prove that:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)​

The value of f(2020) is 39/100.

Given function is,

f(25) = 80

And f(xy) = f(x)/y²   .....(i)

Since

f(25) = 80

Then we define function as

f(x) = x + 55   .....(ii)

Now we can write 2020 = 101 x 20

So f(2020) = f(101x20) = f(101)/20²                from (i)

                                    =  (101 + 55)/400       from(ii)

                                    = 156/400

                                    = 39/100

Hence, f(2020) = 39/100

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The length of segment PQ is equals to the length of segment P'Q' divided by 1.5, that is:

PQ = P'Q'/1.5

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The scale factor for this problem is given as follows:

k = 1.5.

Hence the equation relating the lengths PQ and P'Q' is given as follows:

P'Q' = 1.5PQ

PQ = P'Q'/1.5

(as the length on the dilated figure is the original length multiplied by the scale factor).

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The model predicts that the number of stores will be at a minimum of approximately 8,123 stores in the year 2009, and will increase from there without bound.

A cubic function is a type of polynomial function with the highest degree term being 3. In other words, a cubic function is a function of the form[tex]f(x) = ax^3 + bx^2 + cx + d[/tex], where a, b, c, and d are constants. The graph of a cubic function is a curve that can take on various shapes depending on the values of the coefficients.

b) To find the predicted number of stores in 2020, we need to find the value of the function when x = 20 (since 2020 is 20 years after 2000). We can substitute x = 20 into the function and evaluate:

[tex]y = 10.4x^3 - 403x^2 + 5585x - 8695\\y = 10.4(20)^3 - 403(20)^2 + 5585(20) - 8695\\y = 140,385[/tex]

Therefore, the model predicts that the number of stores in 2020 will be 140,385.

c) To determine if the number of stores ever decreases over the period of years ending in 2020 according to the model, we can look at the behavior of the function. The function is a cubic function with a positive leading coefficient, which means it will have a global minimum (i.e., the lowest point on the graph) and then increase without bound as x approaches positive or negative infinity.

To find the global minimum, we can take the derivative of the function and set it equal to zero:

[tex]y' = 31.2x^2 - 806x + 5585\\0 = 31.2x^2 - 806x + 5585[/tex]

x ≈ 8.68 or x ≈ 22.12

The first solution, x ≈ 8.68, is within the range of interest (2000 to 2020), so we can use it to find the global minimum:

[tex]y = 10.4x^3 - 403x^2 + 5585x - 8695[/tex]

y ≈ 8,123

Therefore, the model predicts that the number of stores will be at a minimum of approximately 8,123 stores in the year 2009, and will increase from there without bound. So according to the model, the number of stores never decreases over the period of years ending in 2020.

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Answer:

x²+14x+49

Step-by-step explanation:

(a+b)²=a²+2ab+b²

(x+7)²=x²+2×7×x+7²=x²+14x+49

The interest rate of the savings account would be = 33.3%

To calculate the interest rate of the savings account, the formula for simple interest should be used. That is;

Simple interest = Principal × time × Rate/100

simple interest = 1250-312.50 = 937.5

Principal amount = $312.50

Time = 9 years

rate = ?

That is;

937.5 = 312.50 × 9 × R/100

make R the subject of formula:

R = 937.5× 100/312.50 × 9

= 93750/2812.5

= 33.3%

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The graph of the function f(x)=−4.6|x+2|+7 is symmetric at x = -2

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

The function f(x)=−4.6|x+2|+7.

The function f(x)=−4.6|x+2|+7 is an absolute value function

An absolute value function is represented as

f(x) = a|x - h| + k

Where the line of symmetry is

x = h

Using the above as a guide, we have the following:

Line of symmetry: x = -2

Hence, the graph of the function is symmetric at x = -2

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The total distance between the buildings is 150 meters. In the event a map placed one is to 5000 scales then it projects one unit on the map represents 5000 units in the actual world.

