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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Determine each of the following as being either true or false. If it is false, explain why.For a normal distribution for which μ = 10 and σ = 5, the z-scores for x = 20 and x = 30 are z = 1.5 and z
The following data were found for the distance y that an object rolled down an inclined plane in time t. Find a quadratic regression model for these data. Predict the distance at 2.5 s. t (s) y
Find the equation of the least-squares line for the given data. Graph the line and data points on the same graph.The speed v (in m/s) of sound was measured as a function of the temperature T (in °C)
Determine the median of the numbers of the given set.Set AA: 3, 6, 4, 2, 5, 4, 7, 6, 3, 4, 6, 4, 5, 7, 3
Use Eq. (22.2) to find the standard deviation s for the indicated sets of numbers.Eq. 22.2Set DD: 105, 108, 103, 108, 106, 104, 109, 104, 110, 108, 108, 104, 113, 106, 107, 106, 107, 109, 105, 111,
Five automobile engines are taken from the production line each hour and tested for their torque (in N · m) when rotating at a constant frequency. The measurements of the sample torques for 20 h of
Whether or not a product passes inspectionIndicate whether the variable is qualitative or quantitative.
The amounts of energy produced by a solar panel on a sample of 10 days are given below. Make a stem-and-leaf plot of the data.9.4 8.5 10.7 9.6 7.2 8.7 8.2 9.1 7.9 9.4
The increase in length y of a certain metallic rod was measured in relation to particular increases x in temperature. Find a quadratic regression model for the given data. x (°C) y (cm) 50.0
If the weights of cement bags are normally distributed with a mean of 60 lb and a standard deviation of 1 lb, use the empirical rule to find the percent of the bags that weigh the following:Between
The thickness of 100 machine parts were measured (to the nearest 0.01 in.) and the grouped data is shown below:Find the mean. Thickness (in.) 0.90 0.91 0.92 0.93 0.94 0.95 0.96 Number 3 9 31 38 12 5 2
Determine each of the following as being either true or false. If it is false, explain why.If the least-squares line for a set of data is y = 2x + 4, the deviation of the data point (2, 6) is 4.
Determine the median of the numbers of the given set.Set BB: 25, 26, 23, 24, 25, 28, 26, 27, 23, 28, 25
The time it takes a worker to complete a taskIndicate whether the variable is qualitative or quantitative.
If the weights of cement bags are normally distributed with a mean of 60 lb and a standard deviation of 1 lb, use the empirical rule to find the percent of the bags that weigh the following:Between
In linear regression, a value of r close to 0 indicates a good fit.Determine each of the following as being either true or false. If it is false, explain why.
Determine the median of the numbers of the given set.Set CC: 0.48, 0.53, 0.49, 0.45, 0.55, 0.49, 0.47, 0.55, 0.48, 0.57, 0.51, 0.46, 0.53, 0.50, 0.49, 0.53
In a random sample, 500 adults aged 30+ were asked which of the following environmentally friendly activities they do or plan to do soon. The results are summarized below:Make a bar graph of these
The pressure p at which Freon, a refrigerant, vaporizes for temperature T is given in the following table. Find a quadratic regression model. Predict the vaporization pressure at 30°F. T (°F) p
Five automobile engines are taken from the production line each hour and tested for their torque (in N · m) when rotating at a constant frequency. The measurements of the sample torques for 20 h of
The thickness of 100 machine parts were measured (to the nearest 0.01 in.) and the grouped data is shown below:Find the standard deviation. Thickness (in.) 0.90 0.91 0.92 0.93 0.94 0.95
Use Eq. (22.3) to find the standard deviation s for the indicated sets of numbers.Eq. 22.3Set BB: 25, 26, 23, 24, 25, 28, 26, 27, 23, 28, 25 S = 2 n(Σκ) - (Σ») n( n − 1)
A particular muscle was tested for its speed of shortening as a function of the force applied to it. The results appear below. Find the speed as a function of the force. Then predict the speed if the
