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1 year ago

What is the GCF of the terms of the polynomial −16y4 + 12y2 – 4y?

Mathematics

1 answer:

Tresset [83]1 year ago

5 0

Answer:

The GCF is - 4y

Step-by-step explanation:

Given the polynomial expression −16y4 + 12y2 – 4y?

If we carefully traverse all the terms we can factor out 4y from all the terms

=-4y(4y³-3y+1) which is similar to the original expression

Hence the greatest common factor GCF = - 4y

The Greatest Common Factor (GCF) is the largest number that will divided evenly into that number.

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Trevor is studying a polynomial function f(x). Three given roots of f(x) are –7, 2i, and 7. Trevor concludes that f(x) must be a

denpristay [2]

Option B

Trevor isn't correct because -2i must also be a root

<em><u>Solution:</u></em>

For the polynomial with roots -7, 2i and 7 their roots can be,

1. ) Real roots

2.) Imaginary roots

The real roots are: -7 and +7

The imaginary root given is: 2i

The imaginary roots come from the square root. So they will be in form of $\pm 2i$

Therefore,

For f(x) with roots -7 and +7 and $\pm 2$ we have,

$f(x)=a(x+7)(x-7)(x-2i)(x+2i)$

Fundamental Theorem of Algebra states that a polynomial will have exactly as many roots as its degree (the degree is the highest exponent of the polynomial).

So for f(x) with 4 roots, degree of f(x) is 4

So option B is correct. Trevor is not correct because –2i must also be a root.

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1 year ago

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Haley is considering two gym membership plans. The plans are detailed here. Plan one $50 for a monthly pass and a $3 fee for eac

vodomira [7]

Well for the first one it'd be y=3x+50 and for the second one it'd be y=10x

5 0

1 year ago

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Captain Jessica has a ship, the H.M.S Crimson Lynx. The ship is two furlongs from the dread pirate Ishaan and his merciless band

Phoenix [80]

Answer:

9/40

Step-by-step explanation:

The probability of event A happening, then event B, is the probability of event A happening times the probability of event B happening given that event A already happened.

In this case, event A is the Captain missing the pirate ship and event B is the pirate hitting the Captain's ship.

The Captain fires first, so her ship can't be sunk before she fires her cannons.

So, the probability of the Captain missing the pirate ship is

3/5

If the Captain missed the pirate ship, the pirate has a normal chance to fire back.

So, the probability of the pirate hitting the Captain's ship given the Captain missing the pirate ship is

3/8

The probability that the Captain misses the pirate ship, but the pirate hits is then the probability of the Captain missing the pirate ship times the probability of the pirate hitting the Captain's ship given the Captain missing the pirate ship.

this is 3/5 X 3/8 = 9/40

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2 years ago

Read 2 more answers

If a random variable X is exponentially distributed with parameter λ=2, then P(X≥1) is equal to

Rasek [7]

Answer:

D. 0.1353

B. 0.0473

Step-by-step explanation:

For an exponentially distributed random variable, the cumulative distribution function is:

$P(x\leq a) = 1 - e^{-\lambda a}\\P(x\geq a) = e^{-\lambda a}$

with parameter λ=2, then P(X≥1) is equal to:

$P(x\geq 1) = e^{-2*1}=0.1353$

D. 0.1353

with parameter λ=1.5, then P(2≤X≤4) is equal to

$P(2\leq x \leq 4) = P(x \leq 4) - P(x\leq 2)\\P(2\leq x \leq 4) =1 - (e^{-1.5*4}) - (1-(e^{-1.5*2}))\\P(2\leq x \leq 4) = 0.0473$

B. 0.0473

7 0

1 year ago

[6+4=10 points] Problem 2. Suppose that there are k people in a party with the following PMF: • k = 5 with probability 1 4 • k =

kirza4 [7]

Answer:

1). 0.903547

2). 0.275617

Step-by-step explanation:

It is given :

K people in a party with the following :

i). k = 5 with the probability of $\frac{1}{4}$

ii). k = 10 with the probability of $\frac{1}{4}$

iii). k = 10 with the probability $\frac{1}{2}$

So the probability of at least two person out of the 'n' born people in same month is = 1 - P (none of the n born in the same month)

= 1 - P (choosing the n different months out of 365 days) = $1-\frac{_{n}^{12}\textrm{P}}{12^2}$

1). Hence P(at least 2 born in the same month)=P(k=5 and at least 2 born in the same month)+P(k=10 and at least 2 born in the same month)+P(k=15 and at least 2 born in the same month)

= $\frac{1}{4}\times (1-\frac{_{5}^{12}\textrm{P}}{12^5})+\frac{1}{4}\times (1-\frac{_{10}^{12}\textrm{P}}{12^{10}})+\frac{1}{2}\times (1-\frac{_{15}^{12}\textrm{P}}{12^{15}})$

= $0.25 \times 0.618056 + 0.25 \times 0.996132 + 0.5 \times 1$

= 0.903547

2).P( k = 10|at least 2 share their birthday in same month)

=P(k=10 and at least 2 born in the same month)/P(at least 2 share their birthday in same month)

= $0.25 \times \frac{0.996132}{0.903547}$

= 0.0.275617

6 0

1 year ago