169+354=523 I think thats what you were asking
ain ABC, AB=x, because=y, and CA=2x. A similarity transformation with a scale factor of 0.5 Maps ABC to MNO, such that vertices M,N and O correspond to A,B,C respectively. If OM=5, what is AB?
We are given: Triangle ABC sides, AB = x, BC = y and CA = 2x.
Another triangle MNO whose vertices M,N and O correspond to A,B,C respectively.
Therefore, AB corresponding to sides MN , BC corresponding to sides NO and CA corresponding to sides OM.
Also, we are given " A similarity transformation with a scale factor of 0.5 Maps ABC to MNO".
That means triangle ABC is dilated by a factor of 0.5.
Each side of the triangle MNO is 0.5 times(half) of Triangle ABC.
We could also say that each side of Triangle ABC is two times of sides of triangle MNO.
We are given side OM = 5 units.
CA = Times of OM = 2 * 5 = 10 units.
CA = 2x = 10 units or 2x=10.
Dividing both sides by 2, we get
[tex]\frac{2x}{2}=\frac{10}{2}[/tex]
x=5.
AB = x.
Therefore, AB = 5 units.
Answer:
Step-by-step explanation:
This is the variable, usually shown on the y-axis, that gets its value from the one on the x-axis.
The Hint say's it starts with (De)
Judy took $30 with her to spend on popcorn and drinks for herself and her friends at the movie theater. The price for each bag of popcorn was $5. The price of each drink was $3. (a) Sketch the graph that represents the situation and label the intercepts. Use one axis to represent the number of bags of popcorn and the other axis to represent the number of drinks. (b) Explain your graph.
helpppppp meeeee PLEASE DUE TOMORROW
Answer: 40,000,000
Population: 400,000,000
40X1010
Step-by-step explanation:
Work the following area application problem.
You own a swimming pool elliptical in shape. You wish to cover it at night to retain its warmth. If the pool measures 18 ft. across at its minor axis and 25 ft. across at its major axis, how much plastic material will you need to cover the pool, assuming you need a 1.5 ft. overhang all around the pool?
Area (to the nearest tenth) = ______ sq. ft.
SInce you need 1.5 feet of overhang, add 3 feet to each axis dimension 1.5 on each side):
Minor Axis = 18 + 3 = 21 feet
Major axis = 25 + 3 = 28 feet
The area of an ellipse is found by multiplying half the minor axis by half the major axis by PI.
1/2 minor axis = 21 / 2 = 10.5
1/2 major axis = 28 / 2 = 14
Using 3.14 for PI
Area = 10.5 x 14 x 3.14 = 147 x 3.14 = 461.6 sq ft
This problem is not as simple as it may appear at first. The area of an ellipse is ...
... A = πab
where a and b are the semi-axes.
Here, it looks like you're expected to choose these to be 1.5 ft longer than half the given axes, so the area of the pool cover is about ...
... A = π(9 ft + 1.5 ft)(12.5 ft +1.5 ft)
... A = 147π ft² ≈ 461.8 ft²
_____
However, adding 1.5 ft of material to an ellipse results in a shape that is not an ellipse, but is slightly larger than the ellipse with the dimensions used above. The area of that may be about 462.5 ft² (found numerically).
Write the rational number as a decimal. Show your work. 5/9 -3/8 -3/11.
I have memorized facts about fractions like these, so can tell you ...
[tex]\dfrac{5}{9}=0.5\overline{5}\\\\-\dfrac{3}{8}=-3\times 0.125=-0.375\\\\-\dfrac{3}{11}=-0.27\overline{27}[/tex]
_____
A fraction with 9 as a denominator is a repeating 1-digit decimal with the decimal digit being the numerator of the fraction.
A fraction with 11 as a denominator is a repeating 2-digit decimal with the two digits being 9 times the numerator of the fraction.
1/8 = 0.125, so any multiple of 1/8 is that multiple of 0.125.
To convert 5/9 - 3/8 - 3/11 into a decimal, you find a common denominator (792), subtract the numerators, resulting in -73/792, and then divide the numerator by the denominator to find the decimal, which is -0.0922.
Explanation:The problem is asking us to write the rational number 5/9 - 3/8 - 3/11 as a decimal. To do this, we need to first subtract these fractions and then convert the result into a decimal.
