Anna, Stephanie, and James all start running around a track at 8:00. Anna completes a lap every 4 minutes, Stephanie finishes a lap every 7 minutes, and James finishes a lap every 6 minutes. What is the earliest time when all three meet back at the beginning?

Answers

Answer 1

Answer:9:24

Step-by-step explanation:

We know that they will meet some time $T$ after 8:00 and that $T$ must be a multiple of 4, 7, and 6. So our job is to find the smallest multiple of those three numbers. Since 4 and 7 share no factors, the first number that is a multiple of both will be $4\cdot7=28$. Next, we must find the smallest multiple of 28 and 6. We can do this in two ways: by listing multiples of 28 until we find one that is a multiple of 6 or by finding what factors of 6 that 28 is missing and multiplying by those factors.

Method 1: The multiples of 28 go 28 (not divisible by 6), 56 (not divisible by 6), 84 (which is divisible by 6!)... So the smallest multiple of 4, 7, and 6 is 84.

Method 2: The factors of 6 are 1,2,3, and 6, so we can write 6 as $2\cdot3$. 28 is divisible by 2 but not by 3, so we must multiply it by 3. We find $28\cdot3=84$ and 84 is therefore the smallest multiple of 4, 7, and 6.

Now we just need to find the time that is 84 minutes after 8:00. Since 9:00 is 60 minutes after 8:00, we just need 24 more minutes after that (since $60+24=84$). The final time is therefore $\boxed{9:24}.$

Answer 2

Hence, the earliest time when all three meet back at the beginning is [tex]9:24[/tex].

What is the division?

Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers.

Here given that,

Anna, Stephanie, and James all start running around a track at [tex]8:00[/tex]. Anna completes a lap every [tex]4[/tex] minutes, Stephanie finishes a lap every [tex]7[/tex] minutes, and James finishes a lap every [tex]6[/tex] minutes.

So, the smallest multiple of [tex]4, 7[/tex] and [tex]6[/tex] is [tex]84[/tex].

Now we just need to find out the time is [tex]84[/tex] minutes so after [tex]8:00[/tex], it would be [tex]9:00[/tex] is [tex]60[/tex] minutes then after [tex]8:00[/tex], we need to move [tex]24[/tex] minutes more after that. The final time is [tex]9:24[/tex].

Hence, the earliest time when all three meet back at the beginning is [tex]9:24[/tex].

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Related Questions

A traveler is walking on a moving walkway in a n airport. The traveler must walk back on the walkway to get a bag he forgot. The traveler's ground speed is 2 ft/s against the walkway and 8 ft/s with the walkway. What is the traveler's speed off the walkway? What is the speed of the moving walkway?

Answers

Answer:

The traveler's speed off the walkway is 4 ft/sec

The speed of the moving walkway is 2 ft/sec

Step-by-step explanation:

pls help me ALAP ,in the class there are 48 students. the number of girls is 3 times the number of boys .how many boys and how many girls are there in the class​

Answers

Answer:

Number of boys = 12

Number of girls = 36

Step-by-step explanation:

Number of boys = x

Number of girls = 3*x = 3x

Total students = 48

x + 3x = 48

   4x = 48

    x = 48/4

    x = 12

Number of boys = 12

Number of girls = 3*12 = 36

CAN SOMEONE PLEASE HELP ME SOLVE THIS!? ASAP PLEASE!!

Find the area of the figure. Round to the nearest hundredth.

Answers

Answer:

Step-by-step explanation:

Break down the figure into a circle of diameter 7 and an 11 by 7 rectangle.

Area of circle = π3.5² = 12.25π ≈ 38.48 square meters

Area of rectangle = 11*7 = 77 square meters

Total area = 38.48+77 = 115.48 square meters

this is the question for

Answers

The answer is choice b

In the following equation, which number is the slope (rate of change) and which is the y-intercept?

y = 32 - 4

Slope:

Y-Intercept:

Answers

Answer: Slope: 3z

Y intercept: -4

Step-by-step explanation:

Are the Triangle similar? Why or why not?

Answers

Answer:

No, they are not similar

Step-by-step explanation:

The three triangle angles should always add up to 180 degrees.

In the smaller triangle, one angle is 90 degrees, so the other 2 angles in that triangle will equal 90 when added.

In the bigger triangle, the 2 other angles are 60 & 70 degrees, amounting to 130 degrees. This means the last angle will be 50 degrees.

In the end, these two triangle are NOT similar because one has a right angle and the other doesn't.

Plz help and show me how to solve these questions

Answers

since -15/16 is a negative number, we can add both sides by 15/16 or subtract both sides by -15/16. Either way works.

p = 1/8 + 15/16

Use common denominator, which is 16:

p = 1(2)/8(2) + 15/16

p = 2/16 + 15/16

p = 17/16

17/16 is an improper fraction. If you want to use a mixed number for your answer, then:

17/16 becomes 1 1/16 (one and one-sixteenth, with 1 being a whole number and 1/16 being a fraction)

Answer: 17/16 or 1 1/16

please i need help!! i’ll put brainliest and 30 points.

