Researchers at a drug company are testing the duration of a new pain reliever. The drug is normally distributed with a mean duration of 240 minutes (4 hours) and a standard deviation of 40 minutes. The drug is administered to a random sample of 10 people. (Round means, standard deviations, and z-scores to the nearest hundredth, if necessary. )

The measure of an angle that goes through 2/8 of a circle is 90°

A circle is a 2-dimensional shape that is round in shape it is equidistant from the center.

A circle has a total angle of 360°

That is the whole complete angle of the circle = 360°

The 2/8 th of the complete angle of the circle = 360 * 2/8

= 360 * 1/4

= 360/4

=90°

Thus, the 90° of the circle is given as 2/8th of an angle of the circle or we can say that the quarter angle of a circle comes out to 90°.

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The amount of water needed for 1/3 cup of rice, is 3/4 cups of water.

The problem asks us to find out how much water is needed for 1/3 cup of rice, given that 2 1/4 cups of water are needed for 1 cup of rice. To solve this problem, we can use a proportion.

A proportion is an equation that says two ratios are equal. In this case, we want to set up a proportion that relates the amount of water needed to the amount of rice.

Let's start by writing down what we know. We know that for 1 cup of rice, we need 2 1/4 cups of water. We can write this as a ratio:

2 1/4 cups water : 1 cup rice

Now we want to figure out how much water we need for 1/3 cup of rice. Let's call the amount of water we need "x" (we don't know what it is yet), and set up another ratio:

x cups water : 1/3 cup rice

We can now set up our proportion by equating these two ratios:

2 1/4 cups water : 1 cup rice = x cups water : 1/3 cup rice

To solve for x, we can cross-multiply and simplify. Cross-multiplying means we multiply the numerator of one ratio by the denominator of the other ratio, like this:

(2 1/4 cups water) * (1/3 cup rice) = (x cups water) * (1 cup rice)

To simplify this, we can convert the mixed number 2 1/4 to an improper fraction:

2 1/4 = 9/4

Now we can substitute these values and multiply:

(9/4 cups water) * (1/3 cup rice) = (x cups water) * (1/1 cup rice)

Multiplying the fractions on the left-hand side gives:

9/12 cups water = (x cups water) * (1/1 cup rice)

Simplifying the fraction on the left-hand side gives:

3/4 cups water = x cups water

So we have found that x, the amount of water needed for 1/3 cup of rice, is 3/4 cups of water. Therefore, if you have 1/3 cup of rice, you would need to use 3/4 cups of water to cook it.

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The given data is an example of a nonlinear function. Therefore, the answer is A.

The given data consists of two sets of numbers, X and Y, where each value of X has a corresponding value of Y. We can observe that the points do not lie on a straight line. Instead, the plotted points form a curved shape, which indicates that the relationship between X and Y is not a linear function.

A linear function is a function where the relationship between the input variable (X) and output variable (Y) is a straight line. In this case, we can observe that as the value of X increases, the value of Y increases at an increasing rate, which means the relationship between X and Y is not linear.

In particular, the relationship between X and Y is a quadratic function since the values of Y are the squares of the corresponding values of X.

Therefore, the answer is A.

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The area of the region bounded by the curves is 4/3 square units.

To find the area of the region bounded by the curves y = 10 - [tex]x^2[/tex] and y = [tex]x^2[/tex] + 8, we need to find the points of intersection between the two curves.
Setting the two equations equal to each other, we have:
10 - [tex]x^2[/tex] = [tex]x^2[/tex] + 8
Simplifying, we get:
[tex]2x^2[/tex] = 2
[tex]x^2[/tex] = 1
x = ±1
Substituting x = 1 into either equation gives us:
y = 10 - [tex]1^2[/tex] = 9
And substituting x = -1 gives us:
y = 10 - [tex](-1)^2[/tex] = 10
So the two curves intersect at the points (1, 9) and (-1, 10).
To find the area of the region bounded by the curves, we need to integrate the difference between the two equations with respect to x, from x = -1 to x = 1:
∫[10 - [tex]x^2[/tex]] - [[tex]x^2[/tex] + 8] dx, from x = -1 to x = 1
= ∫(2 - 2[tex]x^2[/tex]) dx, from x = -1 to x = 1
= [2x - (2/3)[tex]x^3[/tex]] from x = -1 to x = 1
= 4/3
So

The area of the region bounded by the curves y = 10 - [tex]x^2[/tex] and y = [tex]x^2[/tex] + 8 is 4/3 square units.

