6= 7-2/3x what does x equal

If x – 10 is a factor of x2 – 8x – 20, what is the other factor?

Svetach [21]

Answer:

The other factor is $(x+2)$

Step-by-step explanation:

we know that

$(x-a)(x-b)=x^{2}-xb-xa+ab$

$(x-a)(x-b)=x^{2}-(a+b)x+ab$

In this problem we have

$x^{2} -8x-20$

and

$a=10$ -----> because is a factor

substitute and solve for b

$x^{2} -8x-20=x^{2}-(10+b)x+10b$

so

$8=10+b\\b=-2$

Verify in the second equation

$-20=10b$ -----> $-20=10(-2)$ -----> $-20=-20$ --> is ok

The other factor is $(x+2)$

3 0

3 years ago

Read 2 more answers

Lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. a bank conducts inter

Otrada [13]

Part A:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector correctly determined that a selected person is saying the truth has a probability of 0.85
Thus p = 0.85

Thus, the probability that the lie detector will conclude that all 15 are telling the truth if all 15 applicants tell the truth is given by:

 $P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(15)={ ^{15}C_{15}(0.85)^{15}(0.15)^0} \\ \\ =1\times0.0874\times1=0.0874$


Part B:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.25
Thus p = 0.15

Thus, the probability that the lie detector will conclude that at least 1 is lying if all 15 applicants tell the truth is given by:

$P(X)={ ^nC_xp^xq^{n-x}} \\ \\ \Rightarrow P(X\geq1)=1-P(0) \\ \\ =1-{ ^{15}C_0(0.15)^0(0.85)^{15}} \\ \\ =1-1\times1\times0.0874=1-0.0874 \\ \\ =0.9126$

Part C:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The mean is given by:

$\mu=npq \\ \\ =15\times0.15\times0.85 \\ \\ =1.9125$

Part D:

Given that lie detectors have a 15% chance of concluding that a person is lying even when they are telling the truth. Thus, lie detectors have a 85% chance of concluding that a person is telling the truth when they are indeed telling the truth.

The case that the lie detector wrongly determined that a selected person is lying when the person is actually saying the truth has a probability of 0.15
Thus p = 0.15

The probability that the number of truthful applicants classified as liars is greater than the mean is given by:

 $P(X\ \textgreater \ \mu)=P(X\ \textgreater \ 1.9125) \\ \\ 1-[P(0)+P(1)]$

 $P(1)={ ^{15}C_1(0.15)^1(0.85)^{14}} \\ \\ =15\times0.15\times0.1028=0.2312$

8 0

3 years ago

I need help please i’ll give u a brainliest for the right answer

nevsk [136]

Answer:

around 4.1

Step-by-step explanation:

7 0

2 years ago

Rounded to three decial places, the value of the irrational number e is

scoray [572]

E = 2.718281828...
rounded to 3 decimal places
2.718

8 0

3 years ago

Mia has a budget of $250 to spend on a health club membership. The monthly membership fee is $20, and there is a one-time regist

Leokris [45]

So we cant go over $250

35+20n=250

now that i put the question in an expression we can take the 35 away from both sides

35+20n=250
-35. -35
_____________
20n=215

now divide 20 by both sides to get (n) alone

20n=215
________
20

n= 10.75

we round down because we cannot exceed the limit, thus

ANSWER: 10 months

7 0

3 years ago