Write a matrix equation with solution

[12 7 -3 8 9 0 -11 1]

The decimal value of the 2 in the hexadecimal number F42AC16 is 131,072.

To determine the decimal value of the 2 in the hexadecimal number F42AC16, we need to understand the positional value system of hexadecimal numbers. In hexadecimal, each digit represents a power of 16. The rightmost digit has a positional value of 16^0, the next digit to the left has a positional value of 16^1, the next digit has a positional value of 16^2, and so on.

In the given hexadecimal number F42AC16, the 2 is the fifth digit from the right. Its positional value is 16^4. Calculating the decimal value: 2 * 16^4 = 2 * 65536 = 131,072. Therefore, the decimal value of the 2 in the hexadecimal number F42AC16 is 131,072.  None of the provided options (a) 409610, b) 51210, c) 25610, d) 210) matches the correct decimal value of 131,072.

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To meet your requirements for a 7-day supply, you should combine 11 servings of Designer Whey and 2 servings of Muscle Milk.

Let x be the number of Designer Whey servings and y be the number of Muscle Milk servings.
Use the protein requirements to set up an equation:
18x + 32y = 262 (Designer Whey has 18g of protein per serving, and Muscle Milk has 32g per serving)
Use the carbohydrate requirements to set up a second equation:
2x + 16y = 54 (Designer Whey has 2g of carbohydrates per serving, and Muscle Milk has 16g per serving)
Now you have a system of two linear equations:
18x + 32y = 262
2x + 16y = 54
To solve this system, first simplify the second equation by dividing by 2:
x + 8y = 27
Rearrange the simplified equation to isolate x:
x = 27 - 8y
Substitute the expression for x from step 4 into the first equation:
18(27 - 8y) + 32y = 262
Distribute the 18 and simplify the equation:
486 - 144y + 32y = 262
Combine like terms and solve for y:
-112y = -224
y = 2
Substitute the value of y back into the expression for x from step 4:
x = 27 - 8(2)
x = 27 - 16
x = 11

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The probability of having one white ball is 1/20 or approximately 0.05.

To find the probability of selecting one white ball out of three balls, you need to know the number of white balls in the box and the total number of balls in the box. You also need to know whether the balls are being selected randomly or not.

Assuming that there is only one white ball in the box and the rest are some other color, and that the balls are being selected randomly.

The probability of selecting one white ball out of three would be:

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Since there is only one white ball, there is only one way to select one white ball out of three. The total number of ways to select three balls out of six is 6 choose 3, which is equal to 20.

Therefore, the probability of selecting one white ball out of three would be

Probability = (number of ways to select one white ball out of three) / (total number of ways to select three balls)

Probability = 1/20

Probability = approximately 0.05.

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Yes.

It is true that if v1, v2, ..., vp are vectors in Rⁿ, then Span{v1, v2, ..., vp} is the same as the column space of the matrix [v1 v2 ... vp].

True, let A = [v1 v2 ... vp] be the matrix columns are the given vectors.

The column space of A is the set of all linear combinations of the columns of A, which is exactly the same as the span of the vectors v1, v2, ..., vp.

In other words, any vector that can be written as a linear combination of the columns of A is also in Span{v1, v2, ..., vp}, and vice versa.

The tools of linear algebra to study the span of a set of vectors, by considering the column space of the corresponding matrix.

Techniques like row reduction and rank to determine if a set of vectors is linearly independent or spans the whole space Rⁿ.

Yes, the given vectors should be used as the matrix columns in A = [v1 v2... vp].

The span of the vectors v1, v2,..., vp is exactly the same as the column space of A, which is the set of all linear combinations of the columns of A.

This means that any vector that can be expressed as a linear combination of columns from A is also a vector in Spanv1, v2,..., vp and vice versa.

By taking into account the column space of the associated matrix, the techniques of linear algebra may be used to examine the range of a collection of vectors.

To establish if a group of vectors spans the whole space Rn or is linearly independent, use methods like rank and row reduction.

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Answer:

theb correct answer is d VHow does your body’s flexibility naturally change as you age?

Step-by-step explanation:

Answer:  2 vertices

The two vertices in question are (2,0) and (5,0). These are points A and D. These two points are on the x axis, which is the line of reflection. Any point on a line of reflection does not move.

The points (0,-3) and (3,-3) are not on the line of reflection, so they do move and are reflected to another location. Refer to the diagram below.

Concept: "Logos" has had a significant impact on Western thought. Importance: its recognition of the interplay between rational thought and empirical observation Acknowledgement: role of language and discourse in shaping our understanding of the world.

Topic: The concept of "Logos" in Greek philosophy and its significance in modern scientific fields.