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The police dog spends 1/6 of its workday at the police station.

To find the fraction of the police dog's workday spent at the police station, we need to add up the fractions of time spent in each location and subtract them from 1, since the dog spends the rest of the day at the police station.

Fraction of time spent in police car =  [tex]1/3[/tex]

Fraction of time spent in public = [tex]1/2[/tex]

To add these fractions, we need to find a common denominator:

[tex]1/3 = 2/6\\1/2 = 3/6[/tex]

So, the fraction of the dog's day spent at the police station is:

[tex]1 - (2/6 + 3/6) = 1 - 5/6[/tex]

                        = [tex]1/6[/tex]

Therefore, the police dog spends 1/6 of its workday at the police station.

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∠AOD≅∠COB,∠AOB≅∠COD by vertical angle theorem. ΔAOD≅ΔCOB,ΔAOB≅ΔCOD by SAS. ∠DAC≅∠BCA,∠BAC≅∠DCA by CPCTC. AB║CD,AD║BC by converse alternate interior angles theorem

Vertical angles theorem states that perpendicular angles, angles that are contrary each other and formed by two cutting straight lines, are harmonious.

Alternate angle theorem states that when two resemblant lines are cut by a transversal, also the performing alternate interior angles or alternate surface angles are harmonious.

SAS Side angle side

CPCTC Corresponding corridor of harmonious triangles are harmonious.

discourse of alternate interior angle theorem If two alternate interior angles are harmonious also the two lines are resemblant.

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According to given data GR(x) * GR(y) = 3 * 2m - 5

The given monomial is P(x;y) = -mx^3m-1 * y^2m-7, and it is known that GA(P) = 17.

We need to find the values of GR(x) and GR(y), which are the degrees of the monomial with respect to x and y, respectively.

Using the formula GA(P) = GR(x) + GR(y), we get GR(x) + GR(y) = 17.

Now, we can write the monomial as P(x;y) = (-m) * x^(3m-1) * y^(2m-7).

Therefore, GR(x) = 3m-1 and GR(y) = 2m-7.

Multiplying these two values, we get GR(x) * GR(y) = (3m-1) * (2m-7) = 6m^2 - 23m + 7.

Hence, the final answer is GR(x) * GR(y) = 6m^2 - 23m + 7.

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The amount of more sauce needed is 5/12.

Thus we are given that the total amount of sauce required for making the pizza is 2/3 cup.

Thus we already have 1/4 cup of tomato sauce present.

Hence, for making the recipe the leftover amount of sauce will be the difference in the sauce we have got to the sauce required.

Tomato sauce required= Total tomato sauce needed - Sauce already present

Therefore,

Tomato sauce required= 2/3-1/4

Thus we have to make the denominators qual by taking their LCM as the denominator.

The LCM of the denominators comes out to be 12.

Therefore,

[tex]=\frac{8-3}{12}[/tex]

[tex]=\frac{5}{12}[/tex]

Therefore, the amount of sauce required is 5/12.

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The measure of angle x is 77 degrees.

We have two angles given: 65 degrees and 38 degrees. Let's call the measure of angle x as "x".

From the information, we have the measure of the missing angle of the angles in a triangle are 38°, 65° and x. Then we can set up an equation:

x + 65 + 38 = 180 (the sum of the measures of the angles in a triangle is 180)

Simplifying this equation, we get:

x + 103 = 180

x = 77

Therefore, the measure of angle x is 77 degrees.

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Complete question

Find the measure of the missing angle of the angles in a triangle are 38°, 65° and x.

The value of s is, 27 yards

:: Volume of cube with side s, is equal to s³

So, as the given volume is 19,683 cubic yards.

Therefore, it can related as,

s³ = 19,683 (yards)³

So,

s = ∛(19,683) yards

s = 27 yards

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The size of the square that needs to be cut out of each corner to create a box of maximum volume is 5/3 inches.

