Correct answer gets brainliest!!

The cost of one cup of coffee is $2.98.

To find the cost of coffee, we need to first determine the cost of bagels on both days.

On Tuesday, Jenny bought 8 bagels and 3 cups of coffee for a total of $14.45. Let's assume the cost of bagels was x and the cost of coffee was y. Then we can write the equation:

8x + 3y = 14.45

On Wednesday, she bought 4 bagels and 5 cups of coffee for a total of $16.15. Again, assuming the cost of bagels is x and the cost of coffee is y, we can write the equation:

4x + 5y = 16.15

Now we can use these two equations to solve for the cost of coffee (y).

First, let's solve for x in both equations:

8x + 3y = 14.45
8x = 14.45 - 3y
x = (14.45 - 3y)/8

4x + 5y = 16.15
4(14.45 - 3y)/8 + 5y = 16.15
5.725 - 1.5y + 5y = 16.15
3.5y = 10.425
y = 2.98

Therefore, the cost of one cup of coffee is $2.98.

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The Area of tile is 190 cm².

We have a trapezoid whose dimensions are:

base 1 = 12 cm

base 2 = 26 cm

Height= 10 cm

Now, the formula for Area of Trapezoid is

= 1/2 x (sum of parallel base) x height

= 1/2 x (base 1 + base 2) x height

So, Substituting the value of base and height in the above formula we get

Area of Trapezoid

= 1/2 x (12 + 26) x 10

= 1/2 x 38 x 10

= 19 x 10

= 190 cm²

Thus, the Area of tile is 190 cm².

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Answer:

0.6 or 60%.

Step-by-step explanation:

First find the number of favorable outcomes (being trained on any station except the most desirable) and the total number of possible outcomes (being trained on any 4 stations).

Assuming all stations are equally likely to be selected for training, if there are 10 stations in total, the probability of not being trained on the most desirable station is as follows:

1)  Favorable outcomes: Selecting 4 stations out of the 9 remaining stations (excluding the most desirable one): C(9, 4).

2) Total outcomes: Selecting any 4 stations out of the 10 available stations: C(10, 4).

P(not trained on most desirable) = Favorable outcomes / Total outcomes

= C(9, 4) / C(10, 4)

C(9, 4) = 9! / (4! * (9-4)!) = 9! / (4! * 5!) = (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1) = 126

C(10, 4) = 10! / (4! * (10-4)!) = 10! / (4! * 6!) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1) = 210

P(not trained on most desirable) = 126 / 210 = 6 / 10 = 0.6

Therefore, the probability of not being trained on the most desirable station is 0.6 or 60%.

The correct answer  is 2.3 with a repeating decimal is equivalent to the simplified fraction 7/3.

To rewrite 2.3 with a repeating decimal as a simplified fraction, we can use a mathematical technique called algebraic manipulation. We start by letting x be equal to 2.3 with a repeating decimal, and then we subtract x from 10x to eliminate the repeating part of the decimal. 10x - x = 23.3333... - 2.3333... = 21

Simplifying, we get: 9x = 21

Dividing both sides by 9, we get: x = 21/9

This fraction can be simplified further by dividing the numerator and denominator by their greatest common factor, which is 3. x = 21/9 = (21 ÷ 3)/(9 ÷ 3) = 7/3

Therefore, 2.3 with a repeating decimal is equivalent to the simplified fraction 7/3.

Repeating decimals can be challenging to work with, but the technique of algebraic manipulation allows us to convert them to equivalent fractions, which can be easier to understand and work with in many contexts.

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Two circles would be worth of 162 cents.

If one-third of a circle is worth 27 cents, then one circle would be worth 3 times that amount, since there are 3 equal parts in a circle.

So, One circle is worth:

= 27 cents/part × 3 parts/circle

= 81 cents

Now, two circles would be worth twice that amount:

= 81 cents/circle × 2 circles

= 162 cents

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Answer: The answer is option D, line B.

