The total amount of interest earned by the investment in n years is 100 times the product of the annual interest rate and the time period i.e., I = 100 * x * n
The total amount of interest earned by an investment can be calculated using the simple interest formula:
I = P * r * t
Where:
I = the total amount of interest earned
P = the principal investment amount
r = the annual interest rate as a decimal
t = the time period in years
In this case, the principal investment amount is $10,000, the annual interest rate is x percent (as a decimal, x/100), and the time period is n years. So, the total amount of interest earned can be represented by:
I = 10,000 * (x/100) * n
Simplifying this expression, we get:
I = 100 * x * n
Therefore, the total amount of interest earned by the investment in n years is 100 times the product of the annual interest rate and the time period. The units of this value will be dollars, since it represents the amount of interest earned.
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In a survey, 400 people were asked to choose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number 2.
Cards Chosen
Number- 1 2 3 4 5
Frequency- 128 96 48 112 16
The theoretical probability of choosing a card with the number 2 is ?%
The experimental probability of choosing a card with the number 2 is ?%
The theoretical probability is ( < > = ) the experimental probability.
(Type integers or decimals)
Answer:
Theoretical A - 20%
Experimental - 24%
Theoretical B - <
Step-by-step explanation:
The theoretical probability of choosing a card with the number 2 is:
1 out of 5 cards have the number 2, so the probability of choosing a card with the number 2 is 1/5 or 0.2, which is equal to 20%.
The experimental probability of choosing a card with the number 2 is:
Out of the 400 people surveyed, 96 chose the card labeled 2. So the experimental probability is 96/400 or 0.24, which is equal to 24%.
On december 1, after making a concerted effort, management determines that it will be unable to collect $1,200 owed to it by one of its customers. This company uses the allowance method to account for uncollectible accounts.
The answer is that since the company uses the allowance method for uncollectible accounts, it needs to record an allowance for doubtful accounts at the end of each accounting period. This allowance is an estimated amount that represents the portion of accounts receivable that is expected to be uncollectible.
In this specific situation, the company has determined that it will not be able to collect $1,200 owed by one of its customers. Therefore, it needs to adjust the allowance for doubtful accounts to reflect this uncollectible amount. This adjustment will decrease the accounts receivable balance and the net income for the period.
The allowance method is a way of accounting for uncollectible accounts that estimates the amount of accounts receivable that is likely to be uncollectible. This method is used because it is not possible to know exactly which accounts will not be collected. The estimated amount is based on historical experience and other relevant factors, such as economic conditions and the creditworthiness of customers.
When a company determines that a specific account is uncollectible, it needs to adjust the allowance for doubtful accounts to reflect this. This adjustment reduces the accounts receivable balance and the net income for the period. The adjustment is made by debiting the allowance for doubtful accounts and crediting the accounts receivable.
In this situation, the company has determined that it will not be able to collect $1,200 owed by one of its customers. Therefore, it needs to adjust the allowance for doubtful accounts to reflect this uncollectible amount. This adjustment will decrease the accounts receivable balance and the net income for the period. The adjustment is made by debiting the allowance for doubtful accounts and crediting the accounts receivable.
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What is the first step to conducting a statistical study?.
The first step to conducting a statistical study is to clearly define the research question or problem.
This involves identifying the population of interest, the variables to be measured, and the hypothesis or objective of the study. Once the research question is clearly defined, the next step is to design the study, including selecting an appropriate sample size, choosing a sampling method, and determining the data collection method.
It is also important to consider potential sources of bias and confounding factors that may impact the study results. Overall, a well-designed statistical study should be able to produce reliable and accurate results that can be used to draw meaningful conclusions about the population of interest.
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shaq made 8 basketball shots and missed 5. what is the probablility of shaq making a basketball shot
The probability of Shaq making a basketball shot is approximately 0.615 or 61.5%.
The number of likely outcomes divided by the total number of outcomes determines the likelihood that an event will occur.
In this case, the event we are interested in is Shaq making a basketball shot.
The number of favorable outcomes is the number of shots that Shaq made, which is 8.
The total number of possible outcomes is the total number of shots that Shaq took, which is 13 (since he made 8 shots and missed 5).
To find the probability of Shaq making a basketball shot, we need to know the total number of shots he took and the number of shots he made.
The total number of shots Shaq took is [tex]8 + 5 = 13[/tex]
(since he made 8 shots and missed 5).
