Bob is hiking down a 60-mile country trail. He could hike at 10 mph for the first two hours and then go the rest of the way at 30 mph or he could just go the whole way at 20 mph. How long would each of these options take? Which option is the faster?
Answers
Time taken for option two: 20mph (3 hours)
Calculate the time taken by option one, 30 mph:
60=20+30x
40/30=x
4/3 =x
1+1/3=x
It would take (option 1): 2+1+1/3= 3 1/3 hours to complete
It would take (option 2): 3 hours
Therefore, option two is faster.
Hope I helped :)
With the first option the hiking has two stages
Stage 1
Hike for
[tex]speed \: = 10mph[/tex]
for
[tex]time = 2 \: hours[/tex]
The distance covered in this stage 1 can be determined using the formula,
[tex]Speed = \frac{distance}{time \: taken} \\ \\ \\ \\10mph = \frac{distance}{2 \: h} \\ \\ \\ distane = 2 \times 10 = 20miles[/tex]
Stage 2
At this stage,the remaining distance to be covered
[tex] = 60 -20 = 40miles[/tex]
We can again calculate the time take to cover this distance using
[tex]Speed = \frac{distance}{time \: taken} \\ \\ \\ 30mph = \frac{40miles}{time \: taken} \\ \\ \\ time \: taken \: = \frac{40miles}{30mph} \\ \\ \\ \\ time \: taken \: = 1 \frac{1}{3} hours[/tex]
The total time taken for this option
[tex] = 2 \: hours \: + 1\frac{1}{3} hours = 3 \frac{1}{3} \: hours[/tex]
OPTION 2
For this option, the hiker goes 30mph throughout the whole journey for
[tex]speed = \frac{distance}{time \: taken} \\ \\ \\ \\ \\ 30mph = \frac{60}{time \: taken } \\ \\ time \: taken = \frac{60}{30} = 2 \: hours[/tex]
For the first option, it took the hiker 3⅓ hours but for the second option, it took him 2 hours.
[tex]<b>Therefore the second option is faster.</b>[/tex]
Related Questions
Sam deposited $350 into a savings account that paid 5% in simple interest. When he withdrew his money 8 months later, how much interest did he receive?
Answers
I = P x R% x T
I is simple interest
P is principal, which is the amount u deposit in
R% is the rate
And T means the time
However, this question didn't list whether 5% is per annual or per monthly.
Suppose it's oer annual,
From the numbers, we can substitute in
Interest = 350 x (5%/12) x 8
Note that since the amount of time is in months, and one year has 12 months, so we need to change the rate into per monthly.
Interest = 350 x (5%/12) x 8
Answer = $11.66666676
But suppose it's per monthly.
This time we don't need to divide the rate by 12.
Interest= 350 x 5% x 8
=$140
I NEED HELP ASAP WILL GIVE 50 POINTS!!!
This diagram shows a pre-image
△ABC, and its image, A′′B′′C′′, after a series of transformations.
Select from the drop-down menus to correctly complete the statements.
Answers
△ABC is rotated 180 degrees about the origin to become △A'B'C'. Then △A'B'C' is translated 3 units down to become △A"B"C". Because the transformations are both rigid, the pre-image and image are congruent.
In Euclidean Geometry, the mapping rule for the rotation of a geometric figure about the origin by 180° in a clockwise or counterclockwise direction can be modeled by the following mathematical expression:
(x, y) → (-x, -y)
Point A (1, -1) → Point A' (-1, 1)
Point B (4, -2) → Point B' (-4, 2)
Point C (7, 2) → Point C' (-7, -2)
Next, we would apply a translation 3 units down to the new figure (△A'B'C'), in order to determine the coordinates of its image as follows;
(x, y) → (x, y - 3)
A' (-1, 1) → (-1, 1 - 3) = A" (-1, -2).
B' (-4, 2) → (-4, 2 - 3) = B" (-4, -1).
C' (-7, -2) → (-7, -2 - 3) = C" (-7, -5).
Therefore, the resulting figure must be located in the third quadrant as illustrated in the diagram shown above.
you place a 3 3/8 pound weight on the left side of a balance scale and a 1 1/5 pound weight on the right side of a balance. How much weight do you need to add right side to balance the scale?