If the weights of cement bags are normally distributed with a mean of 60 lb and a standard deviation of 1 lb, use the empirical rule to find the percent of the bags that weigh the following:Less than
A fraction f of annual hot-water loads at a certain facility are heated by solar energy. The fractions f for certain values of the collector area A are given in the following table. Find a power
Five automobile engines are taken from the production line each hour and tested for their torque (in N · m) when rotating at a constant frequency. The measurements of the sample torques for 20 h of
In a random sample, 500 adults aged 30+ were asked which of the following environmentally friendly activities they do or plan to do soon. The results are summarized below:Find the relative frequency
The thickness of 100 machine parts were measured (to the nearest 0.01 in.) and the grouped data is shown below:Make a relative frequency table. Thickness (in.) 0.90 0.91 0.92 0.93 0.94 0.95
An airline’s records showed that the percent of on-time flights each day for a 20-day period was as follows:72, 75, 76, 70, 77, 73, 80, 75, 82, 85,77, 78, 74, 86, 72, 77, 67, 78, 69, 80Determine
Use Eq. (22.3) to find the standard deviation s for the indicated sets of numbers.Eq. 22.3Set CC: 0.48, 0.53, 0.49, 0.45, 0.55, 0.49, 0.47, 0.55, 0.48, 0.57, 0.51, 0.46, 0.53, 0.50, 0.49, 0.53 S
Determine the median of the numbers of the given set.Set DD: 105, 108, 103, 108, 106, 104, 109, 104, 110, 108, 108, 104, 113, 106, 107, 106, 107, 109, 105, 111, 109, 108
If the weights of cement bags are normally distributed with a mean of 60 lb and a standard deviation of 1 lb, use the empirical rule to find the percent of the bags that weigh the following:More than
Five AC adaptors that are used to charge batteries of a cellular phone are taken from the production line each 15 min and tested for their direct-current output voltage. The output voltages for 24
The altitude h (in m) of a rocket was measured at several positions at a horizontal distance x (in m) from the launch site, shown in the table. Find the least-squares line for has a function of x. x
An airline’s records showed that the percent of on-time flights each day for a 20-day period was as follows:72, 75, 76, 70, 77, 73, 80, 75, 82, 85,77, 78, 74, 86, 72, 77, 67, 78, 69, 80Determine
The output torque (in J) of a certain engine was measured at various frequencies (in r/min) with the following results. Find a power regression model for these data. Predict the output torque for a
In a random sample, 500 adults aged 30+ were asked which of the following environmentally friendly activities they do or plan to do soon. The results are summarized below:Is it appropriate to use a
Use Eq. (22.3) to find the standard deviation s for the indicated sets of numbers.Eq. 22.3Set DD: 105, 108, 103, 108, 106, 104, 109, 104, 110, 108, 108, 104, 113, 106, 107, 106, 107, 109, 105, 111,
Determine the mean of the numbers of the given set.Set AA: 3, 6, 4, 2, 5, 4, 7, 6, 3, 4, 6, 4, 5, 7, 3
In testing an air-conditioning system, the temperature T in a building was measured during the afternoon hours with the results shown in the table. Find the least-squares line for T as a function of
In a random sample, 500 adults aged 30+ were asked which of the following environmentally friendly activities they do or plan to do soon. The results are summarized below:Make a bar graph of these
Use the following information. At a certain customer call-in center, the customer hold time is normally distributed with a mean of 5.2 min and a standard deviation of 1.4 min.According to the
A standardized math test has a mean score of 200 and a standard deviation of 15. Find and interpret the z-scores of the following math test scores.218
The resonant frequency f of an electric circuit containing a 4-μF capacitor was measured as a function of the inductance L in the circuit. The following data were found. Find a power regression
An airline’s records showed that the percent of on-time flights each day for a 20-day period was as follows:72, 75, 76, 70, 77, 73, 80, 75, 82, 85,77, 78, 74, 86, 72, 77, 67, 78, 69, 80Determine
Five AC adaptors that are used to charge batteries of a cellular phone are taken from the production line each 15 min and tested for their direct-current output voltage. The output voltages for 24
Determine the mean of the numbers of the given set.Set BB: 25, 26, 23, 24, 25, 28, 26, 27, 23, 28, 25
The displacement y of an object at the end of a spring at given times t is shown in the following table. Find an exponential regression model for this. Predict the displacement at 2.5 s. Is this
The pressure p was measured along an oil pipeline at different distances from a reference point, with results as shown. Find the least-squares line for p as a function of x using a calculator. Then
Find and interpret the z-score of a hold time of 8.7 min.Use the following information. At a certain customer call-in center, the customer hold time is normally distributed with a mean of 5.2 min and
A standardized math test has a mean score of 200 and a standard deviation of 15. Find and interpret the z-scores of the following math test scores.179
In a random sample, 800 smartphone owners were asked which type of smartphone they would choose with their next purchase (if they could only choose one). The results are summarized below:Find the
An airline’s records showed that the percent of on-time flights each day for a 20-day period was as follows:72, 75, 76, 70, 77, 73, 80, 75, 82, 85,77, 78, 74, 86, 72, 77, 67, 78, 69, 80Determine
Use the statistical feature of a calculator to find the mean and the standard deviation s for the indicated sets of numbers.Set AA: 3, 6, 4, 2, 5, 4, 7, 6, 3, 4, 6, 4, 5, 7, 3
Five AC adaptors that are used to charge batteries of a cellular phone are taken from the production line each 15 min and tested for their direct-current output voltage. The output voltages for 24
Determine the mean of the numbers of the given set.Set CC: 0.48, 0.53, 0.49, 0.45, 0.55, 0.49, 0.47, 0.55, 0.48, 0.57, 0.51, 0.46, 0.53, 0.50, 0.49, 0.53
The heat loss L per hour through various thicknesses of a particular type of insulation was measured as shown in the table. Find the least-squares line for L as a function of t using a calculator. t
An airline’s records showed that the percent of on-time flights each day for a 20-day period was as follows:72, 75, 76, 70, 77, 73, 80, 75, 82, 85,77, 78, 74, 86, 72, 77, 67, 78, 69, 80Construct a
Use the following information. At a certain customer call-in center, the customer hold time is normally distributed with a mean of 5.2 min and a standard deviation of 1.4 min.What percent of hold
A standardized math test has a mean score of 200 and a standard deviation of 15. Find and interpret the z-scores of the following math test scores.164
Use the statistical feature of a calculator to find the mean and the standard deviation s for the indicated sets of numbers.Set BB: 25, 26, 23, 24, 25, 28, 26, 27, 23, 28, 25
In a random sample, 800 smartphone owners were asked which type of smartphone they would choose with their next purchase (if they could only choose one). The results are summarized below:What is the
The average daily temperatures T (in °F ) for each month in Minneapolis (National Weather Service records) are given in the following table. (1 = Jan, 2 = Feb, etc.).Find a sinusoidal regression
Five AC adaptors that are used to charge batteries of a cellular phone are taken from the production line each 15 min and tested for their direct-current output voltage. The output voltages for 24
Determine the mean of the numbers of the given set.Set DD: 105, 108, 103, 108, 106, 104, 109, 104, 110, 108, 108, 104, 113, 106, 107, 106, 107, 109, 105, 111, 109, 108
A standardized math test has a mean score of 200 and a standard deviation of 15. Find and interpret the z-scores of the following math test scores.233
Each hour, for 20 consecutive hours, a sample of 5 M&M packets are randomly selected and their weights are measured. Explain how these data can be used to make an R control chart.
An airline’s records showed that the percent of on-time flights each day for a 20-day period was as follows:72, 75, 76, 70, 77, 73, 80, 75, 82, 85,77, 78, 74, 86, 72, 77, 67, 78, 69, 80Make a
What happens to the standard error of the mean as n increases? Use the formula for the standard error to help explain your answer.The lifetimes of a certain type of automobile tire have been found to
In an experiment on the photoelectric effect, the frequency of light being used was measured as well as the stopping potential (the voltage just sufficient to stop the photoelectric effect) with the
Find the equation of the least-squares line for the points indicated in the following table. Graph the line and data points on the same graph. X 1 3 5 7 9 y 5 11 17 20 27
For a production process for which there is a great deal of data since its last modification, the population mean μ and population standard deviation σ are assumed known. For such a process, we
If gas is cooled under conditions of constant volume, it is noted that the pressure falls nearly proportionally as the temperature. If this were to happen until there was no pressure, the theoretical
In a random sample, 800 smartphone owners were asked which type of smartphone they would choose with their next purchase (if they could only choose one). The results are summarized below:Use the
In a random sample, 800 smartphone owners were asked which type of smartphone they would choose with their next purchase (if they could only choose one). The results are summarized below:Make a bar
Use the statistical feature of a calculator to find the mean and the standard deviation s for the indicated sets of numbers.Set CC: 0.48, 0.53, 0.49, 0.45, 0.55, 0.49, 0.47, 0.55, 0.48, 0.57, 0.51,
According to the empirical rule, what percent of the batteries have voltages between 1.45 V and 1.55 V?It has been previously established that for a certain type of AA battery (when newly produced),
Determine the mode of the numbers of the given set.Set AA: 3, 6, 4, 2, 5, 4, 7, 6, 3, 4, 6, 4, 5, 7, 3
An airline’s records showed that the percent of on-time flights each day for a 20-day period was as follows:72, 75, 76, 70, 77, 73, 80, 75, 82, 85,77, 78, 74, 86, 72, 77, 67, 78, 69, 80Draw a
The period of a pendulum as a function of its length was measured, giving the following results:Find the equation of the power regression model for these data. Length (ft) Period (s) 1.00 1.10 3.00
Find and interpret the values of r and r2 for the given data.Exercise 7Data from Exercises 7In an electrical experiment, the following data were found for the values of current and voltage for a
For a production process for which there is a great deal of data since its last modification, the population mean μ and population standard deviation σ are assumed known. For such a process, we
Use the statistical feature of a calculator to find the mean and the standard deviation s for the indicated sets of numbers.Set DD: 105, 108, 103, 108, 106, 104, 109, 104, 110, 108, 108, 104, 113,
Find the standard deviation for the indicated sets of numbers. A calculator may be used.The miles traveled in Exercise 15Data from Exercises 15Use the following data. In testing a new electric
What percent of the batteries have voltages between 1.52 V and 1.58 V?It has been previously established that for a certain type of AA battery (when newly produced), the voltages are distributed
In testing a new electric engine, an automobile company randomly selected 20 cars of a certain model and recorded the range (in mi) that the car could travel before the batteries needed recharging.
Determine the mode of the numbers of the given set.Set BB: 25, 26, 23, 24, 25, 28, 26, 27, 23, 28, 25
For a production process for which there is a great deal of data since its last modification, the population mean μ and population standard deviation σ are assumed known. For such a process, we
An airline’s records showed that the percent of on-time flights each day for a 20-day period was as follows:72, 75, 76, 70, 77, 73, 80, 75, 82, 85,77, 78, 74, 86, 72, 77, 67, 78, 69, 80Construct a
For the employees of a certain business, the highest education level is summarized below:Use the frequencies to make a bar graph of these data. Education No high school diploma High school
In testing a new electric engine, an automobile company randomly selected 20 cars of a certain model and recorded the range (in mi) that the car could travel before the batteries needed recharging.
Find and interpret the values of r and r2 for the given data.Exercise 8Data from Exercises 8A particular muscle was tested for its speed of shortening as a function of the force applied to it. The
What percent of the batteries have voltages below 1.54 V?It has been previously established that for a certain type of AA battery (when newly produced), the voltages are distributed normally with μ
Determine the mode of the numbers of the given set.Set CC: 0.48, 0.53, 0.49, 0.45, 0.55, 0.49, 0.47, 0.55, 0.48, 0.57, 0.51, 0.46, 0.53, 0.50, 0.49, 0.53
Find and interpret the values of r and r2 for the given data.Exercise 10Data from Exercises 10In testing an air-conditioning system, the temperature T in a building was measured during the afternoon
For a production process for which there is a great deal of data since its last modification, the population mean μ and population standard deviation σ are assumed known. For such a process, we
For the employees of a certain business, the highest education level is summarized below:Using relative frequencies, make a pie chart of these data. Education No high school diploma High school
Find the standard deviation for the indicated sets of numbers. A calculator may be used.The following data giving the mean number of days of rain for Vancouver, B.C., for the 12 months of the year20,
Find the standard deviation for the indicated sets of numbers. A calculator may be used.The number of apps in ExerciseData from Exercises 19 Use the following data. In a random sample, 30
A manufacturer of drone propellers randomly selects 1000 propellers from the production line each week and inspects them for defects. The number of defective propellers, along with the proportion of

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