a goods train leaves a station at 6 pm followed by an express train which leaves at 8 pm and travels 20 km/hour faster than the goods train. The express train arrives at a station, 1040 km away, 36 minutes before the goods train. Assuming that the speeds of both the trains remain constant between the two stations; calculate their speeds
Answers
Answers:
Goods train has a speed of 80 km per hour
Express train has a speed of 100 km per hour
==========================================================
Explanation:
Check out the diagram below to see the table. For now, refer to table 1.
Each row represents a different train.
We have x as the speed of the slower train (the goods train) and x+20 is the speed of the faster train (express train). These speeds are in km/hr or kph.
The y variable represents the number of hours it takes the goods train to arrive at its destination. The equation formed in the first row is 1040 = xy. This is because distance = rate*time.
Let's solve for y to get
1040 = xy
xy = 1040
y = 1040/x
We'll use this equation later.
-------------------------
The second row of table 1 has x+20 as the speed and y-2-0.6 as the time.
The "-2" represents the fact that the express train is operating for 2 hours less compared to the goods train (because the goods train had a 2 hour head start). Then the "-0.6" indicates we're taking off another 36 minutes, which is equivalent to 36/60 = 0.6 hours.
So overall, the express train is traveling for 2+0.6 = 2.6 fewer hours compared to the goods train. The express train's time value is y-2.6 hours.
With this in mind, we can form this equation for the second row
distance = rate*time
1040 = (x+20)(y-2.6)
We'll now apply substitution to replace y with 1040/x. This is valid because earlier we found that y = 1040/x
------------------------
If we apply that substitution and solve for x, we get the following
\(1040 = \left(x+20\right)\left(y-2.6\right)\\\\1040 = \left(x+20\right)\left(\frac{1040}{x}-2.6\right)\\\\1040 = x\left(\frac{1040}{x}-2.6\right) + 20\left(\frac{1040}{x}-2.6\right)\\\\1040 = 1040 - 2.6x + \frac{20800}{x} - 52\\\\0 = -2.6x + \frac{20800}{x} - 52\\\\x*0 = x*\left(-2.6x + \frac{20800}{x} - 52\right)\\\\0 = -2.6x^2 + 20800 - 52x\\\\-2.6x^2 - 52x + 20800 = 0\\\\\)
Let's now use the quadratic formula to finish things off.
\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-52)\pm\sqrt{(-52)^2-4(-2.6)(20800)}}{2(-2.6)}\\\\x = \frac{52\pm\sqrt{219024}}{-5.2}\\\\x = \frac{52\pm468}{-5.2}\\\\x = \frac{52+468}{-5.2} \ \text{ or } \ x = \frac{52-468}{-5.2}\\\\x = \frac{520}{-5.2} \ \text{ or } \ x = \frac{-416}{-5.2}\\\\x = -100 \ \text{ or } \ x = 80\\\\\)
Ignore the negative solution because we can't have a negative speed.
The only practical solution here is x = 80
This means the goods train has a speed of 80 km/hr.
The express train's speed must be x+20 = 80+20 = 100 km/hr.
------------------------
Now to verify these answers.
If the goods train travels 1040 km and does so at a speed of 80 km/hr, then it travels for 1040/80 = 13 hours. Add this onto 6:00 PM and we arrive at 7:00 AM. This is shown in the first row of table 2 (see below).
If the express train travels 1040 km and its speed is 100 kph, then it travels for 1040/100 = 10.4 hours. This is equivalent to 10 hours, 24 minutes because 0.4 hrs = 0.4*60 = 24 min
If we start at 8:00 PM and elapse 10 hours, then we'll arrive at 6:00 AM. Add on another 24 minutes, and we get to 6:24 AM. Notice how this is 36 minutes before 7:00 AM (because 24+36 = 60). So this confirms that the express train indeed arrives 36 minutes before the goods train does, despite the goods train having that 2 hour head start.
