Player Aled a baseball league in runs batted in for the 2008 regular season Player B, who came in second to player A, had 18 fewer runs batted in for the 2008 regular season Together, these two players
brought home 230 runs during the 2008 regular season. How many runs bafted in did player A and player Beach account for?
Player A had _______runs and player 6 had ______runs batted in for the 2008 regular season

By definition of conditional expectation,

\(\mathrm E\left[ X \mid Y = y \right] = \displaystyle \sum_x x\, p_{X\mid Y}(x \mid y) = \sum_x x \frac{p_{X,Y}(x,y)}{p_Y(y)}\)

where \(p_Y(y)\) is the marginal probability mass function (pmƒ) of Y. We find this by summing up all joint probabilities over the possible values of X :

\(p_Y(y) = \displaystyle \sum_x p_{X,Y}(x,y) = p_{X,Y}(1,y) + p_{X,Y}(2,y) + p_{X,Y}(3,y)\)

Consult the given values of the joint pmƒ. The values you actually list are unclear… if p(1, 1) = 1, then all other probabilities should be 0, so you must mean something else.

To get around this, I'll just make up a valid joint pmƒ of my own, and show you how to get what you need **using this pmƒ**.

\(\begin{array}{c|c|c|c} & A=1 & A=2 & A=3 \\ ---&---&---&--- \\ B=1 & 0.3 & 0.1 & 0.05 \\ B=2 & 0.02 & 0.02 & 0.01 \\B=3 & 0.25 & 0 & 0.25 \end{array}\)

The marginal pmƒ for B is

\(p_B(b) = \begin{cases} p_{A,B}(1,1)+p_{A,B}(2,1)+p_{A,B}(3,1) = 0.45 & \text{if }b = 1 \\ p_{A,B}(2,1)+p_{A,B}(2,2)+p_{A,B}(3,1) = 0.05 & \text{if }b = 2 \\ p_{A,B}(3,1)+p_{A,B}(3,2)+p_{A,B}(3,3)=0.5 & \text{if }b = 3\\0&\text{otherwise}\end{cases}\)

Now get the conditional expectation:

\(\mathrm E\left[A \mid B = b\right] = \begin{cases}\dfrac{1\cdot p_{A,B}(1,1)+2\cdot p_{A,B}(2,1)+3\cdot p_{A,B}(3,1)}{p_B(1)} \approx 1.44 & \text{if }b = 1 \\\\\dfrac{1\cdot p_{A,B}(1,2)+2\cdot p_{A,B}(2,2)+3\cdot p_{A,B}(3,2)}{p_B(2)} = 1.8 & \text{if }b = 2\\\\\dfrac{1\cdot p_{A,B}(1,3)+2\cdot p_{A,B}(2,3)+3\cdot p_{A,B}(3,3)}{p_B(3)} = 2 & \text{if }b = 3\end{cases}\)

If A and B are independent, then \(p_{A,B}(a,b)=p_A(a)p_B(b)\) and it follows that E[A | B] = E[A]. Compute the expectation of A :

\(\mathrm E\left[A\right] = \displaystyle \sum_a a \, p_{A,B}(a,b)\)

\(\mathrm E[A] = \begin{cases}1\cdot p_{A,B}(1,1)+2\cdot p_{A,B}(2,1)+3\cdot p_{A,B}(3,1) = 0.65 & \text{if }b = 1 \\ 1\cdot p_{A,B}(1,2)+2\cdot p_{A,B}(2,2)+3\cdot p_{A,B}(3,2) = 0.9 & \text{if }b = 2\\ 1\cdot p_{A,B}(1,3)+2\cdot p_{A,B}(2,3)+3\cdot p_{A,B}(3,3) = 1 & \text{if }b = 3\end{cases}\)

But E[A | B] ≠ E[A], so A and B are not independent.

The minimum annual interest rate for Kyoko to reach her goal, using daily compounding, is 9.903%.

