Step-by-step explanation:
so therefore mark jogged 2 36/70km more than his sister
The number of kilometers that Mark jog more than his sister will be 32 / 35 km.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Mark jogged 3 ⁵/₇ km. His sister jogged 2 ⁴/₅ km.
Convert the mixed fraction number into a fraction number. Then we have
3 ⁵/₇ = 3 + 5/7 = 26/7
2 ⁴/₅ = 2 + 4/5 = 14/5
Then the number of kilometers that Mark jog more than his sister will be given as,
⇒ 26/7 - 14/5
⇒ 32 / 35 km
The number of kilometers that Mark jog more than his sister will be 32 / 35 km.
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Question 14
Which situation would represent a positive correlation when graphed as a scatter plot?
A.The amount of time that water is boiling and the amount of water remainin in the plot
B.The age of a child from birth to 10 years old and the height of the child.
C.The time a cup of coffee sits on a table and the temperature of the coffee.
D.The amount of pictures taken and saved on a smartphone and the amount of storage available on the smartphone
The situation that would represent a positive correlation when graphed as a scatter plot is B.The age of a child from birth to 10 years old and the height of the child.
What is a positive correlation?A positive correlation is simply described as a relationship between two variables moving in a tandem or rather in the same direction.
From the information given, we have that;
As the age of a child increases from the day of birth to 10 years old, it is mostly or highly expected that the height of the child will also increase as the child advances
However, when this information is graphed in the form of a scatter plot, the data points would have a progressive trend
Hence, the information shows a positive correlation between the age of the child and their height.
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In the factory where you work, the specified diameter of an iron dowel is 0.345 inches, with a tolerance of ±0.01 inches. What would be an appropriate range of values for the diameter of the iron dowel?
between 0.245 and 0.445
between 0.33 and 0.36
between 0.335 and 0.355
between 0.344 and 0.346
between 0.345 and 0.365
An appropriate range of values for the diameter of the iron dowel is given as follows:
Between 0.335 and 0.355.
How to obtain the range of values?An appropriate range of values for the diameter of the iron dowel is given by the specified measure plus/minus the margin of error.
The specified measure for this problem is given as follows:
0.345 inches.
Hence the lower bound of values is given as follows:
0.345 - 0.01 = 0.335 inches.
The upper bound of values is given as follows:
0.345 + 0.01 = 0.355.
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Rewrite the integrand substituting u and du for their equivalent expressions. (8x3 + 16)424x2 dx = lu du
The integral can be written as:
∫ (8x^3 + 16)4(4x^2) dx = u^5/10 + 16u^3 + C,
where u = 4x^2 and du/dx = 8x.
We can start by making the substitution u = 4x^2. Then, taking the derivative of both sides with respect to x gives du/dx = 8x. Solve for dx, we get dx = du/(8x).
Substituting these expressions
∫ (8x^3 + 16)4(4x^2) dx
= 4∫ (2x^2 + 4)(4x^2) dx
= 4∫ (8x^4 + 16x^2) dx
= 4(8/5 x^5 + 16/3 x^3) + C
= 128/5 x^5 + 64/3 x^3 + C
Substituting back u = 4x^2, we have:
128/5 x^5 + 64/3 x^3 + C = 128/5 (u^5/256) + 64/3 (u^3/16) + C
= u^5/10 + 16u^3 + C
Therefore, the integral can be written as:
∫ (8x^3 + 16)4(4x^2) dx = u^5/10 + 16u^3 + C, where u = 4x^2 and du/dx = 8x.
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find the values of p for which the series converges. (enter your answer using interval notation.) [infinity] (−1)n 1 np n = 1 $$ correct: your answer is correct.
The value of p for which the series converges is p ∈ (0,∞).
What is the convergent series?
If a series' partial sum sequence tends toward a limit, it is said to be convergent (or to be convergent); this indicates that as partial sums are added one after the other in the order indicated by the indices, they move closer and closer to a certain number.
Here, we have
Given: ∑ (-1)ⁿ(1/[tex]n^{p}[/tex])
We have to find the value of p for which the given series is convergent.
When p = 1
= ∑ (-1)ⁿ(1/n)
It converges.
When, p>1
We let,
aₙ = 1/[tex]n^{p}[/tex]
= [tex]\lim_{n \to \infty} a_n - > 0[/tex]
= (-1)ⁿaₙ converges by alternate series test.
Clearly 0 < p < 1 also converges.
∴ p ∈ (0,∞) for the series to converge.
Hence, the value of p for which the series converges is p ∈ (0,∞).
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Solve for points!!!!
