Answer: There are 4 people who only go to the game on Saturday.
Step-by-step explanation:
Let the number of people go on Saturday be n(A).
Let the number of people go on Sunday be n(B).
Since we have given that
n(A) = 8
n(B) = 12
n(A∪B) = 16
According to rules, we get that
[tex]n(A)+n(B)-n(A\cap B)=n(A\cup B)\\\\8+12-n(A\cap B)=16\\\\20-n(A\cap B)=16\\\\n(A\cap B)=20-16=4[/tex]
So, n(only go on Saturday) = n(only A) = n(A) - n(A∩B) = 8-4 = 4
Hence, there are 4 people who only go to the game on Saturday.
How many 3 digit pass codes can be made from the digits 0 to 9 if the first number is not allowed to be a 0?
Answer:
total 900 pass codes can be made.
Step-by-step explanation:
Given situation is 3 digit pass codes are required made from the digits 0 to 9.
But the first number is not allowed to be a 0.
So for the third place we have 10 choices ( 0,1,2,3,4,5,6,7,8,9 )
For the second place we have 10 choices ( 0,1,2,3,4,5,6,7,8,9 )
But for the first place we have 9 choices ( 1,2,3,4,5,6,7,8,9 )
( 9 × 10 × 10 ) = 900
Therefore, total 900 pass codes can be made from the digits 0 to 9.
Based on the diagram above, a student determined the hypotenuse of the triangle to be 6√3 Determine if the student's answer is correct. If it is not correct, find the correct length.
A. Yes, the student's answer is correct.
B. No, the hypotenuse should be 12√3
C. No, the hypotenuse should be 6√2
D. No, the hypotenuse should be 12.
Answer:
D) No, the hypotenuse should be 12.
Step-by-step explanation:
Hypotenuse is the side opposite to the 90 degrees angle.
'6' is the opposite side to the given angle i.e. it is opposite from angle 30 degrees.
Step 1: Use the sin formula to find the hypotenuse.
Sin (angle) = opposite/hypotenuse
Step 2: Substitute the values in the formula
Sin (30) = 6/hypotenuse
1/2 = 6/hypotenuse
hypotenuse = 6x2
hypotenuse = 12
Therefore, the answer is option D; No, the hypotenuse should be 12.
!!
Suppose you just received a shipment of thirteen televisions. Three of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
Answer: 0.4083
Step-by-step explanation:
Let D be the event of receiving a defective television.
Given : The probability that the television is defective :-
[tex]P(D)=\dfrac{3}{13}[/tex]
The formula for binomial distribution :-
[tex]P(X=x)=^nC_xp^x(1-p)^{n-x}[/tex]
If two televisions are randomly selected, compute the probability that both televisions work, then the probability at least one of the two televisions does not work is given by :_
[tex]P(X\geq1)=P(1)+P(2)\\\\=^2C_1(\frac{3}{13})^1(1-\frac{3}{13})^{2-1}+^2C_2(\frac{3}{13})^2(1-\frac{3}{13})^{2-2}\\\\=0.408284023669\approx0.4083[/tex]
Hence , the required probability = 0.4083
1) Emily wants to create snack bags for a trip she is going on. She has 6 granola bars and 10 pieces of dried fruit. If the snack bags should be identical without any food left over, what is the greatest number of snack bags Emily can make? Write answer in sentence form.
Answer: 2
Step-by-step explanation:
Given : The number of granola bars = 6
The number of pieces of dried fruit = 10
If the snack bags should be identical without any food left over, then the greatest number of snack bags Emily can make is the greatest common factor (GCF) of 6 and 10.
Since , factors of 6 = 1, 2, 3, 6
Factors of 10 = 1, 2, 5, 10
Hence, the greatest common factor of 6 and 10 = 2
Thus, the greatest number of snack bags Emily can make = 2.
An instructor at a major research university occasionally teaches summer session and notices that that there are often students repeating the class. Out of curiosity, she designs a random sample of students enrolled in summer sessions and counts the number repeating a class. She counts 105 students in the sample, of which 19 are repeating the class. She decides a confidence interval provides a good estimate of the proportion of students repeating a class. She wants a 95% confidence interval with a margin of error at most ????=0.025m=0.025 . She has no idea what the true proportion could be. How large a sample should she take? 250 1537 1500 400
Answer: 1537
Step-by-step explanation:
Given : Margin of error : [tex]E=0.025[/tex]
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=z_{0.025}=1.96[/tex]
The formula to calculate the sample size if prior estimate pf population proportion does not exist :-
[tex]n=0.25(\dfrac{z_{\alpha/2}}{E})^2\\\\\Rightarrow\ n=0.25(\dfrac{1.96}{0.025})^2\\\\\Rightarrow\ n=1536.64\approx1537[/tex]
Hence, she should take a sample with minimum size of 1537 .
