A survey was conducted of students at a high school and at a college to determine students' favorite subjects. The results are shown on the table.

Answer:

Explained below.

Step-by-step explanation:

The random variable X is defined as the number of stars in a given volume of space.

[tex]X\sim \text{Poisson}\ (\lambda=1)[/tex]

The probability mass function of X is:

[tex]p_{X}(x)=\frac{e^{-\lambda}\lambda^{x}}{x!}[/tex]

(7)

Compute the probability of exactly two stars in 16 cubic light-years as follows:

[tex]P(X=2)=\frac{e^{-1}\times 1^{2}}{2!}=\frac{e^{-1}}{2}=\frac{0.36788}{2}=0.18394\approx 0.184[/tex]

(8)

Compute the probability of three or more stars in 16 cubic light-years as follows:

[tex]P(X\geq 3)=1-P(X<3)\\\\=1-P(X=0)-P(X=1)-P(X=2)\\\\=1-\sum\limits^{2}_{x=0}[\frac{e^{-1}\times 1^{x}}{x!}]\\\\=1-0.36788-0.36788-0.18394\\\\=0.0803[/tex]

(9)

In 16 cubic light years there is only 1 star.

Then in 1 cubic light years there will be, (1/16) stars.

Then in 4 cubic light years there will be, 4 × (1/16) = (1/4) stars.

(10)

In 16 cubic light years there is only 1 star.

Then in 1 cubic light years there will be, (1/16) stars.

Then in t cubic light years there will be, [t × (1/16)] stars.

Answer:

For #5 all you have to do is set down to points in order for it to count. The answer is: (0,2) and (3,6)

Step-by-step explanation:

In order to find where exactly you must plot the points, we plug in what we know. In our equation, the 2 is our y intercept, this means that the point is (0,2) (Side Note: here's another example, (0,6) the 6 would be our y intercept)

From the point (0,2) we use the other value given. The other value given in this case, is our slope. When dealing with slope, we use Rise over Run or Rise/Run. This means that from the 2 on the graph, you rise 3 which would be 5 and you run to the right for 4. This now gets you the points (3,6)

Hope this helps with plotting the other questions! :)

(SIDE NOTE: IF THEY GIVE THE VALUE WITH X AS JUST A NUMBER, YOU CAN PLACE A 1 UNDER IT TO TURN IT INTO A FRACTION. FOR EXAMPLE 3X CAN BE TURNED INTO 3/1 WHICH WOULD THEN BE RISE 3 AND RUN 1.

(sooory about the caps, it's just to get your attention.)

Answer:

5=148 and 8=32

Step-by-step explanation:

For this equation we know since the lines are parelle that they will produce the same angle degrees.

so 2,4,6,and 8 are all 32

if we subtract 180 (the dregree of a stright line) from 32 we get 148

so 148 is for 1,3,5, and 7

Answer: $41.472 or $41.50

Step by step solving: First convert 20% to a decimal which is .20 now multiply that by $51.84 which equals 10.368 now subtract that number from 51.84 which equals 41.472

If you are allowed to round to the nearest hundreth then that would be $41.50 before the tip.

Answer:

9-4/5

5/5 = 1

Step-by-step explanation:

Answer:

1

9-4/5 is equal to 5/5 which is equal to 1

Answer:

D

Step-by-step explanation:

Answer:

2.83 inches

Step-by-step explanation:

Let y equal the length of the drawing in inches. Use a proportion to solve for the missing length.

Answer:

[tex]m = \frac{2}{3}[/tex]

Step-by-step explanation:

Use the following equation:

slope [tex](m) = \frac{y^2 - y^1}{x^2 - x^1}[/tex]

Set the variables with the points:

[tex](x_1 , y_1) = (-16 , -6)\\(x_2 , y_2) = (-4 , 2)\\[/tex]

Plug in the corresponding numbers to the corresponding variables in the equation:

[tex]m = \frac{2 - (-6)}{-4 - (-16)}[/tex]

[tex]m = \frac{2 - (-6)}{- 4 - (-16)} = \frac{2 + 6}{16 - 4} = \frac{8}{12}[/tex]

slope [tex]m = \frac{8}{12}[/tex] [tex]= \frac{2}{3}[/tex]  (simplified)

~

Answer:

2/3

Step-by-step explanation:

Answer:

-1.0

Step-by-step explanation:

Answer:

11, there both 8 away so its right in ze middle :D

Step-by-step explanation:

Answer:

(0,4)

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

Step 1: translate the given word problem into solvable algebraic equation.

Let "t" represent the number of tadpoles Joseph caught.

"Wendy caught nine times three more than Joseph caught" can be expressed as 9(t + 3)

Number of Wendy's tadpole = [tex] 9(t + 3) [/tex]

Given that half of Wendy's tadpole and also 6 times Joseph's tadpoles swarm away leaving Wendy with only 3, the following equation can be written:

[tex] \frac{9(t + 3)}{2} - 6t = 3 [/tex]

Step 2: solve for t using the equation created.

