9 sin^2(x/2) I need help rewriting the expression

One of the following statements is Always FALSE: The statement that is always false is d) I, II, and III are Always FALSE.

In this question, we are given three statements, and we need to determine which one is always false. Let's analyze each option:

a) I and II but Not III: This option suggests that statements I and II are false, but statement III may or may not be false. However, we cannot conclude this without further information.

b) I and III but Not II: This option states that statements I and III are false, but statement II may or may not be false. Similarly, we cannot determine the truth value of this option without additional information.

c) II and III but Not I: This option indicates that statements II and III are false, but statement I may or may not be false. As with the previous options, we cannot definitively determine its truth value.

d) I, II, and III are Always FALSE: This option states that all three statements are always false. However, this is not necessarily the case. It is possible that one or more of the statements could be true in specific contexts or under certain conditions.

Since we cannot determine the truth value of options a), b), or c) without more information, the only statement that is always false is d) I, II, and III are Always FALSE.

One of the following statements is Always TRUE:

The statement that is always true is b) I and III but Not II.

In this question, we are given three statements, and we need to identify which one is always true. Let's analyze each option:

a) I and II but Not III: This option suggests that statements I and II are true, but statement III may or may not be true. However, we cannot determine the truth value of this option without further information.

b) I and III but Not II: This option states that statements I and III are true, but statement II may or may not be true. Similarly, we cannot definitively determine the truth value of this option without additional information.

c) II and III but Not I: This option indicates that statements II and III are true, but statement I may or may not be true. As with the previous options, we cannot determine its truth value without more information.

d) I, II, and III are Always TRUE: This option states that all three statements are always true. However, this is not necessarily the case. It is possible that one or more of the statements could be false in certain scenarios.

Since we cannot determine the truth value of options a), c), or d) without more information, the only statement that is always true is b) I and III but Not II.

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Answer:

D) 269.3

Step-by-step explanation:

Rectangular prism volume:

V = whl

V = (12.1)(5.3)(4.2)

V = 269.346

The required answer is P(t) = 9.0066 billion / 1 + (15 billion - 9.0066 billion) e^(0.025 * t)

The Logistic Growth function is:P(t) = PoK / Po + (K - Po) e^(r0*t)

Where,Po is the population at some reference point

           K is the carrying capacity of the population

           ro is the base growth rate of the population

Given that for the year 1999, t = 0 and the population was 6 billion, carrying capacity K = 15 billion, and base growth rate ro = 0.025 per year.Po = 6 billion K = 15 billion r0 = 0.025

We substitute these values into the logistic growth function:

P(t) = PoK / Po + (K - Po) e^(r0*t)

P(t) = 6 billion * 15 billion / 6 billion + (15 billion - 6 billion) e^(0.025 * 0)P(t) = 90 billion / 15 billion + 9 billion

P(t) = 99 billion / 15 billion + 9 billionP(t) = 6.6 + 9 billion = 9.0066 billion

So, the logistic growth function for the world when it had 6 billion people in 1999 with carrying capacity K = 15 billion and base growth rate ro = 0.025 per year is:

P(t) = 9.0066 billion / 1 + (15 billion - 9.0066 billion) e^(0.025 * t)

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The truth value of Proposition 1, [A ⊃ ~(B · Y)] ≡ ~[B ⊃ (X · ~A)], is true when A and B are true, and X and Y are false.

First, we'll evaluate each part of the proposition:

1. A ⊃ ~(B · Y): Since A is true and B · Y is false (due to Y being false), the statement becomes "true ⊃ ~false", which simplifies to "true ⊃ true". This is true.

2. B ⊃ (X · ~A): Since B is true, X is false, and ~A is false, the statement becomes "true ⊃ (false · false)", which simplifies to "true ⊃ false". This is false.

Now, we'll evaluate the equivalence ([A ⊃ ~(B · Y)] ≡ ~[B ⊃ (X · ~A)]): The statement becomes "true ≡ ~false", which simplifies to "true ≡ true". Therefore, the truth value of Proposition 1 is true.

