Triplets Peter, Reeta and Nikita have two ways for getting home from school each day: cycle on a tandem bike or walk. The bike can carry either one or two riders at a time. Regardless of the number of people pedalling, cycling speed is 5 times walking speed. The triplets always leave school at the same time and always use the same path between school and home, whether walking or cycling. The school is 5km from home and their walking speed is 4 kilometres per hour. A On Monday, Nikita and Peter cycle and Reeta walks. On reaching the point four-fifths of the way home the bike gets a puncture, so Nikita and Peter walk the rest of the way home. How far from school is Reeta when the cyclists arrive home?

Answers

Answer 1

The distance between Reeta and the school when the cyclists arrive the home for this case is found being 2 km

How to form mathematical expression from the given description?

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

How to find the speed of an object?

If the object is going linearly, and at constant speed, then the speed of that object is given by the distance it traveled to the time it took to travel that distance.

If the object traveled D distance in T units time, then that object's speed is

[tex]Speed = S = \dfrac{\: Distance \: traveled}{\: Time \: taken} = \dfrac{D}{T} \: \rm unit \: length/unit \: time[/tex]

Given that:

Distance from school to home = 5 kmWalking speed = 4 km / hoursCycling speed = 5 times walking speed = 20 km / hourThey all go and come together to and from school/home.On monday: Nikita and Peter are coming by cycle, and Reeta walks.Cycle punctures at four fifth of the way home = [tex]\dfrac{4}{5} \times 5= 4\: \rm km[/tex] from school (as they're coming towards home, so went from school)After puncture, cyclists walk to home

To find: Disance of Reeta from school when cyclist reach home.

Suppose at time 0 hours, all three people departed from school (on that monday).

After 't' hours, suppose the cycle gets punctured.

Then, as the cycle was going by 20 km / hour speed, so in 't' hours, it must have covered d kilometers (suppose),

then we get:
[tex]S = \dfrac{D}{T}\\\\20 = \dfrac{d}{t}\\\\d = 20 t \: \rm km[/tex]

This distance is measured from school. But we know that this distance is 4 km, so we get:

[tex]20t = 4\\t = \dfrac{4}{20} = 0.2 \: \rm hours[/tex]

The remaining 1 km (as home is 5 km away from school and 4 km is already traveled) is walked by Cyclists. And walking speed is 5 km / hour, so let they take T hours to travel that 1 km walking, then we get:
[tex]S = D/T\\\\5 = \dfrac{1}{T} \\\\T = 0.2 \: \rm hours[/tex]

So, total time cyclists took to reach home from school is: [tex]0.2 + 0.2 = 0.4 \: \rm hours[/tex]

Reeta is walking that whole 5 km.

The time the cyclist reached home, Reeta had walked for 0.4 hours as they had started at the same time, and it took cyclists 0.4 hours to reach home.

Thus, we have:

Time taken  0.4 hours, speed of Reeta = walking speed= 5 km/hour, then we get:

[tex]S = D/T\\D = ST\\D = 5 \times 0.4 = 2 \: \rm km[/tex]

So Reeta was 2 km away from school when cyclists reached home on that monday.

Thus, the distance between Reeta and the school when the cyclists arrive the home for this case is found being 2 km

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Related Questions

PLease Help Me Its A math Problem !!! As what value of x does the function f(x)=2(3)x overtake the function g(x)=2x^2+4x?
Question options:

x = 2


x = 3


x = 4


x = 1

Answers

Answer:

x=2

Step-by-step explanation:

To test when the function f(x) over takes the function g(x)

I just plugged in the x values

X f(x) g(x)

1 6 6

2 12 16

3 18 30

4 24 48

We can see from this table that f(x) is greater than g(x) starting from x=2

Therefore I think x=2 is your answer.

Hope this helps! :)

A survey of 2,000 registered voters is used to predict by how many percentage points a candidate is leading. Of the 2,000 people, 1,240 planned to vote for Candidate A. By how many percentage points is Candidate A leading?

I NEED HELP ASAP THIS IS FOR MATH AND IT A STUDY QUIDE AND I NEED HELP AND IT IS SUPPOSE TO BE TURNED IN TODAY

Answers

760 points I think check I should be correct if not I’ll Take a look

x+2x+6x+18=180. Solve for x.

