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Answer: no

Step-by-step explanation:

an example of a linear equation is x + 1. linear means a straight line. In a linear, the highest exponent on the x opponent is 1. in the equation 3x^2 + 2, the highest exponent on the x opponent is 2 which means this is a quadratic not a linear.

Answer:

a) 17/9

b) 25/39

Step-by-step explanation:

a)  3 2/5 to 1 4/5

17/5 to 9/5

The ration of fractions is 17/5 / 9/5  = 17/9

b) 2 4 /3  to 1 / 5 5

10/3 to 26/5

25/39

a. Given that the GST is 7% of the selling price, we can calculate the GST for different selling prices within the given range.

Selling Price (x) | GST (y)

$30 | $2.10

$31 | $2.17

$32 | $2.24

$33 | $2.31

$34 | $2.38

$35 | $2.45

$36 | $2.52

$37 | $2.59

$38 | $2.66

$39 | $2.73

$40 | $2.80

$41 | $2.87

$42 | $2.94

$43 | $3.01

$44 | $3.08

$45 | $3.15

$46 | $3.22

$46.50 | $3.26

(b) The GST for a selling price of $37.50 is approximately $2.63.

c The selling price for a GST of $3.02 is approximately $43.01.

d. The gradient in this case is approximately 0.0703.

b.It should be noted that we can estimate the GST by taking the average of the two values:

GST = ($2.59 + $2.66) / 2 = $2.625

Therefore, the GST for a selling price of $37.50 is approximately $2.63.

(c) Selling Price = $43 + ($3.02 - $3.01) * (($44 - $43) / ($3.08 - $3.01))

Selling Price = $43 + 0.01 * (1) = $43.01

Therefore, the selling price for a GST of $3.02 is approximately $43.01.

(d) The gradient of the graph represents the rate of change of the GST with respect to the selling price. In this case, the gradient is constant since the GST is a fixed percentage of the selling price.

Gradient = Change in GST / Change in Selling Price

Let's take two points from the table: ($30, $2.10) and ($46.50, $3.26)

Change in GST = $3.26 - $2.10 = $1.16

Change in Selling Price = $46.50 - $30 = $16.50

Gradient = $1.16 / $16.50 ≈ 0.0703

The gradient in this case is approximately 0.0703. This value represents the constant rate at which the GST increases for each unit increase in the selling price. In other words, for every dollar increase in the selling

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The NPV is positive, it is worth taking the Investment.

Net Present Value (NPV) is an assessment method that determines the attractiveness of an investment. It is a technique that determines whether an investment has a positive or negative present value.

This method involves determining the future cash inflows and outflows and adjusting them to their present value. This helps determine the profitability of the investment, taking into account the time value of money and inflation.The formula for calculating NPV is:

NPV = Σ [CFt / (1 + r)t] – CIWhere CFt = the expected cash flow in period t, r = the discount rate, and CI = the initial investment.

The given problem can be solved by using the following steps:

Calculate the present value (PV) of the expected cash inflows:

Year 1: $28,000 / (1 + 0.08)¹ = $25,925.93Year 2: $28,000 / (1 + 0.08)² = $24,009.11Year 3: $28,000 / (1 + 0.08)³ = $22,173.78Total PV = $72,108.82

Calculate the PV of the initial investment: CI = $7,000 / (1 + 0.08)¹ + $35,000 / (1 + 0.08)²CI = $37,287.43Calculate the NPV by subtracting the initial investment from the total PV: NPV = $72,108.82 – $37,287.43 = $34,821.39

Since the NPV is positive, it is worth taking the investment.

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To determine the length of BE, we can use the concept of the triangle's side lengths and apply the Triangle Inequality Theorem.

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, we can apply it to triangle ABC, where AC is the longest side.

Given the lengths AE = 3, DE = 5, and CE = 2, we can conclude that AC > AE and AC > CE.

Now, let's focus on triangle ABE. Since AC is the longest side, we can conclude that AB + BE > AE.

Substituting the known values, we have:

AB + BE > 3

Rearranging the inequality, we get:

BE > 3 - AB

To find the length of BE, we need to determine the value of AB. Unfortunately, the length of AB is not provided in the given information. Therefore, without knowing the value of AB, we cannot determine the exact length of BE.

In conclusion, without additional information or the length of AB, we cannot calculate the exact length of BE.

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-83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

Two or more expressions with an Equal sign is called as Equation.

Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

4357/21 - 4200

Take LCM as 21.

4357-88200/21

-83843/21

=-3992.5

Hence -83843/21 is the partial fraction of Four thousand three hundred fifty seven divided by twenty one minus four thousand two hundred.

