I need this input into MATLAB. I'm so lost on how to code it.
Evaluate the integral sintcos tdt .
I have already solved and found the answer to be -cost 2cost cos t + C 5 9 7
I just need to prove my work with MATLAB
Answers
Answer:
>>syms t
>>f=sin(t)*cos(t);
>>int(f)
Step-by-step explanation:
It's actually pretty easy, just use symbolic variables.
First, create the symbolic variable t using this command:
syms t
Now define the function
f=sin(t)*cos(t)
Finally use the next command in order to calculate the indefinite integral:
int(f)
I attached a picture in which you can see the procedure and the result.
To evaluate the integral of sintcost tdt in MATLAB, use the symbolic math toolbox and the 'int' function.
Explanation:To evaluate the integral sintcost tdt in MATLAB, you can use the symbolic math toolbox. First, define the extended variable t using 'syms t'. Then, determine the integrand using the symbolic expression 'f = sin(t) * cos(t)'. Finally, use the 'int' function to find the integral, 'int(f, t)'.
Here's the MATLAB code:
syms tf = sin(t) * cos(t)
integral_value = int(f, t)
The resulting 'integral_value' will be the evaluated integral.
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Related Questions
A small military base housing 1,000 troops, each of whom is susceptible to a certain virus infection. Assuming that during the course of the epidemic the rate of change (with respect to time) of the number of infected troopers is jointly proportional to then number of troopers infected and the number of uninfected troopers. If at the initial outbreak, there was one trooper infected and 2 days later there were 5 troopers infected, express the number of infected troopers as a function of time.
Answers
Answer:
[tex]I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}[/tex]
Step-by-step explanation:
The rate of infection is jointly proportional to the number of infected troopers and the number of non-infected ones. It can be expressed as follows:
[tex]\frac{dI}{dt}=a*I*(1000-I)[/tex]
Rearranging and integrating
[tex]\frac{dI}{dt}=a*I*(1000-I)\\\\\frac{dI}{I*(1000-I)}=a*dt\\\\\int\frac{dI}{I*(1000-I)}=\int a*dt\\\\-\frac{ln(1000/I-1)}{1000}+C=a*t[/tex]
At the initial breakout (t=0) there was one trooper infected (I=1)
[tex]-\frac{ln(1000/1-1)}{1000}+C=0\\\\-0,006906755+C=0\\\\C=0,006906755[/tex]
In two days (t=2) there were 5 troopers infected
[tex]-\frac{ln(1000/5-1)}{1000}+0,006906755=a*2\\\\-0,005293305+0,006906755=2*a\\a = 0,00161345 / 2 = 0,000806725[/tex]
Rearranging, we can model the number of infected troops (I) as
[tex]-\frac{ln(1000/I-1)}{1000}+0,006906755=0,000806725*t\\\\-\frac{ln(1000/I-1)}{1000}=0,000806725*t-0,006906755\\-ln(1000/I-1)=0,806725*t-0.6906755\\\\\frac{1000}{I}-1=exp^{0,806725*t-0.6906755} \\\\\frac{1000}{I}=exp^{0,806725*t-0.6906755}+1\\\\I=\frac{1000}{exp^{0,806725*t-0.6906755}+1}[/tex]
To review the solution to a similar problem, consult Interactive Solution 1.43. The magnitude of a force vector is 86.4 newtons (N). The x component of this vector is directed along the +x axis and has a magnitude of 72.3 N. The y component points along the +y axis. (a) Find the angle between and the +x axis. (b) Find the component of along the +y axis.
Answers
We have a vector [tex]\vec F[/tex] with a magnitude [tex]F[/tex] of 86.4 N.
a. Let [tex]\theta[/tex] be the angle [tex]\vec F[/tex] makes with the positive [tex]x[/tex]-axis. The [tex]x[/tex]-component of [tex]\vec F[/tex] is
[tex]F_x=(86.4\cos\theta)\,\mathrm N[/tex]
and has a magnitude of 72.3 N, so
[tex]72.3=86.4\cos\theta\implies\cos\theta=0.837\implies\theta=\boxed{33.2^\circ}[/tex]
b. The [tex]y[/tex]-component of [tex]\vec F[/tex] is
[tex]F_y=(86.4\cos33.2^\circ)\,\mathrm N=\boxed{47.3\,\mathrm N}[/tex]
a) The angle between the vector and the +x axis is approximately 33.196°.
b) The component of the force along the +y axis is approximately 47.304 newtons.
Vector analysis of a given force
In this question we should apply the concepts of magnitude and direction of a vector to solve each part. The magnitude ([tex]\|\vec F\|[/tex]), in newtons, is a application of Pythagorean theorem and direction ([tex]\theta[/tex]), in degrees, is an application of trigonometric functions.
a) The angle between the vector and the component along the x axis ([tex]F_{x}[/tex]), in newtons, is found by means of the following expression:
[tex]\theta = \cos^{-1} \frac{F_{x}}{\|\vec F\|}[/tex] (1)
([tex]\|\vec F\| = 86.4\,N[/tex], [tex]F_{x} = 72.3\,N[/tex])
[tex]\theta = \cos^{-1} \left(\frac{72.3\,N}{86.4\,N} \right)[/tex]
[tex]\theta \approx 33.196^{\circ}[/tex]
The angle between the vector and the +x axis is approximately 33.196°. [tex]\blacksquare[/tex]
b) The magnitude of the +y component of the vector force ([tex]F_{y}[/tex]), in newtons, is determined by the following Pythagorean expression:
[tex]F_{y} = \sqrt{(\|\vec F\|)^{2}-F_{x}^{2}}[/tex] (2)
([tex]\|\vec F\| = 86.4\,N[/tex], [tex]F_{x} = 72.3\,N[/tex])
[tex]F_{y} = \sqrt{(86.4\,N)^{2}-(72.3\,N)^{2}}[/tex]
[tex]F_{y} \approx 47.304\,N[/tex]
The component of the force along the +y axis is approximately 47.304 newtons. [tex]\blacksquare[/tex]
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In the 2000 Sydney Olympics, a special program initiated by IOC president Juan Antonio Samaranch allowed developing countries to send athletes to the Olympics without the usual qualifying procedure. Here are the 71 times for the first round of the 100 meter men’s swim (in seconds).60.39 49.93 53.40 51.82 50.46 51.36 50.28 50.19 52.1450.56 52.72 50.95 49.74 49.16 52.57 52.53 52.09 52.4049.75 54.06 53.50 50.63 51.93 51.62 52.58 53.55 51.0749.76 49.73 50.90 59.26 49.29 52.78 112.72 49.79 49.8352.43 51.28 52.22 49.76 49.70 52.90 50.19 54.33 62.4551.93 52.24 52.82 50.96 48.64 51.11 50.87 52.18 54.1250.49 49.84 52.91 52.52 50.32 51.52 52.00 52.85 52.2449.45 51.28 49.09 58.79 49.74 49.32 50.62 49.45Calculate the sample mean and sample standard deviation(use Excel functions).
Answers
Answer:
The means for times for the first round of the 100 meter men’s swim is 52.64789 seconds
The satandar deviation for times for the first round of the 100 meter men’s swim is 7.60182 seconds
Step-by-step explanation:
The sample mean for a set of n data is given by:
[tex]\bar X = \frac{1}{n}\sum{x_i}[/tex]
In other words, the sample mean of the times for 71 times of the first round measured in seconds is:
[tex]\bar X = \frac{1}{71}\sum{x_i} = 52.64789[/tex] seconds
The sample standard deviation for a set of n data is given by:
[tex]S = \sqrt{\frac{1}{n-1}\sum{(x_i - \bar x)^2}}[/tex]
In other words, the sample standard deviation of the times for 71 times of the first round measured in seconds is:
[tex]S = \sqrt{\frac{1}{n-1}\sum{(x_i - \bar x)^2}} = 7.60182[/tex] seconds
There are 18,017 AIDS deaths in 2003, or 34.5% of the 1995 AIDS deaths. Determine the number of AIDS deaths in 1995.
Answers
Answer: There are 52223.18 AIDS death in 1995.
Step-by-step explanation:
Since we have given that
Number of AIDS deaths in 2003 = 18,017
Percentage of deaths of 1995 AIDS deaths =34.5%
Let the number of AIDS deaths in 1995 be 'x'.
According to question, it becomes ,
[tex]\dfrac{34.5}{100}\times x=18017\\\\x=18017\times \dfrac{100}{34.5}\\\\x=52223.18[/tex]
Hence, there are 52223.18 AIDS death in 1995.
2. In an experiment with a mass attached to a spring, a student measures the period of the oscillation t as follows: 1.94 s, 1.96 s, 2.01 s, 1.98 s, 2.02 s, 2.00 s, 1.99 s, 2.01 s, 1.98 s, 1.97 s. a) What is the average and b) standard deviation? Use the instructions for excel to find statistics on a set of similar numbers, round to the correct # sig figs. Zeroes to the right do. ALWAYS include units for a number that has units. These statistics have the same units all the way throug
Answers
Answer: a) The average of this set of numbers is 1.98 s. b) the standard deviation is 0.02 s.
