Answer:
Step-by-step explanation:
To calculate the final account balance for a savings account with an initial deposit of $5,460.75, compounded semiannually with an interest rate of 3.92%, for 51 months, we need to use the formula:
A = P * (1 + r/n)^(nt)
where A is the final account balance, P is the initial deposit, r is the interest rate (as a decimal), n is the number of times the interest is compounded in a year, t is the number of years, and nt is the number of compounding periods.
In this case, n = 2 (since the interest is compounded semiannually), r = 3.92%/100 = 0.0392, t = 51 months / 12 months/year = 4.25 years, and nt = 2 * 4.25 = 8.5.
Substituting the values into the formula, we get:
A = $5,460.75 * (1 + 0.0392/2) ^ (8.5)
A = $5,460.75 * 1.0196^8.5
A = $5,460.75 * 1.2408
A = $6790.32
So, the final account balance if the initial deposit is invested with interest compounded semiannually is $6790.32.
B) Comparing the final account balance of the simple interest account and the compound interest account, we can see that the compound interest account yields a higher balance ($6790.32) than the simple interest account ($6370.51). This is because compounding interest allows for the interest earned in one period to be reinvested, so the interest earns interest in future periods, which increases the overall amount of interest earned over time. In contrast, simple interest is calculated only on the initial deposit, so the amount of interest earned remains constant over time.
B={z∣∣11≤z≤23andzis an even number }
I- uhm, it makes one but, I think that's just an equation...
A right triangle has an area of 36 square units if you draw scaled copies of this triangle using the scale factor in the table, what will the areas of these scaled copies be? Explain or show your reasoning
The areas of the scale factors 2, 3, 5, 1/2 and 2/3 are 144, 324, 900, 9 and 16 square units respectively.
The area of the right triangle = 36 square units
Scale factor of each scaled copies of the right triangles are given
Scale factor = 2
Then the area will be = Area at scale factor 1 × square of scale factor
Substitute the values in the equation
Area = 36 × 2^2
= 36 × 4
= 144 square units
Scale factor = 3
Area = 36 × 3^2
= 36 × 9
= 324 square units
Scale factor = 5
Area = 36 × 5^2
= 36 × 25
= 900 square units
Scale factor = 1/2
Area = 36 × (1/2)^2
= 36 × 1/4
= 9 square units
Scale factor = 2/3
Area = 36 × (2/3)^2
= 36 × 4/9
= 16 square units
Therefore, area of the each scale factor has been found
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The given question is incomplete, the complete question is :
A right triangle has an area of 36 square units if you draw scaled copies of this triangle using the scale factor in the table, what will the areas of these scaled copies be?
Rate my profile pic 1-10
Answer:
10
Step-by-step explanation:
i love how you look like a dinosaur
Use the Distributive Property to figure out (z-5)(z+3)
whats the answer
Using the distributive property, we can write (z-5)(z+3) is equal to [tex]z^2[/tex] - 2z - 15.
Let us expand the expression (z-5)(z+3).
We will distribute the terms in the first set of parentheses (z-5) to the terms in the second set of parentheses (z+3) as follows -
(z-5)(z+3) = z(z+3) - 5(z+3)
Now, we will simplify the expression by distributing z to both terms inside the first set of parentheses, and then distributing -5 to both terms inside the second set of parentheses as follows -
z(z+3) - 5(z+3) = [tex]z^2[/tex] + 3z - 5z - 15
Combining the like terms, we get,
(z-5) (z+3) = [tex]z^2[/tex] - 2z - 15
Therefore, (z-5)(z+3) is equal to [tex]z^2[/tex] - 2z - 15.
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Find the answer pls. this is imo lvl 2 questuin
Answer:
50) i. C 800cm^2
50)ii. B 120cm
Step-by-step explanation:
Use the picture in its given 2-d to mark the unknown measures. Such as, the gray rectangle on top has a bottom that is also 20 and the left side is 15.
The small horizontal jutting out on the left mid-way down is 5cm same as the 5cm just below.
