What is the median of the data: 1, 2, 3, 3, 5, 6, 8


What is the mode of the data: 1, 2, 3, 3, 5, 6, 8


What is the range of the data: 1, 2, 3, 3, 5, 6, 8
i need help fast

∫∫∫e f(x, y, z) dV can be expressed as ∫∫∫e f(x, y, z) dz dy dx for the given solid e bounded by y = 4 - \(x^{2}\) \(z^{2}\) and y = 0.

To express the integral as an iterated integral, we consider the order of integration. In this case, we start with the innermost integral, which integrates with respect to z. The limits of integration for z are determined by the bounds of the solid e, which are given by the surfaces y = 0 and y = 4 - \(x^{2}\) \(z^{2}\)

Next, we move to the middle integral, integrating with respect to y. The limits of integration for y are determined by the intersection points of the surfaces y = 0 and y = 4 - \(x^{2}\) \(z^{2}\). In this case, y ranges from 0 to the value of y determined by the equation 4 - \(x^{2}\) \(z^{2}\) = 0.

Finally, we integrate with respect to x, where the limits of integration for x are determined by the bounds of the solid e. These bounds can be determined by finding the values of x that satisfy the equation 4 - \(x^{2}\) \(z^{2}\) = 0.

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The value of c that makes the equation true is c = 64, when x = 6 and y = 3.

To find the value of c that makes the equation true, we can start by simplifying both sides of the equation using exponent rules and canceling out common factors.

First, we can simplify 3√(x^3) to x√x, and 3√y to y√y, giving us:

x√x/cy^4 = x/4y(y√y)

Next, we can simplify x/4y to 1/(4√y), giving us:

x√x/cy^4 = 1/(4√y)(y√y)

We can cancel out the common factor of √y on both sides:

x√x/cy^4 = 1/(4)

Multiplying both sides by 4cy^4 gives us:

4x√x = cy^4

Now we can solve for c by isolating it on one side of the equation:

c = 4x√x/y^4

We can substitute in the values of x and y given in the problem statement (x>0 and y>0) and simplify:

c = 4x√x/y^4 = 4(x^(3/2))/y^4

c = 4(27)/81 = 4/3 = 1.33 for x = 3 and y = 3

c = 4(64)/81 = 256/81 = 3.16 for x = 4 and y = 3

c = 4(125)/81 = 500/81 = 6.17 for x = 5 and y = 3

c = 4(216)/81 = 64 for x = 6 and y = 3

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Answer:

60

Step-by-step explanation:

0.2x = 12

x=60

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Answer:

Explanation:

The number 43 is basically 40+3

We read "43" as "forty three", in which you can think of having 40 and then an additional 3 on top of that to get 40+3 = 43 overall.

As for the decimal portion, we do the same sort of thing.

The 0.205 breaks up into 0.2 + 0.005

0.2 = 2 tenths

0.005 = 5 thousandths

So that's why 43.205 breaks down into 40+3+0.2+0+0.005; each place value digit corresponds to a term in that expanded sum.

Answer:

"HL" in geometry typically refers to "Hypotenuse-Leg". This term is often used when talking about right-angled triangles, where the hypotenuse is the longest side, opposite the right angle, and the legs are the two shorter sides adjacent to the right angle.

Based on the fact that Raven is trying to decide between two plumbing services, the costs of the service charge are:

The Service cost for Service provider A is:

= 50 x  1.5 + (50 x ((1.75 / 1.5) - 1)

= $83.33

Service cost for Service provider B is:

= Number of hours x Cost per hour

= 60 x 1.75

= $105

The cheaper plumber is Service provider A.

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Answer:

A. The side opposite the 60° angle has a length of √3/2

C.Sin(60°)=√3/2

E.The other acute angle of the triangle is 30°

Step-by-step explanation:

The diagram has been attached to the answer

A. The side opposite the 60° angle has a length of

B. The side opposite the 60° angle has a length of .

C. sin(60°) =

D. sin(60°) =

E. The other acute angle of the triangle is 30°.

Answer

The side opposite the 60° angle has a length of the square root of 3/2

Opposite side of the 60° angle has a length of √3/2

sin(60°) = the square root of 3/2

Sin(60°)=√3/2

The other acute angle of the triangle is 30°

Proof:

Total angle in a triangle=180°

180°-60°-90°

=30°

Answer:

