What is the solution of |x – 6| ≥ 1? 5 < x < 7 x ≤ –7 or x ≥ –5 x ≤ 5 or x ≥ 7 –7 < x < –5

The surface area of the given objects is  1809.56 units².

The Surface Area of a Sphere is :

A = 4πr^2

where r = radius.

the surface area is:  Area = 4π(12)²

The surface Area of a Cylinder:

The surface area of a cylinder is made up of addition of the areas of its two bases :

area of a circle : A = πr²

The curved surface area is then A = 2πrh

The surface area of the two bases of the circles is:

= 2π(5)²

The curved surface area is:

= 2π(5)(12)

Total Surface Area = Area of sphere + Area of bases + Area of curved

Total Surface Area = 4π(12)² + 2π(5)² + 2π(5)(12)

Total Surface Area = 1809.56 units²

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#complete question:

calculate the surface area of a sphere with a radius of 12 units and a cylinder with a radius of 5 units,

There are 17 times that the divisor 36 divides into 614.

A number that divides into another number is termed as divisor. The entire process is called division. The number that is divided by divisor is called dividend.

The quantity that is "left over" after conducting a calculation is referred to as the remnant in mathematics. The integer that remains after multiplying one integer by another to create an integer quotient is known as the remnant in mathematics.The amount that remains after a division is called a remnant. It hasn't been cut in half. Divide a residue by the number it is being divided by to represent it as a fraction. The number being divided by becomes the denominator at the bottom of the fraction, and the remainder becomes the numerator at the top of the fraction.

In this question, 36 is divisor and 614 is dividend

614÷36 =17.06

= 17

hence, the result is 17

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To determine whether the linear transformation T is one-to-one, onto, or neither, we need to analyze the rank and nullity of the transformation.

The rank of T is the dimension of the image space, which is the span of the columns of the transformation matrix. To find the matrix, we can write T(X, Y, Z, W) = (V, W, X, Z) as a matrix equation:

|V|   |0 0 1 0||X|
|W| = |0 1 0 0||Y|
|X|   |1 0 0 0||Z|
|Z|   |0 0 0 1||W|

From this matrix, we can see that the columns are linearly independent, so the rank of T is 4.

The nullity of T is the dimension of the kernel, which is the set of all solutions to the equation T(X, Y, Z, W) = (0, 0, 0, 0). We can set up the augmented matrix for this equation:

|0 0 1 0 0|
|0 1 0 0 0|
|1 0 0 0 0|
|0 0 0 1 0|

Row-reducing this matrix gives:

|1 0 0 0 0|
|0 1 0 0 0|
|0 0 1 0 0|
|0 0 0 1 0|

The only solution is the trivial one, so the nullity of T is 0.

Since the rank of T is equal to the dimension of the domain and the codomain, T is onto. And since the nullity of T is 0, T is also one-to-one. Therefore, the correct answer is "one-to-one and onto".
Hi! To determine whether the linear transformation T: R4 → R4, T(X, Y, Z, W) = (V, W, X, Z) is one-to-one, onto, or neither, let's analyze the properties of this transformation.

1. One-to-one: A linear transformation is one-to-one if different input vectors produce different output vectors.

In this case, T(X, Y, Z, W) = (V, W, X, Z). Observe that every input vector (X, Y, Z, W) uniquely determines the output vector (V, W, X, Z). Thus, this transformation is one-to-one.

2. Onto: A linear transformation is onto if every output vector can be produced by some input vector.

For this transformation, T(X, Y, Z, W) = (V, W, X, Z), every output vector (V, W, X, Z) can be produced by the input vector (X, Y, Z, W). So, the transformation is onto as well.

In conclusion, the linear transformation T: R4 → R4, T(X, Y, Z, W) = (V, W, X, Z) is both one-to-one and onto.

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Answer:

Step-by-step explanation:

¿A qué se llamó feudalismo? ¿Dónde y cuándo se desarrolló?