When you mentally "unfold" the shape to its full rectangular shape and size, all the lengths are marked.
Use:
Area=length×width
and,
Perimeter
=L + w + L + w
There are lots of perimeter formulas, for perimeter, you just add up all the sides all the way around the shape.
see image.
In the linear equation y=2x+3, if x increases by 4 points, how much will y increase?
In the linear equation y=2x+3, if x increases by 4 points, the y will increase by 8 points.
An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation's graph will always be a straight line. A linear equation is expressed using the linear equation formula. There are numerous ways to accomplish this. A linear equation, for instance, can be written in standard form, slope-intercept form, or point-slope form.
According to that,
y=2x+3 is the linear equation.
x will now rise by 4 points.
According to the data given, the calculation is as follows:
x = x + 4
So = 2(x)
= 2(x + 4) + 3
= (2x + 3) + 8
= y + 8
Eight points should be added to the y.
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Need help with this question urgent please
Answer:
Step-by-step explanation:
First, add 7 to all parts of the inequality to isolate x.
-10+7 < 3x-7+7 ≤ 5+7
-3 < 3x ≤ 12
Then divide all sides by 3.
-1 < x ≤ 4
So x is greater than -1 but less than or equal to 4.
This can be written as (-1, 4] in interval notation.
Determine two unique values of 0 in the interval [0, 2pi)such that sin 0 = 1/2. ( picture included)
The two unique values of sin theta in radians are
π/67π/6When is Sin of angle = 1/2The sine function has a range of [-1, 1], so there are multiple angles that correspond to a sine of 1/2.
The most commonly used values are π/6 (30 degrees) and 7π/6 (150 degrees), which are in the first quadrant and second quadrant and have a positive sine value of 1/2.
It's worth noting that there are an infinite number of angles that correspond to a given sine value, since the sine function has period 2π. These angles are related to the angles by adding or subtracting multiples of 2π.
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The height of a hill, h(x), in a painting can be written as a
function of x, the distance from the left side of the
painting. Both h(x) and x are measured in inches.
h(x) = -(x)(x-13)
Mark this and return
4
What is the height of the hill in the painting 3 inches from
the left side of the picture?
O 6 inches
O
13 inches
O 30 inches
O 150 inches
Save and Exit
Next
Submit
The height of the hill in the painting 3 inches from the left side of the picture is 30 Inches. Option C
How to determine the height
From the information given, we have that;
h(x) represents the height of a hill, h(x), in a paintingx represents the distance from the left side of the paintingBoth the height and the distance are measured in inchesWe also have that the function is;
h(x) =-(x)(x-13)
Given that the distance is 3 inches
Substitute the values, we have;
h(3)= -(3)(3-13)
substract the values
h(3) = (-3)(-10)
multiply the values
h(3) = 30 inches
Hence, the value is 30 inches
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Kyle and Tina both think they figured out how to get Triangle ABC to transform to Triangle A'B'C', however they both did it in different ways. Kyle used a sequence of transformations, but Tina was able to do it in just one transformation. Assuming both students are correct, explain what each of them did in order to complete the problem.
Kyle: Rotation about the origin, then reflection across the x axis
Tina: Reflection over the line y = x
What is reflection in geometry?In geometry, reflection refers to a transformation that involves flipping a shape or object over a line, often called the "line of reflection".
This transformation preserves the size and shape of the original object, but changes its orientation by reversing the positions of all its points across the line of reflection.
Considering the image, rotation about the origin, then reflection across the x axis when compare with Reflection over the line y = x. will yield similar result.