Two shipping companies charge different amounts to mail packages. UPS charges
an initial $5 fee, and each pound shipped is an additional $1. Fed Ex charges an
initial $3 fee, and $1.50 for each pound shipped.
a.) How much would each company charge to mail a package weighing 2
pounds?
b.) For what weight package will the two companies charge the same amount?
c.) Which company charges less for a 6-pound package? How much will you
save by choosing this company to ship your 6-pound package?

Answers

Answer:

A. UPS- $7 Fed Ex- $6

B. 4 pounds

C. UPS by one dollar

Step-by-step explanation:

don’t give me a link please just an answer, the right one at least

Answers

Answer:

27.5 mph

Step-by-step explanation:

The mean is the average of the numbers. It is easy to calculate: add up all the numbers, then divide by how many numbers there are. I

After you add up all the numbers you get : 330 mph

330 mph divided by 12 is 27.5

27.5 mph is the answer :)

HELP ME PLEASE!!,I WILL GIVE BRAINLIEST!!

Answers

Answer:

D

Step-by-step explanation:

The answer is correct and cannot be simplified any further. Can I get that brainliest thay you promised me last time?

Hope this helps

Answer:

The Answer is D!

Step-by-step explanation:

A bag contains 36 red balloons, 40 blue balloons, and 24 purple balloons. Find the probability of NOT choosing a purple balloon.
Group of answer choices

A 3/4

B 76%

C 0.25

D 24%

Answers

add the numbers up
36+40+24=100
36+40=76
76/100 simplified is 19/25
19 divided by 25 is 76%
It’s B. All that equals to 100 so divide and it is equal to 76%

PLEASE ANSWER HONESTLY (PLEASE BE HELPFULL I HAVE BEEN STUCK ON THIS PROBLEM) WILL MARK BRANIEST IF CORRECT. (no links my computer is slow and no ctrl c ctrol v if possible
Given a right triangle with leg lengths f and g, and hypotenuse h, if f = 6 inches and g = 8 inches, what is h

Answers

Answer:

I put the answer as a picture because it wouldn't let me write out the equations and use some characters :(

Step-by-step explanation:

Hopefully this helped :))

If the zeroes of a quadratic function, G, are 4 and -2, what is the equation of the axis of symmetry of G

Answers

9514 1404 393

Answer:

  x = 1

Step-by-step explanation:

The axis of symmetry is the vertical line halfway between the zeros.

  x = (4 -2)/2

  x = 1 . . . equation of axis of symmetry

1. Write a multiplication equation and a division equation that this diagram could
represent.
54
18
18
18

Answers

Answer:

54 ÷ 18

18 x 3

Step-by-step explanation:

54 ÷ 18 is 3

and 18 x 3 is 54

We can write the multiplication expression and a division expression as

(54 ÷ 18)(18 x 18)

What is multiplication and division?In math, to multiply means to add equal groups. When we multiply, the number of things in the group increases. Division is the process of splitting a number or an amount into equal parts

Given are the numbers as 54, 18, 18, 18.

We can write the multiplication expression and a division expression as-

(54 ÷ 18)

(18 x 18)

Therefore, we can write the multiplication expression and a division expression as

(54 ÷ 18)(18 x 18)

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50 <8-6x
Pls help ASAP

Answers

Answer:

x = -7

Step-by-step explanation:

X equals negative seven

I have two congruent sides.I also have two congruent angle i am (n) -------- that measures 45 each s

Answers

Answer:

Isosceles triangle

Step-by-step explanation:

Given

Two congruent angles and two congruent sides

Base on the given description, the concept being described is an isosceles triangle, as it has two congruent sides and two congruent angles.

If each angle measures 45 degrees each, then the third angle is 90 degrees.

This is shown below.

[tex]\theta + 45 + 45= 180[/tex] --- angles in a triangle

[tex]\theta + 90= 180[/tex]

Subtract 90 from both sides

[tex]\theta = 90[/tex]

Someone please help ! how do I solve this?

Answers

Answer:

A=14.9

B=25.6

C=25.5

Step-by-step explanation:

[tex]\frac{25,5}{sin71} =\frac{14.9}{sin^{0} } \\\\sinx^{0}=\frac{14.9 sin 71}{25,5} \\\\x=sin ^{-1}(\frac{14.9 sin 71}{25,5} \\\\x=33.54\\\\[/tex]

[tex]180-71-33.54=75.46 \\\\B:\frac{b}{sinB} =\frac{25.5}{sin71} \\[/tex]

[tex]b=\frac{25.5 sin 75.46}{sin 71} \\\\b=26.106\\\\b=26.1\\\\x=33.54[/tex]

hope it helps...

have a great day

Please explain! What is the solution for the inequality below:
12- x<8
Please help!!!!!

Answers

Answer:

The solution for the inequality is x>4.

Carlos needs to paint the outside of the shed in his backyard, including its roof but not including its floor. A rectangular prism with a length of 8 feet, width of 5 feet, and height of 6 feet. What is the total area of the surfaces that he needs to paint? 214 feet squared 230 feet squared 300 feet squared 350 feet squared

Answers

Answer:

It's 230 feet squared! (aka B)

Step-by-step explanation:

I just took the test :)

Answer:

B.) 230 feet squared.

Step-by-step explanation:

I hope this helps!! :)

Calculate the slope of the line that contains the points (-2, -4) and (2, 4).

Answers

Answer:

Slope is 2

Step-by-step explanation:

(-2, -4) and (2, 4)

Slope:

m=(y2-y1)/(x2-x1)

m=(4+4)/(2+2)

m=8/4

m = 2

Last year Rikki sang 960 songs with his rock band. How many songs did he sing per month? How did you get your answer?

Answers

If he sang the same number of songs each month, he sang 80 songs per month.

960/12 (months) = 80 (songs per month)

determine the sum of the prime factor of 675​

Answers

Answer:

5 ÷ 5 = 1 - No remainder! 5 is one of the factors! The orange divisor above are the prime factors of the number 675. If we put all of it together we have the factors 3 x 3 x 3 x 5 x 5 = 675.

Step-by-step explanation:

SPEED RUN

The sum of the prime factor of 675​ is, 8.

What is Addition?

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

Given that;

Number is,

⇒ 675

Now, Factorization of 675 is,

⇒ 675 = 3 x 3 x 3 x 5 x 5

Hence, Prime factors of 675 are 3 and 5.

Thus, The sum of the prime factor of 675​ is,

⇒ 3 + 5

⇒ 8

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Let A = the sum of all 2-digit positive perfect squares. Let B= the sum of all 2-digit positive perfect cubes. Find A – B.

Answers

Answer:

180

Step-by-step explanation:

A = 16 + 25 + 36 + 49 + 64 + 81 = 271

B = 27 + 64 = 91

A - B = 271 - 91 = 180

Write a problem you could represent with the equation 3k - 12 = 6 . Solve the equation and show your solution .

Answers

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3k - 12 = 6}[/tex]

[tex]\large\text{ADD 12 to BOTH SIDES}[/tex]

[tex]\textsf{3k - 12 + 12 = 6 + 12}[/tex]

[tex]\large\text{Cancel out: -12 + 12 because it gives you 0}[/tex]

[tex]\large\text{Keep: 6 + 12 because it helps you solve for k}[/tex]

[tex]\mathsf{6 + 12 = 18}[/tex]

[tex]\large\text{New equation: 3k = 18}[/tex]

[tex]\mathsf{3k = 18}[/tex]

[tex]\large\text{DIVIDE 3 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{3k}{3} = \dfrac{18}{3}}[/tex]

[tex]\large\text{Cancel out: }\mathsf{\dfrac{3}{3}}\large\text{ because that gives you 1 }[/tex]

[tex]\large\text{Keep: }\mathsf{\dfrac{18}{3}}\large\text{ because that helps you solve for k}[/tex]

[tex]\large\text{New equation}\mathsf{\dfrac{18}{3}=k}[/tex]

[tex]\mathsf{\dfrac{18}{3}=18\div3\rightarrow\bf 6}[/tex]

[tex]\boxed{\boxed{\large\text{Answer: \huge\bf k = 6}}}\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

The circumference of a circular pond in the park is 120 meters. Find the area.

The formula for circumference is C = d.

What is the value of the diameter rounded to the nearest whole number?

Answers

Answer:

38.21 in

Step-by-step explanation:

Given data

C= 120meters

We also know that circumference

C=2πr

Substitute

120=2*3.142*r

120= 6.28r

r= 120/6.28

r= 19.10 m

Hence the diamter D

D= r*2

D= 38.21 in

Answer:

1 2 1

Step-by-step explanation:

A B A

5(x – 1) + 3x = 7(x + 1)

What is the solution?

Answers

Answer:

the answer is x=12

2a*5a⁷
what is this in it's smallest form​

Answers

Answer:

Step-by-step explanation:

[tex]2a(5a^7)\\ \\ 2(5)a(a^7)\\ \\ 10a^{(1+7)}\\ \\ 10a^8[/tex]

10a^8 hdhdjshshsusidbsjisosjd

cual es el valor de x en x4 = -8

Answers

Answer:56

Step-by-step explanation:

2x divide 4 from both sides.

If f(x)=x²+1 and g(x)=5x−3, what is f(g(x))?

Answers

Answer:

[tex]25x^{2} -30x+10[/tex]

Step-by-step explanation:

Plug in 5x-3 into f(x) so

[tex](5x-3)^2 + 1 = 25x^2 -30x+10[/tex]

Which term correctly describes the figure shown below?

An obtuse triangle ABC is shown. Angle A is 25 degrees, angle B is 110 degrees, and angle C is 45 degrees. Side AB is 6 meters, side BC is 4 meters, and side AC is 9 meters.
A. acute triangle
B. obtuse triangle
C. parallelogram
D. right triangle

Answers

Answer:

B) obtuse triangle

Step-by-step explanation:

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