If n(U)=16, n(A)=7 and n(B)=12, find greatest n(AUB)

For the given problem, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\)  is  \($\sin^{-1}\frac{x}{a} + C$.\)

A mathematical notion that depicts the area under a curve or the accumulation of a quantity over an interval is known as an integral. Integrals are used in calculus to calculate the total amount of a quantity given its rate of change.

The process of locating an integral is known as integration. Finding an antiderivative (also known as an indefinite integral) of a function, which is a function whose derivative is the original function, is what integration is all about. The antiderivative of a function is not unique since it might differ by an integration constant.

For given problem,

\($\int \frac{1}{\sqrt{a^2-x^2}} dx$\)

Let \($x = a \sin\theta$\) , then \($dx = a \cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2-a^2\sin^2\theta}} a\cos\theta d\theta$\)

\($= \int \frac{1}{\sqrt{a^2\cos^2\theta}} a\cos\theta d\theta$\)

\($= \int d\theta$\)

\($= \theta + C$\)

Substituting back for\($x = a\sin\theta$:\)

\($= \sin^{-1}\frac{x}{a} + C$\)

Therefore, the integral of \(\frac{1}{\sqrt{a^2-x^2}}\) is \($\sin^{-1}\frac{x}{a} + C$.\)

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Answer:

43÷100*2100=903

Step-by-step explanation:

43 devide by 100 because it is a percentage, we always devide percentages by 100. It gives an answer of 0,43.

0,43 multiply by 2100 because we need a cost.

Answer:

The given equation for the path of the football is f(x) = -2(x-3)^2 + 56.

This is a quadratic function in the form f(x) = a(x-h)^2 + k, where a, h, and k are constants.

Comparing this equation to the standard form, we can see that a = -2, h = 3, and k = 56.

Since the coefficient of the squared term is negative, the graph of this quadratic function is a downward-facing parabola.

The maximum height reached by the football occurs at the vertex of the parabola.

The x-coordinate of the vertex is given by x = h = 3.

The y-coordinate of the vertex is given by f(h) = k = 56.

Therefore, the maximum height reached by the football is 56 feet.

Step-by-step explanation:

Answer:

Maximum height = 56 feet

Step-by-step explanation:

The equation is in the vertex form of the quadratic equation, whose general form is:

y = a(x - h)^2 + k, where

Thus, in the equation f(x) = -2(x -3)^2 + 56, (3, 56) is the equation of the vertex (in this case the maximum) and since f(x) represents the height in feet, the max height reached by the football is 56 feet.

Answer:

520

Step-by-step explanation:

4% of 500 is 20

500+20=520

Answer:

Step-by-step explanation:

Given 4% interest on a $500 dollar purchase

So total payment=500x104/100=$520 is the answer

If variation in a process results from common causes alone, the process is said to be in statistical control.

When talking about control charts, being in-control means your process is exhibiting common cause variation and is predictable.

Variation due to the inherent variability in a system of operation is called. special or assignable causes.

Industrial control systems are used by a discipline known as industrial process control in continuous manufacturing processes to produce at a level of consistency, economy, and safety that is impossible to achieve exclusively through manual human control. Process control systems make guarantee that industrial activities are carried out efficiently, dependably, and with as little fluctuation as is practical. They are installed in industrial settings to guarantee throughput, quality, yield, and energy efficiency. Ensure that work is done profitably and safely according to established procedures.

Therefore,

If variation in a process results from common causes alone, the process is said to be in statistical control.

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The expression which describes the given phrase that the product of a number and the difference of the squares of the opposite of seven and four is 33x.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Let's consider that number is x.

Now, the opposite of 7 is -7 and the opposite of 4 is -4.

The difference between square of -7 and -4 is,

(-7)² - (-4)² = 49 - 16 = 33

The product of 33 and x is 33x.

Hence "The expression which describes the given phrase that the product of a number and the difference of the squares of the opposite of seven and four is 33x".