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Answer:

Given that JK = MN, JK = KL, and LM = MN, therefore, by transitive property, we have;

KL ≅ LM

Step-by-step explanation:

The given information are;

The midpoint of the segment JL = The point K

The midpoint of the segment LN = The point M

Given that JK = MN

The two column proof is given as follows;

Statement \({}\)               Reason

1) JK = KL  \({}\)               Definition of the midpoint of segment JL

2) LM = MN  \({}\)            Definition of the midpoint of a segment LN

3) JK = MN   \({}\)            Given

4) KL ≅ LM   \({}\)            Transitive property.

Answer: The answer should be A, Isosceles

Step-by-step explanation: Have a great day!

It is true to say that a subset of data values is a sample.

There are two types of sampling techniques:

Probability (simple random sampling, stratified sampling, etc.) and non-probability (snowball sampling, purposive sampling, etc.) sampling techniques.

Meanwhile, the population refers to the total number of items. It can be items, people, etc. For example, the population would be all the students in an area or all the employees in a company.

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As QR + QS = RS, confirming that QRS is a right triangle.

Hence Option C is the correct answer

To determine whether QRS is a right triangle,

We can use the Pythagorean Theorem,

Which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Using the coordinates given, we can calculate the lengths of the sides QR, QS, and RS using the distance formula.

QR = √[(18-12)² + (15-15)²] = 6

QS = √[(12-12)² + (15-7)²] = 8

RS = √[(18-12)² + (15-7)²] = 10

Now, we can check if the Pythagorean Theorem holds true for QRS.

Option A states that QRS is a right triangle because,

RS² + QS² = RQ².

However, this is incorrect as RQ is not a side of the triangle.

Option B states that QRS is not a right triangle because,

QR² + QS² ≠ RS².

This is also incorrect as we can see that the Pythagorean Theorem does not hold true for this triangle.

Option C states that QRS is a right triangle because,

QR² + QS² = RS².

This is the correct answer as we can see that the Pythagorean Theorem holds true for this triangle. Therefore, QRS is a right triangle.

Option D states that QRS is not a right triangle because,

RS² + QS² ≠ RQ².

This is incorrect as we have already established that RQ is not a side of the triangle.

In conclusion, the correct answer is option C and we can confirm that QRS is a right triangle.

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By analytical geometry, the line y = - 2 · x - 1 represents a line perpendicular to the line shown in the picture. (Correct choice: C)

According to analytical geometry, lines are described by polynomials of the form:

y = m · x + b

Where:

And the equation of the perpendicular line pass through a point of original line and is related to the slope of the line by following relationship:

m · m' = - 1

Where:

First, determine the slope and intercept of the original line:

(x, y) = (0, 1)

1 = m  · 0 + b

b = 1

(x, y) = (2, 0)

0 = m · 2 + b

2 · m + b = 0

m = - b / 2

m = - 1 / 2

Second, calculate the slope of the perpendicular line:

m' = 1 / (- 1 / 2)

m' = - 2

Third, we conclude by discarding options that the equation of the perpendicular line is y = - 2 · x - 1.

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The positive value of c that makes the function f(x) = xe^(-x)ce^(-x) have an absolute minimum at x = -5 is approximately 16.05.

To find the value of c that gives an absolute minimum at x = -5, we need to analyze the behavior of the function. First, we differentiate f(x) with respect to x to find the critical points. The derivative of f(x) is f'(x) = -x^2e^(-2x)ce^(-x). Setting f'(x) = 0 and solving for x, we find x = 0 as a critical point.

However, we are interested in finding the value of c that results in an absolute minimum at x = -5. Plugging x = -5 into f(x), we get f(-5) = -5e^(5)c^(-5)e^(5). Since e^5 is positive, to minimize f(-5), c should be as large as possible. Taking the limit as c approaches infinity, we find that f(-5) approaches 0.

Therefore, c should be a large positive value. Calculating the exact value, we find c ≈ 16.05 gives an absolute minimum at x = -5 for the function f(x).

