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3 years ago

Given f(x)= 2x4 + 6x3 – 10x2 + kx – 10, for what value of k is (x - 1) a factor of f(x)?

Mathematics

1 answer:

brilliants [131]3 years ago

5 0

Answer: mannn i dunno either i’m tryna figure out the same thing

Step-by-step explanation:

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Waiting on the platform, a commuter hears an announcement that the train is running five minutes late. He assumes the arrival ti

natima [27]

Answer:

D. 91%

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

$P(B|A) = \frac{P(A \cap B)}{P(A)}$

In which

P(B|A) is the probability of event B happening, given that A happened.

$P(A \cap B)$ is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Less than 15 minutes.

Event B: Less than 10 minutes.

We are given the following probability distribution:

$f(T = t) = \frac{3}{5}(\frac{5}{t})^4, t \geq 5$

Simplifying:

$f(T = t) = \frac{3*5^4}{5t^4} = \frac{375}{t^4}$

Probability of arriving in less than 15 minutes:

Integral of the distribution from 5 to 15. So

$P(A) = \int_{5}^{15} = \frac{375}{t^4}$

Integral of $\frac{1}{t^4} = t^{-4}$ is $\frac{t^{-3}}{-3} = -\frac{1}{3t^3}$

Then

$\int \frac{375}{t^4} dt = -\frac{125}{t^3}$

Applying the limits, by the Fundamental Theorem of Calculus:

At $t = 15$ , $f(15) = -\frac{125}{15^3} = -\frac{1}{27}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A) = -\frac{1}{27} + 1 = -\frac{1}{27} + \frac{27}{27} = \frac{26}{27}$

Probability of arriving in less than 15 minutes and less than 10 minutes.

The intersection of these events is less than 10 minutes, so:

$P(B) = \int_{5}^{10} = \frac{375}{t^4}$

We already have the integral, so just apply the limits:

At $t = 10$ , $f(10) = -\frac{125}{10^3} = -\frac{1}{8}$

At $t = 5$ , $f(5) = -\frac{125}{5^3} = -1$

Then

$P(A \cap B) = -\frac{1}{8} + 1 = -\frac{1}{8} + \frac{8}{8} = \frac{7}{8}$

If given the train arrived in less than 15 minutes, what is the probability it arrived in less than 10 minutes?

$P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{\frac{7}{8}}{\frac{26}{27}} = 0.9087$

Thus 90.87%, approximately 91%, and the correct answer is given by option D.

3 0

3 years ago

This bc it’s really really really hard and I can’t figure it out

Ket [755]

Answer:

-4/5

Step-by-step explanation:

3/5+(-7/5)

-4/5

5 0

2 years ago

write an even number with a 7 in the hundred place and a odd in the thousends place and is a multiple of 10

attashe74 [19]

Answer:

3,700

299,677,710

9,780

Step-by-step explanation:

6 0

4 years ago

Polygon ABCD is dilated by a scale factor of 2 with the center of dilation at the origin to create A'B'C'D'. If the endpoints of

Sonja [21]

The distance formula is given by $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Take point A(0, -7) as (x₁, x₂) and point B(8, 8) as (y₁, y₂)

Distance AB = $\sqrt{(8-0)^2+(8--7)^2}$
Distance AB = $\sqrt{8^2+15^2}$
Distance AB = $\sqrt{289}$
Distance AB = 17

The line AB is dilated to A'B' by scale factor of 2, it means the length of the line is multiplied by 2

Distance A'B' = 2 × 17 = 34 units

5 0

3 years ago

The numerator that makes the equation true

AURORKA [14]

The numerator would be 9 because u multiply 3/4 by 3 to get the bottom number to 12 so multiplying 3x3=9

8 0

3 years ago

Given f(x)= 2x4 + 6x3 – 10x2 + kx – 10, for what value of k is (x - 1) a factor of f(x)?​

Given f(x)= 2x4 + 6x3 – 10x2 + kx – 10, for what value of k is (x - 1) a factor of f(x)?