What is 20-23 (work does not need to be shown)

The prior probabilities for events A1 and A2 are P(A1) = 0.30 and P(A2) = 0.55. It is also known that P(A1 ∩ A2) = 0. Suppose P(

k0ka [10]

We're given the following probabilities:

$P(A_1)=0.30$

$P(A_2)=0.55$

$P(A_1\cap A_2)=0$

$P(B\mid A_1)=0.20$

$P(B\mid A_2)=0.05$

(a) Yes, $A_1$ and $A_2$ are mutually exclusive. This is exactly what zero probability of their intersection means. The two events cannot occur simultaneously.

(b) Use the definition of conditional probability to expand:

$P(A_1\cap B)=P(A_1)P(B\mid A_1)=0.30\cdot0.20=0.06$

$P(A_2\cap B)=P(A_2)P(B\mid A_2)=0.55\cdot0.05=0.0275$

(c) By the law of total probability,

$P(B)=P(A_1\cap B)+P(A_2\cap B)=0.06+0.0275=0.0875$

(d) Bayes' theorem says

$P(A_1\mid B)=\dfrac{P(A_1)P(B\mid A_1)}{P(B)}=\dfrac{0.30\cdot0.20}{0.0875}\approx0.686$

$P(A_2\mid B)=\dfrac{P(A_2)P(B\mid A_2)}{P(B)}=\dfrac{0.55\cdot0.05}{0.0875}\approx0.314$

3 0

2 years ago

The temperature function (in degrees Fahrenheit) in a three dimensional space is given by T(x, y, z) = 3x + 6y - 6z + 1. A bee i

madam [21]

You're looking for the extreme values of $T(x,y,z)=3x+6y-6z+1$ subject to $x^2+y^2+z^2=9$ . The Lagrangian is

$L(x,y,z,\lambda)=3x+6y-6z+1+\lambda(x^2+y^2+z^2-9)$

with critical wherever the partial derivatives vanish:

$L_x=3+2\lambda x=0\implies x=-\dfrac3{2\lambda}$

$L_y=6+2\lambda y=0\implies y=-\dfrac3\lambda$

$L_z=-6+2\lambda z=0\implies z=\dfrac3\lambda$

$L_\lambda=x^2+y^2+z^2-9=0$

Substituting the first three solutions into the last equation gives

$\dfrac9{4\lambda^2}+\dfrac9{\lambda^2}+\dfrac9{\lambda^2}=9$

$\implies\lambda=\pm\dfrac32$

$\implies x=1,y=2,z=-2\text{ or }x=-1,y=-2,z=2$

At these points, we have

$T(1,2,-2)=28$

$T(-1,-2,2)=-26$

so the highest temperature the bee can experience is 28º F at the point (1, 2, -2), and the lowest is -26º F at the point (-1, -2, 2).

6 0

2 years ago

Gas in Germany cost 1.50 euros per liter. how much is this in dollars per gallon

SIZIF [17.4K]

To solve this problem, you will have to first find how many US Dollars are in 1 Euro. Upon looking this up, I see that currently 1 Euro is worth 1.23 US Dollars. Next, you must calculate how many liters are in a gallon. Looking this up shows that 1 liter is equal to 0.264 gallons.

Since 0.264 is not a whole gallon and we are asked to find the price per gallon, we should next calculate how many liters can fit in a gallon. To do this, we will divide 1 by 0.264, which gives us 3.78. This tells us that 3.78 liters will fit into a gallon.

The cost of 1L of gas in euros is 1.50 Euros. Since we need 3.78L to equal 1 gallon, we can calculate the cost of this to be:

3.78 * 1.50 = €5.67

Earlier we determined that 1 euro is worth 1.23 US Dollars. Our final step is to convert our €5.67 per gallon to dollars per gallon. To do this, we simply have to multiply 5.67 by 1.23. This gives us $6.97.

So, our answer is that the cost is $6.97 per gallon.

Hopefully this is correct and makes sense to you. This is how I would approach the question.

3 0

2 years ago

Refer to the rectangular prism

slavikrds [6]

Answer:

Properties of a Rectangular Prism : A rectangular prism has 8 vertices, 12 sides and 6 rectangular faces. All the opposite faces of a rectangular prism are equal.

Step-by-step explanation:

4 0

1 year ago

Read 2 more answers

Drag numbers to write an equation for the line in slope-intercept form. Numbers may be used once, more than once, or not at all.

vfiekz [6]

Answer:

y = -4x + 5

Step-by-step explanation:

Here, we want to get the equation of the line that passes through the given points

The general form is;

y = mx + b

where m is the slope and b is the y intercept

To find the slope, we use the slope formula

this is ;

m = (y2-y1)/(x2-x1)

(x1,y1) = (0,5)

(x2,y2) = (2,-3)

m = (-3-5)/(2-0) = -8/2 = -4

To get the y-intercept we simply substitute one of the points

But we know that the y-intercept is the y-value when x = 0

From the point we can see (0,5) which means that the y-intercept is 5

so the equation of the line is;

y = -4x + 5

7 0

2 years ago