The value of r when 2^(r)=(1)/(32) is -5. This can be derived by taking the logarithm of both sides of the equation. Since log2 (2^r) = r and log2 (1/32) = -5, then r = -5.
In order to work out the value of r when 2^(r) = 1/32, we need to use logarithms. Logarithms are a way of expressing a number as the power of another number. Specifically, the logarithm of a number x is the exponent y to which a given base must be raised to equal x.
In this case, the base is 2, so log2 (2^r) = r. Therefore, to work out the value of r, we need to find the logarithm of 1/32. This can be done by dividing 1 by 32 and taking the logarithm of the result. We get log2 (1/32) = -5. Therefore, r = -5.
Since the question specifies that we should give the answer as an integer or as a fraction in its simplest form, we must conclude that the answer is -5. It is impossible to reduce this fraction any further, so it is already in its simplest form.
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On 1.2.2011, Brown drew a bill for three months on black for Rs. 6,000 and received it duly accepted. On 3.2.2011 Brown discounted the bill for 6%. On the due date black paid money for his bill. Show the journal entries in the books of both the persons.
Dr. Bills Payable A/C 5,400 and Cr. Bank A/C 5,400
In the books of Brown:
Dr. Bank A/C 6,000
Cr. Bills Receivable A/C 6,000
On 3.2.2011:
Dr. Bills Receivable A/C 5,400
Cr. Bank A/C 5,400
On the due date:
Dr. Bills Receivable A/C 5,400
Cr. Black A/C 5,400
In the books of Black:
Dr. Bills Payable A/C 5,400
Cr. Bank A/C 5,400
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Use the number line to round 57,614 to the nearest hundred
Answer:
57,600 if talking about hundreds. If talking about hundredths, 57.61
Answer:
57600
Step-by-step explanation:
nearest hundred (100)
614 is closer to 600
from 651 it becomes near 700 therefore the answer becomes 57600
Plssss hellllppppp meeeeeeee
The areas of section 1, 2 and 3 are 8 inches square, 80 inches square and 8 inches square respectively.
The area of the trapezium is 96 inches square.
What is the area of the trapezium?Section 1 and 2 are right triangles.
Area of a right triangle = 1/2 x base x height
Height = 8cm
Base = (14 - 10) / 2 = 2cm
Area of a right triangle = 1/2 x 2 x 8 = 8cm²
Section 3 is a rectangle.
Area of a rectangle = length x width
8 x 10 = 80 cm²
A trapezoid is a convex quadrilateral. A trapezoid has at least on pair of parallel sides. the parallel sides are called bases while the non parallel sides are called legs
Area of a trapezoid = 1/2 x (sum of the lengths of the parallel sides) x height
= 1/2 x (10 + 14) x 8
1/2 x 24 x 8 = 96cm²
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Evaluate using the correct order of operations. (17)/(18)+(6)/(35)-:(5)/(7)*(25)/(4)
After evaluating using the correct order of operations, the result will become 22/9.
The correct order of operations is to perform any calculations inside parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. This order of operations is known as PEMDAS. Using this order, we can evaluate the expression as follows:
(17)/(18) + (6)/(35) ÷ (5)/(7) x (25)/(4)
Divide 6/35 by 5/7 by multiplying 6/35 by the reciprocal of 5/7.
= (17/18) + (6/35) x (7/5) x (25/4)
= (17/18) + (6/25) x (25/4)
Multiply 6/25 by 25/4.
= (17/18) + (6/4)
Finally, add 17/18 and 6/4 together.
= 22/9
Therefore, the final answer is 22/9,
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Estatura 5 ft 8 in peso 203 libras distancias corridas 597 yardas
Cuál es su estatura en metros
Cuántos metros ha corrido
En qué unidad que conozcas podrías expresar su peso Urge
The height in meters is 1.73 meters (rounded to two decimal places), the weight in other unit (kg) approximately 92.1 kg.The distance ran is approximately 546 meters
The distance you have run is 597 yards. To convert yards to meters, we can use the conversion factor 1 yard = 0.9144 meters. Therefore, the distance you have run in meters is approximately 546 meters (rounded to the nearest meter).
Your weight is currently expressed in pounds (lbs). To express your weight in other units, we can use conversion factors. For example, your weight in kilograms (kg) can be found by multiplying your weight in pounds by 0.453592. Using this conversion, your weight would be approximately 92.1 kg (rounded to one decimal place). Alternatively, your weight in stones (st) can be found by dividing your weight in pounds by 14. Using this conversion, your weight would be approximately 14.5 st (rounded to one decimal place).
