One important statistic in baseball is a pitcher’s earned run average, or ERA. This number represents the average number of earned runs given up by the pitcher per nine innings. The following table lists the portion of the ERAs for pitchers playing for the New York Yankees and the Baltimore Orioles as of July 22, 2010; the complete data, labeled ERA , are available on the text website.

New York ERA Baltimore ERA
Sabathia 3.13 Guthrie 4.58
Pettitte 2.88 Millwood 5.77
Burnett 4.99 Matusz 5.21
Hughes 3.99 Bergeson 6.51
Vazquez 4.68 Hernandez 4.29
Chamberlain 5.80 Berken 2.50
Gaudin 6.81 Hendrickson 5.23
Rivera 0.98 Albers 4.31
Robertson 4.86 Arrieta 4.87
Park 5.93 Simon 3.14
Mitre 2.88 Ohman 2.57
Logan 3.92 Tillman 7.92
Marte 4.08 Mata 7.79
Aceves 3.00 Meredith 5.40
Moseley 7.50 Uehara 2.92
Melancon 9.00 Castillo 10.13
Albaladejo 5.40 Johnson 6.52
Mickolio 7.36
Gonzalez 18.00

Required:
a. Calculate the mean and the median ERAs for the New York Yankees.
b. Calculate the mean and the median ERAs for the Baltimore Orioles.
c. Based solely on your calculations above, which team is likely to have the better winning record?

1. New York Yankees
2. Baltimore Orioles

LStep-by-step explanation:

(a) To proof this statement choose m = 4 and n = -1, from here we have 2(4) + 7(-1) = 1 as required. Hence th statement is true.

(b) To proof this statement choose m = 1 and n = -1, from here we have 15(1) + 12(-1) = 3 as required. Hence the statement is true.

(c) To proof this statement, suppose m and n are integers, since integers are closed under addition and multiplication then 2m, 4n and 2m + 4n are all integers. Obviously 2m and 4n are even integers, therefore their sum is also an even integer. This contradicts the equation 2m + 4m = 7, hence there do not exist integers m and n that satisfy the statement.

(d) To proof this statement, suppose m and n are integers, then 12m, 15n and 12m + 15n are all integers, since integers are closed under addition and multiplication. Factoring out 3 from the sum, we have: 3(4m + 5n). Therefore 3(4m + 5n) = 1 is a contradiction, because it will give 4m + 5n = 1/3 and addition of two integers can never give a fraction.

(e) To proof this statement, suppose m and n are integers, then 15m + 16n = t can be rewritten as 3(5m) + 8(2n) = t. Since integers are closed under multiplication, then 5m and 2n are integers. Let 5m = r and 2n = s, then we have: 3r + 8s = t as required.

(f) To proof this statement, suppose that m and n are both negative integers, we see that 12m + 15n = 1 is clearly impossible because the sum would be less than 0. Therefore, if there exist integers m and n such that 12m + 15n = 1, then they must be positive.

(g) To proof this statement, suppose m is an integer and has the form 4k + 1 for some integer k, then m + 2 = 4k + 1 + 2 = 4k + 3 = 4k + 4 - 1 = 4(k + 1) - 1. Since k is an integer then k + 1 is an integer because integers are closed under addition. Therefore, put j = k + 1. Hence we have 4j - 1.

(h) suppose that m is odd, then there is an n such that m = 2n + 1, therefore m² = (2n + 1)² = 4n² + 4n + 1 = 4(n² + n) + 1. Here, we need a lemma that says: suppose k is an integer, k(k + 1) is an even integer. This can be proven intuitively, when k is odd, the term in the bracket becomes even, and the whole expression is even. If k is even, then automatically the whole expression becomes even. Hence, our lemma is proven intuitively. This implies that n² + n is an even integer and can be replaced by 2k for some k that is an integer. Therefore, we have 4(2k) + 1 = 8k + 1 as required.

(i) suppose that m and n are odd integers such that mn = 4k - 1 for some k that is an integer. If we assume that neither m nor is in the for 4j - 1, then:

mn = (4a + 1)(4b + 1) for some a and b that are integers. Expanding that we have mn = 4(4ab + a + b) + 1 which is not in the form 4k - 1 for some k that is an integer as assumed. Therefore, if m and n are odd integers such that mn is in the form 4k - 1 for some k that is an integer, then m and n are in the form 4j - 1 for some j that is an integer.

\(x = \frac{10}{\sqrt{2}}\\\\y = 5\)

Answer:

Step-by-step explanation:

9.05737

The length of the radius of the cone to the nearest foot is 5 feet.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, The surface area of a cone is 216π sq units and the height of the cone is  (5/3) times of the radius.

∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.

∴ πrl = 216π.

√{(34/9)r³ = 216.

1.9r³ = 216.

r³ = 113.7.

r = 4.8 feet Or 5 feet.

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Answer:

722.57cm²

Step-by-step explanation:

Below, we have listed six basic equations that can be used to derive the explicit formulas of radius of a cylinder:

Volume of a cylinder: V = π * r² * h ,

Base surface area of a cylinder: A_b = 2 * π * r² ,

Lateral surface area of a cylinder: A_l = 2 * π * r * h ,

Total surface area of a cylinder: A = A_b + A_l ,

Surface Area of Cylinders. To find the surface area of a cylinder add the surface area of each end plus the surface area of the side. Each end is a circle so the surface area of each end is π * r2, where r is the radius of the end. There are two ends so their combinded surface area is 2 π * r2.

The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V=πr2h . ... Therefore, the volume of the cylinder is about 3016 cubic centimeters.

You Can Use Some Of These Points

Answer:

∠w = 50°

∠y = 130°

Step-by-step explanation:

Angles ∠w and ∠y are supplementary angles, which means their sum is 180.

4x + 6 + 12x - 2 = 180

16x + 4 = 180

16x = 176

x = 11

To find the angle measures replace x with 11

∠w = 4x + 6

∠w = 4*11 + 6

∠w = 50°

Now, ∠y

∠y = 12x - 2

∠y = 12*11 - 2

∠y = 130°

The area of the composite figure is 378.5 square feets.

We can decompose this into a rectangle of 30ft by 10ft and a circle whose diameter is 10ft.

Remember that the area of a rectangle of width W and length L is given by:

A = L*W

So the area of this rectangle is:

A = 30ft*10ft = 300ft²

And the area of a circle whose diameter D is:

A = 3.14*(D/2)²

So in this case the area of the circle is:

A = 3.14*(10ft/2)²

A = 3.14*(5ft)² = 78.5 ft²

Then the total area of the composite figure is:

area = 300ft² + 78.5 ft²

area = 378.5 ft²

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The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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The length of the diameter of the sphere is 30 cm.

The surface area of a sphere is given by the formula:

\(A = 4\pi r^2\)

where A is the surface area and r is the radius of the sphere.

We are given that the surface area of the sphere is 900π cubic cm. Therefore:

\(A = 4\pi r^2 = 900\pi\)

Dividing both sides by 4π, we get:

\(r^2 = 225\)

Taking the square root of both sides, we get:

r = 15

The diameter of the sphere is twice the radius, so:

d = 2r = 30

Therefore, the length of the diameter of the sphere is 30 cm.

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Answer:

The number 15/10 is a fraction, specifically a rational number. It can be expressed as the quotient of two integers, where 15 is the numerator and 10 is the denominator. In this case, the fraction is equivalent to 1.5, which is a decimal representation of the rational number.

Step-by-step explanation:

Answer:

Fraction, 15/10 is written out as 15 Over 10

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

Answer:

Step-by-step explanation:

step 1

100%/the total number = percent for one probability

100/5 = 20%

2 and 4 is even.

total even number * percent for one probability = total percent for even number

20% * 2 = 40%

therefore total even number is 40%

The probability is:

Step-by-step explanation:

Remember the formula for probability:

\(\boxed{\!\!\boxed{\bold{Probability=\frac{Favourable~outcome}{total~outcomes}\quad}}\!\!}\)

In this case, the favourable outcome (an even number) is 2, because there are only 2 even numbers in the set.

As for the total outcomes, there are 5 of them, because we have 5 numbers total.

So the probability of choosing an even number is 2/5.

The function that is decreasing on the same interval as the given function f(x) is h(x) = 2x^2 + 8x + 3.

To determine if a function is increasing or decreasing, we look at the sign of its derivative. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.

Taking the derivative of h(x) with respect to x, we get h'(x) = 4x + 8. To find the interval on which h(x) is decreasing, we need to find the values of x for which h'(x) < 0.

Setting h'(x) < 0, we have 4x + 8 < 0. Solving this inequality, we find x < -2.

Therefore, h(x) is decreasing for x < -2. Since the interval where h(x) is decreasing matches the interval for the given function f(x), we can conclude that h(x) = 2x^2 + 8x + 3 is the function that is decreasing on the same interval as f(x).

Overall, the function h(x) = 2x^2 + 8x + 3 is decreasing on the interval x < -2, which aligns with the interval of the given function f(x).

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Answer:

18 years (to the nearest year)

Step-by-step explanation:

Compound interest formula:

\(A=P(1+\frac{r}{n})^{nt}\)

where A is amount, P is principal, r is interest rate (decimal format), n is the number of times interest is compounded per unit 't', and t is time

Given:

\(\implies 4490=2400(1+\frac{0.035}{12})^{12t}\)

\(\implies \dfrac{449}{240}=\left(\dfrac{2407}{2400}\right)^{12t}\)

\(\implies \ln\dfrac{449}{240}=\ln\left(\dfrac{2407}{2400}\right)^{12t}\)

\(\implies \ln\dfrac{449}{240}=12t\ln\left(\dfrac{2407}{2400}\right)\)

\(\implies t=\dfrac{\ln\dfrac{449}{240}}{12\ln\left(\dfrac{2407}{2400}\right)}\)

\(\implies t=17.92277136...\)

Therefore, it would take 18 years (to the nearest year) for the account to reach $4,490

Answer:

Hello middleschoolvibes says he is good at algebra and would like to help you if you post them.

Answer:

Step-by-step explanation:

cot²α csc α+2 cot α csc α-3 csc α

=csc α (cot²α+2cot α-3)

=csc α (cot² α+3cot α- cot α-3)

=csc α[cot α(cot α+3)-1(cot α+3)]

=csc α (cot α+3)(cot α-1)

To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.

Number of temperatures = Sum of temperatures / Mean temperature

In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.

Number of temperatures = 2,516 / 74

Calculating the division:

Number of temperatures ≈ 34.05

Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.

1. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

2. Probability of no breakdowns = (reliability of a single machine)^3. Probability of at least one breakdown = 1 - Probability of no breakdowns

1. To determine how often the computer should be scheduled for maintenance, we need to consider the reliability and the desired level of operational condition. Since the duration for trouble-free operation follows a gamma distribution with a mean of 40 days, this means that, on average, the computer can operate for 40 days before a breakdown occurs.

To ensure operational condition with a 95% probability, we can calculate the maintenance interval using the concept of reliability. The reliability represents the probability that the machine will not break down within a certain time period. In this case, we want the reliability to be 95%, so the probability of not breaking down is 0.95.

Using the gamma distribution parameters, we can find the corresponding reliability for a specific time duration. By setting the reliability equation equal to 0.95 and solving for time, we can find the maintenance interval:

reliability = 0.95

time = maintenance interval

Using reliability and the gamma distribution parameters, we can calculate the maintenance interval.

2. To calculate the probability that at least one of the three machines will break down within the first scheduled maintenance time, we can use the complementary probability approach.

The probability that none of the machines will break down within the first scheduled maintenance time is given by the reliability of a single machine raised to the power of the number of machines:

Probability of no breakdowns = (reliability of a single machine)^3

Since the breakdown times between the machines are statistically independent, we can assume that the reliability of each machine is the same. Therefore, we can use the reliability calculated in the first part and substitute it into the formula:

Probability of at least one breakdown = 1 - Probability of no breakdowns

By calculating this expression, we can determine the probability that at least one of the three machines will break down within the first scheduled maintenance time.

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It's 87 feet I got the answer right

The  height of the tree is estimated as 87 ft.

The height of the tree can be estimated using trigonometric ratios. Therefore,

tan 44° = opposite / adjacent

tan 44° = h / 90

h = 90 tan 44°

h = 90 × 0.9656887748

h = 86.9119897326

h ≈ 87 ft

Therefore, the  height of the tree is estimated as 87 ft.

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Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Answer:

The answer is 5.

Step-by-step explanation:

Hope this helped Mark BRAINLEST!!!

Answer:

5

Step-by-step explanation:

An order-preserving function is one where x < y implies f(x) < f(y). An isomorphism is a one-to-one order-preserving function between two partially ordered sets, while an automorphism is an isomorphism of a set to itself.

In the given excerpt, it explains the concepts of order-preserving functions, isomorphisms, and automorphisms in the context of partially ordered sets.

Order-Preserving Function:

A function f: P -> Q, where P and Q are partially ordered sets, is said to be order-preserving if for any elements x and y in P, if x < y, then f(x) < f(y). In other words, the function preserves the order relation between elements in P when mapped to elements in Q.

Increasing Function:

If P and Q are linearly ordered sets, then an order-preserving function is also referred to as an increasing function. It means that for any elements x and y in P, if x < y, then f(x) < f(y).

Isomorphism:

A one-to-one function f: P -> Q is called an isomorphism of P and Q if it satisfies two conditions:

a. f is order-preserving: For any elements x and y in P, if x < y, then f(x) < f(y).

b. f is onto (surjective): Every element in Q has a pre-image in P.

When an isomorphism exists between (P, <) and (Q, <), it means that the two partially ordered sets have a structure that is preserved under the isomorphism. In other words, they have the same ordering relationships.

Automorphism:

An automorphism of a partially ordered set (P, <) is an isomorphism from P to itself. It means that the function f: P -> P is both order-preserving and bijective (one-to-one and onto). Essentially, an automorphism preserves the structure and order relationships within the same partially ordered set.

These concepts are fundamental in understanding the relationships and mappings between partially ordered sets, particularly in terms of preserving order, finding correspondences, and exploring the symmetry within a set.

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Answer:

Sam would have $22.80 left over

Step-by-step explanation:

28 boxes of nails cost $10.3616

Planks cost $91.84

All together he spent $102.20 on supplies leaving him with $22.80

By inspection, we can see that x = ±√2, since (±√2)⁴ = 2² = 4.

In particular, if \(x^n=n\), which means \(x=n^{\frac1n}\), then \(x^{x^n}=x^n=n\).

Let x = √2. Then

\(x^{x^2}+x^{x^8}=(\sqrt2)^{(\sqrt2)^2}+(\sqrt2)^{(\sqrt2)^8}\)

\(x^{x^2}+x^{x^8}=(\sqrt2)^2+(\sqrt2)^{16}\)

\(x^{x^2}+x^{x^8}=2+256\)

\(x^{x^2}+x^{x^8}=\boxed{258}\)

Answer:

No, because the number in 2011 multiplied by three is less than the number in 2015.

Step-by-step explanation:

i dunno just makes sense

Answer:

I think that it did not because 555*3 is not 900 so it can't equal it.

Step-by-step explanation:

Answer:

x=12

(90-35)-7/4

Answer:

x=12

Step-by-step explanation:

Since the two angles are complementary, both angles add up to 90°.

So, to find the value of the other angle, simply subtract 35 from 90.

90-35=55

Now we know that the expression is equal to 55.

4x+7=55

Subtract 7 from both sides.

4x=48

Divide both sides by 4.

x = 12

its not 65% americans like all

The standard error of the sample proportion is 0.0002275

The standard error of a proportion p in a sample of size n is given by:

\(S= \sqrt{\frac{p(1-p)}{n}}\)

Now it is given that,

Number of people selected is 1000.

So, sample size, n 1000

Americans prefer chocolate = 65%

Thus, proportion, p = 0.65

So, standard error of a proportion is given as,

\(S= \sqrt{\frac{p(1-p)}{n}}\)

\(S= \sqrt{\frac{0.65(1-0.65)}{1000}}\)

\(S= \sqrt{\frac{0.65(0.35)}{1000}}\)

\(S= \sqrt{\frac{0.2275}{1000}}\)

\(S= 0.0002275\)

this is the required standard error of the sample proportion.

Thus, the standard error of the sample proportion is 0.0002275.

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Answer:

UMM...........

Step-by-step explanation:

The only possible value of "a" that satisfies the given equations is a = 5.

The possible values of "a" that satisfy the given equations, let's solve the system of equations:

a + ab = 250 ---(1)

a - ab = -240 ---(2)

We can solve this system by using the method of substitution. Rearranging equation (2), we get:

a = ab - 240 ---(3)

Substituting equation (3) into equation (1), we have:

(ab - 240) + ab = 250

2ab - 240 = 250

2ab = 250 + 240

2ab = 490

ab = 490/2

ab = 245

Now we have the value of "ab."

We can substitute this back into equation (3) to solve for "a":

a = (245) - 240

a = 5

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Answer:

D, because in between -3 and -2 is -2 1/2, and absolute values are not negative, so the answer is 2 1/2, or D

Answer:

C.

Step-by-step explanation: