To design a sine function with a period of 24 and minima and maxima at given times, we scale the function using a coefficient of 2π/24, shift the function to make the peak occur at x=16, and stretch it by a factor of 3 to make it go from 10 to 16.
Explanation:To design a sine function with a period of 24 and minima and maxima at given times, we first need to understand a few concepts about sine functions. The standard sine function, sine(x), has a period of 2π. Therefore, to stretch it to a period of 24 hours, we would scale the function using a coefficient of 2π/24 or π/12. Thus, our function becomes sine((π/12) x).
Next, we want to shift the function so its maximum occurs at t=16. Normally, the sine function peaks at π/2, so we need to shift the function to the right by an amount that makes the peak occur at x=16. This would be 16 - π/2, which gives us the function sine(π/12 x - 16 + π/2).
Finally, to stretch the function vertically to accommodate the minimum and maximum values of 10 and 16, we note that the amplitude of the sine function is usually 1 (from -1 to 1), so we need to stretch it by a factor of (16-10)/2 = 3 to make it go from 10 to 16. This gives us the function y= 3sin((π/12)x - 16 + π/2)+13.
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Suppose 60% of homes in Miami have a swimming pool and 30% have both a swimming pool and a Jacuzzi. What is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool?
Answer:
0.5 is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.
Step-by-step explanation:
We are given the following in the question:
S: Homes in Miami have a swimming pool
J: Homes in Miami have a jacuzzi
[tex]P(S) = 60\% = 0.6\\P(S\cap J) = 30\% = 0.3[/tex]
We have to find the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.
Thus, we have to calculation the conditional probability of having a jacuzzi given the house has a swimming pool.
[tex]P(J|S) = \dfrac{P(J\cap S)}{P(S)}\\\\P(J|S) = \displaystyle\frac{0.3}{0.6} = 0.5[/tex]
0.5 is the probability that a randomly selected home will have a Jacuzzi given that it has a swimming pool.
Find the equation of the plane that is parallel to the vectors left angle 3 comma 0 comma 3 right angle and left angle 0 comma 1 comma 3 right angle, passing through the point (2 comma 0 comma negative 1 ).
Answer:
[tex]x + 3y -z - 3 = 0[/tex]
Step-by-step explanation:
We have to find the equation of plane that is parallel to the vectors
[tex]\langle 3,0,3\rangle, \langle0,1,3\rangle[/tex]
The plane also passes through the point (2,0,-1).
Hence, the equation of plane s given by:
[tex]\displaystyle\left[\begin{array}{ccc}x-2&y-0&z+1\\3&0&3\\0&1&3\end{array}\right]\\\\=(x-2)(0-3) - (y-0)(9-0) + (z+1)(3-0)\\=-3(x-2)-9y+3(z+1)\\\Rightarrow -3x + 6 - 9y + 3z + 3 = 0\\\Rightarrow 3x + 9y -3z -9 = 0\\\Rightarrow x + 3y -z - 3 = 0[/tex]
It is the required equation of plane.
A student who has created a linear model is disappointed to find that herR2 value is a very low 13%. a) Does this mean that a linear model is not appropriate? Explain. b) Does this model allow the student to make accurate predictions? Explain.
Answer:
a) No it doesn't mean that linear model is inappropriate
b) No. The prediction using this model will not be accurate.
Step-by-step explanation:
a)
For answering this part, firstly consider the concept of [tex]R^{2}[/tex]
The [tex]R^{2}[/tex] also known as coefficient of determination is used to determine the amount of variability in dependent variable is explained by the linear model. Lower [tex]R^{2}[/tex] depicts that less variation of dependent is explained by the independent variable using the linear model. The linearity of model is determined by scatter plot. Thus, if the [tex]R^{2}[/tex] is lower, it doesn't mean that linear model is inappropriate.
b)
The predictions made by the model having lower [tex]R^{2}[/tex] value are erroneous. The model is used for prediction if the linear model explains the larger portion of variability in dependent variation. If the predictions made from the model that have lower [tex]R^{2}[/tex] value then the predicted values will not be close to the actual value and thus residuals will not be minimum as residuals are the difference of actual and predicted values.
Find the sales tax and total cost of a Sony Playstation that costs $172.99. The tax rate is
4%. Round your answer to the nearest cent.