Step-by-step explanation:

To find the image of the line y = 2x after a translation of 3 units along the s-axis and 4 units along the y-axis, we need to shift every point on the line 3 units to the right and 4 units up.

The original line y = 2x has a y-intercept of 0 and a slope of 2, which means that for every increase of 1 unit in x, the value of y increases by 2 units. We can represent this line in slope-intercept form as y = 2x + 0.

To shift the line 3 units to the right, we need to subtract 3 from the x-coordinate of every point on the line. This gives us the equation y = 2(x - 3) + 0, which simplifies to y = 2x - 6.

To shift the line 4 units up, we need to add 4 to the y-coordinate of every point on the line. This gives us the final equation y = 2x - 2, which is the equation of a line with a slope of 2 and a y-intercept of -2.

Looking at the graph, we can see that line B has a slope of 2 and a y-intercept of -2. Therefore, line B is the image of the line y = 2x after a translation of 3 units along the s-axis and 4 units along the y-axis.

Therefore, the answer is option D, line B.

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Based on the box and whisker plots, the true statement is C. The Fitness Center has a larger range in employee hourly wages than Fitness Plus.

The range describes the difference between the lowest and highest values.

The range is computed as the difference between the maximum and the minimum.

Range of employee hourly wages at Fitness Center = 7 (15 to 22)

Range of employee hourly wages at Fitness Plus = 6 (14 to 20)

Thus, Option C is correct.

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An airplane flies from its headquarters at night to a city 510 miles away and returns the next morning. The wind speed is approximately -167 mph and is headwind.

To solve this problem, let's assume that the wind speed is represented by 'w' (in mph).

a. We know that the total flying time for the round-trip is 3.9 hours. The first half of the trip, which is 255 miles, is traveled at a speed of 255 mph with no wind. Therefore, the time taken for the first half of the trip is:

Time = Distance / Speed = 255 miles / 255 mph = 1 hour

Since the total flying time is 3.9 hours, the return trip must have taken 3.9 - 1 = 2.9 hours.

Now, we can use the formula: Time = Distance / Speed to calculate the speed of the return trip. The distance for the return trip is also 255 miles.

2.9 hours = 255 miles / (255 mph + w)

To solve for 'w', we rearrange the equation:

2.9(255 mph + w) = 255 miles

739.5 mph + 2.9w = 255 miles

2.9w = 255 miles - 739.5 mph

2.9w = -484.5 mph

w ≈ -167 mph

The wind speed is approximately -167 mph. Since wind speeds are typically reported as positive values, we take the magnitude of the wind speed, which is approximately 167 mph.

Thus, since the wind speed is negative, the wind on the return flight is a headwind.

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The solution is 13 miles per hour strong is the wind on the return flight.

Here, we have,

If the first half of the trip was travelled at the speed of 255 mph and the distance from the headquarters to the city is 510 miles, the time of travel for the first half is:

255 miles ------- 1 hour

510 miles ------- ? hours

= 510/255 × 1/1

= 2 hours

So, since the first half of the journey was at the speed of 255 miles per hour, therefore it took the plane 2 hours to get to the city from the headquarters (covering a distance of 510 miles).

But, if the time for the entire round trip is 3.9 hours, the return time is therefore:

3.9 hours ---------2 hours

= 1.9 hours( so this is the return time)

Since returning will still entail covering the same distance of 510 miles, then the speed of return is:

Speed = distance/time

= 510/1.9 = 268.42 mph.

To determine how strong the wind was on the return, we subtract the speed of the first half of the trip from the speed of the return flight:

= 268.42 - 255

= 13 miles per hour (13 mph)

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Yes, the triangles are congruent.

Given that a figure, where VY ≅ WY and ZY ≅ XY, we need to see whether the triangles ZYV and XYW are congruent,

So, in triangles ZYV and XYW,

VY ≅ WY [given]

ZY ≅ XY [given]

∠ZYV ≅ ∠XYW [vertical angles]

Therefore, the triangles ZYV and XYW are congruent, by SAS rule.

