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Question 3
Elias has a collection of 1,200 baseball trading cards of these cards, 35% are from the American League, 45% are from the National League, and the rest are international
players. How many trading cards are of the international players?

Answer:

£4800

Step-by-step explanation:

principal amount:£800

time:3years

rate:2%

amount= principal*rate*time

£800*2*3

=£4800

The rule that describes a 90° clockwise rotation is (x, y) → (-y, x).

A 90° clockwise rotation in a two-dimensional Cartesian coordinate system involves rotating points 90 degrees in the clockwise direction around the origin (0,0) on the x-y plane.

In this rotation, the new x-coordinate becomes the negative of the original y-coordinate, and the new y-coordinate becomes the original x-coordinate.

So for the given option, we can see clearly that the rule that describes a 90° clockwise rotation is (x, y) → (-y, x).

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Answer:

y = 1/2 x + 1

Step-by-step explanation:

1. Get two point from the graph

Point1 (-2,0)

Point2 (0,1)

2. Find the slope,m

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

=(1-0)/(0-(-2))

=1/2

3. Find b

y= mx + b

substitute x,y from Point2 and m from 2.

1 = 1/2(0) + b

b = 1

Line equation

y = 1/2x + 1

Critical values of t, which are used for hypothesis testing and confidence interval calculations, vary depending on the sample size and the degrees of freedom.

b) degrees of freedom.

Degrees of freedom (df) are calculated based on the sample size and represent the number of independent pieces of information available in the data. It is an important parameter in determining the appropriate critical value to use from the t-distribution table. Therefore, before using the t-table, it is essential to calculate the degrees of freedom of the data set in question.

Options a, c, and d are not correct answers as they do not pertain to the calculation needed before using the t-table.

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Complete Question

Since critical values of t vary by sample size, before using the t table we must first calculate:

a) the Z score.

b) degrees of freedom.

c) the population standard deviation.

d) the sample size.

The degrees of freedom will then determine the critical values of t that should be used in calculating confidence intervals or conducting hypothesis tests. Therefore, it is important to consider the sample size when working with t statistics and using the t table.

To answer your question, before using the t-table, you must first calculate the degrees of freedom. The degrees of freedom are important as they determine the critical values of t based on your sample size. Here's a step-by-step explanation:

1. Obtain your sample data.
2. Determine the sample size (n) by counting the number of data points in your sample.
3. Calculate the degrees of freedom (df) by subtracting 1 from the sample size: df = n - 1.
4. Refer to the t-table with the calculated degrees of freedom to find the critical values of t for your desired level of confidence or significance.

By following these steps, you'll be able to find the appropriate critical values of t based on your sample size before using the t-table.

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Answer:

It is C

Step-by-step explanation:

To get the new coordinates you would move the shape up the y-axis 8 times, and right on the x-axis 8 times as well.

Answer:

C

Step-by-step explanation:

You can either compare two similar points or just count the units on the graph

Thus, at x ≈ 1.4142, the tangent line to the graph of y = x + 2/x is horizontal.

To find the x value where the tangent line of the graph y = x + 2/x is horizontal, we need to determine when the first derivative of the function is equal to 0.

This is because the slope of the tangent line is represented by the first derivative, and a horizontal line has a slope of 0.

First, let's find the derivative of y = x + 2/x with respect to x. To do this, we can rewrite the equation as y = x + 2x^(-1).

Now, we can differentiate:
y' = d(x)/dx + d(2x^(-1))/dx = 1 - 2x^(-2)

Next, we want to find the x value when y' = 0:
0 = 1 - 2x^(-2)

Now, we can solve for x:
2x^(-2) = 1
x^(-2) = 1/2
x^2 = 2
x = ±√2

Since we are looking for a positive x value, we can disregard the negative solution and round the positive solution to four decimal places:
x ≈ 1.4142

Thus, at x ≈ 1.4142, the tangent line to the graph of y = x + 2/x is horizontal.

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1) a = 0.60 , The MAD for this forecast is 4.5 surgeries.