Therefore, the probability of Shaq making a basketball shot is:
total rounds fired / total shots made
[tex]= 8 / 13[/tex]
[tex]= 0.615 or 61.5%[/tex]
So the probability of Shaq making a basketball shot is approximately 0.615 or 61.5%.
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Factor
25m^2 -30mn+ 9n^2
[tex](5m-3n) (5m-3n)[/tex] is the factor of [tex]25m^{2} - 30mn + 9n^{2}[/tex].
Factoring is the method of breaking down an expression into less difficult terms (components) that when multiplied together deliver the original expression. Variables are numbers, expressions, or algebraic quantities that when multiplied together deliver a given product.
Factoring is an imperative tool in variable-based math and is utilized in solving equations, simplifying expressions, and finding common denominators in divisions.
Factorize,
[tex]25m^{2} - 30mn + 9n^{2}\\= 25m^{2} - 15mn - 15mn + 9m^{2} \\= 5m(5m-3n) - 3n (5m-3n)\\= (5m-3n) (5m-3n)[/tex]
Therefore, (5m-3n) (5m-3n) is the factor of 25m^2 -30mn+ 9n^2.
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The surface area of a small toy ball is 10 square inches. If the radius of the ball is doubled, what will be the surface area of the new, larger ball in square inches?.
The surface area of the new, larger ball is 160 square inches.
What is surface area?
The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.
The surface area of a sphere with radius r is given by:
A = 4πr²
If the radius is doubled to 2r, the surface area of the new sphere is:
A' = 4π(2r)² = 4π(4r²) = 16πr²
So the new surface area is 16 times the original surface area.
Since the original surface area is 10 square inches, the new surface area is:
A' = 16(10) = 160 square inches
Therefore, the surface area of the new, larger ball is 160 square inches.
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The size of a company's logo on an envelope is 1/4 the size of the company's logo on a shirt. The logo on the 1 shirt is 8 centimeters wide and 6 centimeters tall. What are the dimensions of the logo on the envelope?
Answer:
Step-by-step explanation:
That's just a simple ratio.
8*1/4 = 2
6*1/4= 1.5
so it would be 2 centimeters wide by 1.5 centimeters tall
(Q1) The circumcenter of a(n) _____ triangle will be in the exterior of the triangle.
The circumcenter of an obtuse triangle will be located in the exterior of the triangle.
Recall that the circumcenter is the point of intersection of the perpendicular bisectors of the sides of a triangle, and it is the center of the circumcircle that passes through all three vertices of the triangle.
In an acute triangle, the circumcenter lies inside the triangle, and in a right triangle, the circumcenter coincides with the midpoint of the hypotenuse. However, in an obtuse triangle, one of the angles measures more than 90 degrees, and the perpendicular bisectors of the two shorter sides intersect outside the triangle, while the perpendicular bisector of the longest side intersects inside the triangle.
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Matt has exactly $1.60 in his pocket. He only has nickels and dimes. There are twice as many nickels as dimes. What is the number of coins in Matt's pocket?
Answer:
24 coins
Step-by-step explanation:
We give the dimes a unknown number like y since the nickels are twice as much we give it 2y we multiply the numbers with their value and form an equation like 2y×5+y×10=160 find the value of y then get value of 2y+y to get the number of coins
(The following passage is an essay published by a British writer in the 1750s.) Pleasure is very seldom found where it is sought. Our brightest blazes of gladness are commonly kindled by unexpected sparks. The flowers which scatter their odors from time to time in the paths of life, grow up without culture from seeds scattered by chance. Nothing is more hopeless than a scheme of merriment. Wits and humorists are brought together from distant quarters by preconcerted invitations; they come attended by their admirers prepared to laugh and to applaud: they gaze a while on each other, ashamed to be silent, and afraid to speak; every man is discontented with himself, grows angry with those that give him pain, and resolves that he will contribute nothing to the merriment of such worthless company. Wine inflames the general malignity, and changes sullenness to petulance, till at last none can bear any longer the presence of the rest. They retire to vent their indignation in safer places, where they are heard with attention, their importance is restored, they recover their good humor, and gladden the night with wit and jocularity. Merriment is always the effect of a sudden impression. The jest which is expected is already destroyed. The most active imagination will be sometimes torpid, under the frigid influence of melancholy, and sometimes occasions will be wanting to tempt the mind, however volatile, to sallies and excursions. Nothing was ever said with uncommon felicity, but by the cooperation of chance; and therefore, wit as well as valor must be content to share its honors with fortune. All other pleasures are