Answer:
a) 117.4
b) 117.9
c) Option A) When there is rounding or grouping, the median can be highly sensitive to small change
Step-by-step explanation:
We are given the following data set in the question:
108.6, 117.4, 128.4, 120.0, 103.7, 112.0, 98.3, 121.5, 123.2
[tex]Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}[/tex]
n = 9
a) Median of the reported blood pressure values
Sorted Values: 98.3, 103.7, 108.6, 112.0, 117.4, 120.0, 121.5, 123.2, 128.4
Median =
[tex]\dfrac{9 + 1}{2}^{th}\text{ term} = 5^{th}\text{ term} = 117.4[/tex]
b) New median of the reported values
Data: 108.6, 117.9, 128.4, 120.0, 103.7, 112.0, 98.3, 121.5, 123.2
Sorted Values: 98.3, 103.7, 108.6, 112.0, 117.9, 120.0, 121.5, 123.2, 128.4
New Median =
[tex]\dfrac{9 + 1}{2}^{th}\text{ term} = 5^{th}\text{ term} = 117.9[/tex]
c) Since median is a position based descriptive statistics, a small change in values can bring a change in the median value as the order of the data may change.
Option A) When there is rounding or grouping, the median can be highly sensitive to small change
The median of the reported blood pressure values is 117.4. If the blood pressure of the second individual is changed to 117.9, the new median would be 117.9. This shows that the median is not sensitive to small changes in rounding or grouping.
Explanation:(a) What is the median of the reported blood pressure values?
To find the median, we need to arrange the blood pressure values in numerical order: 98.3, 103.7, 108.6, 112.0, 117.4, 120.0, 121.5, 123.2, 128.4. Since there are 9 values, the middle value is the 5th value, which is 117.4.
(b) Suppose the blood pressure of the second individual is 117.9 rather than 117.4. What is the new median of the reported values?
If we change the second individual's blood pressure to 117.9, the new order is: 98.3, 103.7, 108.6, 112.0, 117.9, 120.0, 121.5, 123.2, 128.4. Now, there are 9 values and the middle value is the 5th value, which is 117.9. So the new median would be 117.9.
(c) What does this say about the sensitivity of the median to rounding or grouping in the data?
C. When there is rounding or grouping, the median is not sensitive to small changes.
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If a population mean is 300 and the sample mean is 400, the difference of 100 is called:
A.Standard error
B.Sampling error
C.Allowable error
D.None of the above.
Answer:
B. Sample error.
Step-by-step explanation:
Such type of error is called Sample error.
Sample error occurs when
Sample error is a statistical error when an expert fails to choose a sample which symbolizes the whole data population and the outcomes of the sample do not reflect the outcomes from the whole population.
If a population mean is 300 and the sample mean is 400, the difference of 100 is called sampling error. So, option b is correct.
Sampling error represents the difference between the population mean and the sample mean, which arises purely by chance because a sample rather than the entire population is observed.
The other options are incorrect in this context:
Standard error: This measures the spread of the sample means around the population mean.Allowable error: This term refers to the acceptable range of error in forecasting or measurement but is not applicable in this context.One coin in a collection of 65 coins has two heads; the rest of the coins are fair. If a coin, chosen at random from the lot and then tossed, turns up heads six times in a row, what is the probability that it is the two-headed coin?
There is only 1 two-headed coin in the collection of 65 coins.
The probability of selecting the two headed coin is 1/65.
The outcome achieved when any of the other coins is tossed a number of times is based purely on chance.
Although if the 2-headed coin is selected, the only possible outcome is having a head, but It also possible to have 6 heads in 6 tosses with a coin that is not 2-headed.
What we're concerned with, is the probability that the 2-headed coin was selected from the lot of 65 coins, which is 1/65.
Answer:
There is only 1 two-headed coin in the collection of 65 coins.
The probability of selecting the two-headed coin is 1/65.
The outcome achieved when any of the other coins is tossed a number of times is based purely on chance.
Although if the 2-headed coin is selected, the only possible outcome is having a head, but It is also possible to have 6 heads in 6 tosses with a coin that is not 2-headed.
What we're concerned with, is the probability that the 2-headed coin was selected from the lot of 65 coins, which is 1/65.
Step-by-step explanation:
Determine if the collection is not well defined and therefore is not a set. The collection of current NHL players
Answer:
Step-by-step explanation:
The collection of current NHL players cant be defined as some may be on injury so therefore the current NHL players is ill-defined thereby they are described as Not well defined set
Final answer:
A collection of current NHL players is a well-defined set. We can precisely determine what is and is not a member of this set.
