Determine the range of f(x) = |x| + 3

Step-by-step explanation:

If the points are (-1/2, 1/2) and (-2/1, 2/1) then you can enter these into the Slope equation

(y1 - y2) / (x1 - x2)

1/2 - 2/1 = 1/2 - 4/2 = - 3/2 or - 1.5

-1/2 - (-2/1) = - 1/2 + 4/2 = 3/2 or 1.5

So your Slope is -1.5/1.5 = - 1

Answer:

4 : 2 : 5

Step-by-step explanation:

To find the ratio of silver to brown to pink counters in simplest form, we need to divide the number of each type of counter by their greatest common factor.

The greatest common factor of 16, 8, and 20 is 4.

So, we divide each of the numbers by 4:

Silver counters: 16 ÷ 4 = 4

Brown counters: 8 ÷ 4 = 2

Pink counters: 20 ÷ 4 = 5

Therefore, the ratio of silver to brown to pink counters in simplest form is:

4 : 2 : 5

or

2 : 1 : 2.5 (if we prefer to express the ratio in decimal form)

f(x) = 3x^2 + 6 ​

0 = 3x^2 + 6 (Replacing f(x) by 0)

-6 = 3x^2 (Subtracting 6 from both sides of the equation)

-6/3 = x^2 (Dividing by 3 on both sides of the equation)

-2 = x^2 (Dividing)

There are no real solutions. The complex solutions are:

Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

In this scenario, there are four people in a room. Three of them possess pairs corresponding to a Shamir secret sharing scheme, enabling any two people to determine the secret.

The remaining person is a foreign agent who has chosen a pair randomly. Thus, if any two of the three people with the valid pairs collaborate, they can successfully uncover the secret, as per the properties of the Shamir secret sharing scheme.

The presence of the foreign agent does not affect the security of the scheme unless they collaborate with another person possessing a valid pair.

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The factored form of the given trinomial expression: x² + 0x - 9 after using the diamond method is (x + 3)(x - 3).

The diamond method, also known as the box method or the X method, is a visual method for factoring quadratic trinomials of the form ax^2 + bx + c, where a, b, and c are constants.

The diamond method involves four steps:

Step 1: Write down the trinomial in standard form: ax² + bx + c.

Step 2: Draw a box and divide it into four cells by drawing a diagonal line.

Step 3: Write the coefficient a in the upper left cell of the box and the constant term c in the lower right cell.

Step 4: Find two numbers whose product is ac (the product of the coefficients of the leading and constant terms) and whose sum is b (the coefficient of the middle term).

Yes, there is another way to rewrite the trinomial that can make factoring easier. The trinomial x² + 0x - 9 can be rewritten as:

x² - 9

This is a difference of squares because 9 is a perfect square and can be written as 3². So, we can factor this expression using the formula for the difference of squares:

x² - 9 = (x + 3)(x - 3)

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The correlation coefficient is 0.9541. This can be determined from the information provided in the ANOVA table, specifically the regression sum of squares (SSR) and the total sum of squares (SST).

The correlation coefficient, also known as the Pearson correlation coefficient, is a measure of the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where values closer to -1 or 1 indicate a stronger relationship, and values closer to 0 indicate a weaker relationship.

To calculate the correlation coefficient, we can use the formula:

r = sqrt(SSR/SST)

From the ANOVA table provided, we can see that SSR = 12,323.64 and SST = 13,538.4. Plugging these values into the formula gives:

r = sqrt(12,323.64/13,538.4) = 0.9541

Therefore, the correlation coefficient for this model is 0.9541, indicating a strong positive linear relationship between the independent variable and the dependent variable

Complete Question:

Using the following information. Coefficients -12.8094 Intercept Independent variable 2.1794 ANOVA df SS MS F 1 90.0481 Regression Residual Total 12,323.64 1,214.762 13,538.4 12,323.64 136.8550 8 1° 9 What is the correlation coefficient? Multiple Choice 0.9103 0.9541 -0.9541

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Answer:

The expression for Annika is $ 4x and Chris is $ (x + 10).

Step-by-step explanation:

Given that Annika has 4 times more than Bob and Chris has $10 more than Bob. So the expressions will be :

Annika = 4 × x = 4x

Chris = 10 + x

Answer:

Annika has 4x

Chris has (x + 10)

Hope i helped

The number of plastic tubing needed to fit around the edge of the pool is 423.3 ft².