equally uncertain, the general remedy of uneasiness is change of place; almost everyone has some journey of pleasure in his mind, with which he flatters his expectation. He that travels in theory has no inconveniences; he has shade and sunshine at his disposal, and wherever he alights finds tables of plenty and looks of gaiety. These ideas are indulged till the day of departure arrives, the chaise is called, and the progress of happiness begins. A few miles teach him the fallacies of imagination. The road is dusty, the air is sultry, the horses are sluggish, and the postilion (21 brutal. He longs for the time of dinner that he may eat and rest. The inn is crowded, his orders are neglected, and nothing remains but that he devour in haste what the cook has spoiled, and drive on in quest of better entertainment. He finds at night a more commodious house, but the best is always worse than he expected. He at last enters his native province, and resolves to feast his mind with the conversation of his old friends, and the recollection of juvenile frolics. He stops at the house of his friend whom he designs to overpower with pleasure by the unexpected interview. He is not known till he tells his name, and revives the memory of himself by a gradual explanation. He is then coldly received, and ceremoniously feasted. He hastes away to another whom his affairs have called to a distant place, and having seen the empty house, goes away disgusted by a disappointment which could not be intended because it could not be foreseen. At the next house he finds every face clouded with misfortune, and is regarded with malevolence as an unreasonable intruder, who comes not to visit but to insult them. It is seldom that we find either men or places such as we expect them. He that has pictured a prospect upon his fancy, will receive little pleasure from his eyes; he that has anticipated the conversation of a wit, will wonder to what prejudice he owes his reputation. Yet it is necessary to hope, though hope should always be deluded, for hope itself is happiness, and its frustrations, however frequent, are yet less dreadful than its extinction. Overall, the style of the passage is best described as conversational digressive cryptic lyrical E intellectual
This is a passage from an essay published by a British writer in the 1750s.
The writer explores the idea that pleasure is rarely found where it is sought and that unexpected sparks can bring the brightest blazes of gladness.
The writer argues that merriment is often hopeless, as pre-planned schemes of humor can lead to discontent and anger.
Instead, true wit and humor come from chance and cooperation with fortune. The writer also explores the idea of travel and how the anticipation of pleasure is often shattered by the reality of dusty roads, bad food, and disappointing encounters.
Overall, the style of the passage is conversational and digressive, with a lyrical quality to the language.
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What is the relationship between interior and exterior angles of polygons?.
Answer:Each interior angle of a regular polygon with n sides is given by the formula:
Interior angle = (n - 2) x 180 degrees / n
Exterior angle = 180 degrees - Interior angle
Step-by-step explanation: The angle that is formed between one of the polygon's sides and a line that is drawn from the side next to it is called the polygon's exterior angle. The outside point and the inside point at every vertex of a polygon are beneficial, meaning they amount to 180 degrees.
A plane is flying north at 40 miles per hour. There is a 5-mile-per-hour wind blowing on the plane heading east. Draw the vectors and find the resulting vector graphically. List the resulting vector's magnitude.
The resultant vector has a magnitude of approximately 40.31 mph and is pointing in a direction approximately 7.13 degrees east of north.
To draw the vectors and find the resulting vector graphically, we can use the Pythagorean theorem and trigonometric functions.
In the diagram, the 40 mph vector is pointing north, and the 5 mph vector is pointing east. To find the resultant vector, we need to find the magnitude and direction of the vector that starts at the origin and ends at the tip of the 40 mph vector.
Using the Pythagorean theorem, we can find the magnitude of the resultant vector:
magnitude = √((40 mph)² + (5 mph)²)
magnitude = √(1600 + 25)
magnitude = √(1625) ≈ 40.31 mph
To find the direction of the resultant vector, we can use the tangent function:
tan(θ) = opposite/adjacent
θ= tan⁻¹(opposite/adjacent)
θ= tan⁻¹(5/40)
θ≈ 7.13 degrees
Therefore, the resultant vector has a magnitude of approximately 40.31 mph and is pointing in a direction approximately 7.13 degrees east of north.
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A cylindrical drill with radius 3 is used to bore a hole through the center of a sphere of radius 5. Find the volume of the ring-shaped solid that remains. Please round the answer to the nearest hundredth.
If someone in our class gets this right, we get our professors famed crumb cake :) help me out please!
