A bicyclist heads east at 10km/h. After she has traveled 24.2 kilometers, another cyclist sets out in the same direction going 30km/h. About how long will it take the second cyclist to catch up to the first cyclist?

Answers

Answer 1
We know that the first cyclist has traveled 24.2 km at a speed of 10 km/h. Lets use the equation [tex]time= \frac{distance}{speed} [/tex] to find the time of the first cyclist:
[tex]t= \frac{24.2}{10} [/tex]
[tex]t=2.42[/tex]
So, we know that she has traveled for 2.42 hours.
 
We also know that after she has traveled for 2.42 hours another cyclist sets out in the same direction, so if [tex]t[/tex] represents the time of our first cyclist, the time of our second cyclist will be [tex]t-2.42[/tex].

Now we are going to use the equation [tex]distance=(speed)(time)[/tex] to relate the speeds and times of the two cyclist:
For the first one:
[tex]distance=10t[/tex] equation (1)
For the second one:
[tex]distance=30(t-2.42)[/tex] equation (2)

Replace (1) in (2)
[tex]10t=30(t-2.42)[/tex]
The only thing left now is solve for [tex]t[/tex]:
[tex]10t=30t-72.6[/tex]
[tex]-20t=-72.6[/tex]
[tex]t= \frac{-72.6}{-20} [/tex]
[tex]t=3.63[/tex]

We can conclude that the second cyclist will catch up the first cyclist after 3.63 hours.



Related Questions

The measure of angle KMN = ?? degrees

Answers

∠KMN = (1/2)*arc KN . . . . . . this relationship is true of any inscribed angle. (It is a useful relationship to remember.)
  = 95°/2
  = 47.5°

type the correct answer in the box.use numeral instead of words. if necessary, use / for the fraction bar.

Answers

It’s 63°, hope this helps!
For this question, all you have to do is solve the missing angle of the triangle ABD since it has two measurements already and the angle BCD is a reflection of the missing angle.

Since the total degrees of a triangle's angles should add up to 180°, let's add the given angles and then subtract that from 180.

83 + 34 = 117°

180 - 117 = 63°

So, the angle BCD is 63°.
Hope that helped!

Michael surveyed 40 of his friends to determine their favorite season. His data shows that 70% said summer, 10% said winter, 5% said fall, and the rest said spring. What circle graph best represents Michael's data?


Answers

The answer is D.) because 70% was summer which, of course, would be the biggest piece of the pie and would be more than Half of it.

Answer:

Correct answer is D the last on in the pic

What is the square root of 1,563?

Answers

39.5 but if you round than it would be 40

The temperature is 9 degrees below zero

Answers

0-9=-9

Hope this helped☺☺

The mathematical expression for the temperature measured can be obtained as -9°.

What is a Measurement unit?

A measurement unit is a unit to measure certain quantities.

For example, the mass can be measured in kilograms, length can be measured in meter and time can be measured in seconds.

To find the measurement of a new quantity knows units can be used in operation. As to find the unit for speed we use m/s as a unit, where, m is the unit of distance and s is the unit of time.

The given measure of the temperature is 9°.

Since, the convention to take measured figures with the values below zero is negative.

The given temperature can be written as -9°.

Hence, the given temperature can be written as -9°.

To know more about measurement unit click on,

https://brainly.com/question/15402847

#SPJ2

A supermarket conducts a survey to find the approximate number of its customers who like apple juice. What is the population of the survey?

Answers

Final answer:

In a survey conducted by a supermarket to find out how many customers like apple juice, the population of the survey would be all customers of the supermarket. The population in a survey defines the group the research wants to gain information about and determine the applicability of the findings.

Explanation:

In the context of survey research, a population refers to the entire group about which information is wanted. In your scenario, where a supermarket is conducting a survey to find out how many customers like apple juice, the population of the survey would be all customers of the supermarket. It's important to identify the population in a survey because it helps determine the scope of the study and how broadly the findings can be applied.