The concept of "Logos" is central to Greek philosophy and has been interpreted in various ways throughout history. In its most basic sense, "Logos" refers to rational thought, speech, and language. It is often associated with the divine or the cosmic principle that governs the universe, as well as human reasoning and discourse.

The significance of "Logos" can be seen in its influence on modern scientific fields, including biology, psychology, and technology, among others. The term "biology," for example, comes from the Greek words "bios" (life) and "logos" (word or reason), reflecting the idea that the study of life requires both empirical observation and rational analysis.

Similarly, the field of psychology, which deals with the workings of the human mind and behavior, derives its name from the Greek word "psyche," meaning "soul," and "logos," meaning "reason." This reflects the idea that the study of the mind and behavior requires both empirical research and theoretical analysis.

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Translation: The Greek word "logos" is typically interpreted as the pinnacle of Western rationalist civilization, having been established by the first schools of classical philosophy. In reality, he is responsible for the names of many scientific fields, including biology, philology, psychology, technology, and others. Since it requires both mind and action, internal and external, the mental notion and pronouncing the word, the concept of "logos" does not have such an abstract meaning. Topic:____________________________________________________ Principal Concept:

Answer:

Because they are both using (g units rates).

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

first do distributive property

4*5 = 20

4*-2x = -8x

combine like terms

20+3 = 23

now we have: 23-8x = 7

solve for x

8-x = 7-23 = -16

divide by -8

x = -16/-8 = 2

x = 2

Answer:

2

Step-by-step explanation:

20-8x+3=7

-8x+3+20=7

-8x+23=7

-8x=7-23

-8x=-16

x=-16/-8

×=16/8

×= 2/1

x=2

Answer:

$9,481.01

Step-by-step explanation:

The formula for compound amounts is

A = P(1 + r/n)^(nt), where n is the number of compounding periods per year, t is the number of years, P is the initial amount invested and r is the annual interest rate as a decimal fraction.

Here,

A = ($7,200)(1 + 0.023/4)^(12*4)

Evaluating this we get:

A = ($7,200)(1.00575)^48, or

A  = ($7,200)(`1.3168) = $9,481.01

Answer:

9,481.01

Step-by-step explanation:

Answer: 12

Work is provided in the image I attached

The mean proportion of samples made with chocolate liquor would be 0.20, which is the same as the population proportion.

The problem states that 20% of all candies produced by the factory are made with chocolate liquor. This means that the population proportion of candies made with chocolate liquor is 0.20.

If we take a random sample of 500 candies, we can calculate the proportion of candies made with chocolate liquor in that sample. This proportion is called the sample proportion.

The central limit theorem states that, as long as the sample size is large enough, the distribution of sample proportions will be approximately normal, with a mean equal to the population proportion.

In this case, the sample size is 500, which is large enough for the central limit theorem to apply. Therefore, the mean of all sample proportions will be equal to the population proportion, which is 0.20. Therefore, the answer is that the mean proportion of samples made with chocolate liquor would be 0.20.

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Answer:

It is 2/15

Step-by-step explanation:

\( = \sqrt{ \frac{1}{ {6}^{2} } - \frac{1}{ {10}^{2} } } \\ \\ = \sqrt{ \frac{4}{225} } \\ \\ = \frac{ \sqrt{4} }{ \sqrt{225} } \\ \\ = \frac{2}{15} \)

Answer:

3-4y=-1

-4y=-4

y=1

A polynomial with degree 3 and zeros -4 and 31 can be written as (x + 4)(x - 31)(x - 31), which expands to f(x) = x³ - 54x² + 787x - 1196.

A polynomial with degree 3 and zeros -4 and 31 can be written as (x + 4)(x - 31)(x - k), where k is an integer that can be determined by expanding the expression.

Since the polynomial has degree 3 and zeros -4 and 31, we can write it as:

f(x) = a(x + 4)(x - 31)(x - k)

where a is a constant that can be determined by considering the leading coefficient of the polynomial. Since the polynomial has degree 3, the leading coefficient must be a nonzero integer, and we can write:

f(x) = a(x + 4)(x - 31)(x - k)

To determine the value of k, we can use the fact that the polynomial has zeros -4 and 31. This means that f(-4) = f(31) = 0. Substituting these values into the expression for f(x), we get:

f(-4) = a(0)(-35)(-4 - k) = 0

f(31) = a(35)(0)(31 - k) = 0

Since these expressions are equal to 0, it follows that either a = 0 or (4 + k) = 0 and (31 - k) = 0. Since a must be nonzero, we have:

4 + k = 0 and 31 - k = 0

Solving these equations simultaneously, we get k = 31. Substituting this value of k into the expression for f(x), we get:

f(x) = a(x + 4)(x - 31)(x - 31)

Expanding this expression, we get:

f(x) = a(x² - 27x - 496)(x - 31)

Therefore, a polynomial with degree 3 and zeros -4 and 31 can be written as (x + 4)(x - 31)(x - 31), which expands to f(x) = x³ - 54x² + 787x - 1196.

