By the chain rule,
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}[/tex]
Then for all [tex]t[/tex] the first derivative has a value of 7.
By the product rule,
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\right]=\dfrac{\mathrm d\left(\frac{\mathrm dy}{\mathrm dt}\right)}{\mathrm dx}\dfrac{\mathrm dt}{\mathrm dx}+\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm d^2t}{\mathrm dx^2}[/tex]
but [tex]t=x\implies\dfrac{\mathrm dt}{\mathrm dx}=1\implies\dfrac{\mathrm d^2t}{\mathrm dx^2}=0[/tex], so we're left with
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d\left(\frac{\mathrm dy}{\mathrm dt}\right)}{\mathrm dx}[/tex]
By the chain rule,
[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d\left(\frac{\mathrm dy}{\mathrm dt}\right)}{\mathrm dx}=\dfrac{\mathrm d\left(\frac{\mathrm dy}{\mathrm dt}\right)}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}=\dfrac{\mathrm d^2y}{\mathrm dt^2}[/tex]
but [tex]y=7t-2\implies\dfrac{\mathrm dy}{\mathrm dt}=7\implies\dfrac{\mathrm d^2y}{\mathrm dt^2}=0[/tex] so the second derivative is 0 for all [tex]t[/tex].
The derivative dy/dx for the given parametric equations is 7, and the second derivative d2y/dx2 is zero. The slope at t = 9 is 7, and the curve does not exhibit concavity since it is linear.
Explanation:To find dy/dx for the parametric equations x = t and y = 7t - 2, we need to compute the derivatives of both x and y with respect to t and then use the chain rule to find dy/dx as dy/dt divided by dx/dt. Since the derivative of x with respect to t is 1, and the derivative of y with respect to t is 7 (as the derivatives of the constants -2 and 1 are zero), dy/dx equals 7/1, which is 7. To find the second derivative d2y/dx2, we note that since dx/dt is constant (equals 1), the second derivative is zero. Therefore, the concavity of the curve does not change and is neither concave up nor down.
At the given value of the parameter t = 9, the slope of the tangent line is 7, as it is for all values of t. Since the second derivative is zero, the curve is linear and does not exhibit concavity at any point, including t = 9.
You are tasked with building a tower of blocks exactly 10 cm high. You have two types of block to work with. Each block A is 2 cm high, and each block B is 3 cm high. You may use any number of each type of block, and may stack any kind of block on top of any other kind. How many possible towers are there
Answer:
2 possible towers
Step-by-step explanation:
2 possible towers
Step-by-step explanation:
The height of the tower required is 10 cm, and that height may be obtained by 'x' number of blocks A and 'y' number of blocks, knowing its respective height, so 'x' and 'y' must accomplish the equation:
[tex] 10 = 2x + 3y [/ tex]
The maximum value for 'x' is 5; a higher value will give a higher than 10 cm height as a result. So, the possible answers for 'x' are: (0,1,2,3,4,5). Note that both 'x' and 'y' values must be integers, and the only numbers that satisfy that condition are (x = 2, y = 2) and (x = 5, y = 0). The other options for 'x' will give a noninteger value for 'y' because of the equation above.
So, there are just two options.
Assume that there are 365 days in a year, the probability that a person is born on any given day is the same for all days, and everyone’s birthdays are independent.
(a) If there are n people, what is the probability that no one is born in July?
(b) If there are 15 people who are all born in July or August, what is the probability that at least two of these people share the same birthday?
For part a, wouldn't it just be 365^n - 365^31 since there are only 31 days in July? Is there a way to make it more order specific? For b I am still confused on how to make order matter if we are just taking days from July or August. Explanations well appreciated!
