Select all the solutions to the inequality: -2x>10

-10
-8
-5
-2
0
2
5
8
10

Answer:

x<-2

Step-by-step explanation:

17+4x<9

4x<-8

x<-2

The solution is:

Work/explanation:

Recall that the process for solving an inequality is the same as the process for solving an equation (a linear equation in one variable).

Make sure that all constants are on the right:

\(\bf{4x < 9-17}\)

\(\bf{4x < -8}\)

Divide each side by 4:

\(\bf{x < -2}\)

The first statement describes the process of sampling while the second statement introduces the concept of Fourier series, which represents periodic signals as a sum of periodic complex exponentials.

1. The first statement describes the process of sampling in digital signal processing. Sampling refers to the conversion of a continuous-time signal into a discrete-time signal by measuring the signal at regular intervals of time. The resulting digital numbers represent the measurements of the signal at those specific time points. This process is fundamental in digitizing analog signals for various applications such as audio processing, image processing, and telecommunications. Sampling allows for the representation, storage, and manipulation of signals using digital systems.

2. The second statement refers to the concept of Fourier series, which is a mathematical representation of periodic signals. A periodic complex exponential is a waveform that repeats itself after a certain period and is characterized by a complex exponential function. In Fourier series, periodic signals can be expressed as a sum of sinusoidal functions with different frequencies, amplitudes, and phases. These sinusoidal functions are known as harmonics or complex exponentials. The fundamental frequency is the lowest frequency component in the series, and the harmonics are integer multiples of the fundamental frequency. Fourier series is widely used in signal analysis and synthesis, as it provides a powerful tool to analyze and represent periodic signals in terms of their frequency content.

Both sampling and Fourier series are fundamental concepts in digital signal processing and play crucial roles in various applications in engineering, communications, and signal analysis.

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The correct next step Amy could take is to factor (x^2 - 16) on the left side of the equation to yield (x + 4)(x – 4)(x + 2) = 0.

The equation is given as:

\(\mathbf{(x^2 - 16)(x + 2) = 0}\)

The possible next steps are:

1. Expand the equation as follows

\(\mathbf{x^3+2x^2-16x-32 = 0}\)

2. Express x^2 -16 as a difference of two squares as follows

\(\mathbf{(x + 4)(x- 4)(x + 2) = 0}\)

However, the correct step in this case is to factor x^2 - 16 as a difference of two squares to give \(\mathbf{(x + 4)(x- 4)(x + 2) = 0}\)

This is so, because the question says Amy is trying to solve for variable x.

This step will ensure that she gets the possible values of x, unlike expanding the whole equation .

Hence, the correct next step is \(\mathbf{(x + 4)(x- 4)(x + 2) = 0}\)

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The total surface area of the package is the sum of the surface areas of the base and lateral faces, which is 2(12.5 square inches) + 110 square inches = 135 square inches.

What is total surface area ?

Total surface area refers to the sum of the areas of all the faces or surfaces of a three-dimensional object. For example, the total surface area of a rectangular prism is the sum of the areas of all six of its rectangular faces. It is often used in geometry and engineering to determine the amount of material needed to cover or construct a given object.

According to the question:
The package is in the shape of a square prism, which has two congruent rectangular bases and four rectangular lateral faces. The base area of the package is 25 square inches, so each base has an area of 25/2 = 12.5 square inches. Since the jewelry box is a cube with edge length 4.5 inches, it has six faces with area \((4.5 inches)^2 = 20.25 square inches\) each. Therefore, the surface area of the jewelry box is 6(20.25 square inches) = 121.5 square inches.

The lateral faces of the package are also rectangles, with length equal to the height of the package (5.5 inches) and width equal to the perimeter of the base of the package divided by 4. Since the base of the package is a square with side length 5 inches, the perimeter of the base is 4(5 inches) = 20 inches. Therefore, the width of each lateral face is 20/4 = 5 inches. Thus, the surface area of each lateral face is (5 inches)(5.5 inches) = 27.5 square inches, and the total surface area of all four lateral faces is 4(27.5 square inches) = 110 square inches.

Therefore, the total surface area of the package is the sum of the surface areas of the base and lateral faces, which is 2(12.5 square inches) + 110 square inches = 135 square inches.

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We can see that since the values that multiply each component (x & y) are less than an unit, the transformation rule would be a reduction.

Answer:

11 bookshelves

Step-by-step explanation:

96/9 then round up if not whole

7/11, and 63/99 = .636363636 [repeating]

Answer:

A

Step-by-step explanation:

The area of the patio is 192 \(m^{2}\)

An object's area is how much space it takes up in two dimensions. It is the measurement of the quantity of unit squares that completely cover the surface of a closed figure. The square unit, which is frequently expressed as square inches, square feet, etc., is the accepted unit of area.