Answers

=》 Solution;

solving,

x+2x+6x+18=180

or, 9x + 18 = 180

or, x + 18 = 180/9

or, x + 18 = 20

or, x = 20 - 18

or, x = 2

therefore, value of x is 2

now,

i) x = 1 X x = 1 X 2 = 2

ii) 2x = 2 X x = 2 X 2 = 4

iii) 6x = 6 X x = 6 x 2 = 12

no explanation is needed :) please help

Answers

Answer:

187 in^2

Step-by-step explanation:

hope this helps!

y = x -5
x + y = -1
whats the soultion for the systeam of eqations

Answers

Answer:

x = 2

y = -3

Step-by-step explanation:

y = x - 5  -------------------(I)

x + y = -1 ----------------(II)

Substitute y = x -5 in equation (II)

x + (x - 5) = -1

x + x - 5 = -1   {Combine like terms}

   2x - 5 = -1 {Add 5 to both sides}

        2x  = -1 + 5

         2x = 4 {Divide both sides by 2}

           x = 4/2

x = 2

Substitute x = 2 in equation (I)

y = 2 - 5

y = -3

Claire invested $2,300 in an account paying an interest rate of
6
1
4
6
4
1

% compounded annually. Henry invested $2,300 in an account paying an interest rate of
6
3
4
6
4
3

% compounded monthly. To the nearest dollar, how much money would Claire have in her account when Henry's money has tripled in value?

Answers

Using compound interest, it is found that Claire will have $6,186 in her account when Henry's money has tripled in value.

What is compound interest?

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.

For Henry, we have that r = 0.0675, n = 12. The time it takes for the amount to triple is t when A(t) = 3P, hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]3P = P\left(1 + \frac{0.0675}{12}\right)^{12t}[/tex]

[tex](1.005625)^{12t} = 3[/tex]

[tex]\log{(1.005625)^{12t}} = \log{3}[/tex]

[tex]12t\log{(1.005625)} = \log{3}[/tex]

[tex]t = \frac{\log{3}}{12\log{(1.005625)}}[/tex]

t = 16.32.

Then, for Claire, we have that the parameters are as follows:

P = 2300, r = 0.0625, n = 1, t = 16.32.

Hence, the amount is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]A(t) = 2300\left(1 + \frac{0.0625}{1}\right)^{16.32}[/tex]

A(t) = 6186.

Claire will have $6,186 in her account when Henry's money has tripled in value.

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Distributed property 3(4x-5)

Answers

the answer 12x-15
bc you multiply 4 and 3 to get 12x and then you multiply 5 and 3 to get 15

Answer:

Answer below!

Step-by-step explanation:

Alright I'm not too sure on what the question is asking for per your instructions, but I've written out my best explanation on how to use distributive property to solve this equation.

So first, what is the process of distributive property? It basically states whatever is in the parenthesis is multiplied by the outside number.

In simpler terms, each character in the parenthesis is multiplied by the number standing outside of the parenthesis.

So we can go...

(3 x 4x) - (3 x 5) = (12x) - (15)

And there's your answer, 12x - 15! Unless you know what x means, you'll probably just stop there.

Hope this was helpful!

From the options below, choose the two triangles that are congruent

Answers

QRM PRN From the options below, choose the two triangles that are congruent

PLSSSS HELP ME ASAP ILL GIVE YOU BRAINIEST!!!

Answers

Answer:

I believe it would be 8 11/20 ft³

Step-by-step explanation:

16,48,144,...
Find the 6th term.

Answers

Step-by-step explanation:

16, 48, 144

hmmm.

the first thing that comes to mind : it cannot be an addition, as the difference between the 2nd and 3rd numbers is much bigger than the difference between the 1st and 2nd numbers.

so, we try multiplication.

and I see : 16×3 = 48

aha !

48×3 = 144

ok, we found it. the sequence is clearly created by multiplying always the previous number by 3.

so, we have 2 main choices to get the 6th term :

1. simply calculate 144 ×3×3×3 (3 times to get from the 3rd to the 6th term).

2. define the sequence formula and calculate for the 6th term.

1.

144 × 3×3×3 = 144 × 27 = 3,888

2.

a1 = 16

a2 = a1×3 = 16×3 = 48

a3 = a2×3 = a1×3×3 = 16×9 = 144

an = a1 × 3^(n-1) = 16 × 3^(n-1)

a6 = 16 × 3⁵ = 16 × 243 = 3,888

Delta Math: Angle Terminology with Equations

Answers

Answer:

m∠A = 139°

Step-by-step explanation:

Since knowing that:

Supplementary angles = 180 degree

Thus we put that in both equation:

( 7x - 15 ) + ( 2x - 3 ) = 180

Combine like terms & use inverse operations to find the value of x:

( 7x - 15 ) + ( 2x - 3 ) = 180

9x - 18 = 180

9x - 18 + 18 = 180 + 18

9x  = 198

9x/9 = 198/9

x = 22

Hence,  Angle A will have a measure of 7x - 15 which means  7 ×  22 -15 = 154 - 15 = 139°

m∠A = 139°

The measure of Angle B will be 2x - 3 = 2 • 22 - 3 = 44 - 3 = 41°

m∠ B = 41°

Check Answer by add 139 and 31 which equal 180

~lenvy~

A grocery store buys organic
apples for $0.75 per apple. The
store marks up the cost of each
apple by 23%. How much will each
apple cost at the store?