2)a = 0.90, The MAD for this forecast is 3.46 surgeries.

3)Using a 3-year moving average, The MAD for this forecast is 7.0 surgeries.

4)The trend-projection method provides forecasts for years 1 through 6: 46.6, 49.8, 53.0, 56.2, 59.4, and 62.6 surgeries, respectively. The MAD for the trend-projection method is not provided.

Exponential smoothing is a forecasting method that assigns exponentially decreasing weights to historical data, with the most recent data given the highest weight. By adjusting the smoothing factor (a), we can control the responsiveness of the forecast to recent changes. A higher value of a gives more weight to recent data.

In the given scenario, when using exponential smoothing with a = 0.60, the forecast for year 1 (44.0 surgeries) is taken as the initial forecast. The subsequent forecasts are calculated by adding a proportion of the difference between the actual observation and the previous forecast.

This results in the forecasted values of 46.4, 47.4, 50.8, 53.9, and 57.6 surgeries for years 2 through 6, respectively.

Similarly, when using exponential smoothing with a = 0.90, the forecast for year 1 remains the same (44.0 surgeries). The subsequent forecasts are adjusted based on a higher weight given to recent observations.

This leads to the forecasted values of 47.6, 48.0, 52.5, 55.6, and 59.6 surgeries for years 2 through 6, respectively.

On the other hand, the 3-year moving average forecast considers the average of the past three observations to make future predictions. For years 4 through 6, the moving average forecasts are 49.7, 52.3, and 56.3 surgeries, respectively.

Finally, the trend-projection method incorporates both the historical data and the trend observed in the data. It assumes that there is a linear relationship between the time period and the number of surgeries.

By fitting a trend line to the data, the method predicts future values. In this case, the trend-projection method yields the forecasts of 46.6, 49.8, 53.0, 56.2, 59.4, and 62.6 surgeries for years 1 through 6, respectively. The MAD for this method cannot be calculated based on the given information.

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Answer: I believe it is 3.75-

Step-by-step explanation:

David: 3.25

Jenny: 2.25 more than Dan

Dan: 1.75 less than David

  3.25

-  1.75

_______

  1.50

Dan spent 1.50

  1.50

+ 2.25

 3.25

_______

$7.00

To determine the probability that the average shoe size of five randomly chosen women is 9 or more, we need to calculate the z-score for this value and then find the corresponding probability using the Normal distribution.

In summary, we want to find the probability that the average shoe size of five randomly chosen women is 9 or more.

Now, let's explain the answer in more detail. The distribution of women's shoe sizes in the US follows a Normal distribution with a mean of 8 and a standard deviation of 1.5. To calculate the probability, we first need to find the z-score corresponding to a shoe size of 9 or more.

The z-score formula is given by z = (x - μ) / σ, where x is the value of interest, μ is the mean, and σ is the standard deviation. In this case, the value of interest is 9, the mean is 8, and the standard deviation is 1.5. Plugging these values into the formula, we get z = (9 - 8) / 1.5 = 0.67.

Next, we use a standard Normal distribution table or a statistical calculator to find the probability corresponding to the z-score of 0.67. The probability of obtaining a z-score of 0.67 or higher represents the probability that the average shoe size of five randomly chosen women is 9 or more.

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Answer:

y = 5x

Step-by-step explanation:

Form the equation:

y = 5 times x or y = 5x

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

-10°F

Step-by-step explanation:

The integer that represents the change in temperature (°F) is -10°F. The difference between 10 and 0 is 10, however, since the temperature decreased instead of increasing, 10 is negative (-10).  

Answer:

10

Step-by-step explanation:

Option a. The car is 115.47 feet from the building is correct for the given right triangle.

A trigonometric formula known as the rule of sines connects any triangle's sides and angles. It claims that for all three sides of a triangle, the ratio of the length of one side to the sine of the angle opposite that side is the same. In other words, if a triangle has angles A, B, and C opposing its sides and sides a, b, and c, then:

If a/sin(A) = b/sin(B) = c/sin(C), then

If some of the other sides and angles of a triangle are known, this formula can be used to solve for those unknown sides or angles. However, it is restricted to triangles and calls for the measurement of at least one angle and one side's length.