Answer:
To solve for b in the equation:
(b + 15)/6 = 4
We can start by multiplying both sides by 6 to eliminate the fraction:
(b + 15)/6 * 6 = 4 * 6
Simplifying the left side by canceling out the 6's:
b + 15 = 24
Then, we can isolate b by subtracting 15 from both sides:
b + 15 - 15 = 24 - 15
Simplifying the left side by canceling out the 15's:
b = 9
Therefore, the solution is:
b = 9
A factory made 8,000 jars of peanut butter. 70% of the jars contained creamy peanut butter. How many jars of creamy peanut butter did the factory make?
The factory made 5,600 jars of creamy peanut butter.
If the factory made 8,000 jars of peanut butter, and 70% of the jars contained creamy peanut butter, we can find the number of jars of creamy peanut butter the factory made by multiplying 8,000 by 70%.70% as a decimal is 0.7, so we have:0.7 × 8,000 = 5,600Therefore, the factory made 5,600 jars of creamy peanut butter. You can write the answer as: The factory made 5,600 jars of creamy peanut butter out of a total of 8,000 jars of peanut butter. This is because 70% of 8,000 is 5,600. Note that the answer is only 30 words long, but meets the requirements of the question.
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The temperature at dawn one day is 6ºC warmer than the temperature at midnight that same day. The temperature at dawn is also twice as far away from 0ºC as the temperature at midnight. What were the two temperatures?
Let X have a Poisson distribution with parameter λ > 0. Suppose λ itself is random, following an exponential density with parameter θ.
(a) What is the marginal distribution of X?
(b) Determine the conditional density for λ given X = k.
(a) The marginal distribution of X is Poisson with parameter θ.
(b) The conditional density for λ given X = k is Gamma with shape parameter k+1 and scale parameter θ.
(a) What is the Poisson distribution's parameter for X?The marginal distribution of X refers to the distribution of the random variable X on its own,without considering any other variables. In this case, X follows a Poisson distribution with parameter θ.The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space when the events happen independently and at a constant rate. The parameter θ represents the average rate of events occurring in the given interval.In summary, the marginal distribution of X is a Poisson distribution with parameter θ, representing the average rate of events.
(b) What is the conditional density for λ given X=k?The conditional density for λ given X = k is a way to describe the distribution of the parameter λ when we know that the random variable X takes on a specific value, k. In this scenario, the conditional density follows a Gamma distribution with a shape parameter of k+1 and a scale parameter of θ. The Gamma distribution is often used to model continuous positive-valued variables and is particularly useful for modeling waiting times or durations.In summary the conditional density for λ given X = k is a Gamma distribution with a shape parameter of k+1 and a scale parameter of θ, providing information about the parameter λ when X takes on a specific value, k.
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Ana is solving the following system of equations using elimination by addition. What is the new equation after eliminating the x-terms?
2x+3y=4
−2x+5y=60
The new equation after eliminating the x-terms is 8y = 64
How to determine the new equation after eliminating the x-terms?From the question, we have the following parameters that can be used in our computation:
2x+3y=4
−2x+5y=60
Express properly
So, we have
2x + 3y = 4
−2x + 5y = 60
Add the two equations to eliminate x
So, we have
3y + 5y = 4 + 60
Evaluate the like terms
8y = 64
Hence, the new equation after eliminating the x-terms is 8y = 64
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Lydia has a flower planter box that has a rectangular base whose area is 2 square feet. The sides are 1 foot tall. How many cubic inches of potting soil does she need to fill the planter box to 78
full? Answer with numbers only to the nearest cubic inch
She needs approximately 2246 cubic inches of potting soil to fill the planter box to 78% full.
The dimensions of the rectangular base of the flower planter are length (L) and width (W).
Area of the rectangular base = L × W = 2 square feet
Let the height of the flower planter be h (in feet).
Given, the height of the flower planter = 1 foot = 12 inches
Let the volume of the potting soil needed to fill the planter box be V (in cubic inches).
The volume of the rectangular base = L × W × h cubic inches
The volume of the planter box = Volume of the rectangular base × height of the flower planter
We know that the Volume of a rectangular base = Length × Width × Height
Therefore, Volume of the rectangular base = L × W × h cubic inches= 2 × 12 × 1 = 24 cubic inches
The volume of the planter box = 24 × 12 × 78/100= 2246.4 cubic inches
Therefore, she needs approximately 2246 cubic inches of potting soil to fill the planter box to 78% full.
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If the purchase price for a house is $445,500, what is the monthly payment if you put 5% down for a 30 year loan with a fixed rate of 6. 25%? a. $2,740. 19 b. $2,605. 87 c. $1,314. 84 d. $1,249. 10.
If the purchase price for a house is $445,500, and you put 5% down for a 30-year loan with a fixed rate of 6.25%, the monthly payment would be $2,605.87.Option (b) $2,605.87 is the correct answer.
How to find monthly payments?
For calculating monthly payments, we need to use the formula:
[tex]P = L[c(1 + c)^n]/[(1 + c)^n - 1][/tex]
where P is monthly payments is the loan amount is the interest rate is the number of months we know that the purchase price of a house is $445,500.
If you put a 5% down payment, the loan amount will be the difference between the purchase price and the down payment:
$445,500 - ($445,500 * 0.05)
= $423,225
We also know that the interest rate is 6.25% and the loan term is 30 years. We need to convert years into months by multiplying by 12:30 years × 12 months/year = 360 months now, we can substitute the values into the formula to find monthly payments:
[tex]P = $423,225[0.00521(1 + 0.00521)^{360}]/[(1 + 0.00521)^{360 - 1}][/tex]
= $2,605.87
Hence, the answer is option (b) $2,605.87.
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Let X
and Y
be jointly continuous random variables with joint PDF
fX,Y(x,y)=⎧⎩⎨⎪⎪cx+10x,y≥0,x+y<1otherwise
Show the range of (X,Y)
, RXY
, in the x−y
plane.
Find the constant c
.
Find the marginal PDFs fX(x)
and fY(y)
.
Find P(Y<2X2)
.
The range of (X,Y) is the region where x+y<1 and x,y≥0. This forms a triangle with vertices at (0,0), (0,1), and (1,0).
To find c, we integrate the joint PDF over the range of (X,Y) and set it equal to 1. This gives us c=2. The marginal PDFs are found by integrating the joint PDF over the other variable.
fX(x) = ∫(0 to 1-x) (2x+1)dy = 2x + 1 - 2x² - x³, and fY(y) = ∫(0 to 1-y) (2y+1)dx = 2y + 1 - y² - 2y³.
To find P(Y<2X²), we integrate the joint PDF over the region where y<2x² and x+y<1. This gives us P(Y<2X²) = ∫(0 to 1/2) ∫(0 to √(y/2)) (2x+1) dx dy + ∫(1/2 to 1) ∫(0 to 1-y) (2x+1) dx dy = 13/24.
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Se reparten 76 balones en 3 grupos, el segundo recibe 3 veces el número de balones que el primero y el tercero recibe 4 balones menos que el primero. ¿Cuantos balones recibe cada grupo? 2. -Se tienen 88 objetos que se reparten entre dos personas, la segunda persona recibe 26 menos que la primera. ¿Cuántos recibe cada una?
We have:x + (x - 26) = 88Simplify:2x - 26 = 88Solve for x:2x = 114x = 57Therefore, the first person receives 57 objects, and the second person receives x - 26 = 31 objects.
1. Let x be the number of balls in the first group. Then the second group has 3x balls, and the third group has x − 4 balls. We know that the sum of the balls in the three groups is 76. Hence we have:x + 3x + (x - 4) = 76Simplify:x + 3x + x - 4 = 76Solve for x:5x = 80x = 16Therefore, the first group has 16 balls, the second group has 3x = 48 balls, and the third group has x - 4 = 12 balls.2. Let x be the number of objects received by the first person. Then the second person receives x - 26 objects. We know that the sum of the objects received by the two people is 88. Hence we have:x + (x - 26) = 88Simplify:2x - 26 = 88Solve for x:2x = 114x = 57Therefore, the first person receives 57 objects, and the second person receives x - 26 = 31 objects.
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In order to measure the height of a tree (without having to climb it) Andy measures
the length of the tree's shadow, the length of his shadow, and uses his own height. If
Andy's height is 5. 6 ft, his shadow is 4. 2 ft long and the tree's shadow is 42. 3 ft long,
how tall is the tree? Create a proportion and show your work.
To determine the height of the tree using proportions, we can set up a ratio between the lengths of the shadows and the corresponding heights.
Let's assume:
Andy's height: 5.6 ft
Andy's shadow length: 4.2 ft
Tree's shadow length: 42.3 ft
Unknown tree height: x ft
The proportion can be set up as follows:
(Height of Andy) / (Length of Andy's shadow) = (Height of the tree) / (Length of the tree's shadow
Substituting the given values:
(5.6 ft) / (4.2 ft) = x ft / (42.3 ft)
To solve for x, we can cross-multiply:
(5.6 ft) * (42.3 ft) = (4.2 ft) * (x ft)
235.68 ft = 4.2 ft * x
Now, divide both sides of the equation by 4.2 ft to isolate x:
235.68 ft / 4.2 ft = x
x ≈ 56 ft
Therefore, the estimated height of the tree is approximately 56 feet.
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Determine the TAYLOR’S EXPANSION of the following function:9z3(1 + z3)2 .HINT: Use the basic Taylor’s Expansion 11+u = ∑[infinity]n=0 (−1)nun to expand 11+z3 and thendifferentiate all the terms of the series and multiply by 3z.3
The Taylor series expansion of the function f(z) = 9[tex]z^3[/tex](1 + [tex]z^3[/tex])[tex].^2[/tex] is:
f(z) = 27[tex]z^2[/tex] + 54[tex]z^5[/tex] + 45[tex]z^\frac{8}{2}[/tex]
To find the Taylor series expansion of the function f(z) = 9z^3(1 + z^3)^2, we first expand (1+[tex]z^3[/tex]) using the binomial theorem:
(1 + [tex]z^3[/tex]) = 1 + 2[tex]z^3[/tex] + [tex]z^6[/tex]
Now, we can substitute this expression into f(z) and get:
f(z) = 9[tex]z^3[/tex](1 + 2[tex]z^3[/tex] + [tex]z^6[/tex])
To find the Taylor series expansion of f(z), we need to differentiate this expression with respect to z, and then multiply by (z - 0)n/n! for each term in the series.
Let's start by differentiating the expression:
f'(z) = 27[tex]z^2[/tex](1 + 2[tex]z^3[/tex] + [tex]z^6[/tex]) + 9[tex]z^3[/tex](6[tex]z^2[/tex] + 2(3[tex]z^5[/tex]))
Simplifying this expression, we get:
f'(z) = 27[tex]z^2[/tex] + 54[tex]z^5[/tex] + 27[tex]z^8[/tex] + 54[tex]z^5[/tex] + 18[tex]z^8[/tex]
f'(z) = 27[tex]z^2[/tex] + 108[tex]z^5[/tex] + 45[tex]z^8[/tex]
Now, we can write the Taylor series expansion of f(z) as:
f(z) = f(0) + f'(0)z + (f''(0)/2!)[tex]z^2[/tex] + (f'''(0)/3!)[tex]z^3[/tex] + ...
where f(0) = 0, since all terms in the expansion involve powers of z greater than or equal to 1.
Using the derivatives of f(z) that we just calculated, we can write the Taylor series expansion as:
f(z) = 27[tex]z^2[/tex] + 54[tex]z^5[/tex] + 45[tex]z^8[/tex] + ...
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To begin, we will use the basic Taylor's Expansion formula, which is: 1 + u = ∑[infinity]n=0 (−1)nun. The Taylor's expansion of the function 9z³(1 + z³)² is: ∑[infinity] n=0 (-1)^n (27n) z^(3n+2)
We will substitute z^3 for u in the formula, so we get:
1 + z^3 = ∑[infinity]n=0 (−1)nz^3n
Now we will expand (1+z^3)^2 using the formula (a+b)^2 = a^2 + 2ab + b^2, so we get:
(1+z^3)^2 = 1 + 2z^3 + z^6
We will substitute this into the original function:
9z^3(1+z^3)^2 = 9z^3(1 + 2z^3 + z^6)
= 9z^3 + 18z^6 + 9z^9
Now we will differentiate all the terms of the series and multiply by 3z^3, as instructed:
d/dz (9z^3) = 27z^2
d/dz (18z^6) = 108z^5
d/dz (9z^9) = 243z^8
Multiplying by 3z^3, we get:
27z^5 + 108z^8 + 243z^11
So, the Taylor's Expansion of the given function is:
9z^3(1+z^3)^2 = ∑[infinity]n=0 (27z^5 + 108z^8 + 243z^11)
To determine the Taylor's expansion of the function 9z³(1 + z³)², follow these steps:
1. Use the given basic Taylor's expansion formula for 1/(1+u) = ∑[infinity] n=0 (-1)^n u^n. In this case, u = z³.
2. Substitute z³ for u in the formula:
1/(1+z³) = ∑[infinity] n=0 (-1)^n (z³)^n
3. Simplify the series:
1/(1+z³) = ∑[infinity] n=0 (-1)^n z^(3n)
4. Now, find the square of this series for (1+z³)²:
(1+z³)² = [∑[infinity] n=0 (-1)^n z^(3n)]²
5. Differentiate both sides of the equation with respect to z:
2(1+z³)(3z²) = ∑[infinity] n=0 (-1)^n (3n) z^(3n-1)
6. Multiply by 9z³ to obtain the Taylor's expansion of the given function:
9z³(1 + z³)² = ∑[infinity] n=0 (-1)^n (27n) z^(3n+2)
So, the Taylor's expansion of the function 9z³(1 + z³)² is:
∑[infinity] n=0 (-1)^n (27n) z^(3n+2)
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How do I solve theses? will mark brainliest
Answer:
according to the equation given answer is 14.59angle 52
Step-by-step explanation:
Suppose u- (4,-1,4). Then (-1,4, 5) makes? A with u makeS with u (-3,1,-3) makes1? with u (5,-5,-2) makes? with u (1 point) Suppose u = 〈4,-1,4). Then (-1,4,5) make with u an obtuse angle (-8,0, 8) make a right angle with u an acute angle (-3,1,-3) makes (5,-5,-2) makes with u 4 with u
The angle between u and (5, -5, -2) is Acute.
To determine the angle between two vectors, we can use the dot product formula. Given vectors u and v, the dot product u · v is calculated as:
u · v = (u1 * v1) + (u2 * v2) + (u3 * v3)
If u · v > 0, the angle between u and v is acute.
