Some students were surveyed about their favorite type music and school-subject preferences. The results are displayed below. Which of the following is true, according to the graph? There is a much larger preference for science among those who prefer R&B. There is a much larger preference for English among those who prefer rock. There is a much smaller preference for math among those who prefer country. The percentages for class preference are relatively the same among the different music groups.

The given system of equations has exactly one solution for all values of 'a' except when 'a = 3'. When 'a = 3', the system has infinitely many solutions.

To analyze the solutions of the system, we can start by using the method of elimination or substitution to solve it. By subtracting the first equation from the second equation, we obtain:

(2x - 3y + 3z) = 1

Now, let's consider the third equation: x + y + (a² - 8)z = a + 3. By comparing the coefficients, we can determine the conditions for which the system has no solutions, exactly one solution, or infinitely many solutions.

When 'a ≠ 3', the coefficient of z in the third equation (a² - 8) is non-zero, indicating that the system has a unique solution. The equations are independent, and the values of x, y, and z can be determined uniquely.

However, when 'a = 3', the coefficient of z becomes zero (3² - 8 = 1 - 8 = -7). In this case, the system of equations reduces to:

2x - 3y + 3z = 1

z = 0

The second equation implies that z is fixed at zero, but the first equation has two variables (x and y) that are not constrained. Therefore, there are infinitely many solutions for this particular value of 'a'.

In summary, the given system of equations has exactly one solution for all values of 'a' except when 'a = 3'. When 'a = 3', the system has infinitely many solutions.

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Answer:

\(\large \boxed{\sf \ \ \ x-y=-2\sqrt{7} \ \ \ }\)

Step-by-step explanation:

Hello,

it took me some time to understand the correct equations, I believe that you mean

\(x+y=4\\\\x^2+y^2=22\\\\x^4=y^4-176\sqrt{7}\)

So let's play with these equations

\(x^4=y^4-176\sqrt{7}\\\\<=>y^4-x^4=176\sqrt{7}\\\\<=>y^4-x^4=(y^2)^2-(x^2)^2=(y^2-x^2)(y^2+x^2)=(y-x)(y+x)(x^2+y^2)\\\\=176\sqrt{7}\)

So

\(x-y=-\dfrac{176\sqrt{7}}{(x+y)(x^2+y^2)}=-\dfrac{176\sqrt{7}}{4*22}=-2\sqrt{7}=-5.291503...\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

2.3 x 2 = 4.6 kg.

hand = one hand

98 - 4.6 = 94.4

Answer:

Step-by-step explanation:

complex zeros always occur in pairs.

so zeros are -3,4-i,4+i

so fourth zero also intersects x-axis.

Hence there are two x-intercepts only.

The possible prices of the new dress must be any value less than or equal to $45.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

The equation-like form of the formula 5x 4 > 2x + 3 has an arrowhead in place of the equals sign. It is an illustration of inequity. This shows that the left half, 5x 4, is bigger than the right part, 2x + 3. Finding the x numbers for which the inequality holds true is what we are most interested in.

Start with the inequality x ≤ 45

This inequality states that x must be less than or equal to 45.

Therefore, the possible prices of the new dress must be any value less than or equal to $45.

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A population of aardvarks is growing at a rate of 2% per year, there are 714 aardvarks this year and 700 aardvarks were there last year.

An equation is an expression that shows the relationship between two or more variables and numbers.

Let y represent the amount of aardvarks after x years.

It can be represented by the equation:

y = a(1.02)ˣ

If this year there are 714 aardvarks, the amount in the last year is:

714 = a(1.02¹)

a = 700

A population of aardvarks is growing at a rate of 2% per year, there are 714 aardvarks this year and 700 aardvarks were there last year.