Related Questions
which of the following random variables meets the criteria for a hypergeometric distribution? multiple choice question. suppose 30% of the population of have a graduate degree. define x to be the number of adults in a sample of 20 who have earned a graduate degree. the average number of adults who have a graduate degree is 0.7/household. let x be the number of adults in a household who have a graduate degree. out of 50 adults, 10 who have a graduate degree. a sample of 20 is taken. define x to be the number of adults in the sample with a graduate degree.
Answers
The following random variable meets the criteria for a hypergeometric distribution: Out of 50 adults, 10 who have a graduate degree. A sample of 20 is taken. Define x to be the number of adults in the sample with a graduate degree.
A hypergeometric distribution is a type of probability distribution that measures the likelihood of a particular number of successes (in this case, adults with a graduate degree) in a sample without replacement.
A random variable that meets the criteria for a hypergeometric distribution is that which meets these conditions: A sample of size n is taken from a population of size N. The population has k successes and N - k failures.
The hypergeometric distribution is used when sampling is done without replacement, where the sample size is small relative to the population size. The sample size is typically less than 10% of the population size. When you have the information of the population, you can use the hypergeometric distribution.
Out of the options provided, the random variable that meets the criteria for a hypergeometric distribution is, Out of 50 adults, 10 who have a graduate degree. A sample of 20 is taken. Define x to be the number of adults in the sample with a graduate degree.
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Which of the following options have the same value as 80\%80%80, percent of 222222?
Choose 3 answers:
Choose 3 answers:
(Choice A)
A
\dfrac{80}{100}\cdot 22
100
80
⋅22start fraction, 80, divided by, 100, end fraction, dot, 22
(Choice B)
B
80\cdot 2280⋅2280, dot, 22
(Choice C)
C
\dfrac{22}{80}\cdot 100
80
22
⋅100start fraction, 22, divided by, 80, end fraction, dot, 100
(Choice D)
D
0.8\cdot 220.8⋅220, point, 8, dot, 22
(Choice E)
E
\dfrac{4}{5}\cdot 22
5
4
⋅22
Answers
The answer is C. I know bc i just did it
The value same as 80% of 22 is 4/5 x 22.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
80% of 22 that is equals to
= 80/100 x 22
= 8/10 x 22
= 4/5 x 22
Hence, the value same as 80% of 22 is 4/5 x 22.
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Pls help/ The y-intercept of f(x)=(1.6)x is ______________________ the y-intercept of the function in the graph:
Answers
The y-intercept of f(x) = (1.6)x is (a) less than the y-intercept of the function in the graph
How to complete the blank?The equation of the function is given as
f(x) = (1.6)x
To determine the y-intercept, we set x = 0
So, we have
f(0) = 1.6 * 0
Evaluate
f(0) = 0
For the graph, we have
When x = 0, the function has a value of 1
This means that
y-intercept is 1
0 is less than 1
Hence, the y-intercept of f(x) = (1.6)x is (a) less
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F(x,y)=⟨−9,2y⟩, half-circle x 2
+y 2
=1 with y≥0, oriented counterclockwise. (Use symbolic notation and fractions where needed.) ∫ C
F⋅dr
Answers
To evaluate the line integral ∫C F · dr, where F(x, y) = ⟨-9, 2y⟩ and C is the half-circle x^2 + y^2 = 1 with y ≥ 0, oriented counterclockwise, we can parameterize the curve C and then compute the line integral.
Parametrization of the curve C:
Let's parameterize the half-circle C in terms of the angle θ:
x = cos(θ)
y = sin(θ)
To find the limits of integration for θ, we note that the half-circle ranges from θ = 0 to θ = π.
Now, we can calculate dr using the parametrization:
dr = ⟨dx, dy⟩ = ⟨-sin(θ) dθ, cos(θ) dθ⟩
Substituting the values of x, y, and dr into F, we get:
F(x, y) = ⟨-9, 2y⟩ = ⟨-9, 2sin(θ)⟩
Now, we can calculate the line integral using the parameterization and the dot product:
∫C F · dr = ∫θ=0 to π (-9)(-sin(θ)) dθ + ∫θ=0 to π (2sin(θ))(cos(θ)) dθ
Simplifying, we have:
∫C F · dr = 9∫θ=0 to π sin(θ) dθ + 2∫θ=0 to π sin(θ)cos(θ) dθ
Integrating each term separately:
∫θ=0 to π sin(θ) dθ = [-cos(θ)] evaluated from θ=0 to π = [-cos(π)] - [-cos(0)] = 1 - (-1) = 2
∫θ=0 to π sin(θ)cos(θ) dθ = [-cos^2(θ)/2] evaluated from θ=0 to π = [-cos^2(π)/2] - [-cos^2(0)/2] = -(-1/2) - (-1/2) = 0
Therefore, the line integral ∫C F · dr = 9(2) + 2(0) = 18.
The value of the line integral ∫C F · dr is 18.
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Mike is planting flowers in plastic cups for his science fair project. Each of the cups is filled to the top with a mixture of soil, fertilizer, mulch, and sand in different proportions. Each cup contains 1/2 cup of soil, 1/3 cup of fertilizer, and 1/8 cup of mulch. How much sand should he use to fill the cup?
PLZ HURRY
Answers
Answer:
He will need 1/8 of sand to fill the cup
Step-by-step explanation:
For 1/2 i filled half of the cup for 1/3 i made new cup split it in 3 and added it in main cup then for 1/8 made a new cup split it in 8 and added it to main cup the test is sand.
Charles charges $4 an hour to baby-sit. He also adds an extra $10 onto the total for families with more than three children. How much will Charles charge to baby-sit 4 children for 4 hours?
A. $48
B. $26
C. $56
D. $160
Answers
The total amount Charles will charge to baby-sit 4 children for 4 hours is; $26
Since, Charles charges $4 an hour to baby-sit.
Therefore, when Charles is asked to baby-sit for four hours;
His normal charge would be; $4 × 4 = $16.
However, he adds an extra $10 onto the total for families with more than three children;
The total charge is therefore; $16 + $10 = $26.
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Answer:
The total amount Charles will charge to baby-sit 4 children for 4 hours is; $26Since, Charles charges $4 an hour to baby-sit.
Step-by-step explanation:
y = 3 x ² + 1 , if the input is 4 , what us the output
Answers
Answer:
the out put would be 49
Step-by-step explanation:
Solve for p.
7/p = 8/9
Answers
Answer:
Exact Form:
p=63/8
Decimal Form:
p=7.875
Mixed Number Form:
p=7 7/8
Hope this helps :-)
Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE.)
f(x) = 3x2/3 − 2x
I keep getting stuck at taking the first derivative and solving for critical points. So please show all work and even some of the tedious algebra bits included so I can see where I'm messing up?
Answers
The function f(x) = 3x²/3 - 2x has no intercepts, a relative minimum at (1, -1), no points of inflection, and no asymptotes.
Intercepts: To find the x-intercepts, we set f(x) equal to zero and solve for x:
0 = 3x²/3 - 2x
0 = x² - 2x
0 = x(x - 2)
x = 0 or x = 2
Therefore, both x = 0 and x = 2 are not actual x-intercepts, but rather double roots.
Relative Extrema: To find the relative extrema, we take the derivative of f(x) and set it equal to zero,
f'(x) = 2x - 2
0 = 2x - 2
2 = 2x
x = 1
Substituting x = 1 back into the original function, we find f(1) = -1. Therefore, the relative minimum occurs at (1, -1).
f''(x) = 2
Since the second derivative is a constant, it never equals zero. Therefore, there are no points of inflection for this function.
Asymptotes: To determine if there are any asymptotes, we examine the behavior of the function as x approaches positive or negative infinity. Since the highest power of x in the function is 2, the graph does not approach any vertical asymptotes.
For horizontal asymptotes, we look at the limits as x approaches positive or negative infinity:
lim(x→∞) f(x) = lim(x→∞) (3x²/3 - 2x) = ∞
The limits approach positive infinity in both cases, indicating that there are no horizontal asymptotes. Graphically, the function represents a parabola that opens upwards, with a relative minimum at (1, -1).