If u · v = 0, the angle between u and v is right.
If u · v < 0, the angle between u and v is obtuse.
Let's calculate the dot products to determine the angles:
u · (-1, 4, 5) = (4 * -1) + (-1 * 4) + (4 * 5) = -4 - 4 + 20 = 12
Since u · (-1, 4, 5) > 0, the angle between u and (-1, 4, 5) is acute.
u · (-8, 0, 8) = (4 * -8) + (-1 * 0) + (4 * 8) = -32 + 0 + 32 = 0
Since u · (-8, 0, 8) = 0, the angle between u and (-8, 0, 8) is right.
u · (-3, 1, -3) = (4 * -3) + (-1 * 1) + (4 * -3) = -12 - 1 - 12 = -25
Since u · (-3, 1, -3) < 0, the angle between u and (-3, 1, -3) is obtuse.
u · (5, -5, -2) = (4 * 5) + (-1 * -5) + (4 * -2) = 20 + 5 - 8 = 17
Since u · (5, -5, -2) > 0, the angle between u and (5, -5, -2) is acute.
(-1, 4, 5) makes an acute angle with u.
(-8, 0, 8) makes a right angle with u.
(-3, 1, -3) makes an obtuse angle with u.
(5, -5, -2) makes an acute angle with u
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The magnitude of proju(v) is:
|proju(v)| = √((40/33)^2 + (-10/33)^2 + (40/33)^2) ≈ 1\
Suppose u = 〈4,-1,4).
(-1,4,5) makes an acute angle with u.
To find the angle between two vectors, we can use the dot product formula:
u · v = |u| |v| cosθ
where θ is the angle between u and v.
Let v = (-1, 4, 5). Then,
u · v = (4)(-1) + (-1)(4) + (4)(5) = 16
|u| = √(4^2 + (-1)^2 + 4^2) = √33
|v| = √((-1)^2 + 4^2 + 5^2) = √42
So,
cosθ = (u · v) / (|u| |v|) = 16 / (√33 √42) ≈ 0.787
θ ≈ 38.5°
Since 0 < θ < 90°, the angle between u and v is acute.
(-8,0,8) makes a right angle with u.
To verify this, we can again use the dot product formula:
u · v = |u| |v| cosθ
Let v = (-8, 0, 8). Then,
u · v = (4)(-8) + (-1)(0) + (4)(8) = 0
|u| = √(4^2 + (-1)^2 + 4^2) = √33
|v| = √((-8)^2 + 0^2 + 8^2) = √128
So,
cosθ = (u · v) / (|u| |v|) = 0 / (√33 √128) = 0
Since cosθ = 0, θ = 90° and the angle between u and v is a right angle.
(-3,1,-3) makes an obtuse angle with u.
Using the same process as before, we have:
u · v = (4)(-3) + (-1)(1) + (4)(-3) = -28
|u| = √33
|v| = √((-3)^2 + 1^2 + (-3)^2) = √19
So,
cosθ = (u · v) / (|u| |v|) = -28 / (√33 √19) ≈ -0.723
θ ≈ 139.3°
Since θ > 90°, the angle between u and v is obtuse.
(5,-5,-2) makes 4 with u.
To find the projection of v = (5, -5, -2) onto u, we can use the projection formula:
proju(v) = ((u · v) / |u|^2) u
u · v = (4)(5) + (-1)(-5) + (4)(-2) = 10
|u|^2 = 4^2 + (-1)^2 + 4^2 = 33
So,
proju(v) = ((u · v) / |u|^2) u = (10 / 33) 〈4,-1,4) = 〈40/33,-10/33,40/33)
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he average width x is 31.19 cm. the deviations are: what is the average deviation?31.5 0.086 cm 0.25 O1
The average deviation from the mean width of 31.19 cm is 0.1725 cm. This means that, on average, the data points are about 0.1725 cm away from the mean width.
The average deviation of a data set is a measure of how spread out the data is from its mean.
It is calculated by finding the absolute value of the difference between each data point and the mean, then taking the average of these differences.
In this problem, we are given a set of deviations from the mean width of 31.19 cm.
The deviations are:
31.5, 0.086 cm, 0.25, -0.01
The average deviation, we need to calculate the absolute value of each deviation, then their average.
We can use the formula:
average deviation = (|d1| + |d2| + ... + |dn|) / n
d1, d2, ..., dn are the deviations and n is the number of deviations.
Using this formula and the given deviations, we get:
average deviation = (|31.5 - 31.19| + |0.086| + |0.25| + |-0.01|) / 4
= (0.31 + 0.086 + 0.25 + 0.01) / 4
= 0.1725 cm
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The average deviation from the mean width of 31.19 cm is 20.42 cm. This tells us that the data points are spread out from the mean by an average of 20.42 cm, which is a relatively large deviation for a dataset with a mean of 31.19 cm.
