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3 years ago

According to the rational root theorem, which is a factor of the polynomial f(x)=3x^3-5x^2-12x+20?

Mathematics

1 answer:

MakcuM [25]3 years ago

4 0

Answer:

(x-2), (x+2), (3x-5)

Step-by-step explanation:

Factors of 3: ±1, ±3

Factors of 20: ±1, ±2, ±4, ±5, ±10, ±20

Possible factors of the polynomial: ±1, ±2, ±3, ±4, ±5, ±10, ±20, .... (there's a lot more but you probably do not need to list them all)

Pick a number to divide the polynomial by (I picked 2)

(3x³-5x²-12x+20)÷(x-2) = 3x²+x-10

So (x-2) is a factor of f(x) = 3x³-5x²-12x+20

Factor 3x²+x-10 = (3x-5)(x-2) these are the other factors of f(x) = 3x³-5x²-12x+20

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Unit #2 – Lesson #1 Exit Ticket: Is r=7 a solution to the equation shown below? Justify your yes no response. 6x+5=x? - 2

Vikki [24]

(First equation:Multiply 6•7=42. 42+5=47)=(second equation:7 to the 2nd power is 49. 49-2=47 )

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3 years ago

The Department of Motor Vehicles reports that 32% of all vehicles registered in a state are made by a Japanese or a European aut

Mandarinka [93]

Answer: C. a parameter.

Step-by-step explanation:

In statistics, a parameter is a measure ( such as population mean , population proportion... ) generated from the entire population .
A statistics is also a measure( such as sample mean , sample standard deviation , sample proportion,..) but generated from the sample taken from population.

Given : The Department of Motor Vehicles reports that 32% of all vehicles registered in a state are made by a Japanese or a European automaker.

Here, Department as considered the entire population of vehicles registered in a state are made by a Japanese or a European automaker to find the proportion.

Thus , 32% = Population proportion of vehicles registered in a state are made by a Japanese or a European automaker

So , The number 32% is best described as a parameter.

Hence, the correct answer is C. a parameter.

8 0

4 years ago

Which is an equation for the line shown?

tino4ka555 [31]

Answer:

a) x=2

Step-by-step explanation:

at any point of the line x=2

5 0

3 years ago

Read 2 more answers

Simon uses 2/3 cup of sugar to bake a cake. How many cups of sugar does he needs to bake 6 cakes?

vitfil [10]

Answer:

Step-by-step explanation:

2/3x6=4

4 0

3 years ago

A coin is tossed 13 times.

Serga [27]

Answer:

a) 2¹³

b) 0.0873

c) 0.9983

d) 0.9538

Step-by-step explanation:

a) How many different outcomes are possible?

For every toss, there are two possible outcomes (heads or tails), so if we toss the coin 13 times the total of outcomes possible is 2¹³

b) What is the probability of getting exactly 4 heads?

The definition of probability is an event is: number of favourable events/ number of total events.

When we have two possible outcomes p, q and we repeat the experiment multiple times, we apply the Binomial distribution, in this distribution the probability of getting exactly k successes in n trials is given by

$P(X=k) =nCk (p^{k} )(1-p)^{n-k}$ where p represents the probability of success. nCk refers to the combinations of k elements out of n elements.

So we have to know how many different ways we can get exactly 4 heads.

let's name p = probability of getting heads = 0.5

1 -p = probability of getting tails = 0.5

We are going to toss the coin 13 different times and we want to get heads 4 times and tails 9 times.

So, by the Binomial Distribution we would have:

P(X=4) = 13C4 (0.5)⁴(0.5)⁹ = 715 (0.5)¹³ = 0.0873

Thus, the probability of getting exactly 4 heads is 0.0873.

c) What is the probability of getting at least 2 heads?

We are going to use the same binomial distribution but now we need at least to heads, this can be written as 1 - (P(X=0) + P(X=1))

P(X=0) + P(X=1) = 13C0 (0.5)⁰(0.5)¹³ + 13C1 (0.5)¹(0.5)¹² = 0.0001220703125 + 0.0015869140625 = 0.001708984375

1 - 0.001708984375 = 0.998291015625

The probability of getting at least 2 heads is 0.9983

d) What is the probability of getting at most 9 heads?

We are going to use the same binomial distribution but now we need at most 9 heads. This can be written as 1 - (P(X=10) + P(X = 11) + P(X=12) + P(X=13))

1 - (P(X=10) + P(X = 11) + P(X=12) + P(X=13)) =1 -(13C10(0.5)¹⁰(0.5)³ + 13C11(0.5)¹¹(0.5)²+ 13C12(0.5)¹²(0.5)¹ + 13C13(0.5)¹³(0.5)⁰) = 0.95385742188

The probability of getting at most 9 heads is 0.9538

6 0

3 years ago