MATHEMATICS HIGH SCHOOL

Experience shows that a ski lodge will be full (153 guests) if there is a heavy snow fall while only partially full (62 guests) with a light snow fall. What is the expected number of guests if the probability for a heavy snow fall is .40

Answers

Answer 1

Answer:

The expected number of guests if the probability for a heavy snow fall is .40 = 98.4

Step-by-step explanation:

The total number of guests for lodge to be full = 153

During heavy snow fall, the lodge will be full.

The expected number of guests during heavy snow fall = 153

During partial snow fall, the expected number of guests = 62

The probability of heavy snowfall = 0.4

The probability of partial snow fall = 1 - 0.4 = 0.6

The expected number of guests = [(0.4) (153)] + [(0.6) (62)]

= 61.2 + 37.2

= 98.4

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Which of the following is a solution of y > |x| - 6?(-5, 1)
(-1, -5)
(5, -1)

Answers

absolute value of x minus 6 is less than y
one way is to jsut make all the x's positive, then subtract them from 6 and see if they are less

sorry for confusing, just read below

(-5,1)
1>|-5|-6
1>5-6
1>-1
true

(-1,-5)
-5>|-1|-6
-5>1-6
-5>-5
false

(5,-1)
-1>|5|-6
-1>-1
false

answer is (-5,1)

Answer A is the correct one

Let R be the region in the first quadrant bounded by the graph of y=sqrt{x-2} and the line y=2.(a). Find the volume of the solid generated when R is revolved about the x-axis.
(b). Find the volume of the solid generated when R is revolved about the line y=-2.

Answers

Volume of the solid generated when R is revolved about the x-axis is 10π and the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.

What is Graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The volume of the solid generated when R is revolved about the x-axis,

$V=\int\limits^a_b\pi {y^(2) } \, dx$

where a and b are the x-coordinates of the points of intersection of the curve y = √(x-2) and the line y = 2.

Solving y = √(x-2) and y = 2 for x, we get:

x = 6 and x = 2

Limits of integration are a = 2 and b = 6. Substituting y = √(x-2) into the formula for the volume, we get:

V = $\int\limits^6_2\pi\sqrt{(x-2)^(2) } \, dx$

V= π [(6²/2 - 2(6)) - (2²/2 - 2(2))]

=10π

Volume of the solid generated when R is revolved about the x-axis is 10π.

b. The volume of the solid generated when R is revolved about the line y = -2

$V=\int\limits^a_b\pi {(y+2)^(2) } \, dx$

Substituting y = √(x-2) into the formula for the volume, we get:

$V=\int\limits^2_6\pi (√(x-2)+2)^(2) \, dx$

We can simplify this by using the identity:

V =40π/3

Therefore, the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.

Hence, Volume of the solid generated when R is revolved about the x-axis is 10π and the volume of the solid generated when R is revolved about the line y = -2 is 40π/3.

To learn more on Graph click:

brainly.com/question/17267403

#SPJ6

A.) Find the volume of the solid generated when R is revolved about the x-axis.

Please answer question 14

Answers

there are 36 possibilities so
1,1
1,2
1,3
1,4
1,5
1,6
2,1
2,2
2,3
2,4
2,5
2,6
3,1
3,2
3,3
3,4
3,5
3,6
4,1
4,2
4,3
4,4
4,5
4,6
5,1
5,2
5,3
5,4
5,5
5,6
6,1
6,2
6,3
6,4
6,5
6,6

Where are the x-intercepts for f(x) = −4cos(x − pi over 2) from x = 0 to x = 2π?

Answers

recall that to get the x-intercepts, we set the f(x) = y = 0, thus

$\bf \stackrel{f(x)}{0}=-4cos\left(x-(\pi )/(2) \right)\implies 0=cos\left(x-(\pi )/(2) \right)\n\n\ncos^(-1)(0)=cos^(-1)\left[ cos\left(x-(\pi )/(2) \right) \right]\implies cos^(-1)(0)=x-\cfrac{\pi }{2}\n\n\nx-\cfrac{\pi }{2}=\begin{cases}(\pi )/(2)\n\n(3\pi )/(2)\end{cases}$

$\bf -------------------------------\n\nx-\cfrac{\pi }{2}=\cfrac{\pi }{2}\implies x=\cfrac{\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{2\pi }{2}\implies \boxed{x=\pi }\n\n-------------------------------\n\nx-\cfrac{\pi }{2}=\cfrac{3\pi }{2}\implies x=\cfrac{3\pi }{2}+\cfrac{\pi }{2}\implies x=\cfrac{4\pi }{2}\implies \boxed{x=2\pi }$

A total of 60 children signed up for hockey. There were 3 boys for every 1 girl who signed up. How many of the children who signed up for hockey were girls?

Answers

Answer: The answer is 15.

Step-by-step explanation: Given that there are a total of 60 students who signed up for hockey, where there were 3 boys for every 1 girl who signed up. We are to find the number of girls who signed up.

The ratio of the number of boys to the number of girls will be 3 : 1.

Let '3x' and 'x' be the number of boys and number of girls respectively who signed up.

Therefore, we have

$3x+x=60\n\n\Rightarrow 4x=60\n\n\Rightarrow x=15.$