To determine the function f given that f'(x)=6x² – 5 sin x+eˣ and f(0) = 20, we need to integrate f'(x) with respect to x to obtain f(x), and then use the initial condition f(0) = 20 to find the value of the constant of integration.

Integrating f'(x) with respect to x, we have:

f(x) = 2x³ + 5 cos x + eˣ + C

where C is the constant of integration.

Using the initial condition f(0) = 20, we have:

f(0) = 2(0)³ + 5 cos 0 + e⁰ + C = 6 + C = 20

Therefore, the constant of integration is C = 14, and the function f(x) is:

f(x) = 2x³ + 5 cos x + eˣ + 14

To determine the size of the square that needs to be cut out of each corner of a standard piece of notebook paper to create a box of maximum volume, we can start by drawing a diagram of the box and labeling the sides as follows:

| |

| |

| | h

| |

|__________|

L

Let x be the length of each side of the square that is cut out of each corner. Then, the length and width of the base of the box will be L - 2x and 11 - 2x, respectively, and the height of the box will be x. Therefore, the volume V of the box can be expressed as:

V(x) = x(L - 2x)(11 - 2x)

Expanding and simplifying, we get:

V(x) = -4x³ + 46x² - 110x

To find the size of the square that maximizes the volume of the box, we need to find the value of x that maximizes V(x). This can be done by finding the critical points of V(x) and determining whether they correspond to a maximum or minimum.

Taking the derivative of V(x) with respect to x, we get:

V'(x) = -12x² + 92x - 110

Setting V'(x) = 0 and solving for x, we get:

x = 5/3 or x = 11/6

To determine whether these values correspond to a maximum or minimum, we can use the second derivative test. Taking the second derivative of V(x) with respect to x, we get:

V''(x) = -24x + 92

Evaluating V''(5/3) and V''(11/6), we find that:

V''(5/3) = -4 < 0, so x = 5/3 corresponds to a maximum.

V''(11/6) = 20 > 0, so x = 11/6 corresponds to a minimum.

Therefore, the size of the square that needs to be cut out of each corner to create a box of maximum volume is 5/3 inches.

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Answer:

It is a trapezoid

Step-by-step explanation:

Yes, the given points represent the vertices of a trapezoid.

A trapezoid is a quadrilateral with one set of parallel sides. In this case, the parallel sides are AB and CD. The other two sides, AD and BC, are not parallel.

The trapezoid is not isosceles because the two non-parallel sides are not congruent. AD has a length of 6 units, while BC has a length of 4 units.

Here is a diagram of the trapezoid:

A(-4,-1)

B((-4,6)

C(2,6)

D(2,-4)

A trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, sides AB and CD are parallel because they have the same slope. So, the given points do represent the vertices of a trapezoid.

An isosceles trapezoid has two congruent legs (non-parallel sides). In this case, the length of side AD is `sqrt((-4-2)^2+(-1+4)^2)=sqrt(36+9)=sqrt(45)` and the length of side BC is `sqrt((-4-2)^2+(6-6)^2)=sqrt(36+0)=sqrt(36)`. Since `sqrt(45)` is not equal to `sqrt(36)`, the trapezoid is not isosceles.

The volume of the rectangular prism is 200 in³.

The volume of a rectangular prism is found by multiplying its length, width, and height. In this case, the prism has a length of 8 inches, width of 2 inches, and height of 12 and one-half inches. To calculate the volume, you would use the following formula:

Volume = Length × Width × Height

Now, plug in the given dimensions:

Volume = 8 in × 2 in × 12.5 in

Perform the calculations:

Volume = 16 in² × 12.5 in

Volume = 200 in³

So, the rectangular prism has a volume of 200 cubic inches. This means that the space occupied by the prism is equal to 200 cubic inches. The other options provided, such as 16 in³, 22 and one-half in³, and 212 and one-half in³, are not correct because they do not represent the product of the length, width, and height of the given prism. In conclusion, the correct answer for the volume of this rectangular prism is 200 in³.

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The measure of the largest interior angle is  105°.

What is the measure of angle?

When two lines or rays intersect at a single point, an angle is created. The vertex is the term for the shared point. An angle measure in geometry is the length of the angle created by two rays or arms meeting at a common vertex.

Here, we have

Given: The measures of 5 of the interior angles of a hexagon are: 130, 120°, 80, 160, and 155. we have to find the measure of the largest interior angle.

The sum of all the six interior angles of a hexagon is 720°.

As sum of five angles is 130° + 120° + 80° + 160° +155° = 165°

The sixth angle is 720° - 165° = 75°

So the smallest interior angle of the hexagon is 75°.

and the largest exterior angle is 180° -  75° =  105°.

Hence, the measure of the largest interior angle is  105°.

Question: The measures of 5 of the interior angles of a hexagon are: 130, 120°, 80, 160, and 155 What is the measure of the largest exterior angle?

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1) function g is increasing on all intervals of x.

2) the same is true about both s and t.

3) functions s and g have the same x-intercept.

The phrase "function g is ___ on all intervals of x" refers to the behavior of the function g with respect to its input variable x. If we know that g is increasing on all intervals of x, this means that as we move from left to right along the x-axis, the values of g are increasing. In other words, if we were to plot the graph of g, it would be sloping upwards from left to right.

The phrase "the same is true about ____" is asking us to identify another function that has the same behavior as function g. The options given are both s and t, function s, function t, or neither s nor t. Without any further information about s and t, we cannot definitively say whether they are increasing on all intervals of x like g. Therefore, the correct answer is "both s and t," because this option covers the possibility that either s or t may have the same behavior as g.

The phrase "functions ____ have the same x-intercept" refers to the point(s) where the graph of each function intersects the x-axis. If we know that functions s and g have the same x-intercept, this means that they intersect the x-axis at the same point(s). Therefore, the correct answer is "s and g." However, there is no information given to suggest that function t has the same x-intercept as either s or g, so it is not a correct answer option.

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1. decreasing

2. function t

3. s and t

4. x

Got it right on Edmentum

68.2% confidence of the students drink between: 131 and 175 bottles of water per day.

We can use the empirical rule, also known as the 68-95-99.7 rule, to determine the range of values that contain 68.2% of the data in a normal distribution. According to the rule, approximately 68.2% of the data falls within one standard deviation of the mean.

We know that the mean amount of bottled water consumed is 153 bottles, with a standard deviation of 22 bottles. Therefore, one standard deviation below the mean is 153 - 22 = 131 bottles, and one standard deviation above the mean is 153 + 22 = 175 bottles.

Thus, we can say with 68.2% confidence that the number of bottled water consumed by students each day falls between 131 and 175 bottles.

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To determine which postulate can be used to prove that triangle CAT and triangle DOG are congruent, we need information about the side lengths and angles of each triangle. Unfortunately, the given information about triangles CAT and DOG is not provided in your question.

However, I can briefly explain each of the mentioned postulates to help you understand how they can be applied to prove congruence:

1. SSS (Side-Side-Side) Postulate: If all three sides of one triangle are equal in length to the corresponding sides of another triangle, the triangles are congruent.

2. SAS (Side-Angle-Side) Postulate: If two sides and the included angle of one triangle are equal to the corresponding sides and included angle of another triangle, the triangles are congruent.

3. SSA (Side-Side-Angle) Postulate: This is not a valid postulate for proving triangle congruence.

4. ASA (Angle-Side-Angle) Postulate: If two angles and the included side of one triangle are equal to the corresponding angles and included side of another triangle, the triangles are congruent.

5. AAS (Angle-Angle-Side) Postulate: If two angles and a non-included side of one triangle are equal to the corresponding angles and non-included side of another triangle, the triangles are congruent.

Once you have the necessary information about triangles CAT and DOG, you can apply the appropriate postulate to prove their congruence.

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The probability that a randomly chosen part has either a major flaw or a minor flaw is 22% or 0.22.

To find the probability that a randomly chosen cast aluminum part has a flaw (major or minor), we can simply add the percentages of parts with minor flaws and major flaws together.

From the given information, 20% of the parts had minor flaws and 2% had major flaws. When we add these percentages together, we get:

20% (minor flaws) + 2% (major flaws) = 22%

Thus, there is a 22% probability that a randomly chosen part has a flaw, either major or minor. Rounded to two decimal places, this would be written as 0.22.

In summary, by considering the percentages of parts with minor and major flaws, we can determine the overall probability of selecting a flawed part. In this case, the probability is 22% or 0.22 when rounded to two decimal places.

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Step-by-step explanation:

Use Pythagorean theorem for right triangles

c^2 = a^2 + b^2      where c = hypotenuse and   a   and b are the legs

8.6^2 = 5^2 + r^2

8.6^2 - 5^2 = r^2

r = ~ 7  units

The value from the Student's t distribution that we would use to calculate a 95% confidence interval is 2.048

When the population standard deviation, σ, is unknown, we use the sample standard deviation, s, to estimate it. The t-distribution is used to calculate the confidence interval when we have a small sample size (less than 30) and the population standard deviation is unknown.

The value from the t-distribution that we would use to calculate a 95% confidence interval for the mean with a sample size of 28 is the t-value with 27 degrees of freedom, denoted by t(0.025,27) is 2.048.

This value can be obtained from a t-distribution table or calculator, and it represents the number of standard errors away from the mean that corresponds to a 95% confidence interval.

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Answer:

Step-by-step explanation:

P(0,7), Q(6,5), R(5,2), and S(-1,4) form the vertices of a rectangle. To prove this, we need to show that the opposite sides of the quadrilateral are parallel and that the diagonals are equal in length and bisect each other.

To explain this solution in more detail, we can start by finding the slopes of the line segments connecting each pair of points. The slope of a line segment can be calculated using the formula:

slope = (change in y) / (change in x)

For example, the slope of the line segment connecting P and Q is:

slope PQ = (5 - 7) / (6 - 0) = -2/6 = -1/3

We can calculate the slopes of the other line segments in a similar way. If the opposite sides of the quadrilateral are parallel, then their slopes must be equal. We can check that this is true for all pairs of opposite sides:

slope PQ = -1/3, slope SR = -1/3

slope QR = (2 - 5) / (5 - 6) = -3/-1 = 3, slope PS = (4 - 7) / (-1 - 0) = -3/-1 = 3

Next, we can calculate the lengths of the diagonals using the distance formula:

distance PR = sqrt[(5 - 0)^2 + (2 - 7)^2] = sqrt(5^2 + (-5)^2) = sqrt(50)

distance QS = sqrt[(6 - (-1))^2 + (5 - 4)^2] = sqrt(7^2 + 1^2) = sqrt(50)

If the diagonals are equal in length, then we should have distance PR = distance QS, which is indeed the case.

Finally, we need to show that the diagonals bisect each other. This means that the midpoint of PR should be the same as the midpoint of QS. We can calculate the midpoint of each diagonal using the midpoint formula:

midpoint of PR = [(0 + 5)/2, (7 + 2)/2] = (2.5, 4.5)

midpoint of QS = [(6 + (-1))/2, (5 + 4)/2] = (2.5, 4.5)

Since the midpoints are the same, we have shown that the diagonals bisect each other.

Therefore, we have shown that the points P(0,7), Q(6,5), R(5,2), and S(-1,4) form the vertices of a rectangle.

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Answer:

x = 150

Step-by-step explanation:

We know that the total amount of degrees in a circle is 360°.

We also know that a right angle is 90°.

Using this information, and the given 120° angle, we can form the following equation to solve for x:

90° + 120° + x° = 360°

210° + x° = 360°

x° = 360° - 210°

x° = 150°

x = 150

Step-by-step explanation:

120° + 90° + x = 360°

210° + x = 360°

x = 360° - 210°

= 150°

The expression for the total volume of the building is V = L × W × H.

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

To write an expression for the total volume of a building, we'll need to consider the dimensions of the building: length (L), width (W), and height (H). The volume of a rectangular building can be calculated using the formula:

Total Volume (V) = Length (L) × Width (W) × Height (H)

So, the expression for the total volume of the building is V = L × W × H.

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The future value of Payton's investment will be $1,048.29 when he cashes in the bond on the maturity date 15 years from now.

To calculate the future value of Payton's 15-year treasury bond, we can use the formula for compound interest:

FV = PV * (1 + r/n)^(n*t)

where FV is the future value, PV is the present value (or face amount), r is the interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, the present value is $700, the interest rate is 2.5% or 0.025, the interest is compounded quarterly, so n = 4, and the time period is 15 years.

Plugging in the values, we get:

FV = $700 * (1 + 0.025/4)^(4*15)

FV = $700 * (1 + 0.00625)^60

FV = $700 * 1.49756

FV = $1,048.29

Therefore, the future value of Payton's investment will be $1,048.29 when he cashes in the bond on the maturity date 15 years from now.

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Answer:

4.

Step-by-step explanation:

What is elimination method?

In the elimination method you either add or subtract the equations to get an equation in one variable

Lets solve for X first.

We have the equations:

5x+3y=8

4x+y=8

We take the GCM (3) and multiply everything on the bottom by -3 and multiply everything on the top by 1 (which in this case, dont touch the top) which we should now have:

5x+3y=8

-12x-3y=-36

We can now eliminate the Y and add like terms from the top to bottom, from which we should now have remaining:

-7x=-28

Solve for X

x=4

Now that we have 4, plug it in to one of the equations, which we should plug it in to 4x+y=12

4(4)+y=12

Simplify:

16+y=12

Subtract 16 to the other side:

y=-4

So now we got our x and y vaule, from which is how we get the answer (4,-4)

The total lease cost for Clayton's SUV is $23,056.24.

Before any additional fees or deposits, the total lease cost is $421.38 per month for 48 months, which equals:

Total cost of the lease  = $421.38/month x 48 months = $20,236.24

Clayton also paid a $2,500 down payment, a $85 title charge, and a $235 license cost in addition to the monthly lease payments.

The entire cost of the lease is $20,236.24 + $2,500 + $85 + $235 = $23,056.24 in total.

Therefore, the total lease cost for Clayton's SUV is $23,056.24.

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The number of left-handed students in the first trial of the simulation can be found by following the above steps and counting the occurrences of two-digit numbers within the 00-14 range on line 1 of the random-number table.

To find out how many left-handed students occur in the first trial of the simulation, you'll need to follow these steps,
1. Identify the probability range for left-handed students, which is 00-14 as you've mentioned.
2. Start on line 1 of the random-number table.
3. Read each two-digit number on the line and check if it falls within the range 00-14.
4. Count the number of times a number within the 00-14 range appears in the first 10 two-digit numbers (since you're selecting a random sample of 10 students).
5. The count of numbers within the 00-14 range represents the number of left-handed students in the first trial of the simulation.

By doing the aforementioned processes and counting the occurrences of two-digit numbers between the ranges of 00 and 14 on line 1 of the random-number table, it is possible to determine the number of left-handed pupils in the simulation's first trial.

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In the given circle, measure of angle m is 44° and the measure of angle n is 39°. Thus, the value of m is 44 and the value of n is 39

From the question, we are to determine the values of m and n in the given circle

From one of the circle theorems, we have that

The angles at the circumference subtended by the same arc are equal. That is, angles in the same segment are equal.

In the given diagram,

Angle m is in the same segment as the angle that measures 44°

Since angles in the same segment are equal,

Measure of angle m = 44°

Also,

Angle n is in the same segment as the angle that measures 39°

Since angles in the same segment are equal,

Measure of angle n = 39°

Hence,

m ∠m = 44°

m ∠n = 39°

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Dilating the figure by a scale factor of 3, the new coordinates are:

A' (-3, 12)

B' (9, 6)

C' (5886, -6)

D (unknown)

To dilate a figure by a scale factor, we need to multiply the coordinates of each point by the scale factor. Given the scale factor K = 3, we can dilate the figure using the formula:

New x-coordinate = K * original x-coordinate

New y-coordinate = K * original y-coordinate

Let's apply this to the given coordinates:

(-1, 4)

New x-coordinate = 3 * (-1) = -3

New y-coordinate = 3 * 4 = 12

A' (-3, 12)

(3, 2)

New x-coordinate = 3 * 3 = 9

New y-coordinate = 3 * 2 = 6

B' (9, 6)

(1962, -2)

New x-coordinate = 3 * 1962 = 5886

New y-coordinate = 3 * (-2) = -6

C' (5886, -6)

Dilating the figure by a scale factor of 3, the new coordinates are:

A' (-3, 12)

B' (9, 6)

C' (5886, -6)

D (unknown)

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