Explanation:
A collection of current NHL players is a well-defined set. A set is a collection of distinct objects, and in this case, the objects are the current NHL players. It is possible to precisely determine what is and is not a member of this set. We can provide a clear and concise definition of the set by listing the names of all current NHL players.
For example:
Auston Matthews
Connor McDavid
Alex Ovechkin
Sidney Crosby
Nathan MacKinnon
These are just a few examples, but by listing all the current NHL players, we can determine exactly what is included in the set and what is not.
Simplify (4x - 6) – (3x + 6).
1) ×- 12
2)-x - 12
3) x + 12
4) -x + 12
Answer:
1) x-12
Step-by-step explanation:
(4x-6)-(3x+6)
4x-6-3x-6
x-12
Determine whether the data described are qualitative or quantitative. The maximum speed limit on interstate highways.
a. Qualitative
b. Quantitative
The data of the maximum speed limit on interstate highways is quantitative because it is expressible as a numerical value, which is an amount or quantity.
Explanation:The data described, 'the maximum speed limit on interstate highways', is quantitative. This is because data is quantitative when it is expressible as an amount or quantity. In this case, a speed limit is typically represented as a numerical value in miles or kilometers per hour, which is an amount or quantity. Therefore, the data of the maximum speed limit on interstate highways is quantitative.
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The average age of residents in a large residential retirement community is 69 years with standard deviation 5.8 years. A simple random sample of 100 residents is to be selected, and the sample mean age ¯ x x¯ of these residents is to be computed. We know the random variable ¯ x x¯ has approximately a Normal distribution because____________.
a. of the central limit theorem.
b. of the 68‑95‑99.7 rule.
c. the population from which we’re sampling has a Normal distribution.
d. of the law of large numbers.
Answer:
a. of the central limit theorem.
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], a large sample size, larger than 30, can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, the sample size is 100, so it is sufficiently large to use the Central Limit Theorem. The mean of the sample in 69 and the standard deviation of the sample is 0.58.
So the correct answer is:
a. of the central limit theorem.
Draw a line for the axis of symmetry of function f. Also mark the x-intercept(s), y-intercept, and vertex of the function. f(x) = -(x + 1)2 + 4
Answer:
Part A: vertex at (-1,4)
Part B: line of symmetry x =-1
Part C: x-intercept x = -3 and x = 1
Part D: y-intercept y = 3
Step-by-step explanation:
Given f(x) = - (x+1)² + 4
The given equation represents a parabola.
The general equation of the parabola with a vertex at (h,k)
f(x) = (x-h)² + k
Part A: To find the vertex, compare the general equation with the given function.
So, the vertex of the function will be at (-1,4)
Part B: the line for the axis of symmetry of function will be at x =-1
Part C: To find x-intercept, put y = 0
So, - (x+1)² + 4 = 0
- (x+1)² = -4
(x+1)² = 4
x + 1 = ±√4 = ±2
x + 1 = 2 OR x + 1 = -2
x = 1 OR x =-3
x-intercept at x = 1 and x = -3
Part D:To find y-intercept, put x = 0
So, y = - (0+1)² + 4 = -1 + 4 = 3
y-intercept at y = 3
See the attached figure.
Answer:
Vertex at (-1,4)
Line of symmetry x =-1
x-intercept x = -3 and x = 1
y-intercept y = 3
If an angle of 145 is divided into 5 angles with ratios 1: 3: 5: 8: 12, what is the measure
of the 4th largest angle?
Answer:
15 °
Step-by-step explanation:
The five angles are splitted in the ratio 1:3:5:8:12
The 1st biggest angle is at ratio 12
The 2nd biggest angle is at ratio 8
The 3rd biggest angle is at ratio 5
The 4th biggest angle is at ratio 3.
Time solve for the 4th biggest angle, we will find the sum of the ratios:
Therefore, 1 + 3 + 5 + 8 + 12 = 29
Ratio of 4th biggest angle:
= (3)/(29). * 145
= (3 * 45) / 29
= 3 * 5
= 15 °
Which expression is equivalent to 6 minus (negative 8)?
Answer:
6 - (-8)
is 6 + 8
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
Identify the type of sampling used. Thirty-five math majors, 52 music majors and 38 history majors are randomly selected from 447 math majors, 480 music majors and 451 history majors at the state university. What sampling technique is used?
