = 205
Since the coefficient of x^2 is negative, the range is (-∞, 205].
c) The horizontal asymptote of the function is y = -400, which represents the long-term average profit per kilogram of coffee sold. This means that as x gets very large, the profit per kilogram approaches -400. This could happen, for example, if the cost of producing the coffee increased significantly while the price remained the same.
d) To find the amount of coffee that must be sold to make a profit of $4000, we can set P(x) = 4000 and solve for x:
5x - 400x + 600 = 4000
Simplifying, we get:
-395x = -3400
Dividing both sides by -395, we get:
x ≈ 8.61
Therefore, approximately 8.61 kg of coffee must be sold to make a profit of $4000.
Step-by-step explanation:
Complete the ratio table to convert the units of time from hours to weeks or weeks to hours.
Hours:
168 1 week
1,008. ____week
_____. 5 weeks
Answer:
6 weeks and 840 hours
Step-by-step explanation:
There are 168 hours in one week.
24 hrs/day * 7 days = 168 hours
1008 hours ÷ 24 hours(1 day) = 42 days ÷ 7 days in a week = 6 weeks
168 hours/week * 5 weeks = 840 hours
Problem 13 and problem 20 ?
The answers to both questions are as:
(a) the value of the investment after 5 years is $14,917.95, after 10 years is $23,673.58, and after 15 years is $37,337.35,
b) the amount of the final payment is $688.32.
What is compound interest?
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
We can use the formula for compound interest to solve this problem:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time (in years).
(a) For 5 years with semiannual compounding:
n = 2 (compounded semiannually)
r = 0.08 (8% annual rate)
t = 5
[tex]A = 9900(1 + 0.08/2)^{(2*5)}[/tex]
A = $14,917.95
(b) For 10 years with semiannual compounding:
n = 2 (compounded semiannually)
r = 0.08 (8% annual rate)
t = 10
[tex]A = 9900(1 + 0.08/2)^{(2*10)}[/tex]
A = $23,673.58
(c) For 15 years with semiannual compounding:
n = 2 (compounded semiannually)
r = 0.08 (8% annual rate)
t = 15
[tex]A = 9900(1 + 0.08/2)^{(2*15)}[/tex]
A = $37,337.35
Therefore, the value of the investment after 5 years is $14,917.95, after 10 years is $23,673.58, and after 15 years is $37,337.35, assuming the interest is compounded semiannually.
To calculate the final payment, we can first find the balance of the loan at the end of the fifth year, and then use this as the principal to calculate the balance at the end of the tenth year.
The interest rate is 5% per year, compounded quarterly. This means that the quarterly interest rate is:
r = 5% / 4 = 0.0125
Let B be the balance of the loan after 5 years. Then we have:
B = 1000*(1 + r)²⁰- 200*(1 + r)⁴
where the first term is the future value of the initial loan after 5 years, and the second term is the present value of the first payment of $200.
Plugging in the values, we get:
B = 1000*(1 + 0.0125)²⁰ - 200*(1 + 0.0125)⁴
B = 1000*(1.0125)²⁰ - 200*(1.0125)⁴
B = 1346.49
So the balance of the loan after 5 years is $1346.49. We can use this as the principal to calculate the balance at the end of the tenth year, which is the final payment we are looking for.
Let P be the final payment. Then we have:
P = 1346.49*(1 + r)⁴⁰ - 800*(1 + r)²⁰
where the first term is the future value of the balance after 10 years, and the second term is the present value of the second payment of $800.
Plugging in the values, we get:
P = 1346.49*(1 + 0.0125)⁴⁰ - 800*(1 + 0.0125)²⁰
P = 1346.49*(1.0125)⁴⁰ - 800*(1.0125)²⁰
P = 688.32
So the amount of the final payment is $688.32.
hence, the answers to both questions are as:
(a) the value of the investment after 5 years is $14,917.95, after 10 years is $23,673.58, and after 15 years is $37,337.35,
b) the amount of the final payment is $688.32.
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Find the annual percentage rate for an account earning compound interest at a rate of 3.425%
Complete the table to find the APR when compounded semiannually and quarterly.
The APR when compounded semiannually and quarterly would be :
Compounded semi - annually - (1.034543) ^ t - 3.4543%Compounded quarterly - (1.034692) ^ t - 3.4692%How to find the APR ?To find the APR when compounded semi - annually, we first need to find the periodic rate to be :
= Annual rate / 2 semi annual periods
= 3. 425 / 2
= 1.7125%
Then use the Effective Annual Rate (EAR) to find the APR to be:
= ( 1 + periodic rate ) ^ number of periods - 1
= ( 1 + 1. 7125 % ) ² - 1
= 3.4543%
For the APR when compounding quarterly, you can variate the EAR formula to the original version of:
= ( 1 + annual rate / number of periods ) ^ number of periods - 1
= ( 1 + 3. 425 / 4 ) ⁴ - 1
= 3.4692%
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Select the set of numbers that are arranged from greatest to least.
