Five-year-old students at an elementary school were given a 30-yard head start in a race. The graph shows how far the avera

ZanzabumX [31]

Answer:-3 3/5 <1.3

Step-by-step explanation:

5 0

3 years ago

Consider a game in which players roll a number cube to determine the number of points earned. If a player rolls a prime number,

Aleksandr-060686 [28]

Answer:

The expected value of the points earned on a single roll in this game is $\dfrac{1}{6} = 0.1667$ .

Step-by-step explanation:

We are given that consider a game in which players roll a number cube to determine the number of points earned. If a player rolls a prime number, that many points will be added to the player’s total. Any other roll will be deducted from the player’s total.

Assuming that the numbered cube is a dice with numbers (1, 2, 3, 4, 5, and 6).

Here, the prime numbers are = 1, 2, 3 and 5

Numbers which are not prime = 4 and 6

This means that if the dice got the number 1, 2, 3 or 5, then that many points will be added to the player’s total and if the dice got the number 4 or 6, then that many points will get deducted from the player’s total.

Here, we have to make a probability distribution to find the expected value of the points earned on a single roll in this game.

Note that the probability of getting any of the specific number on the dice is $\dfrac{1}{6}$ .

Numbers on the dice (X) P(X)

+1 $\frac{1}{6}$

+2 $\frac{1}{6}$

+3 $\frac{1}{6}$

-4 $\frac{1}{6}$

+5 $\frac{1}{6}$

-6 $\frac{1}{6}$

Here (+) sign represent the addition in the player's total and (-) sign represents the deduction in the player's total.

Now, the expected value of X, E(X) = $\sum X \times P(X)$

= $(+1) \times \frac{1}{6} +(+2) \times \frac{1}{6} +(+3) \times \frac{1}{6} +(-4) \times \frac{1}{6} +(+5) \times \frac{1}{6} +(-6) \times \frac{1}{6}$

= $\frac{1}{6} + \frac{2}{6} + \frac{3}{6} - \frac{4}{6} + \frac{5}{6} - \frac{6}{6}$

= $\frac{1+2+3-4+5-6}{6}$

= $\frac{11-10}{6}= \frac{1}{6}$

Hence, the expected value of the points earned on a single roll in this game is $\frac{1}{6} = 0.1667$ .

4 0

3 years ago

PEF and triangle GHI are similar right triangles.

LekaFEV [45]

Answer: it’s the first 1

Step-by-step explanation:

6 0

2 years ago

Evaluate the expression Arcsec(sqrt 2). Do not use your calculator to answer this question. Do not express answer in decimals.

Igoryamba

Pi/4 radians
You're looking for the angle that has a secant of sqrt(2). And since the secant is simply the reciprocal of the cosine, let's take a look at that.
sqrt(2) = 1/x
x*sqrt(2) = 1
x = 1/sqrt(2)
Let's multiply both numerator and denominator by sqrt(2), so
x = sqrt(2)/2
And the value sqrt(2)/2 should be immediately obvious to you as a trig identity. Namely, that's the cosine of a 45 degree angle. Now for the issue of how to actually give you your answer. There's no need for decimals to express 45 degrees, so that caveat in the question doesn't make any sense unless you're measuring angles in radians. So let's convert 45 degrees to radians. A full circle has 360 degrees, or 2*pi radians. So:
45 * (2*pi)/360 = 90*pi/360 = pi/4
So your answer is pi/4 radians.

5 0

3 years ago

Read 2 more answers

I need help someone help me please <3

ElenaW [278]

Answer:

$y=-\frac{3}{2}x-2$

Step-by-step explanation:

using the y=mx+b equation, where m=slope and b=y-intercept, we can place our known slope and y-intercept to form our answer, $y=-\frac{3}{2}x-2$ :-) hope this helped!

4 0

3 years ago