Answer:
Stratified
Step-by-step explanation:
The stratified sampling is defined as the type of random sampling when the population is divided into non-overlapping groups known as strata and then sample is selected from each of the stratum.
The sampling technique used is stratified sampling because the population is divided into 3 strata math, music and history and then sample of 35,52 and 38 is selected from these 3 strata respectively.
what is the total area of this prism?
T.A=
Answer:
The answer to your question is 61.8 in²
Step-by-step explanation:
Process
1.- Calculate the height of the triangle
3² = h² + 1.5²
h² = 3² - 1.5²
h² = 9 - 2.25
h² = 6.75
h = 2.6 in
2.- Calculate the area of the triangles
Area = [tex]\frac{base x height}{2}[/tex]
Area = [tex]\frac{3 x 2.6}{2}[/tex]
Area = 3.9 in²
There are 2 triangles = 2(3.9) = 7.8 in²
3.- Calculate the area of the rectangles
Area = base x height
Area = 6 x 3 = 18 in²
There are 3 rectangles = 3(18) = 54 in²
4.- Total area
At = 7.8 + 54
= 61.8 in²
Answer:
(104 +16√13) ft
Step-by-step explanation:
49. If a statistician specifies a 5% level of significance, then she will reject the null hypothesis only if her sample result differs from her hypothesized value by an amount that would occur by chance a) Less than 5% of the time. b) More than 5% of the time. c) 95% of the time or more. d) 2.5% of the time or less.
Answer:
The answer is a) less than 5% of the time
Step-by-step explanation:
By definition, the level of significance is the probability that one rejects a null hypothesis of a test when it is true. Denoted as alpha α, it shows how convincing the sample data is and concludes if it is statistically significant.
A level of significaance of 5% or 0.05, shows that you need more convincing power before determining whether you willreject the null hypothesis
By way of rule,
-If p-value ≤ level of significance α , then reject the null hypothesis.
-If p-value ≥ level of significance α , then do not reject the null hypothesis.
This implies that a statistician with a 5% level of significance will reject the null hypothesis if her hypothesized value falls below this mark.
Answer:
c) 95% of the time or more.
Step-by-step explanation:
The level of significance in a statistical research is the probability of rejecting the null hypothesis when it is actually true. A possible example is a significance level of 0.02 which indicates a 2% risk of concluding that a difference exists when there is no actual difference. The lower the significance level, the stronger the evidence required before you can reject the null hypothesis. 5% significance level may imply 95% confidence interval which means the range of values that occurs 95% of the time.
Therefore, rejecting the null hypothesis at 5% significance level means that the alternative hypothesis differs from the null hypothesis by 95% or more of its possible values (95% of the time or more).
Find g(-x) when g(x) = 2x^2 -5x + 5
Answer: g(-x) = 2x^2 +5x + 5
Step-by-step explanation:
This Is a topic under functions in mathematics, it deals with substituting "x" for the new entity that has been placed in the new function you're asked to look for.
Hence, to solve this, we simply substitute "-x" for "x" wherever "x" appears in the equation.
By doing so, we go straight to the given function.
2x^2 -5x + 5
And we go ahead with our substitution which goes thus:
2(-x^2) -5(-x) + 5
On simplifying, we then finally have have:
2x^2 +5x + 5.
This means:
g(-x) = 2x^2 +5x + 5
Data is collected from a:
A. sample
B. population
C. variable
D. None of the above answers is correct
Data is collected from a sample, which is a smaller subset of the population.
Explanation:The correct answer is A. sample. When data is collected, it is usually infeasible or impractical to collect information from an entire population. Therefore, a sample, which is a smaller subset of the population, is selected for data collection and analysis. For example, if we want to know the average height of students in a school, it would be time-consuming and costly to measure the height of every student. Instead, we can select a sample of students from different grades or classrooms to represent the entire population and collect data from them.
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Four fair coins are tossed at once. What is the probability of obtaining 3 heads and one tail? 2
Answer:
There are 16 possible outcomes, all equally likely. There’s only one way to get four heads and only one way to get no heads. That leaves 14 ways to get two or three heads.
There’s four ways to get three heads. The first coin can be the tail, the second can be the tail, the third can be the tail, or the fourth can be the tail.
There’s also four ways to get one head. The first coin can be the head, the second can be the head, the third can be the head, or the fourth can be the head.
That leaves six ways left to get exactly two heads. So 6/16 or 3/8.