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Which expressions are equivalent to 4 � 4b4, b ? Choose all answers that apply: Choose all answers that apply: (Choice A) A � + 2 ( � + 2 � ) b+2(b+2b)b, plus, 2, left parenthesis, b, plus, 2, b, right parenthesis (Choice B) B 3 � + � 3b+b3, b, plus, b (Choice C) C 2 ( 2 � ) 2(2b)
B=3b-b
C= 2b expressions are equivalent to 4 � 4b4, b .
b+2(b+2b)=b+2(3b)=b+6b=7b
3b+b=4b
2(2b)=4b Option B and C produce the outcome 4b. They are the expressions that are comparable to 4b as a result. We can also get an equivalent equation by multiplying or dividing both sides of an equation by the same nonzero value. If x4=2x+7, we can add 4 to both sides to get the following equation, which is equivalent: x4+4=2x+7+4. Of course, both sides of the equation can be made simpler. Constants x=2x+7+4 on the left side cancel each other out. If two systems of equations have the same solution, they are equivalent (s). In algebra, two equations are said to be equivalent if their roots or solutions are the same. The same number, symbol, or expression must be added to or subtracted from both sides of an equation to produce an equivalent equation.
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what is the solution to the number sentence k - 1.6 / 6 = 5.4
Answer:
k = 48.4
Step-by-step explanation:
[tex] \frac{k - 16}{6} = 5.4 \\ 6 \times \frac{(k - 16)}{6} = 5.4 \times 6 \\ k - 16 = 32.4 \\ k = 32.4 + 16 \\ k= 48.4 [/tex]
Q9.
Gavin bought 3 pairs of jeans in the USA.
He paid a total of $72
Gavin sold the 3 pairs of jeans in England,
He sold each pair of jeans for £34.50
£1 = $1.34
Work out Gavin's percentage profit.
Give your answer correct to the nearest whole number.
Answer:
Gavin made a Profit of $66.69 that is 93% Profit
Step-by-step explanation:
First, we calculate the Selling Price of Jeans after converting from GBP to USD on the given rate:
Rate: £1 = $1.34
Quantity: 3
Price in USD = Selling Price per pair * Rate in USD
£34.50 * 1.34 = $46.23 per pair of jeans.
Total Selling Price = Price Per Pair * Quantity
= 46.23 * 3
= $138.69
Total Profit = Total Selling Price - Total Cost Price
= $138.69-$72
= $66.69
Percentage of Profit = Total Profit / Total Cost Price
=66.69 / 72
=92.65
Therefore, the Profit Percentage is 92.65 % the nearest whole number would be 93%
To calculate Gavin's percentage profit, find the difference between the selling price and the buying price, and calculate the percentage of the buying price that the profit represents.
Explanation:To calculate Gavin's percentage profit, we need to find the difference between the selling price and the buying price, and then calculate the percentage of the buying price that the profit represents.
First, convert the selling price of each pair of jeans from pounds to dollars. Since £1 = $1.34, each pair of jeans sold for $34.50 x 1.34 = $46.23.Next, calculate the total selling price by multiplying the selling price of each pair by the number of pairs: $46.23 x 3 = $138.69.Then, calculate the profit by subtracting the total buying price from the total selling price: $138.69 - $72 = $66.69.Finally, calculate the percentage profit by dividing the profit by the total buying price and multiplying by 100: ($66.69 / $72) x 100 ≈ 92.6%.Gavin's percentage profit is approximately 92.6%.
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sita had 4^x . she want to buy a copy at (3*2^x+3) .she needed rs 128 more than how muc she had at the beggning
In the beginning, Sita had Rs. 64 to start with.
What are some rules of exponents?Some common rules of exponents are
xᵃ×xᵇ = xᵃ⁺ᵇ.
xᵃ/xᵇ = xᵃ⁻ᵇ.
Addition and subtraction of exponents is only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.
From the given information the equation can be formed as,
4ˣ + 128 = 3.2⁽ˣ⁺³⁾.
2²ˣ + 2⁷ = 3.2⁽ˣ⁺³⁾.
Putting some arbitrary values of 'x' we gey at x = 3,
64 + 128 = 3.64.
So, In the beginning, she had 4³ rs which is 64 rs.
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7. MP Reason Abstractly The number of customers in a store on the first
day is represented by (6x-3). The number of customers on the second
day is represented by (x - 1). Write an expression to find how many more
customers visited the store on the first day. Then evaluate the expression
if x is equal to 50. (Example 6)
Answer:
6x-3 - (x-1) is the expression.