First, find a common denominator for all three fractions, which is 792. Convert the fractions to have this denominator, to get 440/792 - 297/792 - 216/792. Then, you subtract these three fractions by subtracting the numerators: 440 - 297 - 216 = -73. So, our fraction is -73/792. And finally, divide the numerator by the denominator to convert the fraction into a decimal: -73 ÷ 792 = -0.0922 to four decimal places. Learn more about Converting Fractions to Decimals here:
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NEED HELP NOW 70 POINTS! Divide. 2/3 ÷ 4/5 A.2/8 B.8/15 C.56 D.8/8
Hi,
Solution:
Find Common Denominators,
2/3 = 10/15
4/5 = 12/15
Divide,
10/15 ÷ 12/15 = 0.8333...
Turn into fraction;
0.8333... = 5/6
Answer - C. 5/6
3. A town's population has been decreasing at a constant rate, In 2010, the population was 5,900 By 2012 the population jad dropped to 4,700 Assume the tren contiues
a. Predict te population in 2016
b. Identify the year in which the population will reach 0
4. A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for five year
a. Find the linear function that models the town's population P as a function of the year, t where t is the number of years since the model began
b. Graph y==p(t) Interpret the meaning of the Intercepts.
c. When does the model expect the population to reach 100,000?
5. The weight of a newborn baby is 7.5 pounds. The baby gained one-half pound a month in its first year.
a. Find the linear function that models the baby's weight W as a function of the age of the baby t, in months
b. Fine a reasonable domain and range for the function W
The population of the first town decreases at a rate of 600 people per year, and is predicted to be 2,100 in 2016. The town with an initial population of 75,000 grows at a linear rate, represented by the function P(t) = 75000 + 2500t, with the population expected to reach 100,000 after 10 years.
Explanation:For the first part of your question regarding the town's decreasing population, we need to establish a rate of decrease. The town's population went from 5,900 in 2010 to 4,700 in 2012—this is a decrease of 1,200 over two years, or 600 people per year. Therefore, we can predict that the population will continue to decrease by 600 people per year. In 2016, this suggests the population would be 4,700 (population in 2012) - 600*4 (4 years from 2012 to 2016), which equals 2,100. For identifying the year when the population will reach 0, we use the same rate and find it by using the formula (current population / rate of decrease) + current year. As for the part about the town with an initial population of 75,000 growing at a constant rate, we can model this as a linear function such as P(t) = 75000 + 2500t. This equation states that the population at any given year is the initial population plus the annual growth times the number of years since the model began. In terms of the graph of this function, the y-intercept represents the initial population, while the slope is the constant rate of growth. The model expects the population to reach 100,000 after (100,000 - 75,000) / 2,500 = 10 years.
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63 less than four times a number is equal to the number. what is the number?
Jordan and Sharla are saving money to go on a study abroad trip. They must provide a down payment of $650 to sign up for the trip, and they can pay the remaining balance later. Jordan raises money by mowing lawns in his neighborhood and charges $25 per lawn. Sharla raises money by selling handmade necklaces for $15 each. Sharla raises less money than Jordan does because Sharla 3. only has enough materials to make 40 necklaces. (A) write two constraints to model the problem. Let x respresent the number of lawns Jordan mows and y represent the number of necklaces Sharla sells. (B) can sharla afford the down payment with the money she earns selling her necklaces? Explain your answer . PLEASE HELP its due NOW! I’ll make you brainliest
Point C is the center of the circle. angle ACB measures 49. What is the of arc ADB
If arc ADB is that portion of the circle that is not arc AB, then its measure is ...
... 360° -49° = 311°
_____
The sum of the measures of the arcs of a circle is 360°.
Every month, Ms. Thomas pays her car loan through automatic payments (withdrawals) from her savings account. She pays the same amount on her car loan each month. At the end of the year, her savings account balance changed by −$2,931 from payments made on her car loan. Describe the total change to Ms. Thomas’ savings account balance after making six monthly payments on her car loan. Model your answer using a number sentence.
Answer: -$1465.5
Ms. Thomas pays the 'same' amount as her car loan each month through car payments.
Total amount payed at the end of the year for car loan = -$2931
Change in Ms. Thomas' savings account each month (with respect to car loan) =
-2931/12 = -$244.25
So, to to calculate the total change to Ms. Thomas's savings account balance after paying for car loan for six months, we will simply multiply one month's amount with 6:
-$244.25 x 6 = -$1465.5
Answer:
Answer: -$1465.5
Ms. Thomas pays the 'same' amount as her car loan each month through car payments.
Total amount payed at the end of the year for car loan = -$2931
Change in Ms. Thomas' savings account each month (with respect to car loan) =
-2931/12 = -$244.25
So, to to calculate the total change to Ms. Thomas's savings account balance after paying for car loan for six months, we will simply multiply one month's amount with 6:
-$244.25 x 6 = -$1465.5
Step-by-step explanation:
What is the value of f(x) at x=8? F(8)=
The value of F(8) is 64.
Given that,
the value of f(x) at x=8.Based on the above information, the calculation is as follows:
[tex]F(8) = 8 \times 8[/tex]
= 64
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Rewrite in terms of sin(x) and cos(x).
sin(x+[7pi/4])
The term sin(x+[7pi/4]) can be rewritten in terms of sin(x) and cos(x) using the formula for sine of the sum of two angles. Given A = x and B = 7pi/4, the equation can be simplified to sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2).
Explanation:To rewrite the term sin(x+[7pi/4]) in terms of sin(x) and cos(x), we can use the formula for sine of the sum of two angles. The formula is given by:
sin(A + B) = sinAcosB + cosAsinB
Substituting our given values into this formula, where A = x and B = 7pi/4, we get:
sin(x + [7pi/4]) = sin(x)cos(7pi/4) + cos(x)sin(7pi/4)
Note that cos(7pi/4) = √2/2 and sin(7pi/4) = -√2/2. Therefore:
sin(x + [7pi/4]) = sin(x)(√2/2) - cos(x)(√2/2)
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Solve for x. y=c(x+b)
x = [tex]\frac{y}{c}[/tex] - b
divide both sides by c
x + b = [tex]\frac{y}{c}[/tex] ( subtract b from both sides )
x = [tex]\frac{y}{c}[/tex] - b
The equation solved for x is x = y/c - b.
What is an equation?Two or more expressions with an equal sign are defined as an equation.
The given equation is y = c(x + b).
y = c(x + b)
y/c = x + b
y/c - b = x
Or, x = y/c - b
Hence, the equation solved for x is x = y/c - b.
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Rex galore is taking his written test to get his license. there is an 85% probability of passing the test.
a. what is the probability that he will pass on his first try?
85% is the answer, because it is an 85% chance of him passing, now the chance of him passing twice in a row would be 72.25% because you would multiply 0.85 and 0.85 together.
If you ever swam in a pool and your eyes began to sting and turn red, you felt the effects of an incorrect pH level. pH measures the concentration of hydronium ions and can be modeled by the function p(t) = −log10t. The variable t represents the amount of hydronium ions; p(t) gives the resulting pH level.
Water at 25 degrees Celsius has a pH of 7. Anything that has a pH less than 7 is called acidic, a pH above 7 is basic, or alkaline. Seawater has a pH just more than 8, whereas lemonade has a pH of approximately 3.
Create a graph of the pH function either by hand or using technology. Locate on your graph where the pH value is 0 and where it is 1. You may need to zoom in on your graph.
The pool maintenance man forgot to bring his logarithmic charts, and he needs to raise the amount of hydronium ions, t, in the pool to 0.50. To do this, he can use the graph you created. Use your graph to find the pH level if the amount of hydronium ions is raised to 0.50. Then, convert the logarithmic function into an exponential function using y for the pH.
Recall from 07.02 how to convert a log to an exponential function. The equation y equals b to the power of x is written on the left. The equation x equals log base b of y is written on the right. A double-ended arrow points to both equations. The word exponent is written above the equations with arrows pointing to the x on the left and the x on the right. The word base is written below the equations with arrows pointing to the b on the left and the b on the right.
The pool company developed new chemicals that transform the pH scale. Using the pH function p(t) = −log10t as the parent function, explain which transformation results in a y-intercept and why. You may graph by hand or using technology. Use complete sentences and show all translations on your graph.
p(t) + 1
p(t + 1)
−1 • p(t)
Hello,
Please, see the attached files.