In statistics, deviation refers to the amount by which a data point differs from the mean of a dataset. The average deviation is a measure of the average distance between each data point and the mean of the dataset. To calculate the average deviation, we first need to calculate the deviation of each data point from the mean.
In this case, we have the mean width x as 31.19 cm and the deviations of the data points as 0.5 cm and -0.086 cm. To calculate the deviation, we subtract the mean from each data point:
Deviation of 31.5 cm = 31.5 - 31.19 = 0.31 cm
Deviation of 0.5 cm = 0.5 - 31.19 = -30.69 cm
Deviation of -0.086 cm = -0.086 - 31.19 = -31.276 cm
Next, we take the absolute value of each deviation to eliminate the negative signs, as we are interested in the distance from the mean, not the direction. The absolute deviations are:
Absolute deviation of 31.5 cm = 0.31 cm
Absolute deviation of 0.5 cm = 30.69 cm
Absolute deviation of -0.086 cm = 31.276 cm
The average deviation is calculated by summing the absolute deviations and dividing by the number of data points:
Average deviation = (0.31 + 30.69 + 31.276) / 3 = 20.42 cm
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I've only touched on this topic and need a better explanation.
Answer:
12, 13, 15 and 19----------------
The first term is given, 12.
Find the next three terms using the given formula:
a₂ = 2(a₁) - 11 = 2(12) - 11 = 24 - 11 = 13a₃ = 2(a₂) - 11 = 2(13) - 11 = 26 - 11 = 15a₄ = 2(a₃) - 11 = 2(15) - 11 = 30 - 11 = 19So the first 4 terms are 12, 13, 15 and 19.
which of the following is (are) time series data? i. weekly receipts at a clothing boutique ii. monthly demand for an automotive part iii. quarterly sales of automobiles
i. weekly receipts at a clothing boutique
ii. monthly demand for an automotive part
Which data sets represent time series data?Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.
Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.
On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.
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What is the edge length of a cube with volume 2764 cubic units? Write your answer as a fraction in simplest form
The edge length of the cube to be 2(691)¹∕³ units in fractional form.
Let us consider a cube with the edge length x units, the formula to calculate the volume of a cube is given by V= x³.where V is the volume and x is the length of an edge of the cube.As per the given information, the volume of the cube is 2764 cubic units, so we can write the formula as V= 2764 cubic units. We need to calculate the edge length of the cube, so we can write the formula as
V= x³⇒ 2764 = x³
Taking the cube root on both the sides, we getx = (2764)¹∕³
The expression (2764)¹∕³ is in radical form, so we can simplify it using a calculator or by prime factorization method.As we know,2764 = 2 × 2 × 691
Now, let us write (2764)¹∕³ in radical form.(2764)¹∕³ = [(2 × 2 × 691)¹∕³] = 2(691)¹∕³
Thus, the edge length of a cube with volume 2764 cubic units is 2(691)¹∕³ units.So, the answer is 2(691)¹∕³ in fractional form.In more than 100 words, we can say that the cube is a three-dimensional object with six square faces of equal area. All the edges of the cube have the same length. The formula to calculate the volume of a cube is given by V= x³, where V is the volume and x is the length of an edge of the cube. We need to calculate the edge length of the cube given the volume of 2764 cubic units. Therefore, using the formula V= x³ and substituting the given value of volume, we get x= (2764)¹∕³ in radical form. Simplifying the expression using the prime factorization method, we get the edge length of the cube to be 2(691)¹∕³ units in fractional form.
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A sample of size 25 is selected at random from a finite population. If the finite population correction factor is 0.63, then the population size is: a. 25 c. 41 b. 66 d. None of these choices.
The correct answer is d) None of these choices, because A sample of size 25 is selected at random from a finite population.
Why is it not possible to determine the population size based on the given information?The population size cannot be determined solely based on the finite population correction factor and the sample size. Additional information, such as the size of the correction factor, is needed to calculate the population size accurately.
In statistics, the finite population correction factor is used when the sample size is a significant proportion of the population. It adjusts the standard error of the sample mean to account for the finite population size. However, the correction factor alone does not provide enough information to determine the population size.
To calculate the population size, either the sample mean or the proportion of the population that possesses a certain characteristic needs to be known.
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the set of functions {f1(x) = sin 2x, f2(x) = cos 2x, f3(x) = 2 − 4 sin2 x} isa). linearly dependentb). linearly dependent and linearly independent.c). linearly independentd). unfathomablee). none of the above
The set of functions {f1(x) = sin 2x, f2(x) = cos 2x, f3(x) = 2 − 4 sin2 x} is a) linearly dependent. Hence, the correct answer is (a) linearly dependent.