We can apply this ratio to alter the distance on the map to the actual distance between the buildings or objects in the given case that the distance is shown as 3 centimeters then the actual distance in meters is followed 1 centimeter on the map represents 5000 centimeters in the real world.

1 cm on the map = 5000 cm in the actual world

3 cm on the map = (3 x 5000) cm in the actual world
= 15000 cm in the actual world
To alter cm to meters, we need to can apply division by 100 since there are 100 cm in a meter. So, the actual distance between the two buildings is:
15000 cm / 100 = 150 meters
The real distance between the two buildings is 150 meters.
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Answer: The stemplot shows that the distribution is unimodal and skewed to the right.

The stem values (tens digits) are:

1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4

The leaf values (ones digits) are:

5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 9, 9, 0, 0, 0, 1, 1, 1, 2, 2, 3, 3, 7, 9, 9, 9, 2, 2, 4, 8, 2

The data is unimodal because there is one clear peak in the distribution. The data is skewed to the right because the long tail of the distribution extends to the right, with a few large values pulling the mean to the right.

Therefore, the best description of the shape of this distribution is skewed to the right.

The distance between the installations is given as follows:

126.42 miles.

The Law of Cosines is a trigonometric formula that relates the lengths of the sides of a triangle to the cosine of one of its angles. It is also known as the Cosine Rule.

The Law of Cosines states that for any triangle with sides a, b, and c and angle B opposite to side b, the following equation holds true:

b^2 = a^2 + c^2 - 2ac cos(B)

The parameters for this problem are given as follows:

a = 143, c = 70, B = 62.1º.

Hence the distance b is obtained as follows:

b² = 143² + 70² - 2 x 143 x 70 x cosine of 62.1 degrees

b² = 15981.

[tex]b = \sqrt{15981}[/tex]

b = 126.42 miles.

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Answer:

The appropriate test statistic for testing the null hypothesis that the slope of the population regression line equals 0 is the t-statistic.

The t-statistic for testing the slope coefficient is calculated as follows:

t = (b1 - 0) / SE(b1)

where b1 is the estimated slope coefficient, and SE(b1) is the standard error of the estimated slope coefficient.

From the computer output, we see that the estimated slope coefficient for exercise time is -2.20, and the standard error of the estimated slope coefficient is 0.07.

Therefore, the t-statistic is:

t = (-2.20 - 0) / 0.07 = -31.43

This t-statistic follows a t-distribution with n-2 degrees of freedom, where n is the sample size. The sample size is not given in the output, so we cannot determine the exact degrees of freedom.

First, we need to find the experimental probability (probability using the provided data) of landing on purple.

Experimental probability of purple = # of purple / total #

Experimental probability of purple = 2 / 26 = 1 / 13 (simplified)

Next, we need to consider the probability in the context of 13 spins, as per the question. Our experimental probability tells us that 1 out of every 13 spins will be purple. Therefore, we can expect 1 of the next 13 spins to land on purple.

Answer: 1 spin

Hope this helps!

Therefore , the solution of the given problem of parallel lines comes out to be parallel lines stay parallel option C is correct.

A parallelogram in Euclidean geometry is essentially a straightforward hexagon with two different groups & equal distances. When both sets of sides evenly share a horizontal path, a particular type of quadrilateral known as a parallelogram is created. There are four distinct types of parallelograms, three of them being incompatible. The four distinct forms are slightly parallelograms, rectangular shapes, squares, and parallelograms.

Here,

C. It is untrue that a line may be translated into two parallel lines.

A line can be translated into another line that runs parallel to the first line, but not into two parallel lines.

Every point on the line is rigidly transformed by a translation, which moves all of the points along the line uniformly and in one direction.

After a translation, parallel lines stay parallel.