For example, if you were a marketing manager for an electronics chain store wanting information about the ages of its customers, the population would also be all customers of the store. Similarly, if a radio station wants to know its listeners' preferences, the population would be all listeners of that station. The aim is to collect data that is representative of this population, be it through sampling or other data collection methods.

Learn more about population here:

https://brainly.com/question/15889243

#SPJ12

The population of the supermarket survey is the entire customer base, including individuals with varying shopping frequencies, aimed at determining the approximate number of customers who like apple juice through representative insights from the diverse customer demographic.

The population of a survey refers to the entire group that the survey aims to represent or provide insights into. In this case, the supermarket is conducting a survey to find the approximate number of its customers who like apple juice. The population of the survey, therefore, is the entire customer base of the supermarket.

To determine the population, the supermarket would ideally want to include all its customers who may have preferences or opinions about apple juice. This could include individuals who have shopped at the supermarket recently or regularly. The population might also encompass a broader range, considering both frequent and occasional customers to ensure a more representative sample of the supermarket's clientele.

In summary, the population of the survey is the entire customer base of the supermarket, encompassing individuals who may have opinions or preferences regarding apple juice.

1. Suzette ran and biked for a total of 34 mi in 3.5 h. Her average running speed was 6 mph and her average biking speed was 12.5 mph. How many hours did suzette run

Answers

Final answer:

To find out how many hours Suzette ran, we used a system of equations with the total distance and total time for running and biking. Solving the system, we determined that Suzette ran for 1.5 hours.

Explanation:

To determine how many hours Suzette ran, we can use the total distance and the total time given for running and biking activities, alongside her average speeds for each activity. We will then set up a system of equations that account for the distances and times and solve for the time Suzette spent running.

Let r be the time spent running and b be the time spent biking. We are given:

Total time: r + b = 3.5 hours

Total distance: 6r + 12.5b = 34 miles (6 mph is the running speed, 12.5 mph is the biking speed)

Now we'll solve this system of equations:

Substitute b from the first equation into the second equation: 6r + 12.5(3.5 - r) = 34.

Simplify and solve for r: 6r + 43.75 - 12.5r = 34.

This simplifies further to -6.5r = -9.75, hence r = 1.5.

Suzette ran for 1.5 hours.

Find x and fill in the angle values. Could you also explain how it works? Please and thank you.

Answers

Hello!

Angles 3 and 1 are vertical angles, and angles 2 and 4 are vertical angles. Vertical angles are congruent by definition, so angle 3 is congruent to angle 1, and angle 2 is congruent to angle 4.

The adjacent angles are supplementary (they add to equal 180 degrees) so you can set up an equation to solve for x.

180 = 2x + x
180 = 3x
60 = x

x = 60

To find the measure if each angle, plug in x as needed.

Angle 4 = x
Angle 4 = 60 degrees

Angle 2 = angle 4
Angle 2 = 60 degrees

Angle 3 = 2x
Angle 3 = 2(60)
Angle 3 = 120

Angle 1 = angle 3
Angle 1 = 120

I hope this helps you.

Maggie wants to buy 4 roses, 6 carnations, and 9 tulips. She estimates that she will spend about 14 dollars on these flowers. Do you agree?

Answers

It depends on how much each rose, carnation, and tulips costs. You can then determine if this prediction is accurate.

Hope this helps!

can someone help me with this question?

Answers

D. 5 5/6

Volume = l * b * h
= 2 1/2 * 3 1/2 * 2/3
= 5/2 * 7/2 * 2/3
= 35/6
= 5 5/6

The diameter of a small gear is 16cm. This is 2.5cm more than 1/4 of the diameter of a larger gear. What is the diameter of the larger gear?

Answers

The diametrr of the large gear is 13.5 cm

To find the diameter of the larger gear, we set up an equation based on the information that the smaller gear's diameter is 2.5cm more than a quarter of the larger gear's diameter. Solving this, the diameter of the larger gear is found to be 54cm.

The student has asked for the diameter of a larger gear when given that the diameter of a smaller gear is 16cm, which is 2.5cm more than one quarter of the larger gear's diameter. To find the diameter of the larger gear, we can set up an equation where d represents the diameter of the larger gear.

