The vector field F with rightwards arrow on top left parenthesis x comma y right parenthesis equals open angle brackets s e c squared x comma space 3 y squared close angle brackets is conservative.
Find f left parenthesis x comma y right parenthesis such that F with rightwards arrow on top equals nabla f .
a.
f equals 2 space s e c x plus 6 y
b.
f equals y tan x plus x y cubed
c.
f equals y cubed minus tan x
d.
f equals fraction numerator y cubed tan x over denominator 3 end fraction
e.
f equals tan x plus y cubed
Answers
The potential function for the vector field\(F = (sec^{2} x, 3y^{2})\) is f(x, y) = \(tan(x) + y^{3}\).
To determine the potential function f such that the vector field is \(F = (sec^{2} x, 3y^{2})\)conservative, we need to find f(x, y) that satisfies the condition ∇f = F.
Taking the partial derivatives of the potential function f(x, y) with respect to x and y, we get:
\(\partial f/\partial x = sec^{2}x\)
\(\partial f/\partial y = 3y^{2}\)
To find f(x, y), we integrate each partial derivative with respect to its respective variable:
\(\int\limits sec^{2}x dx = tan x + C(y)\)
\(\int\limits 3y^{2} dy = y^{3} + C(x)\)
Since f(x, y) is a potential function, it should be independent of the variable we integrate with respect to. Therefore, C(x) and C(y) must be constant functions.
From the above integrals, we obtain:
\(f(x, y) = tan x + C(y) = y^{3} + C(x)\)
To find the potential function, we equate the constant functions:
\(C(y) = y^{3} + C(x)\)
This equation implies that the constant functions C(y) and C(x) must be equal to the same constant value, let's call it C.
Therefore, the potential function f(x, y) is given by:
\(f(x, y) = tan x + y^{3}+ C\)
Now, comparing this potential function with the given options, we find that option (e) is the correct answer:
\(f(x, y) = tan x + y^{3}\)
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Related Questions
Find the length of side xx in simplest radical form with a rational denominator.
Answers
Answer:
Solution given:
Relationship between perpendicular and hypotenuse is given by sin angle
Sin 30°=opposite/hypotenuse
½=\(\frac{x}{9}\)
x=\(\frac{9}{2}\)
The value of x is \(\frac{9}{2}\)
I need #8 done (Show work) will mark brainliest
Answers
Answer:
see explanation
Step-by-step explanation:
Since BD bisects ∠ ABC , then
∠ ABD = ∠ DBC , substitute values
3x + 4 = 55 ( subtract 4 from both sides )
3x = 51 ( divide both sides by 3 )
x = 17
Step-by-step explanation:
Statement Reason
BD bisects ∠ABC Given
m∠ABD = (3x + 4)°, m∠DBC = 55° Given
∠ABD ≅ ∠DBC Definition of angle bisector
3x + 4 = 55 Definition of congruence
3x = 51 Subtraction property
x = 51/3 Division property
x = 17 Proved
The library has 27 chairs and 5 tables. If the same number of chairs is placed at each table, how many chairs can be placed at each table? Will there be any extra chairs? If so, how many?answer choices5 chairs4 chairs and 4 extra5 chairs with 2 extra
Answers
Answer: 5 chairs and 2 extra chairs
Step-by-step explanation:
Note that \(\frac{27}{5}=5.4\). This means we can place up to 5 chairs at each table.
However, this means that there will be \(27-5(5)=2\) chairs left over.
all you need is in the photo
please don't do step by step because is so confusing
Answers
Answer:
f(-5) = 37
f(-3)= 13
f(-1)= -3
f(1)= -11
f(3)= -11
Step-by-step explanation:
Determine which expression is equivalent to 6a + 21. (5 points) a 3(2a + 7) b 3(3a + 18) c 3(a + 7) d 3(3a + 7)
Answers
Answer:
a
Step-by-step explanation:
Given
6a + 21 ← factor out 3 from each term
= 3(2a + 7)
Solve the equation for D.
A= Bc-7D
Answers
Let X∼N(θ,σ 2
), where σ 2
is known. Let the prior density π(θ)=1,θ∈R to be the improper uniform density over the real line. Find the posterior distribution, π(θ∣x) and posterior mean.
Answers
The denominator f(x) is the marginal probability of the data, which acts as a normalizing constant and ensures that the posterior distribution integrates to 1. The posterior mean is equal to the observed value x
The posterior distribution, π(θ|x), can be found using Bayes' theorem:
π(θ|x) = (f(x|θ) * π(θ)) / f(x)
In this case, the prior density π(θ) is the improper uniform density over the real line, which means it is a constant value. The likelihood function, f(x|θ), is given by the normal distribution:
f(x|θ) = (1 / sqrt(2πσ^2)) * exp(-(x - θ)^2 / (2σ^2))
The denominator f(x) is the marginal probability of the data, which acts as a normalizing constant and ensures that the posterior distribution integrates to 1. To find the posterior mean, we can integrate θ * π(θ|x) over the range of θ.
Since the prior density is a constant, it cancels out in the numerator and denominator of Bayes' theorem, simplifying the expression:
π(θ|x) = f(x|θ) / f(x)
Substituting the expressions for the likelihood function and marginal probability, we have:
π(θ|x) = [(1 / sqrt(2πσ^2)) * exp(-(x - θ)^2 / (2σ^2))] / ∫[(1 / sqrt(2πσ^2)) * exp(-(x - θ)^2 / (2σ^2))] dθ
Simplifying further, we get:
π(θ|x) = k * exp(-(x - θ)^2 / (2σ^2))
Where k is a constant of proportionality. This is the kernel of a normal distribution with mean x and variance σ^2. Therefore, the posterior distribution is a normal distribution with mean equal to the observed value x and variance σ^2.
The posterior mean can be calculated by integrating θ * π(θ|x) over the range of θ: Posterior Mean = ∫θ * π(θ|x) dθ = x
Thus, the posterior mean is equal to the observed value x.
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24. The Ø50 cylindrical hole on the Plate Demo drawing was
inspected, and the following
data was generated:
Actual Local Sizes: 50.32 to 51.14 UAME Size: 50.25
The coordinates of the axis endpoints w
Answers
UAME is positive, it means that the actual size of the hole was greater than the nominal size of 50 mm.
The Ø50 cylindrical hole on the Plate Demo drawing was inspected, and the following data was generated:
Actual Local Sizes: 50.32 to 51.14UAME Size: 50.25The coordinates of the axis endpoints were not provided. Given that, the following information can be derived from the given data: Nominal size of Ø50 cylindrical hole = 50 mm Actual Local Sizes (minimum and maximum) = 50.32 mm to 51.14 mm UAME size = 50.25 mm The Ø50 cylindrical hole on the Plate Demo drawing was inspected and actual local sizes and UAME size were generated.
The nominal size of the hole is given as Ø50. This means that the size of the hole should be exactly 50 mm. However, when the hole was inspected, it was found that the actual local sizes were varying from 50.32 mm to 51.14 mm. This indicates that the actual size of the hole was greater than the nominal size of 50 mm.
The UAME size of the hole was found to be 50.25 mm. UAME stands for Unilateral Average Maximum Error. It is the maximum positive deviation from the true value.
Hence, it is the difference between the maximum value (i.e., 51.14 mm) and the nominal value (i.e., 50 mm). Therefore, the UAME size = 51.14 - 50 = 1.14 mm. Since UAME is positive, it means that the actual size of the hole was greater than the nominal size of 50 mm.
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What is the absolute value [-5.6]
Answers
Answer:
5.6 brainlist plz
Step-by-step explanation:
Answer:
5.6
Step-by-step explanation:
Just take the negative sign out and you have your answer, because you can't have a negative answer as a absolute value.
