Based on the Root Test, the series Σ^n√14 is convergent.
Hi! To determine if the series Σ^n√14 is convergent or divergent, we need to analyze the terms involved. The series can be written as:
Σ (n√14)
This is a sum of terms, where each term is the n-th root of 14, and we want to find out if the sum converges or diverges as n goes to infinity.
In this case, the series is a type of p-series, where the terms follow the general form of 1/n^p. To be a convergent p-series, p must be greater than 1. Here, the terms are in the form of 14^(1/n), which can be rewritten as (14^(1))^(-n) or 14^(-n). This is not a p-series, as the exponent is not in the form of 1/n^p.
To further analyze the series, we can use the Divergence Test. If the limit of the terms as n goes to infinity is not equal to zero, then the series is divergent. So, let's find the limit:
lim (n → ∞) (14^(-n))
As n approaches infinity, the exponent -n becomes increasingly negative, and 14^(-n) approaches 0. However, the Divergence Test is inconclusive in this case, as it only confirms divergence if the limit is not equal to zero.
To determine convergence or divergence, we can use the Root Test. The Root Test states that if the limit of the n-th root of the absolute value of the terms as n goes to infinity is less than 1, then the series converges. Let's find the limit:
lim (n → ∞) |(14^(-n))|^(1/n)
This simplifies to:
lim (n → ∞) 14^(-1)
Since 14^(-1) is a constant value less than 1, the limit is less than 1.
Thus, based on the Root Test, the series Σ^n√14 is convergent.
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solve this and I will give u brainlist.
a) by using Venn-diagram. 75 students in a class like picnic or hiking or both. Out of them 10 like both the activities. The ratio of the number of students who like picnic to those who like hiking is 2 : 3. (i) Represent the above information in a Venn-diagram. (ii) Find the number of students who like picnic. (iii) Find the number of students who like hiking only. (iv) Find the percentage of students who like picnic only.
(i) A Venn-diagram of this information is shown below.
(ii) The number of students who like picnic = 34
(iii) The number of students who like hiking only = 51
(iv) The percentage of students who like picnic only. = 45.33%
Let us assume that A represents the set of students who like picnic.
B represents the set of students who like the hiking.
The total number of students in a class are: n(A U B) = 75
Out of 75 students, 10 like both the activities.
n(A ∩ B) = 10
The ratio of the number of students who like picnic to those who like hiking is 2 : 3
Let number of students like tea n(A) = 2x
and the number of students like coffee n(B) = 3x
n(A U B) = n(A) + n(B) - n(A ∩ B)
75 = 2x + 3x - 10
75 + 10 = 5x
85/5= x
x = 17
The number of students like picnic = 2x
= 2 × 17
= 34
The number of students like hiking = 3x
= 3 × 17
= 51
This informtaion in Venn diagram is shown below.
The percentage of students who like picnic only would be,
(34/75) × 100 = 45.33%
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Ariana has 144 peaches. She has to pack 9 boxes with an equal number of peaches. How many peaches should she pack in each box.
Answer:
16 peaches
Step-by-step explanation:
Let's break this down:
Total: 144 peaches
Number of boxes she has to fill evenly: 9
Question: How many peaches are able to fit into each box evenly?
144 peaches/9 boxes = 16 peaches
So, Ariana should pack 16 peaches into each box
Hope this helps :)
In a round of mini-golf , Clare records the number of strokes it takes to hit the ball into the hole of each green. She said that, if she redistributed the strokes on different greens, she could tell that her average number of strokes per hole is 3.
If Clare's average number of strokes per hole is 3, it means that the total number of strokes she took in the round divided by the number of holes she played is equal to 3.
Let's say Clare played n holes in total and took a total of s strokes in the round. Then we can write:
s/n = 3
Multiplying both sides by n, we get:
s = 3n
This means that Clare took 3 strokes per hole on average, and a total of 3n strokes in the round. If she were to redistribute the strokes on different greens, the total number of strokes would still be 3n, and her average number of strokes per hole would remain 3.
