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2 years ago

According to the line plot, what is the total distance that was run by the runners who each ran for 1/3 of a mile?

Mathematics

2 answers:

Alik [6]2 years ago

7 0

Answer:

$1\frac{1}{3}$ miles

Step-by-step explanation:

4 runners ran 1/3 of a mile:

4*1/3 = 4/3, or 1 1/3 mile

gladu [14]2 years ago

5 0

Answer:

1 1/3 miles

Step-by-step explanation:

1/3+1/3+1/3+1/3=1 1/3

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Two friends, Sasha and Maria, are growing out their hair. They plan to cut it off at a certain

34kurt

Answer:

13 months, 49 cms

Explanation:

For Sasha, multiply 3 and 13 together for the growth per month. You should get 39, then add the 10 cm Sasha already has. The sum is 49.

For Maria, multiply 13 and 1 for the growth per month. You should get 13, then add the 36 Maria already has. The sum is also 49.

Hope this helps!

8 0

2 years ago

A rumor spreads through a small town. Let y ( t ) be the fraction of the population that has heard the rumor at time t and assum

Ivan

Answer:

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solution

$y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

The rumor reaches 80% at 8.48 days.

Step-by-step explanation:

We know

y(t): proportion of people that heard the rumor

y'(t)=ky(1-y), rate of spread of the rumor

Differential equation

$\frac{dy}{dt} =ky(1-y)$

Solving the differential equation

$\frac{dy}{y(1-y)}=k\cdot dt \\\\\int \frac{dx}{y(1-y)} =k \int dt \\\\-ln(1-\frac{1}{y} )+C_0=kt\\\\1-\frac{1}{y} =Ce^{-kt}\\\\\frac{1}{y} =1-Ce^{-kt}\\\\y=\frac{1}{1-Ce^{-kt}}$

Initial conditions:

$y(0)=0.2\\y(3)=0.4\\\\y(0)=0.2=\frac{1}{1-Ce^0}\\\\1-C=1/0.2\\\\C=1-1/0.2= -4\\\\\\y(3)=0.4=\frac{1}{1+4e^{-3k}} \\\\1+4e^{-3k}=1/0.4\\\\e^{-3k}=(2.5-1)/4=0.375\\\\k=ln(0.375)/(-3)=0.327\\\\\\y=\frac{1}{1+4e^{-0.327t}}$

Value of constant k=0.327 days^(-1)

At what time the rumor reaches 80%?

$y(t)=0.8=\frac{1}{1+4e^{-0.327t}} \\\\1+4e^{-0.327t}=1/0.8=1.25\\\\e^{-0.327t}=(1.25-1)/4=0.0625\\\\t=ln(0.0625)/(-0.327)=8.48$

The rumor reaches 80% at 8.48 days.

8 0

3 years ago

Find the value of c that makes the expression a perfect-square<br>trinomial.<br>• 6) x2 + 26x + c

slava [35]

The value of c would be 169

8 0

3 years ago

Car is driving at 30 kilometers per hour. How far in meters does it travel in 3 seconds?

Alenkasestr [34]

Answer:

25 meters

Step-by-step explanation:

30 km/hr = (30 km/1 hr)*(1000 m/1 km)*(1 hr/60 min)*(1 min/60 sec)

30 km/hr = (30*1000*1*1)/(1*1*60*60) meters per second

30 km/hr = 8.3333333333 m/s (approximate)

----------

The speed or rate is r = 8.3333333333 meters per second approximately, and the time is t = 3 seconds, so,

distance = rate*time

d = r*t

d = 8.3333333333 * 3

d = 24.9999999999

Due to rounding error, the true answer should be d = 25. We can see this if we opted to use the fraction from of 8.3333... instead of the decimal representation which isn't a perfect exact measurement.

4 0

3 years ago

Mr. Berger assigned the following system of equations to be solved for homework. 2x-3y = -12

jeka57 [31]

-4x + 6y = 24
4x + y = -10

7y = 14

y = 2

2x - 6 = -12

2x = -6

x= -3

6 0

3 years ago