f(x) = -2|x+4|+ 1; Find f(-9)

Answer:

Proof is given below

Step-by-step explanation:

I am not sure whether this is an acceptable answer for your teacher. But we can prove this by using proof by example

Wikipedia Definition of Proof By Example
In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof.

The smallest number considered prime is 2. The next higher prime is 3. Since p > q, we set p = 3, q=2 and p-q = 1 which is a perfect square of 1. However, (p+q) = (2+3) = 5 which is not a perfect square of any number, so both p-q and p+q cannot both be perfect squares.

Let's try with another two primes p=7, q = 3

p - q = 4 which is a perfect square of 2. But then p+q = 7 + 3 =10 which is not a perfect square of any number.

So in this case, while p-q is a perfect square, p+q is not which proves that both p-q and p+q cannot both be perfect squares

p - q and p + q cannot both be perfect squares.

Given that p and q are both prime numbers where p> q.

We need to show that p-q and p+q cannot both be perfect squares.

Let's prove by contradiction. Assume that both p - q and p + q are perfect squares. That is, there exist two integers m and n such that:

p - q = m²,

p + q = n²,

where m and n are positive integers.

Now, let's subtract the equations obtained in 1 and 2:

(n²) - (m²) = (p + q) - (p - q)

n² - m² = 2q

Now, let's factor the left side of the equation:

(n + m)(n - m) = 2q

Since q is a prime number, it only has two positive divisors: 1 and q itself. So, there are two possible cases:

Case 1: (n + m) = 2 and (n - m) = q

Adding the above two equations:

(n + m) + (n - m) = 2 + q

2n = 2 + q

Dividing by 2:

n = 1 + q/2

Since p and q are prime numbers, both are odd (greater than 2), and thus, q/2 is not an integer.

So, n cannot be an integer in this case, which contradicts our assumption.

Case 2: (n + m) = q and (n - m) = 2

Adding the above two equations:

(n + m) + (n - m) = q + 2

2n = q + 2

Dividing by 2:

n = (q + 2)/2

Again, since q is an odd prime number, (q + 2)/2 is not an integer, so n cannot be an integer in this case either, which again contradicts our assumption.

Since both cases lead to contradictions, our initial assumption that both p - q and p + q are perfect squares must be false.

Therefore, p - q and p + q cannot both be perfect squares.

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The expected number of tosses until either a head comes up or four tails are obtained is 7/4

Let X be the random variable representing the number of tosses until either a head comes up or four tails are obtained.

Let's consider the first toss. There are two possible outcomes: heads or tails. If a head comes up on the first toss, then we stop and X = 1. If a tail comes up, we need to continue tossing until we get four tails in a row or a head.

Let Y be the random variable representing the number of additional tosses needed if the first toss is a tail. There are two possible outcomes for the second toss: heads or tails. If a head comes up, we stop and X = 2. If a tail comes up, we need to continue tossing until we get three tails in a row or a head.

Similarly, we can define Z as the random variable representing the number of additional tosses needed if the first two tosses are tails. There are two possible outcomes for the third toss: heads or tails. If a head comes up, we stop and X = 3. If a tail comes up, we need to continue tossing until we get two tails in a row or a head.

Finally, let W be the random variable representing the number of additional tosses needed if the first three tosses are tails. There are two possible outcomes for the fourth toss: heads or tails. If a head comes up, we stop and X = 4. If a tail comes up, we need to continue tossing until we get four tails in a row.

We can write X in terms of Y, Z, and W as follows

X = 1 + Y if the first toss is heads

X = 1 + 1 + Z if the first two tosses are tails and the third toss is heads

X = 1 + 1 + 1 + W if the first three tosses are tails and the fourth toss is heads

X = 1 + 1 + 1 + 1 if the first four tosses are tails

Now, we need to compute the expected values of Y, Z, and W.

If the first toss is a tail, the probability of getting another tail on the second toss is 1/2, and the probability of getting a head is also 1/2. Therefore,

E[Y] = 1/2(1) + 1/2(1 + Z)

If the first two tosses are tails, the probability of getting another tail on the third toss is 1/2, and the probability of getting a head is also 1/2. Therefore,

E[Z] = 1/2(1) + 1/2(1 + W)

If the first three tosses are tails, the probability of getting another tail on the fourth toss is 1/2, and the probability of getting a head is also 1/2. Therefore,

E[W] = 1/2(1) + 1/2(4)

Note that the expected value of W is 2, not 3, because if we get three tails in a row, we stop and X = 4.

