If her current wealth is $100 and f 0.25, then she bets $25 and either gains or loses that amount then the probability is 0.139.
It is given that Xj is the amount she has immediately after the j the bet is settled.
In the J+1 the bet, she bets fXj of her welath, which has a probability of win of P and probability of loss of 1-p.
Thus:
Xj+1 = Xj + fpXj - f(1-p)Xj
Xj+1 = Xj (1+fp-f(1-p))
Xj+! = Xj(1+2fp-f)
Taking expected values on both sides
E(Xj+1) = E9Xj)(1+2fp-f)
we can write:
E(Xₙ) = E(Xₙ₋₁)(1+2fp-f)
E(Xₙ) = E(Xₙ₋₂)(1+2fp - f)²
E(Xₙ) = E(Xₙ₋₃)(1+2fp - f)³
Hence we get the required answer.
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solve the inequality 11x > 4(1+3x). record your answer in interval notation
Answer:
(-∞, -4)
Step-by-step explanation:
11x > 4(1+3x)
11x > 4*1+4*3x ==> distribute 4 to 1 and 3x using the distribution property
11x > 4 + 12x ==> simplify
11x-12x > 4 + 12x-12x ==> isolate x by subtracting 12x on both sides
-x > 4
x < -4 ==> when dividing by a negative number, switch the inequality sign
x < -4 can also be written as -∞ < x < -4
This is because x is greater than -∞ but can never equal -∞.
-∞ < x < -4 ==> (-∞, -4)
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use the given information, determine weather you can prove each pair of triangles congruent…
Both triangles are congruent by the SAS congruence theorem.
The congruence statement is, ΔBDC ≅ ΔBDA.
How to Prove that Two Triangles are Congruent by the SAS?The SAS stands for side-angle-side theorem, which means that if we can show that two triangles have two corresponding congruent sides and one pair of corresponding congruent included angle, then both triangles are congruent.
From the information given, we can state the following:
AB ≅ CB, which is one pair of corresponding congruent sides [given]
Angle ABD ≅ angle CBD, which is one pair of corresponding included congruent angles [given]
BD ≅ BD, also one pair of corresponding congruent sides [reflexive property of congruence]
Therefore, we can conclude based on the above information that:
ΔBDC ≅ ΔBDA by the SAS congruence theorem.
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1
You are told that 56% of the pupils in a class are girls.
What is the smallest number of pupils the class could contain?
The smallest number of pupils the class could contain is 25.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100
Since we are told that 56% of the pupils in a class are girls, the smallest number of pupils the class could contain is 25. This will be:
= 14 / 25 × 100
= 56%
This is correct as indicated above.
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Luke invests $800 into an account with a 2.9% interest rate that is compounded semiannually.
How much money will he have in this account if he keeps it for 5 years?
Round your answer to the nearest dollar.
The money he will have in this account if he keeps it for 5 years is $358.
What is meant by compound interest?Compound interest is the term used to describe interest on savings that is calculated using both the initial principal and interest that has accrued over time. You can earn interest on interest, which is known as compound interest.
WE have given $100 and it earns 5% interest annually, you will have $105 at the end of the first year. You will have $110.25 by the conclusion of the second year.
Given,
P = $800
Time t=5 years
Interest rate= 2.9%
Hence, the amount will have in his account is:
=[tex]P(1 + 10 / 2000)^{2t}[/tex]
Here, the interest is compounded semiannually.
[tex]800 (1 + 2.9 / 200)^{10}[/tex]
=$358
Therefore, if the interest rate is compounded semiannually then the money he will have in this account if he keeps it for 5 years is $358.
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(please explain :))A 35 foot ladder is set against the side of a house so
that it reaches up 21 feet. If Elijah grabs the ladder at its
base and pulls it 4 feet farther from the house, how far up
the side of the house will the ladder reach now? (The
answer is not 17 ft.) Round to the nearest tenth of a foot.
Answer:
21.4
Step-by-step explanation:
If the ladder originally reaches up 21 feet on the side of the house, and Elijah pulls it 4 feet farther away from the house, the distance from the base of the ladder to the side of the house will increase by 4 feet. This means that the new distance from the base of the ladder to the side of the house will be 21 feet + 4 feet = 25 feet.
Since the height of the ladder is the same, and the base of the ladder is now 25 feet from the side of the house, the ladder will still reach up 21 feet on the side of the house. Therefore, the new distance from the top of the ladder to the ground will be 25 feet - 21 feet = <<25-21=4>>4 feet.
