If triangle ABC is euilateral solve for x (8x-44)

What is the standard form of (6x^2-8x-7)+(8x^2-76x)

Studentka2010 [4]

Answer: 14x^2 - 84x - 7

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Explanation:

The like terms 6x^2 and 8x^2 combine to 14x^2

The like terms -8x and -76x combine to -84x

Nothing pairs with the -7, so its stays as is.

Standard form is where we list the terms in decreasing exponent order. We can think of -84x as -84x^1 and the -7 as -7x^0. So 14x^2 - 84x - 7 would be the same as 14x^2 - 84x^1 - 7x^0. The exponents count down: 2,1,0.

The final answer is a trinomial since it has three terms. It is also a quadratic because the degree (highest exponent) is 2.

5 0

2 years ago

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

A ball is thrown into the air with an upward velocity of 48 ft/s. Its height h in feet after t seconds is given by the function

Masja [62]

The equation modeling the height of the ball at time,t is given by h=-16t²+48t+6
a. In how many seconds does the ball reach its maximum height?
Time taken for the ball to reach the maximum height will be given by:
h'(t)=-32t+48=0
finding the value of t we get:
32t=48
t=48/32
t=1.5 seconds
Thus the time taken for the ball to reach the maximum time is 1.5 seconds

b] What is the ball’s maximum height?
The maximum height will be:
h(1.5)=-16(1.5)²+48(1.5)+6
h(1.5)=42 fee

3 0

3 years ago

A map of an island is shown on a half-centimetre grid,

SOVA2 [1]

Answer:

The answer is b.

Step-by-step explanation:

4 0

3 years ago

I have $11.60 in dimes and quarters. I have 32 more dimes than quarters. How many dimes and how many quarters do I have?

Kazeer [188]

D=dimes
Q=quarters

D=32+Q
Q=?
D+Q=$11.6
D=(32*10)+Q=
$3.2+Q
$11.6-$3.2=$8.4
Each quarter must include 1 dime from now on because there’s 32 MORE dimes than quarters. $8.4/$0.35=24. (Divide 8.4 dollars by 1quarter+1dime, which is 35 cents.)

35 cents goes into $8.4 dollars 24 times. This means there’s 24 quarters and 24 more dimes. Returning to our original equations,
D=32+24
D=56
Q=24

This follows the rule of having 32 more dimes than quarters and the two add up to the correct amount, $11.60

There’s 56 dimes and 24 quarters

8 0

3 years ago