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(a) The function f = 1A is f-measurable.

(b) For every m ∈ N (m > 1), the set Em is f-measurable.

(a) To show that f = 1A is f-measurable, we need to show that the preimage of any Borel set B in R is f-measurable. Since f can only take values 0 or 1, the preimage of any Borel set B is either the empty set, X, A or X \ A, all of which are f-measurable. Therefore, f is f-measurable.

(b) To show that Em is f-measurable, we need to show that its complement E^c_m is f-measurable. Let E^c_m be the set of points that belong to less than m sets Ak.

Then E^c_m is the union of all intersections of at most m-1 sets Ak. Since each Ak is f-measurable, any finite intersection of at most m-1 sets Ak is also f-measurable. Hence, E^c_m is f-measurable, and therefore Em is also f-measurable.

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The roof area is 468.75 square feet.

To find the roof area, we need to follow these steps:
Determine the rise (vertical distance) using the slope of 9 inches per foot:

Since the run is 10 feet, the rise is 9 inches/foot × 10 feet = 90 inches.
Convert the rise to feet: 90 inches ÷ 12 inches/foot = 7.5 feet.
Calculate the length of the rafter using the Pythagorean theorem:

Rafter length = √(run² + rise²) = √(10² + 7.5²) = √(100 + 56.25) = √156.25 = 12.5 feet.
Determine the total length of the gable roof:

Since the rake slope is 1.25, we have Total length = Rafter length × Rake slope = 12.5 feet × 1.25 = 15.625 feet.
Calculate the roof area:

Roof area = Eaves length × Total length = 30 feet × 15.625 feet = 468.75 square feet.
None of the given options matches the calculated roof area.

It is possible there is a mistake in the question or the provided options.

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Answer:

\(x=5/3\text{ or } x=1\)

Step-by-step explanation:

We have the equation:

\(27x^6-152x^3+125=0\)

We can solve this using u-substitution. Let's let u=x³. Therefore:

\(27(x^3)^2-152(x^3)+125=0\)

Substitute all x³s for u:

\(27u^2-152u+125=0\)

This is now in quadratic form. So, we can use the quadratic formula:

\(u=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\)

Our a is 27, b is -152, and c is 125. So:

\(u=\frac{-(-152)\pm \sqrt{(-152)^2-4(27)(125)}}{2(27)}\)

Simplify:

\(u=\frac{152\pm\sqrt{9604}}{54}\)

Simplify:

\(u=\frac{152\pm 98}{54}\)

Reduce. Divide everything by 2:

\(u=\frac{76\pm49}{27}\)

Split into two cases:

\(u=\frac{76+49}{27}\text{ or } u=\frac{76-49}{27}\)

Solve for each case:

\(u=\frac{125}{27}\text{ or } u=\frac{27}{27}=1\)

Substitute back x³ for our u:

\(x^3=\frac{125}{27}\text{ or } x^3=1\)

Take the cube root of each equation:

\(x=\sqrt[3]{\frac{125}{27}}\text{ or } x=\sqrt[3]1\)

Evaluate:

\(x=5/3\text{ or } x=1\)

And that's our two solutions.

And we're done!

To find the shortest distance from the surface xy + 15x + z^2 = 209 to the origin, we need to minimize the distance function between a point on the surface and the origin.

The distance from a point (x, y, z) on the surface to the origin can be calculated using the distance formula: Distance = √(x^2 + y^2 + z^2). We can express y in terms of x and z using the given equation:  xy + 15x + z^2 = 209; y = (209 - 15x - z^2) / x. Substituting this expression for y in the distance formula, we have: Distance = √(x^2 + [(209 - 15x - z^2) / x]^2 + z^2). To find the shortest distance, we need to minimize this distance function. We can do this by finding the critical points of the distance function and checking for the minimum value. Differentiating the distance function with respect to x and z, we obtain: ∂(Distance)/∂x = (2x - (209 - 15x - z^2) / x^3) / (2√(x^2 + [(209 - 15x - z^2) / x]^2 + z^2)); ∂(Distance)/∂z = (2z - 2z(x^2 + [(209 - 15x - z^2) / x]^2) / (2√(x^2 + [(209 - 15x - z^2) / x]^2 + z^2)).

Setting both partial derivatives equal to zero, we can solve for the critical points. However, solving these equations algebraically may be difficult due to the complexity of the expressions. Alternatively, we can use numerical methods or optimization techniques to find the minimum distance.