Step-by-step explanation: The average is calculated by adding all numbers found in the experiment divided by the number of values. [tex]average = \frac{Sumxi}{n}[/tex]
The standard deviation is given by the square root of the squared sum of the difference between each number and the average divided by the total number of values. For instance, std deviation = [tex]\frac{sqrt{(1.94-1.98)^{2}+(1.96-1.98)^2+(2.01-1.98)^2...}}{11}[/tex] and that is done with all 11 terms of data minus the average to find the standard deviation.
In excel, the average of a certain set of numbers (displayed in cells A1 to A5) can be found by the commands =average(A1:A5). The standard deviation can be found by the commands =stdedv.p(A1:A5) in which p is the population. You can decrease decimals by clicking on the icon displayed in the Ribbon.
x + y = 40
x + 10 = 60
What is the value of x? Of y?
Answers
Answer:
x = 50
y = -10
Step-by-step explanation:
x + y = 40
x + 10 = 60
60 - 10 =x
60 - 10 = 50
x = 50
50 + y = 40
40 - 50 = y
40 - 50 = -10
y = -10
Hey!
------------------------------------------------
Solve for x:
x + y = 40
x + y - y = 40 - y
x = 40 - y
50 - 10 = 40
50 + (-10) = 40
x = 50
y = -10
------------------------------------------------
Solve for x:
x + 10 = 60
x + 10 - 10 = 60 - 10
x = 50
------------------------------------------------
Hope This Helped! Good Luck!
Diff. / Original amount= % of increase or decrease
Answers
Answer:
% increase =[tex]\frac{\text{ Increased number -Original number }}{\text{Original number}} \times 100\%[/tex]
% decrease =[tex]\frac{\text{ Original number - Decreased number }}{\text{Original number}} \times 100\%[/tex]
Step-by-step explanation:
Percentage Increase:
Let there be an original number. If it increased to a certain value we can calculate the percentage increase value with the help of following formula:
% increase =[tex]\frac{\text{ Increased number -Original number }}{\text{Original number}} \times 100\%[/tex]
Percentage Decrease:
Let there be an original number. If it decreases to a certain value we can calculate the percentage decrease with the help of following formula:
% decrease =[tex]\frac{\text{ Original number - Decreased number }}{\text{Original number}} \times 100\%[/tex]
Calculate:
5,500 milliliters(mL) =__liters (L)
Answers
Answer:
5.5 liters
Step-by-step explanation: there are 1000 milliliters in a liter, so divide 5,500/1000
Answer:
5.5 liters
Step-by-step explanation:
because 5500 millilitres is 5.5 liters
Arrivals at a fast-food restaurant follow a Poisson distribution with a mean arrival rate of 16 customers per hour. What is the probability that in the next hour there will be exactly 9 arrivals?
a. 0.7500
b. 0.1322
c. 0.0000
d. 0.0213
e. none of the above
Answers
Answer:
d. 0.0213
Step-by-step explanation:
If a variable follow a poisson distribution, the probability that x events happens in a specific time is given by:
[tex]P(x)=\frac{e^{-a}*a^{x} }{x!}[/tex]
Where a is the mean number of events that happens in a specific time.
So, in this case, x is equal to 9 arrivals and a is equal to 16 customers per hour. Replacing this values, the probability is:
[tex]P(9)=\frac{e^{-16}*16^{9} }{9!}[/tex]
[tex]P(9)=0.0213[/tex]
A bag contains four red marbles, two green ones, one lavender one, three yellows, and one orange marble. HINT (See Example 7.] How many sets of four marbles include none of the red ones?
Answers
Answer: 35
Step-by-step explanation:
Given : A bag contains four red marbles, two green ones, one lavender one, three yellows, and one orange marble.
Total = 4+2+1+3+1=11
To find sets of four marbles include none of the red ones, we need to exclude red marbles when we count the total number of marbles.
Then, the total marbles(exclude red) =11-4=7
Now, the combination of 7 marbles taking 4 at a time is given by :-
[tex]^7C_4=\dfrac{7!}{4!(7-4)!}=\dfrac{7\times6\times5\times4!}{4!3!}=35[/tex]
Hence, the number of sets of four marbles include none of the red ones = 35
Assume that the sales of a certain appliance dealer can be approximaed y sraig were $6000 in 1982 and $ 64,000 in 1987. Let x - O represent 1982 Find the equation giving yearly alesSand then use it to predict the yearly sales in 1990.
Answers
Answer:
[tex]y=11,600x+6,000[/tex]
Yearly sales in 1990: $98,800.
Step-by-step explanation:
We have been given that the sales of a certain appliance dealer can be approximated by a straight line. Sales were $6000 in 1982 and $ 64,000 in 1987.
If at 1982, [tex]x=0[/tex] then at 1987 x will be 5.
Now, we have two points (0,6000) and (5,64000).