Answer:
Step-by-step explanation:
If each day equal chance then p = Prob that a person is borne on a particular day = 1/365
Each person is independent of the other and there are two outcomes either borne in July or not
p = prob for one person not borne in July = (365-31)/365 = 334/365
a)Hence prob that no one from n people borne in July = [tex](\frac{334}{365} )^n[/tex]
b) p = prob of any one borne in July or Aug = [tex]\frac{(31+31) }{365} =\frac{62}{365}[/tex]=0.1698
X- no of people borne in July or Aug
n =15
P(X>=2) =[tex]15C2 (0.1698)^2*(1-0.1698)^{13} +15C3 (0.1698)^3*(1-0.1698)^{12} +...+15C15 (0.1698)^{15}[/tex]
=0.7505
A property contained ten acres. How many lots of not less than 50 feet by 100 feet can be subdivided from the property if 26,000 square feet were dedicated for roads?
Answer:
81 lots of 5,000 square feet fits in the property.
Step-by-step explanation:
The first step is calculate the square feet of the minimum area:
[tex]50 \: feets \times 100 \: feet = 5,000 \:square \: feet[/tex]
Second, from the ten acres we subtract the 26,000 feets of roads:
[tex]1 \: acre = 60 \: feet \times 660\:feet = 43,560\:square\:feet\\43,560 \times 10 = 435,600\\435,600 - 26,000 = 409,600 \:square \: feet\:available[/tex]
Third, we divide the lot area over the available square feet
[tex]\frac{409,600}{5,000} = 81.92[/tex]
81 lots of 5,000 square feet fits in the property.
When the positive integer "n" is divided by 3, the remainder is 2 and when "n" is divided by 5, the remainder is 1. What is the least possible value of "n" I really need this done out step by step and explained in detail. im not grasping it...
Answer:
The number would be 11.
Step-by-step explanation:
Dividend = Divisor × Quotient + Remainder
Given,
"n" is divided by 3, the remainder is 2,
So, the number = 3n + 2,
"n" is divided by 5, the remainder is 1,
So, the number = 5n + 1
Thus, we can write,
3n + 2 = 5n + 1
-2n = -1
n = 0.5,
Therefore, number must be the multiple of 0.5 but is not divided by 3 or 5,
Possible numbers = { 1, 2, 4, 7, 8, 11...... }
Since, 1 and 4 do not give the remainder 2 after divided by 3,
And, 2, 7 and 8 do not give the remainder 1 after divided by 5,
Hence, the least positive integer number that gives remainder 2 and 1 after divided by 3 and 5 respectively is 11.
Given the Arithmetic sequence A1,A2,A3,A4 53, 62, 71, 80 What is the value of A38?
Answer:
[tex]A_{38} = 350[/tex]
Step-by-step explanation:
The 5th term of the arithmetic sequence is 53. We can write the equation:
[tex]a + 4d = 53...(1)[/tex]
The 6th term of the arithmetic sequence is 62. We can write the equation:
[tex]a + 5d = 62...(2)[/tex]
Subtract the first equation from the second one to get:
[tex]5d - 4d = 62 - 53[/tex]
[tex]d = 9[/tex]
The first term is
[tex]a + 4(9) = 53[/tex]
[tex]a + 36 = 53[/tex]
[tex]a = 53 - 36[/tex]
[tex]a = 17[/tex]
The 38th term of the sequence is given by:
[tex] A_{38} = a + 37d[/tex]
[tex]A_{38} = 17+ 37(9)[/tex]
[tex]A_{38} = 350[/tex]
Answer:
[tex]A_{38}=386[/tex]
Step-by-step explanation:
We have been given an arithmetic sequence gas [tex]A_1,A_2,A_3,A_4[/tex] as :53,62,71,80. We are asked to find [tex]A _{38}[/tex].
We know that an arithmetic sequence is in format [tex]a_n=a_1+(n-1)d[/tex], where,
[tex]a_n[/tex] = nth term,
[tex]a_1[/tex] = 1st term of sequence,
n = Number of terms,
d = Common difference.
We have been given that 1st term of our given sequence is 53.
Now, we will find d by subtracting 71 from 80 as:
[tex]d=80-71=9[/tex]
[tex]A_{38}=53+(38-1)9[/tex]
[tex]A_{38}=53+(37)9[/tex]
[tex]A_{38}=53+333[/tex]
[tex]A_{38}=386[/tex]
Therefore, [tex]A_{38}=386[/tex].
Suppose a bank offers a CD that earns 1% interest compounded 353 times per year. You invest $1,282 today. How much will you have (in dollars and cents) after 8 years?
Answer:
1388 dollars 77 cents.
Step-by-step explanation:
Since, the amount formula in compound interest is,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where, P is the principal amount,
r is the annual rate,
n is the number of periods in a year,
t is the number of years,
Given,
P = $ 1,282,
r = 1 % = 0.01,
n = 353,
t = 8 years,
Hence, the amount after 8 years would be,
[tex]A=1282(1+\frac{0.01}{353})^{2824}[/tex]
[tex]=\$ 1388.77244711[/tex]
[tex]\approx \$ 1388.77[/tex]
= 1388 dollars 77 cents.
Find the? inverse, if it? exists, for the given matrix.
[4 3]
[3 6]
Answer:
Therefore, the inverse of given matrix is
[tex]=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}[/tex]
Step-by-step explanation:
The inverse of a square matrix [tex]A[/tex] is [tex]A^{-1}[/tex] such that
[tex]A A^{-1}=I[/tex] where I is the identity matrix.
Consider, [tex]A = \left[\begin{array}{ccc}4&3\\3&6\end{array}\right][/tex]
[tex]\mathrm{Matrix\:can\:only\:be\:inverted\:if\:it\:is\:non-singular,\:that\:is:}[/tex]
[tex]\det \begin{pmatrix}4&3 \\3&6\end{pmatrix}\ne 0[/tex]
[tex]\mathrm{Find\:2x2\:matrix\:inverse\:according\:to\:the\:formula}:\quad \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}[/tex]
[tex]=\frac{1}{\det \begin{pmatrix}4&3\\ 3&6\end{pmatrix}}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}[/tex]
[tex]\mathrm{Find\:the\:matrix\:determinant\:according\:to\:formula}:\quad \det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}\:=\:ad-bc[/tex]
[tex]4\cdot \:6-3\cdot \:3=15[/tex]
[tex]=\frac{1}{15}\begin{pmatrix}6&-3\\ -3&4\end{pmatrix}[/tex]
[tex]=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}[/tex]
Therefore, the inverse of given matrix is
[tex]=\begin{pmatrix}\frac{2}{5}&-\frac{1}{5}\\ -\frac{1}{5}&\frac{4}{15}\end{pmatrix}[/tex]
What is the measure of ∠X?
69°
111°
180°
21°
Which of the following is a true statement about the self-interest assumption?
a.
Self-interest players always maximize money.
b.
Self-interest players will never perform an act of charity.
c.
Self-interest players may sacrifice to punish others.
d.
Self-interest implies that players are selfish.
Answer:
d
Step-by-step explanation:
Self-interest assumption means that an action taken by a person can be termed as self interest if he or she has any basis or reason behind taking such action. The individual always looks for profit and self benefit.Hence they can be treated as selfish.
So, if a person sacrifices his or her own interest so that others can be punished then such act can be termed as self-interest as person concerned is taking such action with a reason behind such act.
Hence, the correct answer is the option (d).
A project manager can interpret several things from data displayed in a histogram. If something unusual is happening, the histogram might be ___________. a. Flat b. Skewed c. Bell-shaped d. S-shaped
Answer:
Skewed
Step-by-step explanation:
A project manager can interpret several things in a histogram. If something unusual happening, the histogram is said to Skewed. When the histogram is Skewed it means that many of the values of the graph are falling on only one side of the mean. It can be either on left side( left skewed) or on the right side called right skewed
Suppose that neighborhood soccer players are selling raffle tickets for $500 worth of groceries at a local store, and you bought a $1 ticket for yourself and one for your mother. The children eventually sold 1000 tickets. What is the probability that you will win first place while your mother wins second place?
Answer:
The probability is 0.001001.
Step-by-step explanation:
Players are selling raffle tickets for $500 worth of groceries at a local store.
You bought a $1 ticket for yourself and one for your mother.
The children eventually sold 1000 tickets.
We have to find the probability that you will win first place while your mother wins second place.
We can find this as :
P(winning) =[tex]1/999=0.001001[/tex]
The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean? 14.7 and 16.9 10.0 and 20.0 16.1 and 18.1 13.2 and 17.6
Answer:
14.7 and 16.9
Step-by-step explanation:
We want to find the confidence interval for the mean when the population standard deviation [tex]\sigma[/tex], is known so we use the [tex]z[/tex] confidence interval for the mean.
The following assumptions are also met;
The sample is a random sample [tex]n\ge 30[/tex]The z confidence interval for the mean is given by:
[tex]\bar X-z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )\:<\:\mu\:<\bar X+z_{\frac{\alpha}{2} }(\frac{\sigma}{\sqrt{n} } )[/tex]
The appropriate z-value for 95% confidence interval is 1.96 (read from the standard normal z-distribution table)....See attachment.
From the question, we have [tex]n=49[/tex], [tex]\sigma=3.8[/tex] and [tex]\bar X=15.8[/tex]
We substitute all these values to get:
[tex]15.8-1.96(\frac{3.8}{\sqrt{49} } )\:<\:\mu\:<\bar 15.8+1.96(\frac{3.8}{\sqrt{49} } )[/tex]
[tex]15.8-1.96(\frac{3.8}{7 } )\:<\:\mu\:<15.8+1.96(\frac{3.8}{7} )[/tex]
[tex]14.7\:<\:\mu\:< 16.9[/tex] correct to one decimal place.
To calculate the 95% confidence interval for the population mean of truck weights on I-475, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / Square Root of Sample Size). Plugging in the given values, we find that the 95% confidence interval is approximately 14.7 to 16.9 tons.
Explanation:To calculate the 95% confidence interval for the population mean, we can use the formula: Confidence Interval = Sample Mean ± (Critical Value) * (Standard Deviation / Square Root of Sample Size). In this case, the sample mean is 15.8 tons, the population standard deviation is 3.8 tons, and the sample size is 49. The critical value for a 95% confidence level is approximately 1.96. Plugging in these values, we get:
Confidence Interval = 15.8 ± (1.96) * (3.8 / √49)
Confidence Interval ≈ 15.8 ± (1.96) * (3.8 / 7)
Confidence Interval ≈ 15.8 ± (1.96) * 0.543
Confidence Interval ≈ 15.8 ± 1.06
Therefore, the 95% confidence interval for the population mean is approximately 14.7 to 16.9 tons.
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You draw a card from a deck. If you get a red card, you win nothing. If you get a spade, you win $5. For any club, you win $10 plus an extra $15 for the ace of clubs. Find the standard deviation of the amount you might win drawing a card.
Answer:
a) The probability is the number of favorable outcomes divided by the number of possible outcomes. There are 52 cards in a deck.
Step-by-step explanation
hope this helps.
A thief steals an ATM card and must randomly guess the correct four-digit pin code from a 9-key keypad. Repetition of digits is allowed. What is the probability of a correct guess on the first try?
Answer: [tex]\dfrac{1}{59049}[/tex]
Step-by-step explanation:
The number of keys on the keypad = 9
The number of digits in the required pin code = 4
If repetition is allowed then , the number of possible codes will be
[tex](9)^5=59049[/tex]
Then , the probability that the choosen pin code is correct is given by :-
[tex]\dfrac{1}{59049}[/tex]
The probability of Geometric distribution formula :
[tex]P(X=x)=(1-p)^{x-1}p[/tex], where p is the probability of success and x is the number of attempt.