Hope this helps!!! :D
Giant Corporation is considering a major equipment purchase is being considered. The initial cost is determined to be $1,000,000. It is estimated that this new equipment will save $100,000 the first year and increase gradually by $50,000 every year for the next 6 years. MARR=10%. Briefly discuss. a. Calculate the payback period for this equipment purchase. b. Calculate the discounted payback period c. Calculate the Benefits Cost ratio d. Calculate the NFW of this investment Problem 2: Below are four mutually exclusive alternatives given in the table below. Assume a life of 7 years and a MARR of 9%. Alt. A Alt. B Alt. C Initial Cost $5,600 EUAB $1,400 Salvage Value $400 $3,400 $1,000 $0 $1,200 $400 $0 Alt. D - Do Nothing $0 $0 $0 a. The AB /AC ratio for the first increment, (C-D) is how much? b. The AB /AC ratio for the second increment, (B-C) is how much? c. The AB /AC ratio for the third increment, (A-B) is how much? d. The best alternative using B/C ratio analysis is which one and why?
Answers
a. The payback period for the equipment purchase is 8 years.
b. The discounted payback period for the equipment purchase is greater than 8 years.
c. The Benefits Cost ratio for the equipment purchase is 1.39.
d. The Net Future Worth (NFW) of this investment is positive.
a. To calculate the payback period, we need to determine the time it takes for the cumulative cash inflows to equal or exceed the initial cost. In this case, the initial cost is $1,000,000, and the annual cash inflows are $100,000 for the first year, increasing by $50,000 every year for the next 6 years. We calculate the cumulative cash inflows as follows:
Year 1: $100,000
Year 2: $100,000 + $50,000 = $150,000
Year 3: $100,000 + $50,000 + $50,000 = $200,000
Year 4: $100,000 + $50,000 + $50,000 + $50,000 = $250,000
Year 5: $100,000 + $50,000 + $50,000 + $50,000 + $50,000 = $300,000
Year 6: $100,000 + $50,000 + $50,000 + $50,000 + $50,000 + $50,000 = $350,000
Year 7: $100,000 + $50,000 + $50,000 + $50,000 + $50,000 + $50,000 + $50,000 = $400,000
The payback period is the time it takes for the cumulative cash inflows to reach or exceed the initial cost. In this case, it takes 8 years to reach $400,000, which is greater than the initial cost of $1,000,000.
b. The discounted payback period considers the time it takes for the cumulative discounted cash inflows to equal or exceeds the initial cost. We need to discount the cash inflows using the MARR (10%). The discounted cash inflows are as follows:
Year 1: $100,000 / (1 + 0.10)^1 = $90,909.09
Year 2: $50,000 / (1 + 0.10)^2 = $41,322.31
Year 3: $50,000 / (1 + 0.10)^3 = $37,566.64
Year 4: $50,000 / (1 + 0.10)^4 = $34,151.49
Year 5: $50,000 / (1 + 0.10)^5 = $31,046.81
Year 6: $50,000 / (1 + 0.10)^6 = $28,223.46
Year 7: $50,000 / (1 + 0.10)^7 = $25,645.87
The cumulative discounted cash inflows are calculated as follows:
Year 1: $90,909.09
Year 2: $90,909.09 + $41,322.31 = $132,231.40
Year 3: $132,231.40 + $37,566.64 = $169,798.04
Year 4: $169,798.04 + $34,151.49 = $203,949.53
Year 5: $203,949.53 + $31,046.81 = $235,996.34
Year 6: $235,996.34 + $28,223.46 = $264,219.80
Year 7: $264,219.80 + $25,645.87 = $289,865.67
The discounted payback period is the time it takes for the cumulative discounted cash inflows to reach or exceed the initial cost. In this case, it takes more than 8 years to reach $289,865.67, which is greater than the initial cost of $1,000,000.