According to the question:
16cm =  1/4d + 2.5cm
To solve for the diameter d, we subtract 2.5cm from both sides and then multiply by 4:

16cm - 2.5cm =  1/4d13.5cm =  1/4d13.5cm times 4 = dd = 54cm

The diameter of the larger gear is therefore 54cm.

find the value of A E B C and D please

Answers

Looks like you've got 3 lines that are all parallel with one transversal diagonally running down the middle. 
Since all of the other lines are parallel to one another, there are only two different angle combinations to be made by the transversal and one of the other lines, one of which being the given 60º angle. 
The other one is found by subtracting that from 180 since a straight angle measures 180º. 
180 - 60 = 120 
The smaller ones are always 60º, and the larger ones are always 120º. 
That means that a = 60, b = 60, and d = 60 
It also means that c = 120 and e = 120. 
Hope this helps!

A paleontologist uncovers a fossil of a saber-toothed cat in California. He analyzes the fossil and concludes that the specimen contain 15% of its original carbon-14. Carbon-14 has a half-life of 5730 years. Use carbon-14 dating to determine the age of the fossil.

Answers

Final answer:

Carbon-14 dating is used to determine the age of fossils by comparing the amount of carbon-14 in the specimen to the amount in the atmosphere. The half-life of carbon-14 is 5730 years, and by analyzing the percentage of carbon-14 remaining, the age of the fossil can be calculated.

Explanation:

Carbon-14 dating is used to determine the age of fossils. Carbon-14 (14C) is a radioisotope that is present in living organisms while they are alive, and it starts to decay after they die. The half-life of carbon-14 is 5730 years, which means that after this time period, half of the original carbon-14 will have decayed.

In the case of the saber-toothed cat fossil, the paleontologist analyzed the specimen and found that it contained 15% of its original carbon-14. By comparing this percentage to the amount of carbon-14 in the atmosphere, which is known, they can determine the age of the fossil.

Since carbon-14 dating is accurate up to about 50,000 years, this method is suitable for dating the fossil. The age of the fossil can be calculated by considering the amount of carbon-14 remaining and the known half-life of the isotope.

what is the volume of this container?

Answers

V = 3*3*4 - 1*3*2 = 36 - 6 = 30 ft³

find the solution x = 3 + y 21x + 8y = -24

Answers

the answer is that y is -3 and x is 0
Answer:
x = 0
y = -3

Explanation:
The first given equation is:
x = 3 + y ............> I
The second given equation is:
21x + 8y = -24 ...........> II

Substitute with I in II and solve for y as follows:
21x + 8y = -24
21(3+y) + 8y = -24
63 + 21y + 8y = -24
29y = -24 - 63
29y = -87
y = -3

Substitute with y in equation I to get x as follows:
x = 3 + y
x = 3 + (-3)
x = 3 - 3
x = 0

Hope this helps :)

how is adding and subtracting decimals similar to and different from adding and subtracting whole number

Answers

Subtracting decimals, just like adding decimals, is similar to subtracting whole numbers. Just like adding decimals, the only difference is that we line up according to the decimal point instead of the last digit.

There isn't any real difference in adding and subtracting decimals from whole numbers but there is just a decimal point in front of the number to make it a decimal.

For example, 2 is a whole number but adding a .0 will make it 2,0 which makes it a decimal.

the floors of houses in japan are traditionally covered by tatami. tatami are rectangle shaped straw mats that measure about 6 feet by 3 feet. if a room is 48 feet by 24 feet, how many tatami are needed to cover the floor

Answers

Oh yikes, this one hasn't been answered in 4 years..

Let's get the area of one tatami, then the one of the floor.
Tatami area: 6*3 = 18 sq. feet

Floor area: 48*24 = 1152 sq. feet

To know how many tatami are needed, we need to divide the floor area by the tatami area:

1152/18 = 64

You'd need 64 tatami to cover the floor

How many playlists can we make with 38 songs if we can repeat 5 songs in each playlist? Use the permutation or combination formula if applicable.