Answer:
all work is shown and pictured
Answer:The total cost of the Sony Playstation is $179.9096
Step-by-step explanation:
The initial or regular cost of the Sony Playstation is $172.99.
The tax rate is 4%. Therefore, the value of the sales tax would be
4/100 × 172.99 = 0.04 × 172.99 = $6.9196
The total cost of the Sony Playstation would be the sum of the regular price and the sales tax. It becomes
172.99 + 6.9196 = $179.9096
The stop-board of a shot-put circle is a circular arc 1.22 m in length. The radius of the circle is 1.06 m. What is the central angle?
Answer:
Central angle= 1.15 radians
Step-by-step explanation:
[tex]Arc\,\,length=s= 1.22\,m\\Radius=r=1.06\,m\\\\Central\,\, angle=\theta=?\\\\Using\\\\ s=r\theta\\\\\theta=\frac{s}{r}\\\\\theta= \frac{1.22}{1.06}\\\\\theta=1.15 \,rad[/tex]
In a sample of 11 men, the mean height was 178 cm. In a sample of 30 women, the mean height was 167 cm. What was the mean height for both groups put together?
Answer:
I'm pretty sure it would be 345, just add the two 178 and 167
Philip ran out of time while taking a multiple-choice test and plans to guess on the last 444 questions. Each question has 555 possible choices, one of which is correct. Let X=X=X, equals the number of answers Philip correctly guesses in the last 444 questions. Assume that the results of his guesses are independent.
What is the probability that he answers exactly 1 question correctly in the last 4 questions?
Answer:
There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
Step-by-step explanation:
For each question, there are only two possible outcomes. Either it is correct, or it is not. This means that we use the binomial probability distribution to solve this problem.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
In this problem we have that:
There are four questions, so n = 4.
Each question has 5 options, one of which is correct. So [tex]p = \frac{1}{5} = 0.2[/tex]
What is the probability that he answers exactly 1 question correctly in the last 4 questions?
This is [tex]P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 1) = C_{4,1}*(0.2)^{1}*(0.8)^{3} = 0.4096[/tex]
There is a 40.96% probability that he answers exactly 1 question correctly in the last 4 questions.
Answer:
0.41
Step-by-step explanation:
kahn
Factor the GCF out of the trinomial on the left side of the equation. (2 points: 1 for the GCF, 1 for the trinomial)2x^2 + 6x - 362(x^2 + 3x - 18)
Answer:
2(x+6)(x-3)
Step-by-step explanation:
Factor the GCF out of the trinomial on the left side of the equation.
[tex]2x^2 + 6x - 36 =2(x^2 + 3x - 18)[/tex]
Greatest common factor of 2, 6, 18 is 2
so GCF is 2
divide each term when we take out GCF 2
so [tex]2(x^2 + 3x - 18)[/tex]
now factor the trinomial
product is -18 and sum is +3
6 times -3 is -18 and 6-3=3
[tex]2(x^2+3x-18)\\2(x+6)(x-3)[/tex]
Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why the system has a unique solution. What must be true of a linear system for it to have a unique solution? Select all that apply.
If the coefficient matrix has a pivot in each column, it means that it is shaped like this:
[tex]A=\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right][/tex]
So, the correspondant system
[tex]Ax = b[/tex]
will look like this:
[tex]\left[\begin{array}{cccc}a_{1,1}&a_{1,2}&a_{1,3}&a_{1,4}\\0&a_{2,2}&a_{2,3}&a_{2,4}\\0&0&a_{3,3}&a_{3,4}\\0&0&0&a_{4,4}\end{array}\right]\cdot \left[\begin{array}{c}x_1\\x_2\\x_3\\x_4\end{array}\right] = \left[\begin{array}{c}b_1\\b_2\\b_3\\b_4\end{array}\right][/tex]
This turn into the following system of equations:
[tex]\begin{cases}a_{1,1}x_1+a_{1,2}x_2+a_{1,3}x_3+a_{1,4}x_4=b_1\\a_{2,2}x_2+a_{2,3}x_3+a_{2,4}x_4=b_2\\a_{3,3}x_3+a_{3,4}x_4=b_3\\a_{4,4}x_4=b_4\end{cases}[/tex]
The last equation is solvable for [tex]x_4[/tex]: we easily have
[tex]x_4=\dfrac{b_4}{a_{4,4}}[/tex]
Once the value for [tex]x_4[/tex] is known, we can solve the third equation for [tex]x_3[/tex]:
[tex]x_3 = \dfrac{b_3-a_{3,4}x_4}{a_{3,3}}[/tex]
(recall that [tex]x_4[/tex] is now known)
The pattern should be clear: you can use the last equation to solve for [tex]x_4[/tex]. Once it is known, the third equation involves the only variable [tex]x_3[/tex]. Once
Assume that about 30% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 140 insurance claims to be processed in the next few days. What is the probability that from 45 to 47 of the claims have been padded?
a. 0.222
b. 0.167
c. 0.119
d. 0.104
e. 0.056
Answer:
For x=45
sample proportion=45/140=0.321
z=(0.321-0.30)/sqrt(0.3*(1-0.3)/140)
z=0.54
For x=47
sample proportion=47/140=0.336
z=(0.336-0.30)/sqrt(0.3*(1-0.3)/140)
z=0.93
Now,
P(0.54<z<0.93)=P(z<0.93)-P(z<0.54)
=0.8238-0.7054
=0.118
So,correct option is 0.119
An airplane has a front nad a rear door that are bother openedto allow passengers to exit when the plane lands. the planehas 100 passengers seated. the number of passengers exitingthrought the front door shougl have
a) a binomial distribution with mean 50
b) a binomial distribution with 100 trials but successprobability not equal to .5
c)a normal didtribution with a standard deviation of5
d) none of the above
Answer:
a) a binomial distribution with mean 50
Step-by-step explanation:
Given that an airplane has a front nad a rear door that are bother opened to allow passengers to exit when the plane lands. the plane has 100 passengers.
These 100 passengers can select either back door or front door with equal probability (assuming)
so probability for selecting front door = 0.5
No of passengers =100
Each passenger is independent of the other
Hence X no of passengers exiting through the front door is binomial with
p =0.5 and n =100
Mean of the variable X = np = 100(0.5) = 50
Variance of X = 100(0.5)(0.5)
Hence std dev = 10(0.5) = 5
So correct answers are
a) a binomial distribution with mean 50
1. Suppose the coefficient matrix of a linear system of four equations in four variables has a pivot in each column. Explain why the system has a unique solution.
2. What must be true of a linear system for it to have a unique solution?
Select all that apply.
A. The system has no free variables.
B. The system has one more equation than free variable.
C. The system is inconsistent.
D. The system is consistent. Your answer is correct.
E. The system has at least one free variable.
F. The system has exactly one free variable.
Answer:its A
Step-by-step explanation:it was
Suppose we want to choose 4 objects, without replacement, from 16 distinct objects (a) How many ways can this be done, if the order of the choices is not relevant? (b) How many ways can this be done, if the order of the choices is relevant?
Answer:
a) 1820 ways
b) 43680 ways
Step-by-step explanation:
When the order of the choices is relevant we use the permutation formula:
[tex]P_{n,x}[/tex] is the number of different permutations of x objects from a set of n elements, given by the following formula.
[tex]P_{n,x} = \frac{n!}{(n-x)!}[/tex]
When the order of choices is not relevant we use the combination formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, we have that:
[tex]x = 4, n = 16[/tex]
(a) How many ways can this be done, if the order of the choices is not relevant?
[tex]C_{16,4} = \frac{16!}{4!(12)!} = 1820[/tex]
(b) How many ways can this be done, if the order of the choices is relevant?
[tex]P_{16,4} = \frac{16!}{(12)!} = 43680[/tex]
We can choose 4 objects from 16 in 1820 ways if order doesn't matter (combination), and in 43680 ways if order does matter (permutation).
Explanation:The subject of this question is combinatorial mathematics. You're being asked to calculate combinations and permutations.
(a) If the order of the choices is not relevant, we are dealing with a combination. The formula for a combination is C(n, r) = n! / [r!(n-r)!], where n is the number of objects and r is the number of objects chosen. In this case, n = 16 and r = 4, so C(16, 4) = 16! / [4!(16-4)!] = 1820 combinations.
(b) If the order of the choices is relevant, we are dealing with a permutation. The formula for a permutation is P(n, r) = n! / (n-r)!. Again, n = 16 and r = 4, so P(16, 4) = 16! / (16-4)! = 43680 permutations.
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Based on a poll, a newspaper reported that between 52% and 68% of voters would be likely to vote for a schoolbond issue. What is the margin of error of the poll?
Answer:
The margin of error of the poll is 8%.
Step-by-step explanation:
This is a confidence interval. A confidence interval has both a lower end and an upper end.
The true proportion is the midpoint between the two ends.
The margin of error is the absolute difference between the proportion and the ends(which is the same, upper end - proportion = proportion - lower end),
In this problem, we have that:
The lower end is 52%.
The upper end is 68%.
The proportion is (52 + 68)/2 = 60%.
The margin of error is 60 - 52 = 68 - 60 = 8%.
Find the mean amount hospitals had to pay in wrong-site lawsuits. Round your answer to the nearest whole dollar.
Answer:
dont see much information here but as far as lawsuits go id aim for the highest answer
Step-by-step explanation:
_____________________________________
A student earned grades of Upper AA, Upper DD, Upper AA, Upper CC, and Upper BB. Those courses had the corresponding numbers of credit hours 44, 22, 22, 33, and 11. The grading system assigns quality points to letter grades as follows: Aequals=4; Bequals=3; Cequals=2; Dequals=1; Fequals=0. Compute the grade point average (GPA) as a weighted mean and round the result with two decimal places. If the Dean's list requires a GPA of 3.00 or greater, did this student make the Dean's list? The grade point average is nothing. (Round to two decimal places as needed.) Did this student make the Dean's list? A. Yes because at least two of the student grades are B or above B. No because the students GPA is not 4.0 C. NoNo because the student has at least one grade lessless than 3 D. NoNo because the student's GPA is lessless than 3.0
Answer:
The grade point average is 2.92The student didn't make the Dean's list because the student's GPA is less than 3.0Step-by-step explanation:
I take the grades as A,D,A,C,B not AA,DD,AA,CC,BB.I take numbers of credit hours as 4,2,2,3,1 not as 44, 22, 22, 33, and 11.Since quality points to letter grades are A=4; B=3; C=2; D=1; F=0, weighted mean is the sum of the qulity points times corresponding credit hours divided by the total credit hours:
[tex]\frac{(4*4) + (1*2) + (4*2) + (2*3) + (3*1)}{12}[/tex] ≈ 2.92
Since 2.92<3.0, the student is not in Dean's list.
An SRS of 350 350 high school seniors gained an average of ¯ x = 22.61 x¯=22.61 points in their second attempt at the SAT Mathematics exam. Assume that the change in score has a Normal distribution with standard deviation σ = 53.63 . σ=53.63. We want to estimate the mean change in score μ μ in the population of all high school seniors. (a) Using the 68 68 – 95 95 – 99.7 99.7 Rule or the z - z- table (Table A), give a 95 % 95% confidence interval ( a , b ) (a,b) for μ μ based on this sample.
Answer: (16.9914, 28.2286).
Step-by-step explanation:
The formula to find the confidence interval for population mean is given by :-
[tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = Sample mean
[tex]\sigma[/tex]= Population standard deviation
n= Sample size.
z* = Critical value.
Let μ be the mean change in score in the population of all high school seniors.
As per given , we have
n= 350
[tex]\overline{x}=22.61[/tex]
[tex]\sigma=53.63[/tex]
The critical z-value for 95% confidence interval is z*= 1.96 [From z-table]
Substitute all the value in formula , we get
[tex]22.61\pm (1.96)\dfrac{53.63}{\sqrt{350}}[/tex]
[tex]=22.61\pm (1.96)\dfrac{53.63}{18.708287}[/tex]
[tex]=22.61\pm (1.96)(2.8666)[/tex]
[tex]=22.61\pm (5.6186)[/tex]
[tex]=(22.61-5.6186,\ 22.61+5.6186) =(16.9914,\ 28.2286)[/tex]
Hence, the 95% confidence interval for [tex]\mu[/tex] is (16.9914, 28.2286).
In a right triangle ΔABC, the length of leg AC = 5 ft and the hypotenuse AB = 13 ft. Find the length of the angle bisector of angle ∠A.
The length of the angle bisector of angle ∠A is approximately 4.62 feet.
To find the length of the angle bisector of angle ∠A in triangle ΔABC, we can use the Angle Bisector Theorem, which states that in a triangle, the angle bisector of a vertex divides the opposite side into segments proportional to the adjacent sides.
In triangle ΔABC, let AD be the angle bisector of ∠A, where D lies on BC. According to the Angle Bisector Theorem:
AC/CD = AB/BD
Given AC = 5 ft and AB = 13 ft, we can plug in these values:
5/CD = 13/BD
To find BD, we use the Pythagorean theorem:
BD = √(AB² - AD²) = √(13² - 5²) = √(169 - 25) = √144 = 12 ft
Now, using the Angle Bisector Theorem:
5/CD = 13/12
Cross-multiply:
5 × 12 = 13 × CD
CD = (5 × 12) / 13 = 60 / 13 ≈ 4.62 ft
You and your friend play a game. You answer 80% of the questions correctly and your friend answers 0.60 of the questions correctly. What is the minimum number of questions in the game?
Answer:
5
Step-by-step explanation:
Assuming both players can answer the same question, the minimum number of questions is the smallest number that when multiplied by either 0.60 or 0.80 yields a whole number.
Let x be the number of questions, solving by trial and error:
[tex]if\ x=2\\x*0.8=1.6\\x*0.6=1.2\\\\if\ x=3\\x*0.8=2.4\\x*0.6=1.8\\\\if\ x=4\\x*0.8=3.2\\x*0.6=2.4\\\\if\ x=5\\x*0.8=4\\x*0.6=3\\\\[/tex]
Therefore, the minimum number of questions in the game is 5.
To find the minimum number of questions in a game where one person answers 80% correctly and another answers 60% correctly, calculate the LCM of the fractions' denominators. The result is 5 questions.
You and your friend have different accuracy rates when answering questions in a game. You answer 80% of the questions correctly, while your friend answers 60% of the questions correctly. To find the minimum number of questions in the game, we need to ensure that both percentages can correspond to whole numbers of questions.
Convert the percentages to fractions: You: [tex]\( \frac{80}{100} = \frac{4}{5} \)[/tex] and your friend: [tex]\( \frac{60}{100} = \frac{3}{5} \)[/tex]To find the smallest number of questions (N) that allows both fractions to be whole numbers, find the Least Common Multiple (LCM) of the denominators (5 in both cases).The LCM of 5 is 5 since it’s the same for both.Thus, the minimum number of questions in the game is 5.In a game with 5 questions:
You would answer 4 out of 5 questions correctly (80%).Your friend would answer 3 out of 5 questions correctly (60%).Therefore, the minimum number of questions in this game is 5.
Let V be the vector space of all 2 X 2 matrices over the field F. Prove that V has dimension 4 by exhibiting a basis for V which has four elements.
Answer:
See the proof below.
Step-by-step explanation:
We can define a basis of V with the following elements:
[tex]X_1=\begin{matrix}1 & 0 \\0 & 0 \end{matrix} [/tex]
[tex]X_2=\begin{matrix}0 & 1 \\0 & 0 \end{matrix} [/tex]
[tex]X_3=\begin{matrix}0 & 0 \\1 & 0 \end{matrix} [/tex]
[tex]X_4=\begin{matrix}0 & 0 \\0 & 1 \end{matrix} [/tex]
So then if we define the basis X as following:
[tex] X = [X_1, X_2, X_3, X_4][/tex]
[tex]X =[\begin{pmatrix}1 & 0\\0 & 0\end{pmatrix},\begin{pmatrix}0 & 1\\0 & 0 \end{pmatrix},\begin{pmatrix}0 & 0\\1 & 0\end{pmatrix},\begin{pmatrix}0 & 0\\0 & 1 \end{pmatrix}[/tex]
We see the the dimension for X is 4 [tex] dim (V) = 4[/tex] since the basis have a dimension of 4 [tex] dim (X) =4[/tex]
Final answer:
The vector space V of all 2 x 2 matrices over a field F has a basis consisting of four matrices which are linearly independent and span V. This basis demonstrates that V has a dimension of 4.
Explanation:
In order to prove that the vector space V of all 2 x 2 matrices over a field F has dimension 4, we need to exhibit a basis for V that consists of four linearly independent elements, which also span V. Consider the following 2 x 2 matrices as the candidate basis elements:
⬑ 1 0 ⬑These matrices are linearly independent and span the vector space of all 2 x 2 matrices. To show linear independence, assume that a linear combination of these matrices equals the zero matrix:
a ⬑ 1 0 ⬑ + b ⬑ 0 1 ⬑ + c ⬑ 0 0 ⬑ + d ⬑ 0 0 ⬑
⬑ 0 0 ⬑ ⬑ 0 0 ⬑ ⬑ 1 0 ⬑ ⬑ 0 1 ⬑
= ⬑ 0 0 ⬑
⬑ 0 0 ⬑
This equation leads to a = b = c = d = 0, which verifies the linear independence. Since we can represent any 2 x 2 matrix as a linear combination of these four basis matrices, they also span V, fulfilling both criteria for a basis. Hence, there are four basis elements, and therefore, the dimension of V is 4.
indicate if the following systems are lineare or non linjear systems d^2x/dt+5dx/dt+10x = 0
Answer: You have only provided one Differential Equation (DE), it looks like you intended listing more.
The equation you wrote contains an incorrect d²x/dt, it is likely to be d²x/dt² + 5dx/dt + 10x = 0, which is linear. Unless it is (dx/dt)² + 5dx/dt + 10x = 0, then it is nonlinear.
Not to worry though, I will explain what linear and nonlinear DE's are.
Step-by-step explanation:
LINEAR DE: This is the kind of DE in which the functions of the dependent variable are linear. There are no powers of the dependent variable and/or its derivatives, there are no products of the dependent variable and its derivative, there are no functions of the dependent variable like cos, sin, exp, etc.
Example:
* 5d²x/dt² + dx/dt - x = 2t
This is linear, as it satisfies all the conditions.
NONLINEAR DE: If any condition explained for linear DE is not satisfied, then it is called nonlinear.
Example:
* d²x/dt² - sinx = 0
This is nonlinear because of the presence of sinx.
* d²x/dt² + xdx/dt = 0
This is nonlinear because of the product of the dependent variable, x, and its derivative, dx/dt.
* d²x/dt² + x² = 0
This is nonlinear because a function of the dependent variable is not linear. You shouldn't have x².
* (dx/dt)³ + 3dx/dt = 0 is equally nonlinear. You can't have nonlinear functions of the dependent variable or its derivatives.
I hope this helps answer the remaining parts of your question.
The Honolulu advertiser stated that in Honolulu there was an average of 661 burglaries per 400,000 households in a given year. In the Kohola drive neighborhood there are 317 homes. Let r be the number of homes that will be burglarized in a year. Compute the probability for r > or equal to 2 round your answer to the nearest ten thousandth.
A)0.3010
B) 0.1013
C) 0.0144
D) 0.0902
E) 0.0369
Answer:
D) 0.0902
Step-by-step explanation:
Data provided in the question:
Probability of burglary, p = [tex]\frac{661}{400,000}[/tex]
= 0.00165
q = 1 - p
or
q = 1 - 0.00165
or
q = 0.99835
Now,
P(r ≥ 2) = 1 - P(r < 2)
= 1 - [ P(0) + P(1) ]
= 1 - [ [tex]^{317}C_0(0.00165)^0(0.99835)^{317-0}+^{317}C_1(0.00165)^1(0.99835)^{317-1}[/tex] ]
[ as P(x) = [tex]^nC_rp^rq^{n-r}[/tex]]
= 1 - [ 0.593 + 0.3168]
= 1 - 0.9098
= 0.0902
Hence,
Option (D) 0.0902
Evaluate the limit using the appropriate Limit Law(s). (If an answer does not exist, enter DNE.) lim x→8 1 + 3 x 5 − 6x2 + x3
Answer:
[tex] [tex] lim_{x \to 8} (1+3\sqrt{x})(1-6x^2 +x^3)[/tex]=[tex]1-384 +512+3\sqrt{8} -18(8)^{5/2} +3 (8)^{7/2} =1223.601[/tex]
And the limit on this case exists.