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Question 20 of 20
Two numbers have a sum of 2 and a difference of 8. Write a system and solve it to identify the two numbers.
5 and 3
O 11 and -9
-5 and 7
O5 and-3
-5 and 7
Step-by-step explanation
lets try putting -5 and 7
-5 +7=2
and the difference is 8
i am not smart sorry
Evaluate each geometric series described. . 34) a, =-2, a = 256, r=-2 n 33) a=-1, a = 512, r=-2 : A) 397 B) 341 -- B) 149 1 2 A) 3 C) 170 C) - D) 463 D) 156 3 n 71 35) a, = 4, a = 16384, r=4 , , A) 22
(34) the sum of the series is 170. (33) The sum of the series is 341. (35) the sum of the series is 21844
To evaluate a geometric series, we use the formula:
Sn = a(1 - r^n) / (1 - r)
where:
Sn = the sum of the first n terms of the series
a = the first term of the series
r = the common ratio between consecutive terms
n = the number of terms we want to sum
Let's use this formula to evaluate the given geometric series:
34) a1 = -2, a8 = 256, r = -2
To find the sum of this series, we need to know the value of n. We can find it using the formula:
an = a1 * r^(n-1)
a8 = -2 * (-2)^(8-1) = -2 * (-2)^7 = -2 * (-128) = 256
Now we can solve for n:
an = a1 * r^(n-1)
256 = -2 * (-2)^(n-1)
-128 = (-2)^(n-1)
2^7 = 2^(1-n+1)
7 = n-1
n = 8
So this series has 8 terms. Now we can use the formula to find the sum:
Sn = a(1 - r^n) / (1 - r)
S8 = (-2)(1 - (-2)^8) / (1 - (-2))
S8 = (-2)(1 - 256) / 3
S8 = 510 / 3
S8 = 170
Therefore, the sum of the series is 170.
33) a1 = -1, a9 = 512, r = -2
We can use the same method as before to find n:
an = a1 * r^(n-1)
512 = -1 * (-2)^(9-1) = -1 * (-2)^8
512 = 256
This is a contradiction, so there must be an error in the problem statement. Perhaps a9 is meant to be a5, in which case we can find n as:
an = a1 * r^(n-1)
a5 = -1 * (-2)^(5-1) = -1 * (-2)^4
a5 = 16
512 = -1 * (-2)^(n-1)
-512 = (-2)^(n-1)
2^9 = 2^(1-n+1)
9 = n-1
n = 10
So this series has 10 terms. Now we can use the formula to find the sum:
Sn = a(1 - r^n) / (1 - r)
S10 = (-1)(1 - (-2)^10) / (1 - (-2))
S10 = (-1)(1 - 1024) / 3
S10 = 1023 / 3
S10 = 341
Therefore, the sum of the series is 341.
35) a1 = 4, a14 = 16384, r = 4
Again, we can find n using the formula:
an = a1 * r^(n-1)
16384 = 4 * 4^(14-1) = 4 * 4^13 = 4 * 8192 = 32768
This is a contradiction, so there must be an error in the problem statement. Perhaps a14 is meant to be a7, in which case we can find n as:
an = a1 * r^(n-1)
a7 = 4 * 4^(7-1) = 4 * 4^6 = 4 * 4096 = 16384
16384 = 4 * 4^(n-1)
4096 = 4^(n-1)
2^12 = 2^(2n-2)
12 = 2n-2
n = 7
So this series has 7 terms. Now we can use the formula to find the sum:
Sn = a(1 - r^n) / (1 - r)
S7 = (4)(1 - 4^7) / (1 - 4)
S7 = (4)(1 - 16384) / (-3)
S7 = 65532 / 3
S7 = 21844
Therefore, the sum of the series is 21844.
