Factorize (2a-b)^2 -4(2a-b) -13

Answer:

C

Step-by-step explanation:

\(\frac{10}{a} =sin 60\\a=\frac{10}{sin~60}\\=\frac{10}{\frac{\sqrt{3} }{2} } \\=\frac{20}{\sqrt{3}} \times\frac{\sqrt{3}}{\sqrt{3}} \\=\frac{20 \sqrt{3}}{3}\)

Answer:

Blue costs 2.875 or 2.88 if rounded, Red costs 3.875 or 3.88 if rounded

Step-by-step explanation:

The simplified complex number is 2i - 2, and its geometric representation would be located at (-2, 2) in the complex plane.

The complex number -2i can be represented geometrically as a point in the complex plane, located at (0, -2).

(a) The complex number -2 + 5i can be represented geometrically as a point in the complex plane, where the real part corresponds to the x-coordinate and the imaginary part corresponds to the y-coordinate. In this case, the point would be located at (-2, 5).

(b) The complex number 5i is a imaginary number and can be represented as a point on the real number line.

(c) The complex number 2 is also a real number and can be represented as a point on the real number line. In this case, the point would be located at 2 on the real number line.

(d) For the complex number -3(2 - i), we can simplify it first:

-3(2 - i) = -6 + 3i

(e)Next, let's represent -6 + 3i geometrically. The point corresponding to this complex number would be located at (-6, 3) in the complex plane.

For the complex number 2i(1 + i), let's simplify it:

2i(1 + i) = 2i + 2i²

Using the fact that i^2 = -1, we can rewrite it as:

2i + 2(-1) = 2i - 2

The simplified complex number is 2i - 2, and its geometric representation would be located at (-2, 2) in the complex plane.

f) Finally, for (-1 + i)², let's compute it:

(-1 + i)² = (-1 + i)(-1 + i) = 1 - i - i + i²

Using the fact that i² = -1, we can simplify it further:

1 - i - i - 1 = -2i

The complex number -2i can be represented geometrically as a point in the complex plane, located at (0, -2).

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The most common error when entering a formula is to reference the wrong cell in the formula.

This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.

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To minimize the function Q = 2x^2 + 3y^2 subject to the constraint x + y = 5, you should choose x = 3 and y = 2.

To minimize the function Q = 2x^2 + 3y^2 subject to the constraint x + y = 5, follow these steps:

Step 1: Express y in terms of x using the constraint.
y = 5 - x

Step 2: Substitute the expression for y into the function Q.
Q = 2x^2 + 3(5 - x)^2

Step 3: Expand and simplify the expression.
Q = 2x^2 + 3(25 - 10x + x^2)
Q = 2x^2 + 75 - 30x + 3x^2
Q = 5x^2 - 30x + 75

Step 4: Find the critical points by taking the first derivative of Q with respect to x and setting it to 0.
dQ/dx = 10x - 30 = 0
10x = 30
x = 3

Step 5: Find the corresponding value of y using the expression from Step 1.
y = 5 - x = 5 - 3 = 2

So, to minimize the function Q = 2x^2 + 3y^2 subject to the constraint x + y = 5, you should choose x = 3 and y = 2.

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Answer: The average amount of pocket change per person is $2.06.

Step-by-step explanation:

To find the average amount of pocket change per person, we need to first add up all the amounts and then divide by the number of people (which is 7 in this case).

Adding up the amounts: $0.00 + $1.25 + $0.02 + $2.00 + $10.75 + $0.40 + $0.00 = $14.42

Dividing by the number of people: $14.42 ÷ 7 = $2.06 So the average amount of pocket change per person is $2.06.

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The resultant vector is 7 units to the left and 5 units down. As a result, graphs option (c) a vector pointing to the left 7 units and down 5 units is the correct answer.

Mathematicians use graphs to visually display or chart facts or values in order to express them coherently. A graph point usually represents a connection between two or more items. A graph, a non-linear data structure, is made up of nodes (or vertices) and edges. Glue the nodes, also known as vertices, together. This graph includes V=1, 2, 3, 5, and E=1, 2, 1, 3, 2, 4, and (2.5). (3.5). (4.5). Statistical graphs (bar graphs, pie graphs, line graphs, and so on) are graphical representations of exponential development. a logarithmic graph shaped like a triangle

We can add vectors geometrically by setting the starting point of the second vector at the terminal point of the first vector and drawing a vector from the first vector's initial point to the second vector's terminal point.

Next we align the starting point of vector v with the terminal point of vector u and draw a vector from the initial point of vector u to the terminal point of vector v:

The resultant vector is 7 units to the left and 5 units down. As a result, option (c) a vector pointing to the left 7 units and down 5 units is the correct answer.