Step-by-step explanation:
If r1 , r2 , and r3 represent rotations from Dn and f 1 , f 2 , and f 3 represent reflections from Dn , determine whether r1 r2 f 1 r3 f 2 f 3 r3 is a rotation or a reflection.
The combined transformation operation r1 r2 f1 r3 f2 f3 r3 is a reflection. This is because a sequence of transformations combining rotations and reflections, when arranged and executed in order, still produces a reflection.
Explanation:The problem is understanding whether the composition of certain transformations, namely rotations (r1, r2, r3) and reflections (f1, f2, f3) from Dn, results in another rotation or a reflection. In mathematics, a composition of transformations means applying several transformations in sequence.
Here, think about the properties of rotations and reflections. A rotation followed by another rotation will result in a rotation. Similarly, a reflection followed by another reflection is equivalent to a rotation. However, a reflection followed by a rotation or vice versa results in a reflection.
The sequence provided is r1 r2 f1 r3 f2 f3 r3. Assuming each transformation in the sequence is executed in order, we can see that it is divided into four segments: rr, rf, fr, and r. The first segment, rr, will result in a rotation. The second segment, rf, will result in a reflection. That reflection followed by the next r, resulting in another reflection. Finally, the last segment is just a rotation. Therefore, reflection followed by a rotation results in a reflection.
So, the combined transformation r1 r2 f1 r3 f2 f3 r3 is a reflection.
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Assume that in the absence of immigration and emigration, the growth of a country's population P(t) satisfies dP/dt = kP for some constant k > 0 (see Equation (1) of Section 1.3). Determine a differential equation governing the growing population P(t) of the country when individuals are allowed to immigrate into the country at a constant rate r > 0. (Use P for P(t).)
dP dt =
What is the differential equation for the population P(t) of the country when individuals are allowed to emigrate at a constant rate r > 0?
dP dt =
Answer:
A) Differential equation for population growth in case of individual immigration is:
[tex]\frac{dP}{dt}=kP+r[/tex]
B) Differential equation for population growth in case of individual emigration is:
[tex]\frac{dP}{dt}=kP-r[/tex]
Step-by-step explanation:
Population growth rate in the absence of immigration and emigration is given as:
[tex]\frac{dP}{dt}=kP--(1)[/tex]
A) When individuals are allowed to immigrate:
Let r be the constant rate of individual immigration given that r >0.
Differential equation for population growth in this case is:
[tex]\frac{dP}{dt}=kP+r[/tex]
B) In case of individual emigration:
Let r be the constant rate of individual emigration given that r >0.
Differential equation for population growth in this case is:
[tex]\frac{dP}{dt}=kP-r[/tex]
A school psychologist wants to test the effectiveness of a new method of teaching logic. She recruits 200 sixth-grade students and randomly divides them into two groups. Group 1 is taught by means of the new method, while group 2 is taught by traditional methods. The same teacher is assigned to teach both groups. At the end of the year, an achievement test (graded on a scale from 1-10) is administered and the results of the two groups are compared. Complete parts (A) through (D) below.
A. What is the response variable in this experiment?
a. The score on the achievement test.
b. The students' ability in Health.
c. The score of Group 2 on the achievement test.
d. The score of Group 1 on the achievement test.
B. Which of the following explanatory variables is manipulated?
a. Intelligence
b. Teacher
c. Method of teaching
d. Grade level
C. How many levels of the treatment are there?
D. What type of experimental design is this?
a. Survey
b. Randomized block design
c. Completely randomized assignment
d. Matched Pair
In a statistical experiment, a response variable is something that “responds” to the changes made in the experiment. The changes are made to the independent variable (also called the manipulated variable).
For the experiment in question:
The response variable is the score on the achievement test.
The explanatory variable that is manipulated is the method of teaching
There are two levels of treatment ( the new teaching method and the traditional treating method)
The type of experimental design used is: Completely randomized assignment
The school psychology experiment's response variable is the score on the achievement test. The manipulated explanatory variable is the method of teaching. There are two treatment levels - the new method and the traditional method of teaching. The experiment follows a completely randomized assignment design.
Explanation:In this experiment conducted by the school psychologist, various aspects come into play.
A. The response variable in this experiment is option a: The score on the achievement test. The response variable is what you measure in the experiment and what is affected during the experiment. In this case, it's the score that the students get on the achievement test at the end of the year.
