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qaws [65]
2 years ago
12

Mark noticed that his bus is late to school 5% of the time. He wants to design a spinner he can use to simulate the situation an

d determine the probability that the bus will be late three times next week. How should Mark divide his spinner to best simulate the situation?
Mathematics
2 answers:
babunello [35]2 years ago
5 0

The more painstaking way would be to divide the spinner up into 100 pieces, and shade in 5 of those pieces. Since 5/100 = 0.05 = 5% this means that landing on any of the 5 pieces has a 5% chance of happening.

A better way to do this is to use 20 slices instead. This works because 5/100 reduces to 1/20 (divide top and bottom by 5). Instead of shading in 5 slices, Mark should shade in 1. If you use a calculator, you should see that 1/20 = 0.05 = 5% as well.

The second option is more practical but even then a spinner with 20 sections is still a lot. I think it might be better for Mark to pull random numbers out of a hat, or let the computer generate random numbers.

zheka24 [161]2 years ago
4 0

Answer:

the answer is 20 equal-sized sections

Step-by-step explanation:

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The population p of a small community on the outskirts of a city grows rapidly over a 20-year period: t05101520p1002004509502000
myrzilka [38]

Answer:

The population of the small community, 5 years into the future, after the initial 20-year period = 4268.

Step-by-step explanation:

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

The exponential function will look like

p = aeᵏᵗ

where a and k are constants.

Take the natural logarithms of both sides

In p = In aeᵏᵗ

In p = In a + In eᵏᵗ

In p = In a + kt

In p = kt + In a.

We then use linear regression to fit the data of In p against t to obtain k and In a.

t | 0 | 5 | 10 | 15 | 20

p | 100 | 200 | 450 | 950 | 2000

In p | 4.605 | 5.298 | 6.109 | 6.856 | 7.601

In p = kt + In a.

y = mx + b

m = k and b = In a

Performing a linear regression analysis on the now-linear relationship between In p and t and also plotting a graph of the variables.

The regression equation obtained is

y = 0.151x + 4.584

The first attached image shows the equations necessary for the estimation of the linear regression parameters.

The second attached image shows the use of regression calculator and the plot of the function In p versus t.

Comparing

y = 0.151x + 4.584

With

In p = kt + In a.

y = In p

k = 0.151

x = t

In a = 4.584

a = 97.905

The exponential function relating p and t,

p = aeᵏᵗ now becomes

p = 97.905 e⁰•¹⁵¹ᵗ

So, to predict the population 5 years into the future, that is 5 years after the 20 year period.

we need p at t=25 years.

0.151 × 25 = 3.775

p(t=25) = 97.905 e³•⁷⁷⁵ = 4268.41 = 4268.

Hope this Helps!!!

7 0
2 years ago
A deli is offering two specials. The roast beef special gives a profit of $2.30 per sandwich, and the turkey special gives a pro
nikklg [1K]

Answer:

The constraints are as follows;

1) 2·x + 2·y ≤ 120

2) 3·x + 4·y ≤ 160

3) x = 2.30

4) y = 3.10

5) P = 2.3·x + 3.10

Step-by-step explanation:

The question is a word problem, with the analysis as follows;

The profit from the roast beef special per sandwich = $2.30

The profit from the turkey special per sandwich = $3.10

The number of slices of bread in the roast beef special = Two slices

The number of slices of cheese in the roast beef special = Three slices

The number of slices of bread in the turkey special = Two slices

The number of slices of cheese in the turkey special = Four slices

The number of slices of bread the deli has  = 120 slices

The number of slices of cheese the deli has = 160 slices

Let 'x' and represent the number of roast beef special and 'y' represent the number of turkey special the deli makes, then we have the constraints as follows;

For the number of slices of bread used;

2·x + 2·y ≤ 120...(1)

For the number of slices of cheese used;

3·x + 4·y ≤ 160...(2)

x = 2.30

y = 3.10

The profit 'P' is given by the following equation

P = 2.3·x + 3.10.

5 0
2 years ago
If the fastest you can safely drive is 65 mi/h, what is the longest time you can stop for dinner if you must travel 569 mi in 9.
stellarik [79]

Divide total miles by speed to get how long it will take to drive:

569 miles / 65 mi/h = 8.75 hours.

Now subtract the time it takes to drive from the total time you can travel:

9.5 hours - 8.75 hours = 0.75 hours.

You can stop for 0.75 hours.

4 0
2 years ago
If mJK=(7x-39) and mML)=87, find x
lilavasa [31]
If two chords of a circle are congruent, then their intercepted arcs are congruent
7x-39 = 87
7x = 87 + 39
7x = 126
x = 126/7
x = 18
5 0
2 years ago
Sita Rahim keeps records of her expenditures. She wants to know how much she spends each month, on the average. Her records for
Scorpion4ik [409]
$2906.17 am average is calculated by dividing the sum of all monthly expenditures by the number of months reported.
7 0
2 years ago
Read 2 more answers
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