Keep in mind you need to use a triple integral to solve this, algebra wont work due to the "caps" on each end of the cylinders. If you can set up the integral I can solve it.
The volume of the ring-shaped solid that remains is approximately 240.90 cubic units, rounded to the nearest hundredth.
Calculating the volume of the solid:The volume of the ring-shaped solid can be found by subtracting the volume of the drilled cylinder from the volume of the original sphere.
To calculate the volume of the cylinder, we use the formula V = πr²h, where r is the radius of the cylinder and h is the height of the cylinder.
To calculate the volume of the sphere, we use the formula V = (4/3)πr³, where r is the radius of the sphere.
Here we have
A cylindrical drill with radius 3 is used to bore a hole through the center of a sphere of radius 5.
Using the formula,
The volume of the sphere V = (4/3)πr³
=> V_sphere = (4/3)π(5³) = 523.60
The volume of the cylinder is given by:
=> V_cylinder = πr²h
Here the height of the cylinder will equal the diameter of the sphere, which is 10. Thus, we have:
=> V_cylinder = π(3)²(10) = 282.86
Now find the volume of the ring-shaped solid by subtracting the volume of the cylinder from the volume of the sphere:
V_ring = V_sphere - V_cylinder = 523.60 - 282.70 = 240.90
Therefore,
The volume of the ring-shaped solid that remains is approximately 240.90 cubic units, rounded to the nearest hundredth.
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Calculate the Light Gathering Power of the hubble space telescope. Compare this to an eye which has an average aperture of 5 mm.
please put the equation and answer.
(THIS IS FOR ASTRONOMY, BRAINLY JUST DOESN'T HAVE ASTRONOMY)
Answer:
The Hubble Space Telescope has a mirror diameter of 2.4 meters (2400 mm), giving it a surface area of approximately 4.5 million mm². Assuming a perfect reflector, the telescope would gather about 4.5 million times as much light as the human eye, which has an average aperture of 5 mm. However, the Hubble's sensors and optics reduce this number somewhat, but it still gathers vastly more light than the human eye, enabling it to observe extremely faint objects in space.
let c be the square oriented counterclockwise with corners (0,0),(5,0),(5,5), and (0,5). if we label the edges of the square as starting from the bottom edge going counterclockwise, then the edges may be linearly parameterized, with , by:
The edges of the square may be linearly parameterized as follows:- The bottom edge from (0,0) to (5,0) can be parameterized as (t, 0) for t in [0, 5].
- The right edge from (5,0) to (5,5) can be parameterized as (5, t) for t in [0, 5], - The top edge from (5,5) to (0,5) can be parameterized as (t, 5) for t in [5, 0]., - The left edge from (0,5) to (0,0) can be parameterized as (0, t) for t in [5, 0].
To linearly parameterize the edges of square C with corners (0,0), (5,0), (5,5), and (0,5), oriented counterclockwise,
we can use the following parameterizations: 1. Bottom edge: from (0,0) to (5,0)
Parameterization: (x, y) = (t, 0), where 0 ≤ t ≤ 5
2. Right edge: from (5,0) to (5,5)
Parameterization: (x, y) = (5, t), where 0 ≤ t ≤ 5
3. Top edge: from (5,5) to (0,5)
Parameterization: (x, y) = (t, 5), where 0 ≤ t ≤ 5
4. Left edge: from (0,5) to (0,0)
Parameterization: (x, y) = (0, t), where 0 ≤ t ≤ 5, These linear parameterizations represent each edge of the square and follow the counterclockwise orientation.
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modeling real life a group spends $277.50 to rent 15 tubes for a float down the ichetucknee river. how many of each type of tube does the group rent?river tubing: 1 person tube 12 dollars and 50 cents, 2 person tube 20 dollars. the group rents one-person tubes and two-person tubes.
The group rented 12 two-person tubes and 3 one-person tubes for their float down the Ichetucknee River.
Let's denote the number of one-person tubes as x, and the number of two-person tubes as y.
From the problem statement, we know that:
x + y = 15 (Equation 1)
And the cost of renting the tubes is $277.50, so:
12.5x + 20y = 277.5 (Equation 2)
Now we can use Equation 1 to solve for x in terms of y:
x = 15 - y
Substituting this into Equation 2, we get:
12.5(15-y) + 20y = 277.5
187.5 - 12.5y + 20y = 277.5
7.5y = 90
y = 12
So the group rented 12 two-person tubes.