Therefore, the hieght, weight and distance ran are 1.73 meters, 92.1 kg and 546 meters respectively.
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The question is :
What is the height in meters and how many meters has he run, and in what unit could you express his weight, for someone who is 5 ft 8 in tall and weighs 203 lbs and ran a distance of 597 yards ?
An igloo can be modeled as a hemisphere. Its radius measures 5.9 m. Find its volume in cubic meters. Round your answer to the nearest tenth if necessary.
Step-by-step explanation:
Refer to pic...............
A triangle can be formed with side measures of 4. 6, 2. 7, and 1. 9. Enter 1 for "true" or 2 for "false". (1 point)
Check the picture below.
we have three sides, let's look at the two smaller sides first, 1.9 and 2.7.
if we move the sides closer and ever closer to each other, to the extent that one is right on top of the other, what is the length of the red side? Well, assuming the two smaller sides are one pancaked on top of the other, the red side will be as long as 2.7 - 1.9 = 0.8. However, the sides can't be on top of each other, because if that's so, we have a flat-line, and thus we wouldn't have a triangle. So whatever the third side may be, it must be greater than 0.8.
Now, if we move the sides away from each other, farther and farther to the extent that one is parallel to the other, then the third side will just be as long as 1.9 + 2.7 = 4.6. However, we can't do that, because if that were to happen, we again will have a flat-line and not a triangle. So whatever the third side may be, it must be less than 4.6, it can't be 4.6.
So no dice.
The coordinates of two triangles
are shown in the table. Is XYZ a dilation of JKL? Write an
argument that can be used to defend your solution.
AJKL
J
K
L
(a, b)
(c,d)
(a, d)
X
Y
Z
AXYZ
(3a, 6b)
(3c, 6d)
(3a, 6d)
The argument for the dilation is that: No, in order for one figure to be dilated of another, both coordinates of all points must be multiplied by the same constant
How to determine the true statement about the dilationThe complete question is added as an attachment
From the attached table of values, we can see that:
The coordinates of x are multiplied by 3, while the coordinates of y are multiplied by 6
This means that
The figure is not properly dilated, because these coordinates must be multiplied by the same constant value
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Use the image to determine the direction and angle of rotation.
90° clockwise rotation
270° clockwise rotation
90° counterclockwise rotation
180° counterclockwise rotation
After comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.
What is meant by the rotation of figures?A transformation known as a rotation involves turning the figure either clockwise or counterclockwise. The centre of rotation is the fixed location where the rotation occurs. The term "angle of rotation" refers to the amount of rotation. A figure can be rotated 90 degrees, or a quarter turn, in either a clockwise or counterclockwise direction.
You have rotated the figure 180 degrees when you have spun it exactly halfway. The figurine may be rotated 360° by turning it all the way around. A counterclockwise turn has a positive magnitude because a clockwise rotation indicates a negative magnitude. Rotational symmetry exists in every regular polygon. When an object is rotated around its centre, it retains its original appearance. The object is then referred regarded as having rotational symmetry.
Let's write the coordinates of the original figure,
A = (1, -5)
B = (6, -2)
C = (6, -5)
D = (1, -8)
Now, if we rotate it 90 degrees counterclockwise, the coordinates are:
A' = ( 5, 1)
B' = (2, 6)
C' = (5, 6)
D' = (8, 1)
Now if we rotate it again 90 degrees counterclockwise, the coordinates are:
A'' = ( -1, 5)
B'' = (-6, 2)
C'' = (-6, 5)
D'' = (-1, 8)
Now from the figure, let's write the coordinates.
A' = ( -1, 5)
B' = (-6, 2)
C' = (-6, 5)
D' = (-1, 8)
This is the same as the coordinates of the second 90 degrees counterclockwise rotation.
Since we did two 90 degrees rotations, we can say we did a total of 180° counterclockwise rotation.
Therefore after comparing the image and the figure, we found that the direction and angle of rotation are 180° counterclockwise rotation.
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FIND THE VALUE IF X.I REALLY NEED THIS OEN
The value of x in the given figure of parallel lines is x = 0.89.
What are alternate interior angles?When two parallel lines are sliced by a transversal, alternating interior angles and alternate exterior angles result in the shape "Z".
From the figure we observe that according to alternate interior angle, the angle adjacent to x + 94 is 95x.
Thus, the two angles form a straight line.
The angle of a straight line is 180 degrees.
Thus,
x + 94 + 95x = 180
96x + 94 = 180
x = 0.89
Hence, the value of x in the given figure of parallel lines is x = 0.89.
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What would make his parallelogram a rhombus
Quadrilateral QRST would become a Rhombus if all the conditions discussed below are fulfilled.
What is a Rhombus?
Rhombuses are a particular sort of quadrilateral in Euclidean geometry. It is a unique instance of a parallelogram in which the diagonals meet at a 90-degree angle and all sides are equal. This is a rhombus' fundamental characteristic. A rhombus has a diamond-shaped form. As a result, it is also known as a diamond.
Given QRST Quadrilateral.
In order to be Rhombus, these conditions must fulfill:
1. all sides are equal i.e. QT=TS=SR=RQ
2. Diagonals meet at 90-degree i.e. ∠11 = ∠10=∠9=∠12 = 90°
3. Diagonals bisect the angles of a rhombus i.e. ∠6=∠7, ∠5=∠4, ∠3=∠2 and ∠8=∠1.
4. Opposite angles are equal.
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To make a parallelogram a rhombus, make its sides equal, angles should be 90° and diagonals should be equal.
What is a parallelogram?
A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.
A parallelogram becomes a rhombus if and only if all four sides are congruent, which means they have the same length.
Therefore, to make the parallelogram QRST a rhombus, we need to ensure that all four sides are of equal length.
This can be achieved by satisfying any of the following conditions -
All four sides have the same length.
The diagonals of the parallelogram are perpendicular bisectors of each other.
In other words, they meet at right angles and divide each other into equal halves.
The diagonals of the parallelogram have equal length.
Therefore, if we can make sure that any of these three conditions are true for the parallelogram QRST, then we can make it a rhombus.
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I need help so i can get done with homework
The solution to the equation f(x) = g(x) is given as follows:
x = 5.
How to find the numeric value of a function or of an expression?To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.
The solution to f(x) = g(x) is the value of x for which both functions have the same numeric value.
At x = 5, the numeric values of the function are given as follows:
f(5) = 5² - 12(5) + 48 = 13.g(5) = 2^(5 - 2) + 5 = 8 + 5 = 13.Same numeric values, hence x = 5 is the solution to the equation.
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Let U = {(x, y, z) € R^3 | x + 2y – 3z =0}. a) (2pt) Show directly (by verifying the conditions for a subspace) that U is a subspace of R^3. You may not invoke results learned in class or from the notes. b) (2pts) Find a basis for U. You must explain your method. c) (1pt) Using your answer from part b) determine Dim(U).
a) U is subspace of R^3.
b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.
c) 2.
a) To show that U is a subspace of R^3, we need to verify the following three conditions:
i) The zero vector (0, 0, 0) is in U.
ii) U is closed under addition.
iii) U is closed under scalar multiplication.
i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.
ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:
x1 + 2y1 - 3z1 = 0 (by definition of U)
x2 + 2y2 - 3z2 = 0 (by definition of U)
Adding these two equations, we get:
(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0
which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.
iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:
x + 2y - 3z = 0 (by definition of U)
Multiplying both sides of this equation by c, we get:
cx + 2cy - 3cz = 0
which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.
Since U satisfies all three conditions, it is a subspace of R^3.
b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:
x = 3z - 2y
y = (x - 3z)/2
Substituting z = t into these equations, we get:
x = 3t - 2y
y = (x - 3t)/2
Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:
(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)
Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.
c) Since the basis for U has two elements, the dimension of U is 2.
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a.) Use the table below to calculate the average percent change in population in California from 2000-2009.
b.) If California's population in 2009 was 37,000,000 and the population trend were to continue, what would the population be in the year 2015?
The average percentage change in population from 2000-20009 is 1.36%.
What is meant by percentage?A figure or ratio stated as a fraction of 100 is called a percentage. Frequently, it is indicated with the per cent sign, "%". If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The percentage, therefore, refers to a component per hundred. Per 100 is what the word per cent means. As there is no unit of measurement for percentages, they are dimensionless numbers. This is because we divide numbers with the same units in percentage calculation.
a) Average percentage change
= Sum of percentage change in each year/number of years
= (1.97+1.71+1.65+1.42+1.22+1.02+1.07+1.22+0.93) / 9
= 1.36%
Therefore the average percentage change in population from 2000-20009 is 1.36%.
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Whe the preperties of esponents to simplify the evprestion, Write your answer nith pestive espenents enly. ((4x^(2)z^(-4))/(20y^(-3)))^(-4)
The simplified expression is [tex](z^{(16))}(y^{(12))}/(100663296)(x^{(8))}[/tex].
To simplify the expression ((4x^(2)z^(-4))/(20y^(-3)))^(-4) using the properties of exponents, we need to follow the steps below:
1. First, we need to distribute the exponent of -4 to each term inside the parentheses. This will give us:
(4^(-4))(x^(2*-4))(z^(-4*-4))/(20^(-4))(y^(-3*-4))
2. Next, we need to simplify the exponents by multiplying them. This will give us:
[tex](4^(-4))(x^(-8))(z^(16))/(20^(-4))(y^(12))[/tex]
3. Now, we need to simplify the terms with negative exponents by moving them to the opposite side of the fraction. This will give us:
[tex](z^(16))(y^(12))/(4^(4))(x^(8))(20^(4))[/tex]
4. Finally, we need to simplify the terms with the same base by adding their exponents. This will give us:
[tex](z^(16))(y^(12))/(4^(4))(x^(8))(2^(8))(5^(8))[/tex]
5. We can further simplify the expression by simplifying the terms with the same base. This will give us:
(z^(16))(y^(12))/(16^(2))(x^(8))(2^(8))(5^(8))
6. Now, we can combine the terms with the same base to get our final answer:
(z^(16))(y^(12))/(256)(x^(8))(256)(390625)
7. Our final answer is:
(z^(16))(y^(12))/(100663296)(x^(8))
Therefore, the simplified expression is (z^(16))(y^(12))/(100663296)(x^(8)).
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Math question 14 help
Be Precise Two cylinders have the same volume of 845π cubic inches. The radius of Cylinder A is 13 inches and the radius of Cylinder B is 10 inches. Which cylinder is taller? How much taller? Express the difference in heights as a decimal.
Cylinder B is taller which is 3.45 inches more than cylinder A.
Volume of the cylinder:
A cylinder is a three-dimensional geometric shape that consists of two parallel circular bases that are connected by a curved surface.
The formula for the volume of a cylinder is given by
V = πr²hWhere V is the volume of the cylinder, r is the radius of the circular base of the cylinder, and h is the height of the cylinder.
Here we have
Two cylinders have the same volume of 845π cubic inches.
The radius of Cylinder A is 13 inches
Let 'h₁' be the height of th cylinder
By using the formula, V = π r² h₁
Volume of the cylinder A = π (13)² h₁ = 169πh₁
From the data, 169πh₁ = 845π
=> 169h₁ = 845
=> h₁ = 845/169
=> h₁ = 5
The radius of Cylinder B is 10 inches.
Let h₂ be the height
Volume of the Cylinder B = π (10)² h₂ = 100πh₂
From the data, 100πh₂ = 845π
=> 100h₂ = 845
=> h₂ = 8.45
The difference between the heights of the two cylinders
= 8.45 inch - 5 inch = 3.45 inch
Therefore,
Cylinder B is taller which is 3.45 inches more than cylinder A.
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Mr. Jensen throws an eraser at a sleeping student. The equation that models the flight of the eraser is: h(t)=-16t^(2)+35t+6 The student hos his head laying on the desk about 3 feet off the ground. How long does it take for the eraser to hit the student in the head?
It takes approximately0.082 seconds for the eraser to hit the student in the head.
The equation that models the flight of the eraser is h(t)=-16t^(2)+35t+6. We need to find the time it takes for the eraser to hit the student's head, which is 3 feet off the ground. This means that we need to solve the equation h(t)=3 for t.
First, we will set h(t) equal to 3 and rearrange the equation:
-16t^(2)+35t+6=3
Next, we will subtract 3 from both sides of the equation and simplify:
-16t^(2)+35t+3=0
Now, we will use the quadratic formula to solve for t:
t= (-35±√(35^(2)-4(-16)(3)))/(2(-16))
Simplifying further, we get:
t= (-35±√(1417))/(-32)
Using a calculator, we can find the approximate values of t:
t≈0.082 or t≈2.27
Since we are looking for the time it takes for the eraser to hit the student's head, we will choose the larger value of t, which is 0.082.
Therefore, it takes approximately0.082 seconds for the eraser to hit the student in the head.
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What are the coordinates of D(2, X) (Triangle XYZ) for X(1, 1), Y(2, 2), and Z(3, 0)?
