Please answer the following:

CLASS 8 SPOT TEST

1.WHAT IS THE PROBABILITY THAT AN INTEGER CHOSEN AT RANDOM BETWEEN 1 TO 10 INCLUSIVE IS EVEN?

2. A BAG CONTAINS 5 WHITE, 4 BLACK AND 1 BLUE BALLS. ONE BALL IS CHOSEN AT RANDOM. WHAT IS THE PROBABILITY THAT IT IS BLACK?

3.FIND THE PROBABILITY OF GETTING AN ODD NUMBER IN A SINGLE TOSS OF A FAIR DIE?

4.A FAIR DIE IS THROWN 900 TIMES. FIND THE NUMBER OF TIMES YOU WOULD EXPECT TO GET A 6.

5.THE PROBABILITY THAT IT WILL BE CLOUDY TOMORROW IS 0.45. WHAT IS THE PROBABILITY THAT IT WILL NOT BE CLOUDY TOMORROW?

Step-by-step explanation:

1. Of the following 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.

Only these 5 are even: 2, 4, 6, 8, 10.

The probability on an even number is 5 / 10 = 0.5 = 50%

2. The total number of balls is 10.

5 WHITE, 4 BLACK AND 1 BLUE

The probability on a black ball is 4 / 10 = 0.4 = 40%

3. A fair die can show the following 6 numbers 1, 2, 3, 4, 5, 6.

Only these 3 are odd: 1, 3, 5.

The probability on an odd number is 3 / 6 = 0.5 = 50%

4. The probability of a six is 1 / 6. If the die is cast for 900 times you can expect it to be 900 * 1 / 6= 900/6 = 150. The number of times you would expect a 6 would be 150.

5. If the probability on a cloudy tomorrow is 0.45, then in mathematics, that defines the propability for an non cloudy tomorrow as 1 - 0.45 = 0.55, which is 55%.

(The total should always add up to 100%).

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

the correct answer would be the third option