Using Equation 1, we can solve for x:
x + y = 15
x + 12 = 15
x = 3
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7.02 Central and Inscribed Angles
pls help
The value of x when central angle is 122 degrees and inscribed angle is (3x + 5) degrees is given by, x = 39.
So the blank will be '39'
Central angle is angle made at center by the end points of an arc of a circle.
Here the central angle in variable is = (3x + 5) degrees
The central angle is = 122 degrees
So by the figure we can see that,
3x + 5 = 122
3x = 122 - 5
3x = 117
x = 117/3
x = 39
So the value of the x is given by, x = 39.
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15. A polygon has the dimensions shown.
(2b + a) in.
W
X
(4a-3) in.
Z
(3a + b-2) in.
Y
Part A
What is the perimeter of triangle WXY?
A 5a + 2b - 5 in.
B 8a3b-5 in.
9a3b-2 in.
D 9a 5b + 2 in.
-
Part B
If triangle WYZ has a perimeter of 4a + 5b - 2
inches, what is the polynomial that represents the
perimeter in inches of polygon WXYZ?
The perimeter of triangle WXY is 3b + 8a - 5.
The polynomial that represents the perimeter of polygon WXYZ is
4a + 8b - 1
We have,
Part A.
The perimeter of triangle WXY.
= (2b + a) + (3a + b - 2) + (4a - 3)
= 3b + 8a - 5
Part B.
WYZ has a perimeter of (4a + 5b - 2).
Now,
The polynomial that represents the perimeter of polygon WXYZ.
= (3b + 8a - 5) + (4a + 5b - 2) - 2(4a - 3)
= 3b + 8a - 5 + 4a + 5b - 2 - 8a + 6
= 4a + 8b - 1
Thus,
The polynomial that represents the perimeter of polygon WXYZ is
4a + 8b - 1
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Find the area of the shaded region. Round to the hundredths place when necessary.
Answer:
√(20^2 + 21^2) = √(400 + 441) = √841 = 29
The diameter of the circle is 29 inches, so the radius is 14.5 inches.
Area of shaded region:
π(14.5^2) - (1/2)(20)(21) = 450.52 in^2
What measurement is equivalent to
1
2
3
yards?
A.
5 feet
B.
48 inches
C.
10,560 feet
D.
126 inches
The [tex]1 \frac{2}{3}[/tex] yards of measurement is equivalent to 5 feet. So, the option A is correct.
Given yards are [tex]1 \frac{2}{3}[/tex] .
Yards: A yard is an English unit of measuring length which is equal to 3 feet or 36 inches or equivalent to 0.9144 meters.
To convert yards into feet we have to use the conversion factor. We know that the 1 yard of value is equivalent to 3 feet. So, to find the value of [tex]1 \frac{2}{3}[/tex] yards we have to multiply the given [tex]1 \frac{2}{3}[/tex] yards by 3.
[tex]1 \frac{2}{3}[/tex] x 3 = [tex]\frac{5}{3}[/tex] x 3 = 5
Hence, from the above explanation, we can conclude that the [tex]1 \frac{2}{3}[/tex] which is equivalent to [tex]\frac{5}{3}[/tex] yards of measurement is equivalent to 5 feet.
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Given question has a mistake, The correct question was "What measurement is equivalent to [tex]1 \frac{2}{3}[/tex] yards? "
____ is A function f(N) that is defined in terms of the same function operating on a value < N.
A recursive function is a function f(N) that is defined in terms of the same function operating on a value < N.
In a recursive function, the function calls itself repeatedly until it reaches a base case, which is a condition that stops the recursion. The function then returns the result of the base case to the previous call, which uses it to compute the final result.
Recursive functions are commonly used in programming for solving problems that can be broken down into smaller subproblems of the same type. They are especially useful for tasks such as traversing trees or searching through graphs.
The process of recursion involves breaking down a problem into smaller, similar subproblems that can be solved using the same approach. This leads to a more elegant and concise solution, as compared to iterative approaches. However, recursive functions can also be less efficient than their iterative counterparts and may have issues with a stack overflow if the recursion depth becomes too large.
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If you are testing the null hypothesis with an alpha value of 0. 05, will the critical value be smaller or larger than if you were testing the alpha value of 0. 01? why?.
