Can someone please help me with this? I'll mark anyone who answers for helping

The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below

Given the following equation

(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)

We start by simplifying the left-hand side of the equation:

(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]

Next, we have the following steps to simplify the expression

= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]

= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]

= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]

= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]

= -4(2p² + 1)/(p²-4) (p² - 1)

Hence, the given identity is proven.

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The angle measures for this problem are given as follows:

θ = 150º and θ = 330º.

The trigonometric expression for this problem is given as follows:

[tex]\theta = \arctan{\left(-\frac{\sqrt{3}}{3}\right)}[/tex]

The solution to the arctangent function is the angle which has the given tangent value.

The angle on the first quadrant with a tangent value of sqrt(3)/3 is given as follows:

θ = 30º.

The quadrants in which the tangent is negative are given as follows:

2nd and 4th.

Hence the equivalent angles are given as follows:

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Answer:

-----------------------------

AB is vertical with same x-coordinates, and BC is horizontal with same y-coordinates.

Hence this is a right triangle.

Its area is:

Answer:

----------------------

Use the following identities:

Apply the identities to the given expression:

Answer:

Step-by-step explanation:

After organizing the data, the researcher must present them so they can be understood by those who will benefit from reading the study. The most useful method of presenting the data is by constructing statistical charts and graphs. There are many different types of charts and graphs, and each one has a specific purpose.

This chapter explains how to organize data by constructing frequency distributions

and how to present the data by constructing charts and graphs. The charts and graphs

illustrated here are histograms, frequency polygons, ogives, pie graphs, Pareto charts,

and time series graphs. A graph that combines the characteristics of a frequency distribution and a histogram, called a stem and leaf plot, is also explained.

Section 2–2 Organizing Data 35

2–3

Objective

Organize data using

frequency

distributions.

1

2–2 Organizing Data

Suppose a researcher wished to do a study on the number of miles that the

employees of a large department store traveled to work each day. The researcher

first would have to collect the data by asking each employee the approximate distance the

store is from his or her home. When data are collected in original form, they are called

raw data. In this case, the data are

1 2 6 7 12 13 2 6 9 5

18 7 3 15 15 4 17 1 14 5

4 16 4 5 8 6 5 18 5 2

9 11 12 1 9 2 10 11 4 10

9 18 8 8 4 14 7 3 2 6

Since little information can be obtained from looking at raw data, the research

Answer:

c

Step-by-step explanation:

its ez

The value of the variable a in the equation is 5 from the calculation here.

We need to square of a number is described as a number that when multiplied by itself give the original number.

Also, index forms are described as those mathematical forms that are used to represent numbers that are too large or small.

From the information given, we have the equation;[tex]a^2[/tex]=25

find the square root of value of 25,

We have;25 = [tex]5^2[/tex]

Substitute the value, we get;[tex]a^2[/tex] =  [tex]5^2[/tex]

Take out the similar factor, this is their exponents.

We then have;

a = 5

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Complete question;

Find the value of a in the equation;a² = 25

Answer:

Assuming you meant to write "x^2 - 4x - 12", there are a few equivalent forms that you could use to represent this expression. One common form is:

(x - 6)(x + 2)

Step-by-step explanation:

This is the factored form of the expression, which shows that it can be written as a product of two linear factors. To see why this is true, you can use the distributive property to expand the product:

(x - 6)(x + 2) = x(x + 2) - 6(x + 2) = x^2 + 2x - 6x - 12 = x^2 - 4x - 12

The surface area of the rectangular prism is 210 in²

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

The surface area of a rectangular prism is the sum of each area for the surface.

Hence:

Surface area = 2(8 in * 5 in) + 2(5 in * 5 in) + 2(8 in * 5 in) = 210 in²

The surface area of the prism is 210 in²

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For the given function 'g':

domain = (-4, -2) ∪ (1, 3]

range = (-5, 4]

If the function is defined as f(x) = y, then the values of x for which the value of function exists, the set of that values is said to be the domain of the function f.

If the function is defined as f(x) = y, then the set of all possible values of the function that is the set of all possible values of y is said to be the range of the function f.

Here given the graph of 'g'.

From the graph we can see that for -4 < x < -2 and 1 < x [tex]\le[/tex] 3 the function has graph.

So the domain = (-4, -2) ∪ (1, 3]

And it is clear that the value of y lies between -5 < y [tex]\le[/tex] 4.

So the range = (-5, 4].

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The sales 12 weeks after release is $586,000 . Option A is the correct answer.