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Answer:

1/2

Step-by-step explanation:

p(event) = (number of desired outcomes)/(total number of outcomes)

How many different outcomes are there? You can choose 1, 2, 3, 4, 5, 6, 7, 8, 9, or 10, so the total number of possible outcomes is 10.

How many outcomes are desired. The desired outcomes are any outcomes with a number 6 or higher. Which numbers are 6 or higher? 6, 7, 8, 9, 10. There are 5 outcomes that are 6 or higher, so there are 5 desired outcomes.

p(event) = (number of desired outcomes)/(total number of outcomes)

p(event) = 5/10 = 1/2

Answer: 1/2

Answer:

3.6

Step-by-step explanation:

\(\frac{2}{3}\)(6a+9)=20.4

4a+6=20.4

4a=14.4

a=3.6

The equation with infinitely many solutions is:

9x + 80 - 1x = 8*(x + 10)

An equation has infinitely many solutions when the dependence on x vanishes.

If you look at the third equation, we get:

9x + 80 - 1x = 8*(x + 10)

If we simplify the left side and expand the right side, we get:

8x + 80 = 8x + 80

So we have the exact same thing in both sides, this means that the equation is true for any value of x, so the equation has infinite solutions.

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This is because the number of pounds can take on an infinite number of values within a range.

The following table shows a series of experiments and associated random variables:ExperimentRandom Variable (x)Values

Continuous or Discrete

a. Take a 15-question examinationNumber of questions answered correctlyDiscreteb. Observe cars arriving at a tollbooth for 1 hourNumber of cars arriving at tollboothDiscretec. Audit 50 tax returnsNumber of returns containing errorsDiscreted. Observe an employee's workNumber of nonproductive hours in a nine-hour workdayDiscretee. Weigh a shipment of goodsNumber of poundsContinuous

The random variable in experiment a is discrete. This is because the number of questions answered correctly can only take on a finite number of values.The random variable in experiment b is also discrete. This is because the number of cars arriving at the tollbooth can only take on a finite number of values.The random variable in experiment c is also discrete. This is because the number of returns containing errors can only take on a finite number of values.The random variable in experiment d is discrete. This is because the number of nonproductive hours in a nine-hour workday can only take on a finite number of values.The random variable in experiment e is continuous.

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The average score is 97

What is average ?

In plain English, an average is a single number chosen to represent a group of numbers; it is often the sum of the numbers divided by the number of numbers in the group. The average of the numbers 2, 3, 4, 7, and 9 is, for instance, 5.

Average, mean, median, and norm all refer to something that sits in the middle. The average is the ratio created by dividing the total number of figures in a set by the total number of figures. scored 85 on tests on average. The term "mean" can refer to the simple average or to a value that lies halfway between two extremes.

Let the grade he got on final test be x

The average of all four grades is 91.

So, we have  

(92+89+86+x)/4 = 91

⇒x=364−267

= 97

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Answer:

see attached

Step-by-step explanation:

The answer is in below picture

Answer:

First table = \(f (n)\) = \(2\) · \((4)^{n-1}\)

Second table = \(f (n)\) = \(3\) · \((2)^{n - 1}\)

Third table = \(f (n)\) = \(2\) · \((6)^{n - 1}\)

I hope this helps you.

The y-intercept is found by setting x=0 on graph , which gives f(0) = (0+7)²(0-1) = -49. The roots are x = -7 and x = 1.

A graph is a visual representation of data, relationships or functions. It typically consists of an x-axis, y-axis and plotted points that represent values or data points.

In a graph, an intercept is the point where the graph intersects with the x-axis or y-axis. The x-intercept is where the graph crosses the x-axis, and the y-intercept is where it crosses the y-axis.

According to the given information:

The intercept is the point at which a function or graph intersects with one of the axes, either the x-axis or y-axis. In the case of the function f(x) = (x + 7)²(x - 1), the y-intercept is found by setting x = 0 and evaluating the function, which gives f(0) = (0 + 7)²(0 - 1) = -49. Therefore, the y-intercept is -49.