Hence the triangles are congruent.

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The formula for y in terms of x, in its simplest form, is y = 80/x.

To begin, let's start by writing out the inverse proportionality relationship between y and a^3:

y ∝ 1/a^3

We can then use the given information that when a = 2, y = 10 to solve for the constant of proportionality.

10 ∝ 1/2^3

10 ∝ 1/8

10(8) = 1

So the formula for y in terms of a is:

y = 8/a^3

Next, we can use the given information that a is directly proportional to x when x = 4 and y = 20.

a ∝ x

a = kx

Substituting this into our formula for y:

y = 8/(kx)^3

y = 8/k^3 * x^-3

Finally, we can solve for the constant of proportionality, k:

When x = 4, y = 20

20 = 8/k^3 * 4^-3

20 = 2/k^3

k^3 = 2/20

k^3 = 0.1

k = (0.1)^(1/3)

Simplifying our expression for y in terms of x:

y = 8/(0.1) * x^-1

y = 80x^-1

Therefore, the formula for y in terms of x, in its simplest form, is y = 80/x.

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Your answer: In the art exhibit, 28 prize-winning pieces of artwork are displayed.

To find the total number of pieces of artwork displayed in the exhibit, you need to multiply the number of rows by the number of artwork pieces in each row.

Step 1: Identify the number of rows and pieces of artwork in each row.
- There are 4 rows of artwork.
- There are 7 pieces of artwork in each row.

Step 2: Multiply the number of rows by the number of artwork pieces in each row.
- 4 rows * 7 pieces of artwork per row = 28 pieces of artwork

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Answer:

6.5 hour  

Step-by-step explanation:

We calculate this using speed distance formula

that is Speed = Distance / Time

When both the person is travelling in the same direction their relative speed would be v1 ( Speed of Darren ) - v2 ( Speed of Darcie)

Thus relative speed is 12 - 8 = 4 mph

By using the above equation

Time = Distance / speed

        = 26 / 4 = 6.5 h

In 6.5 h Darren will be 26 miles ahead of Darcie

The missing angle measures are x = 55 degrees and y = 125 degrees.

The missing angle measures are:

x = 55 degrees

y = 125 degrees

In a triangle, the sum of the three interior angles is always 180 degrees. Therefore, we can find the measure of angle C by subtracting the measures of angles A and B from 180:

angle C = 180 - angle A - angle B = 180 - 35 - 90 = 55 degrees

The measure of the exterior angle ∠DAC is equal to the sum of the measures of angles C and A, so we can find the measure of y by adding the measures of angles C and A:

angle y = angle C + angle A = 55 + 35 = 125 degrees.

Therefore, the missing angle measures are x = 55 degrees and y = 125 degrees.

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Answer:

x=55 degrees

y=145 degrees

Step-by-step explanation:

I got it right.

The false statement regarding evaluating forecasting errors is mean squared error and mean absolute error always agree on which forecast is better. The correct option is mean squared error and mean absolute error always agree on which forecast is better.

- Mean squared error (MSE) is heavily influenced by one single large forecast error because it squares each forecast error, and this is true.
- Mean squared error aggregates forecast errors without canceling out positive and negative forecast errors, which is also true as it squares each error.
- Mean squared error goes beyond averaging out the forecast errors since it squares each error before calculating the mean, so this statement is true as well.

However, MSE and mean absolute error (MAE) don't always agree on which forecast is better because they measure errors differently. MSE penalizes larger errors more than MAE, so they can lead to different conclusions about forecast accuracy. The correct option is mean squared error and mean absolute error always agree on which forecast is better.