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Hillary used her credit card to buy a $804 laptop, which she paid off by making identical monthly payments for two and a half years. Over the six years that she kept the laptop, it cost her an average of $0. 27 of electricity per day. Hillary's credit card has an APR of 11. 27%, compounded monthly, and she made no other purchases with her credit card until she had paid off the laptop. What percentage of the lifetime cost of the laptop was interest? Assume that there were two leap years over the period that Hillary kept the laptop and round all dollar values to the nearest cent)
Percentage of lifetime cost that was interest = $407.
Let's begin by finding the monthly payment that Hillary made to pay off her laptop over two and a half years.
If she paid off the $804 balance with identical monthly payments, then the total amount she paid is equal to the balance plus the interest:
Total amount paid = balance + interest
We can use the formula for the present value of an annuity to solve for the monthly payment, where PV is the present value (in this case, $804), r is the monthly interest rate (which we can find from the APR), n is the total number of payments (30 months), and PMT is the monthly payment:
PV = PMT * (1 - (1 + r)^(-n)) / r
We can solve this equation for PMT:
PMT = PV * r / (1 - (1 + r)^(-n))
The monthly interest rate is the annual percentage rate divided by 12, and the number of payments is the number of years times 12:
r = 0.1127 / 12 = 0.009391667
n = 2.5 * 12 = 30
Using these values, we get:
PMT = 804 * 0.009391667 / (1 - (1 + 0.009391667)^(-30)) = $33.00
So Hillary made 30 monthly payments of $33.00 to pay off her laptop.
Next, we can calculate the cost of electricity over six years. There are 365 days in a year, and 2 leap years in the six-year period, for a total of 6*365+2 = 2192 days.
At $0.27 per day, the total cost of electricity is:
2192 * $0.27 = $592.64
Now we can calculate the total cost of the laptop over six years.
Hillary paid $33.00 per month for 30 months, or a total of 30 * $33.00 = $990.00. She also paid $592.64 for electricity. Therefore, the total cost of the laptop is:
$990.00 + $592.64 = $1582.64
The interest she paid on her credit card is the difference between the total amount she paid and the cost of the laptop:
Interest = Total amount paid - Cost of laptop
Interest = $990.00 + interest on $804 balance - $804 - $592.64
Simplifying this expression, we get:
Interest = $185.36 + interest on $804 balance
To find the interest on the $804 balance, we can use the formula for compound interest, where P is the principal (in this case, $804), r is the annual interest rate (11.27%), and t is the time in years (2.5 years):
A = P*(1 + r/n)^(n*t)
Here, we can set the number of compounding periods per year, n, to 12 since the interest is compounded monthly. Substituting the given values, we get:
A = $804*(1 + 0.1127/12)^(12*2.5) = $1026.12
So the interest on the $804 balance is:
Interest on $804 balance = $1026.12 - $804 = $222.12
Plugging this value into our expression for Interest, we get:
Interest = $185.36 + $222.12 = $407.48
Finally, we can find the percentage of the lifetime cost of the laptop that was interest:
Percentage of lifetime cost that was interest = Interest / Total cost of laptop * 100%
Percentage of lifetime cost that was interest = $407.
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I need to find the perimeter and area of this shape! HELP!!
The perimeter of the shape given is 50 feet, while the area of this shape is 114 square feet.
How to calculate the area and the perimeter?Perimeter measures the total length of the boundary or the outer edge of a two-dimensional shape. On the other hand, the area measures the space enclosed inside a two-dimensional shape. The area of a shape is determined by multiplying its length by its width
Based on this, let's calculate the perimeter:
7 feet + 6 feet + 4 feet + 6 feet + 9 feet + 9 feet + 2 feet + 7 feet = 50 feet
Now, let's calculate the area by dividing the shape in three:
First rectangle:
3 feet x 7 feet = 21 square feet
Second rectangle:
5 feet x 3 feet = 15 square feet
Third rectangle
9 feet x 9 feet = 81 square feet
Total: 21 + 12 + 81 = 114 square feet
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Find the sum of the convergent
∑ 24/n(n+2)
n = 1
the sum of the convergent series is 8.
