____probability is the predicted ratio of favorable outcomes to the total number of outcomes.

Find the remainder when x51+x is divided by x+1

kaheart [24]

Answer:

-2

Step-by-step explanation:

By definition, the remainder is the portion of the dividend that is not evenly divisible by the divisor. Basically, it is what's left over. In this case, -2 is the amount left over after dividing this equation.

3 0

3 years ago

A simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6. respectively. All 10 dice we

kompoz [17]

Answer:

C) a sample distribution of a sample mean with n = 10

$\mu_{{\overline}{X}} = 3.5$

and $\sigma_{{\overline}{Y}} = 0.38$

Step-by-step explanation:

Here, the random experiment is rolling 10, 6 faced (with faces numbered from 1 to 6) fair dice and recording the average of the numbers which comes up and the experiment is repeated 20 times.So, here sample size, n = 20 .

Let,

$X_{ij}$ = The number which comes up on the ith die on the jth trial.

∀ i = 1(1)10 and j = 1(1)20

Then,

$E(X_{ij})$ = $\frac {1 + 2 + 3 + 4 + 5 + 6}{6}$

= 3.5 ∀ i = 1(1)10 and j = 1(1)20

and,

$E(X^{2}_{ij}$ = $\frac {1^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2}}{6}$

= $\frac {1 + 4 + 9 + 16 + 25 + 36}{6}$

= $\frac {91}{6}$

$\simeq$ 15.166667

so, $Var(X_{ij}$ = $(E(X^{2}_{ij} - {(E(X_{ij})}^{2})$

$\simeq 15.166667 - 3.5^{2}$

= 2.91667

and $\sigma_{X_{ij}}$ = $\sqrt {2.91667}[/tex [tex]\simeq 1.7078261036$

Now we get that,

$Y_{j} = \frac {\sum_{j = 1}^{20}X_{ij}}{20}$

We get that $Y_{j}'s$ are iid RV's ∀ j = 1(1)20

Let, ${\overline}{Y} = \frac {\sum_{j = 1}^{20}Y_{j}}{20}$

So, we get that $E({\overline}{Y}) = E(Y_{j})$

= $E(X_{ij}$ for any i = 1(1)10

= 3.5

and,

$\sigma_{({\overline}{Y})} = \frac {\sigma_{Y_{j}}}{\sqrt {20}} = \frac {\sigma_{X_{ij}}}{\sqrt {20}} = \frac {1.7078261036}{\sqrt {20}} [tex]\simeq 0.38$

Hence, the option which best describes the distribution being simulated is given by,

C) a sample distribution of a sample mean with n = 10

$\mu_{{\overline}{X}} = 3.5$

and $\sigma_{{\overline}{Y}} = 0.38$

6 0

2 years ago

What is the inequaliity of 3<-5n+2n and how do you put it on a number line

timama [110]

The inequality would be the negative factor, because -5n+2n is 3n. You would write it on a number line like this.....
Sry, i was just making an educated guess.... RIP....

6 0

3 years ago

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100 is the regular price if you buy one and get the other half price. Explain how this different from getting a 50% discount?

Vinvika [58]

100 = x + x/2

3x/2 = 100

x = 200/3

if there was 50% discount:

buying 1 would be $33.33

buying 2 would be $66.67

4 0

3 years ago

The table represents the change in the boiling point of water at different altitudes. Altitude (in thousands of feet) Boiling Po

Anton [14]

Answers:

1) The dependent variable is the boiling point of water and the independent variable is the altitude.

2) The slope would represent the average decrease of the boiling point of water per every one thousand feet that the altitude increase.

Explanation:

1) given

Table:

<span>Altitude (in thousands of feet)    Boiling Point of Water (Fahrenheit)

(sea level) 0    212
0.5                                               211.1
1.0                                               210
2.0                                               208.4
2.5                                               207.5
3.0                                               206.6
4.0                                               204.8
4.5                                               203.9

2) The independent variable is the input of the function, and the dependent variable is the output of the function.

The input determines the output once the rule is established.

Therefore:

a) the independent variable is the altitude, and
b) the dependent variable is the boiling point of water in Farenheit.

3) The slope of the graph would be:

                 change in the dependent variable          change in boiling point
slope = --------------------------------------------------- = ---------------------------------
</span>                 change in the independent variable          change in altitude

Therefore, the slope represents the average change in the boiling boilin point of water every one thousand feet on change of altitude.

If the relationship is not linear, then the slope is not constant, and you will have different slopes for different parts.

If the slope is negative, means that as the altitude increase the boiling point of water decrease.

You can calculate the slope using any two pair of points (data)

              212 - 210           2
slope =---------------- =   ------- = - 2
                0 - 1            - 1

or, using other pair of points:

                204.8 - 210           -5.2
slope = --------------------- =   --------- = -2.6
                  4.0 - 2.0               2.0

As you see, the slope is not constant. So, the function is not linear.

5 0

3 years ago

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