The interest rate is computed using an online finance calculator that sets the following parameters.

The compounding period involved is 2,555 days for 7 years, based on the assumption that there are 365 days in a year.

N (# of periods) = 2555 days (7 years x 365 days)

PV (Present Value) = $10,000

PMT (Periodic Payment) = $-0

FV (Future Value) = $-20000

Results:

I/Y = 9.903% if interest compound 365 times per year (APR)

I/Y = 10.409% if interest compound once per year (APY)

I/period = 0.027% interest per period

Total Interest = $10,000.00

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Step-by-step explanation:

hope it helps................

9514 1404 393

Answer:

Step-by-step explanation:

It appears term n is the square of the digit 7 prepended with (n-1) sixes. That square is n instances of the digit 4, followed by (n-1) instances of the digit 8, followed by the digit 9.

Then the 5th line of the pattern will be ...

  66667^2 = 4444488889

__

The 7th line of the pattern will be ...

  6666667^2 = 44444448888889

Answer:19/20

1-20=19

1÷20=0.05

0.05=5%

I hope this is good enough:

The unit rate of the relationship will be 10/3. The correct option is C.

The given equation is,

y = 10/3x + 8

The general form of an equation of the line is,

y = mx +  c

here, the slope will be 10/3

Slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for a given change in the independent variable.

The slope of a line is represented by the ratio of the change in the y-axis (vertical) to the change in the x-axis (horizontal) between any two points on the line. It can also be interpreted as the rate of change of the dependent variable with respect to the independent variable.

A positive slope indicates an upward trend, while a negative slope indicates a downward trend. The slope of a line is often denoted by the letter m.

The unit relationship will be 10/3.

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bTo determine the percent of the original price you end up paying after the discounts, we can calculate the final price as a percentage of the original price.

Let's assume the original price of an item is $100.

The first discount reduces the price by 50%, so the price after the first discount is 50% of the original price, which is $100 * 0.5 = $50.

The second discount of 45% is applied to the price after the first discount. The price after the second discount is 45% of $50, which is $50 * 0.45 = $22.50.

Therefore, the final price you end up paying after both discounts is $22.50.\

To find the percent of the original price you end up paying, we divide the final price by the original price and multiply by 100:

Percent of original price = (final price / original price) * 100

In this case, the final price is $22.50 and the original price is $100:

Percent of original price = ($22.50 / $100) * 100

                       = 0.225 * 100

                       = 22.5%

Therefore, you end up paying 22.5% of the original price after the discounts.

It's important to note that the percent of the original price you end up paying will depend on the original price of the item. The calculations above were based on the assumption that the original price was $100. If the original price is different, the resulting percentage will vary accordingly.

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Step-by-step explanation:

1) (3x)^2 = (3x)*(3x)

2) (3x)^2 = 3x * 3x = 9 x^2

Step-by-step explanation:

7equitacion h< y ⚽ de los siguientes dominios

Answer:

Since wave heights at Folly Beach are normally distributed with a mean of 4 feet and a standard deviation of 1.5 feet, we can use the normal distribution formula to find the probability of a wave having a height of exactly 3 feet.

The formula for the normal distribution is:

P(x) = (1 / (σ * sqrt(2π))) * e^(-(x - μ)^2 / (2 * σ^2))

where:

P(x) is the probability density function

σ is the standard deviation

μ is the mean

e is the base of the natural logarithm

x is the value of the variable

Substituting the values given in the problem, we get:

P(3) = (1 / (1.5 * sqrt(2π))) * e^(-(3 - 4)^2 / (2 * 1.5^2))

P(3) = 0.176

Therefore, the probability that a wave has a height of exactly 3 feet is 0.176 or approximately 17.6%.

The domain of the given function is {.........-4, -3, -2, -1, 0, 1, 2, 3, 4,....} the interval notation is (-∞,∞),{x|x∈R}.

The domain and range are defined for a relation and they are the sets of all the x-coordinates and all the y-coordinates of ordered pairs respectively.

The given function is y=2x-6.

Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.

Domain: (-∞,∞),{x|x∈R}

Range: (-∞,∞),{y|y∈R}

Therefore, the domain of the given function is {.........-4, -3, -2, -1, 0, 1, 2, 3, 4,....} the interval notation is (-∞,∞),{x|x∈R}.

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The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:

20m

Step-by-step explanation:

bc 22m rounded to the closest tenth is 20m.

Hopes This Helps :)

Answer:

about 180 cm

Step-by-step explanation:

Answer:

Han's mixture, Claire's mixture

Step-by-step explanation:

I figured out the percentage of orange juice for each person's mixture:

For Claire:

2 1/2 + 1/3 = 2 5/6

2 5/6 as a decimal: about 2.8

Now find what percent of Claire's total mixture was orange juice:

100 * 1/3 / 2.8 = about 11.9%

For Han:

1 2/3 + 1/4 = 1 11/12

1 11/12 as a decimal: about 1.9

Now find what percent of Han's total mixture was orange juice:

100 * 1/4 / 1.9 = 13.2%

So, Han's mixture is stronger, since his has the higher percentage of orange juice concentrate

By solving the equation 2x² + 5x + xy = 2  , we found y'(2) = 1 by differentiation.

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.

The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

To find y'(2) by implicit differentiation, we will need to take the derivative of both sides of the equation with respect to x, using the product rule for the term xy:

\(2x^2 + 5x + xy = 2\)

Differentiating both sides with respect to x, we get:

4x + 5 + x(dy/dx) + y = 0

Now we can solve for dy/dx:

x(dy/dx) + y = -4x - 5

dy/dx = (-4x - 5 - y)/x

To find y'(2), we need to substitute x=2 and y=-8 into the equation we just derived:

y'(2) = (-4(2) - 5 - (-8))/2

y'(2) = (-8 + 5 + 4)

y'(2) = 1

Therefore, y'(2) = 1.

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Answer:

f(x)=x^(2),[2,3]

-2x-h+3

Step-by-step explanation:

The mortality rate will be 180 per 100000 people.

From the information, 595,700 Americans died of (all forms of) cancer and there is a population of 321 million.

Therefore the mortality rate will be:

= 595700 / 321 million

= 0.0018

Therefore the mortality rate will be 180 per 100000 people.

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The measure of the angles formed between parallel lines and their transversals indicates;

9. m∠3 = 97°, m∠5 = 97°, m∠10 = 97°, m∠7 = 83°

Parallel lines are lines that  maintain the are equidistant from each other and have the same slope on the coordinate plane.

The angles formed between the parallel lines and their transversal are;

1. Alternate exterior angles; (c) ∠9 and ∠16
2. Supplementary angles (e);  ∠15 & ∠11

3. Alternate interior angles (a); ∠10 & ∠15

4. Vertical angles (d); ∠12 & ∠15

5. Corresponding angles (b); ∠9 & ∠11

6. None (f); ∠9 & ∠15

7. Supplementary angles (e); ∠13 & ∠14

8. Alternate interior angles; ∠14 & ∠11

9. The alternate interior angles theorem indicates that we get;

(a + 28) = 2·a

Therefore; 2·a - a = 28

2·a - a = a, therefore;

a = 28

∠MNP = (a + 28)° = (28 + 28)° = 56°

10. The alternate interior angles theorem indicates that we get;

5·y° = (2·y + 78)°

Therefore;

5·y - 2·y = 78

3·y = 78

y = 78/3 = 26

The measure of the angle WXZ, m∠WXZ = 5·y°

Therefore; m∠WXZ = 5 × 26 = 130

m∠WXZ = 130°

9. ∠2 ≅ ∠3 (Vertical angles theorem)

m∠2 = m∠3

Therefore; m∠3 = m∠2 = 97°

m∠5 + m∠6 = 180° (Linear pair angles theorem)

m∠5 + 83° = 180°

m∠5 = 180° - 83° = 97°

∠10 and ∠2 are corresponding angles, therefore;

m∠10 = m∠2 = 97°

∠7 and ∠6 are vertical angles, therefore;

m∠7 = m∠6 = 83°

∠9 and ∠3 are same side interior angles, therefore;

m∠9 + m∠3 = 180°

m∠9 = 180° - m∠3

m∠9 = 180° - 97° = 83°
∠8 and ∠6 are linear pair angles, therefore; m∠8 = 180° - 83° = 97°

∠16 and ∠6 are same side exterior angles, therefore;

m∠16 + m∠6 = 180°

m∠16 = 180° - 83° = 97°

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Answer:

Rounded to the nearest hundred, Ms. Sanshes had about 200 more tokens than Mr. Brown

Step-by-step explanation:

567=600 (rounded)

432=400 (rounded)

600-400=200 tokens

Explanation:

This problem is a simple percent chage problem. The absoluge change in price was $12−$8=$4. Relative to the original price, it was 412, which is 0.3333 or 33.33%.

Given:

P = 55% = 0.55

n = 500

Let's find the probability the number of students who say yes, they do won a car is between 270 and 290.

Now, let's first find the mean:

Let's find the standard deviation:

Now, to find the probability, apply the formula:

Solving further, we have:

Where:

P(270 < x < 290) = P(290) - P(270)

Using the standard normal table, we have:

NORMSDIST(-0.44964) = 0.32649

NORMSDIST(1.34892) = 0.91132

Hence, we have:

P(270 ≤ x ≤ 290 = P(290) - P(2870) = 0.91132 - 0.32649 = 0.58483

Therefore, the probability the number of students who say they own a car is between 270 and 290 is 0.585

ANSWER:

0.585

Answer: 63 computers.

Step-by-step explanation:

Let 48 computers be 100%.

If the number of computers sold must increase by 30% in the next month, that means they need to sell 100% + 30% = 130%.

48 computers - 100%

x computers - 130%

x = (48 * 130%) / 100% = 62.4 computers ⇒ 63 computers.

Answer:

1×18=18

2×18=36

18×36= 648 inches squared

Step-by-step explanation:

Multiply both 1 inch and 2 inches by the scale factor of 18. For every one in of the scale model, there is 18 inches of the actual flag. Multiply your scaled number together to get the area.

Hope this helped!

Answer:

m+2m-s

Step-by-step explanation:

Answer:

A: M + 2m - s

Step-by-step explanation:

The coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

Here, we have,

To find the coordinates of Y' and Z', we need to apply the same translation that maps X to X'.

We know that the vector that connects X to X' is (3 - (-1), 1 - 0) = (4, 1).

So, to translate Y to Y', we add the vector (4, 1) to the coordinates of Y:

Y' = Y + (4, 1)

= (2, 3) + (4, 1)

= (6, 4)

Similarly, to translate Z to Z', we add the vector (4, 1) to the coordinates of Z:

Z' = Z + (4, 1)

= (1, -2) + (4, 1)

= (5, -1)

Therefore, the coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

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The number of years the annuity will last if it pays $300 per year is 18 years.

An annuity is an investment that pays the investor a fixed periodic amount for many years in the future.

The annuity payment may be monthly or yearly, as the case may be.

An online finance calculator can compute the annual payment (annuity).

I/Y (Interest per year) = 7%

PV (Present Value) = $3,000

PMT (Periodic Payment) = $-300

FV (Future Value) = $0

Results:

N = 17.795

Sum of all periodic payments = $-5,338.44

Total Interest $2,338.44

Thus, for an annuity with a present value of $3,000, earning 7% per annum and paying $300 per year will last almost 18 years.

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The present value of an annuity is $3,000 and earns 7% per annum.

Find the number of years the annuity will last if it pays $300 per year.