A graph is a visual representation of a function or relationship between variables. In this case, the graph of f(x) = (x + 7)²(x - 1) would show how the output (y-value) of the function changes as the input (x-value) changes. To sketch the graph, we can use a sign table to identify the roots of the function (where it crosses the x-axis) and the sign of the function in each interval. The roots of this function are x = -7 and x = 1 (with a double root at x = -7), and the function is positive to the left of x = -7, negative between x = -7 and x = 1, and positive to the right of x = 1. We can use this information to sketch the graph, making sure to accurately cross the x-axis at each root and passing through the y-intercept of -49.

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Answer:

6

Step-by-step explanation:

A = 4 cm * 3 cm/2

A = 6 cm^2

Answer:

6

Step-by-step explanation:

The graph of the parent absolute value function is decreasing over the interval (-∞, 0). The function exhibits a decreasing behavior as x moves from negative infinity towards zero, where the absolute value decreases.

The parent absolute value function is defined as f(x) = |x|. To determine where the graph of this function is decreasing, we need to identify the intervals where the function's slope is negative.

Let's analyze the behavior of the parent absolute value function:

For x < 0, the function can be rewritten as f(x) = -x. In this interval, the function is a linear function with a negative slope of -1. As x decreases, f(x) also decreases, indicating a decreasing behavior.

For x > 0, the function remains f(x) = x. In this interval, the function is a linear function with a positive slope of 1. As x increases, f(x) also increases, indicating an increasing behavior.

At x = 0, the function is not differentiable since the slope changes abruptly from negative to positive. However, it is worth noting that the function does not strictly decrease or increase at x = 0.

Therefore, we can conclude that the graph of the parent absolute value function is decreasing over the interval (-∞, 0).

In this interval, as x moves from negative infinity towards zero, the function values decrease. The farther away x is from zero (in the negative direction), the larger the absolute value, resulting in a decrease in the function values.

On the other hand, the graph of the parent absolute value function is increasing over the interval (0, ∞), as explained earlier.

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for a two-tailed test at a 12.66% significance level, the critical values of z are approximately +1.53 and -1.53. We are looking for the z-score that corresponds to the area to the right of it (for the positive critical value) equal to 0.0633.

For a two-tailed test at a 12.66% significance level, we need to find the critical value of z.

Step 1: Determine the significance level for each tail.
Since this is a two-tailed test, we need to divide the overall significance level (12.66%) by 2. This gives us 6.33% (or 0.0633 in decimal form) in each tail.

Step 2: Find the z-score associated with the given significance level.
To find the critical value of z, you can use a z-table or an online calculator. We are looking for the z-score that corresponds to the area to the right of it (for the positive critical value) equal to 0.0633.

Using a z-table or calculator, you'll find that the z-score is approximately ±1.53.

So, for a two-tailed test at a 12.66% significance level, the critical values of z are approximately +1.53 and -1.53.

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The ounces of snack mix that Grayson made during the family camping is 41.87 ounces.

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

An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Grayson added 14.52 ounces of peanuts to 27.35 ounces of granola.

Amount of snack mix = 14.52 ounces + 27.35 ounces = 41.87 ounces.

The ounces of snack mix that Grayson made during the family camping is 41.87 ounces.

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The calculated measure of the angle CTZ is 38 degrees

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

This means that

YTA + BTC = 90

So, we have

4y + 6 + 7y - 4 = 90

So, we have

11y = 88

Divide

y = 8

Next, we have

CTZ = 90 - BTC

So, we have

CTZ = 90 - (7y – 4)

This gives

CTZ = 90 - (7 * 8 – 4)

Evaluate

CTZ = 38

Hence, the measure of CTZ is 38 degrees

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In a haplodiploid system, the relatedness of a son to a maternal aunt is 75%.

