a) The first four nonzero terms of the power series for f(x) about x=0 are
e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!
The general term of the power series is (-2)^n (2x)^(2n) / (2n)!
b) The interval of convergence of the power series is (-∞, ∞).
c) To estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series, we can use the Lagrange form of the remainder
|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!
a) To find the power series for f(x) about x = 0, we can use the Maclaurin series formula
f(x) = Σ[n=0 to ∞] (fⁿ(0)/n!) xⁿ
where fⁿ(0) denotes the nth derivative of f evaluated at x=0.
In this case, we have
f(x) = e^6(-2x^2)
fⁿ(x) = dⁿ/dxⁿ(e^6(-2x^2)) = (-2)^n(2x)^ne^6(-2x^2)
So, we can write the power series as
f(x) = Σ[n=0 to ∞] ((-2)^n(2x)^n e^6(0))/n!)
= Σ[n=0 to ∞] ((-2)^n (2x)^n /n!)
To find the first four nonzero terms, we substitute n = 0, 1, 2, and 3 into the above formula
f(0) = e^6
f'(0) = 0
f''(0) = 24
f'''(0) = 0
So, the first four nonzero terms of the power series are:
e^6 - 2x^2 + (2x^4)/2! - (2x^6)/3!
The general term of the power series is
(-2)^n (2x)^(2n) / (2n)!
b) To find the interval of convergence of the power series, we can use the ratio test
lim [n→∞] |((-2)^(n+1) (2x)^(2n+2) / (2n+2)! ) / ((-2)^n (2x)^(2n) / (2n)!)|
= lim [n→∞] |-4x^2/(2n+1)(2n+2)|
= lim [n→∞] 4x^2/(2n+1)(2n+2)
Since this limit depends on the value of x, we need to consider two cases
i) If x = 0, then the power series reduces to the constant term e^6, and the interval of convergence is just x=0.
ii) If x ≠ 0, then the series converges absolutely if and only if the limit is less than 1 in absolute value
|4x^2/(2n+1)(2n+2)| < 1
This is true for all values of x as long as n is sufficiently large. So, the interval of convergence is the entire real line (-∞, ∞).
c) We can use the Lagrange form of the remainder to estimate the error between f(x) and its partial sum g(x) given by the sum of the first four nonzero terms of the power series
|R4(x)| = |f(x) - g(x)| ≤ M |x|^5 / 5!
where M is an upper bound for the fifth derivative of f(x) on the interval [-0.6, 0.6].
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Two cars, one going due east at the rate of 90 km/hr and the other going to south at the rate of 60 km/hr are traveling toward the intersection of two roads. At what rate the two cars approaching each other at the instant when the first car is 0.2 km and the second car is 0.15 km from the intersection ?
The two cars are approaching each other at a rate of 36 km/hr at the given instant.
We can solve this problem by using the Pythagorean theorem and differentiating with respect to time. Let's call the distance of the first car from the intersection "x" and the distance of the second car from the intersection "y". We want to find the rate at which the two cars are approaching each other, which we'll call "r".
At any moment, the distance between the two cars is the hypotenuse of a right triangle with legs x and y, so we can use the Pythagorean theorem
r^2 = x^2 + y^2
To find the rates of change of x and y, we differentiate both sides of this equation with respect to time
2r(dr/dt) = 2x(dx/dt) + 2y(dy/dt)
Simplifying and plugging in the given values
dr/dt = (x(dx/dt) + y(dy/dt)) / r
dr/dt = (0.2 x 90 + 0.15 x (-60)) / sqrt((0.2)^2 + (0.15)^2)
dr/dt = (18 - 9) / sqrt(0.04 + 0.0225)
dr/dt = 9 / sqrt(0.0625)
dr/dt ≈ 36 km/hr
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Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs. y 0 1 2 3 4 ply) 0.60 0.20 0.15 0.03 0.02 (a) Calculate and interpret Hy My = 0.20 (b) In the long run, for what proportion of cartons is the number of broken eggs less than jy? (Round your answer to two decimal places). Enter a number. Does this surprise you? Yes O No 0 + 1 + 2 + 3 + 4 (c) Explain why sy is not equal to = 2.0. 5 This computation of the mean is incorrect because the value in the denominator should equal the maximum y value. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are all equally like O This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when O This computation of the mean is incorrect because it does not take into account the number of partially broken eggs.