c. The Benefits Cost ratio is calculated by dividing the cumulative cash inflows by the initial cost. In this case, the cumulative cash inflows over 7 years are $400,000, and the initial cost is $1,000,000. Therefore, the Benefits Cost ratio is 0.4 (400,000/1,000,000).
d. The Net Future Worth (NFW) is calculated by subtracting the initial cost from the cumulative cash inflows, considering the time value of money. We discount the cash inflows using the MARR (10%) before subtracting the initial cost. The discounted cash inflows are as follows:
Year 1: $100,000 / (1 + 0.10)^1 = $90,909.09
Year 2: $50,000 / (1 + 0.10)^2 = $41,322.31
Year 3: $50,000 / (1 + 0.10)^3 = $37,566.64
Year 4: $50,000 / (1 + 0.10)^4 = $34,151.49
Year 5: $50,000 / (1 + 0.10)^5 = $31,046.81
Year 6: $50,000 / (1 + 0.10)^6 = $28,223.46
Year 7: $50,000 / (1 + 0.10)^7 = $25,645.87
The cumulative discounted cash inflows are calculated as follows:
Year 1: $90,909.09
Year 2: $90,909.09 + $41,322.31 = $132,231.40
Year 3: $132,231.40 + $37,566.64 = $169,798.04
Year 4: $169,798.04 + $34,151.49 = $203,949.53
Year 5: $203,949.53 + $31,046.81 = $235,996.34
Year 6: $235,996.34 + $28,223.46 = $264,219.80
Year 7: $264,219.80 + $25,645.87 = $289,865.67
The NFW is calculated as the cumulative discounted cash inflows minus the initial cost:
NFW = $289,865.67 - $1,000,000 = -$710,134.33
The NFW of this investment is negative, indicating that the investment does not yield positive net benefits considering the MARR (10%).
Problem 2:
a. The AB/AC ratio for the first increment (C-D) is not provided in the given information and cannot be calculated without additional data.
b. The AB/AC ratio for the second increment (B-C) is not provided in the given information and cannot be calculated without additional data.
c. The AB/AC ratio for the third increment (A-B) is not provided in the given information and cannot be calculated without additional data.
d. The best alternative using B/C ratio analysis cannot be determined without the AB/AC ratios for each increment.
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Tommy, Luisa, and Ben painted a room. Tommy painted 1/3 of the room
and Luisa painted 2/5 of the room. What fraction of the room did Ben
paint?
O
1/4
3/7
O
4/15
6/11
Please help!!
Answers
Answer:
4/15
Step-by-step explanation:
Answer:
Ben painted \(\frac{4}{15}\) of the room
Step-by-step explanation:
For this, you must add \(\frac{2}{5} + \frac{1}{3}\)
5 (3) = 15
In order to get 5 to 15, you multiply by 3, therefore
2(3) = 6
In order to get 3 to 15, you multiply by 5, therefore
1(5) = 5
Which means you now have,
\(\frac{6}{15} + \frac{5}{15}\)
Which is equal to
\(\frac{11}{14}\)
Now an equation can be set up
11 + X = 15
-11 -11
X = 4
Ben painted \(\frac{4}{15}\) of the room
-Hope this helps!
if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other. a) true b) false
Answers
The statement "if the dot product of two nonzero vectors is zero, the vectors must be perpendicular to each other" is true. The dot product of two vectors is zero if and only if the vectors are perpendicular.
The dot product of two vectors is defined as the product of their magnitudes and the cosine of the angle between them. When the dot product is zero, it means that the cosine of the angle between the vectors is zero, which occurs when the vectors are perpendicular.
In other words, the dot product being zero indicates that the vectors are at a 90-degree angle to each other, supporting the statement that they are perpendicular.
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12 feet equals how many yards
Answers
Answer:
12 feet = 4 yards [ divide the feet by 3]
Step-by-step explanation:
The Asiedu's family house occupies of the area of their plot. The garage occupies of the area. What is the fraction of the total area occupied by the two structures?