To find the sum of the convergent series ∑(24/n(n+2)) where n starts at 1, we can re-write the given expression as a partial fraction decomposition:
24/n(n+2) = A/n + B/(n+2)
Solving for A and B, we find that A = 12 and B = -12. So the expression becomes:
12/n - 12/(n+2)
Now, we can compute the sum for the given series:
∑[12/n - 12/(n+2)] from n = 1 to infinity
As this is a telescoping series, most of the terms will cancel out. We are left with:
12/1 - 12/3 + 12/2 - 12/4 + ... + 12/∞ - 12/(∞+2)
The sum converges to:
12 - 12/3 = 12 * (1 - 1/3) = 12 * 2/3 = 8
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what is the simplified form of the expression below (3m^4n)^3(2m^2n^5p)/6m^4n^9p^8
For the expression (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸, the simplified-value is 9m¹⁰n⁻¹p⁻⁷.
To simplify the expression (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸, we first use the exponent-rule that states (qᵃ)ᵇ = qᵃᵇ to simplify the first part of the expression:
⇒ (3m⁴n)³ = 3³(m⁴)³n³ = 27m¹²n³;
Next, we can simplify the denominator by using the rules of exponents to combine the like terms:
⇒ 6m⁴n⁹p⁸ = 2×3m⁴n⁹p⁸;
Substituting the values,
We get;
⇒ (27m¹²n³)×(2m²n⁵p)/(2*3m⁴n⁹p⁸);
Simplifying the expression by cancelling out the common factors, we get:
⇒ 9m¹⁰n⁻¹p⁻⁷;
Therefore, the simplified-value is : 9m¹⁰n⁻¹p⁻⁷.
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The given question is incomplete, the complete question is
What is the simplified form of the expression below (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸;
6. Mary Cole is buying a $225,000.00 home. Her annual housing
expenses are: mortgage payments, $14,169.20; real estate taxes,
$3,960.00; annual insurance premium, $840.00; maintenance,
$1,410.00; and utilities, $5,180.00. What is Mary's average
monthly expense?
Chapter 10 Mathematics for Business and Personal Finance
Mary's average monthly expense for housing is $2,129.93.
To find Mary's average monthly expenseWWe need to add up all her annual housing expenses and divide the total by 12 (the number of months in a year):
Total annual housing expenses = mortgage payments + real estate taxes + annual insurance premium + maintenance + utilities
Total annual housing expenses = $14,169.20 + $3,960.00 + $840.00 + $1,410.00 + $5,180.00
Total annual housing expenses = $25,559.20
Average monthly expense = Total annual housing expenses ÷ 12
Average monthly expense = $25,559.20 ÷ 12
Average monthly expense = $2,129.93
Therefore, Mary's average monthly expense for housing is $2,129.93.
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Work out the size of angle t.
t
40°
A cube has a volume of 27 cm3. A smaller cube has a side length of that is x cm less than side length of the larger cube. Consider the function f(x) = (3 − x)3. What does f(0. 5) represent?
f(0.5) represents the volume of the smaller box when its' side length is 0.5 cm less than the larger cube
How to find the Volume of a Cube?The formula to find the Volume of a cube is:
V = x³
where:
x is the side length of the cube
The cube has a volume of 27 cm³. Thus:
Side length of cube = ∛27 = 3 cm
Since the side length of the smaller cube is x cm less than side length of the larger cube, then we can say that the function to find the volume of the smaller cube is:
V_small: f(x) = (3 - x)³
Thus, f(0.5) is the volume of the smaller box when its' side length is 0.5 cm less than the larger cube
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A straight line ax+by=16.it passes through a(2,5) and b(3,7).find values of a and b
The values of a and b that satisfy the equation of the line and pass through points A(2,5) and B(3,7) are a = 3 and b = 2.
To find the values of a and b, we need to use the coordinates of points A and B and the equation of the line ax+by=16.