Putting it all together, we have:

E[X] = 1/2(1) + 1/2(1 + E[Z])

= 1/2(1) + 1/2(1 + 1/2(1) + 1/2(1 + E[W]))

= 1/2(1) + 1/2(1 + 1/2(1) + 1/2(1 + 2))

= 7/4

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Answer:

Step-by-step explanation:

u799

Answer: the first one is C.) The graphs are reflected across the y-axis

the second one is A.) The graphs are the same

Step-by-step explanation:

The graphs are reflected across the y-axis.

Here we have the two functions:

You can remember that for a given function f(x), a reflection over the y-axis is written as:

g(x) = f(-x).

So if we have:

f(x) = 3^x

The reflection over the y-axis gives:

g(x) = 3^(-x).

So we can conclude that the relation between the graphs is that these are reflected across the y-axis.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model. The model assumes that the value of a stock is equal to the present value of all its expected future dividends.

First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17

Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40

Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65

Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92

Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.

The present value of the dividends can be calculated as follows:

PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n)

where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value:

PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)

PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5

PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59

PV ≈ $16.22

Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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The dividend in 2018 was $2.95, and it is expected to grow at a rate of 7.4% for the next five years and 2.6% thereafter. With an equity cost of capital of 8.6%, the value per share at the end of 2018 can be calculated.

To calculate the value per share at the end of 2018, we need to discount the expected future dividends using the dividend-discount model.
The model assumes that the value of a stock is equal to the present value of all its expected future dividends. First, we need to calculate the dividends for each year from 2019 to 2023. We start with the dividend in 2018, which was $2.95. We then increase it by 7.4% each year for the next five years:

Dividend in 2019 = $2.95 * (1 + 7.4%) = $3.17
Dividend in 2020 = $3.17 * (1 + 7.4%) = $3.40
Dividend in 2021 = $3.40 * (1 + 7.4%) = $3.65
Dividend in 2022 = $3.65 * (1 + 7.4%) = $3.92
Dividend in 2023 = $3.92 * (1 + 7.4%) = $4.22

After 2023, the dividend is expected to grow at a rate of 2.6% per year. To find the value per share at the end of 2018, we discount the future dividends to their present value using the equity cost of capital of 8.6%.
The present value of the dividends can be calculated as follows:
PV = (D1 / (1 + r)) + (D2 / (1 + r)^2) + ... + (Dn / (1 + r)^n) where PV is the present value, D1 to Dn are the dividends for each year, r is the equity cost of capital, and n is the number of years.

In this case, n = 5 because we are discounting the dividends for the next five years. Let's calculate the present value: PV = ($3.17 / (1 + 8.6%)) + ($3.40 / (1 + 8.6%)^2) + ($3.65 / (1 + 8.6%)^3) + ($3.92 / (1 + 8.6%)^4) + ($4.22 / (1 + 8.6%)^5)
PV = $3.17 / 1.086 + $3.40 / 1.086^2 + $3.65 / 1.086^3 + $3.92 / 1.086^4 + $4.22 / 1.086^5
PV ≈ $2.91 + $3.07 + $3.24 + $3.41 + $3.59
PV ≈ $16.22
Therefore, the estimated value per share of Procter and Gamble at the end of 2018 using the dividend-discount model is approximately $16.22.

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Answer:

No

Step-by-step explanation:

No, it is not because the 3 dollars is a steady price. A expression will look like 7n+3. Since the 3 dollars is a steady price you can never have a unit rate.

Answer:

It's proportional

Step-by-step explanation:

10-3=7  7/1 = 7

17 - 3= 14 1 4/2 = 7

31 - 3 = 28 28/4 = 7

38 -3 = 35 35/5 = 7

73 - 3 = 70 70/10 = 7

Answer: 16.8

Step-by-step explanation: if x= 15 and y =12 we know that y =.8 of x or 4/5 of x.  Knowing this we can divide x (21) by 5 and get 4.2.  We can then multiply this and get 16.8 which is 4/5 of x(21).  y=16.8

Statistical process control (SPC) is a technique used in quality control to monitor and control a process over time

What is used to periodically check that a process is in statistical control?

a. sampling

b. scrap parts

c. the process is only measured in the beginning 100 percent inspection.

a. Sampling is used to periodically check that a process is in statistical control.