OA) 2.4 x 10; 2.7 x 105; 3.1 x 105
OB) 3.1 x 10; 2.4 x 10;
2.7 x 105
OC) 2.7 x 105;
2.4 x 10¹;
3.1 x 10¹
OD) 3.1 x 10³; 2.7 x 105;
2.4 x 10
The set of numbers arranged from greatest to least is:
OC) 2.7 x 105; 3.1 x 10¹; 2.4 x 10¹0
To see why, let's convert each number to scientific notation, which makes it easier to compare them:
OA) 2.4 x 10 = 24
2.7 x 105 = 270,000
3.1 x 105 = 310,000
OB) 3.1 x 10 = 31
2.4 x 10 = 24
2.7 x 105 = 270,000
OC) 2.7 x 105 = 270,000
2.4 x 10¹ = 24
3.1 x 10¹ = 31
OD) 3.1 x 103 = 3,100
2.7 x 105 = 270,000
2.4 x 10 = 24
As we can see, the set of numbers in option OC is arranged from greatest to least, with 2.7 x 105 being the largest number, followed by 3.1 x 10¹, and then 2.4 x 10¹0 as the smallest number
please help image attached! x=?
Answer:
90°
Step-by-step explanation:
from the figure and the measurements it is a square, the diagonals are perpendicular and form 4 angles of 90°, so 90° is your answer.
A,B and B,C form a right angle at point B. If A = (-3,-1) and B = (4,4), what is the equation of B,C?
Answer:
the equation of line BC is y = (-7/5)x + (48/5).
Step-by-step explanation:
To find the equation of the line that passes through points B and C, we first need to determine the coordinates of point C. Since the angle at B is a right angle, we can use the slope of line AB to find the slope of line BC.
The slope of line AB is:
mAB = (yB - yA) / (xB - xA)
= (4 - (-1)) / (4 - (-3))
= 5/7
Since lines AB and BC are perpendicular, the slope of line BC is the negative reciprocal of the slope of line AB:
mBC = -1 / mAB
= -7/5
Now we can use the point-slope form of the equation of a line to find the equation of line BC. We can use point B as the known point, since we already know its coordinates:
y - yB = mBC(x - xB)
Substituting the values we have:
y - 4 = (-7/5)(x - 4)
Expanding and simplifying:
y - 4 = (-7/5)x + (28/5)
y = (-7/5)x + (48/5)
Which fraction is larger 3/4 or 1/4
Answer:
3/4
Step-by-step explanation:
3/4 is larger because since they have the same denominator (the bottom value), you compare the numerators (the top value). Whichever numerator is bigger gives you the larger fraction.
Answer: 3/4 is larger, this is simply because 3/4 is = 75%
whereas 1/4 = 25%
What is 7% as a decimal ?
Answer: 0.07%
Step-by-step explanation:
Answer:
0.07
Step-by-step explanation:
Easy (7th-grade math)
Answer:
384 cm
Step-by-step explanation:
hope this helps ! good luck on ur assignment! <3
there are 4 types of ice cream, 3 different cones and 3 choices of toppings. how many different ways can an ice cream cone be ordered
Answer:
25
Step-by-step explanation:
Y=4x+2 -6x+2y=8 what is the value x t y
Use the information given below to find tan(a + B)
cos a = 3/5, with a in quadrant IV
tan B = 4/3, with B in quadrant I I I
Give the exact answer, not a decimal approximation.
tan(a + B) = ?
let's bear in mind that on the III Quadrant, sine and cosine are both negative, whilst on the IV Quadrant, sine is negative and cosine is positive, that said
[tex]\cos(\alpha )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{5}}\hspace{5em}\textit{let's find the \underline{opposite side}} \\\\\\ \begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{5}\\ a=\stackrel{adjacent}{3}\\ o=opposite \end{cases} \\\\\\ o=\pm \sqrt{ 5^2 - 3^2} \implies o=\pm \sqrt{ 16 }\implies o=\pm 4\implies \stackrel{IV~Quadrant }{o=-4} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\tan(\beta )=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{3}}\implies \tan(\beta )=\cfrac{\stackrel{opposite}{-4}}{\underset{adjacent}{-3}} \\\\[-0.35em] ~\dotfill\\\\ \tan(\alpha + \beta) = \cfrac{\tan(\alpha)+ \tan(\beta)}{1- \tan(\alpha)\tan(\beta)} \\\\\\ \tan(\alpha + \beta)\implies \cfrac{ ~~\frac{-4}{3}~~ + ~~\frac{-4}{-3} ~~ }{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \cfrac{0}{1-\left( \frac{-4}{3} \right)\left( \frac{-4}{-3} \right)}\implies \text{\LARGE 0}[/tex]
I need help with my homework
To find the length of a line segment in a circle, use the formula [tex]d = 2r[/tex] [tex]sin(t/2)[/tex] , where r is the radius of the circle and t is the angle between the radii. The length of segment DE is [tex]5[/tex] units.