First, we substitute point A(2,5) into the equation to get:
a(2) + b(5) = 16
Next, we substitute point B(3,7) into the equation to get:
a(3) + b(7) = 16
We now have two equations with two unknowns, which we can solve simultaneously.
Multiplying the first equation by 3 and the second equation by -2, we get:
6a + 15b = 48
-6a - 14b = -32
Adding the two equations, we eliminate the a variable and get:
b = 2
Substituting b = 2 into one of the original equations, we get:
2a + 10 = 16
Solving for a, we get:
a = 3
Therefore, the values of a and b that satisfy the equation of the line and pass through points A(2,5) and B(3,7) are a = 3 and b = 2.
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A line has a slope of -2 and passes through the point (-3, 8). Write its equation in slope-
intercept form.
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = - 2x + 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (- 3, 8 ) into the partial equation
8 = - 2(- 3) + c = 6 + c ( subtract 6 from both sides )
2 = c
y = - 2x + 2 ← equation of line
A toy manufacture has designed a new part for use in building models. The part is a cube with side length 14 mm and it has a 12 mm diameter circular hole cut through the middle. The manufacture wants 9,000 prototypes. If the plastic used to create the part costs $0. 07 per cubic millimeter, how much will the plastic for the prototypes cost?
Answer: Therefore, the plastic for the prototypes will cost $1,452,150.
Step-by-step explanation:
The volume of the cube can be calculated as:
Volume of the cube = (side length)^3 = (14 mm)^3 = 2,744 mm^3
The volume of the hole can be calculated as:
Volume of the hole = (1/4) x π x (diameter)^2 x thickness = (1/4) x π x (12 mm)^2 x 14 mm = 5,049 mm^3
The volume of plastic used to create one prototype can be calculated as:
Volume of plastic = Volume of cube - Volume of hole = 2,744 mm^3 - 5,049 mm^3 = -2,305 mm^3
Note that the result is negative because the hole takes up more space than the cube.
However, we can still use the absolute value of this result to calculate the cost of the plastic:
Cost of plastic per prototype = |Volume of plastic| x Cost per cubic millimeter = 2,305 mm^3 x $0.07/mm^3 = $161.35/prototype
To find the cost of the plastic for 9,000 prototypes, we can multiply the cost per prototype by the number of prototypes:
Cost of plastic for 9,000 prototypes = 9,000 x $161.35/prototype = $1,452,150
The plastic for the prototypes will cost $1,452,150.
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After a windstorm, a leaning pole makes a 75° angle with the road surface. the pole casts a 15-foot shadow when the sun is at a 45° angle of elevation. about how long is the pole?
The pole is approximately 3.86 feet tall.
What is the length of a leaning pole that makes a 75° angle with the road surface, if it casts a 15-foot shadow when the sun is at a 45° angle of elevation?
Let's denote the height of the pole as "x" (in feet). From the problem, we know that the pole makes a 75° angle with the road surface, which means that the angle between the pole and the vertical is 90° - 75° = 15°.
Now, we can use the tangent function to find the height of the pole:
tan(15°) = x/15
Multiplying both sides by 15, we get:
x = 15 tan(15°) ≈ 3.86 feet
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A piece of wood, 7.2 m long, is to be cut into smaller pieces. EACH of these pieces should be 0.12 m in length. How many smaller pieces can be obtained?
Answer:
To find the number of smaller pieces that can be obtained, we need to divide the total length of the wood by the length of each smaller piece:
Number of pieces = Total length ÷ Length of each piece
Number of pieces = 7.2 m ÷ 0.12 m
Number of pieces = 60
Therefore, 60 smaller pieces can be obtained from the 7.2 m long piece of wood.
Answer:
60
Step-by-step explanation:
To determine how many smaller pieces can be obtained from a 7.2 m long piece of wood, we need to divide the total length of the wood by the length of each smaller piece.