B. In this experiment, the explanatory variable that is manipulated is option c: Method of teaching. This is because it is the factor that the experimenter is changing in order to measure the effect on the response variable.
C. There are Two levels of the treatment in this experiment. The two modes of teaching – the new method and the traditional method constitute the two levels of treatment.
D. The type of experimental design used here is option c: Completely randomized assignment. The students were randomly divided into two groups for the purpose of the study which fits under this type of experimental design.
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The quantity demanded x for a certain brand of MP3 players is 100 units when the unit price p is set at $80. The quantity demanded is 1100 units when the unit price is $40. Find the demand equation.
p =
Answer:p = (2100 - x)/25
Step-by-step explanation:
According to the law of demand, when the price,p of the brand of MP3 players is is high, the quantity,x of the brand of MP3 players demanded would be low and when the price,p of the brand of MP3 players is is low, the quantity,x of the brand of MP3 players demanded would be high.
To derive the demand equation, we would apply the slope intercept form of equation which is expressed as
y = mx + c
Where
m = slope
c = intercept
The slope, m would be
(y2 - y1)/(x2 - x1)
Slope = (1100 - 100)/(40 - 80) = 1000/-40
Slope = - 25
To find the y intercept, we would substitute m = - 25, y = 1100 and x = 40 into y = mx + c. It becomes
1100 = - 25 × 40 + c
1100 = - 1000 + c
c = 1100 + 1000 = 2100
y = - 25x + 2100
Therefore, the demand equation is
x = - 25p + 2100
25p = 2100 - x
p = (2100 - x)/25
A number is equal to 3 times a smaller number. Also, the sum of the smaller number and 4 is the larger number. The situation is graphed on the coordinate plane below, where x represents the smaller number and y represents the larger number. On a coordinate plane, a line goes through (0, 4) and (2, 6) and another line goes through (1, 3) and (2, 6). Which two equations represent the situation? y = one-third x and y = x minus 4 y = one-third x and y = x + 4 y = 3 x and y = x + 4 y = 3 x and y = x minus 4.
Answer: two equations represent the situation are
y = 3x and y = x + 4
Step-by-step explanation:
The smaller number was represented by x and its values on the x coordinate.
The larger number was represented by y and its values on the y coordinate.
The larger number is equal to 3 times a smaller number. This means that
y = 3x
Also, the sum of the smaller number and 4 is the larger number. This means that
y = x + 4
Answer:
two equations represent the situation are
y = 3x and y = x + 4
Step-by-step explanation:
The share of aggregate income held by middle-income households in 1970 was 62%, whereas that held by upper-income households was 29%. The corresponding figures in 2014 were 43% and 49%, respectively. The models describing the fall and the rise in the share of the aggregate incomes of these two groups are approximately linear over the period under consideration.† (a) Find the mathematical models describing the percent share of aggregate income held by each group from 1970 through 2014. (Let t denote the time, in years, with t = 0 corresponding to the beginning of 1970.) middle-income households y = Incorrect: Your answer is incorrect. upper-income households y = Incorrect: Your answer is incorrect. (b) Find the time when the aggregate income held by upper-income households first exceeded that held by middle-income households. (Give the calendar year in which the change occurred.)
Answer:
a) y = -19/44t +62; y = 5/11t +29
b) 2007
Step-by-step explanation:
(a) The two-point form of the equation of a line is useful when two data points are given.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Middle Income
The two given points are (0, 62), (44, 43), so the equation is ...
y = (43 -62)/(44 -0)(t -0) +62
y = -19/44t +62
__
Upper Income
The two given points are (0, 29), (44, 49), so the equation is ...
y = (49 -29)/(44 -0)(t -0) +29
y = 20/44t +29
y = 5/11t +29
__
(b) The year in which the shares are equal is found by setting the y-values equal:
-19/44t +62 = 5/11t +29
33 = 39/44t
t = (33)(44)/39 ≈ 37.2
The upper income share exceeded the middle income share in the year 1970 +37.2 = 2007.
The mathematical models for the middle-income and upper-income households are y1(t) = 62% - 0.38% * t and y2(t) = 29% + 0.40% * t, respectively. The aggregate income held by upper-income households first exceeded that held by middle-income households in the year 2014.
Explanation:In order to find the mathematical model, we will first determine the slope for each data set. The slope is calculated as the change in y divided by the change in x. Here, 'y' represents the share of aggregate income and 'x' represents time.