Thanks.
Answer:
hey i think the answer is 7
Step-by-step explanation:
Find the distance between 4 2/3 and −5 1/3
Answer:
The distance between these two is 10.
Step-by-step explanation:
In order to find this, we simply need to subtract the values from one another. If the value is then negative, we take the absolute value to find the distance.
4 2/3 - -5 1/3
4 2/3 + 5 1/3
10
U is between C and D.
True Or false
Find 5x − 3y − z if x = −2, y = 2, and z = −3
HELP FAST PLS!! Drag each function to correct location on the image. Identify exponential functions.
Answer:
See the attached
Step-by-step explanation:
An exponential function has the variable in the exponent.
Answer:
Exponential functions: [tex]f(x)=8e^x[/tex],[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex]
Non-exponential functions: [tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex]
Step-by-step explanation:
The general form of an exponential function is
[tex]f(x)=ab^x[/tex]
where, a is initial value and b is growth factor.
It means the variable term i.e., x must be the exponent . In other words we can say that the variable term must be in the power of constant terms.
We need to check whether the given function is an exponential function or not.
The given function is
[tex]f(x)=8e^x[/tex]
It is an exponential function with initial value 8 and growth factor e≈2.718.
Similarly,
[tex]f(x)=e^{-3x}[/tex] and [tex]f(x)=20^{\frac{x}{3}}[/tex] are exponential functions.
[tex]f(x)=5x^{\frac{3}{7}}[/tex], [tex]f(x)=4x^3-6x[/tex] and [tex]f(x)=\sqrt{x}+3x[/tex] are non-exponential functions.
What is the product of -2x^3 + x - 5 and x^3 - 3x - 4? Are the products equal to those of x^3 - 3x - 4 and -2x^3 + x - 5? Explain
I am soooo lost on working this out.
Answer:
Step-by-step explanation:
( -2x³ + x - 5) × ( x3 - 3x - 4)
= ( -2x³)×( x3 - 3x - 4) +(x)×( x3 - 3x - 4) - (5)( x3 - 3x - 4)
= - 2x^6 +6x^4 +8x³ + x^4 - 3x² -4x - 5x³ +15x + 20
= - 2x^6 +7x^4 +3x³-3x²+11x +20
Beth and Mark would like to put some savings in the bank. They most likely will not need this money for 4 years, so Beth wants to put it in a four-year CD. Mark wants to put the money in a passbook savings account. What is the advantage of a CD
Quite often, the CD will earn more interest—even if you have to pay a penalty for early withdrawal.
_____
For example, my local credit union offers 0.10% interest on passbook savings and 1.46% interest on a 4-year CD. One of my local banks offers 0.01% interest on passbook savings, and 0.60% on a 4-year CD.
A CD (Certificate of Deposit) generally offers a higher interest rate than a passbook savings account, which may lead to a greater return on investment. But it has a drawback where money cannot be withdrawn without penalty until a set time period ends.
Explanation:The primary advantage of a CD (Certificate of Deposit) over a passbook savings account is typically a higher interest rate. A CD is a type of timed deposit, meaning that the money is typically put in the bank for a fixed amount of time. During this time, the interest rate is usually higher than that of a typical savings account, allowing for a greater return on the initial investment. Unlike a passbook savings account, however, you cannot withdraw money from a CD without penalty until the time period ends, which in this case is four years. This is an important consideration for Beth and Mark.
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Parallel lines r and s are cut by two transversals, parallel lines t and u.
Which angles are corresponding angles with angle 8?
4 and 12
2 and 10
6 and 14
3 and 9
Answer:
∠4 and ∠12
A is correct
Step-by-step explanation:
Parallel lines r and s are cut by two transversals, parallel lines t and u
r || s and t || u
We are four parallel line. Two parallel line cuts two another parallel line.
Angle 8 is form by intersection of s and t line.
Corresponding angle: When two parallel lines are crossed by transversal line, the angles at matching corners are called corresponding angles.
For angle 8, t || u with s is transveral line.
Thus, ∠8 = ∠12 (By definition of corresponding angle)
For angle 8, s || r with t is transveral line.
Thus, ∠8 = ∠4 (By definition of corresponding angle)
Hence, ∠4 and ∠12 are corresponding angle of ∠8
I need a little help with the second part of b and part c! + can y'all check my explanations please
a. (my answer for context) The system for this word problem is x+y=14; 11.99x+24.99y=245.86 (x is shirts and y is pants)
b. 1. Explain, without solving, which method is most efficient in solving this system: substitution, elimination, graphing, or making a table?
(my answer is substitution, because the solutions to x and y can easily be substituted into the first equation).
b. 2. Explain why the other methods are not as sufficient.
(I need a little help but I'm thinking it's because for this system solving method you basically only have to solve the second equation and then just substitute)
c. How could you simplify the numbers used in this system to simplify the system? Does this new system change your answer to part b? Explain. (What does this mean? How can I answer it?)
Answer:
b. Your answer is appropriate.
c. The decimals can be eliminated by multiplying by 100. (You can also add 0.14 to the problem, adding .01 to each individual price and 0.14 to the total. This will make the second equation be 12x +25y = 246, which makes the numbers slightly easier to work with.) Unfortunately, there don't seem to be any common factors that would reduce the size of the numbers.
Step-by-step explanation:
a. We assume you're finding quantities of shirts and pants for a purchase of 14 total items costing $245.86. If so, your equations are appropriate.
b. The solution for one variable or the other can be found in 6 arithmetic operations using your suggested method. Any other method takes as many or more. (Multiplying the first equation by -11.99 and adding to the second gets you the equivalent of substituting for x in as many operations.)
Graphing can be quick and easy with the right tool. Since you know the solutions are integers, just about any graphing tool will get you close enough.
Another method (using only 5 arithmetic operations) is to calculate the average price of an item as 245.86/14, then figuring the ratio of the difference from the lower price to the total difference in price. Multiplying this ratio by the number of items gives the number of the higher-priced item (pants). (245.86/14 -11.99)/(24.99 -11.99)·14 = 6 This method treats the problem as a "mixture" problem, finding the numbers of each consitutuent that make the average come out what it is.
c. See above for how to simplify the numbers. Done properly, the answer is not changed. (Some people don't work well with decimals or fractions, so like to see those eliminated from the problem. Some folks work better with small integers than with large ones, so like to see the numbers be made as small as possible.)
A company developed a student survey so that students could share their thoughts about school. In 2011, 78,234 students across the United States were administered the survey. In 2012, the company planned to administer the survey to 10 times as many students as we're surveyed in 2011. About how many surveys should the company have printed in 2012? Explain how you found your answer.
Answer:
Company needs to print [tex]782,340[/tex] surveys in 2012.
Step-by-step explanation:
In 2011, 78,234 students participated in the survey.
Now in 2012 it is to be increased by 10 times. So there will be 10 times more students participating in the survey. Therefore they will need as 10 times more surveys.
Number of surveys needed in 2012 = [tex]78,234*10[/tex]
=[tex]782,340[/tex]
Company needs to print [tex]782,340[/tex] surveys in 2012.
If y = 2x^3 + 4x and dx/dt = 2, find dy/dt when x = 4.
dy/dx = 6x² +4 . . . . . using the power rule
dy/dt = (dy/dx)×(dx/dt) = (6(4²) +4)×2
dy/dt = 200 . . . at x=4
The population of a town is 6500 and is increasing at a rate of 4% each year. Create a function for this scenario. At this rate, approximately what will the town's population be in 4 years?
Answer:
[tex]P_4 = 7604.08[/tex]
Step-by-step explanation:
If the population increases at a rate of 4% per annum, then:
In year 1:
[tex]P_1 = P_0 + 0.04P_0[/tex]
Where [tex]P_0[/tex] is the initial population and [tex]P_n[/tex] is the population in year n
In year 2
[tex]P_2 = P_1 + 0.04P_1[/tex]
It can also be written as:
[tex]P_2 = P_0 + 0.04P_0 + 0.04 (P_0 + 0.04P_0)[/tex]
Taking out common factor [tex]P_0[/tex]
[tex]P_2 = (1 + 0.04) (P_0) + 0.04P_0 (1 + 0.04)[/tex]
Taking out common factor (1 + 0.04)
[tex]P_2 = (1 + 0.04) (P_0 + 0.04P_0)[/tex]
Taking out again common factor [tex]P_0[/tex]
[tex]P_2 = (1 + 0.04) (1 + 0.04) P_0[/tex]
Simplifying
[tex]P_2 = P_0 (1 + 0.04) ^ 2[/tex]
So
[tex]P_n = P_0 (1 + 0.04) ^ n[/tex]
This is the equation that represents the population for year n
Then, in 4 years, the population will be:
[tex]P_4 = P_0 (1 + 0.04) ^ 4\\P_4 = 6500(1 + 0.04) ^ 4\\P_4 = 7604.08[/tex]
Solve for x.