Final answer:
To estimate the proportion of students repeating a class with a 95% confidence level and a margin of error of 0.025, the instructor would need a sample size of at least 1537 students.
Explanation:
To calculate the sample size needed for constructing a 95% confidence interval for the proportion of students who are repeating a class with a specified margin of error, we can use the formula for sample size in a proportion:
n = (Z² × p × (1-p)) / E²
Where:
Substituting the values, we get:
Thus, the calculation is:
n = (1.96² × 0.5 × (1 - 0.5)) / 0.025²
n = (3.8416 × 0.25) / 0.000625
n = 0.9604 / 0.000625
n = 1536.64
As we cannot have a fraction of a person, we would round up to the next whole number.
Therefore, the instructor would need to sample at least 1537 students.
Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = −xi − yj + z3k, S is the part of the cone z = x2 + y2 between the planes z = 1 and z = 2 with downward orientation.
The equation of the cone should be [tex]z=\sqrt{x^2+y^2}[/tex]. Parameterize [tex]S[/tex] by
[tex]\vec s(u,v)=u\cos v\,\vec\imath+u\sin v\,\vec\jmath+u\,\vec k[/tex]
with [tex]1\le u\le2[/tex] and [tex]0\le v\le2\pi[/tex]. Take the normal vector to [tex]S[/tex] to be
[tex]\vec s_v\times\vec s_u=u\cos v\,\vec\imath+u\sin v\,\vec\jmath-u\,\vec k[/tex]
Then the integral of [tex]\vec F[/tex] across [tex]S[/tex] is
[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\int_0^{2\pi}\int_1^2(-u\cos v\,\vec\imath-u\sin v\,\vec\jmath+u^3\,\vec k)\cdot(u\cos v\,\vec\imath+u\sin v\,\vec\jmath-u\,\vec k)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle\int_0^{2\pi}\int_1^2(-u^2-u^4)\,\mathrm du\,\mathrm dv[/tex]
[tex]=\displaystyle-2\pi\int_1^2(u^2+u^4)\,\mathrm du\,\mathrm dv=\boxed{-\frac{256\pi}{15}}[/tex]
To evaluate the surface integral, we need to find the flux of the vector field F across the oriented surface S. Given that F(x, y, z) = −xi − yj + z3k, and S is the part of the cone z = x2 + y2 between the planes z = 1 and z = 2 with downward orientation, we can proceed as follows: First, find the unit normal vector to the surface. Next, calculate the dot product between the vector field F and the unit normal vector. Finally, integrate the dot product over the surface S using the downward orientation.
Explanation:To evaluate the surface integral, we need to find the flux of the vector field F across the oriented surface S. Given that F(x, y, z) = −xi − yj + z3k, and S is the part of the cone z = x2 + y2 between the planes z = 1 and z = 2 with downward orientation, we can proceed as follows:
First, we need to find the unit normal vector to the surface. In this case, the unit normal vector is -∇(z - x^2 - y^2)/|∇(z - x^2 - y^2)|. By calculating the gradient and normalizing it, we get the unit normal vector as (2x, 2y, -1)/√(1 + 4x^2 + 4y^2).Next, we calculate the dot product between the vector field F and the unit normal vector. The dot product is -2x - 2y + z^3.Finally, we integrate the dot product over the surface S using the downward orientation. The integral is given by ∫∫S (-2x - 2y + z^3)dS.Learn more about Surface Integral here:https://brainly.com/question/32088117
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Which sampling technique is most desirable in quantitative research? a. random sample b. convenience sample c. purposeful sample d, criterion-based sample
Answer:
d) criterion-based sample
Step-by-step explanation:
Quantitative research analyzes a given data and forms conclusions based on the analytical tools implemented in them. The most commonly used method to gather data is through questionnaires. Now, the generation of the questionnaires is important as the hypothesis you propose must be reflected after analysis of the data i.e., the criterion for each question must be selected carefully.
Answer: A) random sample
Explanation:
Random sample is the best sampling technique for the quantitative research as, random sample comes under the probability sampling and it occurred randomization when the parameters of the sampling frame has the equal opportunity for sampling. When we want to draw the random sample, the research started with the list of elements and members and this list sometimes contain the sampling frame.
divide
(3x^2 + 9x + 7) divide by (x+2)
Answer:
The remainder is: 3x+3
The quotient is: 1
Step-by-step explanation:
We need to divide
(3x^2 + 9x + 7) by (x+2)
The remainder is: 3x+3
The quotient is: 1
The solution is attached in the figure below.
Answer:
[tex]3x+3+\frac{1}{x+2}[/tex]
Step-by-step explanation:
We are to divide the polynomial [tex]3x^2 + 9x + 7[/tex] by [tex]x+2[/tex].
For that, we will first divide the leading coefficient of the numerator [tex]\frac{3x^2}{x}[/tex] by the divisor.
So we get the quotient: [tex]3x[/tex] and will multiply the divisor [tex]x+2[/tex] by [tex]3x[/tex] to get [tex]3x^2+6x[/tex].
Next, we will subtract [tex]3x^2+6x[/tex] from [tex]3x^2 + 9x + 7[/tex] to get the remainder [tex]3x+7[/tex].
Therefore, we get [tex]3x+\frac{3x+7}{x+2}[/tex].
Now again, dividing the leading coefficient of the numerator by the divisor [tex]\frac{3x}{x}[/tex] to get quotient [tex]3[/tex].
Then we will multiply [tex]x+2[/tex] by [tex]3[/tex] to get [tex]3x+6[/tex].
Then, we will subtract [tex]3x+6[/tex] from [tex]3x+7[/tex] to get the new remainder [tex]1[/tex].
Therefore, [tex]\frac{3x^2 + 9x + 7}{x+2}=3x+3+\frac{1}{x+2}[/tex]
Suppose that 15% of people dont show up for a flight, and suppose that their decisions are independent. how many tickets can you sell for a plane with 144 seats and be 99% sure that not too many people will show up.
The book says to do this by using the normal distribution function and that the answer is selling 157 tickets.
Answer: 157 tickets
Explanation:
The people not showing up for the flight can be treated as from Binomial distribution.
The binomial distribution B(n, p) is approximately close to the normal i.e. N(np, np(1 − p)) for large 'n' and for 'p' and neither too close to 0 nor 1 .
Now, Let us assume 'n' = n
and we are given
p=0.15
So now B(n,0.15n) follows Normal distribution
u=n
[tex]\sigma^{2}[/tex] = 0.15n
We have to calculate P(X<144) with 99% accuracy
P(X<144) = P(Z<z)
where;
z= [tex](144-\bar{X})\div \sigma[/tex]
z score for 99% is 2.33
i.e.
[tex](144-\bar{X})\div \sigma = (144-n)/\sqrt{np} = 2.33\\\ (144-n)^{2} = \ np*2.33^{2}\\\ 20736 +n^{2} - 288n = 0.15n*5.43\\\ n^{2} - 288.81n + 20736=0[/tex]
solving this we will get one root nearly equal to 157 and other root as 133
Hence the answer is 157.
segment M'N' has endpoints located at M' (−2, 0) and N' (2, 0). It was dilated at a scale factor of 2 from center (2, 0). Which statement describes the pre-image? segment MN is located at M (0, 0) and N (2, 0) and is half the length of segment M'N'. segment MN is located at M (0, 0) and N (2, 0) and is twice the length of segment M'N' . segment MN is located at M (0, 0) and N (4, 0) and is half the length of segment M'N' . segment MN is located at M' (0, 0) and N (4, 0) and is twice the length of segment M'N' .
Answer:
A. MN is located at M 0,0) and N (2, 0) is half the length of M'N'.
Step-by-step explanation:
MN was dilated with a factor 2 is is half the length of M'N'.
MN is located at M(0,0) and N(2,0) as well as it's length would be half the M'N' length. A further explanation is below.
According to the question,
M'N' is a line with,
M' = (-2, 0)N' = (2, 0)Since,
Center of dilation = N' = (2,0)
Just because M'N' seems to be the dilated image of MN by something like a factor of two. It follows that M must have been at (0,0).It's two units left from the center of dilation.So,
→ [tex]M' = 2\times 2[/tex]
[tex]= 4 \ units[/tex]
Since the dilation is (2, 0), then
→ [tex]M' = (2-4, 0)[/tex]
[tex]= (-2,0)[/tex]
M'N' is twice then MN. Thus the above answer is correct.
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\sum_{n=1}^{\infty } ((-1^n)/n)x^n
Find the interval of convergence.
Answer:
(-1,1).
Step-by-step explanation:
We need to calculate [tex]\lim_{n \to \infty}\frac{| a_{n+1}|}{| a_{n}|} = \frac{1}{R}[/tex] where R is the radius of convergence.
[tex]\lim_{n \to \infty}\frac{\frac{|(-1)^{n+1}|}{|n+1|}}{\frac{|(-1)^{n}|}{|n|}}[/tex]
[tex]\lim_{n \to \infty}\frac{\frac{1}{|n+1|}}{\frac{1}{|n|}}[/tex]
[tex]\lim_{n \to \infty}\frac{|n|}{|n+1|}[/tex]
Applying LHopital rule we obtaing that the limit is 1. So [tex]1=\frac{1}{R}[/tex] then R = 1.
As the serie is the form [tex](x+0)^{n}[/tex] we center the interval in 0. So the interval is (0-1,0+1) = (-1,1). We don't include the extrem values -1 and 1 because in those values the serie diverges.
Without sketching the graph, find the x intercepts and y-intercepts of the graph of the equation 2x+3y=12 What isjare the x-intercept(s)? Select the correct choice below and, il necessary, il in the answer box within your choice ? A. The x intercept(s) isare? O B. There are no x-intercepts (Type an integer or a simplifted fraction Use a comma to separate answers as needed ) Click to select and enter your answeris) and then click Check Answer Clear All 0
Answer:
x-intercept: (6,0)
y-intercept: (0,4)
Step-by-step explanation:
The x-intercepts lay on the x-axis and therefore their y-coordinate is 0.
To find the x-intercept, you set y to 0 and solve for x.
2x+3y=12
Set y=0.
2x+3(0)=12
2x+0 =12
2x =12
Divide both sides by 2:
x =12/2
x =6
The x-intercept is (x,y)=(6,0).
The y-intercepts lay on the y-axis and therefore their x-coordinate is 0.
To find the y-intercept, you set x to 0 solve for y.
2x+3y=12
2(0)+3y=12
0+3y =12
3y =12
Divide both sides by 3:
y =12/3
y =4
The y-intercept is (0,4).
The x-intercept of the equation 2x + 3y = 12 is (6,0) and y-intercept is (0,4).
To find the x-intercept of the equation 2x + 3y = 12, we set y to 0 and solve for x:
2x + 3(0) = 12
2x = 12
x = 6
So, the x-intercept is (6,0).
To find the y-intercept, we set x to 0 and solve for y:
2(0) + 3y = 12
3y = 12
y = 4
The y-intercept is (0,4).
what is the solution of the inequality shown below? c+6>-1
Answer:
c > -7
Step-by-step explanation:
Isolate the variable c. What you do to one side, you do to the other. Subtract 6 from both sides:
c + 6 (-6) > -1 (-6)
c > -1 - 6
Simplify.
c > (-1 - 6)
c > - 7
c > -7 is your answer.
~
Answer:
[tex]\huge \boxed{c>-7}[/tex]
Step-by-step explanation:
Subtract by 6 from both sides of equation.
[tex]\displaystyle c+6-6>-1-6[/tex]
Simplify, to find the answer.
[tex]\displaystyle -1-6=-7[/tex]
[tex]\displaystyle c>-7[/tex], which is our final answer.
A bag contains the letters from the words SUMMER VACATION. You Randomly choose a letter A, and do not replace it. Then choose another letterA.. What is the probability that both letters are A's??
Answer:
1/91
Step-by-step explanation:
SUMMER VACATION
There are 14 letters, 2 of them are A's
P (1st letter is an A) = 2/14=1/7
Then we keep the A
SUMMER VCATION
There are 13 letters, 1 of them is an A's
P (2nd letter is an A) = 1/13
P (1st A, 2nd A) = 1/7 * 1/13 = 1/91
Answer:
1/91
Step-by-step explanation:
Compute the following binomial probabilities directly from the formula for b(x; n, p). (Round your answers to three decimal places.) (a) b(5; 8, 0.25) .023 (b) b(6; 8, 0.65) .259 (c) P(3 ≤ X ≤ 5) when n = 7 and p = 0.55 .745 (d) P(1 ≤ X) when n = 9 and p = 0.1 .613
We know that the binomial theorem for finding the probability of x success out of a total of n experiments is given by:
[tex]b(x;n;p)=n_C_x\cdot p^x\cdot (1-p)^{n-x}[/tex]
(a)
b(5; 8, 0.25)
is given by:
[tex]8_C_5\cdot (0.25)^5\cdot (1-0.25)^{8-5}\\\\=8_C_5\cdot (0.25)^5\cdot (0.75)^3\\\\=56\cdot (0.25)^5\cdot (0.75)^3\\\\=0.023[/tex]
Hence, the answer is: 0.023
(b)
b(6; 8, 0.65)
i.e. it is calculated by:
[tex]=8_C_6\cdot (0.65)^6\cdot (1-0.65)^{8-6}\\\\=8_C_6\cdot (0.65)^6\cdot (0.35)^2\\\\=0.259[/tex]
Hence, the answer is: 0.259
(c)
P(3 ≤ X ≤ 5) when n = 7 and p = 0.55
[tex]P(3\leq x\leq 5)=P(X=3)+P(X=4)+P(X=5)[/tex]
Now,
[tex]P(X=3)=7_C_3\cdot (0.55)^3\cdot (1-0.55)^{7-3}\\\\P(X=3)=7_C_3\cdot (0.55)^3\cdot (0.45)^{4}\\\\P(X=3)=0.239[/tex]
[tex]P(X=4)=7_C_4\cdot (0.55)^4\cdot (1-0.55)^{7-4}\\\\P(X=4)=7_C_4\cdot (0.55)^4\cdot (0.45)^{3}\\\\P(X=4)=0.292[/tex]
[tex]P(X=5)=7_C_5\cdot (0.55)^5\cdot (1-0.55)^{7-5}\\\\P(X=3)=7_C_5\cdot (0.55)^5\cdot (0.45)^{2}\\\\P(X=3)=0.214[/tex]
Hence,
[tex]P(3\leq x\leq 5)=0.745[/tex]
(d)
P(1 ≤ X) when n = 9 and p = 0.1 .613
[tex]P(1\leq X)=1-P(X=0)[/tex]
Also,
[tex]P(X=0)=9_C_0\cdot (0.1)^{0}\cdot (1-0.1)^{9-0}\\\\i.e.\\\\P(X=0)=1\cdot 1\cdot (0.9)^9\\\\P(X=0)=0.387[/tex]
i.e.
[tex]P(1\leq X)=1-0.387[/tex]
Hence, we get:
[tex]P(1\leq X)=0.613[/tex]
To compute binomial probabilities using the formula b(x; n, p), you can substitute the values of x, n, and p into the formula and solve for the probability. For example, b(5; 8, 0.25) represents the probability of getting exactly 5 successes in 8 trials with a success probability of 0.25. (a) b(5; 8, 0.25) = 0.023. (b) b(6; 8, 0.65) = 0.259. (c) P(3 ≤ X ≤ 5) when n = 7 and p = 0.55 is approximately 0.745. (d) P(1 ≤ X) when n = 9 and p = 0.1 is approximately 0.613.
Explanation:Binomial probabilities can be calculated using the formula for b(x; n, p). For example, to calculate b(5; 8, 0.25), you can use the formula:
[tex]b(5; 8, 0.25) = C(8, 5) * (0.25)^5 * (0.75)^3[/tex]
where C(8, 5) represents the number of combinations of 8 items taken 5 at a time. Solving this equation will give you the probability of getting exactly 5 successes in 8 trials with a success probability of 0.25.
Similarly, for b(6; 8, 0.65), you can use the formula:
[tex]b(6; 8, 0.65) = C(8, 6) * (0.65)^6 * (0.35)^2[/tex]
where C(8, 6) represents the number of combinations of 8 items taken 6 at a time. Solving this equation will give you the probability of getting exactly 6 successes in 8 trials with a success probability of 0.65.
(c) To calculate the probability of 3 ≤ X ≤ 5 when n = 7 and p = 0.55, you need to calculate the probabilities of 3, 4, and 5 successes individually and then sum them up.
(d) To calculate P(1 ≤ X) when n = 9 and p = 0.1, you need to calculate the probabilities of 1, 2, 3, ..., 9 successes individually and then sum them up.
The weaknesses of content analysis include:
A. its use influences that which is being studied.
B. if you make a coding error you must recode all of your data.
C. it’s limited to examining social artifacts.
D. it requires special equipment.
E. a researcher cannot use it to study change over time.
Answer: The weaknesses of content analysis include: if you make a coding error you must recode all of your data.
Explanation:
Content analysis is a method for analyse documents,communication artifacts, which might be of various formats such as pictures, audio or video. Content analysis can provide valuable or cultural insights over time through analysis .
But it is more time consuming and subject to increased error . There is no theoretical base in order to create relationship between text. So in case if we make coding error then we must recode all data .
Hence option (B) is correct
Content analysis weaknesses include potential influence on subject under study, the need to recode all data if a coding error occurs, limitation to studying social artifacts, requirement of special equipment, and misconception that it can't study change over time.
Explanation:The weaknesses of content analysis include:
Its use influences that which is being studied. This is a potential bias that can affect the reliability of results as the very act of studying a social artifact can change it.If you make a coding error, you must recode all of your data. This can be time-consuming and introduce additional errors.It's limited to examining social artifacts. This means it might not be a suitable method for all research questions.It requires special equipment. Although not a primary issue, but it may make the method inaccessible for some researchers.A researcher cannot use it to study change over time. This isn't entirely true, content analysis can be longitudinal, studying changes over designated periods.Learn more about Content Analysis here:https://brainly.com/question/32294663
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Suppose that a population of bacteria triples every hour and starts with 400 bacteria. Find an expression for the number n of bacteria after t hours. n(t) = Use it to estimate the rate of growth of the bacteria population after 3.5 hours. (Round your answer to the nearest whole number.)
The bacterial population's growth is represented by the exponential growth function n(t) = 400 * 3^t, where 400 is the initial number of bacteria and t is the time in hours. After 3.5 hours, the population is estimated to be approximately 21236 bacteria.
Explanation:The population of the bacteria can be modeled by an exponential growth function, specifically by considering its constant rate of tripling every hour. If we denote No as the initial number of bacteria, which is 400, and t as the time in hours, the number of bacteria n after time t would be represented by the function n(t) = No * 3^t. In this case, n(t) = 400 * 3^t.
Now, to estimate the rate of growth of the bacteria population after 3.5 hours, we substitute t = 3.5 into the equation which gives n(3.5) = 400 * 3^3.5. Calculating this to the nearest whole number gives approximately 21236, which represents the size of the bacteria population after 3.5 hours. This indicates a significant increase, a characteristic of exponential growth commonly observed in prokaryotes like bacteria under suitable conditions.
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To find an expression for the number of bacteria after t hours, we can use the following formula:
n(t) = 400 * [tex]3^{t}[/tex]
Now, let’s estimate the rate of growth after 3.5 hours:
n(3.5) = 400 * [tex]3^{3.5}[/tex]
Calculating this:
n(3.5) ≈ 400 × [tex]3^{3.5}[/tex] ≈ 400 × 46.8 ≈ 18,706.15
Rounded to the nearest whole number, the estimated population after 3.5 hours is 18,706 bacteria.
3. Find the inverse Laplace transform of F(s) = (-4s-9) / (s^2 + 25-8) f(t) =
[tex]f(s)\Longrightarrow L^{-1}=\{\frac{-4s-9}{s^2+25-8}\}[/tex]
First dismantle,
[tex]L^{-1}=\{-\frac{4s}{s^2+25-8}-\frac{9}{s^2+25-8}\}[/tex]
Now use the linearity property of Inverse Laplace Transform which states,
For functions [tex]f(s),g(s)[/tex] and constants [tex]a, b[/tex] rule applies,
[tex]L^{-1}=\{a\cdot f(s)+b\cdot g(s)\}=aL^{-1}\{f(s)\}+bL^{-1}\{f(s)\}[/tex]
Hence,
[tex]-4L^{-1}\{\frac{s}{s^2+25-8}\}-9L^{-1}\{\frac{1}{s^2+25-8}\}[/tex]
The first part simplifies to,
[tex]
L^{-1}\{\frac{s}{s^2+25-8}\} \\
\frac{d}{dt}(\frac{1}{\sqrt{17}}\sin(t\sqrt{17})) \\
\cos(t\sqrt{17})
[/tex]
The second part simplifies to,
[tex]
L^{-1}\{\frac{1}{s^2+25-8}\} \\
\frac{1}{\sqrt{17}}\sin(t\sqrt{17})
[/tex]
And we result with,
[tex]\boxed{-4\cos(t\sqrt{17})-\frac{9}{\sqrt{17}}\sin(t\sqrt{17})}[/tex]
Hope this helps.
If you have any additional questions please ask. I made process of solving as quick as possible therefore you might be left over with some uncertainty.
Hope this helps.
r3t40
Prove that n is odd if and only if 3n + 6 is odd by contradiction.
Step-by-step explanation:
o - odd number
e - even number
n + e =o, if n is odd...rule 1
n + e = e, if n is even...rule 2
n × o = o, if n is odd...rule 3
n × o = e, if n is even...rule 4
thus if 3n +6 = o,
then 3n must be odd, following rule 1
=> 3n = o, then n is an odd number, following rule 3
Determine if checking 100 applicants to see if they were admitted to Park University is a binomial experiment or not. Explain
Answer:
This is a binomial experiment
Step-by-step explanation:
Binomial experiment is an experiment in which for each trial there are only two outcomes.
In case of the given experiment, it is being asked either the applicants were admitted to the Park university or not, it has only two outcomes, Yes and no. So having only two options as outcomes this experiment is a binomial experiment ..
Find the fixed points of f(x) = 2x - x3 and determine their stability.
Answer with explanation:
⇒ A point k is said to be fixed point of function, f(x) if
f(k)=k.
The given function is
f(x)=2 x - x³
To determine the fixed point
f(k)=2 k - k³=k
→2 k -k -k³=0
→k -k³=0
→k×(1-k²)=0
→k(k+1)(k-1)=0
→k=0 ∧ k+1=0∧k-1=0
→k=0∧ k= -1 ∧ k=1
So, the three fixed points are=0,1 and -1.
To Check Stability of fixed point
1.⇒ f'(x)=2-3 x²
|f'(0)|=|2×0-0³|=0
⇒x=0, is Superstable point.
2.⇒|f'(-1)|=2 -3×(-1)²
=2 -3
= -1
|f'(-1)| <1
⇒x= -1, is stable point.
3.⇒|f'(1)|=2 -3×(1)²
=2 -3
= -1
|f'(1)| <1
⇒x= 1, is also a stable point.
⇒⇒There are two points of Stability,which are, x=1 and , x=-1.
At a certain concert, 73 % of the audience was under 20 years old. A random sample of n = 146 members of the audience was selected. Find the value of , the mean of the distribution of sample proportions.
Answer: p = 0.73
Step-by-step explanation:
Given that,
73% of the audience was under 20 years old :
so, probability (p) = 0.73
n = 146
Mean of the distribution of sample proportion = ?
According to central limit theorem,
np(1-p) ≥ 10
146 × 0.73(0.27) ≥ 10
28.77 ≥ 10
∴ Central limit theorem assumes that the sample distribution of the sample proportion is normally distributed.
Hence, the mean of the distribution of sample proportion:
μ = p = 0.73
Question 2: Find the midpoint between the points (1, 4) and (2, 3).
Question 2 options:
(3, 7)
(1/2, -1/2)
(0, 0)
(3/2, 7/2)
Answer:
The answer is (3/2, 7/2)
Step-by-step explanation:
1+2 = 3
3/2 = 1.5
3+4 = 7
7/2 = 3.5
Answer: last option.
Step-by-step explanation:
Given two points:
[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
You can find the midpoint between them by using the following formula:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Then, given the point (1, 4) and the point (2, 3), you can identify that:
[tex]x_1=1\\x_2=2\\y_1=4\\y_2=3[/tex]
Therefore, the final step is to substitute values into the formula:
[tex]M=(\frac{1+2}{2},\frac{4+3}{2})\\\\M=(\frac{3}{2},\frac{7}{2})[/tex]
Laura is planning to buy two 5-lb bags of sugar, three 5-b bags of flour, two 1-gal cartons of milk, and three 1-dozen cartons of large eggs. The prices of these items in three neighborhood supermarkets are as follows Milk Eggs (1-doren carton) Sugar (5-lb bag) Flour (1-gal carton) (5-lb bag) Supermarket I Supermarket II Supermarket 11 $3.15 $3.79 $2.99 $3.49 $2.99 $2.89 $2.79 $3.29 $3.74 $2.98 $2.89 $2.99 (a) Write a 3x 4 matrix A to represent the prices (in dollars) of the items in the three supermarkets Am (b) Write a 4x1 matrix B to represent the quantities of sugar, flour, milk, and eggs that Laura plans to purchase in the three supermarketts (c) Use matrix multiplication to find a matrix C that represents Laura's total outlay (in dollars) at each supermarket C-
At which supermarket should she make her purchase if she wants to minimize her cost? (Assume that she will shop at only one supermarket.) O supermarket I O supermarket II O supermarket III Need Help? Read It
Answer:
(a, b) see the input matrices in the calculator image below
(c) see the output matrix in the calculator image below
Laura should use Supermarket II.
Step-by-step explanation:
(a) Your data is not clearly identified, so we have assumed that the item costs are listed for one supermarket before they are listed for the next. Then your matrix A will be ...
[tex]A=\left[\begin{array}{cccc}3.15&3.79&2.99&3.49\\2.99&2.89&2.79&3.29\\3.74&2.98&2.89&2.99\end{array}\right][/tex]
__
(b) The column matrix of purchase amounts will be ...
[tex]B=\left[\begin{array}{c}2&3&2&3\end{array}\right][/tex]
__
(c) It is somewhat tedious to do matrix multiplication by hand, so we have let a calculator do it. Some calculators offer easier data entry than others, and some insist that data be entered into tables before any calculation can be done. We have chosen this one (attached), not because its use is easiest, but because we can post a picture of the entry and the result.
[tex]C=\left[\begin{array}{c}34.12&30.10&31.17\end{array}\right][/tex]
Laura's total bill is least at Supermarket II.
_____
As you know, the row-column result of matrix multiplication is the element-by-element product of the 'row' of the left matrix by the 'column' of the right matrix. Here, that means the 2nd row 1st column of the output is computed from the 2nd row of A and the 1st (only) column of B:
2.99·2 +2.89·3 +2.79·2 +3.29·3 = 5.98 +8.67 +5.58 +9.87
= 30.10
Please show work,
A speedboat is traveling 40 knots. How fast is that in miles per hour?
Step-by-step explanation:
thus is basically all I could get I hope that this helps a little bit :)
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = t2 + 35 , y = ln(t2 + 35), z = t; (6, ln(36), 1)
Step-by-step explanation:
i think the answer is 42 to be exacr
Determine if the finite correction factor should be used. If so, use it in your calculations when you find the probability. In a sample of 700 gas stations, the mean price for regular gasoline at the pump was $ 2.837 per gallon and the standard deviation was $0.009 per gallon. A random sample of size 55 is drawn from this population. What is the probability that the mean price per gallon is less than $2.834?
Answer: 0.9932
Step-by-step explanation:
Given : Mean : [tex]\mu=\$2.837\text{ per gallon }[/tex]
Standard deviation : [tex]\sigma = \$0.009\text{ per gallon}[/tex]
a) The formula for z -score :
[tex]z=\dfrac{x-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
Sample size = 55
For x= $2.834 ,
[tex]z=\dfrac{2.834-2.837}{\dfrac{0.009}{\sqrt{55}}}\approx2.47[/tex]
The p-value = [tex]P(z<2.47)=[/tex]
[tex]0.9932443\approx0.9932[/tex]
Thus, the probability that the mean price per gallon is less than $2.834 is approximately 0.9932 .
The question asks about finding the probability that the mean price per gallon of gas is less than $2.834. This is a statistics question and requires calculation of Z-score and the finite correction factor should be considered due to our sample size being more than 5% of the population.
Explanation:The question asks about the probability of a certain mean price per gallon for a sub-sample drawn from a larger population. In statistics, we often use Z-scores to calculate the probability of a score occurring within a standard distribution, but the entire population parameters should be known. Hence, we should use the finite correction factor (a.k.a the population correction factor) due to our sample size being more than 5% of the population.
In this case, the Z-score is calculated as follows:
Z = (X - μ) / (σ/√n)Where X = sample mean = 2.834, μ = population mean = 2.837, σ = standard deviation = 0.009, and n = sample size = 55.The finite correction factor = √((N-n)/(N-1))Now, calculate Z with the finite correction factor and find the corresponding probability from the Z-table.Learn more about Probability here:https://brainly.com/question/32117953
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Use set-builder notation to write the following sets whose elements are terms of arithmetic sequence
A. (2,4,6,8,10,.....)
B. ( 1,3,5,7,....)
Answer:
A. [tex]\text{Set builder}=\{2x:x\in Z,x>0\}[/tex]
B. [tex]\text{Set builder}=\{2x-1:x\in Z,x>0\}[/tex]
Step-by-step explanation:
Set builder form is a form that defines the domain.
A.
The given arithmetic sequence is
2,4,6,8,10,.....
Here all terms are even numbers. The first term is 2 and the common difference is 2.
All the elements are multiple of 2. So, the elements are defined as 2x where x is a non zero positive integer.
The set of all 2x such that x is an integer greater than 0.
[tex]\text{Set builder}=\{2x:x\in Z,x>0\}[/tex]
Therefore the set builder form of given elements is [tex]\{2x:x\in Z,x>0\}[/tex].
B.
The given arithmetic sequence is
1,3,5,7,....
Here all terms are odd numbers. The first term is 1 and the common difference is 2.
All the elements are 1 less than twice of an integer. So, the elements are defined as 2x-1 where x is a non zero positive integer.
The set of all 2x-1 such that x is an integer greater than 0.
[tex]\text{Set builder}=\{2x-1:x\in Z,x>0\}[/tex]
Therefore the set builder form of given elements is [tex]\{2x-1:x\in Z,x>0\}[/tex].
define the variables, write a system if equations corresponding to the problem, and solve the problem. 2. A group of four golfers pays $150 to play a round of golf. Of these four, one is a member of the club and three are nonmembers. Another group of golfers consists of two members and one nonmember and pays a total of $75. What is the cost for a member to play a round of golf, and what is the cost for a nonmember?
Answer: Cost of member = $15 and Cost of non member = $45
Step-by-step explanation:
a) Define variables.
Let x be the cost of member.
Let y be the cost of non member.
b) Write a system of equations:
According to question, we get that
x+3y=$150--------------(1)
2x+y=$75---------------(2)
Now, we need to calculate the cost for a member and a non member.
Using graphing method, we get that (15,45) is the solution set.
Hence, cost of member = $15 and Cost of non member = $45
Please help me with this
Answer:
Option 2: m∠1 = 147°, m∠2 = 80°, m∠3 = 148°
Step-by-step explanation:
Step 1: Consider triangle ABC from the picture attached below.
Lets find angle x
x + 47 + 33 = 180 (because all angles of a triangle are equal to 180°)
x = 100°
Angle x = Angle y = 100° (because vertically opposite angles are equal)
Step 2: Find angle 2
Angle 2 = 180 - angle x (because angle on a straight line is 180°)
Angle 2 = 180 - 100
Angle 2 = 80°
Step 3: Find angle z
48 + y + z = 180° (because all angles of a triangle are equal to 180°)
z = 32°
Angle 3 = 180 - angle z (because angle on a straight line is 180°)
Angle 3 = 180 - 32
Angle 3 = 148°
Step 4: Find angle 1
Angle 1 = 180 - 33 (because angle on a straight line is 180°)
Angle 1 = 147°
Therefore m∠1 = 147°, m∠2 = 80°, m∠3 = 148°
Option 2 is correct
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