Maths-
General
Easy

Question


The line graph shows the wind speed recorded every 2 hours in a town, where x is the number of hours after midnight and  is the wind speed, in miles per hour (mph). What is the greatest average change in wind speed, in miles per hour per hour, between two readings shown in the graph?

The correct answer is: 5 (in miles/ hr)


    HINT :- The greatest average change in wind speed in miles per hour  in the graph can be determined by the slope of the line connecting the two consecutive  points  in the graph .
    Explanation :
    The greatest average change in wind speed in miles per hour  in the graph can be determined by the slope of the line connecting the two consecutive  points  in the graph .
    Step 1 : calculating all possible slopes to find the greatest average speed
    So slope of line connecting the readings (0,5) and (2,9) is
    m= fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 end fraction right parenthesis not stretchy rightwards double arrow m 1 equals fraction numerator left parenthesis 9 minus 5 right parenthesis over denominator left parenthesis 2 minus 0 right parenthesis end fraction equals 2 space left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis
    So slope of line connecting the readings (2,9) and (4,4) is
    m= fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 2 equals fraction numerator left parenthesis 4 minus 9 right parenthesis over denominator left parenthesis 4 minus 2 right parenthesis end fraction equals negative 5 over 2 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis
    So slope of line connecting the readings (4,4) and (6,2) is
    m= fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 3 equals fraction numerator left parenthesis 2 minus 4 right parenthesis over denominator left parenthesis 6 minus 4 right parenthesis end fraction equals negative 1 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis
    So slope of line connecting the readings (6,2) and (8,6) is
    m= fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 4 equals fraction numerator left parenthesis 6 minus 2 right parenthesis over denominator left parenthesis 8 minus 6 right parenthesis end fraction equals 2 left parenthesis fraction numerator in miles over denominator hr end fraction right parenthesis
    So slope of line connecting the readings (8,6) and (10,16) is
    m= fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 5 equals fraction numerator left parenthesis 16 minus 6 right parenthesis over denominator left parenthesis 10 minus 8 right parenthesis end fraction equals 5 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis
    So slope of line connecting the readings (10,16) and (12,8) is
    m= fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 6 equals fraction numerator left parenthesis 8 minus 16 right parenthesis over denominator left parenthesis 12 minus 10 right parenthesis end fraction equals negative 4 left parenthesis fraction numerator space in miles over denominator h r end fraction right parenthesis
    So slope of line connecting the readings (12,8) and (14,12) is
    m= fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 7 equals fraction numerator left parenthesis 12 minus 8 right parenthesis over denominator left parenthesis 14 minus 12 right parenthesis end fraction equals 2 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis
    So slope of line connecting the readings (14,12) and (16,10) is
    m= fraction numerator left parenthesis y 2 minus y 1 right parenthesis over denominator left parenthesis x 2 minus x 1 right parenthesis end fraction not stretchy rightwards double arrow m 8 equals fraction numerator left parenthesis 10 minus 12 right parenthesis over denominator left parenthesis 16 minus 14 right parenthesis end fraction equals negative 1 left parenthesis fraction numerator in miles over denominator h r end fraction right parenthesis
    So the greatest average change in the wind speed  is m5 = 5 (fraction numerator text in miles  end text over denominator text hr end text end fraction) in between the interval (8,6) and (10,16).

    Related Questions to study

    General
    Maths-

    As of 2016, there were 118 known elements. These elements can be described with 10 classifications as summarized in the given table.

    An element is a nonmetal if it is classified as a halogen, noble gas, or other nonmetal. The ratio of all nonmetals to all elements is 10 to k. What is the value of k ?

    As of 2016, there were 118 known elements. These elements can be described with 10 classifications as summarized in the given table.

    An element is a nonmetal if it is classified as a halogen, noble gas, or other nonmetal. The ratio of all nonmetals to all elements is 10 to k. What is the value of k ?

    Maths-General
    General
    Maths-

    As of 2016, there were 118 known elements. These elements can be described with 10 classifications as summarized in the given table.

    The percentage of the 10 classifications that have 11 or more elements is p straight percent sign. What is the value of p ?

    As of 2016, there were 118 known elements. These elements can be described with 10 classifications as summarized in the given table.

    The percentage of the 10 classifications that have 11 or more elements is p straight percent sign. What is the value of p ?

    Maths-General
    General
    Maths-

    The expression 3xy(2y + 3) is equivalent to b x y squared plus 9 x y, where b is a constant. What is the value of b ?

    The expression 3xy(2y + 3) is equivalent to b x y squared plus 9 x y, where b is a constant. What is the value of b ?

    Maths-General
    parallel
    General
    Maths-

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 5 x plus 3 y equals 31 end cell row cell 5 x minus 4 y equals 17 end cell end table
    If (x, y) is the solution to the given system of equations, what is the value of 10x - y ?

    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 5 x plus 3 y equals 31 end cell row cell 5 x minus 4 y equals 17 end cell end table
    If (x, y) is the solution to the given system of equations, what is the value of 10x - y ?

    Maths-General
    General
    Maths-

    A one-digit positive integer will be chosen at random. What is the probability that the chosen integer will be greater than 7 ? (Express your answer as a fraction or decimal, not as a percent.)

    A one-digit positive integer will be chosen at random. What is the probability that the chosen integer will be greater than 7 ? (Express your answer as a fraction or decimal, not as a percent.)

    Maths-General
    General
    Maths-

    Rectangle A has an area of 64 square meters. The length and width of rectangle B are 3 times the corresponding length and width of rectangle A. What is the area, in square meters, of rectangle B ?

    Rectangle A has an area of 64 square meters. The length and width of rectangle B are 3 times the corresponding length and width of rectangle A. What is the area, in square meters, of rectangle B ?

    Maths-General
    parallel
    General
    Maths-

    left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 100
    In the xy-plane, the graph of the given equation is a circle. Which point (x , y) lies on the circle?

    left parenthesis x plus 3 right parenthesis squared plus left parenthesis y minus 7 right parenthesis squared equals 100
    In the xy-plane, the graph of the given equation is a circle. Which point (x , y) lies on the circle?

    Maths-General
    General
    Maths-


    Which equation is the most appropriate exponential model for the data shown in the scatterplot?


    Which equation is the most appropriate exponential model for the data shown in the scatterplot?

    Maths-General
    General
    Maths-

    S left parenthesis t right parenthesis equals 10 left parenthesis 0.5 right parenthesis to the power of t over 29 end exponent
    A sample of strontium-90 will radioactively decay to half the original quantity in approximately 29 years. The function  above models the amount of strontium- 90 , in grams, that remains t years after a 10-gram sample starts to decay. Which of the following is the best interpretation of the number  in the function?

    S left parenthesis t right parenthesis equals 10 left parenthesis 0.5 right parenthesis to the power of t over 29 end exponent
    A sample of strontium-90 will radioactively decay to half the original quantity in approximately 29 years. The function  above models the amount of strontium- 90 , in grams, that remains t years after a 10-gram sample starts to decay. Which of the following is the best interpretation of the number  in the function?

    Maths-General
    parallel
    General
    Maths-

    y equals 1 half x plus 5
    One of the two equations in a linear system is given. The system has no solution. Which equation could be the second equation in this system?

    y equals 1 half x plus 5
    One of the two equations in a linear system is given. The system has no solution. Which equation could be the second equation in this system?

    Maths-General
    General
    Maths-

    The histogram shows the distribution of book prices, in dollars, for the 27 books for sale at a store.

    The first bar represents books with prices of less than straight $ 5. The second bar represents books with prices of at least  but less than straight $ 10, and so on. In which interval will the median price of books for sale be included when the book that costs at least straight $ 35 but less than straight $ 40 is sold?

    The histogram shows the distribution of book prices, in dollars, for the 27 books for sale at a store.

    The first bar represents books with prices of less than straight $ 5. The second bar represents books with prices of at least  but less than straight $ 10, and so on. In which interval will the median price of books for sale be included when the book that costs at least straight $ 35 but less than straight $ 40 is sold?

    Maths-General
    General
    Maths-


    The bar graph shows the frequency of each data value in a certain data set. What is the minimum data value in the data set?


    The bar graph shows the frequency of each data value in a certain data set. What is the minimum data value in the data set?

    Maths-General
    parallel
    General
    Maths-

    A potter is selling vases. The function  gives the total profit p(x) , in dollars, the potter will receive if the vases are sold at a price of x dollars each. The graph of y = p(x) is shown.

    What equation represents the relationship between the price of one vase and the profit?

    A potter is selling vases. The function  gives the total profit p(x) , in dollars, the potter will receive if the vases are sold at a price of x dollars each. The graph of y = p(x) is shown.

    What equation represents the relationship between the price of one vase and the profit?

    Maths-General
    General
    Maths-


    Data set R and data set S are represented in the dot plots shown. The mean for each data set is . Which of the following best describes the relationship between the standard deviation of data set R and the standard deviation of data set S ?


    Data set R and data set S are represented in the dot plots shown. The mean for each data set is . Which of the following best describes the relationship between the standard deviation of data set R and the standard deviation of data set S ?

    Maths-General
    General
    Maths-

    The graph of the line y equals negative 1 half x plus 3 in the xy-plane is translated 2 units to the right. What is the y-intercept of the translated line?

    The graph of the line y equals negative 1 half x plus 3 in the xy-plane is translated 2 units to the right. What is the y-intercept of the translated line?

    Maths-General
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.