To find the new distance from the top of the ladder to the side of the house, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, we have a right triangle with legs of lengths 21 feet (the height of the ladder) and 4 feet (the distance from the top of the ladder to the ground), and we want to find the length of the hypotenuse (the distance from the top of the ladder to the side of the house). We can use the formula c^2 = a^2 + b^2 to find the length of the hypotenuse:
c^2 = 21^2 + 4^2
= 441 + 16
= 457
c = sqrt(457)
= 21.37
Therefore, the distance from the top of the ladder to the side of the house is 21.37 feet, and the ladder will reach up 21.37 feet on the side of the house after Elijah pulls it 4 feet farther away. Round to the nearest tenth of a foot, the ladder will reach up 21.4 feet on the side of the house.
The answer would not be 17 feet because the height of the ladder and the distance from the base of the ladder to the side of the house are two separate and independent quantities. The height of the ladder is a fixed distance and does not change, regardless of the position of the base of the ladder. Therefore, even if Elijah pulls the ladder 4 feet farther away from the house, the height of the ladder will still be 21 feet and the ladder will still reach up 21 feet on the side of the house. The only change will be the distance from the base of the ladder to the side of the house, which will increase by 4 feet.
Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05. Therefore, the null hypothesis ________.
A. should not be rejected
B. must be rejected
C. may or may not be rejected depending on the square root of the sample size
D. is the same as the alternative hypothesis
Consider a two-tailed test with a level of confidence of 99%. The p-value is determined to be 0.05. Therefore, the null hypothesis should not be rejected.
What is null hypothesis?The null hypothesis is a common statistical theory that contends that there is no statistical relationship or significance between any two sets of observed data and measured phenomena for any given single observed variable.
What is alternative hypothesis?An assertion used in statistical inference experiments is known as the alternative hypothesis. It is indicated by Ha or H1 and runs counter to the null hypothesis. Another way to put it is that it is only a different option from the null. An alternative theory in hypothesis testing is a claim that the researcher is testing.
One less than the confidence level, or 0.01, is the test's level of significance. The null hypothesis is not rejected since the p-value of 0.05 exceeds the level of significance of 0.01.
Therefore, the null hypothesis should not be rejected.
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The ______ of an object is a measure of the average kinetic energy of the particles in the object.
a.heat b.temperature c.conductivity d.charge
Answer:
b. temperature
Step-by-step explanation:
It is the measure of average kinetic energy of motion or K.E of a single particle in a system.
Divide 25 by 5,
then add 7.
Answer:
The answer would be 12.
The equation would be (25/5)+7
Step-by-step explanation:
To solve this problem, first divide 25 by 5.
25/5=5
Now, add 7 to 5 for your answer.
The answer would be 12.
The equation would be (25/5)+7
Hope this helps! Have a great day! :D
25÷5=5
5+7=12
12 is your answer
On a number line, the directed line segment from Q to S has endpoints Q at -14 and S at 2. Point R partitions the
directed line segment from Q to S in a 3:5 ratio.
Which expression correctly uses the formula
x; to find the location of point R?
To get the coordinate of point R partitioned by the ratio 3:5, the required
What is partition
To divide (something, as a country) into two or more territorial pieces with distinct political standing is to divide it into parts or shares. to divide or separate by a partition (such as a wall), frequently used with off.
formula will be given as [tex]M(x, y)=\left(\frac{a x_1+b x_2}{a+b}, \frac{a y_1+y_2}{a+b}\right)[/tex]M(x, y) = (ax1+bx2/a+b, ay1+by2/a+b)
The midpoint rule
From the given statement, we have the following information
Point Q = (-14, 0)
Point S = (2, 0)
R = (x, y)
To get the coordinate of point R partitioned by the ratio 3:5, the required formula will be given as M(x, y) = (ax1+bx2/a+b, ay1+by2/a+b)
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1. A woman visits four different places: A, B, C, and D. If, at a given time, she is at point A, then the next hour she will be at point D with 100 percent probability. If she is at point B, then she will be at point A in an hour (with 100 percent probability) If she is at point C, then she will be at point A or B, with equal probabilities (that is, 50 percent each). If she is at point D, then she will be at point B or C with equal probability. a) Write down the stochastic matrix M that describes, given a probability vector, the probability that the woman will be at each of the places during the next hour. (b) Find the steady state vector. (This is a probability vector [positive entries that add up to 11 satisfying Mu- [Hint: you should simply assume that λ-1 is an eigenvalue for M (this is guaranteed for all stochastic matrices) and find the corresponding eigenspace. Divide by a suitable constant to get the steady state vector (c) After many hours pass, what are the probabilities that the woman will be at A? B? C? D? (These are recorded in the steady state vector.)
