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zavuch27 [327]
2 years ago
10

A plant has an initial height of 6 inches and grows at a constant rate of 3 inches each month. A second plant that also grows at

a constant rate has an initial height of 2 inch and is 50 inches tall after 1 year. After how many months are the plants the same height?
Mathematics
1 answer:
Semenov [28]2 years ago
3 0

Answer:

4 months

Step-by-step explanation:

-Let the number of months it takes for their heights to equal be x and let h(x) be the height after x months.

#For plant 1, we equate height after x months as:

h(x)=6+3x

#For plant 2, we equate height after x months and at a constant rate m:

h(x)=2+mx

#we equate and solve for rate of growth, m in plant 2 as below:

h(x)=2+mx\\\\but\  h(12)=50\\\\\therefore r=\frac{50-2}{12}\\\\r=4 \ inches/month

#We then equate the two heights after x months to solve for x:

h(x)_1=h(x)_2\\\\6+3x=2+4x\\\\6-2=4x-3x\\\\x=4

Hence, the plants have the same height after 4 months

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There are 16 track events and 6 field events

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2 years ago
Michael is a basketball player who regularly shoots sets of 2 free-throws. Suppose that each shot has probability 0.60. , point,
Sati [7]

Answer:

0.1306

Step-by-step explanation:

This is a binomial distribution problem

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

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x = Number of successes required = 6

p = probability of success = 0.60

q = probability of failure = 1 - 0.60 = 0.40

P(X = 6) = ⁷C₆ (0.6)⁶ (0.4)⁷⁻⁶ = 0.1306368 = 0.1306

Hope this Helps!!!

4 0
3 years ago
The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integ
Nutka1998 [239]

Answer:

  • equation: (x-3) +(x-1) +(x+1) +(x+3) = -72
  • values: -21, -19, -17, -15

Step-by-step explanation:

When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...

  (x-3) +(x-1) +(x+1) +(x+3) = -72

This simplifies to ...

  4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.

  x = -18 . . . . . . . . the middle number of the sequence

So, the numbers are:

  • -18-3 = -21
  • -18-1 = -19
  • -18+1 = -17
  • -18+3 = -15

_____

A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...

  (x) +(x +2) +(x +4) +(x +6) = -72

and that simplifies to ...

  4x +12 = -72 . . . . . collect terms

  4x = -84 . . . . . . . . subtract 12

  x = -21 . . . . . . . . . . divide by 4

Now, the other three numbers are found by adding 2, 4, and 6 to this one.

3 0
3 years ago
Every autumn, the North American Monarch
Stolb23 [73]

Part A

The equation is d = 50t

This is because the slope of 50 represents how many miles per day the butterflies cover (on average). The y intercept is 0 to indicate that 0 miles have been traveled initially.

You can think of this as the equation y = 50x

If t = 1, then d = 50t = 50*1 = 50 miles have been covered

If t = 2, then d = 50t = 50*2 = 100 miles have been covered

And so on.

==========================================================

Part B

You'll have these values in the bottom row (in the order presented): 50, 100, 150, 200, 250

You can plug in the values t = 1, t = 2, t = 3, t = 4 and t = 5 into d = 50t to find those answers in bold.

Or you could add on 50 each time to generate each new value. We start at 50 since t = 1 corresponds to d = 50.

==========================================================

Part C

You can keep the pattern of 50,100,150, ... going until you reach 2500. Then note the t value that pairs with d = 2500

In my opinion, that's the slower method.

The quicker method is to plug d = 2500 into the equation for part A, and then solve for t.

d = 50t

2500 = 50t

50t = 2500

50t/50 = 2500/50 ....... divide both sides by 50

t = 50

It will take 50 days for the average distance traveled to be 2500 miles.

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