Answers

Answer:

ok so 23 percent more means thats its the oringaly price times 1.23 so

0.75*1.23=9.225

92 cents per apple

Hope This Helps!!!

help me please. don't mine the blue dot on answer A.

Answers

Answer:

2 quarts .

Step-by-step explanation:

4 quarts make a gallon but two is already added

Answer:

2 quarts

Step-by-step explanation:


An airplane flying at 650 miles per hour has a bearing of 54. After flying for 1.5 hours, how far north and how far east will the plane have traveled from its point of departure?

Answers

Answer:

627 miles north

747 miles east

Step-by-step explanation:

Bearing angles are measured east of north, so in (N, E) coordinates, the final position of the plane is ...

 (1.5 h)(650 mi/h)(cos(50°), sin(50°)) = (975cos(50°), 975sin(50°)) mi

 = (626.72, 746.89) mi

The plane will be 627 miles north and 747 miles east of its point of departure.

Given the parallelogram WEST below. Write a proof to show without using the theorem that states that diagonals of a parallelogram bisect each other

Answers

The theorem simply states that diagonals of a parallelogram bisect each other is proven as OA = OC.

How to proof the parallelogram?

From the information, OA = OC and OB = OD. In both triangles AOD and BOC, AD = BC since opposite angles are equal.

Also, ADO = CBO since alternate interior angles are equal. Also, DAO = BCO.

Therefore, OA = OC

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in the figure below, what is the measure of angle x

Answers

Check the picture below.

Helppppppp 50 points!!!!!!!!!!!!!
which angle has its terminal side on the positive y-axis?

2pi radians
pi radians
pi/2 radians
3 pi/2 radians

Answers

Answer:

[tex]\sf \dfrac{\pi}{2}[/tex]

Step-by-step explanation:

Angles are measured in a counterclockwise direction from the positive x-axis (initial side).

Therefore, if an angle's terminal side is on the positive y-axis, the angle will be 90° or [tex]\sf \dfrac{\pi}{2}[/tex] radians.

See attached diagram for visual explanation.

If the angle was [tex]\pi[/tex] then the terminal side would be on the negative x-axis.

If the angle was [tex]\dfrac32\pi[/tex] then the terminal side would be on the negative y-axis.

If the angle was [tex]2\pi[/tex] then the terminal side would be on the positive x-axis and the angle would be one complete revolution of the circle.

A candy company claims that their bags of jellybeans have a mean weight of 9. 45 oz. 125 randomly chosen bags of jellybeans were sampled, and it was discovered that their mean weight was 9. 68 oz, with a standard deviation of 1. 23 oz. Test this hypothesis using a 99% confidence level

Answers

The hypothesis illustrates that C. Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.

How to illustrate the information?

Using a graphing calculator and calculated the t-interval of the jellybean sample using a 99% confidence level:

tInterval 9.68,1.23,125,0.99

It resulted in 9.68 ± 0.287805.

Therefore, we're 99% confident that the weight number of jellybeans would lie between 9.3922 oz and 9.9678 oz.

Therefore, the researcher failed to reject the null hypothesis.

Complete question:

A weight of 9.45 oz lies within this range, therefore, it is possible that the candy company's claim is true.

A candy company claims that their bags of jellybeans have a mean weight of 9.45 oz. 125 randomly chosen bags of jellybeans were sampled, and it was discovered that their mean weight was 9.68 oz, with a standard deviation of 1.23 oz. Test this hypothesis using a 99% confidence level.

A- Reject the null hypothesis. There is not enough evidence to oppose the company's claim.

B- Reject the null hypothesis. There is enough evidence to oppose the company's claim.

C- Fail to reject the null hypothesis. There is not enough evidence to oppose the company's claim.

D- Fail to reject the null hypothesis. There is enough evidence to oppose the company's claim.

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PLEASE I NEED HELP 40PTS


For his phone service, Ryan pays a monthly fee of $10, and he pays an additional $0.06 per minute of use. The least he has been charged in a month is $92.74. What are the possible numbers of minutes he has used his phone in a month? Use m for the number of minutes, and solve your inequality for M.

Answers

you have to subtract from the $92.74 the $10 of the monthly fee, and then that is divided by the additional amount per minute, so that gives us the result I use it 1379 minutes

Solve for X if two adjacent angles form a straight line and their measurements are 2x degrees and 3x degrees

Answers

Use all your techniques of angles to help you

Which of the following points are in the second quadrant of the xy plane?
Check all that apply.
A. (6, -2)
B. (-2, -8)
C. (-7, 6)
D. (2,2)
E. (-4, 2)
F. (4,8)

Answers

Answer:

a

Step-by-step explanation:

 Answer: a and b bc that are in the negative-positive quad

C and E
The quadrants go in the order of the letter c so quadrant one is top right, while quadrant four is bottom right :)

The sum of two numbers is -19. One number is 28 more than the other one. Find the numbers.