[tex]\text{Slope}=\frac{64,000-6,000}{5-0}[/tex]
[tex]\text{Slope}=\frac{58,000}{5}[/tex]
[tex]\text{Slope}=11,600[/tex]
Now, we will represent this information in slope-intercept form of equation.
[tex]y=mx+b[/tex], where,
m = Slope,
b = Initial value or y-intercept.
We have been given that at [tex]x=0[/tex], the value of y is 6,000, so it will be y-intercept.
Substitute values:
[tex]y=11,600x+6,000[/tex]
Therefore, the equation [tex]S=11,600x+6,000[/tex] represents yearly sales.
Now, we will find difference between 1990 and 1982.
[tex]1990-1982=8[/tex]
To find yearly sales in 1990, we will substitute [tex]x=8[/tex] in the equation.
[tex]S=11,600(8)+6,000[/tex]
[tex]S=92,800+6,000[/tex]
[tex]S=98,800[/tex]
Therefore, the yearly sales in 1990 would be $98,800.
In preparing a certain ointment, a pharmacist used 28.35 g of zinc oxide instead of the 31.1 g called for. Calculate the percentage of error on the basis of the desired quantity.
Answers
Answer: 9.70%
Step-by-step explanation:
The formula to find the percentage error is given by :-
[tex]\%\text{ error}=\dfrac{|\text{Estimate-Actual}|}{\text{Actual}}\times100[/tex]
Given : Actual mass of zinc oxide used by pharmacist = 28.35 g
Estimated mass of zinc oxide used by pharmacist =31.1 g
Now, [tex]\%\text{ error}=\dfrac{|31.1-28.35|}{28.35}\times100[/tex]
i.e. [tex]\%\text{ error}=\dfrac{2.75}{28.35}\times100[/tex]
i.e. [tex]\%\text{ error}=9.70017636684\approx9.70\%[/tex]
Hence, the percentage of error on the basis of the desired quantity.= 9.70%
T F IfA and B are similar matrices, then AT=BT
Answers
Answer:
Step-by-step explanation:
We know that for two similar matrices [tex]A[/tex] and [tex]B[/tex] exists an invertible matrix [tex]P[/tex] for which
[tex][tex]B = P^{-1} AP[/tex][/tex]
∴ [tex]B^{T} = (P^{-1})^{T} A^{T} P^{T} \\[/tex]
Also [tex]P^{-1}P = I\\[/tex]
and [tex](P^{-1})^{T} = (P^{T})^{-1}[/tex]
∴[tex](P^{-1})^{T}P^{T} = I[/tex]
so, [tex]B^{T} = (P^{-1})^{T} A^{T} P^{T} = (P^{T})^{-1}A^{T} P^{T}\\B^{T} = A^{T} I\\B^{T} = A^{T}[/tex]
Let P(x), Q(x), R(x) and S(x) denote the following predicates with domain Z:
P(x): x ≤ 0,
Q(x): x2 = 1,
R(x): x is odd
S(x): x = x + 1.
For each predicate, determine its truth value
Answers
Answer: Hi!, first, Z are the integer numbers, so we only will work with them.
P(x): x ≤ 0
ok, this predicate is true if x is less or equal tan 0, and false if x is greater than 0.
so P(x) is true if { x∈Z, x ≤ 0}
Q(x): x2 = 1
Q(x) is true only if 2*x = 1. now, this means that if x=1/2 is true, but 1/2 isnt an integer, then Q(x) is false ∀ x ∈ Z.
R(x): x is odd
R(x) is true if x is odd, we can write odd numbers as x = 2k + 1, where k is a random integer; then:
R(x) is true if x=2k +1, with k∈Z.
S(x): x = x + 1
S(x) is true if x= x+1, if we subtract x from both sides of the equality, we get that S(x) is true if 0=1, and this is absurd, then:
S(x) is false ∀ x ∈ Z.
Weinstein, McDermott, and Roediger (2010) conducted an experiment to evaluate the effectiveness of different study strategies. One part of the study asked students to prepare for a test by reading a passage. In one condition, students generated and answered questions after reading the passage. In a second condition, students simply read the passage a second time. All students were then given a test on the passage material and the researchers recorded the number of correct answers. a. Identify the dependent variable for this study. b. Is the dependent variable discrete or continuous? c. What scale of measurement (nominal, ordinal, interval, or ratio) is used to measure the dependent variable?
Answers
Answer:
Dependent variable: number of correct answers
Step-by-step explanation:
The dependent variable is the number of correct answers, because it is the variable that the researchers were recording as response in the experiment.
As it is a counting, it can only take finite values (0 correct answers, 1 correct answer, 2 correct answers and so on). Then, it can be classified as a discrete variable. Discrete values always represent exact quantities that can be counted. For example, number of passengers per car, or number of cows per acre.
