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Volgvan
3 years ago
12

If you flip three fair coins what is the problility that you will get all three heads

Mathematics
1 answer:
ira [324]3 years ago
6 0
25 percentage chance of getting heads three times in a row
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Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.
lesya692 [45]

Answer:

\displaystyle f(x) = -2(x-2)(x^2+4)

Step-by-step explanation:

We want to find a third degree polynomial with zeros <em>x </em>= 2 and <em>x</em> = 2i and f(-1) = 30.

First, note that by the Complex Root Theorem, since <em>x</em> = 2i is a root, <em>x</em> = -2i must also be a root.

Hence, we will have the three factors:

\displaystyle f(x) = a(x-(2))(x-(2i))(x-(-2i))

Where <em>a</em> is the leading coefficient.

Expand and simplify the second and third factors:

\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}

Hence:

\displaystyle f(x) = a(x-2)(x^2+4)

Since f(-1) = 30:

\displaystyle \begin{aligned}  f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}

In conclusion, third degree polynomial function is:

\displaystyle f(x) = -2(x-2)(x^2+4)

5 0
3 years ago
Eric is saving $60 every week to buy a new laptop that costs $480. He has already saved $180.
Rama09 [41]

Answer:

Step-by-step explanation:

You saved $200 on a laptop you purchased online. If this was a 25% savings from the original price, find the original cost of the laptop.

13,962 results

Math

You saved $200 on a laptop you purchased online. If this was a 25% savings from the original price, find the original cost of the laptop.

7 0
3 years ago
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A 5-kilogram bag of rice costs $16.03. What is the unit price, rounded to the nearest cent?
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3.21 dollars per killogram t t t t t t t t t t t t t t t t t t t

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3 years ago
30 people watched the soccer game last night tickets cost 2.75 each half of these fans bought a program at 1.50 each how much mo
Dima020 [189]
Answer: 105$
Half the ppl paid 1.50 for programs which is 15 x 1.5 = 22.5
30 ppl bought tickets 30x2.75
Add the totals to get 105
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3 years ago
What is the missing number in the factor tree?
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9 because 9x4 equal 36
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