In a haplodiploid system, males develop from unfertilized eggs and are haploid, while females develop from fertilized eggs and are diploid. This means that sons inherit all of their genetic material from their mother, including her alleles from both her haploid sets of chromosomes. Maternal aunts, on the other hand, share one set of haploid chromosomes with their nephew (the son), as they are the sister of his mother. Therefore, the relatedness between a son and his maternal aunt in a haplodiploid system is 0.75 or 75%.

In a haplodiploid system, the relatedness of a son to a maternal aunt can be calculated using the following steps:

1. Determine the relatedness of the son to his mother: In haplodiploid systems, sons are haploid and inherit their single set of chromosomes from their mother. This means that they are 100% related to their mother, as they share all her genes.

2. Determine the relatedness of the maternal aunt to the son's mother: The maternal aunt is a sister of the son's mother. In haplodiploid systems, sisters share 75% of their genes, as they get half of their genes from their mother and the other half from their father (who, as a haploid male, gives all his genes to his daughters).

3. Calculate the relatedness of the son to his maternal aunt: To determine the relatedness of the son to his maternal aunt, multiply the son's relatedness to his mother (100%) by the maternal aunt's relatedness to the son's mother (75%).

Relatedness of son to maternal aunt = (1.0) * (0.75) = 0.75 or 75%

So, in a haplodiploid system, the relatedness of a son to a maternal aunt is 75%.

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The given statement states that for all integers n ≥ 1, the product of the first n terms of the sequence 1 · 2 · 3 · ... · n is equal to n(n-1)(n-2)(n-3) · ... · 4. This can be proven using mathematical induction.

We will prove the given statement using mathematical induction.

Base case: For n = 1, the left-hand side of the equation is 1 and the right-hand side is also 1, so the statement holds true.

Inductive step: Assume the statement holds true for some integer k ≥ 1, i.e., 1 · 2 · 3 · ... · k = k(k-1)(k-2) · ... · 4. We need to prove that it holds for k+1 as well.

Consider the left-hand side of the equation for n = k+1:

1 · 2 · 3 · ... · k · (k+1)

Using the assumption, we can rewrite it as:

(k(k-1)(k-2) · ... · 4) · (k+1)

Expanding the right-hand side, we have:

(k+1)(k)(k-1)(k-2) · ... · 4

By comparing the two expressions, we see that they are equal.

Therefore, if the statement holds true for some integer k, it also holds true for k+1. Since it holds for n = 1, by mathematical induction, the statement holds for all integers n ≥ 1.

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Answer:

x = b-a-y

Step-by-step explanation:

Answer:

X=B-A-Y

Step-by-step explanation:

X+Y=B-A

subtract the y and it will fall onto the other side

so your answer will be x=b-a-y cause the y turned negative to cancel out the y that is ear the x.  

Answer:

Yes, Jean is correct

Step-by-step explanation:

Given

\(73 * \frac{3}{4}\)

Required

Determine the value of the result

When a positive integer is multiplied by a fraction, the result is always less than the integer

Solving further

\(Expression = 73 * \frac{3}{4}\)

\(Expression = \frac{73 * 3}{4}\)

\(Expression = \frac{219}{4}\)

\(Expression = 54.75\)

The result of the expression shows that the resulting value is less than 73.

Hence, Jean is correct

Splitting strategy is one of the technique in mathematics  which help to add  the larger number , two-digit and three digit and so on.

Explanation:

Splitting strategy is one of the mathematical technique :

Therefore, the splitting strategy is mathematical technique to make out work effortless.

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The perimeter of triangle is 66.24 units.

What is triangle?

In Euclidean geometry, any 3 points, once non-collinear, verify a unique triangle and at the same time, a unique plane

Main body:

according to question :

c = 28

let the vertices be A,B,C

∠A= 30°

by using trigonometric ratios,

BC/ AB = sin30°

AB = C = 28

BC/28 = sin30°

BC = 28*sin30°

BC= 28*(1/2)

BC = 14

similarly

AB /CA = cos 30°

28/CA = √3/2

CA = 28*√3/2

CA = 14/√3

CA = 24.24

Hence , perimeter = AB +BC +CA = 28+14+24.24

                              =66.24 units

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