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There are two identical jars on a table: Jar-A has exactly 380 red jelly beans, and Jar-B has exactly 380 black jelly beans. Suppose you took the scoop that holds exactly 20 jelly beans, and filled it with 20 red jelly beans from A and put them into B. After shaking B to mix the jelly beans, scoop 20 jelly beans from B and put them into A.
(a) Choose the correct statement from the following.
1) There are more red jelly beans expected in B than the black jelly beans expected in A.
2) There are more black jelly beans expected in A than the red jelly beans expected in B.
3) The number of red jelly beans expected in B and the number of black jelly beans expected in A are the same.
4) There is not enough information.
(b) Either mathematically or in plain English, justify your answer.
Answers
Option 3) The number of red jelly beans expected in B and the number of black jelly beans expected in A are the same.
(b) Justification: Initially, Jar-A has 380 red jelly beans and Jar-B has 380 black jelly beans. When you scoop 20 red jelly beans from A and put them into B, Jar-B has 380 black jelly beans and 20 red jelly beans. After shaking, you scoop 20 jelly beans from B and put them into A. Since you took out 20 jelly beans from B, it will still have 380 jelly beans. The probability of picking a red jelly bean from B is now 20/380, so you can expect to return approximately
(20/380) × 20 = 20/19 ≈ 1 red jelly bean to A, leaving 19 red jelly beans in B.
Similarly, you can expect to have 20 - 1 = 19 black jelly beans in A,
as you scooped out 20 jelly beans from B. Therefore, the number of red jelly beans expected in B and the number of black jelly beans expected in A are the same.
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3) A car can travel 442 miles on 26 gallons of gasoline. How much gasoline will it need to go 102 miles?
Answers
The car will need 6 gallons of gasoline to travel 102 miles
Explanation:Given that the car travels 442 miles on 26 gallons of gasoline.
Because the more the distance, the more the volume of gasoline used, this is a direct proportion.
So, we have:
\(\begin{gathered} V=\frac{102\times26}{442} \\ \\ =6 \end{gathered}\)It will need 6 gallons.
find the equation of the straight line passing through the point (0,2) which is perpendicular to line y=1/4x+5
Answers
Answer:
y = -4x + 2
Step-by-step explanation:
Given the following data;
Points (x1, y1) = (0, 2)
Perpendicular line = y = ¼x + 5
To find the equation of the straight line passing;
Mathematically, the equation of a straight line is given by the formula: y = mx + c
Where;
m is the slope.x and y are the pointsc is the intercept.From the question, we can deduce that the slope (m) of the perpendicular line is ¼.
y = ¼x + 5 = mx + c
Since the points are perpendicular to the equation of line, it must have a slope that is its negative reciprocal because the slopes of perpendicular lines are negative reciprocals of each other.
Therefore, ¼ = -4
Next, we would write the equation of the straight line using the following formula;
y - y1 = m(x - x1)
Substituting into the formula, we have;
y - 2 = -4(x - 0)
y - 2 = -4x - 0
y - 2 = -4x
y = -4x + 2
London has a collection of 260 coins. How many coins represent 25% of her collection?
Answers
Answer:
65 coins
Step-by-step explanation:
Set this problem up with a porportion.
\(\frac{?}{260} \frac{25}{100}\)
After that, cross multiple and divide.
25 times 260. Then divide by 100. That is then your answer.
Let n = 9 in the T statistic defined in Equ-
ation 5.5-2.
(a) Find to.025 so that P(- to.025 ≤ T ≤ t0.025) = 0.95. (b) Solve the inequality [-t0.025 ≤ T < to.025] so that u is
in the middle.
Answers
a. P(-t0.025 ≤ T ≤ t0.025) = 0.95. b. the specific numerical values for t0.025 may vary based on the degrees of freedom (df) and the desired level of confidence.
(a) To find the value of t0.025 such that P(-t0.025 ≤ T ≤ t0.025) = 0.95, we need to look up the critical value in the t-distribution table or use statistical software.
Since we are looking for a two-tailed confidence interval with a total probability of 0.95, we divide the remaining probability (1 - 0.95 = 0.05) into two equal tails. Each tail will have a probability of 0.05/2 = 0.025
By consulting the t-distribution table or using software, we can find the critical value associated with the upper tail probability of 0.025 and degrees of freedom (df) equal to n - 1 = 9 - 1 = 8. Let's denote this critical value as t0.025.