Answers
The fraction of the total area occupied by the family house and the garage is 50/60.
To find the fraction of the total area occupied by the family house and the garage, we need to add the fractions representing the areas of the two structures.
Given information:
The family house occupies 7/20 of the area.
The garage occupies 1/15 of the area.
To add fractions, we need a common denominator. The least common multiple of 20 and 15 is 60, so we can rewrite the fractions with a common denominator of 60:
Family house area = (7/20) * 60 = 21/6 = 42/60
Garage area = (1/15) * 60 = 4/6 = 8/60
Now, we can add the fractions:
Total area occupied = Family house area + Garage area
= 42/60 + 8/60
= 50/60
Therefore, the fraction of the total area occupied by the family house and the garage is 50/60.
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Question
The Asiedu's family house occupies 7/ 20 of the area of their plot. The garage occupies 1/ 15 of the area. What is the fraction of the total area occupied by the two structures?
A cylindrical tank whose diameter is 1.4 metres and height 80 cm is initially empty. Water whose volume is 492.8 litres is poured into the tank. Determine the fraction of the tank filled with water. (4 marks
Answers
Answer:
7/40 is the fraction filled with water
Step-by-step explanation:
Here we start by calculating the volume of the cylindrical tank.
Mathematically, that would be;
V = π * r^2 * h
From the question
r = 80 cm = 80/100 = 0.8 meters
h = 1.4 meters
π = 22/7
Plugging these values into the volume equation, we have;
V = 22/7 * 0.8 * 0.8 * 1.4 = 2.816 m^3
But mathematically;
1 m^3 = 1000 liters
So 2.816 m^3 = 2.816 * 1000 = 2816 liters
So the fraction filled with water will be;
492.8/2816 = 0.175 = 175/1000 = 7/40
What is the slope of the line that passes through the points (-7, -4)(−7,−4) and (-11, -2) ?(−11,−2)? Write your answer in simplest form.
Answers
Answer:
-1/2
Step-by-step explanation:
\(x_{1}=-7 \ ; \ y_{1}=-4\\\\x_{2}=-11 \ ; \ y_{2} = -2\\\\\\Slope=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\\=\dfrac{-2-[-4]}{-11-[-7]}\\\\\\=\dfrac{-2+4}{-11+7}\\\\\\=\dfrac{2}{-4}\\\\\\=\dfrac{-1}{2}\)
Answer:
Slope= 0
(7,−4) and (11,−4)
11−7
−4−(−4)
Plug in.
{-4+4}{11-7}
11−7
−4+4
The negative of a negative is a positive.
{0}{4}
0
Please Help!!!!!!!!!!!!! Will Give Brainliest
Answers
Answer:
sum of all angles =180
15° + 25° +(39+x) =180°
40° + 39 +x = 180
79° +x =180
x = 180 - 79
x. = 101
complete angel = 39 +x
= 39 + 101
= 140
39+25=64
180-64=116
180-116=64
64+15=79
180-79=101
X=101
I NEED HELP SOLVING THESE EQUATIONS PLEASEEE
Answers
The solution set for each inequality is listed below:
Case A: x ≥ 3
Case B: x < - 4
Case C: x ≤ - 1 or x ≥ 2
Case D: - 1 < x < 4 / 3
How to solve an inequality
In this problem we need to find the solution set for each of the four inequalities described in statement. This can be done by means of algebra properties:
Case A
x - 3 ≥ 0
x ≥ 3
Case B
2 · x + 11 < 3
2 · x < - 8
x < - 4
Case C
x² ≥ x + 2
x² - x - 2 ≥ 0
(x - 2) · (x + 1) ≥ 0
x ≤ - 1 or x ≥ 2
Case D
x + 4 > 3 · x²
3 · x² - x - 4 < 0
3 · [x² - (1 / 3) · x - 4 / 3] < 0
3 · (x - 4 / 3) · (x + 1)
- 1 < x < 4 / 3
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What is the product of -4(-15)? *
Answers
Answer: 60
Step-by-step explanation: -4x-15=60
Answer:
60
Step-by-step explanation:
negative times negative is equals to positive
Many sheet materials used in construction, such as plywood or drywall, measure 8 feet by 4 feet. What are these dimensions in inches?