The number of plastic tubing needed to fit around the area is calculated from the difference between the area of the rectangle and area of the circular pool.

Area of the circular pool is calculated as;

A = πr²

where;

A = π (15 ft / 2)²

A = 176.7 ft²

The area of the rectangle is calculated as follows;

A = length x breadth

A = 20 ft x 30 ft

A = 600 ft²

The number of plastic tubing needed to fit around the edge of the pool is calculated as;

The difference in the area = 600 ft² - 176.7 ft² = 423.3 ft²

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Lisa bowling score is 100.

John bowling score is 282.

What is linear expression?

A linear expression is an algebraic statement where each term is either a constant or a variable raised to the first power.

Given that;

Lisa and John are bowling.

Johns score is three times the difference of Lisa's score and 6.

The sum of their scores is 382.

Now, Let Lisa bowling score = x

Then, John bowling score = 3 (x - 6)

Since, The sum of their scores is 382.

Hence,

x + 3 ( x - 6 ) = 382

After solving,

x + 3x - 18 = 382

4x = 382 + 18

4x = 400

x = 100

Hence, Lisa bowling score = x = 100

And, John bowling score = 3 (x - 6)

                                       = 3 (100 - 6)

                                       = 3 × 94

                                       = 282

Therefore, Lisa bowling score is 100.

And, John bowling score is 282.

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Answer:

90/125*100=9000/125

9000/125=72

72%

Answer:

Its 23

Step-by-step explanation:

7 – 5p + 3q

                 = 7 – 5(1) + 3(7)

                = 7 – 5 + 21

                = 28 – 5

               = 23

Answer: 12 m

Step-by-step explanation:he path of a football has been modeled by the equation:

Answer: 39.06

Step-by-step explanation:

The probability that you are right is 0%.

Alice draws a 2-card hand from a standard 52-card deck, which means there are only four aces in the deck. On the other hand, Bob rolls two dice, each with six sides, so there are only two ways to roll two aces: rolling a double 1 or rolling a double 6. These events are much less likely compared to Alice drawing two aces from the deck.

Given that the game show host tells you that the mystery person obtained two aces, the only possible explanation is that it must be Alice. Bob simply does not have a high enough probability of rolling two aces to be considered as the mystery person in this scenario.

In summary, because Bob's chances of rolling two aces are significantly lower than Alice's chances of drawing two aces, the probability of you being right by guessing Bob is 0%.

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Answer:

it is -5 if I'm not mistaking

Id she walks 2 miles every 12 minutes

2 4 6. 8 10

12 24 26 48 60

60 is an hour therefore she'll walk 10 miles per hour.

Answer:

6 miles per hour

Step-by-step explanation:

12 divided by 2 is 6 miles per hour

Answer:

Step-by-step explanation:

The question has asked who has taken fewer than 15 courses

There are 4 options that are fewer than 15: 10, 8, 8, 13

4/10  (10 is total number of options/students)

To find the percentage you...

Answer: 198 tickets

Step-by-step explanation: 1584/8 = 198

Since 56 pints of Cold Farm ice cream cost $140, and 28 quarts of Cold Farm, ice cream cost $133, hence the large size container is the better deal for Sheldon.

From the table, we are told that 1 pint of Cold farm costs $2.50, this can be written as:

56pints of the cold farm will cost (56 * 2.50) = $140

Similarly, 1 quartz of Cold farm costs $4.75, this can be written as:

28pints of the cold farm will cost (28 * 4.75) = $133

56 pints of Cold Farm ice cream cost $140, and 28 quarts of Cold Farm, ice cream cost $133, hence the large size container is the better deal for Sheldon.

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Answer:

-8p -2

Step-by-step explanation:

(-7p + 10) - (p + 12) =

-7p + 10 - p - 12 =

-8p -2

Answer:

Solution given:

let the two bags of pickle & chips and be x and y.

according to the question

x+2y=$3.25

again

3x+4y=$7.25 is a second equation.

Answer:

x=150

Step-by-step explanation:

i think this is it sorry if not

Answer:

I would say B only IV because all of the others are assuming and there's no way to prove true or not.

Step-by-step explanation:

A diverse workforce can provide a source of competitive advantage by suggesting goods and services that will allow the company to increase its market by catering to a broader customer base.

When an organization embraces diversity and inclusion, it brings together individuals from different backgrounds, cultures, experiences, and perspectives. This diverse pool of employees can offer unique insights and ideas that might otherwise go unnoticed, leading to innovative product development and improved customer experiences.

By having a workforce that represents a wide range of demographics, including race, ethnicity, gender, age, sexual orientation, and more, a company can better understand the needs and preferences of various customer segments. This understanding enables them to develop and market products and services that resonate with a larger audience, ultimately increasing market share and revenue.

A diverse workforce enhances creativity and problem-solving abilities within the organization. Diverse teams bring different ways of thinking and approaching challenges, fostering an environment of innovation and adaptability. This can lead to the development of groundbreaking solutions that meet the evolving demands of an increasingly diverse consumer market.

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Answer:

It should be D, For each there are 4 markers.

Step-by-step explanation:

Given: there are 100 markers and 25 students

So each student, there are 4 markers.

4 x 25 is 100

Therefore the answer is D.

Answer:

Because they are both negative that means they are on the left side so -0.4 is closer to the 0 so less.

Answer:

A) 143

B) 13.79

C) 14

Step-by-step explanation:

Frances can complete 91 oil changes in 7 days.

In 1 day, Frances can complete 91/7 = 13 oil changes.

In 11 days, Frances can complete 13 × 11 = 143 oil changes.

At the market, 5 light bulbs cost $9.85.

1 light bulb costs 9.85/5 =  $1.97.

7 light bulbs cost 1.97 × 7 = $13.79.

Henry can read 5.25 pages in 3 hours.

Henry can read 5.25/3 = 1.75 pages in 1 hour.

In 8 hours, Henry can read 1.75 × 8 = 14 pages.

Answer:

x= 8

Step-by-step explanation:

12x - 8 = 3x + 64

12x - 3x = 64 + 8

9x = 72

x= 72÷9

x = 8

Answer:

x=8

Step-by-step explanation:

12x-8=3x+64 ( collect like terms)

=12x-3x=64+8 (add or subs like terms)

=9x=72 (divided both sign by 9)

=9x/9=72/9=8

x=8

Answer:

54%

Step-by-step explanation:

2750 is nothing but 54100 if you multiply the numerator and denominator by 2. Now that we have a value over 100, we just have to multiply the entire by 100. The denominator will be canceled, and we're left with 54%

Answer:

54%

Step-by-step explanation:

to find a percentage you must have the denominator (bottom number) that is 100

to get the denominator to 100 you must multiply it by 2

that means you multiply the top and bottom by 2

27 * 2 / 50 * 2

54 / 100

a percentage is a number over 100 and this percentage is 54%

The transfer functions for the given systems represented in state space are: a. G(s) = (s+5)/(s²+ s - 10), b. G(s) = (3s² - 13s + 2)/(s³ - 3s² + 4s + 10) and c. G(s) = (7s² - 10s + 24)/(s³ + 9s²+ 28s + 20)

To find the transfer function G(s) = Y(s)/R(s) for each of the given systems represented in state space, we can use the formula:
G(s) = C(sI - A)^-1B + D
where A, B, C, and D are matrices obtained from the given state space representation. Let's find the transfer function for each system:

a. Given state space representation:
x = [ 0  0  -3 ]   x + [ 0 ]   r
       [ 1  0  -2 ]        [ 0 ]
       [ 0  1  -5 ]        [ 0 ]

Output equation: y = [ 1  0  0 ]  x

To find the transfer function, we need to calculate the matrices A, B, C, and D.

A = [ 0  0  -3 ]
      [ 1  0  -2 ]
      [ 0  1  -5 ]

B = [ 0 ]
      [ 0 ]
      [ 0 ]
C = [ 1  0  0 ]
D = [ 0 ]
Now, we can substitute these matrices into the transfer function formula:
G(s) = C(sI - A)^-1B + D

Calculating (sI - A):

sI - A = [ s   0   0 ] - [ 0  0  -3 ] = [ s   0    3 ]
            [ 0   s   0 ]     [ 1  0  -2 ]      [ -1  s   2 ]
            [ 0   0   s ]     [ 0  1  -5 ]      [ 0   -1  s+5 ]

Calculating (sI - A)^-1:

(sI - A)^-1 = [ (s+5)/(s² + s - 10)    3/(s² + s - 10)    3/(s+ s² - 10) ]
                       [ (-1)/(s² + s - 10)    s/(s² + s - 10)    2/(s² + s - 10) ]
                       [ 0   -1/(s² + s - 10)    (s+5)/(s² + s - 10) ]