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Answer:

Angle B would be a obtuse angle

Step-by-step explanation:

Answer:

This is angle obtuse because an obtuse angle is usually 130 degrees

Step-by-step explanation:

Answer:

a = 180 - 92 - 27=61

b = 92 + 27= 119

Step-by-step explanation:

Answer:

Interior Angle A = 180 - (27 +92)

= 180 - (119)

= 61 degrees

Exterior Angle B = 180 - 61

= 119 degrees

The probability of a player's height being between 5' 3" and 5' 8" is approximately 77%.

To calculate the probability of a player's height being between 5' 3" and 5' 8" in a normal distribution, we need to standardize the heights using the z-score formula and then use the standard normal distribution table or a calculator to find the probability.

Step 1: Convert the heights to inches for consistency.

5' 3" = 5 * 12 + 3 = 63 inches

5' 8" = 5 * 12 + 8 = 68 inches

Step 2: Calculate the z-scores for the lower and upper bounds using the average height and standard deviation.

Lower bound:

z1 = (63 - 66) / 2 = -1.5

Upper bound:

z2 = (68 - 66) / 2 = 1

Step 3: Use the standard normal distribution table or a calculator to find the area/probability between z1 and z2.

From the standard normal distribution table, the probability of a z-score between -1.5 and 1 is approximately 0.7745.

Multiply this probability by 100 to get the percentage:

0.7745 * 100 ≈ 77.45

Therefore, the probability of a player's height being between 5' 3" and 5' 8" is approximately 77%.

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Answer:

2/3

Hope that helps!

The probability that at least one of them is a 1 is 0.2778 when a fair set of dice is thrown and the total of the numbers falling above them is even.

Given that,

A fair set of dice is thrown.

We have to find given that the total of the numbers falling above them is even, what is the probability that at least one of them is a 1.

We know that,

A fair set of dice is thrown.

The total of the numbers falling above them is even.

The probability that at least one of them is a 1 is

(5/36)/(8/36)

5/18

0.2778

Therefore, The probability that at least one of them is a 1 is 0.2778 when a fair set of dice is thrown and the total of the numbers falling above them is even.

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39.8631371388 days will be taken by amoeba to produce a population of 1000 .

The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be increased in order to obtain a number x is the logarithm of x to the base b.

So the number of amoebae doubles every cycle (a cycle being four days).  So we just multiply it by 2 every cycle

2 x 2 x 2...

A simple way to write this is using an exponent with a base of 2

2n

where n represents the number of cycles.

2^1 = 2 amoebae after one cycle

2^2 = 4 amoebae after two cycles

2^3 = 8 amoebae after three cycles, and so on

So you can substitute different numbers for n until you find the correct number of cycles, or you can take the base 2 logarithm of the equation.

2n = 1000

log2(2n) = log2(1000)

n = log2(1000)

Remember, n represents the number of cycles, so once you find it you will have to multiply it by the length of each cycle.

log₂(1000) = 9.9657842847 cycles this is the time taken by the amoeba to produce a population of 1000

therefore days taken will be = 9.9657842847 * 4 = 39.8631371388 days

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Answer:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Step-by-step explanation:

The expression you provided is a polynomial in two variables, x₁ and x₂. Let's simplify it step by step:

2x₁²x₂² - x₁x₂ - 3x₁ - 3x₂

To simplify, we can look for common terms that can be factored out:

x₁(2x₁x₂² - x₂ - 3) - 3x₂

Now let's simplify the expression inside the parentheses:

2x₁x₂² - x₂ - 3

Answer:

Should be 5 or 6

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

( 2^5 - 4 ) - 3 × ( 2 + 1 )

= ( 32 - 4 ) - 3 × 3

= 28 - 9

= 19

Answer:

the answer is e

Answer:

C- calculate the mean of the data and find the distance each data point is from the mean, and find the mean of step 2

The Simplified value of the "algebraic-expression" (12x³y² - 18xy)/6xy is 2x²y - 3.

An "Algebraic-Expression" represents a combination of numbers, variables, and arithmetic operations such as addition, subtraction, multiplication, and division, that represents a mathematical relationship or rule.

To simplify the expression, (12x³y² - 18xy)/6xy,  we factor out a common factor of "6xy" from the numerator;

We get,

⇒ (12x³y² - 18xy)/6xy = 6xy(2x²y - 3)/6xy,

The 6xy in the numerator and denominator cancel out,

We get,

⇒ 2x²y - 3

Therefore, the simplified expression is 2x²y - 3.

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The given question is incomplete, the complete question is

Simplify and evaluate the given algebraic expression

(12x³y² - 18xy)/6xy.

Answer:

9.25

13 - 0.75t

Step-by-step explanation:

0.75 * 5 = 3.75

13 - 3.75 = 9.25

hope this helps!

The composition of the two given functions is:

(k°h)(x) = 1/5x

Here we have the functions h(x) = 5x and k(x) = 1/x.

We want to get (k°h)(x), which is equal to:

k(h(x))

Then we have:

k(h(x)) = 1/h(x)

Replacing h(x) we get:

k(h(x)) = 1/h(x) = 1/(5x)

So the composition is just one over 5x.

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Answer:

wrong

Step-by-step explanation:

(a+b)^2=(a+b)(a+b)

=a(a+b)b(a+b)

=a^2+ab+ab+b^2

=a^2+2ab+b^2

i hope it helps you

Answer:

I think option (B) is right answer

The graph of the function y = x⁴ + x³ + 2x² + 9x + 3 is added as an attachment

From the question, we have the following parameters that can be used in our computation:

y = x⁴ + x³ + 2x² + 9x + 3

The above function is a polynomial function that has the following features

Next, we plot the graph using a graphing tool by taking not of the above features

The graph of the function is added as an attachment

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One-half of the dogs in each shelter are between the weights represented by the first and third quartiles, which are approximately 20-55 pounds for the first shelter and 25-65 pounds for the second shelter, respectively.

A box plot is a visual representation of a set of data that shows the median, quartiles, and outliers of the data. The box represents the middle 50% of the data, with the bottom and top edges of the box representing the first and third quartiles, respectively. The line inside the box represents the median, or the middle value of the data set. The "whiskers" extend from the edges of the box to the minimum and maximum values of the data set, but outliers beyond the whiskers are represented as individual points.

Now, let's look at the two box plots showing the weights of dogs in two different animal shelters. One-half of the dogs in each shelter are between the first and third quartiles, which are represented by the edges of the box in each plot.

If we take the first box plot, we can see that the first quartile is approximately 20 pounds and the third quartile is approximately 55 pounds. Therefore, one-half of the dogs in this shelter weigh between 20 and 55 pounds.

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The correct choice is (A): It is possible. Since Cx- v is consistent for every v in R, according to the Invertible Matrix Theorem that makes the 6x6 matrix not invertible. Since it is not invertible, Cx - v does not have a unique solution.

Because there are infinitely many solutions to Cx = v, if the equation Cx- v is consistent for every v in R6, the matrix C has a nontrivial nullspace (the set of all solutions to the homogeneous equation Cx = 0). The Invertible Matrix Theorem states that a matrix is invertible if and only if its nullspace contains the zero vector. As a result, if C's nullspace is nontrivial, C is not invertible.

If C is not invertible, it has no unique inverse, and so Cx- v lacks a unique solution for some v in R6. As a result, for some v, the equation Cx- v may have more than one solution.

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The value of y is 6. When dividing 24 by 4, you get 6.

Answer:

speed and direction of the object in motion

Answer:

b) $1,391.25

Step-by-step explanation:

Noon is at 12pm, so 8am-12pm will be 4 hours.
8821-3256=5565, so the snack bar made $5565 in 4 hours, to find how much it made in 1 hour we need to divide 5565 by 4.

5565/4=1391.25

Answer: I’m unclear on your question

Step-by-step explanation:

I’m sorry I would love to help but I’m not sure what the question is. You’re total percentage here is 65% so I’m wondering if you need to know how much percent is something else which would be 35% but if you upload the rest of the problem then I know lots of people would love to take a look and try to help you solve it.