IS ABC = DEF IF SO , NAME THE CONGRUENCE POSTULATE THAT APPLIES .

IS ABC = DEF IF SO , NAME THE CONGRUENCE POSTULATE THAT APPLIES .

Answers

Answer 1

The congruence postulate that applies is C. Congruent - SSS

What are congruent triangles?

When the properties (i.e length of sides and/or internal angles) of two or more triangles are equal, then it can be said that they are congruent. This congruent relations can be expressed using either of the following postulates: Angle-Side-Side, Side-Angle-Side (SAS), Angle-Angle-Side (AAS), Side-Side-Side (SSS) etc.

Considering the given triangles ABC and DEF, it is was given that:

AB ≅ DE

BC ≅ EF

CA ≅ FD

Therefore, it can be concluded that the two triangles are congruent by Side-Side-Side (SSS) relations. So that the required congruence postulate that applies is C. Congruent - SSS

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Related Questions

What is the value of x? Please help as soon as possible!!

Answers

The value of x based on the triangle is 7 cm.

How to calculate the value of x

From 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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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?

Answers

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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First make a substitution and then use integration by parts to evaluate the integral.
π,0
e^cos(t) sin(2t) dt

Answers

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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(Q1) The circumcenter of a(n) _____ triangle will be in the exterior of the triangle.

Answers

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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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)

Answers

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%.

Theoretical A-20%

Experimental-24%

Theoretical B -

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?

Answers

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

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?.

Answers

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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Factor
25m^2 -30mn+ 9n^2

Answers

[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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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.

Answers

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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Which two dimsoel figure is always a quadiretal

Answers

Rectangle is a two dimensionall figure is always a quadrilateral

What is a rectangle

A 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

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?

Answers

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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Simplify [tex]\frac{9}{8 - \sqrt 3}[/tex]

Answers

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]

What measurement is equivalent to
1
2
3
yards?

A.
5 feet

B.
48 inches

C.
10,560 feet

D.
126 inches

Answers

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? "

shaq made 8 basketball shots and missed 5. what is the probablility of shaq making a basketball shot

Answers

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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What is the relationship between interior and exterior angles of polygons?.

Answers

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.

Answers

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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7.02 Central and Inscribed Angles
pls help

Answers

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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Find the area of the shaded region. Round to the hundredths place when necessary.

Answers

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

A particle moving along a curve in the xy-plane has position.

Answers

The position of a particle moving along a curve in the xy-plane can be described using parametric equations, where x and y are both functions of a third variable, usually time (t).


1. Parametric equations are equations that express the coordinates of a point (x, y) in the xy-plane in terms of a single variable, often time (t). In this case, x = f(t) and y = g(t), where f(t) and g(t) are functions of time.

2. To find the position of the particle at any given time, plug the value of time (t) into both functions, f(t) and g(t), to find the corresponding x and y coordinates. The position of the particle at time t is given by (x(t), y(t)).

3. To visualize the path of the particle, you can plot the curve described by the parametric equations x = f(t) and y = g(t) on the xy-plane. The particle moves along this curve as time progresses.

4. If you need to find the particle's velocity or acceleration, you can calculate the first and second derivatives of the position functions with respect to time.

In summary, the position of a particle moving along a curve in the xy-plane can be described by parametric equations, which relate the x and y coordinates to a third variable, usually time (t). The position of the particle at any given time can be found by plugging in the value of time into the parametric equations.

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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

Answers

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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presents a poll where 48% of 331 americans who decide to not go to college do so because they cannot afford it

Answers

A poll was conducted with 331 Americans who had the option to go to college but did not. The results of the poll showed that 48% of the respondents did not go to college because they could not afford it.

This means that 48% of the 331 respondents chose not to go to college because they did not have the financial means to do so. It is important to note that this result is based on the sample of respondents who were surveyed and may not be representative of the entire population of Americans who did not go to college due to financial reasons.

It is also worth noting that the cost of college can vary widely depending on the institution, location, and field of study, among other factors. Therefore, the financial barriers to college may be different for different individuals and may require different solutions.  

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Full Question: Exercise 6.16 presents the results of a poll where 48% of 331 Americans who decide to not go to college do so because they cannot afford it.

Calculate a 90% confidence interval for the proportion of Americans who decide to not go to college because they cannot afford it, and interpret the interval in context.

lower bound: (please round to four decimal places)

upper bound: (please round to four decimal places) Interpret the confidence interval in context:

90% of Americans choose not to go to college because they cannot afford it

We can be 90% confident that the proportion of Americans who choose not to go to college because they cannot afford it is contained within our confidence interval

We can be 90% confident that our confidence interval contains the sample proportion of Americans who choose not to go to college because they cannot afford it

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.

Answers

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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(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

Answers

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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A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 40 pounds each, and the small boxes weigh 25 pounds
each. There are 110 boxes in all. If the truck is carrying a total of 3500 pounds in boxes, how many of each type of box is it carrying?
Number of large boxes:
Number of small boxes:
5

Answers

Answer:

50 large boxes

Step-by-step explanation:

First, "boxes of two sizes" means we can assign variables:

  Let x = number of large boxes

       y = number of small boxes

 "There are 115 boxes in all"    means    x + y = 115      [eq1]

Now, the pounds for each kind of box is:

    (pounds per box)*(number of boxes)

So,

  pounds for large boxes     +    pounds for small boxes      =    4125 pounds

                 "the truck is carrying a total of 4125 pounds in boxes"

        (50)*(x)                   +              (25)*(y)                  = 4125    [eq2]

It is important to find two equations so we can solve for two variables.

Solve for one of the variables in eq1 then replace (substitute) the expression for that variable in eq2.  Let's solve for x:

   x = 115 - y          [from eq1]

    50(115-y) + 25y = 4125             [from eq2]

     5750 - 50y  + 25y = 4125           [distribute]

     5750 - 25y = 4125

      -25y = -1625

         y = 65             [divide both sides by (-25)]

 There are 65 small boxes.

Put that value into either equation (now, which is easier?) to solve for x:

  x = 115 - y

  x = 115 - 65

  x = 50

Prove that if f and g are each uniformly continuous on R, then the composite function
f o g is uniformly continuous on R.

Answers

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 true about the slopes of perpendicular lines?
A The fractions of the slopes are flipped.
B) Both b and c.
C The slopes are the same.
D) One of the slopes is negative and the other is positive.

Answers

The statement that is true abut the slopes of perpendicular lines is that: D. One of the slopes is negative and the other is positive.

What are the Slopes of Perpendicular Lines?

If two lines are perpendicular, it means that their slope (which is the change in y over x or rise/run along the line) will be negative reciprocal to each other.

For example, if the slope of one line is 2, the slope of any line that is perpendicular to the line must be negative reciprocal to 2, which is -1/2.

If we multiply their slopes together, we must have -1. I.e. 2 * -1/2 = -1. Therefore, if one is negative the other would be positive.

The correct answer is: D. One of the slopes is negative and the other is positive.

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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)

Answers

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.

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?

Answers

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

What is the slope of a line that goes through the origin and the point (6, -4)?

Answers

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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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.

Answers

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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