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\(\sf \longrightarrow \: \:Surface \: area \: of \: cylinder \: = \: 2\pi \: r \: h \: + \: 2\pi \: {r}^{2} \)

\(\sf \longrightarrow \: \: r \: = \: \frac{Diameter}{2} \\ \)

\(\sf \longrightarrow \: \: r \: = \: \frac{12}{2} \\ \)

\(\sf \longrightarrow \: \: r \: = \: \cancel\frac{12}{2} \: \: ^{6} \\ \)

\(\sf \longrightarrow \: \: r \: = \:6 \: ft\)

\(\sf \longrightarrow \: \: h \: = \: 15 \: ft\)

\(\sf \implies \: \:2 \: \times \: \pi \times \: 6 \: \times \: 15 \: \: + \: \: 2 \: \times \: \pi \times \: {6}^{2} \)

\(\sf \implies \: \:2 \: \times \: \pi \times \: 90 \: \: + \: \: 2 \: \times \: \pi \times \: 36\)

\(\sf \implies \: \:180 \: \pi \: + \: \: 72 \: \pi\)

\(\sf \implies \: \:252 \: \pi\)

Hence, the surface area of cylinder is 252 π ft²

(a) To demonstrate graphically that the feasible region is unbounded, we can plot the given constraints on a graph. The first constraint, -2x1 + 3x2 ≤ 12, can be represented by a line. The second constraint, -3x1 + 2x2 ≤ 12, can also be represented by a line. Additionally, we have the constraints x1 ≤ 0 and x2 ≤ 0, which define the non-positive regions of the x1 and x2 axes, respectively. By combining these constraints, we can see that there are no upper bounds on the feasible region in the positive direction for either x1 or x2. This indicates that the feasible region is unbounded.

(b) When the objective is to maximize Z = 4x1 + x2, the model does not have an optimal solution. Since the feasible region is unbounded, we can continuously increase the values of x1 and/or x2, resulting in an infinitely increasing objective function value. Therefore, there is no maximum value for Z in this case.

(c) When the objective is to maximize Z = x1 - x2, the model also does not have an optimal solution. Similar to part (b), the feasible region being unbounded allows us to continuously increase the values of x1 and/or decrease the values of x2, resulting in an infinitely increasing objective function value. Thus, there is no maximum value for Z.

(d) The fact that the model does not have an optimal solution does not mean that there are no good solutions according to the model. It simply implies that the objective function cannot be maximized or minimized within the given constraints. There could still be feasible solutions that satisfy the constraints, but they do not result in an optimal value for the objective function.

(e) To select an objective function for which the model has no optimal solution, we can consider an objective such as Z = x1 + x2. Using the simplex method step by step, we would observe that the algorithm does not terminate and continues to iterate indefinitely. This indicates that Z is unbounded, as the objective function value can increase without bound.

(f) Using a software package based on the simplex method, we can confirm that Z is unbounded for the selected objective function. The software would iterate through the simplex algorithm and indicate that the solution is unbounded, meaning there is no maximum or minimum value for the objective function within the given constraints.

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Answer:

180.....1888888888888888

Answer:

90 degrees

Step-by-step explanation:

Decagon interior angles: 1,440 degrees

1440 - 1170 = 270

270/3 = 90

To find the expected number of times Joan rolls a 3, we use the formula for mean of a binomial distribution.

The correct option is, option (C) 6.

The probability of rolling a number 3 on any given roll is 1/4

If Joan rolls the die 20 times, the number of times she rolls a 3 will follow a binomial distribution with n = 20 (number of trials) and p = 1/4 (probability of success).

The formula for the probability mass function of a binomial distribution is:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where X is the random variable representing the number of successes (the number of times Joan rolls a 3), k is the number of successes, n is the number of trials, p is the probability of success, and (n choose k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items.

Using this formula, we can calculate the probability of rolling a 3 exactly k times out of 20 rolls:

P(X=k) = (20 choose k) * (1/4)^k * (3/4)^(20-k)

To find the expected number of times Joan rolls a 3, we can use the formula for the mean of a binomial distribution:

E(X) = n * p

In this case, E(X) = 20 * 1/4 = 5

Therefore, the expected number of times Joan rolls a 3 is 5.

Since the possible answers are integers, the closest answer to 5 is 6. Therefore, the answer is (C) 6.

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Answer:

AB=6 Units

Step-by-step explanation:

Given the following lengths of rectangle ABCD and its dilation A'B'C'D' respectively

We are to determine the length of AB. To do this, we first determine the dilation factor.