Answers

38(greater than or equal to)5x

Final answer:

The number of playlists that can be created with 38 songs allowing for the repetition of 5 songs is calculated using combinations with repetition, resulting in a total of 850,668 possible playlists.

Explanation:

The question relates to the number of different ways we can create playlists from 38 songs, with the possibility of repeating 5 songs in each playlist. To calculate the number of different playlists that can be made by repeating songs, we need to use combinations with repetition. This is a concept in combinatorics which allows for the selection of items with replacements.

We can represent the problem with a formula used for combinations with repetition: (n + r - 1) choose r, where n is the total number of options (in this case, 38 songs) and r is the number of choices to make (in this case, repeating 5 songs). The formula becomes (38 + 5 - 1) choose 5, which simplifies to 42 choose 5. Using the combination formula, we can compute the total number of possible playlists as follows:

C(42, 5) = 42! / (5!(42-5)!) = 42! / (5!37!) = 850,668

This number represents the total number of playlists we can create with 38 songs, allowing for the repetition of 5 songs on each playlist.

I'll give brainliest to whoever shows there work to the answer. Plz answer quickly.
Which point best approximates the square root of 3?
A
B
C
D

Answers

The answer is B because the square root of 3 is 1.17
Hello there! When solved on a calculator, the square root of 3 is approx. 1.73. C and D are eliminated, because those points are farther on the number line, with C being at 2 and D being at 3. A is way too low, and it's not even close to 1, so A is out. The only point that works in this situation is B. Therefore, the answer is B.

HELP ASAP PLEASE HELP ASAP PLEASE HELP ASAP

The rental car holds 25 gallons of gas and gets 18 miles per gallon. The trip to Yarrow City is 1350 miles. How many times will the car need to be filled up to make the trip?

A. 2
B. 3
C. 4
D. 5

Answers

Your answer would be B. 3
The answer to your question is 3

CeeCee recorded the number of necklaces for sale at 10 different locations and then arranged the numbers from smallest to largest. The numbers of necklaces for sale at the locations were 4, 4, 4, 5, 8, 9, 9, 9, 9, and 9. The mean number of necklaces for sale at the locations was 7.

What is the mean absolute deviation?


A. 0

B. 2

C. 2.2

D. 4.4

Answers

The answer is 2.2. that means it's c.

Hope this helped☺☺

Answer: 2.2

Step-by-step explanation: I am in the test

Sum of 1.08, 2.16, and .003

Answers

the answer is 3.243 for the sum of them 

which phrase correclty describe the location on thr number line of opposite of -8? A a point 8 unit tot he left of -8. B a point 8 unit to the right of -8 C.a point 8 unit to the left of 0 D.a point 8 unit to the right of 0

Answers

I got d
I hope that helped

Helpppp!!!!Im not sure what this is, isn’t the square root of 144 a rational number and the square root of 34 a rational number, too?

Answers

The square root of 144 would be a rational number and square root of 34 is not rational because it can't be fit into a fraction
The answer would be 144

Write the following as a whole number:

19 thousands + 46 hundreds + 32 tens + 57 ones

Answers

23,977 is the answer to this problem, since this is a number problem. 

How many times greater is the value of 5 in 3,590 than the value of 5 in 359 ?

Answers

Answer:

10 times greater is the value of 5 in 3,590 than the value of 5 in 359.

Step-by-step explanation:

To find : How many times greater is the value of 5 in 3,590 than the value of 5 in 359 ?

Solution :

The place value stem is

Thousand     Hundred     Tens    Ones

  1000               100            10         1

The value of 5 in 3,590 is at hundred place

So, [tex]5\times 100=500[/tex]

The value of 5 in 359 is at tens place

So, [tex]5\times 10=50[/tex]

Number of time greater is the value of 5 in 3,590 than the value of 5 in 359 is given by,

[tex]n=\frac{500}{50}[/tex]

[tex]n=10[/tex]

Therefore, 10 times greater is the value of 5 in 3,590 than the value of 5 in 359.

Final answer:

The value of 5 in 3,590 is 10 times greater than the value of 5 in 359 because the 5 in 3,590 represents 500 while in 359 it represents 50.