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Answer:

36is what I got from my calculations

Step-by-step explanation:

4÷1/9

=36

I tried

Answer:

A.

Step-by-step explanation:

Anwer A has the following equation:

\(g(x)=\frac{3}{5}x^2-3\)

In this equation, we can calculated the intercept replacing x by 0, as:

\(g(x)=\frac{3}{5}0^2-3=-3\)

if this is the answer, the graph of g(x) should be through the point (0,-3) and that happens.

Additionally, the roots of the equations are calculated replacing g(x) by 0 and solving for x, so:

\(0=\frac{3}{5}x^2-3\\x_1=\sqrt{5}=2.236\\x_2=-\sqrt{5}=-2.236\)

It means that the graph of g(x) should be through the points (2.236,0) and (-2.236,0) and that happens too.

So, the answer is A, \(g(x)=\frac{3}{5}x^2-3\)

27 is the test score of percentile score of 71 and the score of victor is 71.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given, the teacher recorded unit 4 test scores from class.

The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.

A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.

The percentile rank of a score of 71 on the test is find by formula

\(R_{100} =\frac{100(N < )+\frac{1}{2} N}{N_{t} }\)

=100×4+1/2(1)/15

=400+0.5/15

=400.5/15

=26.7=27th

Now we need to find the score of victor who has 60 th percentile.

\(R_{100} =\frac{100(N < )+\frac{1}{2} N}{N_{t} }\)

60=Score/15

score=71

Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.

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Answer:

104 + 3(90.50)

Step-by-step explanation:

Given the cost expression :

(127.50 - 23.50) + 3(86.50 + 4)

Equivalent expression :

(127.50 - 23.50) + 3(86.50 + 4)

104 + 3(90.50)

Answer:

Mean:  160

Median:  150

Mode:  none

Range:  105

Standard deviation:  35.3

Step-by-step explanation:

Given:

If each value in the data set is multiplied by a constant value, the mean, median, mode, range, and standard deviation will all be scaled by the same amount.

Therefore, if each value in the data set is multiplied by 0.5:

Proof

Data set: {1, 2, 3, 4, 5}

\(\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{1+2+3+4+5}{5} = 3\)

\(\sf Median = 3\)

\(\sf Mode = none\)

\(\sf Range = 5-1=4\)

\(\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{10}{5}}=\sqrt{2}\)

If we multiply each value by 0.5, the new data set is:

{0.5, 1, 1.5, 2, 2.5}

\(\sf Mean\:\mu =\dfrac{\sum x_i}{n}= \dfrac{0.5+1+1.5+2+2.5}{5} = 1.5\)

\(\sf Median = 1.5\)

\(\sf Mode = none\)

\(\sf Range = 2.5-0.5=2\)

\(\sf Standard\:deviation\:\sigma=\sqrt{\dfrac{\sum (x_i-\mu)^2}{n}}=\sqrt{\dfrac{2.5}{5}}=\dfrac{\sqrt{2}}{2}\)

Therefore, if each value in the data set is multiplied by 0.5, the mean, median, mode, range, and standard deviation are all scaled by the same amount.

Answer:

5/1

Step-by-step explanation:

Answer:

5/1

Step-by-step explanation:

The probability that the mean score of the 49 seniors is greater than 20 is 0.0516. To solve this problem, we need to use the central limit theorem, which states that the distribution of sample means from a population with any distribution will approach a normal distribution as the sample size increases.

First, we need to find the standard error of the mean (SEM), which is the standard deviation of the sampling distribution of the mean. We can use the formula SEM = σ / √n, where σ is the population standard deviation, and n is the sample size.

In this case, σ = 6.0 and n = 49, so SEM = 6.0 / √49 = 0.857.

Next, we need to standardize the sample mean using the z-score formula: z = (x - μ) / SEM, where x is the sample mean, μ is the population mean, and SEM is the standard error of the mean.

In this case, x = 20, μ = 18.6, and SEM = 0.857, so z = (20 - 18.6) / 0.857 = 1.63.

Finally, we need to find the probability that a standard normal distribution is greater than 1.63, which is 0.0516 when rounded to 4 decimal places.

Therefore, the probability that the mean score of the 49 seniors is greater than 20 is 0.0516.

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Answer: translation.

Answer:

42.9% or 43%

Step-by-step explanation:

270÷630=0.4285714286

0.4285714286 × 100 = 42.85714286

Rounded - 42.9% or 43%

Answer:

he would only be able to bring 2 friends

Step-by-step explanation:

250- 100= 150    cost of table

150/ 40=3.75   cost of friends

He was would not be able to bring a .75 of a friend so you would have to round down.