Statistical process control (SPC) is a technique used in quality control to monitor and control a process over time. SPC involves collecting and analyzing data on the process, and using statistical methods to determine whether the process is in statistical control (i.e., producing consistent and predictable results) or is out of control (i.e., producing inconsistent or unpredictable results).

One way to monitor a process using SPC is to use sampling. This involves taking a sample of parts or products from the process at regular intervals, and measuring certain characteristics of the sample (such as dimensions, weight, or color). The data collected from the samples can then be analyzed using statistical methods to determine whether the process is in control or out of control.

If the data collected from the samples indicates that the process is out of control (i.e., producing inconsistent or unpredictable results), corrective action can be taken to bring the process back into control. By regularly monitoring and adjusting the process using SPC techniques like sampling, organizations can ensure that their processes are producing consistent and high-quality results.

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The quadrilateral WXYZ is not a square using the distance formula

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

W(-1,1),X(3,4),Y(6,0) and Z(2,3)

The lengths of the sides can be calculated using the following distance formula

Length = √[Change in x² + Change in y²]

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

WX = √[(-1 - 3)² + (1 - 4)²] = 5

XY = √[(3 - 6)² + (4 - 0)²] = 5

YZ = √[(6 - 2)² + (0 - 3)²] = 5

ZW = √[(2 + 1)² + (3 - 1)²] = 13

The sides that are congruent are WX, XY and YZ

This means that WXYZ is not a square

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The unit rate for the turtle crawling is 1 mile per hour

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

Unit rate is the ratio of two different units, and also having a denominator of one.

For every of an hour that the turtle is crawling, he can travel of a mile. Hence:

Unit rate of crawling = 1 mile / 1 hour = 1 mile per hour

The unit rate for the turtle crawling is 1 mile per hour

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Answer:

4 ( n + 2 )

\(4(n + 2)\)

Answer:

12:55

Step-by-step explanation:

12 + 8+ 9 + 10 + 16 = 55

good luck, i hope this helps :)

Answer:

12/55

Step-by-step explanation:

Answer:

5/8 + 1/2 = 1 1/8

1/2 = 4/8

5/8 + 4/8 = 9/8

9/8 = 1 1/8

Those are the steps. Sorry for not doing it right earlier.

Step-by-step explanation:

5/8 + 1/2= 5/8+ 1 · 4/2 · 4 = 5/8+ 4/8 = 5 + 4/8= 9/8

It is suitable to adjust both fractions to a common equal, identical denominator for adding, subtracting, and comparing fractions. The common denominator you can calculate as the least common multiple of both denominators - is LCM(8, 2) = 8. It is enough to find the common denominator, not necessarily the lowest, by multiplying the denominators: 8 × 2 = 16. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - five-eighths plus one-half is nine-eighths.

(a) To compute the limit lim (x,y)→(0,0) x² + y² / xy, we need to evaluate the expression as (x,y) approaches (0,0). We will determine whether the limit exists by considering different paths of approach.

(b) To compute the limit lim (x,y)→(0,0) x² + y² / (x²)(y²), we will also evaluate the expression as (x,y) approaches (0,0) and analyze the existence of the limit using different paths of approach.

(a) Let's consider the limit lim (x,y)→(0,0) x² + y² / xy. If we approach (0,0) along the line y = mx, where m is a constant, the limit becomes

lim (x, mx)→(0,0) x² + (mx)² / x(mx).

Simplifying this expression, we get lim (x,mx)→(0,0) (1 + m²) / m.

This limit does not exist since it depends on the value of m.

Therefore, the limit lim (x,y)→(0,0) x² + y² / xy does not exist.

(b) Now let's consider the limit lim (x,y)→(0,0) x² + y² / (x²)(y²).

Using similar reasoning as in part (a), if we approach (0,0) along the line y = mx, the limit becomes lim (x, mx)→(0,0) x² + (mx)² / (x²)(m²x²).

Simplifying this expression, we get lim (x,mx)→(0,0) (1 + m²) / (m²x²). Since the limit does not depend on x, it becomes lim (x,mx)→(0,0) (1 + m²) / (m²). This limit exists and is equal to 1/m².