Therefore, we find t0.025 such that P(-t0.025 ≤ T ≤ t0.025) = 0.95.
(b) To solve the inequality [-t0.025 ≤ T < t0.025] so that u is in the middle, we need to find the range of values for T that satisfies this condition.
Given the confidence interval is symmetric around the mean, we want to find the range that contains the central 95% of the t-distribution. We already found the critical values -t0.025 and t0.025 in part (a).
The solution to the inequality is -t0.025 ≤ T < t0.025. This range ensures that the population mean (u) will be within the central portion of the distribution, as the tails outside this range contain a cumulative probability of only 5% (0.025 on each side).
By selecting values of T within this range, we can be confident that the corresponding population mean will fall within the middle portion of the distribution.
It's important to note that the specific numerical values for t0.025 may vary based on the degrees of freedom (df) and the desired level of confidence.
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What is the image of the point (-7,5) after a rotation of 180° counterclockwise about
the origin
Answers
Answer:
(7,-5)
Step-by-step explanation:
If a point is rotated 180 degrees (the direction doesn't matter) you change the sign. So if the preimage is positive then the image will be negative and vice-versa.
Answer:
(7,-5)
Step-by-step explanation:
The data set below represents the heights (in inches) of students in a particular high school class: 72 67 62 64 59 71 62 66 67 75 67 62 What is the range of the data set? 0 18 inches 16 inches 0 12 inches 0 75 inches
Answers
The range of the data set is 16 inches.
How many inches is the range of the data set?The range of a data set represents the difference between the highest and lowest values in the set. In this case, the data set consists of the following heights (in inches):
59, 62, 62, 62, 64, 66, 67, 67, 67, 71, 72, 75
To find the range, we need to determine the minimum and maximum values in the set. By sorting the data set in ascending order, we can identify the minimum and maximum values more easily:
59, 62, 62, 62, 64, 66, 67, 67, 67, 71, 72, 75
The smallest value in the set is 59, which is the minimum value, and the largest value is 75, which is the maximum value.
To calculate the range, we subtract the minimum value from the maximum value:
Range = Maximum value - Minimum value
Range = 75 - 59
Range = 16 inches
Therefore, the range of the given data set is 16 inches. This means that the difference between the tallest and shortest student in the class is 16 inches.
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Rocky Mountain Tire Center sells 10,000 go-cart tires per year. The ordering cost for each order is $35, and the holding cost is 40% of the purchase price of the tires per year. The purchase price is $25 per tire if fewer than 200 tires are ordered,$17 per tire if 200 or more, but fewer than 8,000, tires are ordered, and $13 per tire if 8,000 or more tires are ordered.
a) How many tires should Rocky Mountain order each time it places an order?
b) What is the total cost of this policy?
Answers
a) Rocky Mountain should order 200 tires each time it places an order.
b) The total cost of this policy is $17,160.
a) To determine how many tires Rocky Mountain should order each time, we need to consider the different price levels and find the point where it is most cost-effective to order. Let's analyze the three price levels:
If fewer than 200 tires are ordered: The purchase price is $25 per tire.
If 200 or more, but fewer than 8,000 tires are ordered: The purchase price is $17 per tire.
If 8,000 or more tires are ordered: The purchase price is $13 per tire.
Since the ordering cost is $35 per order, it is most cost-effective to order the maximum quantity that falls within the second price level, which is 200 tires.
b) To calculate the total cost of this policy, we need to consider the ordering cost and the holding cost. The holding cost is 40% of the purchase price per tire per year. Let's calculate the total cost:
Total holding cost = (Purchase price per tire * Quantity ordered * Holding cost rate) / 2 = (($17 * 10,000 * 0.4) / 2) + (($13 * 2,000 * 0.4) / 2) = $34,000 + $5,200 = $39,200
Total cost = Total ordering cost + Total holding cost = (Ordering cost per order * Number of orders) + Total holding cost = ($35 * (10,000 / 200)) + $39,200 = $1,750 + $39,200 = $40,950
Therefore, the total cost of this policy is $40,950.