Discrete variables can be divided into nominal (they haven’t an order or a hierarchy, as in the example of cows/acre), ordinal (they follow a natural order or hierarchy), interval (they can be divided into classes) or ratio (they represent relative quantities).
The number of correct answers is an ordinal variable, because they have a natural hierarchy. 1 correct answer it’ s better than 0, and 2 corrects answers are better than 1 and 0. Then, you can order your results: 0, 1, 2, 3, 4, etc.
Find the expansion of tan x about the point X = 0.
Answers
Answer:
[tex]f(x) = x +\frac{1}{3}x^{3}+....[/tex]
Step-by-step explanation:
As per the question,
let us consider f(x) = tan(x).
We know that The Maclaurin series is given by:
[tex]f(x) = f(0) + \frac{f^{'}(0)}{1!}\cdot x+ \frac{f^{''}(0)}{2!}\cdot x^{2}+\frac{f^{'''}(0)}{3!}\cdot x^{3}+......[/tex]
So, differentiate the given function 3 times in order to find f'(x), f''(x) and f'''(x).
Therefore,
f'(x) = sec²x
f''(x) = 2 × sec(x) × sec(x)tan(x)
= 2 × sec²(x) × tan(x)
f'''(x) = 2 × 2 sec²(x) tan(x) tan(x) + 2 sec²(x) × sec²(x)
= 4sec²(x) tan²(x) + 2sec⁴(x)
= 6 sec⁴x - 4 sec² x
We then substitute x with 0, and find the values
f(0) = tan 0 = 0
f'(0) = sec²0 = 1
f''(0) = 2 × sec²(0) × tan(0) = 0
f'''(0) = 6 sec⁴0- 4 sec² 0 = 2
By putting all the values in the Maclaurin series, we get
[tex]f(x) = f(0) + \frac{f^{'}(0)}{1!}\cdot x+ \frac{f^{''}(0)}{2!}\cdot x^{2}+\frac{f^{'''}(0)}{3!}\cdot x^{3}+......[/tex]
[tex]f(x) = 0 + \frac{1}{1}\cdot x+ \frac{0}{2}\cdot x^{2}+\frac{2}{6}\cdot x^{3}+......[/tex]
[tex]f(x) = x +\frac{1}{3}x^{3}+....[/tex]
Therefore, the expansion of tan x at x = 0 is
[tex]f(x) = x +\frac{1}{3}x^{3}+....[/tex].
Use the compound interest formula to compute the total amount accumulated and the interest earned $4500 for 3 years at 5% compounded quarterly The total amount accumulated after 3 years is $5223.40 (Round to the nearest cent as needed.) The amount of interest earned is $ (Round to the nearest cent as needed.)
Answers
To compute the total amount accumulated with compound interest and the interest earned, we utilize the formula for compound interest on the given principal amount, rate of interest, and the period. The interest earned is then computed by subtracting the initial principal amount from the total accumulated amount.
Explanation:The subject of this question is the calculation of compound interest. Given that the principal amount is $4500, the rate of interest is 5%, and the interest is compounded quarterly over a course of 3 years, we first need to compute the total amount accumulated. Using the formula for compound interest:
A = P (1 + r/n)^(nt)
where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (in decimal).
n is the number of times that interest is compounded per year.
t is the number of years the money is invested for.
In this case, P = 4500, r = 0.05 (5% expressed as a decimal), n = 4 (since interest is compounded quarterly), and t = 3. Substituting these values into the formula, we get the total accumulated amount.
The interest earned can subsequently be found by subtracting the original principal amount (P) from the accumulated amount (A).
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what is the reason for each step in the solution of the equation? -6x = -2(x + 12) ? Drag and drop the reasons into the boxes to correctly complete the table.
Answers
Answer:
GivenDistributive propertyAddition propertyDivision propertyStep-by-step explanation:
In step 2, the result of eliminating parentheses is shown. That is done by using the distributive property to multiply -2 by each of the terms inside parentheses, giving ...
(-2)(x) +(-2)(12) = -2x -24
In step 3, 2x is added to both sides of the equation. This eliminates the -2x term on the right, and increases the -6x term on the left to -4x.
In step 4, the equation is divided by -4. This makes the coefficient of x become 1.
The equation -6x = -2(x + 12) can be solved by distributing -2 to elements inside the bracket, re-writing the equation, simplifying it, and then finally solving for 'x', leading to x = 6.
Explanation:The equation shared is a linear equation in one variable, -6x = -2(x + 12). There are main steps to solving this equation:
Distribute the -2: First, distribute the '-2' to both 'x' and '+12' inside the bracket. So, this becomes -2x -24. Set equal to -6x: Now, re-write the equation: -6x = -2x - 24. Simplify: You'll add 2x to both sides of the equation to keep the equation balanced, leading to -4x = -24. Solve for x: Finally, divide both sides by -4 to isolate 'x'. This will result in x = 6.