Answer:C the students were amounting to almost nothing in theater a

Step-by-step explanation:

Answer: -2

Step-by-step explanation: ... well 2 is actually not a whole number so you would consider it an integer if the value of it's integer is less than 0, A simpler way of explaining it is to say that integers include all of the positive and negative versions of whole numbers. 2 is a whole number and an integer. -2 is an integer, but not a whole number, because it is a negative value (less than zero).

If we have a large enough number of samples, the sample mean can provide a reliable estimate of the population mean.

As the number of samples increases, the sample mean can be used to approximate a population mean.

The sample mean is the average value calculated from a subset of the population, which represents the overall population mean when the sample is random and representative.

By taking multiple samples and calculating their means, we can estimate the population mean more accurately.

This is because as the number of samples increases, the sample mean values tend to converge towards the population mean.

This concept is known as the Central Limit Theorem.

Therefore, if we have a large enough number of samples, the sample mean can provide a reliable estimate of the population mean.

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By providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship, we have

(i) \(3^{n/2}\) = O(2^n)

(ii) \(8^{\log n}\) = θ(\(n^2(\log n)^4\) ≤ 3n^3)

(iii) √n + (log n)^5 = O(\((2)^{1/2\times\log n}\))

We have to compare the following function pairs by providing the c and k values in the formal definition when asserting a big O, Ω or θ relationship

i) The first function is \(3^{n/2}\) vs. 2^n

We can write  \(3^{n/2}\) as

\(3^{n/2}\) = \((\sqrt{3})^n\)

\(3^{n/2}\) = (1.732)^n

Clearly, we get for c = 1 and n ≥ 0, then

0 ≤ 1.732n ≤ 2n

Hence, \(3^{n/2}\) = O(2^n)

ii) The second function is \(8^{\log n}\) vs. n^2(log n)^4 + 2n^3

We can write it as

\(8^{\log n}\) = \(n^{\log 8}\)

\(8^{\log n}\) = \(n^{\log 2^3}\)

\(8^{\log n}\) = n^3

For n ≥ 0, c(1) = 1 and c(2) = 3, we have

0 ≤ n^3 ≤ \(n^2(\log n)^4\) ≤ 3n^3

Hence, \(8^{\log n}\) = θ(\(n^2(\log n)^4\) ≤ 3n^3)

iii) The third function is  \((\sqrt{2})^{\log n}\) vs. √n + (log n)^5

We can write \((\sqrt{2})^{\log n}\) as

\((\sqrt{2})^{\log n}\) =  \((2)^{1/2\times\log n}\)

For c = 2 and n ≥ 2, we have

0 ≤ √n + (log n)^5 ≤ \((2)^{1/2\times\log n}\)

Hence, √n + (log n)^5 = O(\((2)^{1/2\times\log n}\))

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The complete question is:

Show your complete work when comparing the following function pairs. provide the c and k values in the formal definition when asserting a big O, Ω or θ relationship(e.g. f(n) is O(g(n)) if there exists C>0 and k≥0 such that f(n)≤Cg(n) for all n≥k).

(i) \(3^{n/2}\) vs. 2^n

(ii) \(8^{\log n}\) vs. n^2(log n)^4 + 2n^3

(iii) \((\sqrt{2})^{\log n}\) vs. √n + (log n)^5

Answer:

18 pounds

Step-by-step explanation:

5 x 3 3/5 =18

Answer:

18(D)

Step-by-step explanation:

Based on your question, it sounds like you are asking about random variables that have a joint probability density function (PDF) of 1/50 over a certain range of values.

In probability theory, a random variable is a variable whose value is determined by chance. It can take on a range of possible values, and the probabilities of each possible value occurring can be described using a probability distribution.

A joint probability density function is a function that describes the probabilities of two or more random variables taking on specific values simultaneously. In your case, you have two random variables that have a joint PDF of 1/50.

Without knowing the specific range of values over which the PDF is defined, it's hard to provide a more detailed answer. However, here are a few general observations about random variables and joint PDFs:

- Random variables can be either discrete or continuous. Discrete random variables take on specific, countable values (e.g. the number of heads in a series of coin tosses), while continuous random variables can take on any value within a certain range (e.g. the height of a randomly selected person).
- A joint PDF is typically used to describe the behavior of two or more continuous random variables. It gives the probability density at each point in the two-dimensional space defined by the values of the two variables.
- The total probability over the entire range of values for a joint PDF must sum to 1. This ensures that the probability of all possible outcomes occurring is equal to 1.