A, D, E

Step-by-step explanation:

I do is big smart

Answer:

3x - 2 = 10

3x = 10 + 2

3x = 12

x = 12/3 = 4

3x - 2 = -10

3x = -10+2

3x = -8

x = -8/3

Your answers are x = -8/3 and x = 4

Answer:

¡¡ Only

Step-by-step explanation:

-8-2x < - 4

-2x < - 4+8

-2x < 4

x > - 2

Answer:

A. The line on the left

B.not sure

C. 20 dollars

Step-by-step explanation:

Applying the trapezoid midsegment theorem, the length of the midsegment of a trapezoid whose bases are 27 and x a+ 8 is determined as: (x + 35) / 2.

According to the trapezoid midsegment theorem, the length of the midsegment of a trapezoid is equal to the sum of the two bases divided by two.

The formula for finding the length of the midsegment of a trapezoid is therefore:

Length of midsegment = (sum of the two bases) / 2.

Given the length of the bases of a trapezoid as 27 and x + 8 respectively, therefore, according to the trapezoid midsegment theorem, we have the equation below:

Length of the midsegment = (27 + x + 8) / 2

Simplify by combining like terms:

Length of the midsegment = (x + 35) / 2

Therefore, the answer is, (x + 35) / 2.

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Total number of eggs = 6 + 19 + 14 + 11 + 23 + 2 = 75 eggs

Total hatched eggs = 6 + 14 + 23 = 43

Therefore, the answer is 57 ( to the nearest whole number)

The statement 'if you have 23 people in a room, there is a 50% chance that 2 of them have the same birthday' is True.

The Birthday Paradox states that with 23 people in a room, there is a 50% chance that two of them have the same birthday . This may seem counterintuitive, but the math behind it works as follows:
Calculate the probability that everyone has a different birthday.
Subtract that probability from 1 to get the probability that at least two people share a birthday.
There are 365 possible birthdays for the first person.
For the second person to have a different birthday, there are 364 remaining options.

For the third person, 363 remaining options, and so on.
The probability of everyone having different birthdays is calculated as:
(365/365) × (364/365) × (363/365) × ... × (343/365)
1 - (calculated probability) = probability that at least two people share a birthday
Using this calculation, the probability is approximately 50% that two people have the same birthday with 23 people in the room.

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Answer:

The answer for the unknown would be:

-12

Step-by-step explanation:

This is because ,

5n+26=19

5n+26=19

31n-31n=19-31n

therefore, (unknown) n= -12

The number will be -1.4 such that the sum of 5 times and 26 is 19.

Arithmetic operators are four basic mathematical operations in which summation, subtraction, division, and multiplication involve.,

Summation = addition of two or more numbers or variable

For example = 2 + 8 + 9

Subtraction = Minus of any two or more numbers with each other called subtraction.

For example = 4 - 8

Division = divide any two numbers or variable called division.

For example 4/8

Multiplication = to multiply any two or more numbers or variables called multiplication.

For example 5 × 7.

Let's say that number is x

Then,

5 times = 5x

So,

5x + 26 = 19

5x = -7

x = -7/5 = -1.4

Hence "The number will be -1.4 such that the sum of 5 times and 26 is 19".

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Answer:

Step-by-step explanation:

The answer is D.

The rule for perpendicular lines is that the slope will be the negative reciprocal. Because this equation is in slope-intercept form, the coefficient of x is the slope. -7/5 becomes 5/7. Our new equation is y=5/7x+b. Plugging in (5,3), we see that b is equal to -4/7. Our equation is then y=5/7x-4/7

A pile of 55 keyboard boxes will be approximately 1983.08 cm tall.

To determine the total height of a pile of 55 keyboard boxes, we need to first calculate the height of a single box and then multiply it by 55.

Given that a single box is 3/2 cm thick, we need to know the dimensions of the box to calculate its height. If we assume that the box has a standard width and length of, say, 30 cm and 20 cm respectively, we can calculate its height using the Pythagorean theorem.

The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is the height of the box, and the other two sides are the width and length.

So, we have:

height^2 = width^2 + length^2

height^2 = 30^2 + 20^2

height^2 = 900 + 400

height^2 = 1300

height = sqrt(1300)

height = 36.0555... cm (rounded to 3 decimal places)

Therefore, the height of a single keyboard box is approximately 36.056 cm.

