What is the solution to the system of equations graphed below?

when joseph travel by train it takes him 3 hours to travel 84 miles at the same rate how many miles he traveled in 5 hours

GalinKa [24]

So you just have to use proportions

3 hours. 5 hours
——-———.=. -------------
84 miles. X

3x=420

Then you divide 3 into 420

So the answer 140 milea

4 0

3 years ago

When describing average home sales prices, explain why the median might be more appropriate measure of center than the mean. Are

Anni [7]

Q. When describing average home sale prices, explain why the median might be more appropriate measure of center than the mean. A. When looking for the average, we usually don't get the approximate price that we are looking for. What we are instead receiving is the rounded figure from the various other prices, rather than finding the "center" price. Whereas, in finding the median, we get the center price (since using median we find the number that is in the approximate middle). That will get us the "core" price for the selection of the homes instead of getting the rounded figure in average. Q. Are all home prices about the same in a city? A. There are no approximate answer for this. This topic is similar to when you are deciding where to start your next business. You need to look at the environment, education, communication etc., before deciding to buy a house. From my point, I would say that not all the houses in the city have the same price. You need to look most at the built-in architectural designs to have a higher price. However, if you look for a some-what luxury house, then you will have more of a lower price.

3 0

3 years ago

Double my tens digit to get my ones digit. Double me and I less than 50

pickupchik [31]

One example of this number is 24, or maybe 12, just follow the rules and you'll have a lot of answers.

6 0

3 years ago

Read 2 more answers

A mass of 1 g is set in motion from its equilibrium position with an initial velocity of 6in/sec, with no damping and a spring c

yan [13]

a) $y(t)=0.0016 sin(94.9t)$ [m]

b) 0.033 s

c) -0.152 m/s

Step-by-step explanation:

a)

The force acting on the mass-spring system is (restoring force)

$F=-ky$

where

k = 9 is the spring constant

y is the displacement

Also, from Newton's second law of motion, we know that

$F=my''$

where

m = 1 g = 0.001 kg is the mass

y'' is the acceleration

Combining the two equations,

$my''=-ky$

This is a second order differential equation; the solution for y(t) is

$y(t)=A sin(\omega t-\phi)$

where

A is the amplitude of motion

$\omega=\sqrt{\frac{k}{m}}=\sqrt{\frac{9}{0.001}}=94.9 rad/s$ is the angular frequency

The spring starts its motion from its equilibrium position, this means that y=0 when t=0; therefore, the phase shift must be

$\phi=0$

So the displacement is

$y(t)=A sin(\omega t)$

The velocity of the spring is equal to the derivative of the displacement:

$v(t)=y'(t)=\omega A cos(\omega t)$

We know that at t = 0, the initial velocity is 6 in/s; since 1 in = 2.54 cm = 0.0254 m,

$v_0=6(0.0254)=0.152 m/s$

And since at t = 0, $cos(\omega t)=1$

Then we have:

$v_0=\omega A$

From which we find the amplitude:

$A=\frac{v_0}{\omega}=\frac{0.152}{94.9}=0.0016 m$

So the solution for the displacement is

$y(t)=0.0016 sin(94.9t)$ [m]

b)

Here we want to find the time t at which the mass returns to equilibrium, so the time t at which

$y=0$

This means that

$sin(\omega t)=0$

We know already that the first time at which this occurs is

t = 0

Which is the beginning of the motion.

The next occurence of y = 0 is instead when

$\omega t = \pi$

which means:

$t=\frac{\pi}{\omega}=\frac{\pi}{94.9}=0.033 s$

c)

As said in part a), the velocity of the mass-spring system at time t is given by the derivative of the displacement, so

$v(t)=\omega A cos(\omega t)$

where we have

$\omega=94.9 rad/s$ is the angular frequency

$A=0.0016 m$ is the amplitude of motion

t is the time

Here we want to find the velocity of the mass when the time is that calculated in part b):

t = 0.033 s

Substituting into the equation, we find:

$v(0.033)=(94.9)(0.0016)cos(94.9\cdot 0.033)=-0.152 m/s$

4 0

3 years ago

At a football stadium, 5% of the fans in attendance were teenagers. If there were 10 teenagers at the football stadium, what was

TiliK225 [7]

Answer:

200 people were at the stadium

Step-by-step explanation:

Let us represent the total number of people at the stadium = x

At a football stadium, 5% of the fans in attendance were teenagers. If there were 10 teenagers at the football stadium

Hence:

5% of total number of people = 10 teenagers

5/100 × x = 10

5x/100 = 10

Cross Multiply

5x = 100 × 10

5x = 1000

Divide both sides by 5

5x/5 = 1000/5

x = 200

The total number of people in the stadium is 200

6 0

3 years ago