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Answer:

e = 3

Step-by-step explanation:

Use the property of the proportion to find e (cross-multiply):

[tex]10 \times e = 6 \times 5[/tex]

[tex]10e = 30[/tex]

Divide both sides of the equation by 10 to make e the subject:

[tex]e = 3[/tex]

Answer:

3

Step-by-step explanation:

6 x 10 = 60

6 x 5 = 30

5/10 = 30/60

30/ 10= 3

60/ 10 = 6

E/6 = 3/6

E=3

The solution is,  that the answer to your question would be that the subject(s) of the sentence is/are the following one/s: Tablet, pens. That is, the correct option would be B.

In this sentence, the PP indicating the location of the tablet of paper and the pens appears in initial position in the sentence.

The sentence sounds odd and is not grammatically correct because in these cases an existential there is introduced.

Take a,

a) In the desk drawer, there are a tablet of paper and some pens

b) *In the desk drawer, are a tablet of paper and some pens

The NP "a tablet of paper and some pens" would function as the subject complement and the existential there acts as grammatical subject filler(a).

Hence, The solution is,  that the answer to your question would be that the subject(s) of the sentence is/are the following one/s: Tablet, pens. That is, the correct option would be B.

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p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

According to the given information we are given that the first term of an arithmetic series is (21 + 1), which simplifies to 22. We are also given that the common difference of the series is 3. Therefore, the second term of the series is 22 + 3 = 25, the third term is 22 + 2(3) = 28, and so on.

To find the nth term of this arithmetic series, we can use the formula for the nth term of an arithmetic sequence:

an = a1 + (n - 1)d

where an is the nth term, a1 is the first term, n is the number of terms, and d is a common difference. We are given that the nth term is (141-5), so we can set up an equation and solve for n:

(141-5) = 22 + (n - 1)3

136 = 22 + 3n - 3

117 = 3n

n = 39

Therefore, there are 39 terms in the arithmetic series.

To find the sum of the first n terms of an arithmetic series, we can use the formula:

Sn = n/2(a1 + an)

where Sn is the sum of the first n terms, a1 is the first term, and an is the nth term. We know that a1 = 22, an = (141-5), and n = 39, so we can substitute these values into the formula:

S39 = 39/2(22 + (141-5))

S39 = 19(136)

S39 = 2584

Therefore, the sum of the first 39 terms of the series is 2584.

Now, we need to write the sum of the first n terms of the series as p(gt - 1), where p, q, and r are integers.

We know that the common difference is 3, so we can write the nth term as:

an = a1 + (n - 1)d

an = 22 + (n - 1)3

an = 3n + 19

Substituting this into the formula for the sum of the first n terms, we get:

Sn = n/2(a1 + an)

Sn = n/2(22 + 3n + 19)

Sn = n/2(3n + 41)

[tex]Sn = 3/2 n^2 + 41/2 n[/tex]

Therefore, p = 3, q = 41, and r = 2, and we can write:

[tex]Sn = 3(gt^2 - t) + 41(gt - t).[/tex]

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Answer:

(-9, 6) This ordered pair is used to find the function value f(-9)=6

or the given function​ value, write a corresponding ordered pair.

Step-by-step explanation:

For the given function​ value, write a corresponding ordered pair.

f(-9) = 6

The ordered pair of each function can be written as (x,y).

For any function, for example, g(x)= 10x, the input is x, and the output y is 10x. So ordered pair is (x,10x)

The given function value is: f(-9) = 6

Here input x=-9 and y value is 6

So, he corresponding ordered pair is (-9, 6)

Therefore, the usefulness of stigma in society depends on how it is applied and the context in which it is used.

Durkheim, one of the founding fathers of sociology, saw deviance as a normal and necessary aspect of society. According to Durkheim, deviance serves several important functions. Firstly, it reinforces social norms by defining what is acceptable and unacceptable behavior. Deviance also provides a sense of unity and reinforces social solidarity within a society by creating a common enemy for people to rally against. Additionally, deviance can facilitate social change by highlighting areas where social norms may be outdated or ineffective.