So, for this equation -6x = -2(x + 12), the solution is x = 6.
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Convert one hour to seconds
Answers
Answer: 3600 seconds
Step-by-step explanation:
Use the following conversions: 1 hour = 60 minutes & 1 minute = 60 seconds
[tex]1\ hour \times \dfrac{60\ minutes}{1\ hour}\times \dfrac{60\ seconds}{1\ minute}\quad =\large\boxed{3600\ seconds}[/tex]
Determine whether the following possible responses should be classified as interval, nominal or ordinal data.
? Ordinal Nominal Interval 1. Heidi's favorite brand of tennis balls
? Ordinal Nominal Interval 2. Number of cars in a parking lot
? Ordinal Nominal Interval 3. Amount of time you spend per week on your homework
? Ordinal Nominal Interval 4. Whether you are a US citizen
Answers
Answer:
1. Nominal data 2. Responses here can't be classified as interval or nominal or ordinal data 3. Responses here can't be classified as interval or nominal or ordinal data 4. nominal
Step-by-step explanation:
1. Heidi's favorite brand of tenis balls is only a "label" in the set of brands that can be regarded. So, because we are dealing with names or "labels" we should classify responses here as nominal data.
2. Possible values for the number of cars in a parking lot are 0, 1, 2, 3, 4,... Besides we can say that 4 cars is twice than 2 cars, and exist a true zero. We can't say that responses here correspond to interval data, in fact, we can say that responses here correspond to the kind of data called ratio data.
3. You can spend zero hours in your homework, so, there exists an absolute zero, besides, to say that you spend 4 hours in your homework is twice that if you spend 2 hours in your homework is meaningful. We can't classify responses here as interval data or ordinal or nominal. We can classify responses here as ratio data.
4. There are only two different responses here, i.e., You are a US citizen or You are not a US citizen. We are dealing with "labels" again, and in general, we can't say there is a better response or stablish an order.
Final answer:
The correct classifications are: Heidi's favorite brand of tennis balls (Nominal), Number of cars in a parking lot (Nominal, with an explanation), Amount of time spent on homework per week (Interval), and Whether you are a US citizen (Nominal).
Explanation:
To determine whether the listed responses should be classified as interval, nominal, or ordinal data, it is essential to understand what each type of data signifies. Nominal data are categories without any order, ordinal data have a meaningful order or ranking but not necessarily consistent differences between rankings, and interval data have a consistent scale and order, but no true zero point.
Nominal: Heidi's favorite brand of tennis balls. This is a category (brand) without a numerical value or order.
Nominal: Number of cars in a parking lot. Although it involves numbers, it is essentially counting the frequency of an item, which falls under ratio data. However, as the question specifically asks among nominal, ordinal, and interval, the correct identification in this context is not provided.
Interval: Amount of time you spend per week on your homework. Time has a consistent scale and can be ordered, but there is no true zero time (you cannot have negative time).
Nominal: Whether you are a US citizen. This is a categorical variable with no inherent order.
Find the point, P, at which the line intersects the plane. x equals negative 3 minus 8 tx=−3−8t, y equals negative 6 plus 5 ty=−6+5t, z equals negative 6 minus 6 tz=−6−6t; negative 7 x plus 2 y plus 8 z equals negative 4−7x+2y+8z=−4 The point, P, at which the line intersects the plane is left parenthesis nothing comma nothing comma nothing right parenthesis,,. (Simplify your answer. Type an ordered triple.)
Answers
Answer:
P = (-18 5/9, 3 13/18, -17 2/3)
Step-by-step explanation:
The given point must satisfy both the equation of the line and that of the plane. We can substitute for x, y, and z in the plane's equation to get ...
-7(-3-8t) +2(-6+5t) +8(-6-6t) = -4
21 +56t -12 +10t -48 -48t = -4
18t -39 = -4 . . . collect terms
18t = 35 . . . . . . add 39
t = 35/18 . . . . . .divide by the coefficient of t
The point is ...
(x, y, z) = (-3-8(35/18), -6+5(35/18), -6-6(35/18))
P = (x, y, z) = (-18 5/9, 3 13/18, -17 2/3)
Find the 100th and the nth term for each of the following sequences.1 , 4 , 7 , 10 , .
Answers
Answer: The value of 100 th term is 298 and the value of n th term is 1+3n.
Step-by-step explanation:
Since we have given that
1,4,7,10............