a) The value of Hy = 1.15
b) The proportion of cartons with less than 1.15 broken eggs is 0.60
c) The answer is B)This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like.
(a) Hy = 0.67, which means that on average, there are 0.67 broken eggs per carton.
Hy = (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1
= 0.67
(b) The proportion of cartons with less than 0.67 broken eggs is 0.60 which is probability of 0 broken eggs.. This may be surprising as the probability of having less than 0.67 broken eggs is only 0.60, but this is due to the fact that the distribution is skewed towards higher values.
(c) Hy is not equal to the simple average of 0, 1, 2, 3, and 4 because the distribution is not symmetrical. The probabilities are weighted towards higher values, which increases the mean. Additionally, the value of zero should be included in the calculation, as it represents a possible outcome. Therefore, the correct formula for Hy is (0*0.60 + 1*0.20 + 2*0.15 + 3*0.03 + 4*0.02)/1 = 0.67.
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--The question is incomplete, answering to the question below--
"Let y denote the number of broken eggs in a randomly selected carton of one dozen eggs.
y 0 1 2 3 4
p(y) 0.60 0.20 0.15 0.03 0.02
(a) Calculate and interpret Hy
(b) In the long run, for what proportion of cartons is the number of broken eggs less than Hy? (Round your answer to two decimal places).
Does this surprise you?
Yes
No
(c) Explain why Hy is not equal to (0 + 1 + 2 + 3 + 4)/5 = 2.0.
A. This computation of the mean is incorrect because the value in the denominator should equal the maximum y value.
B. This computation of the mean is incorrect because it does not take into account that the number of broken eggs are not all equally like
C. This computation of the mean is incorrect because it includes zero in the numerator which should not be taken into account when
D. This computation of the mean is incorrect because it does not take into account the number of partially broken eggs."
please help I know its 9:35 PM I Just need help what this question2.1 × 1.6 =
21
10
×
16
10
= tenths × tenths my parents are gonna kill me help
The value of the expression 2.1 × 1.6 = 3.36.
What are decimals?Decimals are a collection of numbers falling between integers on a number line. They are only an additional mathematical representation of fractions. Decimals allow us to express quantifiable quantities like length, weight, distance, money, etc. with more accuracy. Integers, also known as whole numbers, are represented to the left of the decimal point, while decimal fractions are shown to the right of the decimal point.
Given that the expression is: 2.1 × 1.6.
2.1 × 1.6 can be written as:
2.1 × 1.6 = 21/10 × 16/10
Multiply the numerator and denominator:
21/10 × 16/10 = 336/100
Covert the fraction into decimal:
336/100 = 3.36
Hence, the value of the expression 2.1 × 1.6 = 3.36.
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Examine the following graphed systems of linear inequalities. Select the points below that are solutions to each system of inequalities. Select TWO that apply.
1. 2.
(2,3) (0,0)
(4,3) (4,3)
(-7,6) (6,1)
(-2,3) (2-5)
I need help D: pls
The solution of the graphs are as follows
first graph
(2, 3)(4, 3)second graph
(4, 3)(6, 1)How to find the ordered pair that are solution of the graphThe graphs consist of two sets of equations plotted, each has shade peculiar to the equation.
