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  1. Asked: April 21, 2021In: ,

    Probability and Statistics

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    First, let us confirm that all the class' scores were covered by making sure that the sum of all probabilities is 1. Thus, $\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}=\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{1}{6}=\dfrac{6}{6}=1$. Thus, the scores of the entire class are represented. The LCD of the denominatorsRead more

    First, let us confirm that all the class’ scores were covered by making sure that the sum of all probabilities is 1.

    Thus, \dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}=\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{1}{6}=\dfrac{6}{6}=1.

    Thus, the scores of the entire class are represented.

    The LCD of the denominators is 6x, so let the total number of students in the class be 6x, then 3x students scored 90, 2x students scored 87, and x students scored 89.

    Thus, the average grade of the entire class is given by \dfrac{90(3x)+87(2x)+89x}{6x}=\dfrac{270x+174x+89x}{6x}=\dfrac{533x}{6x}\approx88.83.

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  2. Asked: April 21, 2021In: ,

    Applied Mathematics: Kinematics

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    acedstud

    The relationship between the vertical height, h, the time, t, the initial velocity, u, and the acceleration due to gravity, g, is given by $h=ut+\dfrac{1}{2}gt^2$. Here, $h=56$ m, $u=0$, $g=9.8 m/s^2$. Thus, $56=0\times t+\dfrac{1}{2}9.8t^2\Rightarrow56=4.9t^2\Rightarrow t^2=\dfrac{56}{4.9}=11.42857Read more

    The relationship between the vertical height, h, the time, t, the initial velocity, u, and the acceleration due to gravity, g, is given by h=ut+\dfrac{1}{2}gt^2.

    Here, h=56 m, u=0, g=9.8 m/s^2.

    Thus, 56=0\times t+\dfrac{1}{2}9.8t^2\Rightarrow56=4.9t^2\Rightarrow t^2=\dfrac{56}{4.9}=11.42857143

    \Rightarrow t=\sqrt{11.42857143}\approx3.38 seconds.

    Using, v=u+gt, we have v=0+9.8\times3.38=33.13 m/s.

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  3. Asked: April 21, 2021In: ,

    algebra questions

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    acedstud

    Using a graphing calculator, we can approximate $k$ to be 5.2 or 0.8. (as attached).

    Using a graphing calculator, we can approximate k to be 5.2 or 0.8. (as attached).

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    Attachment

  4. Asked: April 21, 2021In: ,

    Geometry Practice: Circle

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    acedstud

    Let the length of the sides of the original square be $s$, then the diameter of the circle cut-off from the square is $s$. Now, the diagonal of the square cut-off from the circle is equivalent to the diameter of the circle, thus $s$. Now, the area of a square given the length of the diagonal is giveRead more

    Let the length of the sides of the original square be s, then the diameter of the circle cut-off from the square is s.

    Now, the diagonal of the square cut-off from the circle is equivalent to the diameter of the circle, thus s.

    Now, the area of a square given the length of the diagonal is given by half the square of the length of the diagonal.

    Therefore, the area of the square cut-off is \dfrac{s^2}{2}. That is half the square of the length of the sides of the original square.

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  5. Asked: April 21, 2021In:

    How can you identify if the sequence is arithmetic or geometric

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    This answer was edited.

    A sequence is an arithmetic sequence if each term is obtained by the addition or subtraction of a constant from the preceding term. A sequence is a geometric sequence if each term is obtained by the multiplication or division of a constant from the preceding term.

    A sequence is an arithmetic sequence if each term is obtained by the addition or subtraction of a constant from the preceding term.

    A sequence is a geometric sequence if each term is obtained by the multiplication or division of a constant from the preceding term.

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  6. Asked: April 21, 2021In: ,

    Geometry of Motion (kinematics)……………..

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    acedstud

    Note that 1 knot = 1 nautical mile per hour (1 nm/hr). The time spent by the boat to travel from port A to port B is given by $\dfrac{9\text{ nautical mile}}{18\text{ nautical mile per hour}}=0.5\text{ hours}$. The time spent by the boat to travel from port B back to port A is $\dfrac{9\text{ nauticRead more

    Note that 1 knot = 1 nautical mile per hour (1 nm/hr).

    The time spent by the boat to travel from port A to port B is given by \dfrac{9\text{ nautical mile}}{18\text{ nautical mile per hour}}=0.5\text{ hours}.

    The time spent by the boat to travel from port B back to port A is \dfrac{9\text{ nautical miles}}{15\text{ nautical mile per hour}}=0.6\text{ hours}.

    Thus, the total distance traveled is 9 nm + 9 nm = 18 nm, and the total time taken is 0.5 hours + 0.6 hours = 1.1 hours.

    Therefore, the average speed is the total distance traveled divided by the total time taken = \dfrac{18\text{ nautical mile}}{1.1\text{ hours}}\approx16.36\text{ nuatical miles per hour}.

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  7. Asked: April 21, 2021In: ,

    Algebraic Expression

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    An algebraic expression is a mathematics statement where variables and constants are combined using the arithmetic operations of addition, subtraction, multiplication, and division.

    An algebraic expression is a mathematics statement where variables and constants are combined using the arithmetic operations of addition, subtraction, multiplication, and division.

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  8. Asked: April 21, 2021In:

    Circle Problem in mathematics

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    acedstud
    This answer was edited.

    The area, $A$, of a circle of radius, $r$, is given by $A=\pi r^2$. When the radius is decreased by 10%, the new radius is $\dfrac{100\%-10\%}{100\%}r=\dfrac{90\%}{100\%}r=0.9r$. Then, the new area is $A=\pi (0.9r)^2=0.81\pi r^2=0.81\times\text{ area of the original circle}$. Therefore, the new areaRead more

    The area, A, of a circle of radius, r, is given by A=\pi r^2.

    When the radius is decreased by 10%, the new radius is \dfrac{100\%-10\%}{100\%}r=\dfrac{90\%}{100\%}r=0.9r.

    Then, the new area is A=\pi (0.9r)^2=0.81\pi r^2=0.81\times\text{ area of the original circle}.

    Therefore, the new area is an 100% – 81% = 19% decrease from the original area.

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  9. Asked: April 21, 2021In: ,

    Mathematics Problem (Permutation)

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    Any of the 8 swimmers can take the 1st prize. After the first price, there are 7 swimmers left, and any of the 7 swimmers can take the second prize. Similarly, after the second price, there are 6 swimmers left, and any of the 6 swimmers can take the third prize. Therefore, the number of possible outRead more

    Any of the 8 swimmers can take the 1st prize.

    After the first price, there are 7 swimmers left, and any of the 7 swimmers can take the second prize.

    Similarly, after the second price, there are 6 swimmers left, and any of the 6 swimmers can take the third prize.

    Therefore, the number of possible outcomes is 8\times7\times6=336.

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  10. Asked: April 21, 2021In: ,

    Mathematics (Data)

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    acedstud

    The first quartile (Q1) of a set of data is the data point that divides the set of data into the first 25% versus the last 75% after the dataset has been arranged in order (usually ascending order). This is the data point dividing the first half of a dataset into two equal parts after the dataset isRead more

    The first quartile (Q1) of a set of data is the data point that divides the set of data into the first 25% versus the last 75% after the dataset has been arranged in order (usually ascending order). This is the data point dividing the first half of a dataset into two equal parts after the dataset is arranged.

    Thus, arranging the given data in ascending order, we have 56, 59, 59, 62, 63, 64, 66, 67, 73, 77, 78, 78, 83, 84, 85, 86, 90, 97

    There are 18 data points in the dataset, thus there are 9 data points in each half. The first half of the dataset is 56, 59, 59, 62, 63, 64, 66, 67, 73. The halfway (median) is obtained by counting out 4 data points from both ends, which leaves 63 at the center, thus the middle number of the first set is 63 and hence Q1 is 63.

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