When testing the null hypothesis with an alpha value of 0.05, the critical value will be larger than if you were testing the alpha value of 0.01. This is because the alpha value represents the level of significance at which we reject the null hypothesis. A smaller alpha value means we are requiring stronger evidence to reject the null hypothesis, and therefore, the critical value will be higher.
Conversely, a larger alpha value means we are more likely to reject the null hypothesis, and therefore, the critical value will be lower.
When testing a null hypothesis with an alpha value of 0.05, the critical value will be larger compared to testing with an alpha value of 0.01. The reason for this is that the alpha value represents the level of significance or the probability of rejecting the null hypothesis when it is actually true.
A smaller alpha value (e.g., 0.01) indicates a more stringent test, requiring stronger evidence to reject the null hypothesis. As a result, the critical value for a 0.01 alpha level will be smaller, making it more difficult to reject the null hypothesis. Conversely, a larger alpha value (e.g., 0.05) indicates a less stringent test, requiring less evidence to reject the null hypothesis, and the critical value will be larger, making it easier to reject the null hypothesis.
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Simplify [tex]\frac{9}{8 - \sqrt 3}[/tex]
Step-by-step explanation:
[tex] \frac{9}{8 - \sqrt{3} } [/tex]
[tex] \frac{9}{8 - \sqrt{3} } \times \frac{8 + \sqrt{3} }{8 + \sqrt{3} } [/tex]
[tex] \frac{72 + 9 \sqrt{3} }{64 - 9} [/tex]
[tex] \frac{72 + 9 \sqrt{3} }{55} [/tex]
Which two dimsoel figure is always a quadiretal
Rectangle is a two dimensionall figure is always a quadrilateral
What is a rectangleA rectangle is a two-dimensional figure that always exists as a quadrilateral. A rectangle has four straight sides with opposite edges being parallel and equal length; all four interior angles measure 90 degrees for added precision. This characteristic feature makes a rectangle an exemplary example of quadrilaterals.
A rectangle is a type of quadrilateral that shares several properties:
It has four straight sides connected by four equal length sides that run perpendicularly to one another and never intersect or diverge, forming equal interior angles of 90 degrees each (right angles).
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Which two dimensionall figure is always a quadrilateral
Prove that if f and g are each uniformly continuous on R, then the composite function
f o g is uniformly continuous on R.
We have proved that f o g is uniformly continuous on R, as desired.
What is composite function?F(g(x)) or (f g)(x) denotes the combination of the functions f(x) and g(x), where g(x) acts first. It brings together two or more functions to produce a new function.
To prove that the composite function f o g is uniformly continuous on R, we need to show that for any ε > 0, there exists a δ > 0 such that for any x, y ∈ R,
| x - y | < δ implies | (f o g)(x) - (f o g)(y) | < ε
We can start by using the uniform continuity of g to choose a δ1 > 0 such that for any x, y ∈ R,
| x - y | < δ1 implies | g(x) - g(y) | < ε
Now, we can use the uniform continuity of f with ε replaced by δ₁ to choose a δ₂ > 0 such that for any u, v ∈ R,
| u - v | < δ₂ implies | f(u) - f(v) | < δ₁
Finally, we can choose δ = δ₂ to show that for any x, y ∈ R,
| x - y | < δ implies | (f o g)(x) - (f o g)(y) | < ε
To see why this is true, let's assume that | x - y | < δ. Then, by the definition of the composite function,
(f o g)(x) - (f o g)(y) = f(g(x)) - f(g(y))
Now, since | g(x) - g(y) | < δ₁, we know that | f(g(x)) - f(g(y)) | < ε, by the choice of δ₁. And since | x - y | < δ₂ implies | g(x) - g(y) | < δ₁, we have shown that
| x - y | < δ₂ implies | (f o g)(x) - (f o g)(y) | < ε
Therefore, we have proved that f o g is uniformly continuous on R, as desired.
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What is the slope of a line that goes through the origin and the point (6, -4)?
The slope of the line that goes through the origin and the point (6, -4) is -2/3.
To find the slope of a line that goes through two given points (x₁, y₁) and (x₂, y₂), you can use the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
In this case, one of the points is the origin, which has coordinates (0, 0), so x₁ = 0 and y₂ = 0. The other point is (6, -4), so x₂ = 6 and y₂ = -4. Substituting these values into the slope formula gives:
slope = (-4 - 0) / (6 - 0) = -4/6 = -2/3
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on november 2, 2014, a gallup poll reported that 51 percent of americans support legalizing marijuana, while 47 percent oppose legalization. the reported margin of sampling error was /- 4 percent. which of the following inferences can be made from the poll?
Based on the Gallup poll conducted on November 2, 2014, it can be inferred that the majority of Americans are in favor of legalizing marijuana.
The poll reported that 51 percent of Americans support legalization while 47 percent oppose it.
However, it is important to note that the reported margin of sampling error was +/- 4 percent, which means that the actual percentage of Americans who support or oppose legalization could be slightly different from the reported percentages.
The margin of sampling error is a measure of the accuracy of the poll results and indicates the amount of random sampling error that is expected. In this case, the margin of sampling error is relatively small, at +/- 4 percent, which suggests that the poll results are fairly reliable.
Overall, the poll indicates that attitudes towards marijuana legalization have shifted in recent years, with a majority of Americans now supporting legalization. This could have implications for future policy decisions related to marijuana legalization at both the state and federal levels.
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First make a substitution and then use integration by parts to evaluate the integral.
π,0
e^cos(t) sin(2t) dt
The value of the integral ∫[tex]e^{cos(t)[/tex] sin(2t) dt over the interval [0, π] is 0.
What is integration?The summing of discrete data is indicated by the integration. To determine the functions that will characterise the area, displacement, and volume that result from a combination of small data that cannot be measured separately, integrals are calculated.
To evaluate the integral ∫[tex]e^{cos(t) sin(2t)} dt[/tex] over the interval [0, π], we can use integration by parts with the substitution u = sin(t) and dv = [tex]e^{cos(t)cos(t)}dt[/tex]. Then, du = cos(t)dt and [tex]v = e^{cos(t)[/tex].
Using this substitution and the formula for integration by parts:
∫[tex]e^{cos(t) sin(2t)} dt[/tex] = [tex]-e^{cos(t) sin(t)}[/tex] + ∫[tex]e^{cos(t) cos(t)} dt[/tex]
We can use another substitution, z = cos(t), to simplify the integral on the right-hand side:
∫[tex]e^{cos(t) cos(t)} dt = \int e^{z} dz = e^z + C[/tex]
Substituting back to the original integral, we get:
∫[tex]e^{cos(t) sin(2t)} dt = -e^{cos(t) sin(t)} + e^{cos(t)} + C[/tex]
Evaluating the definite integral over the interval [0, π], we get:
∫[0,π] [tex]e^{cos(t) sin(2t)} dt = -e^{cos(\pi ) sin(\pi )} + e^{cos(\pi )} - (-e^{cos(0) sin(0)} + e^{cos(0)})[/tex]
Simplifying the trigonometric terms sin(π) = 0 and sin(0) = 0, and using the fact that cos(π) = -1 and cos(0) = 1, we get:
∫[0,π] [tex]e^{cos(t)[/tex] sin(2t) dt = [tex]-e^{-1} + e^{-1} = 0[/tex]
Therefore, the value of the integral ∫[tex]e^{cos(t)[/tex] sin(2t) dt over the interval [0, π] is 0.
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sam said the square root of a rational number must be a rational number. jenna disagreed. she said that it is possible that the square root of a rational number can be irrational. who is correct and why? jenna is correct because all square roots are irrational numbers. sam is correct because all square roots of rational numbers are rational. an example is startroot 121 endroot
Jenna is actually correct. The square root of a rational number can be an irrational number.
A rational number is defined as a number that can be expressed as a ratio of two integers (i.e., a fraction), where the denominator is not zero. An irrational number, on the other hand, is a number that cannot be expressed as a ratio of two integers.
For example, the number 2 is a rational number because it can be expressed as the ratio 2/1. The square root of 2, however, is an irrational number because it cannot be expressed as a ratio of two integers.
Therefore, it is possible for the square root of a rational number to be irrational. Jenna's argument is correct.
While Sam's example of the square root of 121 is a valid point, it is not a general proof that all square roots of rational numbers are rational.
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What is the value of x? Please help as soon as possible!!
The value of x based on the triangle is 7 cm.
How to calculate the value of xFrom the given figure, we know that the two corresponding lines are parallel and so the two given triangles are congruent to each other.
Therefore, the corresponding sides of these triangles will also be proportional so we can write it as:
5 / 45 = 3 / 2x + 10
10x + 65 = 135
Collect the like terms
10x = 135 - 65.
10x = 70
Divide
x = 70 / 10
x = 7
Therefore, the value of x is 7 cm.
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