The solution of the graph consist of the ordered pair that fall within the parts covered by the two shades
For the first graph by the left, the solutions are
(2, 3)(4, 3)For the second graph by the left, the solutions are
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Question 11 (2 points)
Among the seniors at a small high school of 150 total students, 80 take Math, 41
take Spanish, and 54 take Physics. 10 seniors take Math and Spanish. 19 take Math
and Physics. 12 take Physics and Spanish. 7 take all three.
How many seniors take Math and Spanish, but not Physics?
Note: Consider making a Venn Diagram to solve this problem.
3
10
27
121
There are 3 seniors who take Math and Spanish, but not Physics.
What is Venn Diagram?
A diagram representing mathematical or logical sets pictorially as circles or closed curves within an enclosing rectangle (the universal set), common elements of the sets being represented by the areas of overlap among the circles.
To solve this problem, we can use a Venn diagram to organize the information given about the students.
First, we know that there are 150 seniors in total, so we can label the outer rectangle of the Venn diagram as having a total of 150 students.
Next, we can label the three circles as Math, Spanish, and Physics, with the numbers given in the problem:
80 seniors take Math, so we label the Math circle with 80.
41 seniors take Spanish, so we label the Spanish circle with 41.
54 seniors take Physics, so we label the Physics circle with 54.
We also know that 10 seniors take Math and Spanish, 19 take Math and Physics, 12 take Physics and Spanish, and 7 take all three. We can label these overlaps in the Venn diagram as follows:
The overlap of Math and Spanish is 10.
The overlap of Math and Physics is 19.
The overlap of Physics and Spanish is 12.
The overlap of all three is 7.
To find the number of seniors who take Math and Spanish, but not Physics, we need to subtract the number of seniors who take all three (because they are counted in all three circles) and the number of seniors who take Math, Spanish, and Physics (because they are counted in the overlap of all three circles). Then we add the number of seniors who take only Math and Spanish (because they are not counted in the Physics circle).
Using the formula for the number of elements in the union of three sets, we have:
Math or Spanish or Physics = Math + Spanish + Physics - (Math and Spanish) - (Math and Physics) - (Spanish and Physics) + (Math and Spanish and Physics)
So, the number of seniors who take Math and Spanish, but not Physics is:
Math and Spanish - (Math and Spanish and Physics) + (Math or Spanish or Physics - (Math + Spanish + Physics) + (Math and Spanish and Physics))
= 10 - 7 + (80 + 41 + 54 - 2(10) - 2(19) - 2(12) + 7)
= 3
Therefore, there are 3 seniors who take Math and Spanish, but not Physics.
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If 5 is increased to 9, the increase is what percentage of the original number
Answer: It's a 80% increase
Step-by-step explanation:
the value of the given test statistic lies between the given cutoffs -2.58 and 2.58. it falls in acceptance region.
Here the values -0.94 and 2.12 falls between the points -2.58 and 2.58. The area between is the acceptance region. So we cannot reject the null hypothesis.
The given is an example for two tailed test. A two tailed test is used to determine whether the value is greater than or less than the mean value of the population. It represents the area under both tails or sides on a normal distribution curve.
Here the value of the test statistic lies between -2.58 and 2.58. So the values less than -2.58 and greater than 2.58 fall in the rejection region, where the null hypothesis can be rejected.
a) -0.94 falls between -2.58 and 2.58. So it is in the acceptance region. So null hypothesis is accepted.
b) 2.12 lies between -2.58 and 2.58. It is also in acceptance region. So null hypothesis is accepted.
So in both cases null hypothesis cannot be rejected.
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The complete question is :
f the cutoffs for a z test are -2.58 and 2.58, determine whether you would reject or fail to reject the null hypothesis in each of the following cases and explain why:
a. z = −0.94
b. z = 2.12
What is the slope of the line in the following graph?
Answer:
1/3
Step-by-step explanation:
using rise over run fron the two dots, we can find 2/6, which simplifies down to 1/3
Please answer Full question
(1) 4y-7z is a binomial.
(2) 8-xy² is a binomial.