To create a table of values, we can plug in different values of t and find the corresponding values of s:

t s

0 10

1 19.882

2 26.248

3 31.177

4 35.064

5 38.185

6 40.731

7 42.837

8 44.6

9 46.095

10 47.384

11 48.508

12 49.498

To graph the function, we can plot the values from the table on a coordinate plane. The horizontal axis represents time in weeks, and the vertical axis represents sales in thousands of units. The resulting graph is a curve that starts at (0,10) and increases as t increases.

To estimate the sales 12 weeks after release, we can look at the graph and see that the corresponding value of s is around 49.5 thousand units. Therefore, the answer is about $586,000 (49.5 x 1000 x 12). Option A is the correct answer.

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Answer:

To create a residual plot, you need to first fit a model to the data. Without any information about the problem you are trying to solve or the model you are fitting, I will assume that you are trying to fit a linear regression model to these data points.

First, you would need to find the equation of the line that best fits the data using a regression analysis software or by hand. Let's assume that the equation of the line is:

y = 0.2x + 2.5

where y is the response variable (dependent variable) and x is the predictor variable (independent variable).

Next, you would calculate the predicted values of y (i.e., the values that the model predicts) for each value of x in your dataset, using the equation of the line. For example, for the first data point (13.8, 1.42), the predicted value of y would be:

y_predicted = 0.2 * 13.8 + 2.5 = 5.06

The residual for this data point would be the difference between the actual value of y and the predicted value of y:

residual = 1.42 - 5.06 = -3.64

You would repeat this process for each data point in your dataset, to get a list of residuals.

Answer:

All lines are parallel.

Step-by-step explanation:

Get each equation in Slope-Intercept form:

  1. Divide both sides by 3: [tex]y=-\frac{4}{3}x+\frac{7}{3}[/tex]

  2. No change

  3. Subtract 8x and divide by 6 on both sides: [tex]y=-\frac{4}{3}x-\frac{2}{3}[/tex]

Notice:

a. All slopes are -4/3

b. All y-intercepts are different

Answer:

The correct answer is C, Graph D.

x^2 - 4x + 4 = (x - 2)^2.

The value of expression 14a +7+ 5b+ 2a + 10b will be 16a + 15b + 7

Since Expression is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given the expression as;

14a +7+ 5b+ 2a + 10b

Combine like terms;

14a + 2a + 10b +7+ 5b

16a + 15b + 7

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The probability of Caleb selecting a 5 on the first selection and then selecting a 5 on the second selection after returning the card to the deck and shuffling is 1/9.

There are a total of 12 cards, out of which 4 are 5s. Since Caleb returns the card to the deck and shuffles it, the selection of the first card does not affect the probability of selecting a 5 on the second selection.

Therefore, the probability of selecting a 5 on the first selection is 4/12 = 1/3, and the probability of selecting a 5 on the second selection is also 4/12 = 1/3.

Since the events are independent, we can multiply the probabilities to find the probability of both events occurring:

P(selecting a 5 on first selection and selecting a 5 on second selection) = P(selecting a 5 on first selection) x P(selecting a 5 on second selection)

= (1/3) x (1/3)

= 1/9

Therefore, the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection is 1/9.

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Answer:

x=38.6

Step-by-step explanation:

x=b/cos(alpha)

x=30/cos(39⁰)

x=38.602

There are 1100 many ways can be done that is when catering service offers 5 appetizers, 11 main courses, and 4 desserts.

Given that,

A catering service offers 5 appetizers, 11 main courses, and 4 desserts. A customer is to select 4 appetizers, 9 main courses, and 3 desserts for a banquet.

We have to find how many ways can this be done.

We know that,

Number of appetizers offered = 5

Number of appetizers customer is to select = 4

Number of main courses offered = 11

Number of main courses customer is to select = 9

Number of desserts offered = 4

Number of desserts the customer is to select = 3

So,

To determine the number of ways this can be selected,

By using the combination formula that is

[tex]^nC_r = \frac{n!}{r!(n-r)!}[/tex]
[tex]^nC_r = ^5C_4\times ^{11}C_9\times^4C_3[/tex]

[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!(5-4)!} \times \frac{11!}{9!(11-9)!}\times \frac{4!}{3!(4-3)!}[/tex]

[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!1!} \times \frac{11!}{9!2!}\times \frac{4!}{3!1!}[/tex]

[tex]^5C_4\times ^{11}C_9\times^4C_3 = \frac{5!}{4!} \times \frac{11!}{9!(2)}\times \frac{4!}{3!}[/tex]

[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 5 × 11 × 5 × 4

[tex]^5C_4\times ^{11}C_9\times^4C_3 =[/tex] 1100

Therefore, There are 1100 many ways this can be done.