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a. To approximate the given quantity using Taylor polynomials with n=3, we need to use the formula for the Taylor polynomial of degree n:

Pn(x) = f(a) + f'(a)(x-a) + (1/2!)f''(a)(x-a)^2 + (1/3!)f'''(a)(x-a)^3 + ... + (1/n!)f^(n)(a)(x-a)^n
where f(x) = sinh(x), a = 0. The derivatives of sinh(x) are:
f'(x) = cosh(x), f''(x) = sinh(x), f'''(x) = cosh(x), and so on.
Therefore, the Taylor polynomial of degree 3 for sinh(x) centered at a = 0 is:
P3(x) = x + (1/2!)(x)^3
To approximate sinh(0.24), we substitute x = 0.24 into the formula above:
P3(0.24) = 0.24 + (1/2!)(0.24)^3 = 0.240008
b. To compute the absolute error in the approximation assuming the exact value is given by a calculator, we need to subtract the actual value of sinh(0.24) from the approximation we obtained in part a:
Error = |P3(0.24) - sinh(0.24)| = |0.240008 - 0.241663| = 0.001655
Therefore, the absolute error in the approximation is 0.001655.
To approximate sinh(0.17), we use the same formula and substitute x = 0.17:
P3(0.17) = 0.17 + (1/2!)(0.17)^3 = 0.170005
To compute the absolute error in this case, we subtract the actual value of sinh(0.17) from the approximation we obtained:
Error = |P3(0.17) - sinh(0.17)| = |0.170005 - 0.17031| = 0.000305
Therefore, the absolute error in the approximation for sinh(0.17) is 0.000305.

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Check the picture below.

Keiko used 5/8 yards of green fabric to make the shirt.

To arrive at this answer, we first need to recognize that the question is asking for the amount of green fabric used, and that there are two types of fabric being used - green and blue. The amounts of each fabric are given as fractions of a yard.

To find the amount of green fabric used, we simply need to look at the fraction given for the green fabric, which is 5/8 yards. This means that Keiko used five-eighths of a yard of green fabric. It is already in its simplest form, so the answer is 5/8 yards.

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The expected number of times we roll the dice until the sum of the numbers is seven is 6.

To calculate the expected number of rolls, we need to consider the probabilities of rolling different sums. There are six possible outcomes that result in a sum of seven: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Each of these outcomes has a 1/36 probability since each die has six equally likely outcomes.

Since the expected value is the sum of the products of each outcome and its corresponding probability, we have:

Expected value = (1/36) * 1 + (1/36) * 2 + (1/36) * 3 + (1/36) * 4 + (1/36) * 5 + (1/36) * 6 = 6/36 = 1/6.

Therefore, the expected number of times we roll the dice until the sum of the numbers is seven is 6.

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Answer: The data could be used as a starting point for further research and analysis to investigate any potential causal relationships or underlying factors.

Step-by-step explanation:

The scatterplot shows a positive correlation between U.S. divorce rates and prison rates for drug offenses. The fact that the correlation coefficient is 0.67 indicates a moderate positive linear relationship between the two variables.

However, correlation does not necessarily imply causation. While the data suggests that there may be some association between divorce rates and drug-related prison rates, it does not tell us which variable is causing the other, or if there is any causal relationship at all.

There could be other factors that affect both divorce rates and drug-related prison rates, or there could be a third variable that influences both. Therefore, we cannot draw any causal conclusions from this data alone.

However, the data could be used as a starting point for further research and analysis to investigate any potential causal relationships or underlying factors.

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The system of equations are equivalent

Given data ,

Let the system of equations be represented as A and B

Now , the value of A and B are

y=( -1/3 )x+2/3   be equation (1)

2x+6y=4   be equation (2)

Multiply by 3 on both sides of equation (1) , we get

3y=-x+2

Adding x on both sides , we get

3y+x=2

Multiply by 2 on both sides , we get

6y+2x=4 equation (3)

So , the equation (2) = equation (3)

Hence , they are equivalent

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Answer: ∠D=78

Step-by-step explanation:

Complementary angles have a sum of 90°

∠C + ∠D = 90°

The equation of the plane is -36x + 54y - 14z + 62 = 0.