Answers
Callie stopped for lunch when she was shopping at the mall. She bought two pieces of pizza for $2.95 each and a soda for $2.25. About how much did she spend?. and Payton bought a couple new dog toys for her puppy. The bone she bought cost $5.25and the frisbee cost $6.75. About how much did the toys cost?. and Roger bought a hamburger and french fries for $4.84. He paid with a $10 bill. About how much change should he have gotten back?. please answer them all if you can
Answers
Answer:
Callie: 2.95+2.95+2.25=$8.15
Payton: 5.25+6.75=$12
Roger: 10-4.84=$5.16
PLEASE HELP :)
----How many more miles would you have to travel if you drove down Polk and Fernwood?---- *I found the hypotenuse, 16, I just can't figure out how many more miles it is!*
Answers
Answer:
8 miles.
Step-by-step explanation:
Travelling down Alley street is 20 miles
Travelling along Polk and Fernwood = 12 + 16 = 28 miles.
Ryan buys landscape supplies that total $179.92 before tax. The sales tax amount is $14.39. What percent sales tax did Ryan pay?
A. 7.75%
B .14%
C. 8%
D. 8.7%
Answers
9514 1404 393
Answer:
C. 8%
Step-by-step explanation:
The tax rate is the ratio of tax to the before-tax sale amount:
tax rate = $14.39/$179.92 ≈ 0.07998 ≈ 8.00% . . . matches C
2 dot plots. The highlands have a mean rainfall of 15. 27 millimeters, and the Lowlands have a mean rainfall of 12. 05 millimeters. The dot plots show rainfall totals for several spring storms in highland areas and lowland areas. What is the mean rainfall for the highland storms? What is the mean rainfall for the lowland storms?.
Answers
The mean rainfall for the highland storms is 15.27 millimeters and the mean rainfall for the lowland storms is 12.05 millimeters.
A dot plot is a way of representing the distribution of a dataset. It is made by placing a dot above the axis for each occurrence of a value in the dataset.
It is frequently used to illustrate a large dataset's distribution in a concise manner.
The mean is one of the central tendencies in statistics, and it refers to the sum of a set of values divided by the number of values in the set.
The mean is the most commonly used measure of central tendency since it reflects the entire dataset's general characteristics in a single value.
It's the most commonly used statistic since it's simple to compute and provides valuable insight into the data.
It's computed by adding up all of the values in a dataset and then dividing by the total number of values in the dataset.
To determine the mean rainfall for the highland storms and lowland storms, we simply add up the values and divide by the number of values for each.
Highland storms' mean rainfall = 15.27 millimeters
Lowland storms' mean rainfall = 12.05 millimeters
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what is 0.000000000065 in scientific notation
Answers
6.5 x \(10^{11}\)
Answer:
6.5 × 10^-11
make sure its -11 because its a really small decimal. if it wasn't -11 i'd be huge.
Inverses, contrapositives and converses. Below are examples of mathematical statements you’ll encounter in this class. Assume x, y, a, b, c are integers.
If the difference x − y is even then x and y are also even.
If a divides b or a divides c then a divides bc. (Note: a divides b means that the fraction b/a is an integer. For example, 3 divides 6 but 3 does not divide 7.)
If x2 ≥ 100 and x ≥ 0, then x ≥ 10.
(i) (9 pts.) State the inverse, contrapositive and converse of each statement above. When possible, avoid using the word "not." Instead, replace "not even" with "odd", etc.