(3) ab-a-b can be written as ab - (a + b) which is a binomial.
(4) z²-3z+8 is a trinomial.
What are monomials, binomials and trinomials?In algebra, monomials, binomials, and trinomials are expressions that contain one, two, and three terms, respectively.
A monomial is an algebraic expression with only one term. A monomial can be a number, a variable, or a product of numbers and variables.
A binomial is an algebraic expression with two terms that are connected by a plus or minus sign. For example, 2x + 3y and 4a - 5b are both binomials.
A trinomial is an algebraic expression with three terms that are connected by plus or minus signs.
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Classify into monomials, binomials and trinomials.
(1) 4y-7z
(1) 8-xy²
(v) ab-a-b
(ix) z2-3z+8
The graph of triangle has coordinates E(1,4) F(-1,1) and G(2,-1). Graph triangle of EFG and it’s image after a translation of 3 units left and 1 unit down.
Answer:
Step-by-step explanation:1.4 -1, 1 2, -1
Answer the question below: *
Tasha is planning an expansion of a square flower garden in a city park. If each side of the original garden is
increased by 5 m, the new total area of the garden will be 121 m². Find the length of each side of the original garden.
O 6 meters
O 6.6 meters
O 11 meters
O 16 meters
Sea "x" la longitud de cada lado del jardín original en metros.
La superficie del jardín original es x^2 m².
Si cada lado del jardín original se aumenta en 5 m, el nuevo lado del jardín será de (x+5) metros, y la nueva superficie será (x+5)^2 m².
Según el problema, la nueva superficie total es de 121 m²:
(x+5)^2 = 121
Tomando la raíz cuadrada en ambos lados:
x+5 = 11
Restando 5 en ambos lados:
x = 6
Por lo tanto, la longitud de cada lado del jardín original es de 6 metros.
Por lo tanto, la respuesta correcta es O 6 metros.
x - the length of each side of the original garden
A = x²
( x + 5 )² = 121 /√
x + 5 = 11, or x + 5 = - 11;
x = 11 - 5
x = 6 ( another solution in negative )
Answer:
A ) 6 m
Help please! I have no idea!!!!
The values of the function from the graph are h(7) = 10, h(0) = 9, h(t) = 8, t = 5 and h(t) = 0, t = 4
How to determine the value of the functionGiven that the graph is the graph of height as a function of time
To calculate the values of h(t) from the graph of g(x), we need to follow these steps
Identify the value of t on the x-axis where you want to calculate the value of h(t)Locate that point on the graphWrite the values from the pointUsing the above, we have the following
h(7) = 10
h(0) = 9
h(t) = 8, t = 5
h(t) = 0, t = 4
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Segment AE shown has length of sqrt 20. Which segment is closest in length to sqrt 10?
Segment C has a length of √10, which is the closest to √10 compared to the other segments.
What is Segment?Segment is a customer data platform (CDP) that enables companies to collect, store, and analyze customer data from multiple sources. It helps companies build customer profiles and create personalized experiences for their customers. Segment allows businesses to track website visits, user actions, and other events in real-time, as well as to create custom events and store customer data in a secure and unified data warehouse. With Segment, companies can create powerful customer segmentation, which allows them to target customers with personalized messages and offers. Segment also integrates with various marketing, analytics, and CRM tools to provide a complete picture of customer behavior. It enables companies to build cohesive customer journeys, run campaigns, and optimize their customer experience.
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Complete Question.
how many one-to-one functions are there from a set with five elements to sets with the following number of ele- ments? a) 4 b) 5 c) 6 d) 7
a) Number of one-to-one functions are equal to the zero, because n< m.
b) Number of one-to-one functions are equal to the ⁵P₅ = 120.
c) Number of one-to-one functions are equal to the ⁶P₅ = 720.
c) Number of one-to-one functions are equal to the ⁷P₅ = 2250.
One to one function is a special form of function that defined from one set to another and maps every element of the range to exactly one element of its domain unique output. As we know a set A has m elements and set B has n elements, then
Number of one-to-one functions from set A to Set B = P(n,m) or ⁿPₘ , n≥ m and number of one-to-one functions from set A to Set B = 0 , n< m.Now, we have a domain set with five elements, m = 5
a) Here, another set (co-domain) has 4 elements, n = 4. So, Number of one-to-one functions = 0 , n<m.
b) number of elements in another set,n= 5
So, Number of one-to-one functions = ⁵P₅ = 5!/(5 - 5 )! ( permutation formula)
= 5!/0! = 120
c) Number of elements in another set, n= 6
So, Number of one-to-one functions= ⁶P₅
= 6!/(6 - 5)!
= 6!/1! = 720
d) Number of elements in another set, n
= 7
So, Number of one-to-one functions
= ⁷P₅ = 7!(7 - 5)!
= 7!/2! = 2250
Hence, required value is 2250.
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PLEASE HELP MEEE
whoever answers right gets brainliest!!!
Answer:
[tex]30\leq x[/tex] AND [tex]x \leq 106[/tex]
Notice the valid answer is the one with the AND since need to be both at the same time.
Step-by-step explanation:
Is the one is market, you add 6 to each side and you obtain that answer
[tex]24 \leq x-6\leq 100[/tex]
[tex]24 +6\leq x\leq 100+6[/tex]
[tex]30\leq x\leq 106[/tex]
Question 6 (2 points)
A wire costs $3 per foot. How much will 18 inches of wire cost?
$1.50
$3.00
$4.50
$9
Answer:
$4.50
Step-by-step explanation:
There are 12 inches in a foot. 18 inches is 1.5 feet.
1 foot of wire is $3.00 and a half of foot should be $1.50.
1.5 feet of wire should cost $4.50
1.5 ft × $3/ft
= $4.50
if the slope of the line joining the points (2,4) and (5,k) is 2. find the value of k
10 is the value of k of the slope of the line .
What are slopes called?
Slope, usually referred to as rise over run, is a line's perceived steepness. By dividing the difference between the y-values at two places by the difference between the x-values, we can determine slope.
You may determine a line's slope by looking at how steep it is or how much y grows as x grows. slope categories. When lines are inclined from left to right, they are said to have a positive slope, a negative slope, or a zero slope (when lines are horizontal).
the points (2,4) and (5,k)
formula from slope of two points
slope = y₂ - y₁/x₂ - x₁
substitute the values in formula
slope = 2
slope = k - 4/5- 2
2 =k - 4/3
6 = k - 4
k = 6 + 4
k = 10
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Suppose we want to choose 5 letters, without replacement, from 15 distinct letters
[tex]\text{order does not matter}[/tex]
[tex]\text{sample space}= \text{15 letters}[/tex]
[tex]\text{no repetition}[/tex]
[tex]\text{P(A)}= \text{15C5}= \text{3003 ways}[/tex]
find the closed formula for 3,6,11,18 by relating them to a well known sequence. assume the first term given is
The closed formula for this particular sequence is an = n² + 2.
Take note that the odd numbers 3, 5, 7, 9, and 11 are separate consecutive terms. This shows that the first n odd numbers can be added to the initial term, az, to get the nth term. Hence, the following is how we may represent the nth term a = az + 1 + 3 + 5 + ... + (2n-3) (2n-3). We may utilize the formula for the sum of an arithmetic series to make the sum of odd integers simpler that is 1 + 3 + 5 + ... + (2n-3) = n².
As a result, we get a = az + n^2 - 1. In conclusion, the equation for the series (an)n21, where a1 = az and an is the result of adding the first n odd numbers to az, is as a = az + n^2 - 1. We have the following for the given series where a1 = az = 3.
So, the closed formula for this particular sequence is an = n² + 2.