The situation can be depicted as a right triangle, with building 200 feet, the angle of depression is 30 degrees.

Now,

tan(30) = opposite/adjacent = 200/distance

distance = 200/tan(30) ≈ 115.47 feet

Hence, option a. The car is 115.47 feet from the building is correct for the given right triangle.

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The probability that at least one box in a selection of three candy gift boxes will weigh less than 34 ounces needs to be found.

To calculate the probability, the weight of a box can be considered as the sum of the weights of the individual candies in the box. The weights of the individual candies are normally distributed with known means and standard deviations.

Using the properties of normal distributions, the weights of the boxes can be modeled as normally distributed with a mean of 27 ounces (9 candies x 3 ounces per candy) and a standard deviation of 0.374 ounces (sqrt(4*(0.2^2)+5*(0.3^2)+0.1^2)). Then, the probability of at least one box weighing less than 34 ounces can be calculated using the normal distribution function.

The calculated probability is 0.0569, or approximately 5.69%. Thus, there is a 5.69% chance that at least one of the three selected candy gift boxes will weigh less than 34 ounces.

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The probability that at least one box will weigh less than 34 ounces is approximately 0.117.

To solve this problem, we can use the Central Limit Theorem to approximate the distribution of the total weight of three gift boxes. The mean weight of one gift box is 3*(4)+5*(3) = 27 ounces, and the standard deviation is sqrt((4*(0.2)^2 + 5*(0.3)^2)) = 0.69 ounces.

The probability that one gift box weighs less than 34 ounces is given by the standard normal distribution, which we can find using a z-score of (34-27)/0.69 = 10.14.

The probability that all three boxes weigh at least 34 ounces is (1-0.117)^3 = 0.770, so the probability that at least one box weighs less than 34 ounces is approximately 1 - 0.770 = 0.117.

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We can determine coordinates if point t is between points u and v by checking if u < t < v or v < t < u.

To determine if point t is between points u and v, we need to compare their coordinates. If u < v, then point t is between points u and v if and only if u < t < v. On the other hand, if v < u, then point t is between points u and v if and only if v < t < u.

Whether or not point t is between points u and v depends on the relationship between the coordinates of u and v. If u < v, t must fall between them, and if v < u, t must also fall between them.

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Answer:

-1

Step-by-step explanation:

LCM is 6,after eliminating the fractions,you will arrive at 3-2x=5

-2x=5-3

-2x=2,divide both sides by -2x.

she should use 2 by 6

Step-by-step explanation:

2 divided by 6 will give 0.3 in 1d.p

The distribution A must has a smaller standard deviation. So, option C is correct.

Normal usually refers to the word "normal" in normal distribution.

The normal distribution is somewhat similar where the main observation (mean or its surrounding) occurs frequently and as we go far from mean, its chances decrease.

If we've got a normal distribution, then we can convert it to a standard normal distribution and its values will give us the z score.

If we have

\(X \sim N(\mu, \sigma)\)

(X is following a normal distribution with mean and standard deviation )

then it can be converted to a standard normal distribution as

\(Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)\)

Normal curve A has a wider distribution than Normal curve B.

The distribution A must has a smaller standard deviation.

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Answer:

\(3x^2+4x+8\)

Step-by-step explanation:

To find the value of \(7x^2+6x+9-4x^2-2x-1\)

We need to combine like terms by grouping

\(7x^2-4x^2+6x-2x+9-1\)

= \(3x^2+4x+8\)

Hope this helps :)

Have a great day!

The expression for the number of bacteria after t hours is N(t) = 50e\(^(0.4427t)\) , rounded to four decimal places.

Let N(t) be the number of bacteria after t hours.

Since the culture grows at a rate proportional to its size, we can write:

dN/dt = kN

where k is the proportionality constant.

This is a separable differential equation, which we can solve by separating the variables and integrating:

dN/N = k dt

ln(N) = kt + C

where C is the constant of integration.

To find the value of C, we use the initial condition that the culture initially contains 50 cells:

ln(50) = k(0) + C

C = ln(50)

Substituting C into the previous equation, we get:

ln(N) = kt + ln(50)

Taking the exponential of both sides, we obtain:

N = e\(^(kt + ln(50)) = 50e^(kt)\)

Now we need to find the value of k. We know that after 1.5 hours, the population has increased to 825:

N(1.5) = 825

Substituting this into the previous equation, we get:

825 = 50\(e^(1.5k)\)

Taking the natural logarithm of both sides, we obtain:

ln(825/50) = 1.5k

k = ln(825/50) / 1.5

k ≈ 0.4427

Finally, substituting this value of k into the expression we obtained for N(t), we get:

N(t) = 50e\(^(0.4427t)\)

Therefore, the expression for the number of bacteria after t hours is N(t) = \(50e^(0.4427t)\), rounded to four decimal places.

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Answer:

Step-by-step explanation:

x^3=27

x=sqrt27=3

x=3

Answer:

A) x=3

Step-by-step explanation:

you can type it in the calculator like this: \(\sqrt[3]{27} =3\)

Answer:

-2 is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want to find the slopes of the lines shown in the attached graphs.

The slope of a line is its "rise" divided by its "run":

  m = rise/run

To determine slope from a graph, start at an identified point on the left, and count the grid squares up (+) or down (-) to the same horizontal line as the identified point on the right. This is the "rise". Then count the grid squares horizontally to the identified point. This is the "run". The slope is the ratio of these numbers.

1. rise 4, run 6, slope 4/6 = 2/3

2. rise -3, run 4, slope -3/4

3. rise -6, run 3, slope -6/3 = -2

4. run = 0; division by 0 is "undefined", so the slope is "undefined"

5. rise 4, run 1, slope 4/1 = 4

6. rise 0, run (anything), slope 0/1 = 0

__

Additional comment

It is helpful to remember that a horizontal line has a slope of 0, and a vertical line has a slope that is "undefined." Slope is positive if the line goes up to the right. It is negative if the slope goes down to the right.

Because the slope of a vertical line is "undefined," its equation cannot be written in "slope-intercept" form.

Here, points are marked on the lines. When that is not the case, it usually works well to identify points where the line crosses an intersection of grid lines.

You can also use grid crossings to check your answer for the slope. For example, the line on graph 3 crosses grid intersections that are 2 down and 1 over from the marked points (and other grid intersections), confirming a slope of -2.

The highest EMV (Expected Monetary Value) is for Alternative 2.

The EMV for each alternative is calculated by multiplying the payoff in each state of nature by its probability and summing up the results. For Alternative 1, the EMV can be calculated as follows:

EMV(Alternative 1) = (0.5 * 130) + (0.5 * 150) = 65 + 75 = 140

Similarly, for Alternative 2:

EMV(Alternative 2) = (0.5 * 200) + (0.5 * 140) = 100 + 70 = 170

Comparing the EMVs of both alternatives, we can see that Alternative 2 has a higher EMV of 170, while Alternative 1 has an EMV of 140. Therefore, the highest EMV is associated with Alternative 2.

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Answer:

x < 5/2

Step-by-step explanation:

−4x + 5 > −5

4x + 5− 5 > −5 −5

−4x > −10

−4x/−4 > −10/−4

x < 5/2

Answer:

r = 5.6

Step-by-step explanation:

To solve this problem, we need to isolate r on one side of the equation. To do this, we need to subtract 2.3 from both sides, giving us:

2.3 + r = 7.9

r = 5.6

So, r = 5.6

Hope this helped!

Answer:

5.6

Step-by-step explanation:

2.3+r=7.9

r=7.9-2.3

r=5.6

Answer:

\(y=3\)

Step-by-step explanation:

\(-2(7 - y) + 4 = -4\)

➱ Subtract 4 from both sides:

➱ Divide both sides by -2:

➱ Subtract 7 from both sides:

➱ Divide both sides by -1:

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