4 - 3x
---------- = 5
2
Answer:
x=-2
Step-by-step explanation:
We are given an equation as
[tex]\frac{4-3x}{2} =5[/tex]
and asked to solve for x
Simplify by multiplying both sides by 2. This will get rid of fraction on left side.
4-3x = 10
Grouping like terms by taking 4 to right side
we get right side 10-4 = 6
-3x = 6
To get exact value of x, we divide by -3 on both the sides
x = 6/-3 = -2
Since this is an equation, we get a single value for x
x=-2
and answer is -2
Given fractional expression:
{(4-3x)/2} = 5
→ 4-3x = (5)2
→ 4-3x = 10
→ -3x = 10-4
→ -3x = 6
Therefore, x = -(6/3) = -2
Please show work: This is for my daughter in 7th. Grade; Needed some insight 15 Points, and Brainliest to whom show work with correct answers!
1a - A boat travel 468 kilometers on 117 liters of gasoline. How much gasoline will it need to go 168 kilometers
1B: A car travels 138 miles in 4 hours (With constant speed) How far can it travel in 10 hours (With the same speed)
2A: A boat travels 261 miles in 15 hours (With a constant speed) How much time will it take traveling 180 miles?
2B: A car travels 452 Km. in 5 hours (with a constant speed) How far can it travel in 4 hours?
5A: 50 LBS. of tomatoes cost $200. How much would 2 LBS cost?
5B: A boat travels 381 km. in 6 hours (with a constant speed) How far can it travel in 7 hours (with the same speed)?
5C: A boat travels 427 km. in 43 hours (with constant speed) How much time will it take traveling 459 kilometers?
5D: 11 Kg. of bananas cost $88 how much would 20 kg cost?
Thanks -P-
Answer:
1a. 42 liters
1b. 345 miles
2a. 10 h 20 min 41.4 sec
2b. 361.6 km
5a. $8
5b. 444.5 km
5c. 46 h 13 min 20.9 sec
5d. $160
Step-by-step explanation:
Each of these problems expresses a proportion and asks you to find a missing value. You are given, for example, value 1 and related value 1. You are asked to find value 2 that corresponds to related value 2.
Solving the Proportion
Expressed as a proportion, this looks like ...
... (value 1)/(related value 1) = (value 2)/(related value 2)
If you multiply both sides of this equation by related value 2, you can find value 2.
... (related value 2)/(related value 1)×(value 1) = value 2
Another way to think about it
I like to think of the related values as making a fraction. If the related value 2 is larger than related value 1, the fraction is greater than 1 and the value 2 will be larger than value 1. (This realization can serve as a check on your answer.)
1a. related value 2 = 168 km. This is the value for which you want to find value 2, the number of liters of gasoline. related value 1 has the same units as related value 2 (km), and value 1 has the same units as value 2 (liters).
Then the fraction of interest is (168 km)/(468 km), and it multiplies 117 L. The result is ...
... (168/468)×(117 L) = 42 L
1b. (10 h)/(4 h)×(138 mi) = 345 mi
2a. (180 mi)/(261 mi)×(15 h) ≈ 10.3448 h
2b. (4 h)/(5 h)×(452 km) = 362.6 km
You may have noticed that I keep the units with the numbers. When the same units are in the numerator and denominator, they cancel—the way any common factors cancel. The remaining units will be the units of the answer. This practice of keeping units with numbers can help ensure you're using the right numbers for the right purpose. If the units don't work out, your math has an error.
5a. (2 lb)/(50 lb)×$200 = $8
5b. (7 h)/(6 h)×381 km = 444.5 km
5c. (459 km)/(427 km)×(43 h) ≈ 46.2225 h
5d. (20 kg)/(11 kg)×$88 = $160