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1 year ago

In Martian Poker, the game is played with 8 cards drawn from a 52 card deck.

Mathematics

1 answer:

WITCHER [35]1 year ago

6 0

Step-by-step explanation:

In Martian Poker, the game is played with 8 cards drawn from a 52 card deck.

What is the probability of a Martian drawing “two trips and a pair". They get 2

three of a kinds and a pair.

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Let e1= 1 0 and e2= 0 1 , y1= 4 5 , and y2= −2 7 , and let T: ℝ2→ℝ2 be a linear transformation that maps e1 into y1 and maps

Furkat [3]

Answer:

The image of $\left[\begin{array}{c}4&-4\end{array}\right]$ through T is $\left[\begin{array}{c}24&-8\end{array}\right]$

Step-by-step explanation:

We know that $T:$ $IR^{2}$ → $IR^{2}$ is a linear transformation that maps $e_{1}$ into $y_{1}$ ⇒

$T(e_{1})=y_{1}$

And also maps $e_{2}$ into $y_{2}$ ⇒

$T(e_{2})=y_{2}$

We need to find the image of the vector $\left[\begin{array}{c}4&-4\end{array}\right]$

We know that exists a matrix A from $IR^{2x2}$ (because of how T was defined) such that :

$T(x)=Ax$ for all x ∈ $IR^{2}$

We can find the matrix A by applying T to a base of the domain ( $IR^{2}$ ).

Notice that we have that data :

$B_{IR^{2}}=$ { $e_{1},e_{2}$ }

Being $B_{IR^{2}}$ the cannonic base of $IR^{2}$

The following step is to put the images from the vectors of the base into the columns of the new matrix A :

$T(\left[\begin{array}{c}1&0\end{array}\right])=\left[\begin{array}{c}4&5\end{array}\right]$ (Data of the problem)

$T(\left[\begin{array}{c}0&1\end{array}\right])=\left[\begin{array}{c}-2&7\end{array}\right]$ (Data of the problem)

Writing the matrix A :

$A=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]$

Now with the matrix A we can find the image of $\left[\begin{array}{c}4&-4\\\end{array}\right]$ such as :

$T(x)=Ax$ ⇒

$T(\left[\begin{array}{c}4&-4\end{array}\right])=\left[\begin{array}{cc}4&-2\\5&7\\\end{array}\right]\left[\begin{array}{c}4&-4\end{array}\right]=\left[\begin{array}{c}24&-8\end{array}\right]$

We found out that the image of $\left[\begin{array}{c}4&-4\end{array}\right]$ through T is the vector $\left[\begin{array}{c}24&-8\end{array}\right]$

3 0

1 year ago

An increase in walking has been shown to contribute to a healthier life-style. A sedentary American takes an average of 5000 ste

Zielflug [23.3K]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

H0: µ = 5000

For the alternative hypothesis,

H1: µ > 5000

Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = population standard deviation

n = number of samples

From the information given,

µ = 5000

x = 5430

σ = 600

n = 40

z = (5430 - 5000)/(600/√40) = 4.53

Looking at the normal distribution table, the probability corresponding to the z score is < 0.0001

Since alpha, 0.05 > than the p value, then we would reject the null hypothesis. Therefore, at a 5% level of significance, it can be concluded that they walked more than the mean number of 5000 steps per day.

6 0

1 year ago

A process that produces bottles of shampoo, when operating correctly, produces bottles whose contents weight, on average, 20 oun

valentinak56 [21]

Answer:

a. Descriptive statistics for the sample.

n= 9

mean X[bar]= 20.36

median Me= 20.30

min: 19.70

max: 21.40

standad deviation S= 0.61

b. 95% Confidence interval [19.88; 20.83]

c. Decision: Support H₀

Step-by-step explanation:

Hello!

I don't have excel so I cannot install PHstat, I've used a statistic software called Infostat for the calculations.

There was a random sample of 9 bottles of shampoo taken to test if the process is operating correctly. If it is, the bottles should weight on average 20 ounces (this would be our study parameter)

The study variable is X: the weight of a bottle of shampoo.

X~N(μ;σ²)

Descriptive statistics for the sample.

n= 9

mean X[bar]= 20.36

median Me= 20.30

min: 19.70

max: 21.40

standad deviation S= 0.61

b. 95% Confidence interval.

Since the variable has a normal distribution and the population variance is unknown, the statistic to use to construct this interval is the Students t:

X[bar] ± $t_{n-1; 1- \alpha /2}$ * (S/√n)

20.36 ± $t_{8; 0.975}$ * (0.61/√9)

[19.88; 20.83]

c. You have to test the hypothesis that the production is operating correctly, if it is so, then:

H₀: μ = 20

H₁: μ ≠ 20

α: 0.05

The statistic value is t $_{H0}$ = 1.74

p-value: 0.1198

When you use the p-value to decide on a statistical hypothesis, you should always contrast it with the level of significance using the following rule:

If p-value ≤ α, then you reject the null hypothesis.

If p-value > α, then you do not reject the null hypothesis.

Since the p-value is greater than the significance level, you do not reject the null hypothesis. This means that the average weight of the shampoo bottles is 20 ounces, i.e. the process is operating correctly.

I hope it helps!

5 0

1 year ago

Pedro works as a newspaper deliverer. He receives a base pay plus an additional amount per newspaper delivered. Last week, Pedro

guapka [62]

Answer is

<span>g(x) = 2.5x + 25

</span>5 newspapers, 2.5(5) + 25 = 12.5 + 25 = 37.5
20 newspapers, 2.5(20) + 25 = 50 + 25 = 75

9 0

1 year ago

Read 2 more answers

Jamie made the tree diagram below to show the different choices he has for ordering a pizza for lunch. According to the tree dia

USPshnik [31]

Sizes = Small, Medium and Large, so they has 3 choices for size.

Crust = Thin or thick for each size, so they have 2 choices for crust.

Topping = Tomato or meatball for each one, so they have 2 choices for toppings.

The answer would be:

<span>Three choices for size, two choices for crust, and two choices for topping</span>

8 0

1 year ago

Read 3 more answers