To find the height of a pile of 55 keyboard boxes, we can simply multiply the height of a single box by 55:

height of pile = 36.056 cm x 55

height of pile = 1983.08 cm

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Answer:

x  =  6 ,  − 6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solving for x

1. 2x - 2 ≥ 0 ⇒ 2x ≥ 2 ⇒ x ≥ 1

2. 2x - 2 < 0 ⇒ 2x < 2 ⇒ x < 1

Where the radius of the ballon is given, the time taken to fill the balloon is: is 55.23 minutes or 55 minutes approximately.

The volume of a sphere is given by the formula:

V = (4/3)π³
V = Volume
r = Radius

Since the ballon is leaking at the rate of 26 cubic feet per minute, it means that  the change of volue of the ballon is alow 26 cubic feet per minute.

If we replace the value for r (which is 7) in the above formula, we have:

V = (4/3) x 3.14 x 7³
V = 1436ft³

Thus, the time taken for the ballon to get empty is:

1436.03/26
= 55.23 mi
To the nearest minutes, that would be

55 minutes.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Air is leaking from a spherical-shaped advertising balloon at the rate of 26 cubic feet per minute. If the radius of the ball is 7 feet, to the nearest minute,how long would it take for the balloon to empty fully ? Round your answer to the nearest minute. Use the approximate of value of π, that is 3.14.

The total force exerted by the water on the semicircular plate is zero Newtons.

To find the total force exerted by the water on the semicircular plate, we need to calculate the hydrostatic force acting on each infinitesimally small element of the plate and then integrate these forces over the entire surface.

The hydrostatic force exerted by a fluid on a submerged surface is given by the formula:

F = ∫∫P dA,

where F is the total force, P is the pressure at a given point on the surface, and dA is the differential area element.

In this case, since the water comes up to the top of the plate, the pressure at any point on the plate is equal to the pressure at the water surface. The pressure at a given depth in a fluid is given by the equation:

P = ρgh,

where ρ is the density of the fluid, g is the acceleration due to gravity, and h is the depth below the surface.

In the case of the semicircular plate, the depth h varies depending on the position on the plate. At any point (x, y) on the plate, the depth can be expressed as:

h = R - y,

where R is the radius of the semicircular plate and y is the distance from the top of the plate.

Substituting the expression for h into the pressure equation, we have:

P = ρg(R - y).

Now, we can calculate the force exerted on each infinitesimal element of the plate:

dF = P dA = ρg(R - y) dA.

Since the plate is symmetric about the x-axis, we can integrate the force over the entire plate by integrating with respect to x from -R to R and with respect to y from 0 to R:

F = ∫[-R,R] ∫[0,R] ρg(R - y) dA.

To set up the integral, we need to express dA in terms of x and y. Since the plate is a semicircle, we can use polar coordinates:

x = r cosθ,

y = R - r sinθ,

dA = r dr dθ.

Now, we can rewrite the integral:

F = ∫[0,R] ∫[0,π] ρg(R - (R - r sinθ)) r dr dθ.

Simplifying the expression:

F = ∫[0,R] ∫[0,π] ρg r² sinθ dr dθ.

Evaluating the inner integral:

F = ∫[0,R] [-ρg/3 r³ cosθ]₀ᴿ dθ.

Evaluating the outer integral:

F = [-ρg/3 R³ sinθ]₀ᴾ.

Since the sine of π is zero and the sine of 0 is zero, the total force simplifies to:

F = [-ρg/3 R³ (sin(π) - sin(0))].

F = [-ρg/3 R³ (0 - 0)].

F = 0.

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Answer:

reflex angle EOC = 250°

Step-by-step explanation:

reflex angle EOC

= angle COA + angle DOA + angle DOB + angle BOE

angle DOB = 40° (given)

angle DOB + angle DOA = 180° (linear pair)

angle DOA = 180° - 40°

angle DOA = 140°

angle COA + angle DOA = 180° (linear pair)

angle COA = 180° - 140°

angle COA = 40°

angle COA + angle BOE = 70° (given)

angle BOE = 70° - 40°

angle BOE = 30°

Now,

we have,

reflex angle EOC = 40° + 140° + 40° + 30°

= 250°

Answer: A; Yes

Step-by-step explanation:

Plug in the ordered pair into the equation: 2(-2) + (1) = -3

Solve: -4 + 1 = -3

-3 = 3 ; (-2, 1) is a solution for 2x + y = -3

Now, repeat the same process for the second equation:

(1) = 2(-2) + 5

1 = -4 + 5

1 = 1 ; (-2, 1) is a solution for y = 2x + 5

The variance for the given data set: Year 1 = 16%; Year 2 = 6%; Year 3 = -25%; Year 4 = -3% is 0.0344.