For the middle-income households, the slope (m1) is: m1 = (43% - 62%)/(2014 - 1970) = -0.38% per year. So, the equation becomes: y1(t) = 62% - 0.38% * t.
For the upper-income households, the slope (m2) is: m2 = (49% - 29%)/(2014 - 1970) = 0.40% per year. So, the equation becomes: y2(t) = 29% + 0.40% * t.
To find out when the aggregate income held by the upper-income households first exceeded that held by middle-income households, we set the two equations equal to each other and solve for 't'. This gives us t = (62% - 29%)/(0.40% + 0.38%) = 43.7, or roughly 44 years after 1970 which is the year 2014.
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Evaluate the line integral Z C z2 dx 2y dy 2xz dz where C is any closed curve in the space.
Answer:
Some other information should be given, I have added those necessary information, should in case you come across a similar question on line integral.
Step-by-step explanation:
To evaluate line integral, some other information has to be given, Assume (so when you see a similar question, you will know how to evaluate line integral) as part of the question X =t2, Y = 2t and Z = 3t and at interval 0≤t≤1
A step by step explanation and calculation has been attached.
Use De Morgan's law to select the statement that is equivalent to: "It is not true that the employee received a large bonus and has a big office."
a. The employee received a big bonus or has a big office.
b. The employee did not receive a big bonus and does not have a big office.
c. The employee did not receivę a big bonus or does not have a big office.
d. The employee received a big bonus and has a big office
Answer:
c. The employee did not receive a big bonus or does not have a big office.
Step-by-step explanation:
From the original statement, "It is not true that the employee received a large bonus and has a big office.", it can be concluded that the employee either has a big office, received a large bonus or neither. That is, either one, the other, or neither conditions are met.
Applying De Morgan's law:
a. This leaves out the possibility that both conditions are not met
b. This only considers that both conditions are not met
c. This statement means that one of the conditions are not met, which is correct.
d. This assumes both conditions are true, which is incorrect.
The statement equivalent to the negation of both an employee receiving a large bonus and having a big office is that the employee did not receive a big bonus or does not have a big office. Hence the correct
To apply De Morgan's laws to the statement "It is not true that the employee received a large bonus and has a big office," we need to negate the conjunction and change the 'and' to 'or' while negating each of the individual statements within the conjunction. De Morgan's laws tell us that the negation of a conjunction is equivalent to the disjunction of the negations. So the statement becomes:
The employee did not receive a large bonus or does not have a big office.
Therefore, the correct answer is (c) The employee did not receive a big bonus or does not have a big office.
Given f(x)= a×e−bx , where a = 1 and b = 6,
calculate g(x)=dfdx and obtain g(1) (that is, evaluate the derivative of f(x) at x = 1).
Report your answer with three significant figures.
Answer:
g(1) = -0.015
Step-by-step explanation:
We are given he following in the question:
[tex]f(x) = ae^{-bx}[/tex]
For a = 1 and b = 6, we have,
[tex]f(x) = e^{-6x}[/tex]
We have to find the the derivative of f(x) with respect to x.
[tex]g(x) = \dfrac{d(f(x))}{dx} = \dfrac{d(e^{-6x})}{dx}\\\\g(x) = -6e^{-6x}\\\\g(1) = \dfrac{d(f(x))}{dx}\bigg|_{x=1} = -6e^{-6} = -0.015[/tex]
Thus, g(1) = -0.015
10 granola bars and twelve bottles of water cost $23. 5 granola bars and 4 water bottles of water of water coat $10. how much does one granola and one water bottle cost
Answer:
One granola costs $1.40.
One water bottle costs $0.75.
Step-by-step explanation:
This question can be solved by a simple system of equations.
I am going to say that
x is the cost of each granola bar.
y is the cost of each bottle of water.
The first step is building the system:
10 granola bars and twelve bottles of water cost $23.
This means that:
10x + 12y = 23.
5 granola bars and 4 water bottles of water of water cost $10
This means that:
5x + 4y = 10
So we have to solve the following system of equations:
10x + 12y = 23
5x + 4y = 10
I am going to multiply the second equation by -2, and use the addition method. So:
10x + 12y = 23
-10x - 8y = -20
10x - 10x + 12y - 8y = 23 - 20
4y = 3
y = 0.75
y = 0.75 means that each water bottle costs 75 cents.
5x + 4y = 10
5x = 10 - 4y
5x = 10 - 4*0.75
5x = 7
x = 1.4.
x = 1.4 means that each granola costs $1.40.
