Compare the key features of f(x)=2x-3 and the
linear function g shown below.
23. What do the slopes and the y intercepts
indicate about the linear functions f and g?
Answers
Answer:
f slopes was [tex]\frac{3}{2}[/tex] ,the y intercepts was -3
g slopes was [tex]-\frac{1}{3}[/tex],the y intercepts was -2
Step-by-step explanation:
g slopes :
functions g has point (0,-2) and (3,-3)
the slopes =[tex]\frac{-2-(-3) }{0-3} =-\frac{1}{3}[/tex]
Related Questions
78 POINTS BRANLIEST CHECK WILL DELETE U IF WRONG ANSWER
Answers
Answer:
Below
Step-by-step explanation:
For the boxes:
the sum of all three angles = 180 for a triangle
soooo : 28 + x-4 + 2x = 180
then x = 52 via algebra
Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) 5 f(x) a = 2 1 + x
Answers
The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....
Given that,
We have to get the first four nonzero terms of the series for f(x), centering at the specified value of a, use the definition of a Taylor series. (Separate your responses into a list using commas.)
f(x)=5/1+x and a=2
We know that,
Take
f(x)=5/1+x and a=2
f(2)=5/1+2=5/3
f'(x)=-5/(1+x)² f'(2)=-5/(1+2)²=-5/9 (differentiating)
f''(x)=10/(1+x)³ f''(2)=10/(1+2)³=10/27
f'''(x)=-30/(1+x)⁴ f'''(2)=-30/(1+2)⁴=-30/81=-10/27
Using the taylor series
F(x)=f(a)-(x-a)f'(a)+(x-a)²/2!f''(a)-(x-a)³/3!f'''(a)+....
F(x)=f(2)-(x-2)f'(2)+(x-2)²/2f''(2)-(x-2)³/3!f'''(2)+....
F(x)=5/3-(x-2)(5/9)+(x-2)²/2(10/27)-(x-2)³/6(-10/27)+....
F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....
Therefore, The first four nonzero terms of the series for f(x) from the taylor series is F(x)=5/3-5/9(x-2)+5/27(x-2)²-5/81(x-2)³+....
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The box below is opened by pressing any two buttons
whose numbers multiply together to give 12√6.
Select all of the numbers on buttons that can be used
as part of a pair to open the box.
3√2
4√3
3
√6
4√6
4√2
3√4
4
12√2
Answers
The multiplication that will give a value of 12✓6 from the numbers will be:
3✓2 × 4✓3
3 × 4✓6
How to illustrate the expression?It should be noted that addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, it should be noted that:
3✓2 × 4✓3 = 12✓6
3 × 4✓6 = 12✓6
It should be noted both scenarios highlight the given value of 12✓6.
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a movie production company is releasing a movie with the hopes that many viewers will return to see the movie in the theater for a second time. their target is to have 40 million viewers, and they want more than 40% of the viewers to want to see the movie again. they show the movie to a test audience of 140 people, and after the movie they asked them if they would see the movie in theaters again. of the test audience, 66 people said they would see the movie again.
Answers
As per the concept of hypothesis, the value of p is 0.47 the value of the static hypothesis is 4.3893 and the statistical division when the alpha = 0.05 is 0.1085.
What is meant by hypotheses?
in math, hypotheses refers a an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.
Here we have given that, a movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a 2nd time. The target is to have 40 million viewers and they want more than 40% of the viewers to return to see the movie again.
And they show the movie to a test audience of 140 people.
Of the test audience, 66 people said they would see it again.
And we have to determine, the p-value is, the p-value for the test statistic.
And the statistical division when the alpha = 0.05 and explain the managerial conclusion for this situation.
Based on the question, the null hypothesis is,
H0: P = 3
H1: P > 0.03
Here we know that they show the movie to a test audience of 140 people.
So, n = 140
Here the test audience, 66 people said they would see it again.
So, x = 66
Therefore, the value of p is,
=> 66/140 = 0.47
Then the test hypothesis is,
=> Z = (0.47 - 0.3) / √[(0.3(1 - 0.3))/140]
When we simplify this one, then we get,
=> Z = 4.3893
Therefore, value of the static hypothesis is 4.3893.