Rocky Mountain Tire Center should order 200 tires each time it places an order, resulting in a total cost of $40,950 for this policy. This ordering quantity and cost analysis allows Rocky Mountain to make efficient and cost-effective decisions in managing their inventory.
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Please try your best
Answers
Answer:
y= - 4/1x + 5
Step-by-step explanation:
Answer:
y=-4x+5
Step-by-step explanation:
4 equals the slope (rise over run) and 5 equals the y-intercept
1. Find the missing side with the Pythagorean Theorem.
(a? + b² = c? where c is the hypotenues)
2. Find: sin(e), cos(O), and tan(0) using SOH CAH TOA
opp
adj
орр
sin(0)
cos(O) = tan(0) =
hyp
hyp
adj
Answers
Answer:
I wrote 0 as theta here!
Step-by-step explanation:
c²=a²+b²
or, 37²=a²+12²
or, 1369=a² + 144
or, a² = 1369-144
or, a² = 1225
so, a = 35
The missing side is 35.
sin(0) = p/h = 35/37
cos(0) = b/h = 12/37
tan(0) = p/b = 35/12
which expression is a possible leading term for the polynomial function graphed below? –18x14 –10x7 17x12 22x9
Answers
Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.
The leading term of a polynomial function is the term containing the highest power of the variable. Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.
The degree of a polynomial function is the highest degree of any of its terms.
If a polynomial has only one term, then the degree of that term is the degree of the polynomial and is also called a monomial.
For example, consider the given function:Now, observe the degree of the function, which is 14, as the highest exponent of the function is 14.
Thus, the term containing the highest power of the variable x is -18x¹⁴.
Therefore, among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.
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Please help!............
Answers
using visual cues identify each pair of angles on the diagram below
Answers
The special angles pairs that are formed are identified below.
What are the Special Angle Pairs?Special angle pairs are formed by a transversal and the parallel lines it cuts across.
Based on the image given, the special angle pairs are given as follows:
Corresponding angles:
∠1 and ∠5
∠4 and ∠8
∠2 and ∠6
∠3 and ∠7
Alternate interior angles:
∠3 and ∠5
∠4 and ∠6
Consecutive interior angles:
∠4 and ∠5
∠3 and ∠6
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3. If h(x) = 7 (-x/2) + 3 find h(8)
Answers
Answer:
found 8
Step-by-step explanation:
Given parallelogram L M N O below, LP = 81 If PN = -7x-3 solve for x
Answers
-7x=81+3
-7x/7=84/-7
Solution
X=-12
Answer:-12x
Step-by-step explanation:
just trust me on this
PLZ HELP ME WITH THIS MATH!!!!!!!!
Answers
Answer:
The surface area is 200
Step-by-step explanation:
For the triangles, the width is 6 and the height is 4; so you would multiply 1/2·w·h (1/2·6·4) = 12
For the two side rectangles, the width is 5 and the height is 8; so you would multiply w·h (5·8) = 40
And for the middle rectangle, the width is 6 and the height is 8; so you would multiply w·h (6·8) = 48
Since there are two triangles you would double the 12, same for the rectangles.
And then you get 200; bam. Sorry, I'm sleep-deprived
Here are the statements
Answers
Answer:
Step-by-step explanation:
the answer is c
Someone please help with this math
Answers
prove that any graph of minimum degree at least three contains a cycle of even length.
Answers
Answer:
a cycle is a sequence of non-repeated vertices and the degree of a graph is the number of neighbors the vertex has.
. The product of two integers is -84. One of them is 4, find the other integer.
Answers
Answer:
Answer :-Product of two integers = - 84
One integer = 4
Other integer = x
\(4 \times x = - 84 \\ 4x = - 84 \\ x = \frac{ - 84}{4} \\ x = - 21\)
⎆ The value of the other integer is - 21
Which equation represents the line that passes through the points (6,7) and ( -3,-2)
Answers
Answer:
y=x+1
Step-by-step explanation:
Find the Equation Using Two Points and i got y=x+1
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