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Answer:

Local Minimum: (-2.5, -2), (0, -2)

Local Maximum: (1, 2)

Answer:

-3/-2

Step-by-step explanation:

If you want to find the distance, the formula is y -y over x-x

The tests commonly used to determine the strength properties of such materials are 3-point load test, direct tension test, cylinder split test.

In this method, a lone loading along length is applied at diametrically end points. Due to this loading cylinder splits into two parts.

Brittle ceramics are typically not subjected to tensile tests. These materials are challenging to mold into the right test structure, they are challenging to handle without breaking, and it is challenging to align the test samples to prevent bending stresses that could damage the samples.

A three-point bending apparatus is used to measure the stress-strain behavior of brittle ceramics, and from the results, an equivalent modulus of elasticity is calculated.

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The relative frequency distribution of the values of the mean of these 15,504 different samples would specify the sampling distribution of the mean.

The sampling distribution of the mean refers to the distribution of sample means obtained from repeated sampling from the same population.

In this case, we have 15,504 different samples of size 5 drawn from a population of 20 hospitals.

Each sample has its own sample mean. The relative frequency distribution of these sample means would specify the sampling distribution of the mean.

The sampling distribution of the mean is important in statistics because it allows us to make inferences about the population mean based on the distribution of sample means.

It helps us understand the variability of sample means and provides a basis for constructing confidence intervals and conducting hypothesis tests.

Therefore, the relative frequency distribution of the mean values from the different samples would describe the characteristics of the sampling distribution of the mean..

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To find the total distance, Divide distance already walked by percentage:

8 / 0.55 = 14.55 km

She already walked 8 so now subtract:

14.55 - 8 = 6.55 km left to walk

A sequence of rigid transformations is applied to quadrilateral URST. Shifting an object along a straight path without any rotation or reflection is called translation, which is a type of transformation used in this quadrilateral.

Based on the given coordinates of the quadrilateral URST and its transformed image U'R'S'T', let's analyze the transformations applied to each vertex,

Translation vector = (x'-x, y'-y)

U' = (-6, 0) - (-1, -2) = (-5, 2)

R' = (-2, 1) - (3, -1) = (-5, 2)

S' = (1, 0) - (6, -2) = (-5, 2)

T' = (-3, -2) - (2, -4) = (-5, 2)

We observe that the translation vector is (-5, 2) for each vertex.

Therefore, Translation: 5 units left, 2 units up

Rule: (x, y) → (x - 5, y + 2)

Therefore, only translation transformation is used.

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(C) Regression analysis is the statistical method commonly used to estimate the level and trend in a time series by modeling the relationship between the data and independent variables.

Regression analysis is the statistical method used to estimate the level and trend in a time series. Time series data represents observations taken at different points in time and is commonly used to analyze trends and patterns over time.

Regression analysis allows us to model the relationship between a dependent variable (in this case, the time series data) and one or more independent variables (such as time or other relevant factors). By using regression analysis, we can identify the underlying trend in the time series and estimate its level.

The regression model captures the relationship between the dependent variable (the time series) and the independent variable(s) by fitting a line or curve that best represents the data. This line or curve helps to identify the overall trend and level of the time series.

While moving average, simulation method, covariance analysis, and correlation analysis are useful techniques in analyzing time series data, they are not specifically designed to estimate the level and trend in a time series. Therefore, (C) regression analysis is the most appropriate method for estimating the level and trend in a time series.

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If a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1, the final formula for the cubic polynomial is f(x) = x³ - 3x² + 12x - 6.

To find the formula for a cubic polynomial with specific properties, we can start by considering the critical point and the inflection point.

Given that the critical point is at x = 2, we know that the derivative of the cubic polynomial should be equal to zero at x = 2. This means that the slope of the polynomial at x = 2 is zero. Taking the derivative of the cubic polynomial, we have:

f'(x) = 3ax² + 2bx + c.

Setting this equal to zero and substituting x = 2, we get:

3a(2)² + 2b(2) + c = 0.

12a + 4b + c = 0.

Now, let's consider the inflection point at (1,4). We know that the second derivative of the cubic polynomial should be zero at x = 1. Taking the second derivative, we have:

f''(x) = 6ax + 2b.

Setting this equal to zero and substituting x = 1, we get:

6a(1) + 2b = 0.

6a + 2b = 0.

Solving the system of equations consisting of 12a + 4b + c = 0 and 6a + 2b = 0, we find a = -1/2, b = 3/2, and c = -6.