Then the p-value = 0.1085 at 5% level of significance.
Here, 0.1085 < 4.3893,
Therefore, the null hypothesis is not rejected.
Therefore, p-value = 0.1085, and we will not reject the null hypothesis.
So, the value of the static hypothesis is greater than the null hypothesis and the value of p so the value of not rejects the null hypothesis.
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Find x , y ( 10 points)
Answers
Answer:
x = 15
y = 4
Step-by-step explanation:
18/6 = x/5
3/1 = x/5
x = 15
12/y = 3/1
3y = 12
y = 4
manny has just filled out his deposit ticket for his savings account. he hands it to the teller and the teller hands it back to manny. the teller explains to manny that the deposit ticket cannot be accepted in its current form. what must manny do to the deposit ticket in order for the teller to process the deposit ticket? a deposit ticket. the ticket has not been signed for cash back. the date is december 16. a. manny forgot to sign the deposit ticket for less cash back
Answers
The manny must do his signature on the deposit ticket in order to get deposited the cashback ticket.
What is cashback?
Cashback is a type of reward program offered by some retailers and online merchants that gives customers money back for making purchases. It is a way for retailers to reward customers for their loyalty and encourage them to keep coming back to their store. Cashback can be offered in the form of a fixed amount, a percentage of the purchase price, or a combination of both. Cashback rewards may be paid in cash or as credits to the customer's account, and they may be used to purchase additional items from the store or to offset future purchases.
When teller sees the deposit ticket he must have seen that it is not signed by manny hence he returned this to manny now manny just have to do one work that to sign that deposit ticket after that teller will accept that deposit ticket and manny will get his required cashback easily in his bank account
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Answer:
a edge
Step-by-step explanation:
for what natural values of n are the value of the following expression equal to a natural number: 36-n^2/n^2
Answers
Answer:
All natural numbers
Step-by-step explanation:
I'm assuming that you mean 36-(n^2/n^2)
A natural number is a positive integer
n^2/n^2 is always 1 for natural numbers.
so 36-1=35 which is a natural number
A senior accounting major at Midsouth State University has job offers from four CPA firms. To explore the offers further, she asked a sample of recent trainees how many months each worked for the firm before receiving a raise in salary. The sample information is submitted to Minitab with the following results: Analysis of Variance Source Factor df Ss MS F 3 28.17 9.39 5.37 0.133 15 26.26 1.75 18 54.43 Total What is the decision rule? (Round your answer to 2 decimal places.) eject H0 if F> At the 0.01 level of significance, is there a difference in the mean number of months before a raise was granted among the four CPA firms? Do not reject O Reject
Answers
Treatment remains the same. Do not Reject.
Test Statistics:
[tex]f = \frac{\text{treatment}}{\text{error}} = 5.37[/tex]
Reject Null Hypothesis if [tex]f > f(a, a-1, N-a)[/tex]
Critical Value [tex]f(0.01, 3, 15) = 5.42 \text{ (From F Table)}[/tex]
[tex]\because 5.37 < 5.417[/tex]
We fail to Reject [tex]H0[/tex]
[tex]\therefore[/tex] Do not Reject.
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Put the slope intercept form
Answers
At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping.
Relaxed time (seconds)
Jumping time (seconds)
26
21
47
40
30
28
22
21
23
25
45
43
37
35
29
32
Answers
The test statistic is 1.507 and the corresponding p value is 0.175539
Fail to reject H₀ because the p value is greater than the significance level 0.05.
There is enough evidence to warrant rejection of the claim that the mean difference between their jumping and relaxed times would be zero.
To find the mean and standard deviation for the paired differences, prepare the table:
Calculate the value of d bar:
d bar = ∑d/n
= 5+7+...+(-3)/8
= 14/8
= 1.75
Calculate the standard deviation of the (d)
Sd = √(d₁-dbar)²/n-1
= √(5-1.75)²+(7.1-75)²+..+(-3-1.75)²/8-1
= √10.785714
= 3.284
The mean and standard deviation of the eight girls were timed to see how long they could be zero.
Null hypothesis H₀: meand = 0
Alternative hypothesis H₁ : mean d ≠ 0
Level of significance α = 0.05
Decision rule : Reject H₀ when p value < 0.05 level of significance.
The null hypothesis is the 8 girls mean difference between their jumping and relaxed time is equal to the zero and alternative hypothesis is the 8 girls mean difference between their jumping and relaxed time is not equal to the zero.
from the available info, d bar = 1.75 Sd = 3.284
Calculate the test statistic value.
t = 1.75 - 0/3.284/√8
= 1.507
calculate the degree of freedom.
df = n-1
= 8-1
= 7
Calculate the p value of the test
P value = (=TDIST(1.507,7,2)) (use MS Excel function)
= 0.175539
Hence the test statistic is 1.507 and the corresponding p value is 0.175539
Fail to reject H₀ because the p value is greater than the significance level 0.05.
There is enough evidence to warrant rejection of the claim that the mean difference between their jumping and relaxed times would be zero.
There is no evidence to warrant rejection of the claim that the mean difference between their jumping and relaxed times would be zero.
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Find f(-1) f(x)=1/3(3)^x
algebra 1
Answers
Answer:
1/9
Step-by-step explanation:
f(-1)=1/3(3)^-1
f(-1)=1/3(1/3)
f(-1)=1/9
. if x1, x2, x3 are independent random variables that are uniformly distributed over (0, 1), compute the probability that the largest of the three is greater than the sum of the other two.
Answers
The probability that the largest of the three random variables is greater than the sum of the other two is:P(x1 > x2 + x3) = 1/4
The probability of an event occurring is equal to the number of favorable outcomes divided by the total number of outcomes. In this case, the total number of outcomes is 8, since each of the three random variables can take on any value between 0 and 1 independently. The favorable outcomes are those in which x1 is greater than the sum of the other two variables, which is 1/4 of the total number of outcomes. Therefore, the probability that the largest of the three random variables is greater than the sum of the other two is 1/4.
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Eduardo is painting a rectangular wall that is 96 inches high and 120 inches long. What is the area of the wall?
Answers
Answer:
The area of the wall is:
11520 inches²
Step-by-step explanation:
Area of a rectangle = high * long
Then:
Area = 96 inches * 120 inches
Area = 11520 inches²
Determine which of the following sets is a subspace of Pn for an appropriate value of n.A: All polynomials of the form p(t) = a + bt2, where a and b are inB: All polynomials of degree exactly 4, with real coefficientsC: All polynomials of degree at most 4, with positive coefficients
Answers
All polynomials of the form p(t) = a + bt2, where a and b are in sets is a subspace of Pn for an appropriate
Step-by-step explanation:Consider the following subsets of Pn given by
The 0 vector of V is in W.
- Given v,w in W then v+w is in W.
- Given v in W and a a real number, then av is in W.
So, for us to check if the three subsets are a subset of Pn, we must check the three criteria.
First property:
Hence the first criteria is not met. Then, W2 is not a subspace of Pn.
For W1 and W3, note that if a= 0, then we have p(t) =0, so the zero polynomial is in W1 and W3.
W1 and W3 are subspaces of Pn for n= 2
and W2 is not a subspace of Pn.
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Consider the figure shown.
What is the value of q?
A 25°
B 72°
C 108°
D 180°
Answers
The value of ∠q is 72 degree. So the option B is correct.
In the given question we have to find the value of q.
The given options are:
A 25 degree
B 72 degree
C 108 degree
D 180 degree
As we know that the angle of straight line is 180 degree.
From the given diagram we can see that the two angel of one line that is cut by another line, is given.
So the third angle of one line that is cut by another line is
25 + 83 + x = 180
x + 108 = 180
Subtract 108 on both side, we get;
x = 72
Using the corresponding angle theorem
∠q = 72 degree
Hence, the value of ∠q is 72 degree. So the option B is correct.
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Find a formula for the general term an of the geometric sequence:
{ 10/3, 10/9, 10/27, 10/81, 10/243}
Express the common ratio r as a fraction and place in parentheses!
an = __________
Answers
Answer: [tex]\displaystyle \frac{10}{3}\left(\frac{1}{3}\right)^{n-1}[/tex]
======================================================
Explanation:
a = 10/3 is the first term
r = 1/3 is the common ratio
Multiply each term by r = 1/3 to get the next term.
Example:
(10/3)*(1/3) = 10/9
We then plug those two items into the formula
[tex]a_n = a(r)^{n-1}[/tex]
to end up with the answer shown above.
The value of n is a positive integer.
Convert from point slope form to slope intercept form.
Slope U/D, (5,0)
Please help me!!!!!!!
Answers
Answer:
x = 5
Step-by-step explanation:
assuming you mean the slope of the line id undefined and passes through (5, 0 )
A line with an undefined slope is a vertical line parallel to the y- axis with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (5, 0 ) with x- coordinate 5 , then
x = 5 ← equation of line
Students pay $2 per ticket and adults pay $5 per ticket. Although the stadium is filled to its capacity of
2000, 254 of those seats are given free of charge to band members, pep squad members, and faculty members. the ticket-booth manager reports to the athletic director that the total income from the sale of tickets for the current game is $5766. How many student and adult tickets were sold?
Answers
The number of students and adult ticket sold are 988 and 758 respectively .
How to find the number of student and adult tickets?Students pay $2 per ticket and adults pay $5 per ticket. The stadium is filled to its capacity of 2000 but 254 of those seats are given free of charge to band members, pep squad members, and faculty members.
The total income from the sale of tickets for the current game is $5766.
The number of student and adult tickets that were sold can be calculated as follows:
let
x = number of student ticket sold
y = number of adult ticket sold
Hence, using equation,
Students pay $2 per ticket and adults pay $5 per ticket and the total total sale is 5766.
2x + 5y = 5766
The stadium is filled to its capacity of 2000 but 254 of those seats are given free. This means the actual number of people that paid for the seats is 2000 - 254 = 1746.
x + y = 2000 - 254
x + y = 1746
Combine the equation
2x + 5y = 5766
x + y = 1746
multiply equation(ii) by 2
2x + 5y = 5766
2x + 2y = 3492
subtract equation(ii) from equation(i)
3y = 2274
y = 2274 / 3
y = 758
x = 1746 - 758
x = 988
Therefore,
number of student tickets = 988
number of adult tickets = 758
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3) Sally is in a long-jump competition. Her first jump is 5.7m. Her second jump is
6.2m. What is her percentage increase in jump length?
Answers
The percentage increase in her jump length would be 8.77%.
What is a percentage increase?
The percentage increase formula is the ratio of value increased to the original value and multiplied by 100. It is expressed in percentage. If there is an increase in the value of anything, then there is an increase in percentage.
The initial jump was 5.7m and the second jump is 6.2m
By using the percentage increase formula, we can write
Percentage increase = (final value - initial value)/|Final value| * 100
= ((6.2 - 5.7)/6.2)*100
= 8.77%
Hence, the percentage increase in her jump length would be 8.77%.
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A tank is full of water. The tank is a right circular cylinder lying on its side (length is parallel to horizon), with radius 2 m, and length 5 m. Find the work required to pump the water out of a spout that rises 2 m above the tank. Set up the integral, but do NOT evaluate. The base of a solid is a circular disk with radius
Answers
The integral for the work required to pump the water out of a spout that rises 2 m above the tank is
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
Integral
An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function (indefinite integral).
Given that:
r = 2m
l = 5m
sinθ = [tex]\frac{x}{r}[/tex]
dv = 2l [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
Let p be the density of water and g be the acceleration due to gravity.
dm = p dv
dw = dmg (h + r - x)
dw = pg (h + r - x) dx
dw = 2l pg (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
w = ∫dw
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
Therefore, the integral for the work required to pump the water out of a spout that rises 2 m above the tank is
w = ∫ lower power (-r) to upper power (r + h) 2pgl (h + r - x) [tex]\sqrt{r^{2} + x^{2} }[/tex] dx
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organizations interested in making sure that accused persons have a trial of their peers often compare the distribution of jurors by age, education, and other socioeconomic variables. one such study in a large southern county provided the following information on the ages of 1,000 jurors and the age distribution countywide. Soc. Age 21-40 41-50 51-60 Over 60 Total 399 212 Number of jurors Age % countywide 231 158 1,000 42.1 22.9 15.7 19.3 100 a. Display the above data using appropriate graphs. b. Is this significant evidence of a difference between the age distribution of jurors and the countywide age distribution? c. Does there appear to be an age bias in the selection of jurors?
Answers
Yes, it is significant evidence of a difference between the age distribution of jurors and the countrywide age distribution.
No, there is no age bias in the selection of jurors.
P Oi Ei ( Oi-Ei) ^2/Ei
0.421 399 421 1.149643705
0.229 231 229 0.017467249
0.157 158 157 0.006369427
0.193 193 193 1.870466321
1 1000 1000 3.043946702
The above can be represented in graphs.
Now,
Ei = n × pi
TS = 3.04394672
From TS < value
Value (7.81472)
We fail to reject the null hypothesis at 5% value of significance
No, there is no age bias in the selection of jurors.
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Please help!!!!!!!!!!
Answers
Answer: [tex]6^{\frac{1}{12} }[/tex]
Step-by-step explanation:
Rewrite This Integral As An Equivalent Iterated Integral In The Five Other Orders. (Assume Y(X) = Squareroot X And Z(Y) = 8 Y)
Answers
The given integral is:
∫ ∫ ( x) ×(8 × (√ x)) dx dy
By changing the order in which we integrate with respect to the variables x and y, we can rewrite this integral as an iterative integral of the other five orders. The other five commands are:
a. ∫ ∫ (√ x) ×(8 × (√t x)) dy dx
b. ∫ ∫ (8 × (√ x)) × (√ x) dx dy
c. ∫ ∫ (8 × (√ x)) × (√ x) dy dx
d. ∫ ∫ (√ x) × (√x) dx (8 × y)
e. ∫ ∫ (√ x) × (√ x) (8 * y) dx
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suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of per hour. suppose also that a sample culture of bacteria is obtained from this population. find the size of the sample after two hours. round your answer to the nearest integer.
Answers
The size of the sample after two hours with an initial population of 1000 and a growth rate of 11% is found to be 1246.
A pattern of data that exhibits larger increases over time, forming the curve of an exponential function, is said to exhibit exponential growth. The formula of continuous exponential growth is P=P₀e^{rt} where P is the population after time t, P₀ is the initial population, and r is the growth rate.
Given P₀ is 1000 bacteria, r is 11% = 0.11, and t is 2 hours. Then, the size of the sample after two hours is,
[tex]\begin{aligned}P&=P_0e^{rt}\\&=1000e^{0.11\times2}\\&=1000e^{0.22}\\&=1000\times1.246\\&=1246\end{aligned}[/tex]
The answer is 1246.
The complete question is -
Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of 11% per hour. Suppose also that a sample culture of 1000 bacteria is obtained from this population. Find the size of the sample after two hours. Round your answer to the nearest integer.
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FILL IN THE BLANK. when model building using the build-down method, you want to start with the complete 2nd-order model and build down to the most______model.
Answers
when model building using the build-down method, you want to start with the complete 2nd-order model and build down to the most data model.
when working on a workbook which requires a team of people to work with you on the workbook, it is important you create transparency and also ensure you complete the workbook on time.
one very important way to complete the task on time is to share the workbook with your team so that they can input their own contributions towards the task, this practice ensures speedy completion of the task. and reduces the level of errors which might have occurred if you where working on it alone.
granting access to the workbook is a very good way to create trust and transparency.
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in certain areas of the city, the Electricity power is cut randomly in a rate of 3/day find the probability that in any given day there are at least 7 cuts at most 4 cuts.
Answers
Answer: This comes out to be 0.1031.
Step-by-step explanation:
in this case, we are given that the rate of power cuts in the city is 3/day, so the rate parameter for our Poisson distribution is $\lambda=3$. We want to find the probability that there are at least 7 cuts but at most 4 cuts in a given day. This means we need to find the probability that $k=7$, $k=8$, $k=9$, ..., $k=4$. We can use the formula for the probability mass function to find the probability for each of these values of $k$ and add them together to get the total probability.
200 g of water in a glass is at 10.0°C when an ice cube is placed in the glass. What is the temperature of the water after it has transferred 4,200 J of thermal energy to the ice cube? °C
Answers
Answer:
20.0°C
Step-by-step explanation:
To find the final temperature of the water after it has transferred thermal energy to the ice cube, we need to use the equation:
Q = cmΔT
where Q is the amount of thermal energy transferred, c is the specific heat capacity of the substance, m is the mass of the substance, and ΔT is the change in temperature.
In this case, we are given that Q = 4,200 J and m = 200 g. The specific heat capacity of water is 4.184 J/g°C.
Substituting these values into the equation gives us:
4,200 J = (4.184 J/g°C)(200 g)(ΔT)
Solving for ΔT gives us:
ΔT = 4,200 J / [(4.184 J/g°C)(200 g)] = 10°C
Since the initial temperature of the water was 10.0°C, the final temperature of the water is 10.0°C + 10°C = 20.0°C.
Therefore, the temperature of the water in the glass is 20.0°C after it has transferred 4,200 J of thermal energy to the ice cube.
A fair die is rolled six times. Calculate the probability of obtaining exactly two 3s. (Round your answer to four decimal places.)
Show work in steps so I can understand how to set up the problem and solve it better. Been stuck on this for awhile! Thanks
Answers
The Total Probability of getting exactly two 3s in two throws is 1/36
What is Probability?
A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Solution:
Probability of Obtaining 3 in the first throw = 1/6
Since, the number of possible outcome is 11 and total outcomes are 6
Similarly the probability of getting 3 in the second throw is 1/6
Therefore, total probability = 1/6 * 1/6 = 1/36
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a recipe asks for 223cups of raisins. how many cups of raisins are needed to make 12of a recipe? multiply. express the answer in simplest form. enter the answer in the box.
Answers
The anwer of number of cups of raisins required for 12 recipes needing 223 cups of raisins each are 2676.
Multiplication operation will be required to find the number of cups of raisins. The expression to be formed for calculation is-
Total number of cups = number of recipes × number of cups for one recipe
Keep the values in formula to find the total number of cups
Total number of cups = 12 × 223
Performing multiplication on Right Hand Side of the equation
Total number of cups = 2676
Thus, 2676 cups are required for recipe.
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If a nonlinear system depends on a parameter, then the equilibrium points can change as the parameter varies. In other words, as the parameter changes, a bifurcation can occur. Consider the one-parameter system family of systems dx = x2 – a =-y(+2+1), where a is the parameter.(a) Show that the system has no equilibrium points if a < 0. (b) Show that the system has two equilibrium points if a > 0. (c) Show that the system has exactly one equilibrium point if a = 0. (d) Find the linearization of the equilibrium point for a = 0 and compute the eigenvalues of this linear system.
Answers
If a<0, then there is no x-null lines, the system has no equilibrium points.
If a=0, it has only one equilibrium points.
If a>0, the system has two equilibrium points.
Points are (-√a,0) and (√a,0)
The system changes from no fixed points to two fixed points when it increases through a=0.
a is a bifurcation point.
The Jawbian matrix,
J = [tex]\left[\begin{array}{ccc}2x&0\\-2xy&x^{2}-1\\\end{array}\right][/tex]
Now,
J[0,0] = [tex]\left[\begin{array}{ccc}0&0\\0&-1\\\end{array}\right][/tex] =0
J[-√a,0] = [tex]\left[\begin{array}{ccc}-2\sqrt{a} &0\\0&-a-1\\\end{array}\right][/tex] = 2a√a + 2√a
If a=0, then it will be a live equilibrium, one of the values are 0, For a>0, the point (-√a,0) is sink and (√a,0) is a saddle points.
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