Step-by-step explanation:
We want to find the following limit:
[tex] lim_{x \to 8} (1+3\sqrt{x})(1-6x^2 +x^3)[/tex]
First we can distribute the polynomials like this:
[tex] lim_{x \to 8} (1-6x^2 +x^3+3\sqrt{x} -18 x^{5/2} +3x^{7/2})[/tex]
And Now we can use the distributive property for the limit and we got:
[tex] lim_{x \to 8} 1 - 6 lim_{x \to 8} x^2 + lim_{x \to 8} x^3 +3 lim_{x \to 8} \sqrt{x} -18 lim_{x \to 8} x^{5/2} + 3 lim_{x \to 8} x^{7/2}[/tex]
And now we can evaluate the limit and we got:
[tex] [tex] lim_{x \to 8} (1+3\sqrt{x})(1-6x^2 +x^3)[/tex]=[tex]1-384 +512+3\sqrt{8} -18(8)^{5/2} +3 (8)^{7/2} =1223.601[/tex]
And the limit on this case exists.
To solve limit problems in mathematics, limit laws are often very useful. In this specific case, as the function is a polynomial and defined for all real number values, a direct substitution of x=8 into the function is sufficient. Therefore, the limit as x approaches 8 for function 1 + 3x5 - 6x2 + x3 is calculable.
Explanation:In the field of mathematics, limit laws are used quite frequently for evaluating limits. In this case, we want to calculate the limit as x approaches 8 for the function 1 + 3x5 - 6x2 + x3.
For a given polynomial function like this one, an easy and very straightforward approach is to substitute the value x is approaching (in this scenario, x = 8) directly into the polynomial function.
So, after substitution, our function becomes: 1 + 3*(8)^5 - 6*(8)^2 + (8)^3. Simplifying it further, the limit as x approaches 8 of this function gives us a definite numeric value.
Always remember while applying limit laws, you might at times need the limit laws to evaluate complex limit problems but in this given scenario, direct substitution works perfectly fine because this polynomial function is defined for all real number values of X.
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Let R be the region bounded by the following curves. Use the disk or washer method to find the volume of the solid generated when R is revolved about the y-axis.
y= square root of (x/2) , y=0 , x=2
Answer:
3.2 pi
Step-by-step explanation:
Given 3 curves are:
y = square root ( x / 2)
y = 0
x = 2
Use washer method for hollow volumes.
Step 1: Compute A (y)
A ( y ) = pi * ( f_1 (y) ^2 - f_2 (y) ^2)
where,
f_1 (y) is the function further away from y axis
f_2 (y) is the function closer to y axis
f_1 (y) = 2
f_2 (y) = 2*y^2
A ( y ) = pi * ( 2 ^2 - (2*y) ^2)
A (y) = pi * (4 - 4*y^2)
A (y) = 4*pi * (1 - y^2)
Step 2: Compute V (y)
[tex]V = \int\limits^1_0 {A (y)} \, dy \\V = 4*pi\int\limits^1_0 {1 - y^2} \, dy\\\\V = 4 * pi* (y - 0.2 y^5) \limits^1_0\\\\V = 4*pi*(1 - 0.2)\\\\V = 3.2 pi[/tex]
Answer: V = 3.2 pi
Samples of skin experiencing desquamation are analyzed for both moisture and melanin content. The results from 100 skin samples are as follows: melanin content high low moisture high 13 10 content low 47 30 Let A denote the event that a sample has low melanin content, and let B denote the event that a sample has high moisture content. Determine the following probabilities. Round your answers to three decimal places (e.g. 98.765).
a) P(A)
b) P(B)
c) P (A|B)
d) P (BA)
Answer: a. 0.40 b. 0.23 c . 0.435 d . 0.25
Step-by-step explanation:
melanin content Total
high low
moisture high 13 10 23
content low 47 30 77
Total 60 40 100
Let A denote the event that a sample has low melanin content, and let B denote the event that a sample has high moisture content.
a) Total skin samples has low melanin content = 10+30=40
P(A)=[tex]\dfrac{40}{100}=0.40[/tex]
b) Total skin samples has high moisture content = 13+10=23
P(B) =[tex]\dfrac{23}{100}=0.23[/tex]
c) A ∩ B = Total skin samples has both low melanin content and high moisture content =10
P(A ∩ B) =[tex]\dfrac{10}{100}=0.10[/tex]
Using conditional probability formula , [tex]P (A|B)=\dfrac{P(A\cap B)}{P(B)}[/tex]
[tex]P (A|B)=\dfrac{0.10}{0.23}=0.434782608696\approx0.435[/tex]
d) [tex]P (B|A)=\dfrac{P(A\cap B)}{P(A)}[/tex]
[tex]P (B|A)=\dfrac{0.10}{0.40}=0.25[/tex]
A study of king penguins looked for a relationship between how deep the penguins dive to seek food and how long they stay underwater. For all but the shallowest dives, there is a linear relationship that is different for different penguins. The study report gives a scatterplot for one penguin titled "The relation of dive duration (DD) to depth (D)." Duration DD is measured in minutes, and depth D is in meters. The report then says, "The regression equation for this bird is: DD = 2.64 + 0.01 D."What is the slope of the regression line? __________?(Round your answer to the nearest hundredth.)
Answer:
The slope of the regression line is 0.01.
Step-by-step explanation:
The given regression equation for this bird is
[tex]DD=2.64+0.01D[/tex] .... (1)
where, DD is dive duration measured in minutes, and D is depth in meters.
The slope intercept form of a line is
[tex]y=mx+b[/tex] .... (2)
where, m is slope and b is y-intercept.
On comparing equation (1) and (2), we get
[tex]y=DD,x=D,m=0.01,b=2.64[/tex]
Since, m=0.01, therefore the slope of the regression line is 0.01.
How many 7/8 cup servings are in 1/2 of a cup of juice? (in simplest fraction form)
The result is [tex]\frac{4}{7}[/tex]
Step-by-step explanation:
In this problem, we are asked to find how many 7/8 cup servings are in 1/2 of a cup of juice.
Mathematically, this is equivalent to divide 1/2 by 7/8. So we can write:
[tex]\frac{1/2}{7/8}[/tex]
This can be rewritten as a multiplication by reversing the denominator:
[tex]\frac{1}{2}\cdot \frac{8}{7}[/tex]
Now we can perform the multiplication of both the numerator and the denominator:
[tex]\frac{1\cdot 8}{2\cdot 7}=\frac{8}{14}[/tex]
And simplifying (dividing by 2),
[tex]\frac{8}{14}=\frac{4}{7}[/tex]
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There are 4/7 servings of 7/8 cup in 1/2 cup of juice.
To determine the number of 7/8 cup servings in 1/2 of a cup of juice, divide the 1/2 cup of juice by 7/8 cup.
Now, the reciprocal of 7/8 and multiplying it by 1/2.
Reciprocal of 7/8 = 8/7
Now, perform the multiplication:
= (1/2 cup) * (8/7)
= (1 * 8) / (2 * 7)
= 8/14
= 4/7
Therefore,4/7 servings of 7/8 cup in 1/2 cup of juice.
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Find the vector representing the area of the triangle ABC where A=(4,5,6), B=(6,4,5) and C=(5,4,6) oriented so that it faces upward.
Answer: Area of triangle is √3 / 2
Step-by-step explanation:
The explanation can be found in the attached in picture
Which table represents the graph of a logarithmic function with both an x-and y-intercept?
Answer:
The answer is B
Step-by-step explanation:
Answer:
B. The second graph
Step-by-step explanation:
edge 2021 math assignment
For wages less than the maximum taxable wage base, Social Security contributions (including those for Medicare) by employees are 7.65% of the employee's wages.
(a) Find an equation that expresses the relationship between the wages earned (x) and the Social Security taxes paid (y) by an employee who earns less than the maximum taxable wage base.
Answer:
y = 0.0765x
Step-by-step explanation:
We have that:
y is the total taxes paid.
x is the total wages earned.
The total taxes paid is a function of the total wages earned.
For wages less than the maximum taxable wage base, Social Security contributions (including those for Medicare) by employees are 7.65% of the employee's wages.
So 7.65% of the total wages earned are paid in taxes. We write the percentage as a decimal, so 7.65/100 = 0.0765
So the answer for a) is:
y = 0.0765x
The relationship between the wages earned (x) and the Social Security taxes paid (y) can be expressed as a linear equation. The equation is y = 0.0765x, which means for every dollar earned, 7.65 cents are paid towards Social Security taxes.
Explanation:The relationship between the wages earned (x) and the Social Security taxes paid (y) can be expressed as a linear equation. Since the contribution is 7.65% of the wages, the equation becomes y = 0.0765x, where x stands for the wages earned, and y represents the employee's Social Security taxes paid.
This equation means that for every dollar earned, 7.65 cents are paid towards Social Security taxes. So, if an employee earns $1000, you would substitute x with 1000 to find the taxes payable. That is y = 0.0765 * 1000, which equates to $76.50
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