Nathan runs around the inside lane of a circular track that has a radius of 29 m.
Rachel runs in the outer lane, which is 2.5 m further from the centre of the track.
How much longer is the distance Rachel runs each lap? Give your answer to 2
decimal places.

Answers

Answer 1

Hey there! I'm happy to help!

The distance around a circle is the circumference. To find it, you multiply the diameter of the circle by pi (we will use 3.14).

First, let's find the circumference of Nathan's circle. We see that the radius is 29. The diameter is twice the radius, so the diameter is 56. We multiply this by 3.14, giving us 175.84 m.

We see that Rachel is 2.5 m further from the center than Nathan's, so her radius is 31.5 m. We multiply by two to give us the diameter, giving us 63. We multiply this by 3.14, giving us 197.82.

Now, we subtract Nathan's lap distance from Rachel's to see how much longer her's is.

197.82-175.84=21.98

Therefore, the distance Rachel runs is 21.98 meters longer than the distance Nathan runs.

Have a wonderful day! :D


Related Questions

Mary earns $28,000 a year. One week she grossed $658.00. She had sold $1673.19 worth of merchandise. what is the rate of her commission?

Answers

Answer:

Her commission rate is 7.44%

Step-by-step explanation:

The parameters given are;

The amount Mary earns annually = $28,000

The amount Mary grossed during a week = $658.00

The amount Mary had sold during the week to make the amount grossed during the week = $1673.19

Given that Mary makes $28,000 per year

Therefore;

The amount Mary earns per week = Amount earned per year/52

The amount Mary earns per week =  $28,000/52 = $538.46

The amount extra she made on commission = $658.00- $538.46= $119.54

The commission rate = Commission earned/(Amount of merchandise sold)×100

The commission rate = 119.54/1673.19 × 100 = 7.14%

Her commission rate = 7.44%

Someone please help! Thank you

Answers

Answer:

110

Step-by-step explanation:

the sum of straight angle is 180

the sum of angle of triangle=180

angle E=180-120=60

triangle BDE: <B=180-60-90=30

<B in triangle ACB=180-(130+30)=20)

in traingle ACB: <A = 180-(90+20)=70

angle x=180-70=110 degrees

PLEASEEEEE I don't understand this question.

Answers

Answer:

  262°

Step-by-step explanation:

The relationship between the angle at B (82°) and the arcs of the circle, CGF and CDF, is that the angle is half the difference of those arcs. Of course the sum of those arcs is 360°, since together they make a full circle. So. we have ...

  CGF +CDF = 360

  (CGF -CDF)/2 = 82

We need to solve this system of equations to find CGF.

__

Multiplying the second equation by 2 and adding the first, we get ...

  2((CGF -CDF)/2) +(CGF +CDF) = 2(82) +(360)

  2CGF = 524 . . . . . simplify

  CGF = 262 . . . . . . divide by 2

The measure of arc CGF is 262°.

_____

Alternate solution

Here's another way to get there. Arc CDF is the supplement to angle B, so is ...

  CDF = 180° -∠CBF

Of course, arc CGF is 360° minus arc CDF, so ...

  CGF = 360° -(180° -∠CBF)

  CGF = 180° +∠CBF . . . . . simplify . . . please note this is a general solution

Then ...

  arc CGF = 180° +82° = 262°.

plzzzz answer right away will mark BRAINLIST AND FIVE STARS PLUS The table below shows the possible outcomes of rolling a six-sided number cube and flipping a coin. A 7-column table with 2 rows. Column 1 has entries H, T. Column 2 is labeled 1 with entries H 1, T 1. Column 3 is labeled 2 with entries H 2, T 2. Column 4 is labeled 3 with entries H 3, T 3. Column 5 is labeled 4 with entries H 4, T 4. Column 6 is labeled 5 with entries H 5, T 5. Column 7 is labeled 6 with entries H 6, T 6. What is the probability of getting a number less than 3 and a tails? StartFraction 1 over 12 EndFraction StartFraction 1 over 6 EndFraction One-fourth One-third

Answers

Answer:

P((1 or 2) and Tail) = 1/6 = StartFraction 1 over 6

Step-by-step explanation:

A six-sided die and a coin.

Probability of getting <3 and tail.

P((1 or 2) and Tail)

= 2/6 * 1/2

= 1/6

Answer:

1/6

Step-by-step explanation:

Complete the general form equation of the parabola that passes through (4, -11) with vertex at : (2, -3).

Answers

Answer:

Step-by-step explanation:

You're given a coordinate in the form of (x, y) and you're also given the vertex in the form of (h, k). We will use those in the vertex form of the equation

[tex]y=a(x-h)^2+k[/tex] and solve for a. Filling in:

[tex]-11=a(4-2)^2-3[/tex] which simplifies a bit to

[tex]-11=a(2)^2-3[/tex] and a bit more to

[tex]-11=4a-3[/tex]. Add 3 to both sides to get

-8 = 4a so

a = -2

The equation, then, is

[tex]y=-2(x-2)^2-3[/tex]

A ladder placed against a vertical wall subtends an angle of 45 degree with the wall. The distance between the foot of the ladder and the wall is 15m, calculate the length of the ladder, correct to the nearest whole number.​

Answers

Answer:

we can calculate it by applying trigonometric ratios

Step-by-step explanation:

tan 45 = length of wall/distance between ladder and wall

1 = length of wall/15

length of wall = 15m

(length of wall[tex])^{2}[/tex] + (distance between ladder and wall[tex])^{2}[/tex] = (length of ladder[tex])^{2}[/tex]

length of ladder = [tex]\sqrt{15^{2} + 15^{2} }[/tex]

                           = [tex]\sqrt{450}[/tex]

                           = 21.21 m

Select all the sentences that can be represented by the equation 25+p=38 A.25 is more than 38 is p B.25 times as much as p is 38 C.38 is p more than 25

Answers

Answer:

Option C: 38 is p more than 25

Step-by-step explanation:

the equation 25 + p = 38

can be read as 38 is 25 plus p units, or similarly ;

38 is p units more than 25.

Therefore from the three sentences you are showing, only the last one (option C) is the correct one.

Please answer this in two minutes

Answers

Answer:

I answered it

Step-by-step explanation:

I answered it

Answer:

∠ V ≈ 33.6°

Step-by-step explanation:

Using the cosine ratio in the right triangle

cos V = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{UV}{TV}[/tex] = [tex]\frac{5}{6}[/tex] , thus

∠ V = [tex]cos^{-1}[/tex] ([tex]\frac{5}{6}[/tex] ) ≈ 33.6° ( to the nearest tenth )

4) The diameter of a circle measures 16 mm. What is the
circumference of the circle? use 3.14 for ł, and do not
round your answer.(be sure to include the correct unit in
your answer)
16mm

Answers

Answer: 50.24 mm

Step-by-step explanation:

Circumference= 2πr

C = 2 x 3.14 x 8mm

C = 50.24 mm

Answer:

Step-by-step explanation:

d=16mm

therefore r=8mm

therefore circumference = 2pi r = 2* 3.14*8

=50.42cm

hope it helps

Solve the inequality
-6w-16>44

Answers

[tex]-6w-16>44[/tex]

Add both sides by 16

[tex]-6w>60[/tex]

Divide both sides by -6 (Note: Since we're dividing by a negative number, the inequality symbol needs to be reversed)

[tex]w<-\dfrac{60}{6}[/tex]

[tex]w<10[/tex]

This is the solution to the inequality. Let me know if you need any clarifications, thanks!

Can someone plz help me? If you answer you are a real life savor

Answers

Answer:

x = 2; y = 6.

Step-by-step explanation:

If the two triangles will be congruent by the HL Theorem, the hypotenuses and side lengths have to be equal. That means that...

x + 3 = y - 1

2x - 1 = y - 3

x + 3 = y - 1

y - 1 = x + 3

y = x + 4

2x - 1 = y - 3

y - 3 = 2x - 1

y = 2x + 2

2x + 2 = x + 4

x = 2

y = 2x + 2

y = 2 * 2 + 2

y = 4 + 2

y = 6

y = x + 4

y = 2 + 4

y = 6

Hope this helps!

PLZZ HELP Fill in the blank with the correct response. The slope of the graph of y = x is ___a0.

Answers

Answer:

1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = x ← is in slope- intercept form

with slope m = 1

Answer:

1

Step-by-step explanation:

Given the geometric sequence where a1 = −1 and the common ratio is 7, what is the domain for n? A. All integers B. All integers where n ≥ −1 C. All integers where n ≥ 0 D. All integers where n ≥ 1

Answers

Answer:

D

Step-by-step explanation:

Hello, This is a geometric sequence where the first term is [tex]a_1=-1[/tex].

It means that the sequence is [tex](a_n)_{n\geq 1}[/tex].

In other words, as the common ratio is 7 the sequence is defined by

[tex]a_1=-1[/tex]

[tex]a_{n+1}=a_n\cdot 7 \ \ \text{ for n }\geq 1[/tex]

For instance, we can estimate the first terms:

[tex]a_1=-1\\\\a_2=7a_1=-7\\\\a_3=7a_2=-49[/tex]

And we know that we can even find a formula for the [tex]n^{th}[/tex] term of the sequence by:

[tex]a_n=a_1\cdot 7^{n-1}=-7^{n-1}[/tex]

Now, to answer the question, the domain for n is all integers where [tex]n\geq 1[/tex].

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

D.) would be the correct answer

Plz help!
i Cant answer it​

Answers

Answer: (4,90)

Step-by-step explanation:

In a coordinate pair, the first number represents the x-axis and the second represents the y-axis.

Hope it helps <3

Answer:

C (4,90)

Step-by-step explanation:

In the graph, the point P is on 4 along the x-axis,

and 90 on the y-axis,

therefore making it's coordinates (4, 90).

Hope this helped! :)

A point with coordinates (a, b) is plotted on a coordinated plane. The values of a and b can be any positive or negative integer.

What must be true about the point ( a, b)?
A) It is flipped across the
y- axis from the original point

B) it is flipped across the
x-axis from the original point

C) it is in the quadrant diagonal to the original point

D) it is in the same quadrant as the original point, but in a different location

Answers

Answer:

I think it's x-axis.

Step-by-step explanation:

but me could me wrong

Answer:

The correct answer to this question would be C.

Step-by-step explanation:

took the test. Hope this helps!

p=E/x+Y express x in terms of p,e and y​

Answers

Answer:

x = E/(p - y)

Step-by-step explanation:

p - y = e/x

x(p-y) = e

x = e/(p-y)

Answer:

Hey there!

p=e/x+y

p-y=e/x

x(p-y)=e

x=e/(p-y)

Hope this helps :)

27. The area of a square plot is 0.0324 hectares. It was fenced using 3
strands of wire. What was the total length of wire used?
O A 72
O 8.144 m
O com
O 0.216​

Answers

Answer: 0.216 km .

Step-by-step explanation:

Given, The area of a square plot is 0.0324 hectares.

Since , 1 hectare =10,000 meters

Then, the area of a square plot = 10,000 x 0.0324

= 324 meters

Area of square = side²

[tex]\Rightarrow\ (\text{side})^2=324\\\\\Rightarrow\ \text{side}=\sqrt{324}=18\ m[/tex]

Perimeter = 4(side) = 4 x 18 = 72 m

Since it  was fenced using 3  strands of wire.

So, Total length of wire used =  3 (Perimeter) = 3 (72)m

= 216 m

Hence, the total length of wire used 216 m.

In km , 216 m = 0.216 km   [ 1 m = 0.001 km]

Hence, the correct option is 0.216 km .

In the lab, Charmaine has two solutions that contain alcohol and is mixing them with each other. Solution A is 12% alcohol and Solution B is 40% alcohol. She uses 800 milliliters of Solution A. How many milliliters of Solution B does she use, if the resulting mixture is a 32% alcohol solution

Answers

Answer: Charmaine wil use 2000 mL of solution B

Step-by-step explanation: Suppose that volume of solution B for the mixture is J.

Volume of solution A used is [tex]V_{A}[/tex] = 0.12*800

Volume of solution B used is [tex]V_{B}[/tex] = 0.4*J

Volume Total is V = 800 + J

0.12*800 + 0.4*J = 0.32(800 + J)

96 + 0.4J = 256 + 0.32J

0.08J = 160

J = 2000

Volume of solution B is 2000mL or 2L.

Pls solve this question. (If its right will give brainliest) X is 1 SOLVE FOR Y 210=60x+50y

Answers

Answer:

Step-by-step explanation:

I don't say u must have to mark my ans as brainliest but if it has really helped u plz don't forget to thank me....

Answer:

3

Step-by-step explanation:

210=60(1)+50y

210=60+50y

-60  -60

150=50y

divide

y=3

HELP ME PLEASE Given that the universal set is all real numbers, write the complement of set A. Set A: {Irrational numbers}

Answers

Answer: The complement is Q, the set of the rational numbers.

Step-by-step explanation:

Ok, here we can use the fact that the set of all the real numbers is equal to the union of the set of the rational numbers and the set of the irrational numbers. (Remember that Q, the rational numbers, also does include the set of the integer numbers))

Then, if the universal set is R, we have that the universal set is:

R = Q + I

Where Q = set of rational numbers and I = set of irrational numbers.

