Which of the following choices best describes the expression (2x + 1) − (x + 32)

There are two games involving flipping a coin. In the first game you win a prize if you can throw between 45% and 55% heads. In

Nina [5.8K]

Answer:

d) 300 times for the first game and 30 times for the second

Step-by-step explanation:

We start by noting that the coin is fair and the flip of a coin has a probability of 0.5 of getting heads.

As the coin is flipped more than one time and calculated the proportion, we have to use the <em>sampling distribution of the sampling proportions</em>.

The mean and standard deviation of this sampling distribution is:

$\mu_p=p\\\\ \sigma_p=\sqrt{\dfrac{p(1-p)}{N}}$

We will perform an analyisis for the first game, where we win the game if the proportion is between 45% and 55%.

The probability of getting a proportion within this interval can be calculated as:

$P(0.45$

referring the z values to the z-score of the standard normal distirbution.

We can calculate this values of z as:

$z_H=\dfrac{p_H-\mu_p}{\sigma_p}=\dfrac{(p_H-p)}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_H-p)>0\\\\\\z_L=\dfrac{p_L-\mu_p}{\sigma_p}=\dfrac{p_L-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p_L-p)$

If we take into account the z values, we notice that the interval increases with the number of trials, and so does the probability of getting a value within this interval.

With this information, our chances of winning increase with the number of trials. We prefer for this game the option of 300 games.

For the second game, we win if we get a proportion over 80%.

The probability of winning is:

$P(p>0.8)=P(z>z^*)$

The z value is calculated as before:

$z^*=\dfrac{p^*-\mu_p}{\sigma_p}=\dfrac{p^*-p}{\sqrt{\dfrac{p(1-p)}{N}}}=\sqrt{\dfrac{N}{p(1-p)}}*(p^*-p)>0$

As (p*-p)=0.8-0.5=0.3>0, the value z* increase with the number of trials (N).

If our chances of winnings depend on P(z>z*), they become lower as z* increases.

Then, we can conclude that our chances of winning decrease with the increase of the number of trials.

We prefer the option of 30 trials for this game.

8 0

3 years ago

Plz help<br>which line segment is a reflection of AB in the x-axis

k0ka [10]

I think it would be (F,E)

5 0

3 years ago

Read 2 more answers

Mrs. Gilbert is interested in determining how many students spend 4 or more hours doing homework each week. She asks every stude

docker41 [41]

Answer:

C. Biased, because she only asked students on honor roll.

Step-by-step explanation:

Since Mrs. Gilbert's goal was to find how many students that spent >4 hours and not how many students that earned Honor Roll that spent >4 hours, the data is biased. Choose C.

4 0

3 years ago

Need help with two of these! Thank you

astraxan [27]

Step-by-step explanation:

17) 3x+5-12+4x+2x

3x+4x+2x +5-12

8x-7

if x =6

8*6-7 =48-7

= 41

18.) 9(3x-4y+8)

27x-36y+72

6 0

3 years ago

Q(x)=4x2-3x3+8x is it a cubic trinomial

Norma-Jean [14]

Answer:

Yes

Answer: x = 0

Step-by-step explanation:

Yes it is.

Down is the answer how to solve this equation and the steps.

Step 1 :

Equation at the end of step 1 :

qx - (((4 • (x2)) - 3x3) + 8x) = 0

Step 2 :

Equation at the end of step 2 :

qx - ((22x2 - 3x3) + 8x) = 0

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors :

qx + 3x3 - 4x2 - 8x =

x • (q + 3x2 - 4x - 8)

Equation at the end of step 4 :

x • (q + 3x2 - 4x - 8) = 0

Step 5 :

Theory - Roots of a product :

5.1 A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

5.2 Solve : x = 0

Solution is x = 0

Solving a Single Variable Equation :

5.3 Solve q+3x2-4x-8 = 0

In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.

Answer: x = 0

Hope this helps.

7 0

3 years ago