When is it necessary to use three points to name an angle? If CP bisects and DPB , what is the measure of angle CPB?

The curve with equation y=e^2x/4+3e^x has one stationary point.find the exact value of the coordinates of this point

Softa [21]

$y=\dfrac{e^{2x}}{4+3e^x}$
$\implies y'=\dfrac{2e^{2x}(4+3e^x)-3e^xe^{2x}}{(4+3e^x)^2}$
$\implies y'=\dfrac{8e^{2x}+3e^{3x}}{(4+3e^x)^2}$

Stationary points occur where the derivative is zero. The denominator is positive for all $x$ , so we only need to worry about the numerator.

$8e^{2x}+3e^{3x}=e^{2x}(8+3e^x)=0$

$e^{2x}>0$ for all $x$ , so we can divide through:

$8+3e^x=0\implies e^x=-\dfrac83$

But $e^x>0$ for all $x\in\mathbb R$ , so this function has no stationary points...

I suspect there may be a typo in the question.

6 0

3 years ago

What is the probability that a random person who tests positive for a certain blood disease actually has the disease, if we know

xeze [42]

Answer:

Step-by-step explanation:

Hello!

Any medical test used to detect certain sicknesses have several probabilities associated with their results.

Positive (test is +) ⇒ P(+)

True positive (test is + and the patient is sick) ⇒ P(+ ∩ S)

False-positive (test is + but the patient is healthy) ⇒P(+ ∩ H)

Negative (test is -) ⇒ P(-)

True negative (test is - and the patient is healthy) ⇒ P(- ∩ H)

False-negative (test is - but the patient is sick) ⇒ P(- ∩ S)

The sensibility of the test is defined as the capacity of the test to detect the sickness in sick patients (true positive rate).

⇒ P(+/S) = P(+ ∩ S)

P(S)

The specificity of the test is the capacity of the test to have a negative result when the patients are truly healthy (true negative rate)

⇒ P(-/H) = P(- ∩ H)

P(H)

For this particular blood disease the following probabilities are known:

1% of the population has the disease: P(S)= 0.01

95% of those who are sick, test positive for it: P(+/S)= 0.95 (sensibility of the test)

2% of those who don't have the disease, test positive for it: P(+/H)= 0.02

The probability of a person having the blood sickness given that the test was positive is:

P(S/+)= P(+ ∩ S)

P(+)

The first step you need to calculate the intersection between both events + and S, for that you will use the information about the sickness prevalence in the population and the sensibility of the test:

P(+/S) = P(+ ∩ S)

P(S)

P(+/S)* P(S) = P(+ ∩ S)

P(+ ∩ S) = 0.95*0.01= 0.0095

The second step is to calculate the probability of the test being positive:

P(+)= P(+ ∩ S) + P(+ ∩ H)

Now we know that 1% of the population has the blood sickness, wich means that 99% of the population doesn't have it, symbolically: P(H)= 0.99

Then you can clear the value of P(+ ∩ H):

P(+/H) = P(+ ∩ H)

P(H)

P(+/H)*P(H) = P(+ ∩ H)

P(+ ∩ H) = 0.02*0.99= 0.0198

Next you can calculate P(+):

P(+)= P(+ ∩ S) + P(+ ∩ H)= 0.0095 + 0.0198= 0.0293

Now you can calculate the asked probability:

P(S/+)= P(+ ∩ S) = 0.0095 = 0.32

P(+) 0.0293

I hope it helps!

6 0

3 years ago

For the following statements 11 - 16 write TRUE or FALSE.

andrezito [222]

Answer:11 is false. Through any two points there is exactly one line. 12 is true. 13 is true. 14 is true. 15 is false. Two planes intersect at a line. 16 is false. A line and a plane would intersect at a point

Step-by-step explanation:

4 0

3 years ago

Solve the equation.9x^2 + 16 = 0

REY [17]

Step 1

Given;

$9x^2+16=0$

Required: To solve the equation.

Step 2

Solve the equation

$\begin{gathered} 9x^2+16-16=0-16 \\ 9x^2=-16 \\ \frac{9x^2}{9}=\frac{-16}{9} \\ x^2=-\frac{16}{9} \\ \sqrt{x^2}=\pm\sqrt{\frac{-16}{9}} \\ x=\sqrt{-\frac{16}{9}},\:x=-\sqrt{-\frac{16}{9}} \\ x=i\frac{4}{3},\:x=-i\frac{4}{3} \end{gathered}$

Answer;

$x=\frac{4}{3}i,\text{ -}\frac{4}{3}i$

4 0

1 year ago

Select the correct function.

erma4kov [3.2K]

Check the picture below.

so let's use those two points the line passes through to get its slope.

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-12}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-12-0}{4-2}\implies \cfrac{-12}{2}\implies -6$

8 0

3 years ago