To learn more about arithmetic sequences, refer to:
Your question is incomplete. The complete question is:
Find the closed formula for the sequence (an)n21. Assume the first term given is az. an = 3, 6, 11, 18, 27... Hint: Think about the perfect squares.
The simple interest formula 1 =
PRT
100
gives the interest I on a principal P
invested at a rate of R% per annum for
Tyears.
a) Find the interest when GH 2500 is
invested at 5% p.a. for 4 years.
b) Find the principal that gains an interest
of GH 2590 in 5 years at 7% per
annum,
The interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.
The principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.
What is simple interest ?
Simple interest is a type of interest that is calculated on the principal amount of a loan or investment at a fixed rate for a specified period of time. It is based only on the principal amount, and does not take into account any interest earned on previous periods.
The formula for simple interest is:
I = P * R * T
where:
I is the interestP is the principal amountR is the interest rate per periodT is the number of periodsAccording to the question:
a) Using the simple interest formula, we have:
I = (P * R * T) / 100
Substituting P = GH 2500, R = 5%, and T = 4 years, we get:
I = (2500 * 5 * 4) / 100 = 500
Therefore, the interest earned on GH 2500 at 5% p.a. for 4 years is GH 500.
b) Using the same formula, we can solve for the principal P:
I = (P * R * T) / 100
2590 = (P * 7 * 5) / 100
2590 = (35P) / 100
35P = 2590 * 100
P = (2590 * 100) / 35
P ≈ GH 7400
Therefore, the principal that gains an interest of GH 2590 in 5 years at 7% per annum is approximately GH 7400.
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please help me 60 points
Answer:
Matt would walk 8 miles in to hours.
Step-by-step explanation:
15 minutes is 1/4 of an hour, meaning it would be 1/8 of 2 hours.
1 mile times 8 = 8 miles
Hope that helps!
Part B
Draw
parallel to
. You can draw
any length and place it anywhere on the coordinate plane, but not on top of
.
Find and record the ratio, n, of the length of
to the length of
. Then, multiply the lengths of
and
by n and record the resulting lengths.
In a diagram,
Then,
[tex]\dfrac{DE}{BC}=n[/tex]
For example, suppose that n=2; thus,
[tex]DE=2BC\longrightarrow2\times CA[/tex]
We can form a new triangle DEF whose side EF is parallel to CA; therefore,
[tex]\longrightarrow EF=2CA[/tex]
Instructions: Use the following data set to find the sample statistics for the
following data set. (Round answers to the nearest hundredth, if necessary.
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45,
47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
1.
2.
<<>>
11
4. Mode =
(>>
3. Median =
=
11
By using sample standard deviation - (1) N or n = 20
(2) X or μ = 43.4
(3) σ = 9.78 and s = 10.04
Why does sample standard deviation exist?
When we talk about a sample standard deviation, we're not talking about population standard deviation. The average amount by which a group of values deviates from their mean is shown by the statistical measure of variability known as the standard deviation.
We are given with the following data set below;
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.
(2) The formula for calculating Mean of the data, i.e. X or μ is given by;
Mean = 51 +48+ 42+ 43+ 48 + 48 + 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42/20
= 868/20 = 43.4
So, the value of X or μ is 43.4.
(3) The formula for calculating population standard deviation () is given by;
Standard deviation, σ = √(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20
= 9.78
Similarly, the formula for calculating sample standard deviation (s) is given by;
Sample Standard deviation, s =
√(51 - 43.4)² + (48 - 43.4)² + .........+(42 - 43.4)²/20 - 1
= 10.04
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What triangles are similar to triangle ABC?
Answer:
A right angled triangle is similar to triangle ABC
Step-by-step explanation:
If you tilt the triangle and put it straight, you'll see that angle C is equal to 90°
And if a triangle has one angle of 90° then it is a right angled triangle
Hope you understand :)
The number 0 is an element of the set of natural numbers.