Using point-slope form, the coordinate of D(2, X) is 2 units away from point X(1, 1).
What is the coordinates of D(2, X)To find the coordinates of point D, we need to know the location of point X on the line YZ. We can use the slope-intercept form of the equation of a line to find the equation of the line passing through points Y and Z:
slope m = (y2 - y1) / (x2 - x1) = (0 - 2) / (3 - 2) = -2
Using the point-slope form of the equation of a line with point Y(2, 2) and slope m = -2:
y - y1 = m(x - x1)
y - 2 = -2(x - 2)
y - 2 = -2x + 4
y = -2x + 6
Now we can substitute x = 2 into the equation of the line to find the y-coordinate of point D:
y = -2x + 6
y = -2(2) + 6
y = 2
Therefore, the coordinates of point D are (2, 2).
So, D(2, 2) is the point that lies on line YZ and is 2 units away from point X(1, 1).
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The following equation models the amount of aspirin in a person's blood in milligrams, t hours after ingesting a dose: f(t) = 300 * (1/2) ^ (1/30)
a. How much aspirin is in the dose?
b. Find and interpret ƒ (60).
c. When will the aspirin level be less than 10 milligrams?
A. The amount of aspirin in the dose is 22.066 milligrams.
B. ƒ (60) = 7.483 milligrams
This means that 60 hours after ingesting a dose of 22.066 milligrams of aspirin, the amount of aspirin in the person's blood will be 7.483 milligrams.
C. The aspirin level will be less than 10 milligrams after approximately 45.06 hours.
a. The initial amount of aspirin in the dose can be found by evaluating f(0):
f(0) = 300 * (1/2)^(1/30) ≈ 22.066
Therefore, there are approximately 22.066 milligrams of aspirin in the dose.
b. We can find f(60) by substituting t = 60 into the equation:
f(60) = 300 * (1/2)^(1/30 * 60) ≈ 7.483
Therefore, there are approximately 7.483 milligrams of aspirin in the person's blood 60 hours after ingesting the dose. This is significantly less than the initial amount of 22.066 milligrams, indicating that the aspirin is being metabolized and eliminated from the body over time.
c. We want to solve for t when f(t) < 10:
300 * (1/2)^(1/30t) < 10
Dividing both sides by 300:
(1/2)^(1/30t) < 1/30
Taking the natural logarithm of both sides:
ln[(1/2)^(1/30t)] < ln(1/30)
Using the properties of logarithms:
(1/30t)ln(1/2) < ln(1/30)
Simplifying:
-0.6931t < ln(1/30)
Dividing both sides by -0.6931 (which is ln(1/2)):
t > ln(1/30) / (-0.6931)
t > 45.06
Therefore, the aspirin level will be less than 10 milligrams after approximately 45.06 hours.
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Please help me I am stuck what do I do I multiply?
Answer:
See below.
Step-by-step explanation:
I'm sure the question is asking to solve for ∠BDC, but we'll solve for all of the angles.
We should note that we have a Given Exterior Angle.
What is an Exterior Angle?An Exterior Angle is an angle that is formed by extended lines.
An exterior angle is equal to the combined sum of the two nonadjacent, and interior angles.
Using what we learned, ∠BCD and ∠CDB will equal ∠DBE°.
Let's turn this problem into an equation.
60° + ∠BDC = 120°
Subtract 60 from both sides.
∠BDC = 60°.
We can also identify that ∠CBD is a linear pair with ∠DBE.
A Linear Pair is 2 adjacent angles that add up to 180°. Linear Pairs are straight lines with one line intersecting in between.
Meaning that ∠CBD + ∠DBE = 180°.
∠CBD + 120° = 180°.
∠CBD = 60°.
We can identify that this triangle is an Equilateral Triangle. An Equilateral Triangles is a triangle that has all congruent sides and angles.
Our final answers are;
∠BDC = 60°.
∠CBD = 60°.
Write the first five terms of a sequence, don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence.
Formula explicitly = n² + 2 n, where n is a full number and the first 5 numbers of the sequence would be 4, 8, 12, 20, and 24.
The sequence:Let 4,8,12,20,24 be the sequence's first five terms.
Let me define the terms explicit formula and recursive formula.
The generic formula to find any term in a series is known as the explicit formula.
Also, if we know the (n-1)th term of the series, we can use the recursive formula to find the nth term.
Thus, the sequence's explicit formula is,
Y equals 4 n, where n is any positive integer.
And this is the recursive formula.
Y = 4 (n-1), and we can find the nth term by using the (n-1)th term.
Initial term = 4 = 4 1
Term two = 8 = 4 2
Term three =12=43
Fourteenth term = 16 = 4 4
.....................
...........................
.................................
(n-1) th term =4 × (n-1)
nth term =4 × n
The universal and recursive formula is obtained by applying the straightforward technique of examining the first, second, and direction of the next term.
You stated that you did not desire a simpler sequence.
Think about the sequence's first five terms: 0, 3,8, 15, and 24.
Well stated formula =n2 + 2 n
Recursive equation: (n-1)
²+2(n-1)
If you examine the sequence, neither geometry nor arithmetic applies.
First term =0=0²+0×0
Second term =3=1+2=1²+2 × 1
Third term =8=4+4=2²+2×2
Fourth term =15=9+6=3²+2×3
Fifth term =24=16 +8=4²+2×4
In the explicit formula, n is a whole number and n²+2n.
Therefore, the formula explicitly = n² + 2 n, where n is a full number and the first 5 numbers of the sequence would be 4, 8, 12, 20, and 24.
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2. Determine the minimum number of faces and the minimum number of edges possible for each of the following polyhedral Prism b. Pyramid c. Polyhedron E: E: 6 V: 5 v: 4 E: 6 v: 4 3 If possible catal
Prism:
- Minimum number of faces: 5 (2 bases and 3 lateral faces)
- Minimum number of edges: 9 (3 edges on each base and 3 lateral edges)
Pyramid:
- Minimum number of faces: 4 (1 base and 3 lateral faces)
- Minimum number of edges: 6 (3 edges on the base and 3 lateral edges)
Polyhedron:
- Minimum number of faces: 4 (a tetrahedron)
- Minimum number of edges: 6 (a tetrahedron)
a. A prism is a polyhedron with two parallel congruent bases and rectangular faces connecting the bases. The minimum number of faces for a prism is 5: two bases and three rectangular faces. The minimum number of edges for a prism is 9: three edges connecting each vertex of one base to the corresponding vertex of the other base, and six edges connecting the vertices of the rectangular faces to the vertices of the bases.
b. A pyramid is a polyhedron with a polygonal base and triangular faces connecting the base to a common vertex. The minimum number of faces for a pyramid is 4: one polygonal base and three triangular faces. The minimum number of edges for a pyramid is 6: one edge for each side of the polygonal base, and three edges connecting each vertex of the base to the common vertex.
c. A polyhedron is a three-dimensional shape with flat faces and straight edges. The minimum number of faces and edges for a polyhedron depends on the specific shape, and there is no general formula to determine the minimum values. For example, a tetrahedron has 4 triangular faces and 6 edges, while a cube has 6 square faces and 12 edges. The minimum number of faces and edges for a polyhedron can be calculated by examining the shape and its properties, such as symmetry and number of vertices.
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Question is in the picture above
The values of the variables in the kite are:
x = 50°
y = 58°
z = 32°
How to find the values of the variables in the kite?Since a kite is symmetrical. Thus, it has two opposite and equal angles
Also, the line of symmetry divides the kite angle into equal angles and similar triangles. We have:
In ΔABO:
x + 90° + 40° = 180° (angle sum in a triangle)
x + 130 = 180
x = 180 - 130
x = 50°
In ΔBCO:
y + 90° + 32° = 180° (angle sum in a triangle)
y = 180 - 122
y = 58°
In ΔCDO:
z = 32° (congruent triangles)
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Consider the following time series data: month 1 2 3 4 5 6 7 value 24 13 20 12 19 23 15 a. Construct a time series plot. What type of pattern exists in the data? b. Develop a three-week moving average for this time series. Compute mse and a fore- cast for month 8. C. Use a 5 0. 2 to compute the exponential smoothing values for the time series. Compute mse and a forecast for month 8. D. Compare the three-week moving average forecast with the exponential smoothing forecast using a 5 0. 2. Which appears to provide the better forecast based on mse? e. Use trial and error to find a value of the exponential smoothing coefficient a that results in a smaller mse than what you calculated for a 5 0. 2
Therefore by increasing [tex]\alpha[/tex] smoothing characteristics we can achieve minimum MSE which is good for forecasting in exponential smoothing.
How to solveTherefore the pattern of the data is a horizontal pattern in time series.
The given data can be summarized as follows:
Week Value
1 24
2 13
3 20
4 12
5 19
6 23
7 15
a) To calculate a two-week moving average, we first need to calculate the average of the first two weeks:
[tex]MA_{1}=\frac{24+13}{2}=18.5[/tex]
Then we can calculate the moving average for the second week as follows:
[tex]MA_{2}=\frac{13+20}{2}=16.5[/tex]
Similarly, we can calculate the moving averages for the rest of the weeks:
Week Value Two-Week Moving Average
1 24
2 13 18.5
3 20 16.5
4 12 16.0
5 19 15.5
6 23 21.0
7 15 19.0
The forecast for the fourth week is the moving average for the second week (16.5), and the forecast for the fifth week is the moving average for the third week (16.0), and so on. The forecast error is the difference between the forecast value and the actual value.
Week Value Two-Week Moving Average Forecast Forecast Error
1 24
2 13 18.5
3 20 16.5
4 12 16.0 16.5 -4.5
5 19 15.5 16.0 3.0
6 23 21.0 15.5 7.5
7 15 19.0 21.0 -6.0
The mean squared error (MSE) is the average of the squared forecast errors:
MSE= [tex]\frac{(-4.5)^{2}+3^{2}+7.5^{2}+(-6)^{2}}{4}=33.375[/tex]
The forecast for the eighth week is the moving average for the seventh week (19.0).
b) To calculate a three-week moving average, we first need to calculate the average of the first three weeks:
[tex]MA_{2}=\frac{24+13+20}{3}=19.0[/tex]
Then we can calculate the moving average for the third week as follows:
[tex]MA_{3}=\frac{13+20+12}{3}=15.0[/tex]
Similarly, we can calculate the moving averages for the rest of the weeks:
Week Value Three-Week Moving Average
1 24
2 13
3 20 19.0
4 12
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Which of the following are subspaces of R3 ?
(i) {(x,y,z)| z = (x+y)2}
(ii) {(x,y,z)| x=10z}
None of the other choices is correct
(ii) only
(i) and (ii)
(i) only
The correct answer is (i) and (ii). Both of the sets are subspaces of R3 because they satisfy the three criteria of a subspace. The first set, {(x,y,z)| z = (x+y)2}, is a set of all triplets (x,y,z) such that z = (x+y)2. The second set, {(x,y,z)| x=10z}, is a set of all triplets (x,y,z) such that x = 10z. Neither of the other choices are correct.
make [t] the subject.
The expression which represents t as the subject of the formula is; t = (p + 4s) / √(s (3s - p)).
What is the expression for t as the subject of the formula?As evident in the task content; it follows that the expression which represents t as the subject of the formula is to be determined.
Given; ( (p + 4s) / t )² = s (3s - p)
(p + 4s) / t = √(s (3s - p))
t = (p + 4s) / √(s (3s - p))
Ultimately, the correct expression is; t = (p + 4s) / √(s (3s - p)).
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A village in alaska is sometimes visited by polar bears. In fact, bear visits form a poisson process of rate 1 visits per month. At each visit a group of bears shows up; the size of a group is equal to 1,2, or 3 with equa
The probability for the bear visits using Poisson process of rate one visits per month is given by ,
P(X=i, Y=j) j=i j=2i j=3i
X=i e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i! 2/3^i× e^(-1)/i!
Bear visits form a Poisson process of rate 1 visit per month.
Number of visits in a month = Poisson distribution with parameter λ = 1.
Let X be the number of visits in a month.
And Y be the total number of bears in the month.
Probability of X and Y is equal to ,
P(X = i, Y = j), for i = 0, 1, 2, 3 and j = i, 2i, or 3i.
Law of total probability for P(X = i, Y = j) for each i and j.
P(X = i, Y = i)
= P(X = i) × P(Y = i | X = i)
= e^(-λ) × λ^i / i! × 1/3^i
= e^(-1) × 1^i / i! × 1/3^i
= e^(-1) (1/ i!) × 1/3^i
Now,
P(X = i, Y = 2i)
= P(X = i) × P(Y = 2i | X = i)
= e^(-λ) × ( λ^i / i!) × [(1/3)^i + 2(1/3)^(i-1)(2/3)]
= e^(-1) / i! × [1/3^i + 4/3^i-1]
For,
P(X = i, Y = 3i)
= P(X = i) × P(Y = 3i | X = i)
= e^(-λ) × λ^i / i! × (1/3)^i × 2
= 2e^(-1) / i! × 1/3^i
Therefore, the probability of the size of bears for given condition is equal to,
P(X=i, Y=j) j=i j=2i j=3i
X=i e^(-1)(1/ i!) × 1/3^i 1/3^i + 4/3^(i-1) × e^(-1)/i! 2/3^i× e^(-1)/i!
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The given question is incomplete, I answer the question in general according to my knowledge:
A village in Alaska is sometimes visited by polar bears. In fact, bear visits form a Poisson process of rate 1 visits per month. At each visit a group of bears shows up; the size of a group is equal to 1,2, or 3 with equal opportunity. Find the probability for each size.
List of covered course outcome in this assignment: 1) Understand the meaning and the applications of statistical inference and confidence interval (1,3,6) Question 1 (50 points): Let A be the first two digits of your AUM ID number. For example: for an ID 34567, A = 34. A statistics instructor wants to know how students in a class of 105 students did on their last test. The instructor asks the A students sitting in the front row to state their latest test score. a) What is the sample? (5 points) b) What is the population? (5 points) c) What is the variable of interest? (5 points) d) Do you think that the sample is representative of the population? Can you generalize the result that you get from the sample to the population? Why? Why not? Discuss (5 points) .) (e) Suppose that the sample mean is 82.4 and assume that the test scores are normally with a population variance of 38.2. Construct a 90% confidence interval on the mean test score of the students i. Write the appropriate formula. (5 points) . ii. Find the necessary table value. (5 points) iii. Substitute the quantities into your formula. (5 points) iv. Calculate the confidence interval. (10 points) v. Interpret your interval. (5 points)
The 90% confidence interval for the mean test score of the students is (81.06, 83.74), which means that we can be 90% confident that the true mean test score of the population is between 81.06 and 83.74.
a) What is the sample? (5 points)
The sample is the set of A students sitting in the front row who stated their latest test scores.
b) What is the population? (5 points)
The population is the entire class of 105 students who took the test.
c) What is the variable of interest? (5 points)
The variable of interest is the mean test score of the students.
d) Do you think that the sample is representative of the population? Can you generalize the result that you get from the sample to the population? Why? Why not? Discuss (5 points).
The sample may or may not be representative of the population. It is difficult to say for certain without knowing the overall distribution of test scores for the population. If the sample is randomly selected and the distribution of the sample is similar to the distribution of the population, then the results from the sample can be generalized to the population. However, if the sample is not randomly selected, then the results may not be reliable for generalization to the population.
e) Suppose that the sample mean is 82.4 and assume that the test scores are normally with a population variance of 38.2. Construct a 90% confidence interval on the mean test score of the students i. Write the appropriate formula. (5 points)
The appropriate formula for a 90% confidence interval is:
Mean ± (1.645 * (Standard Error of the Mean))
ii. Find the necessary table value. (5 points)
The necessary table value is 1.645, which is the critical value associated with a 90% confidence interval.
iii. Substitute the quantities into your formula. (5 points)
Mean ± (1.645 * (Standard Error of the Mean))
82.4 ± (1.645 * (Standard Error of the Mean))
iv. Calculate the confidence interval. (10 points)
Standard Error of the Mean = (Population Variance/Sample Size)0.5
Standard Error of the Mean = (38.2/105)0.5
Standard Error of the Mean = 0.8244
Confidence Interval = 82.4 ± (1.645 * 0.8244)
Confidence Interval = 82.4 ± 1.34
Confidence Interval = (81.06, 83.74)
v. Interpret your interval. (5 points)
The 90% confidence interval for the mean test score of the students is (81.06, 83.74), which means that we can be 90% confident that the true mean test score of the population is between 81.06 and 83.74.
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3: Find the value of X
4: Find the measure of angle JML
Step-by-step explanation:
3.
the sum of all internal angles in a quadrilateral is always 360°.
so, the internal angle at x is given by
360 = 40 + 80 + 110 + inner angle
inner angle = 360 - 40 - 80 - 110 = 130°
an inner and an outer angle combined are together always 180°.
so,
130 + x = 180
x = 50°
4.
first, again, the sum of all inner angles is 360°.
this is a parallelogram. that means the diagonally opposing angles are equal.
so, the angle opposite of the 38° angle is also 38°.
that leaves
360 - 38 - 38 = 284°
for the 2 (again equal) remaining angles :
284 = 2 × angle
each of these remaining angles is then
284/2 = 142°
the angle JML is one of them.
so,
angle JML = 142°