[tex] \frac{9(t + 3)}{2} - 6t = 3 [/tex]

Add 6t to both sides

[tex] \frac{9(t + 3)}{2} - 6t + 6t = 3 + 6t [/tex]

[tex] \frac{9(t + 3)}{2} = 3 + 6t [/tex]

Multiply both sides by 2

[tex] \frac{9(t + 3)}{2}*2 = (3 + 6t)*2 [/tex]

[tex] 9(t + 3) = 2(3 + 6t) [/tex]

[tex] 9t + 27 = 6 + 12t [/tex]

Collect like terms

[tex] 9t - 12t = 6 - 27 [/tex]

[tex] -3t = -21 [/tex]

Divide both sides by -3

[tex] t = 7 [/tex]

Joseph caught 7 tadpoles

idkStep-by-step explanation:

Answer:

0 The product will be smaller than both the factors.

0 There will be a zero in the tenths place.

0 The answer is 0.04.

Answer:

8

Step-by-step explanation:

Mary needs 8 boxes to put 96 muffins in dozens so 96÷12 gives you 8

Answer:

[tex] {a}^{2} + 2ab + {b}^{2} [/tex]

Answer:

(a + b) × (a + b)

Step-by-step explanation:

(a + b)²

(a + b) × (a + b)

Answer:

0 degrees faranhiet

Step-by-step explanation:

when you add 14 and -5 you get 9 then the question says 9 degrees cooler so that would translate to the problem 9 - 9 which you get zero.

Answer:

No, triangle B is a reflection of triangle A.

Step-by-step explanation:

The points of triangle A are reflected across the dotted line. So as a result triangle B is a reflection of triangle A.

Answer:

No

Step-by-step explanation:

Its a reflection because even if you did rotate it it would never be in that orientation.

Answer:

t=x+3

y = (x+3)^2 + 5

y = x^2+6x + 9 + 5

y= x^2 + 6x + 14

Answer:

5 times x-3?

Step-by-step explanation:

Sorry if its wrong i didn't really understand what you wanted.

Answer:

h(x) = (x-6)(x+2)

k(x) is not further factorable

Step-by-step explanation:

h(x) = x²-4x-12

      = (x-6)(x+2)

k(x) = x²-4x+8

not further factorable

Answer:

1/6

Step-by-step explanation:

9: 9,18,27,36,45,54,63,72,81,90

10: 10,20,30,40,50,60,70,80,90,100

Since, 90 is the LCM of 9 and 10 that turns into your denominater then your equation turns into this...

5/90 x 3/90

The denomineter stays the same so you get 90 then 5 x 3 equals 15 so you get 15 and in total that gives you 15/90. Divide the top and bottom by the greatest number that will divide both numbers exactly which gives you 1/6

HOPE THIS HELPED :D

Answer:

219.42858852

Step-by-step explanation:

Answer:

x= 6, -7

Step-by-step explanation:

Answer:

- 1/2

Step-by-step explanation:

Just took the test

The value of cot (b) using trigonometry is -1/2 when tan b = -2.

Since we are given that tan(b) = -2 and the terminal side of angle b is in quadrant II, determine the value of cot(b).

In quadrant II, the sine and cosine values are positive, while the tangent and cotangent values are negative.

Given:

tan(b) = -2

The cotangent (cot) of an angle is the reciprocal of the tangent:

cot(b) = 1 / tan(b)

Now, substituting the given value of tan(b):

cot(b) = 1 / (-2)

cot(b) = -1/2

So, the value of cot(b) is -1/2.

Learn more about Trigonometry here:

https://brainly.com/question/11016599

#SPJ4

Answer:

I think it B or C but hope I can help :)

Step-by-step explanation:

Answer:

f(x)= -(x-2)^2+2

Step-by-step explanation:

the same valuve needs the be added to both sides

f(x)+?= -x^2+4x+?-2

to complete the square -x^2+4x-4= -(x-2)^2 add the -4 to the expression

f(x)+?= -x^2+4x-4-2

since -4 was added to the right side, also add -4 the the left side

f(x)-4= -x^2+4x+?-2

now factor out the negative sign from the expression

f(x)-4= -(x^2-4x+4)-2

using a^2-ab+b^2=(a-b)^2

f(x)-4= -(x-2)^2-2

move the constant the the right side and change its sign

f(x)= -(x-2)^2-2+4

now calculate the sum

f(x)= -(x-2)^2+2

Answer: h/3 + 7.5 = w

Answer:

C.1%

Step-by-step explanation:

Answer:

force = 100 m/s/25 s = 4 m/s^2

Answer:

c

Step-by-step explanation: