In Game 1, Emerson struck out 30 times in 90 times at bat. In Game 2, he struck out 40 times in 120 times at bat. In Game 3, Emerson struck out 42 times in 140 times at bat.

Part A
Drag numbers to complete the proportion to represent the percent of strike outs per at-bats.
Numbers may be used once or not at all.



Part B
What percentage of times at bat did Emerson actually hit the ball?

Assuming birthdays are uniformly distributed throughout the week, the probability that two strangers passing each other on the street were both born on Friday is (1/7) * (1/7) = 1/49.

Since birthdays are assumed to be uniformly distributed throughout the week, each day of the week has an equal chance of being someone's birthday. There are a total of seven days in a week, so the probability of an individual being born on any specific day, such as Friday, is 1/7.

When two strangers pass each other on the street, their individual birthdays are independent events. The probability that the first stranger was born on Friday is 1/7, and the probability that the second stranger was also born on Friday is also 1/7. Since the events are independent, we can multiply the probabilities to find the probability that both strangers were born on Friday.

Thus, the probability that two strangers passing each other on the street were both born on Friday is (1/7) * (1/7) = 1/49. This means that approximately 1 out of every 49 pairs of strangers would both have been born on Friday.

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Answer:

1000 km^3

Step-by-step explanation:

1 km=1000m

1 cubic kilometer is equivalent to 1,000,000,000 cubic meters, due to cubing the conversion factor of 1,000 (meters per kilometer).

1 cubic kilometer is equivalent to 1,000,000,000 (one billion) cubic meters. When converting units, you need to remember the relationships between those units. In this case, 1 kilometer is equivalent to 1000 meters. Therefore, to convert from cubic kilometers to cubic meters, you need to cube the conversion factor (1000 meters/kilometer). Hence, 1 cubic kilometer = 1,000^3 cubic meters = 1,000,000,000 cubic meters.

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To express the quadratic function f(x) = x^2 - 18x + 63 in standard form, we need to complete the square.

First, we can factor out the coefficient of x^2, which is 1: f(x) = 1(x^2 - 18x + 63), Next, we want to find the value that completes the square for the expression inside the parentheses,

which is (-18x + 63). To do this, we take half of the coefficient of x, which is -9, square it, and add it to both sides: f(x) = 1(x^2 - 18x + 81 - 81 + 63).

Notice that we added and subtracted 81 inside the parentheses, which is the value we got from (-9)^2. This allows us to write the expression as a perfect square trinomial, which can be factored as: f(x) = 1[(x - 9)^2 - 18].

Finally, we can simplify this expression by distributing the 1 and adding 63 outside the brackets: f(x) = (x - 9)^2 - 18 + 63, So the quadratic function f(x) in standard form is: f(x) = (x - 9)^2 + 45.

Note that standard form for a quadratic function is usually written as ax^2 + bx + c, where a, b, and c are constants. In this case, we factored out the coefficient of x^2, which is why our standard form expression doesn't have an "a" term.

A quadratic function in standard form is written as f(x) = a(x - h)^2 + k, where a, h, and k are constants. Our goal is to rewrite the given function in this format. So, the standard form of the given quadratic function is: f(x) = (x - 9)^2 - 18

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Answer:

\(\frac{8}{6} = \frac{20}{15}\)

Step-by-step explanation:

It appears that a is the missing value that needs to be solved. The equal sign means that the two values are equal to each other and the other not equal sign means that they don't equal each other.

Whenever dealing with two fractions that equal each other, you can use the fraction cross-product property, where you would multiply the numerator with the denominator and vice versa.

\(\frac{8}{a} = \frac{20}{15} \\\\8 \times 15 = 20 \times a\\\\120 = 20a\\\\a = 6\)

So, the fraction would be

\(\frac{8}{6} = \frac{20}{15}\)

Answer:

\(\sqrt{60}\)

Step-by-step explanation:

Use the Pythagorean theorem a^2 + b^2 = c^2

In this case you are given a and c, so set the equation up like

2^2 + b^2 = 8^2

b^2 = 8^2 - 2^2

b =\(\sqrt{8^{2} -2^{2} }\)

b =\(\sqrt{60}\)

Answer:

120

Step-by-step explanation:

The formula is A = bh

12 x 10 = 120

a.  If we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

b. Michael's substitution satisfies the requirement for u to be differentiable.

(a) i. Kayla's proposed substitution of u as (3 - 2x) will not work in this case. The reason is that when using the u-substitution method, it is necessary for the chosen u to be differentiable, meaning that its derivative du/dx should exist and be non-zero. However, if we let u = (3 - 2x), then the derivative du/dx would be -2, which is not equal to zero. This indicates that the substitution does not satisfy the requirement for u to be differentiable.

ii. Kayla's idea of always picking the most inside factor as u does not work for all u-substitutions. There can be cases where choosing the most inside factor may not lead to a valid substitution that simplifies the problem or makes integration easier. It is important to consider the properties of the function and choose a suitable substitution accordingly.

(b) i. Michael's proposed substitution of u as 3√3 - 2x will work in this case. If we let u = 3√3 - 2x, then the derivative du/dx would be -2, which is non-zero. Therefore, Michael's substitution satisfies the requirement for u to be differentiable.

ii. Michael's idea of always picking the most complicated factor as u also does not hold true for all u-substitutions. The choice of u depends on various factors, including the structure of the function, simplification possibilities, and making the integration process more manageable. It is not necessarily the case that the most complex factor will always result in a successful substitution.

It is important to consider the specific characteristics of the function and apply appropriate judgment in choosing the substitution u to simplify the problem effectively.

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The sampling procedure being used to collect completion time data in this scenario is based on paired samples or dependent samples.

In paired samples, each observation in one sample is uniquely linked or paired with an observation in the other sample. In this case, the workers are randomly selected, and each worker is assigned to use both production methods, one after the other. The completion time for each worker is measured under both methods, creating paired or dependent observations.

By using paired samples, the company can compare the completion times of the same workers using different production methods. This approach helps eliminate individual differences and other sources of variability among workers, focusing solely on the comparison between the two methods.

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The required expression will be -10 ÷ (-2/5).

Given are the numbers -10, -5/2,-2/5, or 5,

An expression is the numbers, symbols and operators grouped together that show the value of something.

Using the numbers,

-10 ÷ (-2/5).

Hence, -10 ÷ (-2/5) will be the expression.

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The answer is the lower bound theorem identifies -2 as a lower bound for the real zeros of f(x). The upper bound theorem does not specify any upper bound for the real zeros of (x)

The Lower bound theorem states that "If the terms of a polynomial are arranged in descending order of their degrees, then the absolute value of the quotient of the constant term and the coefficient of the term of the highest degree gives a lower bound for the absolute value of its zeros." Let's examine whether the lower bound theorem identifies -2 as a lower bound for the real zeros of f(x) and whether 3 is an upper bound for the real zeros of (x).

As f(x) = 56 = x + 17x² + 11x + 23Since f(x) is not arranged in descending order of their degrees, we have to rearrange it as follows. 17x² + 11x + x + 23 + 56 = 17x² + 12x + 79 on rearranging the equation we have: 17x² + 12x + 79 = 0Hence the constant term is 79 and the coefficient of the term of the highest degree is 17. Thus, using the lower bound theorem, we can evaluate that a lower bound for the absolute value of the zeros of the polynomial is 79/17 ≈ 4.65 Since -2 is less than the calculated lower bound of 4.65, it is indeed a lower bound for the real zeros of f(x). Now, for (x), the constant term is 0, and the coefficient of the term of the highest degree is 1. Thus, using the upper bound theorem, we can evaluate that an upper bound for the absolute value of the zeros of the polynomial is 1/0, which is equal to infinity. Since infinity is not a number, 3 cannot be an upper bound for the real zeros of (x).

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Answer:

=> B.125

Step-by-step explanation:

=> 180°- 55°{ linear pair }

=> 125°

The measure of angle COE = 125

Answer:

Step-by-step explanation:

If you are asking how much money were the drinks?

Then, the answer is $6.75. This is because 19.25 - 12.50 = 6.75

If you are asking how much money per drink, then the answer is $1.35

Answer:

1/6

Step-by-step explanation:

1/3×2/4 = 2/12

2/12 = 1/6

For each n ≥ 0, the natural filtration Gn satisfies Gn ⊆ Fn. show that for each n ≥ 0, Gn ⊆ Fn, we need to demonstrate that the natural filtration Gn is a subset of the filtering Fn.

The natural filtration Gn is defined as the sigma-algebra generated by the process {Xn}n≥1 up to time n. This means that Gn contains all the information available up to time n.