Calculating C(sI - A)^-1B:
C(sI - A)^-1B = [ 1  0  0 ] [ (s+5)/(s²+ s - 10)    3/(s²+ s - 10)    3/(s²+ s - 10) ] [ 0 ] = (s+5)/(s²+ s - 10)
Finally, adding D:
G(s) = (s+5)/(s² + s - 10) + 0 = (s+5)/(s²+ s - 10)

b. Given state space representation:
x = [ 2  0  -3 ]   x + [ 1 ]   r
       [ -3  5  -5 ]        [ 4 ]
       [ -8  3  -4 ]        [ 6 ]

Output equation: y = [ 1  3  6 ]  x

Following the same steps as above, we find:

A = [ 2  0  -3 ]
      [ -3  5  -5 ]
      [ -8  3  -4 ]

B = [ 1 ]
      [ 4 ]
      [ 6 ]

C = [ 1  3  6 ]

D = [ 0 ]

Calculating (sI - A):

sI - A = [ s-2   0    3 ]
            [ 3   s-5   5 ]
            [ 8   -3   s+4 ]

Calculating (sI - A)^-1:
(sI - A)^-1 = [ (s+5)/(s³ 3s² + 4s + 10)    3/(s³ - 3s² + 4s + 10)    3/(s³ - 3s²+ 4s + 10) ]
                       [ (-3)/(s³ - 3s² + 4s + 10)    (s+2)/(s³ - 3s²+ 4s + 10)   5/(s³ - 3s²+ 4s + 10) ]
                       [ 8/(s³- 3s²+ 4s + 10)   -3/(s^3 - 3s² + 4s + 10)    (s-5)/(s³ - 3s² + 4s + 10) ]

Calculating C(sI - A)^-1B:

C(sI - A)^-1B = [ 1  3  6 ] [ (s+5)/(s³- 3s² + 4s + 10)    3/(s³ - 3s² + 4s + 10)    3/(s³ - 3s² + 4s + 10) ] [ 1 ] = (3s² - 13s + 2)/(s³ - 3s² + 4s + 10)

Finally, adding D:

G(s) = (3s² - 13s + 2)/(s³ - 3s² + 4s + 10) + 0 = (3s² - 13s + 2)/(s³- 3s²+ 4s + 10)

c.  Given state space representation:
x = [ 3  1  -3 ]   x + [ 5 ]   r
       [ -5  -8  -6 ]        [ -3 ]
       [ 2  7  2 ]        [ 2 ]

Output equation: y = [ 0  5  2 ]  x

Following the same steps as above, we find:

A = [ 3  1  -3 ]
      [ -5  -8  -6 ]
      [ 2  7  2 ]

B = [ 5 ]
      [ -3 ]
      [ 2 ]

C = [ 0  5  2 ]

D = [ 0 ]

Calculating (sI - A):

sI - A = [ s-3   -1    3 ]
            [ 5   s+8   6 ]
            [ -2   -7   s-2 ]

Calculating (sI - A)^-1:

(sI - A)^-1 = [ (s² - 6s + 9)/(s³ + 9s² + 28s + 20)    (-s+2)/(s³ + 9s² + 28s + 20)    (-3)/(s^3 + 9s² + 28s + 20) ]
                       [ (-5)/(s³+ 9s² + 28s + 20)    (s²- 10s + 4)/(s³ + 9s² + 28s + 20)    (-6)/(s³ + 9s² + 28s + 20) ]
                       [ (2)/(s³+ 9s² + 28s + 20)   (7)/(s³+ 9s² + 28s + 20)    (s² - 8s + 6)/(s³+ 9s² + 28s + 20) ]

Calculating C(sI - A)^-1B:

C(sI - A)^-1B = [ 0  5  2 ] [ (s- 6²s + 9)/(s³ + 9s² + 28s + 20)    (-s+2)/(s³ + 9s² + 28s + 20)    (-3)/(s³ + 9s² + 28s + 20) ] [ 5 ] = (7s² - 10s + 24)/(s³+ 9s² + 28s + 20)

Finally, adding D:

G(s) = (7s² - 10s + 24)/(s³ + 9s² + 28s + 20) + 0 = (7s²- 10s + 24)/(s³ + 9s²+ 28s + 20)

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