Answers
Answer:
[tex]2\frac{7}{40}[/tex] pounds
Step-by-step explanation:
Given information:
Weight on the left side = [tex]3\frac{3}{8}[/tex] pounds
Weight on the right side = [tex]1\frac{1}{5}[/tex] pounds
We need to balance both sides.
Let x be the weight which is added to the right side to balance the scale.
[tex]3\frac{3}{8}=1\frac{1}{5}+x[/tex]
[tex]\frac{24+3}{8}=\frac{5+1}{5}+x[/tex]
[tex]\frac{27}{8}=\frac{6}{5}+x[/tex]
Subtract 6/5 from both sides.
[tex]\frac{27}{8}-\frac{6}{5}=x[/tex]
[tex]\frac{135-48}{40}=x[/tex]
[tex]\frac{87}{40}=x[/tex]
[tex]2\frac{7}{40}=x[/tex]
Therefore, [tex]2\frac{7}{40}[/tex] pounds weight is added to the right side to balance the scale.
Please help me!!
Solve for B:
C = sqrt(A^2 + B^2)
Answers
c^2 = a^2+b^2 now subtract a^2 from both sides
c^2 - a^2 = b^2 Now take the square root of both sides
b = +- sqrt(c^2-a^2)
Final answer:
To solve for B in the equation C = sqrt(A^2 + B^2), you square both sides of the equation, subtract A^2 from both sides, and then take the square root of the result to find B = sqrt(C^2 - A^2).
Explanation:
The equation C = sqrt(A^2 + B^2) is representative of the Pythagorean theorem, which is used in mathematics to relate the sides of a right triangle. To solve for B, we must isolate B on one side of the equation. Here's how you can do it:
Begin with the equation C = sqrt(A^2 + B^2).Square both sides of the equation to eliminate the square root, getting C^2 = A^2 + B^2.Subtract A^2 from both sides to get B^2 = C^2 - A^2.Finally, take the square root of both sides to solve for B, which gives B = sqrt(C^2 - A^2).This gives us the magnitude of B in terms of A and C.
How do you convert 0.45 (45 being repeated) to a fraction?
Answers
~ThePirc
0.454545(45 being repeated)
45 / 100 = 9 / 20 (Divided by 5)
Hope this helps :))
~Top
Help me Solve this and explain to me the steps thank you
Answers
recall that a flat-line is always 180°, also recall that all interior angles in a triangle are 180°, therefore x + 95 + 54 = 180. Surely you'd know what "x" is.
Look at ΔABC. Which triangle is congruent to ΔABC by the ASA criterion? triangle 1 triangle 2 triangle 3 triangle 4
Answers
hope it helps
Answer:
Triangle 4
Step-by-step explanation:
Congruent triangles are identical in all aspects. They have identical sides and angles.
The ASA the Angle Side Angle criterion.
Congruent triangles should be able to "close up" on each other if one triangle is placed on top of the other. Let's look at the triangle in question.
The triangle ABC is made distinct by the lines on it.
The lines mark the different angles on the triangle.
By looking at the triangle and comparing, Triangle satisfies the ASA criterion
Take a look at the figure. What is the value of y?
A. y = 32 B. y = 64 C. y = 14 D. y = 16
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What is 435 000 in standardform?
Answers
A bracelet was marked up $50 from cost, which amounts to a 20% increase. Find the original cost of the bracelet.
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The following are two sets of class scores (you may consider these scores to be normally distributed). Julia received the two scores marked with an asterisk. Did she do better or worse on the second test? Why? (16 points) First Test 48 *56 61 60 39 49 5 57 52 51 Second Test 75 81 63 *74 59 88 77 79 76 69 67
Answers
First let’s find the mean and standard deviation for both test and then we can calculate the probability of getting that score in his respective test and compare.
First test
P(x < 56)
P(z < 56-47.80/16.38)
P(z<0.50) = 1 – 0.3085 = 0.6915 or 69 percentile
Second test
P(x < 74)
P(z < 74 – 73.45 / 8.37)
P(z<0.07) = 1 – 0.4721= 0.5279 or 53 percentile
The probability for this normal distribution also means the percentile, so we can say that in the first test she was in the 69 percentile while in the second test she was in the 53 percentile. Therefore, she did worse in the second test
Julia did better on the first test compared to the second test.