Then, the complement of the set A =  I = irrational numbers, is equal to:

R - I = Q + I - I = Q

Then the set of the rational numbers is the complement of the set A.

please help Evaluate 5 - (3/2) to the 3 power A.) 13/8 B.) 9.5 C.) 18.5 D.) 2197/8

Answers

Answer: THE ANSWER IS A

Step-by-step explanation:

5-(3/2)^3

=13/8

im a math god

ratio
simplify

4x:9=7:3

Answers

Answer:

4x:9=7:3 can be written as

[tex] \frac{4x}{9} = \frac{7}{3} [/tex]

Cross multiply

We have

4x(3) = 9 × 7

12x = 63

Divide both sides by 12

[tex]x = \frac{21}{4} \: \: \: \: \: or \: \: \: 5 \frac{1}{4} [/tex]

Hope this helps you

Answer:

[tex]\boxed{x=\frac{21}{4}}[/tex]

Step-by-step explanation:

[tex]4x:9=7:3[/tex]

Turn ratios to fractions.

[tex]\frac{4x}{9} =\frac{7}{3}[/tex]

Cross multiplication.

[tex]4x \times 3 = 9 \times 7[/tex]

Simplify.

[tex]12x=63[/tex]

Divide both sides by 12.

[tex]x=\frac{63}{12}[/tex]

[tex]x=\frac{21}{4}[/tex]

James determined that these two expressions were equivalent expressions using the values of y=4 and yu 6. Which
statements are true? Check all that apply
7x+4 and 3x+5+4x-1
When - 2. both expressions have a value of 18.
The expressions are only equivalent for X-4 and X- 6.
The expressions are only equivalent when evaluated with even values.
The expressions have equivalent values for any value of x.
The expressions should have been evaluated with one odd value and one even value.
When - 0, the first expression has a value of 4 and the second expression has a value of 5.
The expressions have equivalent values if X-

Answers

Answer with explanation:

Two or more Algebraic expressions are said to be equivalent, if both the expression produces same numerical value , when variable in the expressions are replaced by any Real number.

The two expressions are

1. 7 x +4

2. 3 x +5 +4 x =1

Adding and subtracting Variables and constants

→7 x +5=1

→7 x +5-1

→7 x +4

→ When x=2,

7 x + 4 =7×2+4

=14 +4

=18

So, Both the expression has same value =18.

→So, by the definition of equivalent expression, when ,you substitute , x by any real number the two expression are equivalent.

Correct options among the given statement about the expressions are:

1.When x = 2, both expressions have a value of 18.

2.The expressions have equivalent values for any value of x.

3.The expressions have equivalent values if x = 8.

Hi! Can I have some help on this math question...

Question C please!

Please explain it as I am very confused!

15 Points

- Thanks!​

Answers

Answer:

β = 22.5°

Step-by-step explanation:

In a triangle, the sum of interior angles must add up to 180°.

Since the angle marked with corners is equal to 90°, we can write an equation to solve for β.

3β + β + 90° = 180°

4β = 180° - 90°

4β = 90°

β = 90° / 4

β = 22.5°

Answer:

T is equal to R

Hope this helps.....

PLSSSSS HELPPPPP Subtract 6/7-3/x

Answers

Answer:

[tex]\huge\boxed{\dfrac{6}{7}-\dfrac{3}{x}=\dfrac{6x-21}{7x}}[/tex]

Step-by-step explanation:

[tex]\dfrac{6}{7}-\dfrac{3}{x}=\dfrac{(6)(x)}{(7)(x)}-\dfrac{(7)(3)}{(7)(x)}=\dfrac{6x}{7x}-\dfrac{21}{7x}=\dfrac{6x-21}{7x}[/tex]

I promise I will mark as brainiest

Answers

There are 18 rectangles inside the playing field.  And if you include the fence around the field, that makes 19.

HELPPPP,Which of the following choices is the length of AB if A (-3, -2) and B (5, -4)? AB = 2 AB = 68 AB = 4 None of these choices are correct

Answers

Answer: [tex]\sqrt{68}[/tex] units is the exact length of AB

===============================================

Explanation:

Use the distance formula to get this answer. The idea is you subtract the x coordinates together, and do the same for the y coordinates as well. Square each result and add up those squares. The last step of the formula is to apply the square root to get the distance from A to B, which is also the length of segment AB.

[tex]d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\\\d = \sqrt{(-3-5)^2+(-2-(-4))^2}\\\\d = \sqrt{(-3-5)^2+(-2+4)^2}\\\\d = \sqrt{(-8)^2+(2)^2}\\\\d = \sqrt{64+4}\\\\d = \sqrt{68}\\\\[/tex]

Therefore, [tex]AB = \sqrt{68}[/tex]

which of the following product? assume y>0 3 square root(y^2 square root 4+ square root 8y)

Answers

Answer:

  [tex]6y^2\sqrt{10}+12\sqrt{5y}[/tex]

Step-by-step explanation:

Use the distributive property and the rules for forming and simplifying square roots.

  (√a)(√b) = √(ab)

  √(a²b) = a√b

__

  [tex]3\sqrt{10}\cdot(y^2\sqrt{4}+\sqrt{8y})=(3\sqrt{10})(2y^2) +(3\sqrt{10})(\sqrt{8y})\\\\=6y^2\sqrt{10}+3\sqrt{80y}\\\\=6y^2\sqrt{10}+3\sqrt{(4^2)(5y)}\\\\=\boxed{6y^2\sqrt{10}+12\sqrt{5y}}\qquad\text{matches the first choice}[/tex]

Answer:

   a

Step-by-step explanation:

Which of the following represents the factorization of the polynomial below?
2x2 +11x +5

Answers

Answer:

(2x + 1)(x + 5)

Step-by-step explanation:

2x² + 11x + 5 =

= 2x² + 10x + x + 5

= 2x(x + 5) + (x + 5)

= (2x + 1)(x + 5)

Long Division of x^3-3x^2-10x+24 ÷x-2

Answers

Answer:

see explanation

Step-by-step explanation:

  x - 2 |    x² - x - 12

          ------------------------

          x³ - 3x² - 10x + 24

          x³  - 2x²    ↓       ↓      ← subtract terms from terms above

         --------------------------

               - x²    - 10x + 24

               - x²   + 2x       ↓          ← subtract terms from terms above

         ----------------------------

                       - 12x + 24

                       - 12x + 24           ← subtract terms from above terms

          ----------------------------

                                    0 ← remainder

Since remainder is zero then (x - 2) is a factor

and quotient = x² - x - 12 , thus

x³ - 3x² - 10x + 24 = (x - 2)(x² - x - 12) = (x - 2)(x - 4)(x + 3)

Other Questions
Sten thinks of a number and gives his friends some clues about it. "My number rounded to the nearest ten, nearest hundred, and nearest thousand gives the same value each time." Which choice is Sten's number? A. 735,619 B. 423,006 C.958,598 D.517,996 Which expression is equivalent to *picture attached* g If the Fed is concerned about a possible recession, it ________ the federal funds rate and, in response, longterm interest rates ________ by a ________ amount than the change in shortterm rates. A. lowers; increase; smaller B. lowers; decrease; smaller C. raises; decrease; larger D. raises; increase; smaller E. raises; increase; larger If (5^4)m=5^12 What is the value of M Given: Circumscribed XYZ XY=7, YZ=8. ZX=5 Find: AX, BY, CZ What height will the object reach? 12 points. Will give brainliest. When you use Word's Email option to share a document, you should edit the _____ line to let the recipient know the email is from a legitimate source. If the external vapor pressure is 2.0 atm , what is the vapor pressure of the water at its boiling point? Which are examples of voter fraud? Check all that apply. 1. using fake identification to vote 2. refusing to let people register to vote 3. demanding a tax be paid for voting rights 4. preventing specific groups from voting 5. using intimidation to influence voters 6. counting votes incorrectly Name the hydro carbon.... I really need your help guyz Education reforms implemented by David Hall's government included higher teacher salaries, mandatory kindergartenattendance, and If you take $100 out of your piggy bank and deposit it in your checking account, how did M1 change? Did M2 change? Assuming that there are no new loans created from the deposit.\ challenges that confront a marriage couple in the Ghanian society What are the remaining angle measures if the figure isto be a parallelogram?mZB=mZC=m2D = What is the measure of work cell at Chris Ellis Commercial Laundry has a workstation with two machines, and each unit produced at the station needs to be processed by both of the machines. (The same unit cannot be worked on by both machines simultaneously.) Each machine has a production capacity of 5 units per hour. The throughput time of the work cell=nothing minutes per unit (enter your response as a whole number).What is the process time of the work cell in minutes per unit? HELP ASAP PLEASEEEEE C is the center of the circle. Find the length of DGE A. s= 161 over 18 pie B. s= 343 over 35 pie C. s= 343 over 18 pie D. s= 343 over 9 pie Simplify the expression.(4+2i)-(1-i) What does Eric Ames name as being the most challenging aspect of managing his finances? 3. What is the degree of the polynomial 3x^4 + 2x^2 + 5x? *