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Answer:

i think its b sorry if  it's wrong

Step-by-step explanation:

The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40

Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;

f( - 4 ) = 15

g( - 2 ) = 5

Substitute the given parameters into the expression to have:

3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5

= 45 - 5

= 40

Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40

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Answer:

f'(x) = 2x, so f'(-2) = 2(-2) = -4.

The solution of the equation is x = -1.

Given is an equation we need to solve it,

3x/4 + 3 - 2x = -1/4 + x/2 +5

Multiplying the equation by 4 both the sides,

3x + 12 - 8x = -1 + 2x + 20

Combining the like terms,

3x - 8x - 2x = 20 - 1 - 12

3x - 10x = 7

-7x = 7

x = -1

Hence the solution of the equation is x = -1.

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The following expression is equivalent to [tex]x^{-5/3}[/tex] as option B that is 1/∛x⁵.

A fraction is a numerical representation of a part or a portion of a whole. It is expressed as one integer (numerator) divided by another integer (denominator), separated by a horizontal line.

Here,

We can rewrite [tex]x^{-5/3}[/tex]as [tex](1/ x^{^(5/3)})[/tex].

The negative exponent in the numerator tells us that we need to move the term to the denominator of a fraction and change the sign of the exponent to make it positive. Similarly, the fractional exponent in the denominator indicates that we need to take the reciprocal of the term and change the sign of the exponent to make it positive.

Therefore, we can rewrite [tex]x^{-5/3}[/tex] as:

[tex](1/ x^{^(5/3)})[/tex]

or

[tex]x^{-5/3}[/tex] = [tex](1/ x^{^(5/3)})[/tex]

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Complete question:

Which of the following is equivalent to [tex]x^{-5/3}[/tex]?

The total cost equation can be written as:

Total Cost = 32000 + 9000L

What is total cost?

Total cost refers to the complete amount of money or resources that are required to produce or obtain a particular good or service. It includes all of the expenses associated with production, such as labor costs, materials costs, overhead costs, and any other costs necessary to manufacture or acquire the product.

The total cost equation can be expressed as:

Total Cost = Fixed Cost + Variable Cost

where Fixed Cost is the cost that does not vary with the number of laptops manufactured and sold, and Variable Cost is the cost that depends on the number of laptops manufactured and sold.

In this case, the fixed monthly cost is $32,000 and it does not depend on the number of laptops manufactured and sold. The variable cost is the cost of manufacturing each laptop, which is $9,000 per laptop.

If L is the number of laptops manufactured and sold per month, then the variable cost can be expressed as 9000L. Therefore, the total cost equation can be written as:

Total Cost = 32000 + 9000L

This equation represents the total cost of manufacturing and selling L laptops per month. The fixed cost of $32,000 is added to the variable cost of $9,000 per laptop multiplied by the number of laptops sold, L, to obtain the total cost.

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Complete question: A business manufactures and sell laptops. Each laptop is sold for 14000.the fixed monthly cost is 32000 and it cost 9000 to manufacture each laptop. let L be number of laptops manufactured and sold per monthly. What is the total cost equation?

Answer:learn how to spell :)

Step-by-step explanation:

For the function "f (x) = 120/x²", the domain of the function "f" is (b) All non zero real numbers.

The "Domain" of a function is the set of all possible "input-values" for which the function is defined. In this case, the function is defined as:

f (x) = 120/x²

The only restriction on the input values is that the denominator cannot be equal to zero, because division by zero is undefined.

So, the domain of the function f is all non-zero real numbers.

Therefore, the correct option is (b): All non-zero real numbers.

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The given question is incomplete, the complete question is

Given that f (x) = 120/x², What is the domain of the function f ?

(a) only positive integers,

(b) All non zero real numbers,

(c) only negative integers,

(d) All real numbers including zero.

a) The formula relating y to t is: y = 45.1 * e^(-0.693/19 * t) b) there will be approximately 30.1 mg of the substance present after 9 minutes.

(a) The general formula for exponential decay is y = y0 * e^(-kt), where y is the amount at time t, y0 is the initial amount, k is the decay constant, and e is Euler's number.

To find the decay constant, we can use the fact that the half-life is 19 minutes. The formula for half-life is t1/2 = ln(2) / k, where ln(2) is the natural logarithm of 2.

Substituting t1/2 = 19 and ln(2) = 0.693 into the formula gives:

19 = 0.693 / k

k = 0.693 / 19

So the formula relating y to t is:

y = 45.1 * e^(-0.693/19 * t)

(b) To find how much will be present in 9 minutes, we can plug t = 9 into the formula we found in part (a):

y = 45.1 * e^(-0.693/19 * 9) ≈ 30.1 mg

So, there will be approximately 30.1 mg of the substance present after 9 minutes.

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Answer: 34,650 permutations