You want to make sure to bring the - over both the "x" and the "-1". You end up with the expression 5x-2. I need more info to "evaluate the expression", it is not possible to evaluate it currently because of limited information on what the expression would equal.
How much would $100 invested at 6% interest compounded monthly be
worth after 20 years? Round your answer to the nearest cent.
A (t) = P(1+r/n)^nt
Answer:
D
Step-by-step explanation:
[tex]100(1 + \frac{016}{12}) ^{12(20)}[/tex]
331.02
Answer:
D. $220.00
Explanation :
Pt(1+r/n) n
HELP DUE TONIGHT!!!
The volume of the cone in terms of π is 96π inches³.
How to find the volume of a cone?The cone has a base radius of 6 inches and the height of the cone is 8 inches. Therefore, the volume of cone can be found as follows:
volume of cone = 1 / 3 πr²h
where
r = radius of the coneh = height of the coneTherefore,
r = 6 inches
h = 8 inches
Hence,
volume of cone = 1 / 3 × π × 6² × 8
volume of cone = 1 / 3 × π × 36 × 8
volume of cone = 12 × 8 × π
volume of cone = 96π inches³
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If f(x)=-2x+4 and g(x)=x^2-5x, find all values of x for which f(x)=g(x)
The values of x for which f(x) = g(x) are -1 and 4
How to determine the values of xFrom the question, we have the following parameters that can be used in our computation:
f(x) = -2x + 4
g(x) = x^2 - 5x
Using the above as a guide, we have the following:
Plot the graphs of f(x) and g(x) on the same planeWrite out the x coordinate of the intersectionUsing the above as a guide, we have the following:
x = -1 and x = 4
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g is most data likely to be skewed or symmetric? there is no right or wrong here but discuss and take a side on the issue.
Most data is likely to be skewed following a particular trait because when considering real life data, it is likely that it may concentrate on one end of the values on the real line as there is high uncertainty that exists with real life.
There is very little confidence that the population would behave in expected ways.
The skewed distribution implies the distribution that is not symmetrical. If a distribution is skewed it can be skewed to the left i.e. mean lies to the left of the center or skewed to the right i.e. mean lies to the right of the center of the distribution.
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Fill in the table using this function rule.
y = 4x+2
X
-2
0
2
4
y
0
0
0
0
X
D
The table is completed using this function rule y = 4x + 2 is given below.
x -2 0 2 4
y -8 2 10 18
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The function is given below.
y = 4x + 2
At x = - 2, the value of 'y' is given as,
y = 4 × (-2) + 2
y = - 8 + 2
y = - 6
At x = 0, the value of 'y' is given as,
y = 4 × (0) + 2
y = 0 + 2
y = 2
At x = 2, the value of 'y' is given as,
y = 4 × (2) + 2
y = 8 + 2
y = 10
At x = 4, the value of 'y' is given as,
y = 4 × (4) + 2
y = 16 + 2
y = 18
The table is completed using this function rule y = 4x + 2 is given below.
x -2 0 2 4
y -8 2 10 18
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Step-by-step explanation:
Please here it is.
Given y = 4x + 2
A room is 11 ft by 20 ft. It needs to be painted. The ceiling is 8 ft above the floor. There are two windows in the room, each one is 3 ft by 4 ft. The door is 2.5 ft by 6.5 ft.
Part 2
a) Find the area of the walls and ceiling to be painted.
b) One gallon of paint covers 71.41 sq ft. How many gallons are needed to paint the room?
c) At $18.32 a gallon, what is the cost to paint the room?
The required answers are,
a) 675.75 [tex]ft^2[/tex]
b) 9.46 gallons or we can say that 10 gallons needed.
c) $183.2
What is Area:The amount of unit squares that cover a closed figure's surface is its area. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity. The term “area” refers to the space inside the boundary or perimeter of a closed shape.