Explanation:To determine whether Julia did better or worse on the second test, we need to compare her score on the first test with her score on the second test. For the first test, Julia received a score of 56 and for the second test, she received a score of 74. To determine which score is better, we can compare their positions in the distribution of scores.
First, we can calculate the mean and standard deviation of the scores for each test. For the first test, the mean is 49.9 and the standard deviation is 12.8. For the second test, the mean is 73.6 and the standard deviation is 7.3.
Next, we can calculate the z-scores of Julia's scores on each test. A z-score represents the number of standard deviations a data point is from the mean. For the first test, Julia's z-score is 0.16, and for the second test, her z-score is -0.2538.
Since a higher z-score indicates a better performance relative to the mean, Julia did better on the first test than the second test.
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The drama club at smith valley middle school is selling cookie dough in order to raise money for costumes. if each tub cookie dough costs $4.75, how many tubs must members sell to make $570.00?
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Ans: 120 tubs
A car was moving 110 km/h how long did it take to go 25.5 miles?
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Determine the graph
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john and brian work for a toy manufacturers putting stuffing in teddy bears. On average, john can stuff x teddy bears in one day and brian can stuff y in one day. They both the same number of days,t. What does the expression (x +y)t represent? A. the number of teddy bears John can stuff in t days B.the number of teddy bears Brian can stuff in t days C. the number of teddy bears John and Brian can stuff in t days D.the number of teddy bears John and Brian can stuff in one day
Answers
Answer:
C
Step-by-step explanation:
Because The Equation Represents how many of those thingy's were stuffed
Ethan buys a video game on sale. If the video game usually costs $39.99, and it was on sale for 20% off, how much did Ethan pay?
Answers
Ethan paid $31.99 for the video game on sale.
How to calculate the discount?To calculate the discount that Ethan obtained in the price of his video game, we do the following operations:
We divide the total price by one hundred and multiply the result by the discount, in this case 20.
$39,99 ÷ 100 = $0,3999$0,3999 × 20 = $7,998Subsequently, we subtract the result of the previous operation (value of the discount) from the total value of the video game.
$39,99 - $7,998 = $31,992
According to the above, the value that Ethan paid for the video game was $31,992
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Answer: $31.99
Step-by-step explanation:
$39,99 ÷ 100 = $0,3999
$0,3999 × 20 = $7,998
$39,99 - $7,998 = $31,992
Jack's mother gave him 505050 chocolates to give to his friends at his birthday party. He gave 333 chocolates to each of his friends and still had 222 chocolates left.
Write an equation to determine the number of friends (x)(x)left parenthesis, x, right parenthesis at Jack's party.
Find the number of friends at Jack's party.
Answers
Answer:
16
This seems to have been miswritten. So I went ahead and just put it as 50, 3 and 2Explanation:
Okay, so Jack started with 50 chocolates and ended with 2.
The simple way to calculate it would be by realizing that Jack only distributed 48 chocolates. We can find how many times 3 fits into 48 by dividing 48÷3=16.
Using algebra, we substitute the value we want to find with x. Here what we want to find is the number of friends that were at Jack's party.
We know that he started with 50 chocolates, then distributed 3× the number of friends present (which is x).
We write that down as 50−3x
(It's minus because when chocolates are distributed, Jack is taking away from what he has.)
We know that after this, there were only 2 chocolates left, so it's
50−3x=2
Then we proceed by moving all the numbers to the right until only x is left:
−3x=2−50
−3x=−48
x=−48−3
x=16
Conclusion: The number of people that attended the party was 16.
Answer:
The equation is 3x+2=50
There were 16 friends at Jack's party.
Step-by-step explanation:
I JUST TOOK THE TEST
The larger of two supplementary angles measures 20° less than four times the measures of the smaller angle .find the degree measure of each angle
Answers
From that knowledge we can write up some equations.
Let angle 1 = x, and angle 2 = y
x + y = 180
"The larger of two supplementary angles measures 20° less than four times the measure of the smaller angle"
(Let x be the larger angle)
x+20 = 4y
Since there are two different equations, and two variables, this means we have a set of simultaneous equations.
We can solve this via the substitution method or the elimination method.
I choose to solve it via the substitution method cause of personal preference.
x + y = 180 => x = 180- y
x+20 = 4y => x = 4y - 20
Make them equal each other..
