A standard number cube is rolled 180 times. Predict how many times a 3 or a 5 will be the result.

The function f(t) = 4t2 − 8t + 6 shows the height from the ground f(t), in meters, of a roller coaster car at different times t.

gregori [183]

Answer:

The correct option is 3.

Step-by-step explanation:

The vertex form of a parabola is

$f(x)=a(x-h)^2+k$ .... (1)

where a, h, and k are integers, and interpret the vertex of f(t). (h,k) is the vertex of the parabola.

The given function is

$f(x)=4t^2-8t+6$

It can be written as

$f(x)=4(t^2-2t)+6$

If an expression is defined as $x^2+bx$ , then we need to add $(\frac{b}{2})^2$ to make it perfect square.

In the expression $t^2-2t$ the value of b is -2. So, we nned to add and subtract $(\frac{-2}{2})^2$ in the parenthesis.

$f(x)=4(t^2-2t+1^2-1^2)+6$

$f(x)=4(t^2-2t+1)+4(-1)+6$

$f(x)=4(t-1)^2-4+6$

$f(x)=4(t-1)^2+2$ .... (2)

The vertex form of the parabola is $f(x)=4(t-1)^2+2$ .

From (1) and (2), we get h=1 and k=2. It means the vertex of the parabola is (1,2). Vertex of upward parabola is point of minima. So the minimum height of the roller coaster is 2 meters from the ground.

Therefore the correct option is 3.

4 0

3 years ago

Suppose the average height of all humans is normally distributed with a mean of 72 inches and a variance of 18 inches.

nignag [31]

Answer:

a) P(75 < x < 80 ) = 0.2088

b) The probability that average height of all humans less than 65

P( X < 65 ) = 0.0495

Step-by-step explanation:

Step(i):-

Given mean of the Population = 72

Given variance of the Population = 18 inches.

Standard deviation of the Population = √18 = 4.242

Let 'x' be the random variable in Normal distribution

a)

Given X₁ = 75

$Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{75-72}{4.242} = 0.70721$

Given X₂= 80

$Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{80-72}{4.242} = 1.885$

The probability that average height of all humans between 75 and 80

$P(75 < X < 80 ) = P(0.70721 < Z < 1.885)$

= | A ( 1.885) - A( 0.70721|

= 0.4699 - 0.2611

= 0.2088

P(75 < x < 80 ) = 0.2088

b)

Step(ii):-

Given X₁ = 65

$Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{65-72}{4.242} = -1.650$

The probability that average height of all humans less than 65

P( X < 65 ) = P( Z < - 1.650 )

= 1 - P( Z > 1.650)

= 1 - ( 0.5 + A (1.650))

= 0.5 - A( 1.65)

= 0.5 - 0.4505

= 0.0495

The probability that average height of all humans less than 65

P( X < 65 ) = 0.0495

4 0

3 years ago

Which one is correct

g100num [7]

Answer:C.

Step-by-step explanation:

8 0

3 years ago

PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU B

lions [1.4K]

Answer:

2/11

Step-by-step explanation:

Let's say x = 0.18181818..

Then, 100x = 18.1818181....

so, if you put x in the repeating decimal in 18.1818,

you get the equation,

100x = 18+x

so, 99x = 18

x = 18/99 = 2/11

3 0

3 years ago

Read 2 more answers

Christopher scored 7 more than two times the questions Mathew scored on the math test. If Christopher scored 87 on the math test

viktelen [127]

Answer:

40

Step-by-step explanation:

To solve this, we can create an equation that represents this situation. Since Christopher score 7 more than twice what Mathew scored, the equation will be:

C = 2M + 7

(Variables are representative of the first letter of each name)

Seeing as Christopher scored 87, we can put that into the equation and solve for M.

So, the equation will be:

87 = 2M + 7

Subtract 7 from both sides in order to isolate variable M on the right side.

80 = 2M

Now solve for M, which is 40 (divide both sides by 2).

7 0

3 years ago