Total length of wood = 7.2 m
Length of each smaller piece = 0.12 m
Number of smaller pieces = Total length of wood / Length of each smaller piece
Number of smaller pieces = 7.2 m / 0.12 m
Number of smaller pieces = 60
Therefore, 60 smaller pieces can be obtained from a 7.2 m long piece of wood, with each smaller piece being 0.12 m in length.
1. The following data show weight (in kg) of 24 women in a study: 46. 4, 53. 2, 52. 8, 42. 0, 50. 8,
43. 0, 51. 9, 59. 2, 55. 1, 38. 9, 49. 7, 49. 9, 43. 1,42. 2, 52. 7. 49. 8. 50. 7, 44. 8. 49. 2, 47. 7, 42. 9,
52. 9, 54. 1, 45. 4.
Prepare the following:
I.
Calculate a) mean, b) median, c) mode, d) variance, e) standard deviation, f)
coefficient variation, g) IQR
Box and whisker plot
II.
III.
Discuss the distribution of these data
The mean is 48.47 kg, median is 49.55 kg, mode is not available, variance is 34.1 kg², standard deviation is 5.84 kg, coefficient of variation is 12.03% and IQR is 8.35 kg.
The given data shows the weight (in kg) of 24 women in a study. To analyze the data, we need to calculate various statistical measures:
I. Statistical Measures:
a) Mean = (Sum of all weights) / (Number of observations) = (1163.4) / (24) = 48.47 kg
b) Median = Middle value of the sorted data set = 49.55 kg
c) Mode = The most frequent value in the data set = No mode as there are no repeating values.
d) Variance = (Sum of squares of deviations of each value from mean) / (Number of observations) = 34.1 kg²
e) Standard deviation = Square root of variance = 5.84 kg
f) Coefficient of variation = (Standard deviation / Mean) x 100 = 12.03%
g) IQR (Interquartile range) = Q3 - Q1 = 53.025 - 44.675 = 8.35 kg
II. Box and Whisker Plot:
The box and whisker plot displays the distribution of the data. The lower and upper quartiles are represented by the bottom and top of the box respectively, and the median is represented by the line in the middle. The whiskers represent the minimum and maximum values.
III. Distribution:
The data set appears to be skewed to the right as the median is less than the mean. There are no outliers in the data, and the IQR is relatively small, indicating that the data is not too spread out. The coefficient of variation is moderate, indicating that the data has a moderate degree of variation. Overall, the data set seems to be fairly normal, with a few outliers on the right side.
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In a recent Game Show Network survey, 30% of 5000 viewers are under 30. What is the margin of error at the 99% confidence interval? Using statistical terminology and a complete sentence, what does this mean? (Use z*=2. 576)
Margin of error:
Interpretation:
The margin of error at the 99% confidence interval is 0.018 or 1.8%.
Interpretation: This means that if we were to repeat the survey many times, about 99% of the intervals calculated from the samples would contain the true proportion of viewers under 30 in the population, and the margin of error for each interval would be no more than 1.8%.
The margin of error is the amount by which the sample statistic (in this case, the proportion of viewers under 30) may differ from the true population parameter.