I hope this helps! If you have any further questions or clarifications, please let me know.
It seems that you are asking about random variables with a joint probability density function (pdf) of 1/50. Random variables are quantities that can take on different values according to some probability distribution. When two or more random variables are considered together, their relationship can be described using a joint pdf. In this case, the joint pdf is 1/50, indicating that the probability of a specific combination of these random variables is 1/50.

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Given data:

The given function.

A function is a relation in which every value of x has a unique value of y.

Thus, to make the given set a function the correct order pair is (6, 3).

a) The null hypothesis (H0): The population mean completion time under new management is equal to or greater than 14.4 minutes. The alternative hypothesis (Ha): The population mean completion time under new management is less than 14.4 minutes. b) The type of test statistic to use is a one-sample z-test, since the sample size is small and the population standard deviation is known. c) The calculated test statistic is approximately -1.632. d) The p-value is slightly greater than 0.05. e) Based on the p-value being greater than the significance level (0.05), we fail to reject the null hypothesis.

a) The null hypothesis (H0): The population mean completion time under new management is equal to or greater than 14.4 minutes.

The alternative hypothesis (Ha): The population mean completion time under new management is less than 14.4 minutes.

b) Since the sample size is small (n = 12) and the population standard deviation is known, we will use a one-sample z-test.

c) The test statistic for a one-sample z-test is calculated using the formula:

z = (\(\bar x\) - μ) / (σ / √n), where \(\bar x\) is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Plugging in the values from the problem:

z = (13.8 - 14.4) / (1.8 / √12) ≈ -1.632

d) To find the p-value, we will compare the test statistic to the critical value from the standard normal distribution. At a significance level of 0.05 (α = 0.05), for a one-tailed test, the critical value is -1.645 (approximate).

The p-value is the probability of obtaining a test statistic more extreme than the observed test statistic (-1.632) under the null hypothesis. Since the test statistic is slightly larger than the critical value but still within the critical region, the p-value will be slightly greater than 0.05.

e) Since the p-value (probability) is greater than the significance level (0.05), we fail to reject the null hypothesis. This means that we do not have enough evidence to support the claim that the population mean completion time under new management is less than 14.4 minutes at the 0.05 level of significance.

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The new exchange rate is 12.5 SEK: $1.

The Swedish krona trades at 10 SEK: $1. If the kroner weakens by 20% vs. the USD, the new exchange rate will be 12.5 SEK : $1.

Since we are looking for the exchange rate between Swedish krona and the dollar, let us find how many dollars we can buy with one Swedish krona initially.

10 SEK: $1 is the exchange rate. One can buy 1 dollar for every 10 SEK.

20% weakening of SEK would imply that one needs to spend more SEK to purchase the same amount of USD.

Since we have 20% depreciation, 1 dollar should now cost more than 10 SEK.

20% of 10 is 2, which means 2 SEK is now lost.

10 SEK - 2 SEK = 8 SEK

Now, 1 dollar is worth 8 SEK. Now we will reverse the ratio for the new exchange rate: 1/8 = 0.125, which means that 1 USD is worth 0.125 SEK.

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Answer:

Irrational

Step-by-step explanation:

The constant \(\pi\), or "pi", is an irrational mathematic constant that corresponds to a non-terminating (never-ending decimal). Because there are an infinite number of digits in pi, pi cannot be expressed as a fraction and therefore is irrational.

Multiplying or adding a rational number does not make pi rational, and therefore the desired answer is (D) Irrational.

The area of the polygon is 80 units².

What is a Polygon?

A polygon is a plane figure made up of line segments connected to form a closed polygonal chain. The segments of a closed polygonal chain are called its edges or sides.

Dividing the polygon into parts marked in the attached figure so as to calculate the area easily.