The resulting probability is 100%
How to calculate probability?
The general formula to calculate the probability is
=> P(B) = (n(B)/N(S)
where,
P(B) is the probability of an event 'B'.
n(B) is the number of favorable outcomes of an event 'B'.
n(S) is the total number of events occurring in a sample space.
Given,
A woman visits four different places: A, B, C, and D. If, at a given time, she is at point A, then the next hour she will be at point D with 100 percent probability. If she is at point B, then she will be at point A in an hour (with 100 percent probability) If she is at point C, then she will be at point A or B, with equal probabilities (that is, 50 percent each). If she is at point D, then she will be at point B or C with equal probability.
Here we have given that,
Number of places = 4 (A, B, C, D)
Initial point = A
Point D probability = 100%
For Point B to A probability = 100%
For point C to A or B probability = 50%
For point D to B and C probability = 50%
Now, here we need to find the probabilities that the woman will be at.
Like the women will spend three hours of travelling in the point A, B and C, then the probability of the points are calculated as,
=> 1 + 0.5 + 0.5 - 1
=> 2 - 1 = 1
Therefore, the resulting probability is 100%.
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Find the length of an arc on a circle whose radius is 10 cm and whose central angle subtends a central angle of 20º
Select all irrational numbers.
√3/16
√4/16
√9/16
√3/4
√9/4
From the given numbers root (3/4) and root (9/4) irrational numbers.
What are irrational numbers?
Irrational numbers are the set of real numbers that cannot be expressed in the form of a fraction, p/q where p and q are integers. The denominator q is not equal to zero (q ≠ 0). Also, the decimal expansion of an irrational number is neither terminating nor repeating.
Here,
root(3/16) is a rational number
root(9/16) is a rational number.
Therefore, from the given numbers root(3/4) and root(9/4) are the irrational numbers.
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Select the values that make the inequality h < 2 true.
(Numbers written in order from least to greatest going across.)
The inequality is: h less than equal to 2 That is the Numbers written in order from least to greatest going across
To find:
The values that make the given inequality true.
We have,
h less than equal to 2
It means the value of h must be less than or equal to 2.
In the given options, the list of numbers which are less than or equal to 2 is
-6, -3, -1, 1, 1.9, 1.99, 1.999, 2
The list of numbers which are greater than 2 is
2.001, 2.01, 2.1, 3, 5, 7, 10
Therefore, the first 8 options are correct and the required values are -6, -3, -1, 1, 1.9, 1.99, 1.999, 2.
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Which of the following are solutions to the equation below?
Check all that apply.
x² + 6x + 9 = 20
A. x= 2√5-3
B. x= √3+ 20
C. x= -2√5 +3
D. x = -√3+20
☐ Ex= 2√5 +3
OF x=-2√5-3
The solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.
What is a quadratic equation?
Any equation of the form where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
x = [-b± (√b²-4ac )] / 2a
The quadratic equation:
x²+6x+9=20
x²+6x -11 = 0
a = 1, b = 6, c = -11
x₁,₂ = [-6±√6² - 4.1.(-11)]/2(1)
x = -3 + 2√5 , x = -3 - 2√5
Thus, the solution to the equation x²+6x+9=20 is x = -2√5 - 3 or x = 2√5 -3 option option (B) and option (D) are correct.