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There are 191 different patterns of mail delivery possible for the 19 houses on the northern side of the street, satisfying the given conditions.

To determine the number of different patterns of mail delivery in this scenario, we can use a combinatorial approach.

Let's consider the possible patterns based on the number of houses in a row that receive mail on the same day: If no houses in a row receive mail on the same day: In this case, all 19 houses would receive mail on different days. We have a single pattern for this scenario.

If one house in a row receives mail on the same day: We have 19 houses, and we can choose one house in a row that receives mail on the same day in 19 different ways. The remaining 18 houses would receive mail on different days. So, we have 19 possible patterns for this scenario.

If two houses in a row receive mail on the same day: We have 19 houses, and we can choose two houses in a row that receive mail on the same day in C(19, 2) = 19! / (2! * (19-2)!) = 171 different ways. The remaining 17 houses would receive mail on different days. So, we have 171 possible patterns for this scenario.

Therefore, the total number of different patterns of mail delivery in this scenario is: 1 (no houses in a row) + 19 (one house in a row) + 171 (two houses in a row) = 191 different patterns.

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Answer:

The original temperature was -18°F

Step-by-step explanation:

x°F + 24°F = 6°F

or, x°F = 6°F - 24°F

so, x°F = -18°F

Answer:

It is C

Step-by-step explanation:

Khan Academy I use it trust me

Answer:

7/20 or 7 out of 20 could be graphic novels

Step-by-step explanation:

The equation that could be used to determine x is (\(x^{2}\) + 8x - 308).

As per the question, the small integer is x. So, the large integer will be (x + 8).

Also, the question mentions that their product is 308. Representing the given information in mathematical equation form -

x (x + 8) = 308

Performing multiplication on Left Hand Side of the equation

x² + 8x = 308

Shifting 308 from Right Hand Side to the Left Hand Side of the equation. the equation that will form is -

x² + 8x – 308 = 0

On solving this quadratic equation, we will get the negative numbers, which will validate our formed equation.  

x² + 8x – 308 = 0

x² + 22x - 14x – 308 = 0

x (x + 22) - 14 (x + 22) = 0

(x + 22) (x - 14) = 0

x = -22 and 14

Since the numbers are negative, hence, value of small number is -22.

Large number = -22 + 8

Large number = -14

Thus, the small and large number is -22 and -14.

Therefore, the correct equation is x² + 8x – 308 = 0.

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The complete question is -

Two negative integers are 8 units apart on the number line and have a product of 308. Which equation could be used to determine x, the smaller negative integer? x² + 8x – 308 = 0 x²  – 8x + 308 = 0 x²  + 8x + 308 = 0 x²  − 8x − 308 = 0

The expected value of the game is then: E(X) = $10(0.4018) + (-$1)(0.5982) = -$0.1816

Let X be the random variable representing the winnings in the game. Then X can take on two possible values: $10 or $-1. Let p be the probability of winning $10, and q be the probability of losing $1.

To find p, we need to calculate the probability of getting at least one five in a 5-card hand. The probability of not getting a five on a single draw is 47/52, so the probability of not getting a five in the 5-card hand is \((47/52)^5\). Therefore, the probability of getting at least one five is 1 - \((47/52)^5\) ≈ 0.4018. So, p = 0.4018 and q = 1 - 0.4018 = 0.5982.

The expected value of the game is then:

E(X) = $10(0.4018) + (-$1)(0.5982) = -$0.1816

This means that, on average, you can expect to lose about 18 cents per game if you play many times.

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Answer:

FV= $123,879.85

Step-by-step explanation:

Giving the following information:

Montlhy deposit (A)= $100

Monthly interest rate (i)= 0.09/12= 0.0075

Number of periods (n)= 12*26= 312 months

To calculate the future value, we need to use the following formula:

FV= {A*[(1+i)^n-1]}/i

A= monthly deposit

FV= {100*[(1.0075^312) - 1]} / 0.0075

FV= $123,879.85

False , the variance and standard deviation are not measures of central location

Given data ,

The variance and standard deviation are not measures of central location but measures of dispersion or spread of a dataset

Measures of central location include the mean, median, and mode, which represent the typical or central value of a dataset

The variance and standard deviation are measures of dispersion or spread in a dataset. They provide information about how the values in a dataset are spread out around the mean.

In order to understand the variability or dispersion of data points within a dataset, one must take into account both the variance and standard deviation. They provide information on the range of values and aid in calculating how far away from the mean certain data points are. In statistics and data analysis, these metrics are frequently used to comprehend and evaluate the variance of various datasets.

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The center height of the semi-elliptical arch of a bridge with a span of 120 feet and a height of 10 feet at a distance of 10 feet from the center is estimated to be around 10.534 feet.

Let's denote the height of the arch at the center as h. We can use the equation of a semi-elliptical arch to solve for h.

The equation of a semi-elliptical arch is given by:

y = a√(1 - x²/b²)

where:

We are given that the span of the arch is 120 feet, so b = 60. We are also given that the height of the arch at a distance of 10 feet from the center is 10 feet, so we can plug in x = 10 and y = 10 to get:

10 = a√(1 - 10²/60²)

Simplifying, we get:

Therefore, the height of the arch at its center is approximately 10.534 feet.

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Answer:

the second one

Step-by-step explanation:

Answer:

The one you clicked is correct

Step-by-step explanation:

The equation is the same as \(-5\frac{4}{5} +2\frac{2}{3}\)

If you flip the 2 terms, you get: \(2\frac{2}{3}-5\frac{4}{5}\)

Then, \(-5\frac{4}{5}\)  multiplied by +1 is \(2\frac{2}{3}+(-5\frac{4}{5})\)

According to the question The equilibrium constant \((K_{eq})\) relates the concentrations of reactants and products \(K_{eq} \ for\ 2AB \rightleftharpoons 2A + 2B \ is\ 49.\)This indicates that the equilibrium position favors formation of products.

The equilibrium constant \((K_{eq})\) relates the concentrations of reactants and products in a chemical reaction at equilibrium. In the given reaction,

\(A + B \rightleftharpoons AB, the\ K_{eq}\ is\ 7\).

When considering the reaction \(2AB \rightleftharpoons 2A + 2B\), the stoichiometric coefficients are doubled on both sides. According to the principles of equilibrium, the equilibrium constant for the modified reaction can be obtained by squaring the original \(K_{eq}\).

Therefore, the \(K_{eq}\) for \(2AB \rightleftharpoons 2A + 2B is (K_{eq})^2 = (7)^2 = 49\). This indicates that the equilibrium position favors the formation of products in the double reaction compared to the original reaction.

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Answer:

0.14

Step-by-step explanation:

1/7 = 0.142

Since 2<5 the answer is 0.14.

Answer:

angle one

Step-by-step explanation:

Answer:

Step-by-step explanation:

You want a formula for the volume of the given figure, which is a hemisphere of radius r atop a cylinder of the same radius and height r.

The volume of a sphere is given by ...

  V = (4/3)πr³

The volume of a cylinder is given by ...

  V =  πr²h

The given figure is composed of half a sphere, and a cylinder. The total volume will be the sum of the volumes of these parts.

  total volume = 1/2(sphere volume) + (cylinder volume)

Using a height of r for the cylinder, we can substitute the above formulas to get ...

  total volume = 1/2(4/3πr³) +(πr²·r)

  total volume = 2/3πr³ + πr³ = (2/3 +1)πr³

  total volume = (5/3)πr³

When the height is 12 inches, the radius is 6 inches, so the volume of the object is ...

  total volume ≈ (5/3)(3.14)(6 in)³ = 1130.4 in³

About 1130.4 cubic inches of glass will be needed for a paperweight that is 12 inches tall.

The correct option for the midpoint of the line segment , where (-1,-2) and (4,-2), is  (1.5,-2).

To find the midpoint of a line segment, we use the midpoint formula, which states that the coordinates of the midpoint (M) are the average of the coordinates of the endpoints.

