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Svetllana [295]
2 years ago
5

-2.5d ≥ 30 10-x ≤35 Please help thanks!

Mathematics
1 answer:
Natasha2012 [34]2 years ago
4 0

Answer:

1) d ≤ -12

2) x ≥ -25

Step-by-step explanation:

-2.5d ≥ 30

2.5d ≤ -30

d ≤ -12

10 - x ≤ 35

-x ≤ 25

x ≥ -25

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2 years ago
Show that 3 · 4^n + 51 is divisible by 3 and 9 for all positive integers n.
-BARSIC- [3]

Answer:

Step-by-step explanation:

Hello, please consider the following.

3\cdot 4^n+51=3\cdot 4^n+3\cdot 17=3(4^n+17)

So this is divisible by 3.

Now, to prove that this is divisible by 9 = 3*3 we need to prove that

4^n+17 is divisible by 3. We will prove it by induction.

Step 1 - for n = 1

4+17=21= 3*7 this is true

Step 2 - we assume this is true for k so 4^k+17 is divisible by 3

and we check what happens for k+1

4^{k+1}+17=4\cdot 4^k+17=3\cdot 4^k + 4^k+17

3\cdot 4^k is divisible by 3 and

4^k+17 is divisible by 3, by induction hypothesis

So, the sum is divisible by 3.

Step 3 - Conclusion

We just prove that 4^n+17 is divisible by 3 for all positive integers n.

Thanks

4 0
3 years ago
There are four activities on the critical path, and they have standard deviations of 1, 2, 4, and 2. what is the probability tha
Sauron [17]
The expected completion time is μ = 40 weeks.
The random variable, X = 38 weeks (the probable time)

If the standard deviation is σ, then the z-score is z = (x - μ)/σ.

Let us test the given standard deviations.
When σ=1,
z = (38-40)/1 = -2
From standard tables,
P(x<=38) = P(z<=-2) = 0.0228 =2.3%

When σ=2,
z = (38*40)/2 = -1
P(x<=38) = P(z<=-1) = 0.1587 = 15.9%

When σ=4,
z = (38-40)/4 = -0.5
P(x<=38) = P(z<=-0.5) = 0.3085 = 30.9%

Answers:
z=1 => 2.3%
z=2 => 16% (approx)
z=4 => 31% (approx)

7 0
2 years ago
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