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Exercises 57 and 58 refer to the following setting. In Exercises 14 and 18 of Section we examined the probability distribution of the random variable the amount a life insurance company earns on a 5 -year term life policy. Calculations reveal that and Life insurance If four 21 -year-old men are insured, the insurer's average income is
where is the income from insuring one man. Assuming that the amount of income earned on individual policies is independent, find the mean and standard deviation of . (If you compare with the results of Exercise 57 , you should see that averaging over more insured individuals reduces risk.)
the mean and standard deviation of the random variable X, which represents the income from insuring four 21-year-old men, is 2000 and 27.22, respective
Mean: $2,000
Standard Deviation: $741.42
The mean of the random variable X is calculated by taking the sum of the products of the probability of each outcome and the corresponding value of X. The probabilities of each outcome, in this case, are 0, 0.38, 0.59, and 0.03, respectively. The corresponding values of X are $1000, 2000, 3000, and 4000$. Thus, the mean of X is calculated as:
Mean =[tex]$\sum_{i=1}^{N} P(X = x_i)*x_i[/tex]
= 0*1000 + 0.38*2000 + 0.59*3000 + 0.03*4000
= 2000
The standard deviation of the random variable X is calculated by taking the square root of the sum of the products of the probability of each outcome and the square of the difference between the corresponding value of X and the mean. The probabilities of each outcome, in this case, are 0, 0.38, 0.59, and 0.03, respectively. The corresponding values of X are $1000, 2000, 3000, and 4000$. The mean of X is 2000. Thus, the standard deviation of X is calculated as:
Standard Deviation = [tex]$\sqrt{\sum_{i=1}^{N} P(X = x_i)(x_i - \mu)^2}[/tex]
= [tex]\sqrt{(0(1000-2000)^2[/tex] + [tex]0.38*(2000-2000)^2[/tex] + [tex]0.59*(3000-2000)^2 + 0.03*(4000-2000)^2)}[/tex]
= [tex]\sqrt{741.42} = 27.22$[/tex]
Therefore, the mean and standard deviation of the random variable X, which represents the income from insuring four 21-year-old men, is 2000 and 27.22, respective
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Given the following linear function, sketch the graph of the function and find the domain and range.
2
f(x)=²x-3
The domain and range of the given function is a set of al real numbers and as such;
Domain : (-∞,∞)
Range : (-∞,∞)
What is the domain and range of the Linear Function?We are given the function as f(x)= -3x+7.
In order for us to sketch the graph of this given function, we need to make a function table
Lets assume some random number for x and find out f(x)
x f(x) = -3x + 7
-2 -3(-2) + 7 = 13
-1 -3(-1) + 7 = 10
0 -3(0) + 7 = 7
1 -3(1) + 7 = 4
We now plot the points as shown in the graph attached
Domain is defined as the set of all x values for which the function is defined while Range is defined as the set of all y values for which the function is defined
In this case, there is no restriction for x and y and as such the domain and range is a set of all real numbers
Domain : (-∞,∞)
Range : (-∞,∞)
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Complete question is;
Given the following linear function sketch the graph of the function and find the domain and range. ƒ(x) = -3x + 7
A student made a mistake while using similar triangles to find the missing side length indicated by the letter z in the diagram Analyze the student's work and find the state. Explain what was done incorrectly and find the correct solution Student's work to find the value of x
The students ratio expressed in fraction as 6/4 = 4/x is incorrect for the similar triangles, and the correct ratio is x : 3 = 10 : 6 expressed in fraction as x/3 = 10/6. The value for x = 5.
How to calculate for x for the similar trianglesSince the triangles are similar, it implies that the length 3 of the smaller triangle is similar to the length x of the larger triangle,
Also the length 6 of the smaller triangle is similar to the length of the larger triangle (4 + 6 = 10).
So it will be wrong to write 6/4 = 4/x, rather the correct fraction will be;
x : 3 = 10 : 6
which when expressed as fraction, we get;
x/3 = 10/6
x = (10 × 3)/6
x = 30/6
x = 5
Therefore, the students expression 6/4 = 4/x is incorrect representation for the lengths of the similar triangles. And the correct expression is x/3 = 10/6, which gives us the value of x equal to 5.
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Determine which answers in in the solution that will make the equation true
Answer:
9
Step-by-step explanation:
3p + 6 = 5p – 12
6 + 12 = 5p – 3p
18 = 2p
p = 18/2
p = 9
rate as brainliest
thank you
Answer:
The answer would be 9.
Step-by-step explanation:
If you plug in 18 for both of them, the answer would be:
60=78
If you plug in 9 for both of them, the answer would be:
33=33
If you plug in 0 for both of them, the answer would be:
6=-12
If you plug in -9 for both of them, the answer would be:
-21=-57
So, 9 would be the best choice.