The midpoint formula is given by:

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Let's apply this formula to find the midpoint of the line segment AB:

x1 = -1, y1 = -2 (coordinates of point A)

x2 = 4, y2 = -2 (coordinates of point B)

Using the midpoint formula:

M = ((-1 + 4) / 2, (-2 + (-2)) / 2)

 = (3 / 2, -4 / 2)

 = (1.5, -2)

Therefore, the midpoint of the line segment , with endpoints (-1,-2) and (4,-2), is (1.5, -2).

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The parameters to the Poisson distribution, to find the probability of exactly 3 arrivals in one thousandth of a​ minute, are given as follows:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following mass probability function:

\(P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}\)

The parameters are listed and explained as follows:

A company has 6000 arrivals of Internet traffic over a period of 13,710 thousandths of a minute, hence the mean of the distribution is given as follows:

μ = 6000/13719.

The parameter x represents the number of arrivals in each thousandth of a minute, hence it is given as follows:

x = 3.

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Step-by-step explanation:

uploading the picture is an excellent way to make sure we get the original problem definition.

but I just answered this (even without the picture). so, you need it again ?

Answer:

y-intercept: 20

x-intercept: 5

Step-by-step explanation:

First, you want to rearrange the equation to make y on one side

2y=20-4x

Next, the y-intercept is 20.

Then to find the x-intercept, you have to make the equation equal to 0.

20-4x=0

Now, you solve for x.

20-4x=0

-4x=-20

-x=5

x=5

The x-intercept is 5.

A rational number is a number that can be written in the form of p/q where q is not equal to zero.

The rational numbers are -100, -14.5, -2, -2/3, 0,10, 15, 20 1/6.are rational.

A rational number is a number that can be written in the form of p/q where q is not equal to zero.

We have,

-100, -14.5, -2, -2/3, 0, 19, 15, 20, 1/6

-100 = -100/1

It is in the form of p/q.

It is a rational number.

-14.5 = -145/10

It is in the form of p/q.

It is a rational number.

-2 = -2/1

It is in the form of p/q.

It is a rational number.

-2/3 = -2/3

It is in the form of p/q.

It is a rational number.

0 = 0/1

It is in the form of p/q.

It is a rational number.

19 = 19/1

It is in the form of p/q.

It is a rational number.

15 = 15/1

It is in the form of p/q.

It is a rational number.

20 = 20/1

It is in the form of p/q.

It is a rational number.

1/6

It is in the form of p/q.

It is a rational number.

We see that all the numbers given are rational numbers.

Thus,

The rational numbers are -100, -14.5, -2, -2/3, 0, 10, 15, 20 1/6.

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Answer:

We can convert the dimensions of the cubic block from meters to decimeters, since there are 10 decimeters in a meter.

0.255 meters = 2.55 decimeters

The volume of a cube is given by the formula:

Volume = (side length)^3

Plugging in the given value of 2.55 decimeters, we get:

Volume = (2.55 dm)^3

Volume = 16.419375 dm^3

Therefore, the volume of the cubic block in cubic decimeters is approximately 16.42 dm^3.

The volume of this block in cubic decimeters is 0.255 meters on a side is 0.000251485 dm³

The volume of the cubic block of concrete can be found by calculating the volume of a cube. The formula for the volume of a cube is V = s^3, where s is the length of the side of the cube.

The side of the cube is 0.255 meters, so the volume is calculated by cubing 0.255.

The volume of the block is 0.0251485m^3.

1m^3 = 1000dm^3.
So, the volume of the block in cubic decimeters is 0.000251485dm^3.

To summarize, the volume of a cubic block of concrete that is 0.255 meters on a side is 0.000251485 dm³.

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Answer:

45

Step-by-step explanation:

rate : 9 minutes per mile

5 x 9 = 45

Answer:

45 minutes

Step-by-step explanation:

18= 2miles

18/2= 9 minutes  (1 mile)

18+18+9= 45