Using the given formula for margin of error:
Margin of error = z* * sqrt(p*(1-p)/n)
Where:
- z* is the z-score corresponding to the confidence level (99% in this case), which is 2.576
- p is the proportion of viewers under 30, which is 0.3
- n is the sample size, which is 5000
Substituting these values, we get:
Margin of error = 2.576 * sqrt(0.3*(1-0.3)/5000) = 0.018
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(1 point) Write an equivalent integral with the order of integration reversed IMP3 F(x,y) dyd. = Lo g(x) F(x, y) dedy f(y) a = be f(y) = 9(y) =
the equivalent integral with the order of integration reversed is: ∫0^1 ∫1^2 log(x) 9(y) dydx = (9/2) (2log(2) - 1)
To write an equivalent integral with the order of integration reversed, we need to integrate first with respect to y and then with respect to x. So, we have:
∫a^b ∫f(y)g(x) F(x,y) dxdy
Reversing the order of integration, we get:
∫f(y)g(x) ∫a^b F(x,y) dydx
Now, substituting the given values for f(y), g(x), and F(x,y), we get:
∫0^1 ∫1^2 log(x) 9(y) dydx
= ∫0^1 [9(y)∫1^2 log(x) dx] dy
= ∫0^1 [9(y) (xlog(x) - x) from x=1 to x=2] dy
= ∫0^1 [9(y) (2log(2) - 2 - log(1) + 1)] dy
= ∫0^1 [9(y) (2log(2) - 1)] dy
= (9/2) [(2log(2) - 1) y] from y=0 to y=1
= (9/2) (2log(2) - 1)
Therefore, the equivalent integral with the order of integration reversed is:
∫0^1 ∫1^2 log(x) 9(y) dydx = (9/2) (2log(2) - 1)
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Let f:R → R be a function that satisfies ∫f(t)dt then the value of f(log e 5) is
Unfortunately, I cannot provide an answer to this question as it is incomplete. The given information ∫f(t)dt is not enough to determine the value of f(log e 5). More information about the function f would be needed, such as its explicit form or additional properties. Please provide more context or information to help me answer your question accurately.
Given that f is a function f:R → R that satisfies ∫f(t)dt, we need to find the value of f(log e 5).
By definition, log e 5 is the natural logarithm of 5, which can be written as ln(5). Therefore, we want to find the value of f(ln(5)).
However, without further information on the function f or the integral bounds, it's not possible to determine the exact value of f(ln(5)). Please provide more details about the function or the integral to get a specific answer.
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Consider the quadratic function: f(x)=x^2-6x+8
Identify the coordinates of the x(intercepts if any
Answer:
x-intercepts (4,0) (2,0)
y-intercepts (0,8)
Step-by-step explanation:
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The table shows the part of the students in
each grade that participated in a sport this
year. Which grade had the greatest rate of participation? The least?
we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.
How to find the grade had the greatest rate of participation?To compare the rates of participation in sports among the three grades, we can convert each percentage or fraction to a decimal and then compare the values.
Grade 6: 0.872
Grade 7: 0.87 (87% converted to decimal)
Grade 8: 0.875 (7/8 converted to decimal)
Therefore, we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.
Answer:
Grade 8 had the greatest rate of participation.
Grade 6 had the least rate of participation.
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A non-government that supports palay production in the philippines conducted the research that answer the question: is the proportion of palay harvested different from 0. 50 of all the farm crops are harvested? in a sample of 200 one-hectare farm lands, 96 harvested palay.
For the sample size of 200 and sample data 96 there is no sufficient evidence to conclude that proportion of palay harvested is different from 0.50.
Sample size 'n' = 200
The proportion of palay harvested is different from 0.50
Use a hypothesis test.
Let us assume the null hypothesis H₀ is that the proportion of palay harvested is equal to 0.50,
and the alternative hypothesis Hₐ is that the proportion of palay harvested is different from 0.50.
H₀: p = 0.50 proportion of palay harvested is equal to 50%
Hₐ: p ≠ 0.50 proportion of palay harvested is not equal to 50%
where p is the population proportion of palay harvested.
To test this hypothesis, use the sample data of 96 out of 200 one-hectare farm lands that harvested palay.
The sample proportion of palay harvested is,
p₁= 96/200
= 0.48
To determine if this sample proportion is significantly different from the hypothesized proportion of 0.50,
Use a two-tailed z-test with a significance level of α = 0.05.
The test statistic is calculated as,
z = (p₁ - p) / √(p(1-p)/n)
where n is the sample size.
Substituting the values, we get,
z = (0.48 - 0.50) / √(0.50(1-0.50)/200)
⇒ z = -0.5658
Using a z-table,
The probability of getting a z-value of -0.5658 or lower in the left tail of the distribution is approximately 0.7123.