The labeling theory of deviance suggests that deviance is not a characteristic of the individual but rather a product of the social reaction to their behavior. The process of labeling a person as deviant can have a significant impact on their self-identity and can lead to further deviant behavior. Primary deviance refers to the initial act of deviance, whereas secondary deviance refers to the subsequent behavior that occurs after a person has been labeled as deviant.

Stigma, or the negative social label attached to deviant behavior, can have both positive and negative consequences for society. On the one hand, stigma can help to reinforce social norms and discourage deviant behavior. However, it can also lead to discrimination and marginalization of individuals who are labeled as deviant, which can have negative impacts on their life chances and well-being. Therefore, the usefulness of stigma in society depends on how it is applied and the context in which it is used.

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The four angles, one in each quadrant, with a common reference angle of with 285° are: 15°, 165°, 195°, 345°

A common reference angle is an angle that is shared by multiple angles in different quadrants when measured from the x-axis. The reference angle for an angle measured in degrees can be found by subtracting the nearest multiple of 90 degrees that is less than the angle.

For the angle 285°, the nearest multiple of 90 degrees that is less than it is 270°. Therefore, the reference angle for 285° is 285° - 270° = 15°.

Using this reference angle, we can find an angle in each quadrant with a common reference angle with 285° as follows:

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Answer:

m∠R=x=37°; m∠QOR=53°

Step-by-step explanation:

Any line that is tangent to a circle (such as QR) is perpendicular to the circle's radius (QO). Therefore, ΔOQR is a right triangle, with the right angle at Q.

1. You can use  90 + (x+16) + x = 180   or    (x+16) + x = 90 to solve for x.

2. If needed, you can then use the solution from step 1 to find the measure of ∠QOR.

Translating the shape S by the vector (  -1 , - 3 ) would lead to S ' with vertices of ( 1, -2 ), ( 1, -1 ), ( 3, -2 ), and (3, 1).

Given that the translation vector is negative, this means that you would have to subtract the corresponding values of the vector from the x and y coordinates of each vertex.

The vertices of the new shape S' would be :

Vertex 1: (2 , 1 ) + ( -1, -3 ) = ( 2 - 1 , 1 - 3 ) = ( 1, -2 )

Vertex 2: ( 2, 2 ) + ( -1, -3 ) = ( 2 - 1, 2 - 3 ) = ( 1, - 1 )

Vertex 3: ( 4, 1 ) + (-1 , -3 ) = ( 4 - 1 , 1 - 3) = (3 , -2)

Vertex 4: ( 4, 4 ) + (- 1, -3 ) = (4 - 1, 4 - 3 ) = (3 , 1 )

In conclusion, the translated vertices would be ( 1, -2 ), ( 1, -1 ), ( 3, -2 ), and (3, 1).

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Answer:

Step-by-step explanation:

The margin of error represents the range of values within which the true population mean is likely to fall with a certain level of confidence. To calculate the range of values for the actual mean number of hours spent in meetings in a week, we can use the formula:

(actual mean) = (sample mean) ± (margin of error)

Substituting the given values, we get:

(actual mean) = 4.3 ± 1.1

To find the range of values, we need to compute the upper and lower bounds of this interval:

Lower bound = 4.3 - 1.1 = 3.2 hours

Upper bound = 4.3 + 1.1 = 5.4 hours

Therefore, the actual mean number of hours spent in meetings in a week is between 3.2 and 5.4 hours.

14.4 is the value of x in triangle .

What is known as a triangle?

Three vertices make up a triangle, a three-sided polygon. The angles of the triangle are formed by the connection of the three sides end to end at a single point. 180 degrees is the sum of the triangle's three angles.  

                                Triangular shapes have three vertices, three angles, and three sides. 180 degrees is the sum of a triangle's three interior angles. The length of a triangle's two longest sides added together exceeds the length of its third side.