Since it forms an A.P. in which
a = 1
d = [tex]4-1 =3[/tex]
So, the value of 100 th term is given by
[tex]a_{100}=a+(n-1)d\\\\a_{100}=1+(100-1)\times 3\\\\a_{100}=1+99\times 3\\\\a_{100}=1+297\\\\a_{100}=298[/tex]
And the value of n th term is given by
[tex]a_n=1+3n[/tex]
Hence, the value of 100 th term is 298 and the value of n th term is 1+3n.
A pawnshop with a monthly interest rate of 3.15 percent would have an annual interest rate of percent. (Round your answer to 2 decimal places.) Multiple Choice 3.15 31.50 3780 18.90 6.30
Answers
Annual is 1 year.
1 year has 12 months.
Multiply the monthly rate by 12:
3.15 x 12 = 37.80%
Is the following relation a function?
Yes
No
Answers
Answer: This represents a function
Step-by-step explanation: In this problem, we are given a relation in the form of a mapping diagram and we are asked if it represents a function. The easiest way to do this problem is to first translate the mapping diagram into a list of ordered pairs.
(6,-2) (-2,2) (4,1) (-1,1)
Now to determine if the relation is a function, we can simply look at the x coordinates of each ordered pair. Notice that all of them are different so the relation must be a function. It's important to understand that even though two of the Y coordinates are the same, this relation is still a function because the y coordinates do not have any effect on whether or not the relation is a function.
The admissions office of a private university released the following data for the preceding academic year: From a pool of 4200 male applicants, 30% were accepted by the university, and 30% of these subsequently enrolled. Additionally, from a pool of 3300 female applicants, 35% were accepted by the university, and 30% of these subsequently enrolled. What is the probability of each of the following?
a) A male applicant will be accepted by and subsequently will enroll in the university?
b) A student who applies for admissions will be accepted by the university?
c) A student who applies for admission will be accepted by the university and subsequently will enroll?
Answers
Answer:
(a) 0.09 (b) 0.322 (c) 0.0966
Step-by-step explanation:
Let's define first the following events
M: an applicant is a male
F: an applicant is a female
A: an applicant is accepted
E: an applicant is enrolled
S: the sample space
Now, we have a total of 7500 applicants, and from these applicants 4200 were male and 3300 were female. So,
P(M) = 0.56 and P(F) = 0.44, besides
P(A | M) = 0.3, P(E | A∩M) = 0.3, P(A | F) = 0.35, P(E| A∩F) = 0.3
(a) 0.09 = (0.3)(0.3) = P(A|M)P(E|A∩M)=P(E∩A∩M)/P(M)=P(E∩A | M)
(b) P(A) = P(A∩S) = P(A∩(M∪F))=P(A∩M)+P(A∩F)=P(A|M)P(M)+P(A|F)P(F)=(0.3)(0.56)+(0.35)(0.44)=0.322
(c) P(A∩E)=P(A∩E∩S)=P(A∩E∩(M∪F))=P(A∩E∩M)+P(A∩E∩F)=0.0504+P(E|A∩F)P(A|F)P(F)=0.0504+(0.3)(0.35)(0.44)=0.0966
A lady buys 20 trinkets at a yard sale.
The cost of each trinket is either $0.30
or $0.65. If she spends $8.80, how
many of each type of trinket does she
buy?
Answers
Answer:
Lady purchased 12 trinkets costing $0.30 each and 8 trinkets costing $0.65 each.
Step-by-step explanation:
A lady buys total number of trinkets = 20
Cost of each trinket is either $0.30 or $0.65.
Let the number of trinkets is x she purchased for $0.30 and y for $0.65
Then x + y = 20 --------(1)
Since she spends total amount = $8.80
Then the equation will be
0.30x + 0.65y = 8.80 ---------(2)
We replace x = (20 - y) from equation (1) to equation (2)
0.30(20 - y) + 0.65y = 8.80
6 - 0.30y + 0.65y = 8.80
0.35y + 6 = 8.80
0.35y = 8.80 - 6
0.35y = 2.80
y = [tex]\frac{2.80}{0.35}[/tex]
y = 8
Now we put y = 8 in equation (1)
x + 8 = 20
x = 20 - 8
x = 12
Therefore, lady purchased 12 trinkets costing $0.30 each and 8 trinkets costing $0.65 each.
A computer assembling company receives 24% of parts from supplier X, 36% of parts from supplier Y, and the remaining 40% of parts from supplier Z. Five percent of parts supplied by X, ten percent of parts supplied by Y, and six percent of parts supplied by Z are defective. If an assembled computer has a defective part in it, what is the probability that this part was received from supplier Z?
Answers
Answer:
There is a 33% probability that this party was received from supplier Z.