The variance given the following returns:

Year 1 = 16%, Year 2 = 6%, Year 3 = -25%, Year 4 = -3% is 0.0344.

In probability theory, the variance is a statistical parameter that measures how much a collection of values fluctuates around the mean.

Variance, like other statistical measures, is used to describe data.

A variance is a square of the standard deviation, which is a numerical term that determines the amount of dispersion for a collection of values.

Variance provides a numerical estimate of how diverse the values are.

If the data points are tightly clustered, the variance is small.

If the data points are spread out, the variance is large.For a given data set, we may use the following formula to compute variance:

\($$\sigma^2 = \frac{\sum_{i=1}^{N}(x_i-\mu)^2}{N-1}$$\)

Where \($$\sigma^2$$\) is variance, \($$\sum_{i=1}^{N}$$\) is the sum of the data set, \($$x_i$$\) is each data point, \($$\mu$$\) is the sample mean, and \($$N-1$$\) is the sample size minus one.

In the above question, we will calculate the variance for the given data set:

Year 1 = 16%; Year 2 = 6%; Year 3 = -25%; Year 4 = -3%.

\($$\mu=\frac{(16+6+(-25)+(-3))}{4}=-1.5$$\)

Using the formula mentioned above,

\($$\sigma^2 = \frac{\sum_{i=1}^{N}(x_i-\mu)^2}{N-1}$$$$\)

=\(\frac{[(16-(-1.5))^2 + (6-(-1.5))^2 + (-25-(-1.5))^2 + (-3-(-1.5))^2]}{4-1}$$\)

After solving this expression,

\($$\sigma^2=0.0344$$\)

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Answer:

y=30

Step-by-step explanation:

it equals 30 because 2y+y=90. So now you know 3y=90. divide both sides by 3 so you can isolate the y. 90/3=30.

I have 90 because of the right angle. That is a 90-degree angle.

In general, to evaluate the function f(x) at a specific value of x, we substitute that value into the expression for f(x) and simplify.

In mathematics, a function is a relation between two sets, where for every element in the first set (called the domain), there is exactly one element in the second set (called the range) that the function maps to. In simpler terms, a function is a rule that assigns each input value from the domain to exactly one output value in the range. Functions are usually represented by a formula or equation that describes the relationship between the input and output values. For example, the function f(x) = 2x + 1 maps every input value of x to an output value that is twice the input value plus 1.

Here,

To evaluate the function f(x) = 4x - 6, we substitute the given values of the independent variable into the expression for f(x) and simplify.

For example:

f(0) = 4(0) - 6 = -6

f(1) = 4(1) - 6 = -2

f(2) = 4(2) - 6 = 2

f(-1) = 4(-1) - 6 = -10

f(3a) = 4(3a) - 6 = 12a - 6

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Answer:

2

Step-by-step explanation:

all of those equal 31

Answer:

31

Step-by-step explanation:

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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As per the concept of exponents, the quotient of 1.782 x 10⁹ and 8.1 x 10⁶ in scientific notation is 2.2 x 10²

Exponents

Exponents refers the method of expressing large numbers in terms of powers.

Given,

Here we have the expressions 1.782 x 10⁹ and 8.1 x 10⁶ .

Now, we have to find the quotient of this in a scientific notations.

In order to solve this one we have to separate the decimal term and the exponent terms,

As per the law of exponents, the exponent part is gives the quotient,

=> 10⁹/10⁶

=> 10⁹⁻⁶

=> 10³

Now, we have to perform the division on the decimal part, then we get,

=> 1.782/8.1

=> 0.22

In order to convert this into scientific notation, we can rewritten these value as,

=> 2.2 x 10⁻¹ x 10³

=> 2.2 x 10 ⁻¹ ⁺ ³

=> 2.2 x 10²

Therefore, the resulting value is 2.2 x 10².

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Answer:2.2 x 10².

Step-by-step explanation: