The partial sums will cease to change when the terms of the series become smaller than the smallest representable number in the floating-point system.
In floating-point arithmetic, there is a finite range of representable numbers and a limited precision for calculations. When dealing with infinite series, the terms are added or subtracted sequentially, but due to the limitations of numerical precision, there is a point at which the terms become too small to affect the sum significantly.
For the series 1/n, as n increases, the terms approach zero but never actually reach zero. Eventually, the terms become smaller than the smallest representable number in the floating-point system, and at this point, they essentially contribute zero to the sum. As a result, the partial sums of the series will cease to change beyond this point.
It's important to note that although the sum of the series may appear to be finite in floating-point arithmetic, mathematically, the series diverges and does not have a finite sum. The convergence to a finite value in floating-point arithmetic is a result of the limitations of numerical representation and precision. A divergent infinite series, such as the sum of 1/n from n=1 to infinity, can have a finite sum in floating-point arithmetic due to the limitations of numerical precision.
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Use the inverse matrices to find and (24) ? 7 - 2 2 2 A-1 B-1 = 2 1 3 4 4. 3 4 2 11 (b) (47) b 100 -100 co (24) JUD .11
To find the value of matrix A given A⁻¹ and B⁻¹, we can use the formula A = (A⁻¹)⁻¹ * B⁻¹.
Given A⁻¹ = [[2, 7], [-2, 2]] and B⁻¹ = [[2, 1], [3, 4], [4, 3], [2, 11]], we can calculate A as follows:
Step 1: Calculate the inverse of A⁻¹: (A⁻¹)⁻¹
(A⁻¹)⁻¹ = [[2, 7], [-2, 2]]⁻¹
To find the inverse of a 2x2 matrix, we use the following formula:
[[a, b], [c, d]]⁻¹ = (1 / det([[a, b], [c, d]])) * [[d, -b], [-c, a]]
Step 2: Calculate the determinant of A⁻¹: det([[2, 7], [-2, 2]])
det([[2, 7], [-2, 2]]) = (2 * 2) - (7 * -2) = 4 + 14 = 18
Step 3: Calculate the inverse of A⁻¹: (A⁻¹)⁻¹
(A⁻¹)⁻¹ = (1 / 18) * [[2, -7], [2, 2]] = [[2/18, -7/18], [2/18, 2/18]]
Step 4: Calculate A = (A⁻¹)⁻¹ * B⁻¹
A = [[2/18, -7/18], [2/18, 2/18]] * [[2, 1], [3, 4], [4, 3], [2, 11]]
Performing matrix multiplication, we get:
A = [[2/18 * 2 + (-7/18) * 3, 2/18 * 1 + (-7/18) * 4],
[2/18 * 2 + 2/18 * 3, 2/18 * 1 + 2/18 * 4]]
Simplifying the calculations, we find:
A = [[-1/3, -2/3],
[2/9, 4/9]]
Therefore, the value of matrix A is [[-1/3, -2/3], [2/9, 4/9]].
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Chloe has a bag of marbles with 5 blue marbles, 1 white marbles, and 3 red marbles.
Find the following probabilities of Chloe drawing the given marbles from the bag if the first marble(s) is(are) returned to the bag after they are drawn.
a) A Blue, then a red =
b) A red, then a white =
c) A Blue, then a Blue, then a Blue =
a) The probability of Chloe drawing a blue marble, then a red marble, with replacement is (5/9) * (3/9) = 15/81 ≈ 0.185.
b) The probability of Chloe drawing a red marble, then a white marble, with replacement is (3/9) * (1/9) = 3/81 ≈ 0.037.
c) The probability of Chloe drawing three blue marbles in a row, with replacement, is (5/9) * (5/9) * (5/9) = 125/729 ≈ 0.172.
For each probability, we multiply the probabilities of drawing each marble consecutively, taking into account that the marble is returned to the bag after each draw. The denominator is 9 because there are a total of 9 marbles in the bag. The numerators reflect the number of marbles of each color in the bag.
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A store has 125 scientific calculators.
Brand x sells for $20 each; Brand y sells
for $15 each. If the total selling price
of the calculators is $2,275, how many
of each calculator does the store have?
Answer:
Brand x: 80
Brand y: 45
Step-by-step explanation:
x + y = 125
20x + 15y = 2275
-20x - 20y = -2500
(+) 20x + 15y = 2275
--------------------------------
-5y = -225
y = 45
x + y = 125
x + 45 = 125
x = 80
Answer:
Brand x: 80
Brand y: 45
1 - m∠QRU = _____ °.
2 - m∠VUW = _____ °.
3 - m∠TUW = _____ °.
Answer:
Step-by-step explanation:
74
The total cost (in dollars) of producing x food processors is C(x)=2500+20x-0,1x². (A) Find the exact cost of producing the 71st food processor. (B) Use the marginal cost to approximate the cost of producing the 71st food processor.
(A) The exact cost of producing the 71st food processor is $3415.90. (B) Using the marginal cost approximation, the cost of producing the 71st food processor is approximately $5.80.
The cost of producing the 71st food processor can be found by substituting x = 71 into the cost function C(x) = 2500 + 20x - 0.1x². (A) The exact cost of producing the 71st food processor is C(71) = 2500 + 20(71) - 0.1(71)² = 2500 + 1420 - 504.1 = $3415.90.
The marginal cost represents the change in cost when one additional unit is produced. It can be approximated by calculating the difference between the cost of producing x+1 units and x units and dividing it by the change in quantity. In this case, the marginal cost is the derivative of the cost function, which is given by C'(x) = 20 - 0.2x. To approximate the cost of producing the 71st food processor using the marginal cost, we can evaluate C'(x) at x = 71. (B) C'(71) = 20 - 0.2(71) = 20 - 14.2 = $5.80. Therefore, the approximate cost of producing the 71st food processor using the marginal cost is $5.80.
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HELPPPPPPPPPP!!!!!!!!!!!!
a
252 cm sq.
b
324 cm sq.
c
144 cm sq.
d
21 cm sq.
What is the volume of a hemisphere with a diameter of 7.6 m, rounded to the nearest tenth of a cubic meter?
Answer:114.9m^3
Step-by-step explanation:
simplify the expression ((-1)^5/(-2)-3)^2
Answer:
Sure! Let's simplify the expression step by step:
((-1)^5/(-2)-3)^2
= (-1/2 - 3)^2 // Since (-1)^5 = -1
= (-7/2)^2
= 49/4
Therefore, ((-1)^5/(-2)-3)^2 simplifies to 49/4.
Jenica bowls three games and scores an average of 116 points per game. She scores 105 on her first game and 128 on her second game. What does she need to score on her third game to get a mean score of 116?
Answer:
115 points on her third game.
Step-by-step explanation:
To find the answer add the first and second games together.
128 + 105 = 233 ÷ 2 = 116.5 (then divide by two because there is two games).
This is the average of two games. To find the average of THREE games try different numbers to see which number works.
233 + 110 = 343 ÷ 3 = 114.3
(so we have to try a higher number than 110).
233 + 112 = 345 ÷ 3 = 115 on average (still not enough).
233 + 115 = 348 ÷ 3 = 116. (we found the answer!)
233 + 115 = 348 ÷ 3 = 116
what is the area of the circle to the nearest square foot?
Answer:
G. 113
Step-by-step explanation:
We know that the diameter = 12, so the radius = 6.
area of circle = πr²
= π (6²)
= 36π
= 113.0973355 . . .
≈ 113 ft²
Find the volume of the following. Round to nearest hundredths place:
Use 3.14 for II
+
7 mi
2 mi
Answer:
volume of cone=1/3×pi×r²×h
volume of cone =1/3×22/7×(2mi)²×7mi
volume of cone =29.32mi³
Help me please!!!!!!!!!!!!!!!
Answer:
reflection over y axis
Step-by-step explanation:
If an augmented matrix [ A b ] is transformed into [ C d ] by elementary row operations, then the equations Ax = b and Cx = d have exactly the same solution sets.
true false
If an augmented matrix [ A b ] is transformed into [ C d ] by elementary row operations, then the equations Ax = b and Cx = d have exactly the same solution sets is true.
Elementary row operations are specific operations that can be performed on the rows of a matrix. These operations include:
Swapping two rows.Multiplying a row by a non-zero scalar.Adding a multiple of one row to another row.When we apply elementary row operations to an augmented matrix [ A b ], we are essentially performing the same operations on the corresponding system of linear equations Ax = b. The purpose of these operations is to simplify the matrix or system of equations, but they do not change the solution set.
Each elementary row operation corresponds to an equivalent algebraic operation on the system of equations. For example, swapping two rows corresponds to rearranging the order of equations, multiplying a row by a scalar corresponds to multiplying both sides of the equation by the same scalar, and adding a multiple of one row to another row corresponds to adding or subtracting equations.
Since elementary row operations preserve the equivalence between the matrix and the system of equations, any solution that satisfies the original system Ax = b will also satisfy the transformed system Cx = d. Similarly, any solution that satisfies Cx = d will also satisfy Ax = b.
Therefore, the solution sets of the original system Ax = b and the transformed system Cx = d are exactly the same.
Therefore, If an augmented matrix [ A b ] is transformed into [ C d ] by elementary row operations, then the equations Ax = b and Cx = d have exactly the same solution sets is true.
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Which is greater? 40 mm or 3 m
and how do I show my work for that?
correct=brainliest
Answer:
The answer is 1 meter
Step-by-step explanation:
One meter is equal to 1000 mm
An author of a book gets 3% of the price of each book sold. He received $24,380. How many copies of the book were sold, if each book was sold for $32.00?
Please Explain
divide the number by 32 then divide what you get by 3 and last times 100 equals 25,395.83333333 round it if you want to to 25,395.8
9) A carton contains 2 litres of tropical juice. The juice consists of 25% mango juice, 30% pineapple juice, and the rest is guava juice. Find how many millilitres of each juice went into the carton of tropical juice.
The carton of tropical juice contains 500 ml of mango juice, 600 ml of pineapple juice, and 900 ml of guava juice.
To find the amount of each juice that went into the carton of tropical juice, we'll calculate the quantities based on the given percentages.
Let's denote the volume of mango juice as M (in milliliters), the volume of pineapple juice as P, and the volume of guava juice as G. Since the total volume of the carton is 2 liters, we have 2000 milliliters as the total volume.
According to the given information, mango juice accounts for 25% of the total volume, pineapple juice accounts for 30%, and the remaining volume is guava juice.
We can express these relationships as equations:
M + P + G = 2000 (Equation 1)
M = 0.25 * 2000 (Equation 2)
P = 0.30 * 2000 (Equation 3)
G = 2000 - (M + P) (Equation 4)
From Equation 2, we have M = 0.25 * 2000 = 500 ml.
From Equation 3, we have P = 0.30 * 2000 = 600 ml.
Substituting these values into Equation 4, we get:
G = 2000 - (500 + 600) = 900 ml.
Therefore, the quantities of each juice that went into the carton of tropical juice are as follows:
Mango juice: 500 ml
Pineapple juice: 600 ml
Guava juice: 900 ml
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Ashley got 18 out of 42 questions correct on the test. How many more questions would she have
needed to get comect to receive a 70% on the testi
Let f:R" + R" be a linear transformation. Prove that f is injective if and only if the only vector v ERM for which f(v) = 0 is v = 0.
If f(u1) = f(u2), then u1 = u2, demonstrating that f is injective.
To prove that a linear transformation f: R^n -> R^m is injective if and only if the only vector v in R^n for which f(v) = 0 is v = 0, we need to establish both directions of the statement.
Direction 1: f is injective implies the only vector v such that f(v) = 0 is v = 0.
Assume that f is injective. We want to show that if f(v) = 0 for some vector v in R^n, then v must be the zero vector, v = 0.
Suppose there exists a non-zero vector v in R^n such that f(v) = 0. Since f is a linear transformation, it satisfies the property that f(0) = 0, where 0 represents the zero vector in R^n.
Now, consider the vector u = v - 0 = v. Since f is linear, it must satisfy the property that f(u) = f(v - 0) = f(v) - f(0) = 0 - 0 = 0.
Since f(u) = 0, and f is injective, it implies that u = 0. However, we initially assumed that v is a non-zero vector. Therefore, we have reached a contradiction.
Hence, if f(v) = 0 for some vector v in R^n, then v must be the zero vector, v = 0.
Direction 2: The only vector v such that f(v) = 0 is v = 0 implies that f is injective.
Now, assume that the only vector v in R^n such that f(v) = 0 is v = 0. We want to show that f is injective.
Let u1 and u2 be two arbitrary vectors in R^n such that f(u1) = f(u2). We need to prove that u1 = u2.
Consider the vector u = u1 - u2. Since f is linear, we have:
f(u) = f(u1 - u2) = f(u1) - f(u2) = 0.
Since f(u) = 0, and the only vector v such that f(v) = 0 is v = 0, it follows that u = 0. This implies that u1 - u2 = 0, which means u1 = u2.
Therefore, if f(u1) = f(u2), then u1 = u2, demonstrating that f is injective.
By proving both directions, we have established that f is injective if and only if the only vector v in R^n for which f(v) = 0 is v = 0.
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Myrtle needs to borrow $200 and is hoping to get a paid day loan with an annual percentage rate (ARP) of less than 50%. if a company charges her $30 in fee for the loan, what is the minimum loan term needed that would give Myrtle her desired APR?
A. 90 DAYS
B. 100 DAYS
C. 110 DAYS
D. 120 DAYS
Answer:
110 days :)
hope it help!
whats 24/3 but not 8?
Answer: well, it =8 and it doesn’t have different answer so that all I have to tell you.
Step-by-step explanation: Hope this help I guess :^ sorry if you don’t want this kind of answer.
From Monday through Friday Sydney works in the bookstore on one day and in the tutoring center where on another doing on Saturday and Sunday Sydney cooks food 50% of the days how many days does Sidney work in a week what percent of Monday through Friday does Sidney work
Answer: The other 50%
Step-by-step explanation:
do perpendicular lines intersect at a 60 degree angle?
Answer:
Perpendicular angles create a 90 degree angle
Step-by-step explanation:
Find the number of subsets in the set (x l x is a day of the week)
a. 124
b. 256
c. 127
d. 128
Please help! Due tonight.
The lateral area of the pyramid is 126 metres squared.
How to find the lateral area of a pyramid?The diagram above is a pyramid. The lateral area of the pyramid can be found as follows:
lateral area of the pyramid = 1 / 2 pl
where
p = perimeter of the basel = height of the pyramidTherefore,
p = 7 × 3 = 21 metres
l = 12 metres
Hence,
lateral area of the pyramid = 1 / 2 × 21 × 12
lateral area of the pyramid = 21 × 6
lateral area of the pyramid = 126 metres²
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a hollow copper wire with an inner diameter of 1.1 mm and an outer diameter of 2.2 mm carries a current of 10 a.
A hollow copper wire with an inner diameter of 1.1 mm and an outer diameter of 2.2 mm carries a current of 10 A.
The given scenario describes a hollow copper wire with an inner diameter of 1.1 mm and an outer diameter of 2.2 mm that carries a current of 10 A. To determine certain characteristics of the wire, we can utilize the concepts of current, diameter, and material properties.
Firstly, the current of 10 A represents the magnitude of electric current flowing through the wire. This current is a measure of the rate at which electric charges are moving through the conductor.
The dimensions of the wire, specifically the inner and outer diameters, provide insights into its cross-sectional area. By calculating the difference between the outer and inner radii (1.1 mm and 2.2 mm, respectively), we can determine the thickness of the wire's walls. This thickness directly affects the wire's resistance and conductivity.
Copper is known for its excellent electrical conductivity, which allows for efficient current flow. Its resistivity is relatively low compared to other materials. This property ensures that the wire experiences minimal losses and heat generation while carrying the current of 10 A.
In conclusion, the provided information about the hollow copper wire's dimensions and current helps us understand key aspects such as current flow, wire thickness, and the conductive properties of copper. These factors are crucial in determining the wire's electrical behavior and efficiency.
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fyou plant tomato plants in your garden and divide them into four plots. all of the plants are the same variety, and receive the same amount of water and sunlight. you add a different fertilizer to each plot. one plot receives no fertilizer at all. at the end of the month you count how many tomatoes were produced by each plant. the independent variable is the
The independent variable in this scenario is the type of fertilizer added to each plot.
The independent variable is the factor that the researcher deliberately manipulates or changes in order to observe its effect on the dependent variable, which is the number of tomatoes produced by each plant in this case.
In the experiment, the researcher is interested in investigating how different fertilizers affect the growth and yield of tomato plants. To determine this, four plots are created, with each plot receiving a different type of fertilizer. This allows for a comparison of the effects of the different fertilizers on the dependent variable, which is the number of tomatoes produced.
By controlling other factors such as the tomato variety, amount of water, and sunlight, the researcher ensures that any differences observed in tomato production can be attributed to the independent variable, which is the type of fertilizer.
This setup allows for a systematic investigation of the relationship between the independent variable and the dependent variable in order to draw meaningful conclusions about the impact of fertilizers on tomato plant growth.
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nadine+mixes+a+juice+solution+that+is+made+from+3+gallons+of+an+80%+juice+solution+and+1+gallon+of+a+20%+juice+solution.+what+is+the+percent+concentration+of+the+final+solution?+25%+50%+65%+70%
The percent concentration of the final juice solution is 65%. The final solution is composed of 65% pure juice.
To compute the percent concentration of the final juice solution, we can calculate the weighted average of the two individual solutions based on their percentages and volumes.
The 80% juice solution is 3 gallons, which means it contains 0.8 * 3 = 2.4 gallons of pure juice.
The 20% juice solution is 1 gallon, which means it contains 0.2 * 1 = 0.2 gallons of pure juice.
The total volume of the final solution is 3 + 1 = 4 gallons.
The total amount of pure juice in the final solution is 2.4 + 0.2 = 2.6 gallons.
To calculate the percent concentration, we divide the amount of pure juice by the total volume and multiply by 100:
Percent concentration = (Pure juice / Total volume) * 100
Percent concentration = (2.6 / 4) * 100
Percent concentration = 65%
Therefore, the percent concentration of the final juice solution is 65%.
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Helppppp me pls asp plssss
I need some help with this, just like Rocky, ASAP!
Answer:
12 possible roots
Step-by-step explanation:
we can use the rational zeros theorem which says that in order to find the possible roots for a polynomial we need to divide the factors of the constant by the factors of the coefficient of the leading term
which in this case is:
±(1, 2, 3, 4, 6, 12)/(1)
±1, 2, 3, 4, 6, 12
so we have 12 possible roots