Answer:one granola costs $1.4
One bottle of water costs $0.75
Step-by-step explanation:
Let x represent the cost of one granola.
Let y represent the cost of one water bottle.
10 granola bars and twelve bottles of water cost $23. It means that
10x + 12y = 23 - - - - - - - - - - - 1
5 granola bars and 4 water bottles of water of water cost $10. It means that
5x + 4y = 10 - - - - - - - - - - - 2
Multiplying equation 1 by 1 and equation 2 by 2, it becomes
10x + 12y = 23
10x + 8y = 20
Subtracting, it becomes
4y = 3
y = 3/4 = 0.75
Substituting y = 0.75 into equation 1, it becomes
10x + 12 × 0.75 = 23
10x + 9 = 23
10x = 23 - 9 = 14
x = 14/10 = 1.4
Compute the line integral of the vector field F=⟨3zy−1,4x,−y⟩F=⟨3zy−1,4x,−y⟩ over the path c(t)=(et,et,t)c(t)=(et,et,t) for −9≤t≤9
Answer:
Step-by-step explanation:
NOTE: If either of the products is not defined, type UNDEFINED for you answer. If the product is defined, type the dimension in the form mxn with NO spaces in betwee.
Answer:
a) Dimension of AB is DEFINED
b) Dimension of BA is UNDEFINED
Step-by-step explanation:
A matrix is always represented with (mxn) rows and columns. the rows are the elements in the horizontal line while the columns make up the elements in the vertical line. however, there are rules in multiplication of matrix.
To multiply matrix, multiply elements in the rows of the first matrix by the elements in the columns of the second matrix. for example if you're multiplying a 3by2 matrix by a 2by3 matrix, the resulting matrix will be a 3by3 matrix from (mxn) -rows and columns.
from the question, matrix A is a 3by5 (3x5) matrix i.e it has 3rows and 5columns.
matrix B is a 5by2 (5x2) matrix i.e it has 5rows and 2columns. multiplying AB = (3x5) X (5x2), hence the resultant matrix will be a 3by2 (3x2) and this shows that multiplication or dimension of AB is DEFINED.
As for the multiplication of BA = (5x2) X (3x5), from this multiplication, it is not possible as such we can't determine any resultant matrix, this makes multiplication or dimension of BA to be UNDEFINED.
Let C(x) be the statement "x has a cat," let D(x) be the statement "x has a dog," and let F(x) be the statement "x has a ferret." Express each of these statements in terms of C(x), D(x), F(x), quantifiers, and logical connectives. Let the domain consist of all students in your class. a) A student in your class has a cat, a dog, and a ferret. b) All students in your class have a cat, a dog, or a ferret. c) Some student in your class has a cat and a ferret, but not a dog. d) No student in your class has a cat, a dog, and a ferret. e) For each of the three animals, cats, dogs, and ferrets, there is a student in your class who has this animal as a pet.
a) A student in your class has a cat, a dog and a Ferret is Ex(C(x)∧D(x)∧F(x)).
b) All students in your class have a cat, a dog or a Ferret is ∀x(C(x)∨D(x)∨F(x)).
c) Some student in you class has cat and Ferret but not a dog is Ex(C(x)∧D(x)∨¬F(x)).
The various types of logical connectives include conjunction (“and”), disjunction (“or”), negation (“not”), conditional (“if . . . then”), and biconditional (“if and only if”).
Let C(x) : x has a cat
D(x) : x has a dog
F(x) : x has a Ferret
a) A student in your class has a cat, a dog and a Ferret.
Ex(C(x)∧D(x)∧F(x))
b) All students in your class have a cat, a dog or a Ferret.
∀x(C(x)∨D(x)∨F(x))
c) Some student in you class has cat and Ferret but not a dog
Ex(C(x)∧D(x)∨¬F(x))
Therefore,
a) A student in your class has a cat, a dog and a Ferret is Ex(C(x)∧D(x)∧F(x)).
b) All students in your class have a cat, a dog or a Ferret is ∀x(C(x)∨D(x)∨F(x)).
c) Some student in you class has cat and Ferret but not a dog is Ex(C(x)∧D(x)∨¬F(x)).
Learn more about the logical connectives here:
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The statements can be expressed using logical connectives and quantifiers in mathematical logic. They express different combinations of students owning cats, dogs, and ferrets.