OA. True
B. False
SUBI
it is false. 0 is not a natural number. it is a whole number
This problem explores some questions regarding the fishery model
dt
dP
=P(1−P)−h
If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of
h
. Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. For what values of
h
does there exist a fixed point?
a) The expression for the stable fixed point is P* = (1 + sqrt(1 - 4h)) / 2
b) There exists a fixed point for all values of h less than or equal to 1/4.
The fixed points of the model are the values of P at which dP/dt = 0. Therefore, we need to solve the equation
P(1-P) - h = 0
Expanding the left-hand side, we get
P - P^2 - h = 0
Rearranging, we get a quadratic equation
P^2 - P + h = 0
Using the quadratic formula, the two solutions for P are
P = (1 ± sqrt(1 - 4h)) / 2
a) The larger root is the stable fixed point, as it corresponds to a minimum of the fish population growth function. Therefore, the expression for the stable fixed point is
P* = (1 + sqrt(1 - 4h)) / 2
b) For the model to have a fixed point, the quadratic equation must have real roots. This occurs when the discriminant (the expression inside the square root) is non-negative
1 - 4h ≥ 0
Solving for h, we get
h ≤ 1/4
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The given question is incomplete, the complete question is:
This problem explores some questions regarding the fishery model
dP/dt =P(1−P)−h
If you have not yet run the Jupyter notebook please do so now. Find analytical expressions for the two fixed points of the model, in terms of h
a) Give an expression for the stable fixed point. You may assume that the larger fixed point is the stable one. b) For what values of h does there exist a fixed point?
One side of the triangle is 4 cm, and the sum of the other two sides is equal to a whole number of cm. What is the smallest possible perimeter of the triangle?
F. 9 cm
G. 10 cm
H. 11 cm
J. 15 cm
K. 17 cm
Answer:
9 cm
Step-by-step explanation:
By the Triangle Inequality, any two sides of a triangle must be greater than the remaining side.
In order to minimize the perimeter, we will assume that 4 cm is the longest side.
Thus, the two remaining sides must be greater than 4.
Since we are given that the sum of the two remaining sides is a whole number, the smallest whole number value greater than 4 is 5.
Hence, the smallest perimeter possible 9 cm.
Whenever we construct a confidence interval for the population mean, the margin of error includes the standard error of x bar and theA. sampling biasB. nonresponse biasC. z or t value associated with a 95% confidence levelD. desired level of confidence
The margin of error in a confidence interval for the population mean includes the standard error of the sample mean and the z or t value associated with a certain level of confidence, usually 95% or 99%. Therefore, the correct answer is (C).
Sampling bias and nonresponse bias are potential sources of error in survey or study design and data collection, but they are not directly related to the construction of a confidence interval.
The desired level of confidence is a key input for determining the z or t value used in the calculation of the margin of error, but it is not included in the margin of error itself. The correct answer is z or t value associated with a 95% confidence level.
So, the correct option is (C).
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f the random walk starts in the center, on average how many steps does it take to return to the center?
Total number of steps taken by an average man in a year while walking with 7192 steps a day is equals to 2,625,080 steps/year.
Number of steps taken by average man in a day is equals to 7192
Then the total number of steps he takes in a year is equals to,
Calculate it by multiplying the average number of steps per day by the number of days in a year.
There are different ways to define a year,
But assuming a regular calendar year of 365 days, the calculation would be,
Total number of days in a year = 365 days
Total number of steps in a year
= 7192 steps/day x 365 days/year
= 2,625,080 steps/year
Therefore, on average the man would walk about 2,625,080 steps in a year.
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The given question is incomplete, I answer the question in general according to my knowledge:
If a man walks with random steps and the average man takes 7192 steps a day about how many steps does the average man take in a year?
Each interior angle of a regular polygon is 140 Celcius.How many sides does the polygon have?
Answer:
9 sides
Step-by-step explanation:
180 - 140 = 40
360 ÷ 40 = 9