To find the equation of the plane through these three points, we first need to find two vectors in the plane. We can do this by subtracting p0 from Q0 and R0, respectively:

Q0 - p0 = <3-(-3), 2-(-2), -5-(-5)> = <6, 4, 0>

R0 - p0 = <2-(-3), 0-(-2), 4-(-5)> = <5, 2, 9>

Next, we can take the cross product of these two vectors to get the normal vector to the plane:

<6, 4, 0> x <5, 2, 9> = <-36, 54, -14>

We can use this normal vector, along with any of the three points, to write the equation of the plane in point-normal form:

-36(x - (-3)) + 54(y - (-2)) - 14(z - (-5)) = 0

Simplifying and rearranging terms, we get the equation of the plane:

-36x + 54y - 14z + 62 = 0

Therefore, the equation of the plane through the points p0(-3,-2,-5), Q0(3,2,-5), and R0(2,0,4) is -36x + 54y - 14z + 62 = 0.

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Answer: We can conclude that approximately 95.45% of the screws produced by the factory have a length between 5.3 cm and 5.7 cm.

Step-by-step explanation:

We know that the distribution is normal with a mean of 5.5 cm and a standard deviation of 0.1 cm. We want to find the percentage of data that lies between 5.3 cm and 5.7 cm.

To do this, we can use the standard normal distribution, which has a mean of 0 and a standard deviation of 1. We first need to standardize the values of 5.3 cm and 5.7 cm using the formula:

z = (x - mu) / sigma

where x is the value we want to standardize, mu is the mean, sigma is the standard deviation, and z is the corresponding z-score.

For 5.3 cm:

z = (5.3 - 5.5) / 0.1 = -2

For 5.7 cm:

z = (5.7 - 5.5) / 0.1 = 2

We can now use a standard normal distribution table or calculator to find the area under the curve between z = -2 and z = 2. This area represents the percentage of data that lies between 5.3 cm and 5.7 cm.

Using a standard normal distribution table or calculator, we find that the area under the curve between z = -2 and z = 2 is approximately 0.9545. This means that approximately 95.45% of the data lies between 5.3 cm and 5.7 cm.

Therefore, we can conclude that approximately 95.45% of the screws produced by the factory have a length between 5.3 cm and 5.7 cm.

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If we are to estimate the first derivative of f(x) = e-x-x2 at x= 5 using the step size h = 0.5, the correct statements are:

A) The result of the forward difference ≈ -9.5087.

B) The result of the central difference ≈ -10.0070.

D) Halving the step size h will halve the error of the backward and forward differences and quarter the error of the central difference.

To estimate the first derivative of f(x) = e^(-x-x^2) at x = 5 using the step size h = 0.5, we can calculate the forward difference, central difference, and backward difference approximations.

The forward difference approximation is given by:

f'(x) ≈ [f(x + h) - f(x)] / h

Substituting the values:

f'(5) ≈ [f(5 + 0.5) - f(5)] / 0.5

f'(5) ≈ [f(5.5) - f(5)] / 0.5

Similarly, the central difference approximation is given by:

f'(x) ≈ [f(x + h) - f(x - h)] / (2h)

Substituting the values:

f'(5) ≈ [f(5 + 0.5) - f(5 - 0.5)] / (2 * 0.5)

f'(5) ≈ [f(5.5) - f(4.5)] / 1

And the backward difference approximation is given by:

f'(x) ≈ [f(x) - f(x - h)] / h

Substituting the values:

f'(5) ≈ [f(5) - f(5 - 0.5)] / 0.5

f'(5) ≈ [f(5) - f(4.5)] / 0.5

To evaluate the statements:

A) The result of the forward difference is approximately -9.5087: We can calculate this approximation using the formula above.

B) The result of the central difference is approximately -10.0070: We can calculate this approximation using the formula above.

C) The result of the backward difference is approximately -10.5053: We can calculate this approximation using the formula above.

D) Halving the step size h will halve the error of the backward and forward differences and quarter the error of the central difference: This statement is correct. When we halve the step size h, the error in the forward and backward differences will decrease by a factor of 2, and the error in the central difference will decrease by a factor of 4.

Therefore, the correct statements are:

A) The result of the forward difference ≈ -9.5087.

B) The result of the central difference ≈ -10.0070.

D) Halving the step size h will halve the error of the backward and forward differences and quarter the error of the central difference.

Your question is incomplete but most probably your full question was

If We Are To Estimate The First Derivative Of F(X) = E-X-X2 At X= 5 Using The Step Size H = 0.5, Which Of The Following Statement Are Correct? (Select Multiple Answers) A) The Result Of Forward Difference ≈ -9.5087. B) The Result Of Central Difference ≈ -10.0070. C) The Result Of Backward Difference ≈ -10.5053. D) Halving The Step Size H Will Halve The

If we are to estimate the first derivative of f(x) = e-x-x2 at x= 5 using the step size h = 0.5, which of the following statement are correct? (Select multiple answers)

A) The result of forward difference ≈ -9.5087.

B) The result of central difference ≈ -10.0070.

C) The result of backward difference ≈ -10.5053.

D) Halving the step size h will halve the error of the backward and forward differences and quarter the error of the central difference.

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The value of y = -651. To find the value of y when x = -10 and z = 20, given that y varies jointly as x and z and y = 179 when x = -5 and z = -11, follow these steps:

Step 1: Understand that "y varies jointly as x and z" means y = kxz, where k is the constant of variation.

Step 2: Use the given values (y = 179, x = -5, z = -11) to find k. Substitute these values into the equation:
179 = k(-5)(-11)

Step 3: Solve for k:
179 = 55k
k = 179 / 55
k = 3.2545 (rounded to the nearest hundredth)

Step 4: Use the found value of k (3.2545) and the new values of x (-10) and z (20) to find the new value of y:
y = (3.2545) (-10)(20)
Step 5: Calculate y:
y = -651
So, when x = -10 and z = 20, y = -651.

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True. The index of a radical expression must always be a positive integer.

The index of a radical expression, which is represented by the "√" symbol, refers to the root being taken. The index indicates the degree of the root and must be a positive integer greater than zero.

For example, if we have √x, the index is 2, indicating that we are taking the square root of x. Similarly, if we have ∛x, the index is 3, indicating that we are taking the cube root of x.

The index being a positive integer is a requirement for the proper interpretation of the radical expression. Non-integer or negative indices are not defined within the realm of real numbers.

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The area of the garden will be 800 square centimetres.

An area is a mathematical concept that refers to the extent or size of a two-dimensional surface or region. It is a measurement that quantifies the amount of space contained within the boundaries of a shape or object.

The unit of measurement for an area depends on the system being used. In the metric system, the most common unit is the square meter (m²), while in the imperial system, units such as square feet (ft²) or square inches (in²) are used.

From the given figure the area of the quadrilateral will be calculated as,

Area = 2 x ( L + W)

Area = 2 x ( 20 + 20 )
Area = 800 square centimetres

Therefore, the area will be 800 square centimetres.

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Answer: yes I do believe

The probability that the mean score of the 49 seniors is greater than 20 is 0.0516. To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means from a population with any distribution will approach a normal distribution as the sample size increases.

First, we need to find the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the mean. We can use the formula SEM = σ / √n, where σ is the population standard deviation, and n is the sample size.

In this case, σ = 6.0 and n = 49, so SEM = 6.0 / √49 = 0.857.

Next, we need to standardize the sample mean using the z-score formula: z = (x - μ) / SEM, where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.

In this case, x = 20, μ = 18.6, and SEM = 0.857, so z = (20 - 18.6) / 0.857 = 1.63.

Finally, we need to find the probability that a standard normal distribution is greater than 1.63, which is 0.0516 when rounded to 4 decimal places.

Therefore, the probability that the mean score of the 49 seniors is greater than 20 is 0.0516.

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