Nina and Jo both ran an 8 km race. Nina took 55 minutes to run the whole race. Jo started the race 3 minutes later than Nina but caught up when they had both travelled 6 km. If Nina and Jo both ran at constant speeds, what is Jo's speed to 2 dp?

Answers

Answer 1

Answer:

Step-by-step explanation:

First we figure out how fast Nina can run. If Nina can run 8 km in 55 minutes, then her rate is

[tex]\frac{8km}{55min}=.145\frac{km}{min}[/tex] and we can use that in a d = rt table:

                 d        =        r        *        t

Nina                            .145

Jo

Now we can fill in the distance which is 6 for both, since that is the distance where they met:

                d        =        r       *        t

Nina         6        =     .145

Jo             6        =

Now we go to the info given about the time. If Jo started the race 3 minutes after Nina, that means that Nina is running 3 minutes longer than Jo. Filling in the time info:

                d        =        r        *        t

Nina          6       =       .145    *      t + 3

Jo              6       =         r       *         t

As you can see, right now we have 2 unknowns in Jo's row. But we don't have to! We will go to Nina's row where the only unknown is time and solve for t. If d = rt, then

6 = .145(t + 3) and

6 = .145t + .435 and

5.55 = .145t so

t = 38.379 minutes. This means that Jo was running 38.379 minutes when she caught up to Nina (it took Nina 3 minutes longer than that to go 6 km since she was already running for 3 minutes when Jo started the race). If Jo's time is 38.379, we can use that in her row for t and solve for r. If d = rt, then

6 = r(38.379) and

r = .16 km/min

Let's check it without the rounding (rounding takes away from the accuracy). If 6 = .145(t + 3) and Nina's rate not rounded is .145454545 and t = 38.37931034, then, rewriting without rounding:

6 should equal .145454545( 38.37931034 + 3)

6 ?=? .145454545(41.37931034)

6 ?=? 6.0 so

Jo's rate is .16 km/min rounded


Related Questions

Jada walks dogs to earn money. The points in this graph represent the total amount of money Jada earns based on the number of hours she walks dogs. Jada wants to purchase a new jacket that costs $32.

How many hours does Jada need to walk dogs to earn enough money to buy the jacket?


6 hours

7 hours

8 hours

9 hours

Answers

Answer:

8 hours

Step-by-step explanation:

In 4 hours she earns 16 dollars

Since this is proportional ( goes through zero), we can multiply by 2

8 hours = 32 dollars

Jada needs to walk the dog for, 8 hours.

4x8 = 32

how would 3 over 5

be Classified ​

Answers

Answer:

3/5 is expressed as 60% in terms of Percentage.

Let's convert the fraction 3/5 into percent. Now, 60/100 is expressed as 65% in terms of percentage.

Pls help me and thank you!

Answers

Answer:

Substitute your answer for Step 1 into the second equation to solve for Z.

If f (x) = 2 x + 5 and three-halves are inverse functions of each other and f (x) = 2x + 5, what is

Answers

Answer:

See explanation

Step-by-step explanation:

The question has conflicting details

[tex]f(x) = 2x + 5[/tex]

[tex]f(x) = 2x + 5[/tex] and three halves doesn't sound correct.

So, I will take f(x) as

[tex]f(x) = 2x + 5[/tex]

Next, solve for the inverse function

Replace f(x) with y

[tex]y = 2x + 5[/tex]

Swap x and y

[tex]x = 2y + 5[/tex]

Make 2y the subject

[tex]2y = x-5[/tex]

Make y the subject

[tex]y = \frac{x-5}{2}[/tex]

Replace y with the inverse sign

[tex]f^{-1}(x) = \frac{x-5}{2}[/tex]

So, now we can calculate any value from the original function and from the inverse function.

For instance:

[tex]f^{-1}(7) = \frac{7-5}{2} = \frac{2}{2} = 1[/tex]

[tex]f(1) = 2*1 + 5 = 2+5=7[/tex]

HELP ME!
Line segment EQ consists of the points ____________. ???

Answers

you forgot to post the picture

Answer:

{F, G, H, I, J, K, L, M, N, O, P}

are the points between segment EQ :)

Carl is filling flowerpots with soil. Each flowerpot is a cylinder with a radius of 7cm and a height of 10 cm. If Carl has 24,000 cubic centimeters of soil, how many flowerpots can he fill?