Therefore, the formula for the cubic polynomial is:

f(x) = -1/2x³ + 3/2x² - 6x + d.

The leading coefficient is 1, so we have:

f(x) = x³ - 3x² + 12x + d.

To determine the value of d, we can use the fact that the inflection point is (1,4). Substituting x = 1 and y = 4 into the equation, we get:

4 = 1 - 3 + 12 + d.

4 = 10 + d.

d = -6.

Therefore, the final formula for the cubic polynomial is:

f(x) = x³ - 3x² + 12x - 6.

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Complete question is:

Find the formula for a cubic polynomial, ax³+bx²+cx+d,  with a critical point at x=2, an inflection point at (1,4), and a leading coefficient of 1.

Answer:

12 hours

Step-by-step explanation:

Time taken by pipe A = 24 hours

Time taken by pipe B = 36 hours

Time taken by pipe C = 32 hours

To find:

How long would it take the three pipes to fill the pool if pipe B is turned on 3 hours after pipe A and pipe C is turned on 1 hour after pipe B?

Solution:

First of all, let us assume the total capacity of the pool.

Let us take LCM of 24, 36 and 32.

LCM of 24, 36 and 32 = 288

Let the total capacity of the pool = 288 units

Total units filled by pipe A in one hour = \(\frac{288}{24} = 12\ units\)

Total units filled by pipe B in one hour = \(\frac{288}{36} = 8\ units\)

Total units filled by pipe C in one hour = \(\frac{288}{32} = 9\ units\)

Now, for the first 3 hours, only pipe A operates, so units filled in first three hours = \(12\times 3 =36\ units\)

For the next one hour, A and B both operate together, so units filled in the next 1 hour = 12 + 8 = 20 units

Total number of units filled in 4 hours = 36 + 20 = 56 units

Units to be filled to completely fill the pool = 288 - 56 = 232 units

Now, after the 4th hours, all the pipes operate together.

So, number of units filled in each hour = 12 + 8 + 9 = 29 units

Time taken to fill 232 units = \(\frac{232}{29} = 8\ hours\)

Total time taken = 4 + 8 = 12 hours

Answer:

2/-5

Step-by-step explanation:

(-2) - (-4) = 2

(-6) - (-1) = -5

Answer:

-2/5

Step-by-step explanation:

you have to do y2-y1 over x2-x1

then you plot in your points :

y2=-2

y1=-4

x1=-1

x2=-6

after you do that you need to subtract them and that's how you will get your  answer.

The best conclusion amongst the following options is Paulina's statement that most of the class made between a 71 and 80.What is a conclusion?

A conclusion is an explanation or reasoning based on the observations and data. It is the final decision that is made by analyzing the information gathered. It is very important to make a correct conclusion as it reflects the accuracy of the data gathered and analyzed by an individual.

What is the given information? Joe said the average grade was a 75.Collin said almost 15% made between a 91 and a 100.Paulina said most of the class made between a 71 and a 80. Quannah said that most of the students understood the concepts that were not tested. Amongst these options, the statement made by Paulina is more precise, clear, and based on the data given. She used the term "most," which means the largest part or majority. Therefore, we can say that the majority of the class's grades were between 71-80. Hence, Paulina's conclusion is the best.

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The p-value is 0.05 or less if the chi-square statistic is 3.84 or more.

The p-value is 0.05 or less if the chi-square statistic is 3.84 or more. This indicates that there is a statistically significant difference between the observed and expected frequencies, and we reject the null hypothesis at a 5% significance level.

A statistical technique called the chi-squared test is used to assess whether there is a significant discrepancy between observed and predicted data. The test is frequently employed in disciplines like biology, sociology, and psychology to analyse categorical data.

The chi-squared test's fundamental premise is to contrast observed frequencies of a collection of categorical data with expected frequencies that would be anticipated if the data were distributed in a particular way. The test determines whether there is a statistically significant difference between the observed and anticipated frequencies.

The goodness-of-fit test and the test of independence are the two primary categories of chi-squared tests.

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Answer:

5! (5 factorial) or 120 ways

Step-by-step explanation:

You can arrange P different ways. R can be arranged only 4 different ways because Pwill be in one of the spots. Next, you can arrange "I" 3 different ways because P and R are already arranged in 2 spots, meaning you cant put "I" there. Next, S can be arranged in 2 different ways for the same reason. And lastly, M can only be arranged in 1 different way because the other spots are taken.

You can put it in any order. For example, M could be arranged 5 ways and P could be arranged in 1 way. You will still get 120 ways

Hopefully this helped. The explanation might be a bit confusing but I tried my best. I'm not good with explaining my solutions but I always try

Answer:

120

Step-by-step explanation:

took the test and i got it right

Answer:

To find all the real zeros of a polynomial function algebraically, use the Rational Root Theorem to generate a list of possible rational zeros and use synthetic division to test each possible zero. The zeros that remain after testing all the possible zeros are the real zeros of the polynomial function.

To find all the real zeros of a polynomial function algebraically, you can use the Rational Root Theorem and synthetic division. The Rational Root Theorem states that if a polynomial function has integer coefficients, then any rational zero (i.e., a zero that can be expressed as a fraction) must have a numerator that is a factor of the constant term and a denominator that is a factor of the leading coefficient.

Here are the steps you can follow:

1. Write the polynomial function in descending order of degree, with all like terms combined.

2. Use the Rational Root Theorem to generate a list of possible rational zeros. This list will be a set of all the possible fractions that can be formed by dividing a factor of the constant term by a factor of the leading coefficient.

3. Use synthetic division to test each possible zero. Start with the smallest possible denominator and work your way up. If a possible zero is not a zero of the polynomial function, cross it off the list.

4. Repeat step 3 until all the possible zeros have been tested. The zeros that remain are the real zeros of the polynomial function.

For example, let's say we have the polynomial function f(x) = x^3 - 6x^2 + 11x - 6.

Write the polynomial function in descending order of degree: f(x) = x^3 - 6x^2 + 11x - 6.

Use the Rational Root Theorem to generate a list of possible rational zeros: ±1, ±2, ±3, ±6.

Use synthetic division to test each possible zero. We start with x = 1:

1 │ 1 -6 11 -6

│ 1 -5 6

└─────────────

1 -5 6 0

Since the remainder is zero, we have found a zero of the polynomial function at x = 1. We can write the factorization f(x) = (x - 1)(x^2 - 5x + 6).

Now we use synthetic division to test the other possible zeros:

2 │ 1 -6 11 -6

│ 2 12 46

└─────────────

1 -4 23 40

x = 2 is not a zero of the polynomial function.

3 │ 1 -6 11 -6

│ 3 15 78

└─────────────

1 -3 26 72

x = 3 is not a zero of the polynomial function.

-1 │ 1 -6 11 -6

│ -1 7 -4

└────────────

1 -7 18 -10

x = -1 is not a zero of the polynomial function.

-2 │ 1 -6 11 -6

│ -2 16 -50

└────────────

1 -8 27 -56

x = -2 is not a zero of the polynomial function.

-3 │ 1 -6 11 -6

│ -3 27 -102

└────────────

1 -9 38 -108

x = -3 is not a zero of the polynomial function.

6 │ 1 -6 11 -6

Hope this helps, I'm sorry if it doesn't! :]

Answer:

45 levels

Step-by-step explanation:

60% of 75 is 45 i think

To assign the 50 students to two independent groups, a randomization procedure can be used. The procedure involves first listing all the students in a random order. It minimizes bias and ensures an equal chance of assignment to either group.

To assign 50 students to two independent groups using randomization, follow these steps:

1. Start with a list of all 50 students.

2. Assign a unique number to each student, such as from 1 to 50.

3. Use a random number generator to generate 25 distinct random numbers from 1 to 50. These random numbers will represent the students for the first independent group.

4. The remaining 25 students, represented by the numbers not selected in step 3, will form the second independent group.

5. Assign the students to their respective groups based on the random numbers.

This procedure ensures that the students are assigned to two independent groups through randomization, reducing potential biases and ensuring a fair distribution of students across the groups.

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Answer: $7.65 for a dozen/12

Step-by-step explanation: 2.55 x 3

Answer: 17/33

Step-by-step explanation:

Or means add the 2 probabilities

There are a total of 33 outcomes.

getting a small clip is 15/33

getting a medium clip is 12/33

add the two probabilities 15/33 +12/33 = 17/33

I'm sure of my numbers.  I think the question is off or answers  

Answer:

The answer is A

Answer:

it should be 4 3/8 but sorry if it's wrong <3

Answer:

The circumference is 50.24 in

Step-by-step explanation:

The circumference formula is C = 2πr where C = Circumference, π = pi and r = radius. We know that r = 8 and π = 3.14 and that we're solving for C, so we can substitute those values into the equation to get C = 2 * 3.14 * 8 = 50.24 in.

Answer:

neither

Step-by-step explanation:

parallel looks like this ---->     =====    it is equal facing eachother

and perpendicular looks like this -----> Г it is on 90⁰

Edit: thx for 5stars vote :)