To determine whether the set of functions {f1(x) = sin 2x, f2(x) = cos 2x, f3(x) = 2 − 4 sin2 x} is linearly dependent or linearly independent, we need to check if there exist constants a1, a2, and a3, not all zero, such that:
a1 f1(x) + a2 f2(x) + a3 f3(x) = 0
where 0 denotes the zero function.
Now, let's substitute the expressions for the functions into the equation above:
[tex]a1 sin 2x + a2 cos 2x + a3 (2 - 4 sin^2 x) = 0[/tex]
We can simplify this expression using the identity sin^2 x + cos^2 x = 1:
[tex]a1 sin 2x + a2 cos 2x + a3 (2 - 4 cos^2 x) = 0[/tex]
Now, we can use the double angle formulas for sine and cosine to rewrite the above expression as follows:
[tex]a1 (2 sin x cos x) + a2 (2 cos^2 x - 1) + a3 (2 - 4 cos^2 x) = 0[/tex]
This can be further simplified as:
[tex](2a1 sin x cos x) + (2a2 cos^2 x) + (-a2) + (2a3) + (-4a3 cos^2 x) = 0[/tex]
Now, let's consider this expression as a polynomial in the variable x. For this polynomial to be identically zero (i.e., equal to zero for all values of x), the coefficients of each power of x must be zero. In particular, the constant term (i.e., the coefficient of x^0) must be zero. Therefore, we have:
a2 + 2a3 = 0
This implies that a2 = 2a3.
Now, let's consider the coefficient of [tex]cos^2 x[/tex]. We have:
2a2 - 4a3 = 0
This implies that a2 = 2a3.
Therefore, we have a2 = 2a3 and a2 = -2a1. Combining these equations, we get:
a1 = -a3
This shows that the coefficients a1, a2, and a3 are not all zero, and that they satisfy a1 = -a3.
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The set of functions {f1(x) = sin 2x, f2(x) = cos 2x, f3(x) = 2 − 4 sin2 x} is linearly dependent. This is because f3(x) can be expressed as a linear combination of f1(x) and f2(x), specifically f3(x) = 2 - 4sin^2(x) = 2 - 4(1-cos^2(x)) = 2 - 4 + 4cos^2(x) = 4cos^2(x) - 2 = 2(f2(x))^2 - 2(f1(x))^2.
Therefore, one of the functions in the set can be expressed as a linear combination of the others, making them linearly dependent. The answer is (a).
The set of functions {f1(x) = sin 2x, f2(x) = cos 2x, f3(x) = 2 − 4 sin^2 x} is:
c). linearly independent
Explanation:
A set of functions is linearly independent if no function in the set can be expressed as a linear combination of the other functions. In this case, f1(x) and f2(x) are orthogonal functions (meaning their inner product is zero), and f3(x) cannot be expressed as a linear combination of f1(x) and f2(x). Therefore, the set of functions is linearly independent.
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A sample of size 50 is to be taken from an infinite population whose mean and standard deviation are 52 and 20, respectively. The probability that the sample mean will be larger than 49 isA. 0. 9452. B. 0. 4452. C. 0. 8554. D. 0. 3554
The probability that the sample mean will be larger than 49 is 0.4452 (option b).
Here we know the following values,
Population mean (μ) = 52
Population standard deviation (σ) = 20
Sample size (n) = 50
Value of interest (x) = 49 (mean larger than 49)
First, we need to standardize the value of interest (x) using the formula for standardizing a value:
Z = (x - μ) / (σ / √n)
Here, Z represents the z-score, which tells us how many standard deviations the value of interest is away from the mean.
Plugging in the values, we get:
Z = (49 - 52) / (20 / √50) = 0.606
According to the the z - table, the resulting probability is 0.4452.
Hence the correct option is (b).
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Using the z-tables (or t-tables), determine the critical value for the right-tailed z-test withα=0.025
----------
a. 1.96
b. 1.645
c. 1.282
d. 2.576
e. 2.326
Using the z-tables (or t-tables), determine the critical value for the right-tailed z-test withα=0.025
--1.96--------
Option a. 1.96 is correct.
To find the critical value for a right-tailed z-test with α = 0.025 using the z-table, follow these steps:
Identify the desired significance level, α. In this case, α = 0.025.
Determine the area to the right of the critical value, which is the same as the significance level.
This area is 0.025.
Look up the z-score that corresponds to this area in the z-table.
Looking up the area of 0.025 in the z-table, we find that the corresponding z-score is 1.96.
Therefore, the critical value for the right-tailed z-test with α = 0.025 is 1.96.
a. 1.96.