Using geometric probability , the probability of a correct guess on the first try is given by :-
[tex]P(X=1)=(1-\dfrac{1}{59049})^{1-1}(\dfrac{1}{59049})=\dfrac{1}{59049}[/tex]
a parking lot is filled with 260 cars. 1/2 of the vehicles are suvs. 1/3 are sub compact cars. the rest are luxury cars. how many cars in the lot are luxury cars?
Answer:
The total number of luxury cars are 43.
Step-by-step explanation:
Consider the provided information.
It is given that there are 260 cars in the parking lot out of 1/2 are SUVs.
Total number of SUV cars = [tex]260\times{\frac{1}{2}=130}[/tex]
Out of 260 cars 1/3 are sub compact cars.
Total number of sub compact cars = [tex]260\times{\frac{1}{3}}=86.66\approx{87}[/tex]
Therefore the total number of luxury cars are:
260 - 130 - 87 = 43
Therefore, the total number of luxury cars are 43.
A given binomial distribution has mean-4 and variance-2. What is the probability of success? Explain your answer.
Answer: 0.5
Step-by-step explanation:
We know that the mean and variance of a binomial distribution with probability of success p is given by :-
[tex]\text{Mean}:\mu=np\\\\\text{Variance}:\sigma^2=np(1-p)[/tex], where n is the total number of trials .
Given : A given binomial distribution has
[tex]\text{Mean}:\mu=np=4.......(1)\\\\\text{Variance}:\sigma^2=np(1-p)=2............(2)[/tex]
Now we substitute , the value of np from (1) in (2), we get
[tex]4(1-p)=2\\\\\Rightarrow\ 1-p=\dfrac{2}{4}\\\\\Rightarrow\ p=1-\dfrac{1}{2}\\\\\Rightarrow\ p=\dfrac{1}{2}=0.5[/tex]
Hence, the probability of success (p) = 0.5
Give an approximation of underroot(3) correct to hundredths. (Round to two decimal places as needed.)
Answer: 1.75
Step-by-step explanation:
To find the value of [tex]\sqrt{3}[/tex]
[tex]\text{Let , }y=\sqrt{x}[/tex]
[tex]\text{And Let x = 4 and }\Delta x=-1[/tex]
Now,
[tex]\Delta y=\sqrt{x+\Delta x}-\sqrt{x}\\\\=\sqrt{3}-\sqrt{4}=\sqrt{3}-2\\\\\Rightarrow\ \sqrt{3}=\Delta y+2[/tex]
Since dy is approximately equals to [tex]\Delta y[/tex] then ,
[tex]dy=\dfrac{dy}{dx}\Delta x\\\\=\dfrac{1}{2\sqrt{x}}\times(-1)=\dfrac{1}{2\sqrt{4}}\times(-1)=-0.25[/tex]
Thus , the approximate value of [tex]\sqrt{3}=-0.25+2=1.75[/tex]
The newly elected president needs to decide the remaining 5 spots available in the cabinet he/she is appointing. If there are 15 eligible candidates for these positions (where rank matters), how many different ways can the members of the cabinet be appointed
To calculate the number of different ways the members of the cabinet can be appointed, we can use the concept of permutations. Using the formula for permutations, it is found that there are 3003 different ways the members of the cabinet can be appointed.
Explanation:To calculate the number of different ways the members of the cabinet can be appointed, we can use the concept of permutations. Since there are 15 eligible candidates for the remaining 5 spots, and the order in which the members are appointed matters, we can use the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of candidates and r is the number of spots available. In this case, we have:
P(15, 5) = 15! / (15 - 5)!
Calculating this gives us:
P(15, 5) = 15! / 10!
P(15, 5) = (15 × 14 × 13 × 12 × 11) / (5 × 4 × 3 × 2 × 1)
P(15, 5) = 3003
Therefore, there are 3003 different ways the members of the cabinet can be appointed.
y''-4y=cosx find general solution.
Answer:
Step-by-step explanation:
[tex]y''-4y=cosx[/tex]
The auxialary equation and solutions are as follows:
[tex]m^2-4=0\\m=2,-2[/tex]
General solution is
[tex]y=Ae^{2x} +Be^{-2x}[/tex]
Right side =cosx
Particular Integral
= [tex]\frac{cosx}{-1-4} =\frac{-cosx}{5}[/tex]
Hence full solution is
Are Sin(x) and e^x linearly independent? Justify.
Answer:
yes they are linearly independent
Step-by-step explanation:
By definition of linear dependence we have if f(x) and g(x) be 2 functions
if they are linearly dependent then we can write
f(x) = αg(x)...........(i) where α is an arbitrary constant
in our case we can see that the range of sin(x) is only from [-1,+1] while as [tex]e^{x}[/tex] has range from [0,∞]
thus we cannot find any value of α for which (i) is valid
Alvin is 15 years older than Elga. The sum of their ages is 89. What is Elga's age?
Answer:
Elga is 37 years old.
Step-by-step explanation:
Let 'x' be the age of elga.
Alvin's age is: x + 15
Given that the sum of their ages is 89, we have that:
x + 15 + x = 89
2x = 89 - 15
2x = 74
x = 74/2 = 37
Elga is 37 years old.
Answer:
Elga is 37 years old.
Step-by-step explanation:
Alvin (A) is 15 years older than Elga (E).
The sum their anges (A and E) is 89.
So the system we have is:
A=15+E
A+E=89
We are going to input 15+E for A in A+E=89 since first equation says A+15+E.
A+E=89 with A=15+E
(15+E)+E=89
15+E+E=89
15+2E=89
Subtract 15 on both sides:
2E=89-15
2E=74
Divide both sides by 2:
2E/2=74/2
E=74/2
E=37
Elga is 37 years old.
A=15+E=15+37=52 so Alvin is 52 yeard old.
52+37=89.
and
52=15+37.
The road map indicates that it is 10 miles from Vacaville to Fairfield. From the information on the road map, it follows that Vacaville and Fairfield really are 10 miles apart. what type of argument?
Answer: Inductive argument.
Step-by-step explanation:
An argument can have one or more premises but there is only one conclusion to it.The arguments are of two types : Inductive (uses pattern or signs to get a conclusion ) and deductive (Uses general facts or defines or theory to decide any conclusion)
The given argument : The road map indicates that it is 10 miles from Vacaville to Fairfield. From the information on the road map, it follows that Vacaville and Fairfield really are 10 miles apart.
The given argument is the argument that is based on signs (maps are signs) which comes under inductive arguments.
Thus, the given argument is an inductive argument.
The argument which concludes that Vacaville and Fairfield are 10 miles apart based on the information from a road map is an example of a deductive argument, specifically, a syllogism.
Explanation:The argument you're describing here falls under the category of a deductive argument. Specifically, it is an example of a syllogism, which is a form of deductive reasoning consisting of two premises and a conclusion. The premises in this case are 'The map says there are 10 miles between Vacaville and Fairfield' and 'The map is correct'. Therefore, the conclusion is 'There are 10 miles between Vacaville and Fairfield'.
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3 is what percent of 40
Answer:
1.2
Step-by-step explanation:
The following situation can be modeled by a linear function. Write an equation for the linear function and use it to answer the given question. Be sure you clearly identify the independent and dependent variables. Is a linear model reasonable for the situation described? You can rent time on computers at the local copy center for an $8 setup charge and an additional $5.50 for every 10 minutes. How much time can be rented for $25?
Select the correct choice below and fill in the answer box to complete your choice. A. The independent variable is rental cost (r), in dollars, and the dependent variable is time (t), in minutes. The linear function that models this situation is t equals to . (Simplify your answer. Do not include the $ symbol in your answer.)
B. The independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. The linear function that models this situation is r equals .
(Simplify your answer. Do not include the $ symbol in your answer.)
How many minutes can be rented for $25. (Round to the nearest minute as needed.)
A linear model reasonable for this situation
The situation can be modelled by the linear function r = $5.50t/10 + $8, where 't' is time and 'r' is cost. For a $25 rental, approximately 31 minutes can be rented. A linear model is appropriate as the cost increases steadily with time.
Explanation:In this case, the independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. Here, 't' is the time on the computer, and 'r' is the total cost.
The linear function for this situation would be r = $5.50t/10 + $8. Note that $5.50t/10 is the cost per minute (as the rate is $5.50 every 10 minutes), and $8 is the setup fee.
To calculate how much time can be rented for $25, we solve for 't' when r = $25. $25 = $5.50t/10 + $8 gives t = (25 - 8) x 10/5.5, or roughly t = 31 minutes.
A linear model is reasonable for this situation as the cost of renting the computer increases steadily with time.
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The correct option is B. The independent variable is time (t), in minutes, and the dependent variable is rental cost (r), in dollars. The linear function that models this situation is r equals . The cost equation is r = 8 + 0.55t, with t as the independent variable and r as the dependent variable. For $25, approximately 31 minutes can be rented.
The given situation can be modeled by a linear function where the total rental cost depends on the time rented. Here, the independent variable is time (t) in minutes, and the dependent variable is rental cost (r) in dollars.
Option B: The linear function that models this situation is:
→ r = 8 + 0.55t
To find the time that can be rented for $25:
→ Set r = 25 and solve for t:
→ 25 = 8 + 0.55t
Subtract 8 from both sides:
→ 17 = 0.55t
Divide both sides by 0.55:
→ t = 30.91 (approximately)
Rounding to the nearest minute, the time that can be rented is 31 minutes.
Find a parametric representation for the surface. The part of the hyperboloid 4x2 − 4y2 − z2 = 4 that lies in front of the yz-plane. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of u and/or v.)
"in front of the [tex]y,z[/tex] plane" probably means [tex]x\ge0[/tex], in which case
[tex]4x^2-4y^2-z^2=4\implies x=\sqrt{1+y^2+\dfrac{z^2}4}[/tex]
We can then parameterize the surface by setting [tex]y(u,v)=u[/tex] and [tex]z(u,v)=v[/tex], so that [tex]x=\sqrt{1+u^2+\dfrac{v^2}4}[/tex].
The part of the hyperboloid in front of the yz-plane is represented parametrically by x(u,v)=2*cos(u), y(u,v)=-2*sinh(v), and z(u,v)=sinh(u).
Explanation:The surface of the hyperboloid lies in front of the yz-plane and is described by the equation 4x² − 4y² − z² = 4. A common form of parameterization for this type of surface uses hyperbolic functions. Therefore, a parametrization for the part of the hyperboloid lying in front of the yz-plane can be given in terms of u and v as follows:
x(u,v) = 2*cos(u) y(u,v) = -2*sinh(v) z(u,v) = sinh(u)
In this parametric form, u can range over all real numbers to cover the entire surface in front of the yz-plane, while v can oscillate between -∞ to +∞ to provide a full representation of the surface.
Learn more about Parametric Representation of Hyperboloids here:https://brainly.com/question/32515441
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Consider the differential equation 4y'' â 4y' + y = 0; ex/2, xex/2. Verify that the functions ex/2 and xex/2 form a fundamental set of solutions of the differential equation on the interval (ââ, â). The functions satisfy the differential equation and are linearly independent since W(ex/2, xex/2) = â 0 for ââ < x < â.
Check the Wronskian determinant:
[tex]W(e^{x/2},xe^{x/2})=\begin{vmatrix}e^{x/2}&xe^{x/2}\\\frac12e^{x/2}&\left(1+\frac x2\right)e^{x/2}\end{vmatrix}=\left(1+\frac x2\right)e^x-\frac x2e^x=e^x\neq0[/tex]
The determinant is not zero, so the solutions are indeed linearly independent.
To verify a fundamental set of solutions for the given differential equation, one must demonstrate that the functions e^{x/2} and xe^{x/2} satisfy the equation and that their Wronskian is non-zero, indicating linear independence.
Explanation:The student's question pertains to verifying whether a given set of functions, e^{x/2} and xe^{x/2}, form a fundamental set of solutions for the differential equation 4y'' - 4y' + y = 0. A set of solutions is fundamental if the functions are linearly independent and satisfy the differential equation. Linear independence can be proved by calculating the Wronskian, which must be non-zero over the given interval. To show that these functions are solutions, they must be substituted into the differential equation to check if it holds true.
To check for linear independence, we can compute the Wronskian:
W(e^{x/2}, xe^{x/2}) = |which simplifies to e^{x} (1 - (x/2)) that is non-zero for all real numbers x, proving linear independence.
To verify if the functions satisfy the differential equation, we substitute each function into the equation. The derivatives of e^{x/2} and xe^{x/2} are taken, and then these are plugged into the equation to confirm that it yields zero.
25 points T a classroom there are 15 men and 3 women. If teams of 4 members are formed and X is the random variable of the number of men in the team. a. Provide the probability function for X. X f(x) b. What is the expected number of men in a team?
The height of a photograph is 40 cm greater than the width, and the area of the photograph is 896 cm2what is the height of the photograph?
Answer:
Height = 56 cm
Step-by-step explanation:
let the width of photograph be = 'w' cm
let the Height of photograph be = 'h' cm
Now it is given that height is 40 cm greater than width
=> h = w + 40 cm.............................(i)
Now it is given that area of photograph = [tex]896cm^{2}[/tex]
We know that area = [tex]Width^{}[/tex]x[tex]Height^{}[/tex]
Thus we have [tex]h^{}[/tex] x [tex]w^{}[/tex]=[tex]896cm^{2}[/tex]
Applying value of 'h' from equation i we get
[tex](w+40^{})[/tex]x[tex]w^{}[/tex]=[tex]896cm^{2}[/tex]
[tex]w^{2} +40w=896cm^{2}[/tex]
This is a quadratic equation in 'w' whose solution in standard form is given by
w=[tex]\frac{-b\mp\sqrt{b^{2}-4ac}}{2a}[/tex]
upon comparing with standard equation we see that
a =1
b=40
c=896
applying values in the formula we get
w=[tex]\frac{-40\mp\sqrt{40^{2}-4\times 1\times- 896}}{2 \times1 }[/tex]
w1 = 16 cm
w2 = -56 cm
We discard -56 cm since length cannot be negative thus
width = 16 cm
Height = 40+16 cm = 56 cm
Problem 2: Suppose that a 3 Ã 5 coefficient matrix A has a pivot in each of the three rows. If we augment A to represent a linear system, would this system have solutions (be consistent) or have no solutions (be inconsistent)? Explain your answer
The cost of health insurance is $1,200 per year. The cost of an operation for a dramatic injury is $500,000. The chances of someone needing such an operation are 47.3% over a twenty year period. From a purely financial point of view, are you better off taking out the insurance or not? Choose the best answer.
Question options: No. The insurance company must make a profit.
Yes. The cost of the insurance is less than the probability cost of the operation
No. The probality of needing the operation is less than 50%.
Yes. Buying insurance is always a good idea.
Answer:
yes. The cost of the insurance is less than the probability cost of the operation
Step-by-step explanation:
yes. The cost of the insurance is less than the probability cost of the operation
The cost of health insurance = $1200
Cost of dramatic injury operation= $500,000
chances of need of operation= 47.3% over a 20 years period
the amount of pay insurance after 20 years= [tex]20\times 1200= 240,00[/tex]
probable of cost operation= 0.473*500,00= $236,500
clearly the cost of insurance is less than the probable cost of operation.