Explanation:

The question asks how many times greater the value of 5 in 3,590 is compared to the value of 5 in 359. In the number 3,590, the 5 is in the hundred's place, meaning it has a value of 500 (5 x [tex]10^2[/tex]). In the number 359, the 5 is in the ten's place, meaning it has a value of 50 (5 x [tex]10^1[/tex]). To find out how many times greater one value is than the other, we divide the larger by the smaller

So, 500 divided by 50 equals 10. This means the value of 5 in 3,590 is 10 times greater than the value of 5 in 359.

A rectangular prism measures 2 2/5 inches by 3 1/5 inches by 2 inch. Priya said, it takes more cubes with edge length 2/5 inch cubes than cubes with edge length 1/5 to pack the prism. Do you agree?

Answers

I don't agree.
Cubes with the edge length of 2/5 have a volume of 0.064 while 1/5 edge length had a volume of 0.008 it will take 8 times more cubes to fill it with the 1/5 edge length squares than the 2/5 edge length squares.

No, she is not correct.

The volume of cubes with side 2/5 inches is : [tex](\frac{2}{5}) ^{3}[/tex] = 8/125 [tex]in^{3}[/tex]

and the volume of cubes with side 1/5 inches is : [tex](\frac{1}{5} )^{3}[/tex] = 1/125 [tex]in^{3}[/tex]

The cubes with sides 1/5 inches have 8 times lesser volume than that of the cubes with sides 2/5 inches.

So, to fill up the same volume, we would require 8 times more cubes of side 1/5 inches than cubes of side 2/5 inches.

Learn more:

https://brainly.com/question/23984629

Three consecutive even integers add to −6. What are these integers?

Answers

Let's consider the smallest even integer = x.

then second even integer = (x + 2).

and third even integer = (x + 4).


So three consecutive even integers would be x, (x + 2), and (x + 4).

The sum of these numbers is -6. Its equation would be as follows :-

x + (x + 2) + (x + 4) = -6

3x + 6 = -6

3x = -6 - 6

3x = -12

x = -4


So first number = x = -4

second number = (x + 2) = -2

third number = (x + 4) = 0

Hence, three consecutive even integers are -4, -2, and 0

Answer:

-4, -2, and 0

Step-by-step explanation:

1. All numbered streets runs parallel to each other. Both 3rd and 4th Streets are intersected by King Ave. as shown:

(a) Suppose a car is traveling east on 4th Street and turns onto King Avenue heading northeast. What is the measure of the angle created by the car's turning? Explain your answer.
(b) Suppose a car is traveling southwest on King Avenue and turns left onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.
(c) Suppose a car is traveling northeast on King Avenue and turns right onto 3rd Street. What is the measure of the angle created by the car's turning? Explain your answer.

Answers

Q1)
As shown in the diagram attached, the angle made between 4th street and king avenue if car is traveling from the west side is 75°. 
when the car is travelling from the east side and is supposed to take a turn towards north east lets call the angle it makes with the turn as x.
4th street is a straight road, therefore straight line 
 and sum of angles of a straight line is 180°.x and 75 are supplementary angles. 
Therefore x + 75° = 180°
x = 105°
therefore the angle it makes in the turn is 105°

Q2)
When the car is travelling south west and turns left towards 3rd street, the angle it makes is termed as y. when 2 parallel lines are cut by a transversal, x° and y° are corresponding angles. 
This means that the angle at which transversal cuts 3rd street and 4th street to the left are both equal. these are called corresponding angles.
this means that x = y
as derived in the previous question, x = 105°, 
hence, y = 105°.

Q3)
When the car is travelling north east and turns right onto 3rd street, lets name the angle it makes with the turn as z.
angles y and z are called vertically opposite angles. When 2 straight lines cut each other, the opposite angles formed are equal to each other.
Therefore y = z.
as derived in the previous question y = 105°. 
since y = z
hence, z = 105°


Answer:

the guy is right except number 2

Step-by-step explanation:

if the car turns left that means it went west and since 4th and 3rd street are parallel and King Ave. is a transparent then street 4 and 3 have the same angles. y is 75 and a vertical that means the car makes a 75 degrees angles .

sorry for the bad explanation

Suppose MyBook has roughly 1,000,000 users, and as each member signs up for an account, he or she is assigned a number. Which of these would result in the smallest sample size using systematic sampling?
A. Surveying every 25,000th number
B. Surveying every 250th number
C. Surveying every 25th number
D. Surveying every 2500th number

Answers

Final answer:

In systematic sampling, a higher n-value (every nth number) means fewer members are selected, thus smaller sample size. Therefore, surveying every 25,000th number results in the smallest sample size.

Explanation:

In systematic sampling, every nth member of a population is chosen for sampling. The smaller the value of n, the larger the sample size will be, because you're selecting a member more frequently. When we compare the options given: A. 25,000, B. 250, C. 25, and D. 2500, we see that option A (the 25,000th member), will result in the smallest sample size. In this scenario, for a total user base of 1,000,000, selecting every 25,000th member would produce approximately 40 samples (1,000,000 / 25,000 = 40), which is less than what you'd get with the other options.

Learn more about Systematic Sampling here:

https://brainly.com/question/28807640

#SPJ12

Other Questions
Area of a square with sides of length 1/3 yard .how did you get 1/9 PLEASE PLEEEASE HELP ME IM BEGGING YOU WITH ALL MY HEART YOU GET 20 POINTS Solve for m:(m-4)^3 = (1/8)^-1 Which relation is a function of x? A point charge of +1.0 C is moved in the direction of an electric field, and it has a change in electric potential difference energy of 10.0 J. What was the change in electric potential difference? 1 C = 10^-6 C 1.0 108 V 1.0 107 V +1.0 107 V +1.0 108 V, A bicycle store costs $1700 per month to operate. The store pays an average of $75 per month. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even? Homologous chromosomes undergo crossing over during _______ of meiosis. prophase i and ii of meiosis. prophase i of mitosis. prophase ii of meiosis. prophase i of meiosis. anaphase ii of meiosis. What is the purpose of the exposition in a story?to provide a resolution to the conflictto increase the suspense or conflict in the storyto provide an exciting turning point in the storyto fill in bacjground information for the reader DO NOT ANSWER JUST TO GET THE POINTS which popular song had a profound social effect and was used to raise funds for famine victims Analyze significant foreign policy events during the Truman, Eisenhower, Kennedy, Johnson, and Nixon administrations. You are purchasing a spread and want to avoid trans fatty acids. which would you avoid since it is the most likely to contain trans fatty acids? If PQRS is a parallelogram, what is the value of Y With the rise of nation-states, new countries discovered nationalism, or a pride in common ethnic heritages, cultures, and beliefs. However, nationalism often created negative consequences. In a few sentences, explain the drawbacks of nationalism. What might go wrong? please help asap! 54 points answer asap Malia created a correct function table using the equation g = 4f. Which table could be Malia's?A.B.C. Read this passage:This argument appeals to the wheelchair ethos of the wealthy, upper-middle class American slob. If Rainbow Bridge is worth seeing at all, then by God it should be easily, readily, immediately available to everybody with the money to buy a big powerboat. Why should a trip to such a place be the privilege only of those who are willing to walk six miles? Or if Pike's Peak is worth getting to, then why not build a highway to the top of it so that anyone can get there? Anytime? Without effort?Edward Abbey, How would you best describe the tone the author is using in this passage?A. GloomyB. RegretfulC. FunnyD. Sarcastic A person who is interested in the role of genetics in health might pursue a career in A)endocrinology B)gene therapy C)neuroscience D)sports medicine order these units from smallest to largest:cm,um,km,mm,m,nm,dm,pm. then give each a measurement in terms of meters. What was the significance of george kennan's long telegram? The Bill and Melinda Gates Foundation hires you as a consultant to determine how best to use $20 billion to save the world. Whats your plan? Which of the following is the most acidic: HBrO3, HFO3, HIO3, and HClO3?