Answers

Answer:

16 pots

Step-by-step explanation:

We first need to find out the amount of dirt that can be filled into a single flowerpot.

We use the formula to find the cylinder's volume.

π[tex]r^{2}[/tex][tex]* h[/tex]

Height is equal to ten, Radius is equal to 7.

49π [tex]* 10[/tex]

≈ 1539.38

25,000 divided by 1539.38

≈ 16.24

He can fill 16 pots fully.

Can someone help me please

Answers

Answer:

yes what would u like help with

pls answer the underline questions​

Answers

Answer:

What is the question?

Step-by-step explanation:

I will edit this and answer when you comment the question in this answer.

3/4 part of a rope is 150m. find the length of 7/10 part of the rope
Please help ASAP with step by step explanation.

Answers

Answer:

140m

Step-by-step explanation:

3/4 = .75

x/.7 = 150/.75

multiply both sides by .7

x = 150/.75 * .7

x = 140m

HEEELPPPPPPPPPPPPPPPPPPP ill give 20 brainlists

Answers

Answer:

B

Step-by-step explanation:

i think it is.....................

b is the best answer :) good luck

What is the vertex of the graph of the function below? y= x2 - 4x + 3

A. (2.-1)

B. (1,-1)

C. (1,0)

D. (2,0)​

Answers

The correct answer is A. (2, -1)
Answer: A

Step by step explanation

Express it in slope-intercept form.

Answers

Answer:

y = 3/2 x -3

Step-by-step explanation:

the line passes (0, -3) and (2, 0)

the slope = (0+3)/(2-0) = 3/2

the equation :

y-0= 3/2(x -2)

y = 3/2 x - 3

Mary has a rectangular driveway. She measures it and finds out it is 14 1/4 feet long by 17 1/2 feet wide. She wants to know how many square feet of paint she will need to completely cover the driveway.

Answers

Answer:

253.75 square feet

253 feet is the answer

The graph shown is a scatter plot:
Which point on the scatter plot is an outlier?

Answers

Answer:

D is the outlier

Step-by-step explanation:

An outlier is a point that is far from the other points

We can draw a line that roughly represents an equation for the points

A,B ,C are all near the line

D is not along the line

Find the quotient.the fraction
8 1/3 divided by 4 1/2​

Answers

Answer:

[tex]8 \frac{1}{3} \div 4 \frac{1}{2} = \frac{50}{27} = 1.851 = 1 \frac{23}{27} [/tex]

Here is some information about a holiday.
7 night holiday
$340 per person
8% discount if you book before 31 March

On 15 February, Naseem books this holiday for 2 people.
Calculate the total cost of his holiday.

Answers

Answer:

$625.6

Step-by-step explanation:

Information about the holiday:

7 night holiday

$340 per person

8% discount if you book before 31 March

Number of people Naseem booked the holiday for = 2

Date of booking of the holiday = 15 February

Total cost of the holiday per person = cost per person - discount before March 31

= $340 - 8% of $340

= 340 - 8/100 * 340

= 340 - 0.08 * 340

= 340 - 27.2

= $312.8

Total cost of the holiday for 2 persons = 2 × Total cost of the holiday per person

= 2 * $312.8

= $625.6

Find the percentage decrease ???​

Answers

Step-by-step explanation:

Price of a book costing sh.250

reduced to sh.200

percentage decrease on the price = (250-200)/250×100

= 20%

Find the width of the rectangular prism which has Surface area of 10 CM2, length of 2cm and height of 1 cm

Answers

Answer:

width is 1 cm

Step-by-step explanation:

The SA of a rectangular prism is SA = 2(lw + wh + hl)

We are given the length, the height, and the SA, and we need to find the width. So we plug in the known values into this equation:

10 = 2(2w + w + 1*2)

10 = 2(3w+2)

10 = 6w+4

6=6w

w=1

We can check the answer by plugging in all the values into the equation:

10 = 2(2*1+1*1+1*2)

10 = 2(5)

10 = 10

7- write the equation of the line that passes through points A(6,1) and B(9,4)
I

Answers

Answer:y=x-5

Step-by-step explanation: Use (y2-y1)/(x2-x1) fill those in and get (4-1)/(9-6) which is 3/3 and that is 1 for the slope. Now fill in y=1x with a given coordinate and try to find the y-intercept so we would do 1=1(6) and we need to make the right side equal to the left so we subtract 5. Ending us with y=x-5.