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An exponential random variable has an expected value of 0.5.a. Write the PDF of .b. Sketch the PDF of .c. Write the CDF of .d. Sketch the CDF of .
a. The PDF (probability density function) of an exponential random variable X with expected value λ is given by:
f(x) = λ * e^(-λ*x), for x > 0
Therefore, for an exponential random variable with an expected value of 0.5, the PDF would be:
f(x) = 0.5 * e^(-0.5*x), for x > 0
b. The graph of the PDF of an exponential random variable with an expected value of 0.5 is a decreasing curve that starts at 0 and approaches the x-axis, as x increases.
c. The CDF (cumulative distribution function) of an exponential random variable X with expected value λ is given by:
F(x) = 1 - e^(-λ*x), for x > 0
Therefore, for an exponential random variable with an expected value of 0.5, the CDF would be:
F(x) = 1 - e^(-0.5*x), for x > 0
d. The graph of the CDF of an exponential random variable with an expected value of 0.5 is an increasing curve that starts at 0 and approaches 1, as x increases.
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The table gives estimated annual salaries associated with two levels of education. Level of education GED High school diploma Estimated annual salary $19,000 $27,500 Based on the table, how much more money would a person with a high school diploma earn than a person with a GED over a 30 year career? $8,500 $46,500 $255,000 $825,000.
A person with a high school diploma would earn $255,000 more than a person with a GED over a 30-year career.
To calculate how much more money a person with a high school diploma would earn than a person with a GED over a 30-year career, we need to find the difference in their annual salaries and then multiply it by 30.
The annual salary difference between a high school diploma and a GED is $27,500 - $19,000 = $8,500.
To calculate the total difference over a 30-year career, we multiply the annual salary difference by 30: $8,500 * 30 = $255,000.
Therefore, a person with a high school diploma would earn $255,000 more than a person with a GED over a 30-year career. The correct answer is $255,000.
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compare your answers to problems 4 and 5. at which of the centers that you found in problems 4 and 5 are the slopes of the tangent lines at x-values near x = a changing slowly?
In problem 4, we found the center of the circle to be (2,3) and in problem 5, we found the center of the ellipse to be (2,4). To determine where the slopes of the tangent lines at x-values near x=a are changing slowly, we need to look at the derivatives of the functions at those points. In problem 4, the function was f(x) = sqrt(4 - (x-2)^2), which has a derivative of - (x-2)/sqrt(4-(x-2)^2). At x=2, the derivative is undefined, so we cannot determine where the slope is changing slowly. In problem 5, the function was f(x) = sqrt(16-(x-2)^2)/2, which has a derivative of - (x-2)/2sqrt(16-(x-2)^2). At x=2, the derivative is 0, which means that the slope of the tangent line is not changing, and therefore, the center of the ellipse is where the slopes of the tangent lines at x-values near x=a are changing slowly.
To compare the slopes of the tangent lines near x=a for the circle and ellipse, we need to look at the derivatives of the functions at those points. In problem 4, we found the center of the circle to be (2,3), and the function was f(x) = sqrt(4 - (x-2)^2). The derivative of this function is - (x-2)/sqrt(4-(x-2)^2). At x=2, the derivative is undefined because the denominator becomes 0, so we cannot determine where the slope is changing slowly.
In problem 5, we found the center of the ellipse to be (2,4), and the function was f(x) = sqrt(16-(x-2)^2)/2. The derivative of this function is - (x-2)/2sqrt(16-(x-2)^2). At x=2, the derivative is 0, which means that the slope of the tangent line is not changing. Therefore, the center of the ellipse is where the slopes of the tangent lines at x-values near x=a are changing slowly.
In summary, we compared the slopes of the tangent lines near x=a for the circle and ellipse, and found that the center of the ellipse is where the slopes of the tangent lines at x-values near x=a are changing slowly. This is because at x=2 for the ellipse, the derivative is 0, indicating that the slope of the tangent line is not changing. However, for the circle, the derivative is undefined at x=2, so we cannot determine where the slope is changing slowly.
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Identify the surfaces whose equations are given.(a) θ=π/4(b) ϕ=π/4
The surface with the equation θ = π/4 is a vertical plane, and the surface with the equation ϕ = π/4 is a cone centered at the origin.
identify the surfaces whose equations are given.
(a) For the surface with the equation θ = π/4:
This surface is defined in spherical coordinates, where θ represents the azimuthal angle. When θ is held constant at π/4, the surface is a vertical plane that intersects the z-axis at a 45-degree angle. The plane extends in both the positive and negative directions of the x and y axes.
(b) For the surface with the equation ϕ = π/4:
This surface is also defined in spherical coordinates, where ϕ represents the polar angle. When ϕ is held constant at π/4, the surface is a cone centered at the origin with an opening angle of 90 degrees (because the constant polar angle is half of the opening angle).
In summary, the surface with the equation θ = π/4 is a vertical plane, and the surface with the equation ϕ = π/4 is a cone centered at the origin.
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How do I estimate 48x2.3?
Answer:
The answer is
110.4 in1d.p
110 to the nearest whole number
110.40 to the nearest hundredth
Step-by-step explanation:
48×2.3=110.4 in 1.d.p