The word "area" refers to a free space. A shape's length and width are used to compute its area.

Length of swimming pool=18 m

Width of swimming pool=8 m

Area of swimming pool= 18*8 = 144\(m^{2}\)

Width of patio=3m

Total length of swimming pool=18+2(3)=24 m

Total width of swimming pool=8+2(3)=14 m

Total area=24*14=336 \(m^{2}\)

Area of patio= total area - Area of swimming pool

                     =336-144

                     =192 \(m^{2}\)

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Answer:

64, 289, 400, 0

Step-by-step explanation:

Answer:

64, 400, 289 , 0 are perfect square.

follow me!

Answer:

Its the first one y=x3 - 3

Step-by-step explanation:

Answer:

y = x – 3

Step-by-step explanation:

y = x³ – 3 [cubic function]

y = x² – 3 [square function / quadratic]

y = x – 3 [linear function]

y = √x – 3 [square root function]

Answer:

-360y^9z^2

\(-360y^9z^2\)

Step-by-step explanation:

Step 3 is unnecessary (the statement is already given, plus you haven't proven the triangle is isosceles anyway).

After, omit step 5 and jump straight to 6.

After this, step 6 is the statement that used to be step 5, which is true by CPCTC.

Then, you can prove the required statement by definition from this.

Using algebraic expressions, the value of x in the diagram given is calculated as: x = 4

An algebraic equation is an equation that has an unknown variable (i.e. x) and digits, which can be used to solve a problem.

Algebraic expression for Mat A is: 4x + 3

Algebraic expression for Mat B is: 2x + 11

We would have the following algebraic equation:

4x + 3 = 2x = 11

Solve for the value of x

4x - 2x = 11 - 3

2x = 8

x = 8/2

x = 4

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If you provide the desired standard error value, I can help you calculate the corresponding population standard deviation.

The standard error is a measure of the variability or uncertainty of a sample mean. It is calculated by dividing the population standard deviation by the square root of the sample size. Therefore, if we want the standard error to be smaller, the population standard deviation should be larger.

To determine how large the population standard deviation needs to be, we need to specify a desired standard error value. Without that information, it is not possible to provide a specific answer. The relationship between the population standard deviation and the standard error is inversely proportional, so as the population standard deviation increases, the standard error decreases.

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Answer: 1.5 pounds

Step-by-step explanation: 16 oz(one pound) + 8oz(half a pound)= 24oz

The vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

To determine if the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly independent, we need to find the scalars a, b, and c that satisfy the equation:

a * [-5 4 5] + b * [2 -1 5] + c * [-17 16 45] = [0 0 0]

If the only solution is a = b = c = 0, the vectors are linearly independent. If there are other solutions where a, b, and c are not all zero, the vectors are linearly dependent.

Let's form a matrix with these vectors as columns:

|-5  2 -17|
| 4 -1  16|
| 5  5  45|

Now, we can row reduce this matrix to its reduced row echelon form (RREF):

| 1 -2  5|
| 0  1 -3|
| 0  0  0|

From the RREF, we can write the system of linear equations:

x - 2y + 5z = 0
y - 3z = 0

Solving this system, we get:

y = 3z
x = 2y - 5z = 6z - 5z = z

Since z can be any scalar, we have infinitely many solutions where not all of a, b, and c are zero. For example, when z = 1, we get x = 1 and y = 3. So, the scalars (1, 3, 1) make the equation true.

Thus, the vectors [-5 4 5], [2 -1 5], and [-17 16 45] are linearly dependent with scalars (1, 3, 1) as an example of a non-zero solution.

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The probability in each case scenario as described in the task content are as follows;

a) P(a) = 7/16

b) P(b) = 7/16

c) P(c) = 7/16

d) P(d) = 7/16

Given: There are 14 freshmen and 18 sophomore students and the students were selected with replacement.

a) The required probability that the 2nd student is also a freshman if the first student was a freshman since the selection is with replacement is simply;

P(a) = 14/32 = 7/16.

b) The probability that the 2nd student was a

freshman if the first student was a sophomore is;

P(b) = 14/32 = 7/16.

c). The required probability that the 2nd student is also a freshman if the first student was a freshman since the selection is with replacement is simply;

P(c) = 14/32 = 7/16.

d) The probability that the 2nd student was a

freshman if the first student was a sophomore is;

P(d) = 14/32 = 7/16.

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Answer:

A(2, -1)

B(6 -1)

C(4, -4)

Not my strongest point but thats seems right

The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Answer:

$51.2

Step-by-step explanation:

If you subtract 64 to 20% then you end up with $51.2

he will need to save 30 dollars a month

Step-by-step explanation:

Answer:

The Quadratic Formula uses the "a", "b", and "c" from "ax2 + bx + c", where "a", "b", and "c" are just numbers; they are the "numerical coefficients" of the quadratic equation they've given you to solve.