The filtering Fn, on the other hand, is defined as the sigma-algebra generated by the random variables {Xk}k≤n, which includes all the information up to and including time n.

Since Gn contains all the information up to time n and Fn includes all the information up to and including time n, it follows that Gn is a subset of Fn, i.e., Gn ⊆ Fn.

Therefore, for each n ≥ 0, the natural filtration Gn satisfies Gn ⊆ Fn.

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The sum of the first 7 terms of the sequence 6, -4, 8/3 is -154/3.

The given sequence is 6, -4, 8/3, which appears to be an arithmetic sequence.

To find the sum of the first 7 terms, we first need to determine the common difference (d) and the nth term formula.

The difference between consecutive terms is constant, so d = -4 - 6 = -10 and 8/3 - (-4) = 20/3.

The nth term formula for an arithmetic sequence is an = a1 + (n-1)d.

Now, let's find the 7th term (a7):

a7 = 6 + (7-1)(-10) + 6(20/3) = -52/3.

The sum of the first 7 terms (S7) can be calculated using the arithmetic series formula:

S7 = n(a1 + a7) / 2, where n is the number of terms.

Substituting the values, we get S7 = 7(6 + (-52/3)) / 2 = 7(-22/3) = -154/3.

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The type of chart that would work best to show a comparison between the number of cable and satellite TV subscribers is bar chart.

A bar chart or bar graph is a chart or graph that conveys categorical data with rectangular bars with heights or lengths proportional to the values which they represent. The bars may be plotted vertically or horizontally. A vertical bar chart is also called a column chart.

A bar chart is used when we want to show a distribution of data points or present a comparison of metric values between different subgroups of our data. From a bar chart, we can preview which groups are the highest or most common, and how the other groups compare to the others.

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Answer:A triangle has a perimeter of 165 cm. The first side is 65 cm less than twice the second side. The third side is 10 cm less than the second side. Write and solve an equation to find the length of each side of the triangle.

The sides can be found by taking the square root of the area. , where = side. . So the length of a side is 6.3 cm.

Step-by-step explanation:

To verify the mean and standard deviation for the given data, we can calculate them using the formulas:

Mean:

\(\[\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i\]\)

Standard Deviation:

\(\[s = \sqrt{\frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2}\]\)

where \(\(n\)\) is the sample size and \(\(x_i\)\)  are the individual weights measured by the experts.

For the given data: 14.28, 14.34, 14.26, and 14.32 grams, we have:

Mean:

\(\[\bar{x} = \frac{14.28 + 14.34 + 14.26 + 14.32}{4} = 14.30\]\)

Standard Deviation:

\(\[s = \sqrt{\frac{(14.28 - 14.30)^2 + (14.34 - 14.30)^2 + (14.26 - 14.30)^2 + (14.32 - 14.30)^2}{3}} = 0.0365\]\)

To construct a 99% confidence interval for the true average weight of a Phoenician tetradrachm, we can use the formula:

Confidence Interval:

\(\[\text{{CI}} = \bar{x} \pm t_{\alpha/2} \times \frac{s}{\sqrt{n}}\]\)

where \(\(t_{\alpha/2}\)\) is the critical value corresponding to the desired confidence level and \(\(n\)\) is the sample size.

For a 99% confidence level, with \(\(n = 4\)\) and degrees of freedom \(\(n-1 = 3\)\) , the critical value  \(\(t_{\alpha/2}\)\)  can be found from the t-distribution table or using statistical software. Let's assume \(\(t_{\alpha/2} = 4.604\)\) :

Confidence Interval:

\(\[\text{{CI}} = 14.30 \pm 4.604 \times \frac{0.0365}{\sqrt{4}}\]\)

Simplifying the expression, we get:

Confidence Interval:

\(\[\text{{CI}} = 14.30 \pm 4.604 \times 0.01825\]\)

Now we can calculate the lower and upper bounds of the confidence interval:

Lower bound:

\(\[14.30 - 4.604 \times 0.01825 = 14.2184\]\)

Upper bound:

\(\[14.30 + 4.604 \times 0.01825 = 14.3816\]\)

Therefore, the 99% confidence interval for the true average weight of a Phoenician tetradrachm is (14.2184, 14.3816) grams.

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Maria can arrange the books on her shelf in (n-2)! ways, where n represents the total number of books excluding the first and last spots.