Explanation:The statements can be expressed in terms of C(x), D(x), F(x), quantifiers, and logical connectives as follows:
a) ∃x (C(x) ∧ D(x) ∧ F(x)): This states that there exists a student 'x' such that 'x has a cat, a dog, and a ferret'. b) ∀x (C(x) ∨ D(x) ∨ F(x)): This states that for all students 'x', 'x has a cat, a dog, or a ferret'. c) ∃x (C(x) ∧ F(x) ∧ ¬D(x)): This states that there exists a student 'x' such that 'x has a cat and a ferret, but not a dog'. d) ¬∃x (C(x) ∧ D(x) ∧ F(x)): This states that there does not exist a student 'x' such that 'x has a cat, a dog, and a ferret'. e) ∃x C(x) ∧ ∃x D(x) ∧ ∃x F(x): This states that for each animal (cats, dogs, ferrets), there exists a student 'x' that has this animal as a pet. Learn more about Mathematical Logic here:https://brainly.com/question/30928478
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A top-fuel dragster ran a 1/4-mile (1320 ft) race. It had traveled 1305.48 feet after 3.58 seconds and it traveled the entire 1320 feet in 3.61 seconds. What was its speed, approximately, in feet per second at the end of the race? In miles per hour?
The speed approximately of this top-fuel dragster is given as 330 miles per hour.
How to solve for the speedWe have 1320 feet distance in 3.61 sec
then we have 1305.48 feet in 3.58
Such that 1320-1305.48 = 14.52 feet
we have to do the conversions of feet into miles and seconds to become hours
1 mile = 5280feet
hence we have 14.52 feet as 14.52/5280
= 0.00275miles
then 0.03 seconds to hour = 0.03/3600
= 0.0000083
Speed = distance / time
0.00275miles/ 0.0000083
= 330 miles per hour
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To find the speed of the top-fuel dragster at the end of the race, divide the total distance traveled by the time taken. The speed at the end of the race is approximately 365.098 ft/s or 249.340 mph.
Explanation:To find the speed of the top-fuel dragster at the end of the race, we can divide the total distance traveled (1320 ft) by the time it took to cover that distance (3.61 s). This will give us the average velocity of the dragster.
So, the speed at the end of the race is approximately 365.098 ft/s.
To convert this speed to miles per hour, we can multiply it by the conversion factor 0.6818. This gives us the speed of the dragster at the end of the race in miles per hour, which is approximately 249.340 mph.
It can be helpful to classify a differential equation, so that we can predict the techniques that might help us to find a function which solves the equation. Two classifications are the order of the equation -- (what is the highest number of derivatives involved) and whether or not the equation is linear .
Linearity is important because the structure of the the family of solutions to a linear equation is fairly simple. Linear equations can usually be solved completely and explicitly. Determine whether or not each equation is linear:
1. (1+y2)(d2y/dt2)+t(dy/dt)+y=et
2. t2(d2y/dt2)+t(dy/dt)+2y=sin t
3. (d3y/dt3)+t(dy/dt)+(cos2(t))y=t3
4. y''-y+y2=0
Answer:
Second-order nonlinear ordinary differential equation. Second-order linear ordinary differential equation. Third-order linear ordinary differential equation. Second-order nonlinear ordinary differential equationStep-by-step explanation:
The objective is to determine whether or not each of the following equation is linear:
[tex](1+y^2)\frac{d^2y}{dt^2} + t \frac{dy}{dt} = e^t[/tex] [tex]t^2\frac{d^2y}{dt^2} + t \frac{dy}{dt} +2y= \sin t[/tex] [tex]\frac{d^3y}{dt^3} + t \frac{dy}{dt} + \cos (2t) y = t^3[/tex] [tex]y''-y+y^2 = 0[/tex][tex](1)[/tex]
We can rewrite this equation in the form
[tex](1+y^2)y''(t) +ty'(t) = e^t[/tex].
As we can see, this is an second-order nonlinear differential equation, because of the term [tex]1+y^2[/tex] next to [tex]y''(t)[/tex].
[tex](2)[/tex]
We can rewrite this equation in the form
[tex]t^2y''(t) + t y'(t) +2y= \sin t[/tex].
This is an second-order linear ordinary differential equation.
[tex](3)[/tex]
We can rewrite this equation in the form
[tex]y'''(t)+ t y' + \cos (2t) y = t^3[/tex]
This is an third-order linear ordinary differential equation.
[tex](4)[/tex]
This is an second-order nonlinear ordinary differential equation, because of the term [tex]y^2[/tex].