Step-by-step explanation:

Answer:

Step-by-step explanation:

55 - 20% = 44

5.5% of 44 = 2.42

2.42 + 44 = 46.42

hope this helps. :]

The probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

To calculate the probability of rolling all six numbers at least once when rolling a six-sided die 12 times, we can use the concept of permutations.

The total number of possible outcomes when rolling a six-sided die 12 times is 6^12 since each roll has six possible outcomes. This represents the denominator of our probability calculation.

Now, let's calculate the numerator, which represents the number of favorable outcomes where we get all six numbers at least once. We can use the concept of derangements (or the principle of inclusion-exclusion) to determine this.

A derangement is a permutation in which none of the elements appear in their original position. In our case, we want to find the number of derangements for a set of six elements (the six numbers on the die).

The formula to calculate the number of derangements for a set of n elements is given by n! * (1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!).

Using this formula, we can calculate the number of derangements for six elements:

Number of derangements = 6! * (1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!) = 265

Therefore, the numerator of our probability calculation is 265.

Finally, we can calculate the probability by dividing the numerator by the denominator:

Probability = Number of favorable outcomes / Total number of possible outcomes = 265 / 6^12

Calculating this value:

Probability ≈ 0.0263

So, the probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

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Answer:

\((x^{2}-9)(x^{2} -1)\)

Step-by-step explanation:

Step 1: Find what adds to _ and multiples to_

It needs to multiple to the 'c' term or 9

It needs to add to the 'b' term or -10

Step 2: Find the numbers

We know -9 and -1 make 10 and multiple to 9

-9 x -1 = 9

-9 + (-1) + -10

Step 3: Write equation in form a(x-r)(x-s)

a = 1

r = -9

s = -1

Plug in the equation to get the factored form of the equation:

\((x^{2}-9)(x^{2} -1)\)

Therefore the factored form of the equation is \((x^{2}-9)(x^{2} -1)\)

Quadratic equations are also a type of algebraic fractions that have factors.

The factor of \(x^{4} - 10x^{2} + 9 = (x -3)(x + 3)(x - 1)(x + 1)\)

In order to completely factor \(x^{4} - 10x^{2} + 9\) we would apply the formula:

a(x-r)(x-s)

To find the variables a, x, r and s, we have to love at the coefficients of \(x^{2}\) which is -10 and the term 9 and find out what can we multiply together to give us 9 and add together to give us -10

That would be , -9 and - 1 because:

-9 x -1 = 9

-9 + (-1) = -10

Hence: the value for a = 1

, r = -9  and s = -1

Putting this into the equation:

1(x -(-9)(x - (-1))

Hence, we have:

\((x^2-9)( x^{2} - 1)\)

Factorizing the above expression further, we have

\((x - 3)(x + 3)(x - 1)(x + 1)\)

Therefore, the factor of \(x^{4} - 10x^{2} + 9 = (x -3)(x + 3)(x - 1)(x + 1)\)

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Answer: Answer:

A. is your answer

When using the Slope Method, your answer is y - 5 = 4(x - 2).

Feel free to give brainliest.

Have a great day everyone!

Answer:

y = 45°

Step-by-step explanation:

4 sides = 360°

(2y+1)° + y° + 112° + 112° = 360°

2y + y = 360 - 112 - 112 - 1

3y = 135

y = 135÷3

= 45°

the next number in the series is 17.

The given series of numbers is a sequence of prime numbers. To find the next number, we need to identify the next prime number after 13.

The next prime number after 13 is 17.

what is series?

In mathematics, a series is the sum of the terms of a sequence. It is a sequence of numbers that are added together in a specific order. Each term in the series is typically obtained by applying a rule or formula to the preceding terms.

For example, the series 1 + 2 + 3 + 4 + 5 + ... is the sum of all positive integers. In this case, the terms of the series are generated by adding the next positive integer to the sum of the previous terms.

Series can be finite, meaning they have a specific number of terms, or they can be infinite, meaning they continue indefinitely.

Series are an important concept in mathematics and have applications in various fields such as calculus, number theory, and probability.

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The child advocate collects data by randomly selecting 4 out of the 25 state orphanages. In each of the four selected orphanages, the child advocate surveys every child.

This approach allows the child advocate to obtain information from a representative sample of children in state orphanages. By surveying every child in the selected orphanages, the child advocate ensures that no child is excluded from the data collection process. This method provides a comprehensive understanding of the experiences, needs, and concerns of the children in the four chosen orphanages.

By collecting data in this manner, the child advocate can gather valuable insights that can inform policies and interventions to improve the well-being and support for children in state orphanages.

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