Hope this helps! :D
A random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations in parts a through d. Calculate a 95% confidence interval for ju for each of these situations. a. n=70, X = 27 b. n = 150, x= 115 c. n= 80. x = 18 d. n = 80, x=5.33 e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a through d? Explain. (Round to two decimal places as needed.) (Round to two decimal places as needed.) (Round to two decimal places as needed.) d. (ID) (Round to two decimal places as needed.) e. Choose the correct answer below. O A. No, since the sample sizes are large in 2 30), the condition guarantees that the sampling distribution of x is approximately normal. O B . No, since the confidence level is at least 90%, the underlying distribution need not be normal. OC. No, since the sample was randomly selected from the target population, the sampling distribution of x is guaranteed to be approximately normal. OD. Yes, the underlying distribution must be normal for the validity of these confidence intervals O E. No, since the sample sizes are large in 230) and randomly selected from the target population, the condition guarantees that the sampling distribution of x is approximately normal.
As per the 95% confidence interval for the population mean is (31.042, 42.958).
What is meant by confidence interval?
In math, A normal distribution with a mean, μ and standard deviation, σ is used to estimate the confidence interval for the unknown population mean.
Here we have given that the random sample of n measurements was selected from a population with unknown mean and standard deviation o = 20 for each of the situations.
And we need to find the 95% confidence interval for ju for each of these situations.
Here we are given the following data:
• Sample size, n=70
• Sample mean, ¯x=37
• Population standard deviation, σ=20
Then the 95% confidence interval for the population mean is defined as:
=> x±z0.01/2×σ√n
Here by applying Excel function for the confidence coefficient:
=> NORM.INV(0.01/2,0,1)
Then we get,
=> 37±2.58×20√75(31.042, 42.958)
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Find the measure of
Answer:
<MON = 102°
Step-by-step explanation:
Alternative Interior Angles so both of those angle equal to each other.
(12x + 30) = (9x + 48)
Get x to one side by subtracting.
12x - 9x + 30 = 48
3x + 30 = 48
Subtract 30 to both side to get x by itself.
3x = 18
Divide 3 to both side to solve for x.
x = 6
Plug x = 6 into <MON = (9x + 48)
9*6 + 48 = 54 + 48 = 102°
Write a function that takes as arguments: the data frame you generated above from importing the Walmart dataset a state abbreviaton (e.g. AR) and, then, the function returns a pandas Data Frame with 2 columns: 1) a column called date that contains the date (note that date must be properly ordered) 2) a column called cumsum that contains the cumulative (i.e. running) sum of the number of stores over time opened in that state Please tell how to use cumsum function for number of stores and then another column that has respective dates.
The cumsum function returns the cumulative sum of an array whose size is not 1 from the dataset that is imported from Walmart.
Create an array of the number of stores in each state along with the date opened. You can then use the cumsum option to find the total number of stores Walmart has over the states.
For instance, to find cumulative sum of integers 1 to 6, we have
A = 1:6;
B = cumsum(A)
It yields the output:
1, 3, 6, 10, 15, 21
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a satellite traveling in a circular orbit 1,000 miles above the earth passes directly over a tracking station at noon. assume that the satellite takes 2 hours to make an orbit and that the radius of the earth is 4,000 miles. find the distance between the satellite and tracking station at 12:03 p.m. draw a picture (using the idea of orbits like above), then solve.
The distance between the satellite and tracking station at 12:03 p.m is 1271.55 miles.
Given that :
TS = 1000 miles
Orbital time = 2 hours
Let T be tracking station.
S be satellite position.
R be a satellite position at 12:03 p.m
Time = 12:03 - 12:00 = 3 min
SR = Satellite speed × time
Orbital distance = 2πR
= 2π(4000 + 1000)
= 10000 π miles
Orbital speed = [tex]\frac{satellite distance}{satellite time}[/tex]
= [tex]\frac{10,000\pi }{2}[/tex]
= 5000 π miles/hour
= [tex]\frac{5000 \pi }{60}[/tex] miles/min
Distance SR = Orbital speed × time
= [tex]\frac{5000 \pi }{60}[/tex] × 3
= 250 π miles
Using pythagoras theorem in triangle TSR
[tex]TR^{2}[/tex] = [tex]TS^{2} + SR^{2}[/tex]
= [tex]\sqrt{TS^{2} + SR^{2} }[/tex]
= [tex]\sqrt{1000^{2} + 250 \pi ^{2} }[/tex]
TR = 1271.55 miles
Therefore, the distance between the satellite and tracking station at 12:03 p.m is 1271.55 miles.