Please help. Thank you

Answers

Given:

[tex]PQRS\sim TUVW[/tex]

In the given figure, PS=x, RS=35, UV=20, VW=25 and TW=15

To find:

The scale factor from PQRS to TUVW.

Solution:

We have,

[tex]PQRS\sim TUVW[/tex]

We know that the corresponding sides of similar figures are proportional. The scale factor is the ratio of one side of image and corresponding side of preimage.

The scale factor is:

[tex]k=\dfrac{VW}{RS}[/tex]

[tex]k=\dfrac{25}{35}[/tex]

[tex]k=\dfrac{5}{7}[/tex]

Therefore, the scale factor from PQRS to TUVW is [tex]k=\dfrac{5}{7}[/tex].

What is the common ratio between successive terms in the sequence?
27, 9, 3, 1,
,
1,
3
O-3
mp

Answers

Answer:

1/3

Step-by-step explanation:

If it was supposed to be a negative answer, there would be negative numbers in the sequence. So that narrows it do to 3 and 1/3. And now we know that 27*3 isn't 9 but 27*1/3=9 and so on.

Answer:

your answer will have to be 3

Step-by-step explanation:

from 27 to 9, we divided by 3

from 9 to 3, we divided by 3

from 1 to 1/3, we divided by 3

from 1/3 to 1/9, we divided by 3

from 1/9 to 1/27, we divided by 3

so basically the common ratio will have to be 3

QUICK I NEED HELP! I WILL MARK BRAINLIEST!

Answers

Answer:

go a head what can i help you with

Answer:

Step-by-step explanation:

[tex]y_A = 9x -3x - 4 \\y_A = 6x - 4\\\\y_B = 12x - 4\\\\y_C = 5x + x - 4\\y_C = 6x -4[/tex]

Standard equation of a line with slope, m and y - intercept b is y = mx + b.

Clearly. for  the second equation has a different coefficient for x.

a ) The coefficient for x , is the slope of the line.

     Though the y - intercept for each equation is same = - 4.

    For example :

  Expression A = 2 , when x = 1

  Expression B = 8 , when x = 1

  Expression C = 2 , when x = 1

b) From above :

        [tex]y_A \ and \ y_C \ are \ the \ same \ expression.[/tex]

c) Expression A and  C are equivalent because the coefficient of x

    is the same  for A and  C.

 

Please solve 3^(x+3) + 3^(x+4)/3 = 162​

Answers

3x+9+x+4=162
4x+13=162
4x=162-13
4x=149
x=149/4
x=37.2
So the answer is : X = 149\4

Question 54 of 98
Which expression uses the associative property to make it easier to evaluate
20(3-6)
O A. 20(6)
B. 20(-5)
c. - 6)20
D. (20 - )6
SUBMIT

Answers

submitdjememendixodme ejej

Can someone explain this to me please

Answers

Answer:

c. 36·x

Step-by-step explanation:

Part A

The details of the circle are;

The area of the circle, A = 12·π cm²

The diameter of the circle, d = [tex]\overline {AB}[/tex]

Given that [tex]\overline {AB}[/tex] is the diameter of the circle, we have;

The length of the arc AB = Half the the length of the circumference of the circle

Therefore, we have;

A = 12·π = π·d²/4 = π·[tex]\overline {AB}[/tex]²/4

Therefore;

12 = [tex]\overline {AB}[/tex]²/4

4 × 12 = [tex]\overline {AB}[/tex]²

[tex]\overline {AB}[/tex]² = 48

[tex]\overline {AB}[/tex] = √48 = 4·√3

[tex]\overline {AB}[/tex] = 4·√3

The circumference of the circle, C = π·d = π·[tex]\overline {AB}[/tex]

Arc AB = Half the the length of the circumference of the circle = C/2

Arc AB = C/2 = π·[tex]\overline {AB}[/tex]/2

[tex]\overline {AB}[/tex] = 4·√3

∴ C/2 = π·4·√3/2 = 2·√3·π

The length of arc AB = 2·√3·π cm

Part B

The given parameters are;

