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Korvikt [17]
3 years ago
8

Biking at 8 mph, it takes Kristen 1/4 hour to reach the train station to go to work. Kristen then takes the train to work, and i

t takes another 1/4 hour for her to get to work when the train travels 24 mph. How far does Kristen travel to work?
Mathematics
1 answer:
devlian [24]3 years ago
4 0

Answer:

8 miles.

Step-by-step explanation:

Biking at 8 miles per hour for 1/4 an hour is equal to biking 2 miles.

Riding the train at 24 miles per hour for 1/4 an hour is equal to riding 6 miles.

2 miles + 6 miles = 8 miles.

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If one batch of play dough uses 1/8 cup of salt how many batches of Play-Doh could you make if you had 3 cups of salt?
Neporo4naja [7]

Answer:

3 / (1/8) = 24

Step-by-step explanation:

3 0
3 years ago
The equation y = 13x describes the amount of money Sarah earns, where x is the number of hours she works
enot [183]

Answer:

A) $14/hr B) Austin

Step-by-step explanation:

A)

If he earns $140 in 10 hours you can divide 140 by 10 to find out how much he makes per hour

B)

Sarah makes $13/hr which is $1 less than Austin

8 0
3 years ago
Each unit on the grid stands for one miles determine two ways to calculate the distance from josie's house to annies
Novosadov [1.4K]
I encountered this problem before but it had an accompanying image and list of answer choices.

I'll attach the image and include the list of options. 

Each unit on the grid stands for one mile. Determine two ways to calculate the distance from Josie's house to Annie's house.
A) Distance Formula and Slope Formula
B) Midpoint Formula and Slope Formula
C) Distance Formula and Midpoint Formula
<span>D) Distance Formula and Pythagorean Theorem
</span>
My answer is: D.) Distance formula and Pythagorean Theorem.

When looking at the image, I can visualize a right triangle. I'll simply get the measure of the long and short legs and solve for the hypotenuse. 
Since the distance formula is derived from the Pythagorean theorem, it can be used to determine the distance from Josie's house to Annie's house.

8 0
3 years ago
Consider the following equation of the form dy/dt = f(y)dy/dt = ey − 1, −[infinity] &lt; y0 &lt; [infinity](a) Sketch the graph
kotegsom [21]

Complete Question:

The complete question is shown on the first uploaded image

Answer:

a) The graph of  f(y) versus y. is shown on the second uploaded image

b) The critical point is at y = 0  and the solution is asymptotically unstable.

c)The phase line is shown on the third uploaded image

d) The sketch for the several graphs of solution in the ty-plane  is shown on the fourth uploaded image

Step-by-step explanation:

Step One: Sketch The Graph of  f(y) versus y

Looking at the given differential equation

       \frac{dy}{dt} = e^{y} - 1 for -∞ < y_{o} < ∞

 We can say let \frac{dy}{dt} = f(y) =e^{y} - 1

Now the dependent value is f(y) and the independent value is y so to sketch is graph we can assume a scale in this case i cm on the graph is equal to 2 unit for both f(y) and y and the match the coordinates and after that join the point to form the graph as shown on the uploaded image.

Step Two : Determine the critical point

   To fin the critical point we have to set   \frac{dy}{dt} = 0

       This means e^{y} - 1 = 0

                          For this to be possible e^{y} = 1

                          which means that  e^{y} = e^{0}

                          which implies that y = 0

Hence the critical point occurs at y = 0

meaning that the equilibrium solution is y = 0

As t → ∞, our curve is going to move away from y = 0  hence it is asymptotically unstable.

Step Three : Draw the Phase lines

A phase line can be defined as an image that shows or represents the way an ODE(ordinary differential equation ) that does not explicitly depend on the independent variable behaves in a single variable. To draw this phase line , draw the y-axis as a vertical line and mark on it the equilibrium, i.e. where  f(y) = 0.

In each of the intervals bounded  by the equilibrium draw an upward

pointing arrow if f(y) > 0 and a downward pointing arrow if f(y) < 0.

      This phase line would solely depend on y does not matter what t is

On the positive x axis it would get steeper very quickly as you move up (looking at the part A graph).

For  below the x-axis which stable (looking at the part a graph) we are still going to have negative slope but they are going to be close to 0 and they would take a little bit longer to get steeper  

Step Four : Draw a Solution Curve

A solution curve is a curve that shows the solution of a DE (deferential equation)

Here the solution curve would be drawn on the ty-plane

So the t-axis(x-axis) is its the equilibrium  that is it is the solution

If we are above the x-axis it is going to increase faster and if we are below it is going to decrease but it would be slower (looking at part A graph)

5 0
3 years ago
Natalie works in a doughnut shop. She packs doughnuts into boxes that each hold 12 doughnuts.
ehidna [41]

Answer:

16

Step-by-step explanation:

If each box holds 12 doughtnuts, and she packed a total of 1,272.

Then 1,272/12 is 16.

Therefore, she needs 16 boxes

4 0
3 years ago
Read 2 more answers
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