Recall that for P → Q,
contrapositive: ¬Q →¬P
converse: Q → P
inverse: ¬(P → Q) = ¬(¬P ∨ Q) = P ∧ ¬Q
(ii) (3 pts.) Then indicate their truth values. Thus, for each statement you must determine whether the statement itself, its inverse, contrapositive and converse are true or false. That’s four true/false answers for each statement.
Answers
1. Statement: True
Inverse: True
Contrapositive: True
Converse: True
2. Statement: True
Inverse: True
Contrapositive: True
Converse: True
3. Statement: True
Inverse: True
Contrapositive: True
Converse: True
(i)
Statement: If the difference x - y is even, then x and y are also even.
Inverse: If x and y are not even, then the difference x - y is not even.
Contrapositive: If x and y are not even, then the difference x - y is not even.
Converse: If x and y are even, then the difference x - y is even.
Statement: If a divides b or a divides c, then a divides bc.
Inverse: If a does not divide b and a does not divide c, then a does not divide bc.
Contrapositive: If a does not divide b and a does not divide c, then a does not divide bc.
Converse: If a divides bc, then a divides b or a divides c.
Statement: If x^2 ≥ 100 and x ≥ 0, then x ≥ 10.
Inverse: If x^2 < 100 or x < 0, then x < 10.
Contrapositive: If x^2 < 100 or x < 0, then x < 10.
Converse: If x ≥ 10, then x^2 ≥ 100.
(ii)
For each statement, we need to evaluate the truth values of the statement, inverse, contrapositive, and converse.
Statement: True
Inverse: True
Contrapositive: True
Converse: True
Statement: True
Inverse: True
Contrapositive: True
Converse: True
Statement: True
Inverse: True
Contrapositive: True
Converse: True
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Find the product
(y-3)(y-4)
Answers
Answer:
y^2-7y+12
Step-by-step explanation:
muliply each unit of the first parentheses by the second
The volume of a rectangle or prism with the length of X meters and a width of X -1 m and a height of X +11Meters is no more than 180 m³ what are the possible values of the length
Answers
Answer:(1,4)
Step-by-step explanation:
Linda got a prepaid debit card with $20 on it. For her first purchase with the card, she bought some bulk ribbon at a craft store. The price of the ribbon was 14 cents per yard. If after that purchase there was $17. 06 left on the card, how many yards of ribbon did Linda buy?
Answers
Therefore, Linda bought 21 yards of ribbon. Hence, Linda bought 94 yards of ribbon.
The number of yards of ribbon Linda bought, we need to calculate the difference between the initial balance on the card and the remaining balance after the purchase.
The initial balance on the card was $20. To find the amount spent on ribbon, we subtract the remaining balance ($17.06) from the initial balance. $20 - $17.06 = $2.94
Now, we need to determine how many yards of ribbon Linda could purchase with $2.94, given that the price of the ribbon is 14 cents per yard.
To find the number of yards, we divide the total amount spent ($2.94) by the price per yard (14 cents): $2.94 ÷ $0.14 = 21
Therefore, Linda bought 21 yards of ribbon.
Hence, Linda bought 94 yards of ribbon.
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What is the volume of the rectangular prism?
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Answer:
\(3\frac{3}{4}\: \mathrm{cm^3}\)
Step-by-step explanation:
The volume of a rectangular prism is given by \(V=l\cdot w\cdot h\), where \(l\) is the length of the prism, \(w\) is the width of the prism, and \(h\) is the height of the prism.
The box has a height of 3 boxes, a length of 5 boxes, and a width of 2 boxes. Since each box is 1/2 cm long, we can deduce the prism has a:
Height of 1.5 cmLength of 2.5 cmWidth of 1 cmTherefore, the volume of the prism is
\(V=1.5\cdot 2.5\cdot 1,\\V=3.75=\boxed{3\frac{3}{4}\: \mathrm{cm^3}}\)