180 - y = 4y - 20
200 = 5y
40 = y
Now that we know y we can sub it into any equation to find x
x + 20 = 4y
x + 20 = 4(40)
x + 20 = 160
x = 140
So the angles are 40° and 140°
We want to create a system of equations that allows us to find the values of two supplementary angles.
We will find that the larger angle measures 140° and the smaller one measures 40°.
------------------------
Two angles A and B are supplementary if their measures add up to 180°, so we have:
A + B = 180°.
Let's assume that B is the larger one, we also do know that:
"The larger is 20° less than 4 times the smaller"
Then we can write:
B = 4*A - 20°.
Then our system of equations is:
A + B = 180°.
B = 4*A - 20°.
To solve it we need to isolate one variable in one of the equations and replace it on the other equation. Here we can see that B is already isolated on the second equation, so we can replace it in the first one to get:
A + B = 180°.
A + (4*A - 20°) = 180°
Now we can solve this for A:
A + (4*A - 20°) = 180°
5*A - 20° = 180°
5*A = 180° + 20° = 200°
A = 200°/5 = 40°
Now that we know the value of A we can get the value of B:
B = 4*A - 20° = 4*40° - 20° = 140°
Then the larger angle measures 140° and the smaller measures 40°
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Find the next two numbers in the sequence 1, 5, 17, 53, 161, _____, _____
Answers
17 = 5 + 12
53 = 17 + 36
161 = 53 + 108
485 = 161 + 324
The next two numbers are 161 and 485.
The required missing term of the given sequence is given as 485 and 1457.
What is a sequence?The sequence is a pattern of placing the values in a specified manner.
here,
5 = 1 + 4
Since, [tex]b_0 = 4[/tex] and [tex]a_0 = 1[/tex]
17 = 5 + 12
So, the general term is given as
[tex]a_n = a_{n-1} + b_{n}[/tex]
Where, [tex]b_n = 3b_{n-1}[/tex]
For 6 th term
6 the term = 161 + 3(108)
6 the term = 485
For the 7th term
7th term = 485 + 3(324)
7th term = 1457
Thus, the required missing term of the given sequence is given as 485 and 1457.
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An isosceles right triangle has leg lengths of 4 centimeters. What is the length of the altitude drawn from the right angle to the hypotenuse?
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The altitude is also 2Sqrt(2) because the altitude is an angle bisector of the 90 degree angle which bisects the hypotenuse, and the other 2 angles of the large right triangle are 45 degrees.
If two standard six-sided dice are tossed, what is the probability that a 5 is rolled on at least one of the two dice? express your answer as a common fraction.
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1/12 is the probability that a 5 is rolled on at least one of the two dice
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that two standard six-sided dice are tossed,
We need to find the probability that a 5 is rolled on at least one of the two dice.
When we roll two dice there is a possibiltiy of 36 outcomes.
In these 36 outcomes atleast one of the dice should show 5.
There are 36 possible rolls
(5, x), (x, 5) and (5, 5) are the possible outcomes with 5 on any of the dice.
x represents any number from one to five.
So the probability that a 5 is rolled on at least one of the two dice is 3/36
which is equal to 1/12.
Hence, 1/12 is the probability that a 5 is rolled on at least one of the two dice
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Belinda keeps a record of her expenses for the week as shown: Bus fare $8.70 Lunch out $7.35 Hair cut $16 Movie rental $5.95 What is the total of Belinda’s expenses for the week? a. $22.16 b. $23.60 c. $37.90 d. $38.00 Please select the best answer from the choices provided A B C D
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Bus fare $8.70
Lunch out $7.35
Haircut $16.00
Movie rental $5.95
Total = 8.70 + 7.35 + 16.00 + 5.95 = $38.00
Answer: d. $38.00
Final answer:
Belinda's total expenses for the week are the sum of her bus fare, lunch out, hair cut, and movie rental, which adds up to d. $38.00.
Explanation:
To calculate the total of Belinda's expenses for the week, we should add up each of the expenses mentioned. This includes the bus fare, lunch out, hair cut, and movie rental. Here's how we do it step-by-step:
Bus fare: $8.70Lunch out: $7.35Hair cut: $16.00Movie rental: $5.95Now, let's add them up:
$8.70 (Bus fare) + $7.35 (Lunch out) + $16.00 (Hair cut) + $5.95 (Movie rental)
When we sum these amounts, we get $8.70 + $7.35 + $16.00 + $5.95 = $38.00.