However, the value of this limit depends on the constant m, indicating that the limit lim (x,y)→(0,0) x² + y² / (x²)(y²) does not exist.

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Answer:

dollars per mile

$0.90 per mile

Step-by-step explanation:

Since you are interested in the price of a 42-mile ride, you need a unit cost of dollars per mile. The time the trip takes does not matter.

unit price in dollars per mile = (price)/(number of miles)

unit price = $50.40/(56 miles) = $0.90/mile

Answer the unit price is $0.90 per mile

Answer:

-1/6 n < -9

Step-by-step explanation:

Negative one-sixth of a number

-1/6 n

is less than -9

-1/6 n < -9

The answer is , an approx. value of m such that the equation cos(x) = mx has exactly two solutions is m = 1 and m = -0.3183

To find an approximate value of m such that the equation cos(x) = mx has exactly two solutions, we can use the fact that the graph of y = cos(x) intersects the line y = mx at exactly two points.

The graph of y = cos(x) is a periodic function with a maximum value of 1 and a minimum value of -1.

Since we want the line y = mx to intersect the graph of y = cos(x) at exactly two points, the slope m must satisfy the condition -1 ≤ m ≤ 1.

Furthermore, for the line y = mx to intersect the graph of y = cos(x) at exactly two points, the line must pass through the maximum and minimum points of the graph of y = cos(x).

These occur at x = 0 and x = π.

At x = 0, we have cos(0) = 1 and the equation cos(x) = mx becomes 1 = m(0), which simplifies to m = 1.

At x = π, we have cos(π) = -1 and the equation cos(x) = mx becomes -1 = m(π), which simplifies to m = -1/π.

Therefore, an approx. value of m such that the equation cos(x) = mx has exactly two solutions is m ≈ 1 and m ≈ -0.3183 (rounded to four decimal places).

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Answer:

a₁ = 8 and r = 16

Step-by-step explanation:

the sequence has a common ratio r between consecutive terms and is therefore geometric , that is

r = \(\frac{a_{2} }{a_{1} }\) = \(\frac{2^{7} }{2^3}\) = \(2^{(7-3)}\) = \(2^{4}\) = 16

r = \(\frac{a_{3} }{a_{2} }\) = \(\frac{2^{11} }{2^7}\) = \(2^{(11-7)}\) = \(2^{4}\) = 16

r = \(\frac{a_{4} }{a_{3} }\) = \(\frac{2^{15} }{2^{11} }\) = \(2^{(15-11)}\) = \(2^{4}\) = 16

the first term a₁ = 2³ = 8

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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Answer:

multiplication

Step-by-step explanation:

Answer:

n=11

Step-by-step explanation:

an=a1+(n-1)d

14=-36+(n-1)5

14=-36+5n-5

14+36+5=5n

55=5n

n= 11

Answer:

Step-by-step explanation:

Pa:

14/84 = 2/12

28/84 = 4/12

7/84 = 1/12

35/84 = 5/12

Pb:

1/8

3/8

1/8

3/8

Answer:

10

Step-by-step explanation:

a^2 +b^2=c^2

6^2 +8^2 = c^2

6×6 is 36

8×8 is 64

36+64 = 100

So 100=c^

Now you need to square root 100

Which is 10

:) I hope that helps

This is Pythagoras theorum

A and b are the shorter sides and make an L shape

The longer side is always c

If you are able to rearrange formulas, I think that would help you a ton x

Answer:

Step-by-step explanation:

12 x 3 = 36

answer is 36

Answer:

12 x 3 = 36

Step-by-step explanation:

value of x is 11.

hope this answer helps you dear....take care and may u have a great day ahead!

The color gradient will vary depending on the height values, with distinct colors representing different average heights. This visualization makes it easier to compare average heights across gender and age groups.

If you drag the average height measure to the color box and select the mark type to be a square, each cell in the table will be represented by a square. The color of the square will correspond to the average height of patients within that particular gender and age group. So, for example, if the average height of male patients aged 20-30 is 6 feet, the corresponding square in the table will be colored to indicate this height range.
When you drag the average height measure to the color box and select the mark type as a square, the cells in the table will display square-shaped marks. Each square's color will represent the average patient height for each specific gender and age group.

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