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Find the 3rd order Taylor polynomial of the function f(x)= √x centered at 4 and then use this polynomial to approximate √14.03. Show at least 8 decimal places in your answer.
The 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is expressed as f(x) ≈ P3(x) = a₀ + a₁(x - 4) + a₂(x - 4)² + a₃(x - 4)³.
Here, a₀, a₁, a₂, and a₃ are the coefficients that need to be calculated. To find these coefficients, we must use the Taylor series formula and the derivatives of f(x) evaluated at 4.
The Taylor series formula is Pn(x) = f(a) + f'(a)(x-a) + (f''(a)/2!) (x-a)² + (f'''(a)/3!) (x-a)³ + ... +[tex](f^(n)(a)/n!) (x-a)^n[/tex].
The derivatives of f(x) evaluated at 4 are f'(4) = 1/2, f''(4) = -1/8, f'''(4) = -1/16.
Using these values, the coefficients of the 3rd-order Taylor polynomial can be calculated as a₀ = 2, a₁ = 1/2, a₂ = -1/8, and a₃ = -1/16.
Therefore, the 3rd-order Taylor polynomial of the function f(x)= √x centered at 4 is P3(x) = 2 + (1/2)(x - 4) - (1/8)(x - 4)² - (1/16)(x - 4)³.
Using this polynomial to approximate √14.03, we have P3(14.03) = 2 + (1/2)(14.03 - 4) - (1/8)(14.03 - 4)² - (1/16)(14.03 - 4)³ ≈ 3.76401097.
Therefore, the approximation of √14.03 using the 3rd-order Taylor polynomial is 3.76401097 to 8 decimal places.
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What is the simplified form of each expression?
The simplified form of an expression is the expression written in its simplest form, usually achieved by combining like terms and removing unnecessary parentheses.
when the base and leg side of right triangle are the same what is the angel measure fo the hypotenuse?
the measure of the hypotenuse angle must be 180 - (45 + 45) = 90 degrees .The angle measure of the hypotenuse in this case would be 45 degrees.
In right triangles, the angles of the triangle always add up to 180 degrees. Since the base and leg side of the triangle have the same measure, the two angles opposite of them must both be 45 degrees. Thus, the measure of the hypotenuse angle must be 180 - (45 + 45) = 90 degrees.In right triangles, the sum of the angles is always 180 degrees. The base and leg of a right triangle have the same measure, thus the angles opposite of them must both be equal. This means that the two angles add up to 90 degrees. Subtracting 90 from 180 degrees gives us the angle measure of the hypotenuse, which is 90 degrees.
180° - (45° + 45°) = 90°
Therefore, the angle measure of the hypotenuse in this case is 90°
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anova 7. a large marketing firm uses many photocopying machines, several of each of four different models. during the last six months, the office manager has tabulated for each machine the average number of minutes per week that it is out of service due to repairs, resulting in the following data: model g: 56 61 68 42 82 model h: model k: 74 77 92 63 54 25 36 29 56 44 model m: 78 105 89 112 61 perform an analysis of variance to decide whether the difference among the means of the four samples can be attributed to chance.state the conclusion.
The null and alternative hypothesis of the number models are
H₀ : There is no difference among the means of four samples models.
H₁ : There is difference among the means of four samples models.
Given that,
Many photocopiers are used by a large marketing company, several of each of the four models. The office manager calculated for each machine the typical amount of minutes per week that it is out of commission due to repairs over the previous six months, yielding the following information:
Model g: 56 61 68 42 82
Model h: 74 77 92 63 54
Model k: 25 36 29 56 44
Model m: 78 105 89 112 61
We have to find the null and alternative hypothesis.
We know that,
So,
H₀ : There is no difference among the means of four samples models.
H₁ : There is difference among the means of four samples models.
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7
The Spinner is a ride that straps people to the edge of a circle
and spins. If riders are traveling 25 mph and the radius of the
wheel is 15 feet, find the angular speed in rpm.
To find the angular speed in rpm, we need to use the formula for tangential speed, which is the speed at which an object moves along a circular path. The formula for tangential speed is:
v = r * omega
where v is the tangential speed, r is the radius of the circle, and omega is the angular speed.