Since Maria has already decided to place "Pride and Prejudice" in the first spot and "Little Women" in the last spot, the remaining books can be arranged in between these two fixed positions. The number of ways to arrange the books in the remaining spots depends on the total number of books excluding the first and last spots.

Let's say Maria has a total of n books (including "Pride and Prejudice" and "Little Women"). Since these two books are fixed, she needs to arrange the remaining (n-2) books in the remaining spots.

The number of ways to arrange (n-2) books is given by (n-2)!. The factorial (n!) represents the number of ways to arrange n distinct objects.

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We have the piecewise-defined function

and we want to calculate f(4). Informally, you can think of a piecewise-defined function as a function defined in branches. To calculate the value of an argument, you must look for the branch in which the argument lies, and then apply the formula of that branch.

In our case, note that 4 lies in the upper branch (4 is less or equal to 4); then,

Answer:  D.gallons

Step-by-step explanation:

Kilogram is a unit of mass

Now, Pounds, Tons and Ounces are also units of mass.

But Gallons is a unit of volume, where 1 gal = 3.785 L

Then you never can represent an amount of mass using units for volume, which means that gallons is incommensurabe with kilograms.

the correct option is D

The curve is given by \(x = y^2,\)so we can express the integral as:

\(∫c x^3 y^4 dx = ∫c (y^2)^3 y^4 dx = ∫c y^10 dx\)

To find the limits of integration, we need to determine the values of y for the endpoints of the curve. At the starting point (0, 0), we have y = 0, and at the endpoint (4, 2), we have y = 2^(1/2). Therefore, the integral becomes:

\(∫c x^3 y^4 dx = ∫0^(2^(1/2)) y^10 dx = [1/11 y^11]_0^(2^(1/2)) =\)\(2^(11/2) / 11\)

Therefore, the value of the integral is \(2^(11/2) / 11\)

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Answer:

D

Step-by-step explanation:

The cost of purchasing a football helmet and jersey is 3x + $11, where "x" represents the cost of the jersey in dollars.

Let's denote the cost of the football jersey as "x" dollars. According to the given information, the cost of the football helmet is $11 more than twice the cost of the jersey.The cost of the helmet can be expressed as: 2x + $11.To determine the cost of purchasing both the helmet and jersey, we add the costs of the individual items together:

Total cost = cost of jersey + cost of helmet

Total cost = x + (2x + $11)

Simplifying the expression:Total cost = 3x + $11

Therefore, the cost of purchasing a football helmet and jersey is 3x + $11, where "x" represents the cost of the jersey in dollars.

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The probability of obtaining x or fewer individuals with the characteristic is P(x), where P(x) is a cumulative probability. Here, x represents the number of individuals with the given characteristic, and the cumulative probability means the probability of getting a result of x or fewer individuals (as opposed to the probability of getting exactly x individuals).

To calculate this probability, you need to use a probability distribution that corresponds to the given situation. For example, if the situation involves a binomial distribution, then you would use the binomial probability formula to find P(x).This formula is P(x) = Σ [ nCx * p^x * (1-p)^(n-x) ] , where n is the total number of individuals in the population, p is the probability of an individual having the given characteristic, and Cx is the number of combinations of n items taken x at a time. The summation (Σ) goes from x = 0 to x = x. To use this formula, you would plug in the values of n, p, and x, and then calculate the sum. The answer will be a probability value between 0 and 1. In general, you can find the probability of obtaining x or fewer individuals with the characteristic by adding up the probabilities of all possible outcomes from 0 to x.

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y = (-11/55)x + 11  is the linear equation in slope-intercept form that relates the height y of the ramp to the distance x from the curb.

To write a linear equation in slope-intercept form that relates the height y of the ramp to the distance x from the curb, we need to use the slope-intercept form of a linear equation: y = mx + b.

We know that the ramp is 11 inches off the ground at the curb, which means that the y-intercept (where the ramp meets the curb) is 11 inches:

y = mx + 11

To find the slope (m), we need to use the information that the other end of the ramp rests on the street 55 inches from the curb. We can use the formula for slope:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) are the coordinates of the curb (0, 11) and (x2, y2) are the coordinates of the other end of the ramp (55, 0).

m = (0 - 11) / (55 - 0) = -11/55

Now we can substitute the slope and the y-intercept into the equation:

y = (-11/55)x + 11

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