Now in the given question,
Area of Walls:
[tex]A(walls)=2(11*8)+2(20*8)\\A(walls)=2(88)+2(160)\\A(walls)=176+320\\A(walls)=496 ft^2[/tex]
Area of 2 windows:
[tex]A(windows)=2(3*4)\\A(windows)=2*12\\A(windows)=24 ft^2[/tex]
Area of door:
[tex]A(door)=2.5*6.5\\A(door)=16.25 ft^2[/tex]
Area of walls to be painted:
[tex]=A(walls)-A(windows)-A(door)\\=496-24-16.25\\=455.75ft^2[/tex]
Area of ceiling:
[tex]A(ceiling)=11*20\\A(ceiling)=220ft^2[/tex]
(a) Now total area to be painted:
A(walls to be painted)+ A(ceiling)=A(total)
[tex]A(total)=455.75 ft^2+220ft^2\\A(total)=675.75 ft^2[/tex]
(b) Number of Gallons:
coverage=71.41 ft^2 /gallon
675.75 ft^2/71.41 ft^/gal=gallons needed
9.46 gal= 10 gallons needed(approx)
(c) Cost of Paint:
You would need to buy 10 gallons at $18.32/gallon to have sufficient paint
cost=10 gallons x $18.32/gallon
=$183.2
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5-121. For parts (a) and (b), rewrite the expression without parentheses. For (c) and (d), solve each equation.
a. 2x(x + 3)
b. (3x + 2)(x-3)
c. 4y -2(6-y) = 6
d. x(2x-4)= (2x + 1)(x-2)
The value of the expressions are;
a. 2x² + 6
b. 3x² - 6x + 2x -6
c. y = 3
d. x = 2
How to solve the expressionsFrom the information given, we have
a. 2x(x + 3)
expand the bracket
2x² + 6
b. (3x + 2)(x-3)
expand the bracket
3x² - 6x + 2x -6
c. 4y -2(6-y) = 6
expand the bracket
4y - 12 + 2y = 6
collect like terms
6y = 18
Then,
y = 3
d. x(2x-4)= (2x + 1)(x-2)
expand bracket
2x² - 4x = 2x² - 4x + x - 2
collect like terms
x = 2
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Compare the two ratios by entering >, <, or = in the box. 1:8 3:4
[tex] \frac{1}{8} < \frac{3}{4} [/tex]
A ladder which is 6.9 m long is placed on the ground 2.9 m from a vertical wall and then leaned over to the wall. How high up the wall can the ladder reach? Give your answer rounded to 1 DP.
Not sure but i think it's 6.3.
Pythagoras theorem
a²+b²=c²
6.9 is the hypotenuse (c)
2.9 is the base (b)
a is the altitude of the wall or the height of the wall (a)
a²+2.9²=6.9²
a= 6.3
Solve this(the best answer and explanation gets brainliest)
Answer: 5/12
Step-by-step explanation:
- For the ease of the problem, turn them into improper fractions, so it would be:
13/3 divided by 14/5 divided by 26/7
- Next, let's turn the equation from division to multiplication. This can be done by flipping the fractions of everything being divided, so:
13/3 times 5/14 times 7/26
- We can cross out some parts of the fraction, like 13 and 26, 14 and 7, which simplifies our equation to:
1/3 times 5/2 times 1/2 = 5/12
Answer:
[tex]\dfrac{5}{12}[/tex]
Step-by-step explanation:
Given equation:
[tex]4 \frac{1}{3} \div 2 \frac{4}{5} \div 3 \frac{5}{7}[/tex]
Convert the mixed numbers into improper fractions:
[tex]\dfrac{4 \times 3+1}{3} \div \dfrac{2 \times 5+4}{5} \div \dfrac{3 \times 7+5}{7}[/tex]
[tex]\dfrac{13}{3} \div \dfrac{14}{5} \div \dfrac{26}{7}[/tex]
[tex]\textsf{Apply the fraction rule:} \quad \dfrac{a}{c}\div\dfrac{b}{d}=\dfrac{a}{c}\times \dfrac{d}{b}[/tex]
[tex]\dfrac{13}{3} \times \dfrac{5}{14} \times \dfrac{7}{26}[/tex]
Multiply the fractions:
[tex]\dfrac{13\times5\times7}{3 \times14 \times 26}[/tex]
[tex]\dfrac{455}{1092}[/tex]
The greatest common factor of 455 and 1092 is 91.
Therefore, divide the numerator and denominator by the GCF:
[tex]\dfrac{455 \div 91}{1092\div 91}=\dfrac{5}{12}[/tex]
suppose you drive 0.6 miles on a road so that the vertical distance changes from 0 to 150 feet. what is the angle of elevation of the road? (note there are 5280 feet in a mile)
Angle of elevation = tan-1 (150/3168).Angle of elevation = 5.0°The angle of elevation of the road is 5.0°.
In order to calculate the angle of elevation of a road, we need to know the vertical distance it has changed and the horizontal distance it has travelled. In this case, we have a vertical distance of 150 feet and a horizontal distance of 0.6 miles. Since there are 5280 feet in a mile, this is equivalent to 3168 feet .Using the formula for angle of elevation, we can calculate the angle of elevation for this road Angle of elevation = tan-1 (vertical distance/horizontal distance)Angle of elevation = tan-1 (150/3168).Angle of elevation = 5.0°Therefore, the angle of elevation of the road is 5.0°.
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answer for this and example
Answer:
e would equal a half because it's in the middle
Ethan is planning for his retirement. He has narrowed it down to two investment options. The first is an IRA where monthly payments are made, in the amount of $416.66, for 30 years. The second is a Roth IRA where annual payments are made, in the amount of $5000, for 30 years. If both compound interest at a rate of 2.5%, determine which account will yield the largest future value for Ethan, and how much greater that value will be than that of the other account. Round your final answer to the nearest cent.
To compare the two investment options, we must compute the future value (FV) of each account after 30 years of compounding at a 2.5% rate.As an outcome, the IRA will have a future value that is $107,116.33 greater than the Roth IRA.
How to find IRA?We have monthly payments of $416.66 for 30 years, or 360 months, on the IRA. Using the following formula to calculate the future value of an annuity:
[tex]FV = PMT * [(1 + r)^n - 1] / r[/tex]
We can calculate the future value of the IRA using the following formula: where PMT is the monthly payment, r is the monthly interest rate (2.5% / 12), and n is the number of payments (360):
[tex]FV IRA = 416.66 * [(1 + 0.025/12)^360 - 1] / (0.025/12) = $358,888.91[/tex]
We have annual payments of $5000 for 30 years on the Roth IRA. Using the following formula to calculate the future value of a lump sum:
[tex]PV * (1 + r)n = FV[/tex]
where PV is the present value (the lump sum), r is the annual interest rate (2.5%), and n is the number of years (30), we can calculate the Roth IRA's future value:
5000 * (1 + 0.025)30 = $251,772.58 FV Roth
As a result, the IRA will outperform the Roth IRA in terms of future value by:
$358,888.91 - $251,772.58 = $107,116.33 FV IRA - FV Roth
As a result, the IRA will have a future value that is $107,116.33 greater than the Roth IRA.
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During a 36 - year period, lightning killed 2,457 people in the United States. Assuming that rate holds true today and is constant throughout the year. Find the probability that tomorrow: (a) No one in the United States will be struck and killed by lightning. (b) One person will be struck and killed.
(c) More than one person will be struck and killed.
Answer: A
Step-by-step explanation: This is how to solve: 3239 / (36 *365)
That's 0.246499239 kills per day, so none died
I hope this helped!
Ahhh pls help!
A cruise ship made a trip to Vancouver and back. The trip to Vancouver took 6 hours, and the trip back took 9 hours. The ship averaged a speed of 12 km/h (kilometers per hour) on the trip back. What was the ship's average speed on the trip to Vancouver?