In this case, we are given that v = 25 mph and r = 15 feet. We can solve for omega by dividing both sides of the equation by r:
omega = v / r
Substituting the given values, we get:
omega = 25 mph / 15 feet
To convert the units of speed from mph to feet per second, we need to use the conversion factor that 1 mph is equal to 5280/3600 feet per second. We can use this conversion factor to rewrite the expression for omega in terms of feet per second:
omega = (25 mph * (5280/3600)) / 15 feet
This simplifies to:
omega = 0.7222 feet/second
Next, we need to convert the angular speed from feet per second to rpm. To do this, we need to use the formula for converting from linear speed to angular speed, which is:
omega = (v * 60) / (2 * pi * r)
where v is the linear speed, r is the radius of the circle, and omega is the angular speed in rpm.
In this case, we are given that v = 0.7222 feet/second and r = 15 feet. We can solve for omega by plugging these values into the formula and simplifying:
omega = (0.7222 feet/second * 60) / (2 * pi * 15 feet)
= 0.7222 feet/second * 60 / (2 * pi * 15 feet)
= 0.7222 * 60 / (2 * pi * 15)
= 4.3332 / (2 * pi * 15)
= 0.2821 / (pi * 15)
Therefore, the angular speed in rpm is 0.2821 / (pi * 15), or approximately 0.0046 rp
Leslie gathered this data revealing the distance traveled and the cost of ticket when taking a commuter train between six different pairs of stations
The cost for two stations that are 10 miles apart will be $8.21.
What is cost?
Cost denotes the amount of money that a company spends on the creation or production of goods or services. It does not include the markup for profit. From a seller's point of view, cost is the amount of money that is spent to produce a good or product.
Given equation is;
y = 0.354x+4.669
Where x represents the number of miles traveled.
For measuring the cost for two stations that are 10 miles apart;
x=10
Putting in given equation
y=0.354(10)+4.669
y=3.54+4.669
y=8.209
Rounding off to nearest hundredth;
y=$8.21
The cost for two stations that are 10 miles apart will be $8.21
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let x and y be i.i.d. unif(0, 1). (a) compute the covariance of x y and x y . (b) are x y and x y independent studysoup
If x and y be i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero.
Yes, x y are x y independent studysoup.
Here x and y be i.i.d. unif(0, 1)
The i.i.d stands for independent and identically distributed
unif means that the uniformly distributed
Here x and y are i.i.d unif (0,1)
The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable
Here we have to find the covariance of x + y and x - y
According to the properties of covariance
Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0
Because Cov(x, x) = Cov (y, y)
Cov(y, x) = Cov(x, y)
Therefore, the covariance of x+y and x - y is 0.
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Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.)
y = 5 - x2
(1) units (width)
(2) units (height)
The length of the rectangle is 1.054 units and the width of the rectangle is 4.72 units.
Length times width equals the area of a rectangle. Let's assume that x represents length and y represents width. To determine the dimensions of the rectangle, we must apply y values to the area formula, differentiate with respect to x, and then set differentiate to zero.
Parabola: [tex]y=5-x^{2}[/tex]
The equation of parabola indicates that it opens down and the axis of symmetry is x=0. So we can take the vertices of the rectangle on the x-axis as [tex]A=(-x,0)[/tex] and [tex]D=(x,0)[/tex]). The other two vertices above the x-axis on the parabola will be [tex]B=(-x, 5-x^{2} )[/tex] and [tex]C=(x,5-x^{2} )[/tex]
Dimensions of the rectangle will be,
[tex]x-(-x)=2x[/tex] and [tex](5-x^{2} )[/tex]
Area of the rectangle (A) = [tex]2x(5-x^{2} )[/tex]
Area function when differentiated (A′) = [tex]2x(-2x)+(5-x^{2} )(2)[/tex]
A′= [tex]-4x^{2} + 10 -2x^{2}[/tex]
A′= [tex]-6x^{2} +10[/tex]
Critical points for maxima and minima ⟹ [tex]-6x^{2} +10=0[/tex]
⟹ [tex]10=6x^{2}[/tex]
⟹ [tex]x^{2} = \frac{10}{6}[/tex]
⟹ [tex]x= \sqrt \frac{10}{6}[/tex]
⟹ [tex]x=[/tex] ±[tex]0.527[/tex]
Maximum area of 2X2 rectangle(square)
A= [tex]2*0.527(5- 0.527^{2} )[/tex] = [tex]4.97[/tex] [tex]units^{2}[/tex]
Length = 2x = 1.054 units
Width = [tex](5-x^{2} )[/tex] = 4.72 units
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