What is the formula for circle segment length?We can use the similar triangles property to find the missing length of segment DE in the given figure. Because triangles ABD and CBE are similar, we can use a proportion to find the length of DE:
[tex]CB/BE = AB/BD[/tex]
With the given values, we get:
[tex]3/6 = 5/(5 + DE)[/tex]
When we simplify and solve for DE, we get:
[tex]3(5 + DE) = 6 * 5 \s15 + 3DE = 30[/tex]
[tex]3DE = 15 \sDE = 5[/tex]
Therefore, segment DE has a length of 5 units.
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Solve for x. Round to the nearest tenth.
x =
(35 points)
The value of x rounded to the nearest tenth is equal to 24.3 units.
How to determine the value of x?In order to determine the value of x, we would apply basic trigonometry. From the information provided about this right angled triangle, we can logically deduce the following parameters:
Adjacent side (Adj) = xHypotenuse (Hyp) = 26.Angle = 21 degrees.Therefore, we would use the cosine trigonometry to determine the value of x as follows:
Cosθ = Adj/Hyp
Cos21 = x/26
x = 26cos21
x = 26(0.9336)
x = 24.3 units.
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Write the polynomial in standard form. Then classify the polynomial by degree and by number of terms.
7x² +9x² - 6x²
Write the polynomial in standard form.
(Simplify your answer.)
Answer:
Step-by-step explanation:
When we combine like terms, we get:
7x² +9x² - 6x² = (7+9-6)x² = 10x²
So the polynomial in standard form is 10x².
The degree of the polynomial is 2 (since the highest power of the variable x is 2) and the number of terms is 1 (since there is only one term). Therefore, we classify this polynomial as a quadratic monomial.
SOMEONE PLEASE HELP ME!!
Measure of the arc or angle indicated is 150.9 degrees.
Describe Arc?In geometry, an arc is a portion of the circumference of a circle or any other curved shape. It is defined by two endpoints and all the points on the curve that lie between them. An arc is usually named by its two endpoints, with a small arc symbol above them to indicate that it is an arc.
The length of an arc can be calculated using the formula:
Arc length = (central angle/360) x 2πr
where r is the radius of the circle, and the central angle is the angle subtended by the arc at the center of the circle, measured in degrees.
The measure of an arc is the degree measure of the central angle subtended by the arc. A semicircle is an arc that subtends a central angle of 180 degrees, and a full circle is an arc that subtends a central angle of 360 degrees.
Since DE and PE are chords of the circle, and they intersect at point P, we can use the intersecting chords theorem to find the length of DP. Let x be the length of DP. Then:
DP * PE = DE * PC
x * (x + PE) = ([tex]\frac{CE}{2}[/tex]) * ([tex]\frac{CE}{2}[/tex])
x² + x(PE) - [tex]\frac{CE}{2}^{\frac{2}{4} }[/tex] = 0
Since angle DPE is 60 degrees, we can use the law of cosines to find PE. Let y be the length of PE. Then:
y² = DE² + DP² - 2 * DE * DP * cos(60)
y² = ([tex]\frac{CE}{2}[/tex])² + x^2 - ([tex]\frac{CE}{2}[/tex]) * x
Substitute this expression for y^2 into the equation for x and simplify:
[tex]x^{2} +x((\frac{CE}{2})^{2} + x^{2} -\frac{CE}{2} *x)^{0.5} -(\frac{CE}{2} ^{\frac{2}{4} } )=0[/tex]
Solve for x:
x = [tex]\frac{CE^{2} -4*(CE^{2} -3*\frac{CE}{2} ^{2} )^{0.5} }{4}[/tex]
x = [tex]\frac{3}{4} *\frac{CE^{2} }{CE^{2} -12}[/tex]
Now we can find the measure of the CD arc by using the formula for the central angle:
CD arc = [tex]2*arctan(\frac{DP}{CE})[/tex]
CD arc = [tex]2*arctan(\frac{x}{\frac{CE}{2} } )[/tex]
CD arc = [tex]2* arctan(CE^{2} -4*(CE^{2} -3*\frac{(\frac{CE}{2} ^{2})^{0.5}}{CE^{2}-12 } ))[/tex]
Simplifying this expression, we get:
[tex]CD arc=2*arctan(2*3^{\frac{1}{2} } -1)[/tex]
CD arc ≈ 150.9 degrees.
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Measure of the arc or angle indicated in the given figure is 150.9 degrees.
Describe Arc?In geometry, an arc is a portion of the circumference of a circle or other curved shape. It is defined by his two endpoints and all midpoints of the curve. Arcs are usually named after their two endpoints, with a small arc symbol above them to indicate that they are arcs.
Arc Length = (Center Angle/360) x 2πr
where r is the radius of the circle and the central angle is the angle the arc makes at the center of the circle, measured in degrees.
The arc measurement is the angle of the central angle defined by the arc. A half circle is an arc that spans a central angle of 180 degrees, and a full circle is an arc that spans a central angle of 360 degrees.
Since DE and PE are chords of the circle and intersect at P, we can use the chord rule to find the length of DP. Let x be the length of DP. Then:
DP × PE = DE × PC
x × (x + PE) = (CE/2) × (CE/2)
x² + x(PE) - [tex]\frac{CE}{2} ^{\frac{2}{4} }[/tex] = 0
Since angle DPE is 60 degrees, we can use the law of cosines to find PE. Let y be the length of PE. Then:
y² = DE² + DP² - 2 × DE × DP × cos(60)
y² = ([tex]\frac{CE}{2}[/tex])² + x² - ([tex]\frac{CE}{2}[/tex]) × x
Substitute this expression for y² into the equation for x and simplify:
[tex]x^{2} +x((\frac{CE}{2} ^{2}) + x^{2} - \frac{CE}{2}*x)^{0.5} -[/tex] [tex]\frac{CE}{2} ^{\frac{2}{4} }[/tex] = 0
Solve for x:
x = [tex]\frac{CE^{2} - 4*(CE^{2}-3*\frac{CE}{2} ^{2})^{0.5} }{4}[/tex]
x = (3/4) × (CE²/CE²-12)
Now we can find the measure of the CD arc by using the formula for the central angle:
CD arc = 2arc tan(DP/CE)
CD arc = 2arc tan [x/(CE/2)]
CD arc = 2arc tan (CE² - 4 × (CE² - 3 × [tex]\frac{(\frac{CE}{2} ^{2}) ^{0.5} }{CE^{2}-12 }[/tex] )
Simplifying this expression, we get:
CD arc ≈ 150.9 degrees.
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need statements 1 and 2 answered by Friday March 23, 2023 at 10am
I will give you some intuitive remarks for some inspiration on the proofs.
For the first one, notice that if m divides n then n = pm where p is a integer.
Since n and m are both natural numbers p then must be a natural number as well.
Now we know that basically we want to prove that if a is congruent to b mod n then a is congruent to b mod "a factor of n" (this is cause n = pm).
Tell me if you need more clarification.
For the second proof, I would just draw a Venn diagram and prove that the two intersections cover identical regions.
Use the quadratic formula to solve the equation 2 - 5x-9=0
The answer is x = 5±√61/2, I really hope this helps (:
View the photo and solve the probability
Therefore, the probability that at least one of the next six births is a girl is 1 - 0.033 = 0.967 (rounded to three decimal places).
What is Probability?Probability is a measure of the likelihood that an event will occur. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
To calculate the probability of an event, you divide the number of ways that event can occur by the total number of possible outcomes. For example, if you flip a fair coin, there are two possible outcomes - heads or tails - and each has an equal probability of 0.5 (or 50%) of occurring.
Given by the question.
To find the probability that at least one of the next six births is a girl, we can find the probability that all six of them are boys and subtract it from 1.
The probability that one birth is a girl is 1 - 0.513 = 0.487.
The probability that all six births are boys is. [tex]0.513^{6}[/tex] = 0.033.
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A school gym is 97 feet long and 61 feet wide. What is its perimeter?
Answer:
316
Step-by-step explanation:
Which of the following is the product of the rational expressions show below?
Answer:
−(3x2+−xx−5)
Step-by-step explanation:
the cost for3.8 pounds of shrimp is 18.05 . find the unit price in dollars per pound. if necessary round it to the nearest cent
The unit price in dollars per pound is $4.75 (rounded to the nearest cent).
What is profit and loss?
Mathematicians use the profit and loss formula to calculate market prices for goods and to assess how lucrative a company is. There is a selling price and a cost price for every commodity. We can determine the profit made or loss suffered for a specific commodity based on the values of these prices. Cost price, fixed, variable, and semi-variable costs, selling price, marked price, list price, margin, etc. are some of the key words that are discussed in this article.
To find the unit price in dollars per pound, we need to divide the total cost by the total weight:
Unit price = Total cost / Total weight
In this case, the total weight is 3.8 pounds and the total cost is $18.05.
Unit price = $18.05 / 3.8 pounds
Unit price = $4.75 per pound (rounded to the nearest cent)
Therefore, the unit price in dollars per pound is $4.75 (rounded to the nearest cent).
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