17² = 9² + X²

289 = 81 + x²

289 - 81 = x²

208 = x²

 x = √208

     = 14.4

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If  u = - 3i + 2i,  v = 2i - 2j and w = - 4j, 5u(3v - 4w) is a scalar quantity with a value of 440.

To evaluate the expression 5u(3v - 4w), we need to first perform the scalar multiplication and then the vector subtraction. We can start by computing the scalar multiplication of 3v - 4w:

3v - 4w = 3(2i - 2j) - 4(-4j) = 6i + 14j

Next, we can perform the scalar multiplication of u and the vector 6i + 14j:

5u(3v - 4w) = 5(-3i + 2j)(6i + 14j)

Expanding the product, we get:

5(-18i² + 36ij + 42ij - 28j²)

Since i² = j² = -1, we can simplify this expression as:

5(18 + 70) = 440

Therefore, 5u(3v - 4w) is a scalar quantity with a value of 440.

The key concept used in this problem is the distributive property of scalar multiplication over vector addition and subtraction. This property allows us to simplify expressions that involve scalar multiplication and vector operations by distributing the scalar to each component of the vector.

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The individual that will be paying the most for their purchase is: B.edgar paid with a credit card and paid the minimum payment each month

The individual that will pay the most according to the data provided is Edgar. Edgar's payment is spread out to the longest length of time. So, he will have to pay the added dues for extending his payment.

Usually, the person who pays cash pays the least amount while the person who pays in installments is charged for additional time spent in making the payment.

Complete Question:

Each of the following people bought a watch that costs $300. Which of the following people will pay the most for their purchase A.Sarah paid cash B.edgar paid with a credit card and paid the minimum payment each month C.susan paid with a credit card and paid the minimum payment plus 30 each month D. Sean paid with a credit card and paid the full balance the first of the month

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Answer:

let the children be x

let the dog be y

for the heads

x+y = 14 --- eqn 1

for the legs

2x + 4y = 40 ----- eqn2

since the children have 2 legs each and the dogs have 4 legs each

x + y = 14

2x+4y=40

through elimination method

multiply eqn1 by 2 and multiply eqn2 by 1

2x + 2y = 28

2x + 4y = 40 , then subtract

-2y = -12

to get y divide both sides by -2

y = 6

since in eqn 1

x+y=14

x = 14-y = 14-6 = 8

x = 8, y = 6

the children are 8 while the dogs are 6

The subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

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

O = (3, 2)

A = (-7, 5)

B = (-7, 2)

The distance between (or length of) the coordinates is calculated as

Length = √[(x2 - x1)² + (y2 - y1)²]

Using the above as a guide, we have the following:

OB = √[(3 -- 7)² + (2 - 2)²]

OB = √[(3 -- 7)² + 0²]

OB = √[(3 -- 7)²]

OB = 3 -- 7

AB = √[(-7 -- 7)² + (5 - 2)²]

AB = √[0² + (5 - 2)²]

AB = √[(5 - 2)²]

AB = 5 - 2

Hence, the subtraction expressions to calculate the lengths are OB = 3 -- 7 and AB = 5 - 2

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Answer:

x = 0, -1, -3

Step-by-step explanation:

Move all terms to the left side and set equal to zero. Then set each factor to equal zero.

Total area to paint: (15 + 10) - 1.5 = 23.5 sq ft

Calculate the area of each wall, subtract the door area, and sum the areas.

Front and back walls: (3 * 2.5) * 2 = 15 sq ft

Next, we calculate the area of the side walls:

Side walls: (2 * 2.5) * 2 = 10 sq ft

Door area: 1.5 * 1 = 1.5 sq ft

Total area to paint: (15 + 10) - 1.5 = 23.5 sq ft

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The Complete Question

Kara wants to paint the four outside walls of her dog's house, excluding the roof and door. The dog house measures 3 feet in length, 2 feet in width, and 2.5 feet in height. The door is 1.5 feet tall and 1 foot wide. What is the area of the surface she needs to paint?