The length of [tex]\overline {OF}[/tex] = The length of [tex]\overline {FB}[/tex]

Angle D = angle B

The radius of the circle = 6·x

The measure of arc EF = 60°

The required information = The perimeter of triangle DOB

We have;

Given that the base angles of the triangles DOB are equal, we have that ΔDOB is an isosceles triangle, therefore;

The length of [tex]\overline {OD}[/tex] = The length of [tex]\overline {OB}[/tex]

The length of [tex]\overline {OB}[/tex] = [tex]\overline {OF}[/tex] + [tex]\overline {FB}[/tex] = [tex]\overline {OF}[/tex] + [tex]\overline {OF}[/tex] = 2 × [tex]\overline {OF}[/tex]

∴ The length of [tex]\overline {OD}[/tex] = 2 × [tex]\overline {OF}[/tex] = The length of [tex]\overline {OB}[/tex]

Given that arc EF = 60°, and the point 'O' is the center of the circle, we have;

∠EOF = The measure of arc EF = 60° = ∠DOB

Therefore, in ΔDOB, we have;

∠D + ∠B = 180° - ∠DOB = 180° - 60° = 120°

∵ ∠D = ∠B, we have;

∠D + ∠B = ∠D + ∠D = 2 × ∠D = 120°

∠D = ∠B = 120°/2 = 60°

All three interior angles of ΔDOB = 60°

∴ ΔDOB is an equilateral triangle and all sides of ΔDOB are equal

Therefore;

The length of [tex]\overline {OD}[/tex] = The length of [tex]\overline {OB}[/tex] = The length of [tex]\overline {DB}[/tex]  = 2 × [tex]\overline {OF}[/tex]

The perimeter of ΔDOB = The length of [tex]\overline {OD}[/tex] + The length of [tex]\overline {OB}[/tex] + The length of [tex]\overline {DB}[/tex] = 2 × [tex]\overline {OF}[/tex] + 2 × [tex]\overline {OF}[/tex] + 2 × [tex]\overline {OF}[/tex] = 6 × [tex]\overline {OF}[/tex]

∴ The perimeter of ΔDOB = 6 × [tex]\overline {OF}[/tex]

The radius of the circle = [tex]\overline {OF}[/tex] = 6·x

∴ The perimeter of ΔDOB = 6 × 6·x = 36·x

The function f is defined by f(x) = (x − 2) 2 − 3 for x > −2. The function g is defined by g(x) = 2x+6 x−2 for x > 2. Find fg(7).

Answers

Answer:

[tex]fg(7)=143.95[/tex]

Step-by-step explanation:

We are given that

[tex]f(x) = (x -2)^2 -3[/tex] for x > −2

[tex]g(x) = 2x+6x^{-2}[/tex] for x > 2

We have to find fg(7)

[tex]fg(7)=f(g(7))[/tex]

[tex]=f(2(7)+6(7)^{-2})[/tex]

=[tex]f(14+\frac{6}{49})[/tex]

=[tex]f(\frac{692}{49})[/tex]

692/49>-2

fg(7)=[tex](\frac{692}{49}-2)^2-3[/tex]

=[tex]146.95-3[/tex]

Hence, [tex]fg(7)=143.95[/tex]

Please help me out for the question is it

A.275 centimeters

B.94 centimeters

C.144 centimeters

D.85 centimeters

You’ll be marked as brainliest

Answers

I think c because from what remember taking this test

can someone please help for brainlest

Answers

Answer:125√3:6

Step-by-step explanation:

Find angle N and arc NQ. See the image below.

Answers

Answer:

Angle N=32

Arc NQ=106

Step-by-step explanation:

Angle N is a inscribed angle of Arc MP so that means Angle N measures 32.

Angle NPQ is a inscribed angle of Arc NQ so that means Arc NQ is twice the measures of NPQ so

Arc NQ=106

Put these numbers in order from least to greatest.

0.92,0.43, and 9/10

Answers

Answer:

0.43,9/10,0.92

Step-by-step explanation:

Answer:

0.43, 9/10, 0.92

Step-by-step explanation:

9/10=0.9=0.90

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