Therefore, the total of Belinda's expenses for the week is $38.00, which corresponds to option D.
How many sides does a polygon have if the sum of its interior angles is 2340?
Answers
(n-2)180=sum
(n-2)180=2340
n-2=2340/180
n-2=13.5
n=13.5+2
n=15.5
However, the problem is that a polygon cannot have "half" as side. Therefore, there might be a problem in the question or there is no solution to such a question.
Hope I helped :)
What is the definition to an equation?
Answers
OR
A mathematical statement that 2 expresion are equal.
You are to construct a€cylindrical can out of tin that encloses a volume of exactly 100 cubic inches. to three significant figures, which dimensions (r and h) will give you the tin can that requires the least amount of metal?
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The formula for volume of cylinder is:
V = π r^2 h
since volume is 100 cubic inches, so:
100 = π r^2 h
Rewriting in terms of h:
h = 100 / π r^2
The least amount of metal means least amount of surface area needed. The surface area of cylinder is:
A = 2 π r h + 2 π r^2
insert the value of h in terms of r:
A = 2 π r (100 / π r^2) + 2 π r^2
A = 200 r-1 + 2 π r^2
Take the 1st derivate and set to 0, dA/dr = 0:
dA/dr = - 200 r-2 + 4 π r
0 = - 200 r-2 + 4 π r
200 / r^2 = 4 π r
r^3 = 50 / π
r = 2.52 inches
So height h is:
h = 100 / π r^2
h = 100 / π (2.52)^2
h = 5.01 inches
Answers:
r = 2.52 inches
h = 5.01 inches
The length of a rectangle is 4 inches greater than the width. The perimeter of the rectangle is 24 inches. What are the dimensions of the rectangle?
length = 12 in.; width = 8 in.
length = 8 in.; width = 6 in.
length = 8 in.; width = 4 in
length = 6 in.; width = 2 in.
Answers
By using the formula for the perimeter of a rectangle and substitution, it is determined that the dimensions of the rectangle are 6 inches for the length and 2 inches for the width.
Explanation:This is a traditional problem in algebra that we can solve using known formulas and principles.
The perimeter of a rectangle is calculated using the formula 2(l+w), where 'l' stands for length and 'w' stands for width. In this problem, we know the perimeter (P) is 24 inches, and we know the length (l) is the width (w) + 4 inches.
We can set up and solve an equation using these facts. Replace 'l' in the equation with '(w + 4)' and solve for 'w': 2[(w + 4) + w] = 24, which simplifies to 2w + 8 = 12, and finally, w = 2.
Having found 'w', we can find 'l' by substituting 'w' in our equation of 'l', l = w + 4 = 2 + 4 = 6.
Therefore, the length is 6 inches and the width is 2 inches.
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What is the equation of a line that passes through the point (4, 2) and is perpendicular to the line whose equation is y= x/3−1 ?
Answers
y= -3x+b
Now, we can substitute in the point given to find the intercept.
2= -3(4)+b
2= -12+b
b=14
Finally, put in everything we've found to finish the equation.
y= -3x+14
I need a little help please Brainliest
Answers
For the first image, the median range would be 88. In order to find the median, you'll place all your numbers in numerical order (smallest to largest). If there are an odd amount of numbers, find the one directly in the middle. If there is an even amount, you'll take the two most central ones and find the mean, that will tell you the median. Therefore, B (88) would be the answer to your first one.
The second one would be C (20.4). It's asking for the mean. In order to find the mean of a set of numbers, you'll simply add up all of the numbers and divide by how many numbers are in your number set. That gives you the mean.
Greatest common factor
Answers
That's because 2 is the greatest number that can go into both 8 and 14.
A bag contains 3 yellow, 1 red, and 2 green beads. Charlene draws a bead, keeps it out, then draws another bead. What’s the probability that Charlene drew the red bead, then a green bead? Write your answer in simplified form.
Answers
P(drew a red bead) = 1/6
without replacing
P(drew a green bead) = 2/5
P(both events) : 1/6 * 2/5 = 2/30 reduces to 1/15 <=