Answers

Answer:

-47

Step-by-step explanation:

28+ ___=-19

28+x= -19

-28 -28

_________

X= -47

28+-47= -19

Consider today’s stock listing for rayje clothiers, shown below. 52 wk high 52 wk low symbol div. close net change 225.80 169.96 raj 25.10 200.43 13.74 today, you sold the 459 shares of rayje clothiers that you purchased yesterday. how much profit did you make? a. $13,985.73 b. $11,520.90 c. $5,338.17 d. $6,306.66

Answers

If he sold the 459 shares of rayje clothiers that you purchased yesterday. The amount of profit is: d. $6,306.66.

Profit

Using this formula

Profit=Net change×Number of shares sold

Where:

Net change=$13.74

Number of shares sold=459 shares

Let plug in the formula

Profit=$13.74×459 shares

Profit=$6,306.66

Therefore the amount of profit is: d. $6,306.66.

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2 1/2 x 2 1/4
Multiply, write the answer as a mixed number in the simplest form.

Answers

Answer:

5 1/2

Step-by-step explanation:

2x2=

4

2 x 1/2 =

1

2 x 1/4=

1/2

1+1/2=

1 1/2+4 =

5 1/2


A toy ball can be modeled as a sphere. Eva measures its diameter as 15.7 cm. Find the
ball's volume in cubic centimeters. Round your answer to the nearest tenth if necessary

Answers

Answer:

[tex]v = 2064.2 {cm}^{3} [/tex]

Step-by-step explanation:

we first consider the formula for the volume of a sphere

[tex]v = \frac{4}{3} \pi {r}^{3} [/tex]

we were given diameter of 15.7cm.

we can find the radius by dividing the diameter by 2

because two times a radius makes a diameter.

[tex] \frac{15.7}{2} = 7.9cm[/tex]

we have the radius as 7.9cm.

and we know pi (π) to be 3.14 or 22/7.

but in this case, we use 3.14.

now let's substitute the values in the formula

[tex]v = \frac{4}{3} \times 3.14 \times {7.9}^{3} [/tex]

and we will get

[tex]v = 2064.19 {cm}^{3} [/tex]

but the nearest 10th will be

[tex]v = 2064.2 {cm}^{3} [/tex]

Answer: is 2026.3 cm ^3

Step-by-step explanation:

A data set has the following characteristics: mean: 4.9 median: 6 mode: 6 variance: 4 the z-score is the number of a data value is away from the .

Answers

The z-score is the number of standard deviations while the data value is away from the mean.

What Is a Z-Score?

The Z-score is said to be a kind of numerical measurement that is known to show or depicts the value's relationship one has to the mean of a group of values.

WE have given a mean: 4.9 median: 6 mode: 6 variance: 4

The Z-score is often measured usually in terms of standard deviations that arise from the mean. It means that if a Z-score is 0, it shows that the data point's score is the same as the mean value.

Learn more about z-score:

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Answer:

standard deviations, mean.

Step-by-step explanation:

EDGE2022

How many 2-centimeter cubes can fit into a rectangular prism with dimensions 12cmx20cmx4cm?

Answers

Answer:

  120 cubes

Step-by-step explanation:

This kind of problem can be easier to work if you rewrite the prism dimensions in terms of cube dimensions. For 2 cm cubes, the prism dimensions are ...

12 cm = 6 cube lengths20 cm = 10 cube lengths4 cm = 2 cube lengths

As always, the volume of the rectangular prism is the product of its dimensions:

  V = (6)(10)(2) = 120 cubes

120 2-cm cubes will fit int the rectangular prism.

please help me it’s due today at 9:10am :(
I will give brainliest please help me

Answers

1) 720 inches³

2) 900 inches³

3) 120 inches³

hope it helps...!!!

For each of 7 weeks babysitting, Kelly made the following dollar amounts:

16, 28, 28, 32, 21, 18, 35

What is the first quartile of this data?

a
35
b
28
c
32
d
16
e
18

Answers

Answer:

28

Step-by-step explanation:

in order to find first quartile find median:

median =32

since there are 6 data points lets split the data set into 2 groups of 3 data points each

the median of the first group is the first quartile and the median of the second group is the third quartile

group 1: 16 28 28

median=28

1st quartile=28

Find the volume 18in 7in 30in 12in

Answers

Answer:

1890 in³

Step-by-step explanation:

The formula to find the volume of a triangular prism: 1/2 x b x h x l, where b is the base, h is the height and l is the length.

1) Substitute the given values in the image into the formula above.

= 1/2 x 18 x 7 x 30

= 1/2 x 126 x 30

= 1/2 x 3780

= 1890

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