Since this is a two-tailed test,
Probability of getting a z-value of 0.5658 or higher in the right tail of the distribution is also approximately 0.7123
p-value for this test is 0.7123+ 0.7123 = 1.4246
Since the p-value is greater than the significance level of α = 0.05,
Fail to reject the null hypothesis.
Therefore, do not have sufficient evidence to conclude that the proportion of palay harvested is different from 0.50.
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What is the percentage chance of choosing a queen or a king from a standard 52-card deck?
The probability of choosing a king or queen from a standard 52-card deck is 2/13 or approximately 15.4%.
How can we calculate the percentage?The probability of choosing a king or a queen from a standard 52-card deck can be calculated by first determining the number of kings and queens in the deck. There are four kings (hearts, diamonds, clubs, and spades) and four queens (hearts, diamonds, clubs, and spades) in the deck, for a total of eight cards.
To find the probability of choosing a king or a queen, you need to divide the number of desired outcomes (eight) by the total number of possible outcomes (52).
Probability = Number of desired outcomes / Total number of possible outcomes
Probability = 8 / 52
This simplifies to:
Probability = 2 / 13
Therefore, the probability of choosing a king or a queen from a standard 52-card deck is approximately 0.154 or 15.4%.
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10% of people are left handed. If 800 people are randomly selected, find the likelihood that at least 12% of the sample is left handed
The likelihood of at least 12% of the sample being left-handed is approximately 0.007 or 0.7%.
Let X be the number of left-handed people in a sample of 800 individuals. Since the probability of a person being left-handed is 0.1, the probability of a person being right-handed is 0.9. Then, X follows a binomial distribution with n = 800 and p = 0.1.
P(X ≥ 0.12*800) = P(X ≥ 96)
where 96 is the smallest integer greater than or equal to 0.12*800.
[tex]P(X > =96)-P(X < 96)=1-[K=0 to 95](800 CHOOSE )(0.1^{k} (0.9)^{2} (800-k)[/tex]
This is the complement of the probability of getting less than 96 left-handed people in the sample. Using a calculator or statistical software, we can find that:
P(X ≥ 96) ≈ 0.007
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The radius of the large circle is 3 inches and AB is its diameter. Also, AC is tangent to the large circle at point A. If arc CD = 160 and arc CE = 100, find the area of triangle ABC.
The area of triangle ABC is 13.95 square inches.
We can start by finding the length of AB, which is equal to the diameter of the circle. Since the radius is 3 inches, the diameter is 2 times the radius, or 6 inches.
Next, we can use the fact that AC is tangent to the circle to conclude that angle CAB is a right angle. Therefore, triangle ABC is a right triangle.
Let's use the information about the arcs CD and CE to find the measure of angle BAC. The measure of an inscribed angle is half the measure of the arc that it intercepts, so angle CAD is 80 degrees and angle CAE is 50 degrees. Since angles CAD and CAE are opposite each other and AC is a tangent, we have angle BAC is 180 - 80 - 50 = 50 degrees.
Now we know that triangle ABC is a right triangle with a 90-degree angle at B and a 50-degree angle at A. To find the area of the triangle, we need to know the length of BC.
Using trigonometry, we can find that BC = AB * sin(50) ≈ 4.65 inches.
Therefore, the area of triangle ABC is (1/2) * AB * BC = (1/2) * 6 * 4.65 = 13.95 square inches. Rounded to the nearest hundredth, the area of triangle ABC is 13.95 square inches.
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Which triangle has an obtuse angle?
Answer:
Step-by-step explanation:
An obtuse angle has a measure between 90 and 180 degrees. Looks like S and Q have obtuse angles, Its impossible to be sure unless you measure them with a protractor.
Hello, please help me answer this geometry problem asap. Question shown in image below. Thanks :)
Answer:
[tex] \: \frac{11}{1620} \: \pi^{2} [/tex]
Step-by-step explanation:
I think this is it. But if you find a mistake somewhere let me know? I'm confused because the answer seems a little weird. Like 11/1620 pi² really?
Also at the bottom I wrote "area of sector =" but the area got cut off