For triangle, DEF

Area = \(\frac{1}{2} bh\)

        = \(\frac{1}{2}\) × 3 × 4

       = 6 units²

For triangle BCD

Area = \(\frac{1}{2}bh\)

        = \(\frac{1}{2}\) × 2 × 4

        = 4 units²

For trapezoid ABFG,

Area = \(\frac{1}{2} (a + b) h\)

        = \(\frac{1}{2}\) × (5.5 + 12) × 8

        = 70 units²

Hence, total area = 6 + 4 + 70

                             = 80 units².

Therefore, the total area of the polygon is 80 units².

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Option B is correct. 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet. This can be obtained by using the formula of density.

Given that there are 22 goldfishes,

mass of tank = 22 goldfishes

volume of tank = 56 cubic feet

                      = 22/56

                      = 0.39 goldfish per cubic feet

Hence 0.39 goldfish per cubic feet is the density of the tank given that there are 22 goldfishes and volume of the tank is 56 cubic feet.

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Answer: 0.39 goldfish

Step-by-step explanation:

Answer:

YES!

Step-by-step explanation:

UwU

Answer:

30 pages

Step-by-step explanation:

Because if he reads 10 pages in 1/3 of a hour 1/3 of an hour is 20 mins so x2 means 30 pages

Step-by-step explanation:

cars : trucks = 3 : 5

there are 3 + 5 = 8 parts of the whole that is shared between cars and trucks.

these 8 parts (or the whole) are in total 360.

therefore, 1 part = 360/8 = 45

cars get 3 parts of the whole parking lot, that is

45 × 3 = 135 cars

trucks get 5 parts of the whole parking lot, that is

45 × 5 = 225 trucks

The mean life of a 14C atom is approximately 8,267 years.

For a radioactive substance, the mean life M is defined as the average amount of time it takes for half of the atoms in a sample to decay.

In this case, we have the equation for the mass of a radioactive substance

m(t) = m(0) \(e^{kt}\)

where m(0) is the initial mass, k is a negative constant, and t is time.

To find the mean life of a 14C atom, we need to find the value of M when k = -0.000121.

First, we need to solve for t when the mass of a sample of 14C is half of its initial mass:

0.5m(0) = m(0) \(e^{-0.000121t}\)

Dividing both sides by m(0), we get

0.5 =  \(e^{-0.000121t}\)

Taking the natural logarithm of both sides:

ln(0.5) = -0.000121t

Solving for t

t = ln(0.5) / (-0.000121)

t ≈ 5,732 years

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Note that the expression that is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0 is:  42x²∛3x (Option B). Even if x = 0, then none of the answers would apply because the expression would automatically = 0.

To prove the above lets us factor and rewrite the radicand in exponential form as follows:

8x² ∛(5³ * 3x) + 2∛(3x⁶ * x)

Rework the expression using

ⁿ√ab = ⁿ√a * ⁿ√b:8x² * ∛5³ * ∛3x + 2∛x⁶ * ∛3x

Simplify the expression 8x² * 5∛3x + 2x² ∛3x

Multiply the monomials to get:
40x² ∛3x+2x²∛3x; Taking the coefficients for the like terms we have:

(40 + 2)x² ∛3x

Calculate the sum to get 42x²∛3x

Thus the simplified version of  8x² ∛375x + 2∛3x⁷, if x ≠ 0 is: 42x²∛3x

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Full Question:

Select the correct answer. Which expression is equivalent to 8x² ∛375x + 2∛3x⁷, if x ≠ 0

A) 42x³

B) 42x²∛3x

C) 10x⁴∛125x

D) 10x²∛125x³

Answer:

17.4

Step-by-step explanation:

The Hundredths place is above four so it has to be the next number up

Answer:17.40

Step-by-step explanation:

17.37 rounded to the nearest tenth is, 17.40, because when rounding, you see if the number is 5 or up ( that means you round it up.)

The denim fabric costs $4 per meter and the cotton fabric costs $3 per meter.

To find out the cost per meter of each type of fabric, we can set up a system of two equations. Let d be the cost per meter of denim fabric and c be the cost per meter of cotton fabric. Then, we have:

3d + 5c = 22 (equation 1)

6d + 2c = 28 (equation 2)

We can use equation 2 to solve for one of the variables in terms of the other. Solving for c, we get:

c = 14 - 3d (equation 3)

We can substitute equation 3 into equation 1 and solve for d:

3d + 5(14 - 3d) = 22

Simplifying this equation, we get:

4d = 3

Therefore, d = 0.75, which means the denim fabric costs $0.75 per meter.

We can then use equation 3 to find the cost per meter of cotton fabric:

c = 14 - 3(0.75) = 11.25/2 = $5.625

Therefore, the cotton fabric costs $5.625 per meter.

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Answer:

10%×110

10/100×110

11

Answer:

Click at the above pic and the ans will appear.

Hope it helps :)

Option D. The faculty should use the median to make their argument. The median will be lower than the mean since the mean is influenced by the few extremely high salaries.

Mean is the average of any data set whereas the median is the middle value we get after arranging the data in ascending order.

So for example, if the salaries of any 5 faculty members are as follows:

$10,000 , $50,000 , $80,000 , $150,000 , $160,000

Mean= (10,000+50,000+80,000+150,000+160,000) / 5

Mean= $90,000

Median= (5+1) / 2

Median= 6/2

Median= 3rd value

As the data is already arranged in ascending order, Median is $80,000

Hence, if the faculty want to give the community the impression that they deserve higher salaries, they should advertise the median of their current salaries.

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Answer:

h(x) is the image after f(x) is horizontally stretched by a scale factor of 4

Step-by-step explanation:

Given

\(h(x) = \frac{1}{4}x^2\)

\(f(x) = x^2\)

Required

Compare h(x) to f(x)

We have:

\(h(x) = \frac{1}{4}x^2\)

Substitute \(f(x) = x^2\)

\(h(x) = \frac{1}{4}f(x)\)

This means that f(x) is stretched horizontally by a scale factor of 4 to get h(x)

The three objects that make up the Alpha centauri system, given their description, are all D. stars.

Alpha Centauri is a star system that consists of three stars, not planets, asteroids, or comets. The three stars are named Alpha Centauri A, Alpha Centauri B, and Proxima Centauri.

Alpha Centauri A and B are similar to the Sun, while Proxima Centauri is a smaller and cooler red dwarf star. The three stars in the Alpha Centauri system produce light and rotate on their own axis, and the system is located an average of 4 light-years from Earth.

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18. An infant weighs 11 pounds which is equivalent to 4.98 kg. Using the 100/50/20 Rule, the required amount of fluid per day for an infant between 11-20 kg is 50 ml/kg/day. So, the required amount of fluid per day in ml is 4.98 kg x 50 ml/kg/day = 249 ml/day.

19. A child weighs 31lbs and 8 ozs which is equivalent to 14.21 kg. Using the 100/50/24 Rule, the required amount of fluid per day for a child over 20 kg is 20 ml/kg/day. So, the required amount of fluid per day in ml is 14.21 kg x 20 ml/kg/day = 284.2 ml/day.

If no oral fluids are consumed, the hourly IV flow rate to maintain proper hydration would be: 284.2 ml/day / 24 hours/day = 11.8 ml/hour.

The question is about fluid requirements for infants and children, and it is using the 100/50/20 Rule for Daily Fluid Requirements (DFR) to calculate the required amount of fluid per day for different weight ranges. The 100/50/20 Rule is a guideline used to determine the appropriate amount of fluid that infants and children should receive on a daily basis based on their weight. The rule states that for infants and children up to 10 kg, the recommended fluid intake is 100 ml/kg/day, for those between 11-20 kg it is 50 ml/kg/day, and for those over 20 kg it is 20 ml/kg/day.

The question also asking about the hourly IV flow rate to maintain proper hydration if no oral fluids are consumed.

This subject is part of pediatrics, more specifically in the field of fluid and electrolyte balance and management.

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Answer:

-1, 2, 4

Step-by-step explanation:

f(x) is the function's value at any given x.  In other words, it's your function's y coordinate.  You're looking for where the y coordinate is zero - so, in other words, the x intercepts.  Luckily for you, all the x-intercepts here are clearly marked and they were kind enough to give you the coordinates.