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Just a correction, the characteristic roots of the equation are [tex]y = 7[/tex] and [tex]y = -\frac{1}{2}[/tex], thus, we should test for:
[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
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Question a:
First, we find the derivatives, thus:[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]
[tex]y^{\prime\prime} = 49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}[/tex]
Now, we replace into the equation:[tex]2y^{\prime\prime} - 13y^{\prime} - 7y = 0[/tex]
[tex]2(49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}) - 13(7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}) - 7(Ae^{7x} + Be^{-\frac{x}{2}}) = 0[/tex]
[tex]98Ae^{-7x} + \frac{1}{2}Be^{\frac{x}{2}} - 91Ae^{-7x} + \frac{13}{2}e^{-\frac{x}{2}} - 7Ae^{7x} - 7Be^{-\frac{x}{2}} = 0[/tex]
[tex]98Ae^{-7x} - 91Ae^{-7x} - 7Be^{-\frac{x}{2}} + \frac{1}{2}Be^{\frac{x}{2}} + \frac{13}{2}e^{-\frac{x}{2}} - 7Be^{-\frac{x}{2}} = 0[/tex]
[tex]0A + 0B = 0[/tex]
[tex]0 = 0[/tex], thus, we found the identity, and for each constant A and B, the following is a solution.
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Question b:
[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]
Since [tex]y(0) = 3[/tex][tex]A + B = 3 \rightarrow B = 3 - A[/tex]
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[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]
Since [tex]y^{\prime}(0) = -5[/tex][tex]7A - \frac{1}{2}B = -5[/tex]
Using [tex]B = 3 - A[/tex]
[tex]7A - \frac{3}{2} + \frac{A}{2} = -5[/tex]
[tex]\frac{14A}{2} + \frac{A}{2} = -\frac{10}{2} + \frac{3}{2}[/tex]
[tex]\frac{15A}{2} = -\frac{7}{2}[/tex]
[tex]15A = -7[/tex]
[tex]A = -\frac{7}{15}[/tex]
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Then, B is given by:
[tex]B = 3 - A = 3 - (-\frac{7}{15}) = \frac{45}{15} + \frac{7}{15} = \frac{52}{15}[/tex]
Thus, the values are: [tex]A = -\frac{7}{15}, B = \frac{52}{15}[/tex]
A similar problem is given at https://brainly.com/question/2456414
A linear regression equation and multiple linear regression equations can be used to calculate y if one is given the x values. However, a logistic regression equation cannot be used to calculate y when one is given x value.
a. True
b. False
Answer:
FALSE
Step-by-step explanation:
First, define y and x.
In statistics, we have what we call variables. Variables are items or symbols that can take on various values. We have dependent variables - whose values are derived from other variables in an equation - and independent variables - whose values are given and are used to determine the values of dependent variables.
Usually, y represents the dependent variable while x represents the independent variable. So the simplest form of regression equation is
y = f (x)
Said as "y is a function of x"
A logistic regression equation can be used to calculate y when x values are given.
Here, the independent variable function (the X function) is a logistic function and it is used to find a binary dependent variable (a Y value, out of two possible values).
In logistic regression equations, the value of Y is not numerical like 1, 0.2, 3/4, and so on. It is categorical, e.g.
Black/White, Gain/Lose, Pass/Fail, Eat/Drink, etc.
uppose cattle in a large herd have a mean weight of 1158lbs and a standard deviation of 92lbs. What is the probability that the mean weight of the sample of cows would differ from the population mean by less than 12lbs if 55 cows are sampled at random from the herd
Answer:
Hence the probability that the mean weight of the sample of 55 cows would differ from the population mean by less than 12 lbs is 0.66545.
Step-by-step explanation:
How to divide 6,558 by 4 in long division
This is the solution to your question.
Leo is running in a 5-kilometer race along a straight path. If he is at the midpoint of the path, how many kilometers does he have left to run?
Answer:
2.5 km left
The midpoint is half of 5, which is 2.5, so he'll still have 2.5 km left to complete
What is 10 + 15k equivalent
Plz hurry
Answer:
if you mean 15k as is 15 thousand then the answer would be 15,010
What are the lengths of the legs of a right triangle in which one acute angle measures 19° and the hypotenuse is 15 units long?
9514 1404 393
Answer:
opposite: 4.88adjacent: 14.18Step-by-step explanation:
SOH CAH TOA is a mnemonic intended to remind you of the relevant trig relations.
Sin = Opposite/Hypotenuse ⇒ opposite = 15×sin(19°) ≈ 4.88 units
Cos = Adjacent/Hypotenuse ⇒ adjacent = 15×cos(19°) ≈ 14.18 units
Answer:
For plato users the correct option is D.
Step-by-step explanation:
D. 4.9 units, 14.2 units
Expand -11(5-p) can someone answer that please
Answer:
-55 +11p
Step-by-step explanation:
-11(5-p)
Distribute
-11*5 -11*(-p)
-55 +11p
Write out the first 5 terms of the following sequence:
9514 1404 393
Answer:
2, 1, -1/2, -1/4, 1/8
Step-by-step explanation:
Use n = 1 through 4:
[tex]a_{1+1}=\dfrac{(-1)^{1+1}\cdot a_1}{2}\ \Rightarrow\ a_2=\dfrac{1\cdot2}{2}=1\\\\a_3=\dfrac{(-1)^3\cdot 1}{2}=-\dfrac{1}{2}\\\\a_4=\dfrac{(-1)^4\cdot(-\dfrac{1}{2})}{2}=-\dfrac{1}{4}\\\\a_5=\dfrac{(-1)^5\cdot(-\dfrac{1}{4})}{2}=\dfrac{1}{8}[/tex]
The first 5 terms are ...
2, 1, -1/2, -1/4, 1/8
2. The two equal sides of an isosceles triangle each have a length of 4x + y - 5. The perimeter of the triangle is
10x + 4y - 18. Determine the length of the third side. Explain how you found your answer. (4 marks)
9514 1404 393
Answer:
2x +2y -8
Step-by-step explanation:
If the equal sides are 'a' and the third side is 'b', then the perimeter is ...
P = a +a +b = 2a +b
The length of the third side is then ...
b = P -2a . . . . . . subtract 2a from both sides
Substituting the given expressions, we find ...
b = (10x +4y -18) -2(4x +y -5)
b = 10x +4y -18 -8x -2y +10
b = 2x +2y -8 . . . . the length of the third side
I need help with this
Answer:
C
Step-by-step explanation:
In the graph given, we can expect the x axis to be horizontal and the y axis to be vertical. This means that the arm span represents y and the height represents x.
Therefore, if a girl on her team is 63 inches tall, we can say that y=x+2, and since height is x, y = 63 + 2 = 65
For a certain company, the cost for producing x items is 40x+300 and the revenue for selling x items is 80x−0.5x2. The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!
Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)
Part b: Find two values of x that will create a profit of $300.
The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1). The order of the list does not matter. To enter a−−√, type sqrt(a).
Part c: Is it possible for the company to make a profit of $15,000?
Answer:
The profit is maximum when x = 40.
Step-by-step explanation:
Cost function, C = 40 x + 300
Revenue function, R = 80 x - 0.5 x^2
The profit function is
[tex]P = R - C\\\\P = 80 x - 0.5 x^2 - 40 x - 300\\\\P = - 0.5 x^2 + 40 x - 300\\\\\frac{dP}{dx} = - x + 40\\\\So, \frac{dP}{dx} = 0\\\\-x + 40 = 0 \\\\x = 40[/tex]
So, the profit is maximum when x = 40 .
The probability I take a nap today is 4/5. The probability I will take a nap and a bubble bath today
is 1/5. What is the probability I will take a bubble bath today, given that I took a nap?
Use Bayes Theorem to compute that probability. I will denote bath as [tex]B[/tex] and nap as [tex]N[/tex], the probability will be denoted as [tex]P(B)[/tex] or [tex]P(N)[/tex].
By Bayes Theorem
[tex]P(B\mid N)=\frac{P(N\mid B)\cdot P(B)}{P(N)}[/tex]
Which reads,
"What is the probability of [tex]B[/tex] given [tex]N[/tex]".
We know that [tex]P(N\mid B)[/tex] is 1 because we already took a bath. So the formula simplifies to,
[tex]P(B\mid N)=\frac{P(B)}{P(N)}[/tex]
Now insert the data,
[tex]P(B\mid N)=\frac{1/5}{4/5}=\boxed{\frac{1}{4}}[/tex]
So the probability that you will take a bath is [tex]0.25[/tex] after you have taken a nap.
Hope this helps. :)
Need help due tomorrow
Answer:
[tex]Given:[/tex] Δ ABC ≈ ΔDEF
[tex]therefor:[/tex] A(ΔABC)/A(ΔDEF)=(BC)²/(EF)²
⇒ 34/A(ΔDEF)=9²/(13.5)²
⇒34/A(ΔDEF)=81/182.25
⇒A(ΔDEF)=34×182.25/81
⇒Area of ΔDEF=76.5 cm²
----------------------------------
Hope it helps...
Have a great day!!!
leave your answer in simplified radical form.
Answer:
The .jpeg file is the answer. Others are formulas that I use to solve.
Nicole was shopping at a local department store and had a budget of $60. She was
buying shorts (s) priced at $10 and t-shirts (t) priced at $8. She was heading to the
checkout stand when she saw a sign that said all t-shirts are 40% off. Write and simplify
an equation that Nicole could use to find the possible combinations of shorts and t-shirts
she could buy for $60.
Answe YEAH BOIIIIII!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
a. A contest entrant has a 0.002 probability of winning $12,165. If this is the only prize and the fee is $35, then find the expected value of winning the contest. b. The probability of winning a lottery is 0.125. What is the probability of winning AT LEAST ONCE in twelve trials?
Answer:
The right answer is:
(a) -10.67
(b) 0.7986
Step-by-step explanation:
(a)
According to the question,
X P(X) X.P(X) X2.P(X)
12130 0.002 24.26 294274
-35 0.998 -34.93 1222.55
Now,
[tex]\Sigma x.P(x) = -10.67[/tex]
or,
[tex]\Sigma x^2.P(x) = 295496.35[/tex]
hence,
The mean will be:
[tex]\Sigma x.P(x) = -10.67[/tex]
(b)
According to the question,
n = 12
p = 0.125
q = 1 - p
= 0.875
Now,
⇒ [tex]P(X=x) = \binom{n}{x} p^x q^{n-x}[/tex]
By substituting the values, we get
⇒ [tex]P(X \geq 1)=1-(\binom{12}{0} 0.125^0. 0.875^{12-0})[/tex]
⇒ [tex]=1-(1 (0.125^0) (0.875^{12}))[/tex]
⇒ [tex]=1-(1(1.0)(0.2014))[/tex]
⇒ [tex]=1-(0.2014)[/tex]
⇒ [tex]=0.7986[/tex]
Dodi bicycles 14mph with no wind. Against the wind, Dodi bikes 10mi in the same time it takes to bike 20mi with the wind. What is the speed of the wind?
Answer:
4.67 mph
Step-by-step explanation:
Speed with no wind = 14 mph
Let wind speed = w mph
Thus;
Speed with wind = 14 + w
Speed against the wind = 14 - w
Now, we are told that against the wind he bikes 10 miles.
Thus, from; time = distance/speed, we have;
Time = 10/(14 - w)
Also, we are told he biked 20 miles with the wind. Thus;
Time = 20/(14 + w)
We are told the times he used in both cases are the same.
Thus;
10/(14 - w) = 20/(14 + w)
Divide both sides by 10 to get;
1/(14 - w) = 2/(14 + w)
Cross multiply to get:
1(14 + w) = 2(14 - w)
14 + w = 28 - 2w
w + 2w = 28 - 14
3w = 14
w = 14/3
w = 4.67 mph
A pizza is to be cut into fifths. Each of these fifths is to be cut into thirds. What fraction of the pizza is each of the final pieces?
A study by researchers at a university addressed the question of whether the mean body temperature of an animal is 98 6°F Among other data, the researchers obtained the body temperatures of 109 healthy animals. Suppose you want to use those data to decide whether the mean body temperature of healthy animals is less than 98.6°F.
Required:
a. Determine the null hypothesis
b. Determine the alternative hypothesis
Answer:
H0 : μ ≥ 98.6
H1 : μ < 98.6
Step-by-step explanation:
The population mean temperature, μ = 98.6
The null hypothesis takes up the value of the population mean temperature as the initial truth ;
The alternative hypothesis on the other hand is aimed at using a sample size of 109 to establish if the mean temperature is less than the population mean temperature.
The hypothesis ;
Null hypothesis, H0 : μ ≥ 98.6
Alternative hypothesis ; H1 : μ < 98.6
If f(x) = x³ - 2, find f(3)
Answer:
25
Step-by-step explanation:
Assuming the equation is f(x) = x³ - 2
Plug in 3 for x
f(3) = 3³-2
= 27-2
=25
Answer:
25!
I hope it's helpful
In the diagram attached, ΔABC has coordinates A(1,1), B(4,1), and C(4,5).
Given the function rule
f(x, y) → (x − 5, −y − 2)
Describe the transformation as completely as possible.
The diagram is attached-- Thanks in advance!
(No this is not homework, I was using a study guide I found online to study for a test.)
Answer:
Step-by-step explanation:
ΔABC has the vertices as A(1, 1), B(4, 1) and C(4, 5).
Rule for the transformation has been given as,
f(x, y) → (x - 5, -y - 2)
By this rule vertices of the transformed image will be,
A(1, 1) → A'(1 - 5, -1 - 2)
→ A'(-4, -3)
B(4, 1) → B'(4 - 5, -1 - 2)
→ B'(-1, -3)
C(4, 5) → C'(4 - 5, -5 - 2)
→ C'(-1, -7)
What is
the solution to the system of equations graphed below?
Solve 2x2 - 9x - 5 = 0 by factoring.
AS IN THE PICTURE...........
A test is divided into 4 sets of problems with the same number pf problems in each set. Alice correctly solves 35 problems. How many problems are on the test if Alice solved more than 60 percent of all the problems, but less than 65 percent of all problems? Give all possible answers.
Answer:
54, 55, 56, 57, 58
Step-by-step explanation:
Answer:
56 problems
Step-by-step explanation:
Set up an equation.
[tex]\frac{3}{5}x<35<\frac{13}{20}x[/tex]
Why do we do this? We are told that she solved MORE than 60%, or [tex]\frac{3}{5}[/tex], and LESS than 65%, or [tex]\frac{13}{20}[/tex]. Therefore, if we set the TOTAL number of problems to x, we have an equation we can solve.
[tex]\frac{3}{5}x<35<\frac{13}{20}x\\[/tex]
Multiply all parts of the inequality by 20 to get rid of the denominators.
[tex]20*\frac{3}{5}x<20*35<20*\frac{13}{20}x\\ \\12x<700<13x[/tex]
Now we can solve TWO individual inequalities to isolate the x variable.
[tex]12x<700\\x<\frac{700}{12}\\x < 175/3\\x<58[/tex]
We can approximate 175/3 to about 58 (rounding down). We will sometimes round down when we have to deal with whole numbers.
The second inequality is as follows.
[tex]13x>700\\x>700/13\\x>53[/tex]
Therefore, we can combine the two inequalities.
[tex]53<x<58[/tex]
There were in between 53 and 58 questions. Since the number of questions must be a whole number, there can be 54, 55, 56, 57, OR 58. Why does 58 also work? When you plug 58 back into the original equation, you get that it STILL works. This is due to the fact that inaccuracies in computations allow you to round UP.
However, the last thing to keep in mind is that there are four sections with an equal number of questions. Meaning, the final answer has to be a multiple of four. The only multiple of 4 is 56; therefore, the final answer is 56.
Work out the length x. 14 cm 7 cm Х
Answer:
If you want the area of something with the sides 14cm and 7cm then it would be 98 cm.
Step-by-step explanation:
Area = length * width
Area = 14 cm * 7 cm
Area = 98 cm
3|3x+4|-7=5 please help
Answer:
[tex]x = 0[/tex]
Step-by-step explanation:
[tex]3 |3x + 4| - 7 = 5[/tex]
Add 7[tex]3 |3x + 4 | = 12[/tex]
Divide by 3.[tex] |3x + 4| = 4[/tex]
Remove the absolute value signs and left with:[tex]3x + 4 = 4[/tex]
Subtract[tex]3x = 0[/tex]
[tex]x = 0[/tex]
Verify if : (-30) x ( 13.+ (-3)] =[(-30) x 13] + [(-30) (-3)]
the following 3 shapes are made up of square, circles, and semi circles. Find the Area and perimeter of the shaded area. Write your answer as a completely simplified exact value in terms of pi
Answer:
Perimeter = 18 + 9pi
Area = 81 - 20.25*pi
Step-by-step explanation:
Perimeter = 9 + 9 + 2(2 pi r)/2 The twos cancel out.
Perimeter = 18 + 9*pi
Area of the square = 9 * 9 = 81 cm^2
Area of the 2 semicircles = 2 * pi * r^2/2
r = d/2
d = 9
r = 9/2 = 4.5
Area of the 2 semicircles = 2 (pi * 4.5^2)/2
Area of the 2 semicircles = 20.25 pi
Area of the blue figure = 81 - 20.25 pi
1. Suppose you have a variable X~N(8, 1.5). What is the probability that you have values between (6.5, 9.5)
Answer:
0.6826 = 68.26% probability that you have values in this interval.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
X~N(8, 1.5)
This means that [tex]\mu = 8, \sigma = 1.5[/tex]
What is the probability that you have values between (6.5, 9.5)?
This is the p-value of Z when X = 9.5 subtracted by the p-value of Z when X = 6.5. So
X = 9.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 8}{1.5}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
X = 6.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6.5 - 8}{1.5}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587
0.8413 - 0.1587 = 0.6826
0.6826 = 68.26% probability that you have values in this interval.
Which sets of values belong to the domain and range of a relation?
Answer:
Domain: input values, independent variables
Range: output vales, dependent variables
Step-by-step explanation:
Think of it like a graph: the domain are the x-values and the range is the y-values. if you're doing a problem with time, the time will go on the x-axis and cannot be influenced by the y-values, but the y-vales are depending on what the x-values are (independent/dependent). for the input/output, usually when solving equations on a graph, you plug in the x-value and find the y-value. you're INPUTTING the x-value to receive the OUPUT.
Domain = set of allowed inputs
The input x is the independent variable as it can do whatever it wants without relying on y.
-------------------------
Range = set of possible outputs
The output is the dependent variable. It depends on what the input x is. Often, we make y the output dependent variable.
-------------------------
For example, with y = 2x+5, we can plug in anything we want for x (it doesn't need to look to y for guidance or anything). Once we pick something for x, it will directly determine what y is.
Let's say we picked x = 10. That would mean y = 2x+5 = 2*10+5 = 25. The input x = 10 in the domain leads to y = 25 in the range. We see that the output y = 25 depends entirely on the independent input x = 10.