Step-by-step explanation:
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
[tex]P = \frac{P(B).P(A/B)}{P(A)}[/tex]
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
-In your problem, we have:
P(A) is the probability of a defective part being supplied. For this probability, we have:
[tex]P(A) = P_{1} + P_{2} + P_{3}[/tex]
In which [tex]P_{1}[/tex] is the probability that the defective product was chosen from supplier X(we have to consider the probability of supplier X being chosen). So:
[tex]P_{1} = 0.24*0.05 = 0.012[/tex]
[tex]P_{2}[/tex] is the probability that the defective product was chosen from supplier Y(we have to consider the probability of supplier Y being chosen). So:
[tex]P_{2} = 0.36*0.10 = 0.036[/tex]
[tex]P_{3}[/tex] is the probability that the defective product was chosen from supplier Z(we have to consider the probability of supplier Z being chosen). So:
[tex]P_{2} = 0.40*0.06 = 0.024[/tex]
So
[tex]P(A) = P_{1} + P_{2} + P_{3} = 0.012 + 0.036 + 0.024 = 0.072[/tex]
P(B) is the probability of the supplier chosen being Z, so P(B) = 0.4
P(A/B) is the probability of the part supplied being defective, knowing that the supplier chosen was Z. So P(A/B) = 0.06.
So, the probability that this part was received from supplier Z is:
[tex]P = \frac{0.4*0.06}{0.072} = 0.33[/tex]
There is a 33% probability that this party was received from supplier Z.
if 4 divides a^2-3b^2, then at least one of the integers a and b is even.
Answers
Step-by-step explanation:
The proof can be done by contradiction. Suppose both a, and b weren't even. So that a, and b are both odd. This means they both look like
[tex]a=2k+1,~~b=2l+1[/tex] (for some integers k and l)
So, let's compute what [tex]a^2-3b^2[/tex] would be in this case:
[tex]a^2-3b^2=(2k+1)^2-3(2l+1)^2=4k^2+4k+1-3(4l^2+4l+1)[/tex]
[tex]= 4k^2+4k+1-12l^2-12l-3=4k^2+4k-12l^2-12l-2 [/tex]
[tex]=4(k^2+k+3l^2-3l)-2[/tex]
which notice wouldn't be divisible by 4. This shows then that since [tex]a^2-3b^2[/tex] is divisible by 4, at least one of the integers a and b is even.
4,275.50= 391/2 of ____
Answers
Answer:
The required value for the blank is 21.8696
Step-by-step explanation:
Consider the provided information,
4,275.50= 391/2 of ____
Replace blank with x.
4,275.50 = 391/2 of x
Use sign of multiplication for "of".
[tex]4,275.50 = \frac{391}{2} \times x[/tex]
Solve the above expression for x.
[tex]x=\frac{4,275.50\times 2}{391} [/tex]
[tex]x=21.8696 [/tex]
Thus, the required value for the blank is 21.8696
Use the row operations tool to solve the following system of equations, obtaining the solutions in fraction form.
12x + 2y + z = 4
3x + 3y - 4z = 5
2x - 2y + 4z = 1
Give the values for x, y, and z with the fractions reduced to lowest terms (for example 4/7 rather than 8/14).
x = ____
y = ____
z = ____
Answers
Answer:
[tex]x=\frac{45}{4}, y=-\frac{201}{4}, z=-\frac{61}{2}[/tex]
Step-by-step explanation:
We start by putting our equation in a matricial form:
[tex]\left[\begin{array}{cccc}12&2&1&4\\3&3&-4&5\\2&-2&4&1\end{array}\right][/tex]
Then, we multiply the second row by 4 and substract the first row:
[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\2&-2&4&1\end{array}\right][/tex]
Now, multiply the third row by 6 and substract the first row:
[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\0&-14&23&2\end{array}\right][/tex]
Next, we will add [tex]\frac{7}{5}[/tex] times the second row to the third row:
[tex]\left[\begin{array}{cccc}12&2&1&4\\0&10&-17&16\\0&0&\frac{-4}{5}&\frac{122}{5}\end{array}\right][/tex]
Now we can solve [tex]\frac{-4}{5} z=\frac{122}{5}[/tex] to obtain
[tex]z=-\frac{61}{2}[/tex]
Then [tex]10y-17\frac{-61}{2}=16[/tex] wich implies that
[tex]y=\frac{16-\frac{17*61}{2}}{10} =\frac{\frac{32-17*61}{2}}{10}=\frac{-1005}{20}=\frac{-201}{4}[/tex]
Finally
[tex]x=\frac{4-2*\frac{-201}{4}+\frac{61}{2}}{12} =\frac{\frac{8+201+61}{2}}{12}=\frac{270}{24}=\frac{135}{12}=\frac{45}{4}[/tex].
[tex]z=-\frac{61}{2}\\ y=-\frac{201}{4} \\x=\frac{45}{4}[/tex]