\(D$ilation Factor =\dfrac{B'C'}{BC} =\dfrac{9.5}{3.8} =2.5\)

Therefore:

\(\dfrac{A'B'}{AB} =2.5\\\\\dfrac{15}{AB} =2.5\\$Cross multiply \\ 2.5 AB =15 \\AB=15 \div 2.5\\$Therefore, AB=6 Units\)

Answer:

6 units

Step-by-step explanation:

edge 2022

Answer:

n=-9

Step-by-step explanation:

Solution for -8-5n=64+3n equation: Simplifying -8 + -5n = 64 + 3n Solving -8 + -5n = 64 + 3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3n' to each side of the equation. -8 + -5n + -3n = 64 + 3n + -3n Combine like terms: -5n + -3n = -8n -8 + -8n = 64 + 3n + -3n Combine like terms: 3n + -3n = 0 -8 + -8n = 64 + 0 -8 + -8n = 64 Add '8' to each side of the equation. -8 + 8 + -8n = 64 + 8 Combine like terms: -8 + 8 = 0 0 + -8n = 64 + 8

Answer:

Answer is -6t

Step-by-step explanation:

\({ \tt{ = (6 \cos(20\pi t) \cos(\pi) + 6\sin(20\pi t) \sin(\pi) ) + 6 \sqrt{3} ( \cos(20\pi t) \cos( \frac{\pi}{2} ) + \sin(20\pi t) \sin( \frac{\pi}{2} )) }} \\ = { \tt{ (- 6t + 0) + (0 + 0)}} \\ = { \tt{ - 6t}}\)

Note that π is 180°

Answer:

√61

Step-by-step explanation:

→ Find the distance between y coordinates

2 --4 = 6

→ Find distance between x coordinates

2--3 = 5

→ Find distance

√6² + 5² = √36 + 25 = √61

Step-by-step explanation:

1. The length is one more thrice it's width. The height is 4 more than it width. We can represent the

\((3x + 1)(x + 4)\)

\((3 {x}^{2} + 13x + 4)x = 720\)

Multiply it by x.

\(3 {x}^{3} + 13 {x}^{2} + 4x = 720\)

\( 3{x}^{3} + 13 {x}^{2} + 4 x - 720\)

The possible roots

The possible roots are plus or minus is1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360, and 720. By a long list of substitution, 5 is a root. So this means that x=5. So the width has to be

\(x = 5\)

2. First. we apply the Rational Root Theorem so the possible roots are plus or minus 1,2,3,6.

Let check via synethic division to see which are roots.

Let try 1 and -1 first. If we plug 1 into the equation, we get

\(1 - 2 - 5 + 6 = 0\)

So 1 or (x-1) is a solution. Since it's a solution we can divide this into our original polynomial to get us a new polynomial that is more simplified. If we apply synthetic division, we get a new polynomial in

\( {x}^{2} - x - 6\)

We can then factor this into

\((x - 3)(x + 2)\)

So our roots or factors is

\((x - 1)(x - 3)(x + 2)\)

Answer:

1,200

Step-by-step explanation:

The formula for Simple Interest is I=prt p=principal r=rate expressed as decimal t=time in years

I=1,000*0.05*4

0.05 because 5% in decimal form it’s 0.05

4 because 48months dived by 12= 4 years

200=1,000*0.05*4 The interest is 200 but they are asking for the total value so then you add the amount you initiated with 1,000+200=1,200

This pseudocode outlines the basic steps for implementing the discretized PID controller in a digitized environment.

Here's the pseudocode for implementing the discretized PID controller in a digitized environment:

```

Read input signal

Initialize controller outputs

While loop until process is stopped:

   Calculate error = setpoint - process variable

   Calculate PID outputs using PID formula

   Compute new control output using PID outputs and discretized controller

   Apply control output to the process

End while loop

```

In this pseudocode, you first read the input signal and initialize the controller outputs. Then, in a loop that continues until the process is stopped, you calculate the error by subtracting the setpoint from the process variable.

Next, you calculate the PID outputs using the PID formula. After that, you compute the new control output by combining the PID outputs with the discretized controller. Finally, you apply the control output to the process. The loop continues until the process is stopped.

This pseudocode outlines the basic steps for implementing the discretized PID controller in a digitized environment.

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Answer:

more than 5 sacks

Step-by-step explanation:

1 1/4 sack of flour per day

5 days

5 * 1 1/4

Change to an improper fraction

5 * (4*1+1)/4

5 * 5/4

25/4

Change to a mixed number

6 1/4 sacks

Answer:

more than

Step-by-step explanation:

1 1/4 = mon - fri

1 1/4 * 5 (days) = 6.25

6.25 > 5

Answer:

32

Step-by-step explanation:

f(6)=6^2-4

f(6)=36-4

f(6)=32

Answer:

f(6)=32

Step-by-step explanation:f(6)=6^2 -4

f(6)=36-4

f(6)=32

The correct statement is :David started at 0 instead of 2

A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.

Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3

The right steps are

Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5

Thus 2+3=5 which is the required answer

but David addes 2-3=-1 which is incorrect.

Hence, David started at 0 instead of 2

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Answer: x = 3

Step-by-step explanation: 10 x + 20 = 5x + 35

                                              10 x + 20 - 5x = 35

                                                5x = 35 - 20

                                                  5x = 15

                                                    x = 3

Answer:

x=3

Step-by-step explanation:

5(2x+4)=5x+35

10x+20=5x+35

10x-5x=35-20

5x=15

x=3

The dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

Let's assume that the width of the rectangle is x meters. According to the given information, the length of the rectangle is 3 meters less than double the width, which can be expressed as 2x - 3.

The area of a rectangle is given by the formula: Area = Length × Width. In this case, the area is given as 14 m². Therefore, we can write the equation:

(x)(2x - 3) = 14

Expanding the equation:

2x² - 3x = 14

Rearranging the equation to standard form:

2x² - 3x - 14 = 0

To solve this quadratic equation, we can factor it or use the quadratic formula. In this case, let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In our equation, a = 2, b = -3, and c = -14. Plugging in these values into the quadratic formula:

x = (-(-3) ± √((-3)² - 4(2)(-14))) / (2(2))

x = (3 ± √(9 + 112)) / 4

x = (3 ± √121) / 4

x = (3 ± 11) / 4

Simplifying further:

x = (3 + 11) / 4 or x = (3 - 11) / 4

x = 14 / 4 or x = -8 / 4

x = 7/2 or x = -2

Since the width cannot be negative, we discard the negative solution. Therefore, the width of the rectangle is 7/2 meters.

Now, we can substitute the value of x into the expression for the length:

Length = 2x - 3

Length = 2(7/2) - 3

Length = 7 - 3

Length = 4 meters

Thus, the dimensions of the rectangle are width = 7/2 meters and length = 4 meters.

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Answer: 12

Step-by-step explanation:

The answer is 12 because:

sizes are 3

toppings are 4

Using the Fundamental Counting Principal you multiple the selections

( 3 x 4=12)

So just learn the fundamental counting principal and it'll be easier. :)

The number of unique ways that you can order a bag of popcorn if you can only select one topping is 12 ways.

Combinations in probability refer to sequences of outcomes where the order does not matter.

Combinations are a way to calculate the total outcomes of an event where the order of the outcomes does not matter. To calculate combinations, we will use the formula nCr = n! / r! × (n - r)! where n represents the total number of items, and r represents the number of items being chosen at a time.

We are given the 3 different sizes of popcorn as;

Small

Medium

Large

Now, we are told that an order of popcorn comes with 4 different topping choices. Thus;

A number of unique ways that you can order a bag of popcorn are;

N = 3×4 = 12 unique ways

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Answer:

x>3

Step-by-step explanation:

Step-by-step explanation:

1 - subtract 10 from both sides so (4x+10-10>28-2x-10)

2 - Simplify (4x>-2x+18)

3 - Add 2x to both sides (4x+2x>-2x+18+2x)

4 - Simplify (6x>18)

5 - Divide both side by 6 (6x/6>18/6)

6 Simplify which gives you (x>3)

Answer:       x>3

Step-by-step explanation:

1- subtract 10 from both sides so (4x+10-10>28-2x-10)

2 - Simplify (4x>-2x+18)

3 - Add 2x to both sides (4x+2x>-2x+18+2x)

4 - Simplify (6x>18)

5 - Divide both side by 6 (6x/6>18/6)

6 Simplify which gives you (x>3)

Answer:  work out how many whole numbers there are by dividing the numerator by the denominator.

Step-by-step explanation:

Answer:

n=132

Step-by-step explanation:

Answer:

132

Step-by-step explanation:

n/12=11

n=11*12

n=132

Answer:

1: 544

2: 2,355.52

3:28, 288

Answer:

B

Step-by-step explanation:

since 28 is the amount of time it takes for him to mow a lawn, we have to have an answer that involves time, which is B.    

The rejection point condition for the hypothesis test is 2.576.

In a local ice-skating contest, there were two judges and 15 contestants. Each judge was asked to rate each contestant on a 7-point scale. The most successful candidates received a rating value of 7, while the least successful candidates received a rating value of 1. It appears that the bivariate normal probability distribution assumption was severely violated. The City Council wants to know whether the judges have similar opinions in rating ice-skating competitors. At a significance level of 0.01, the rejection point condition for the hypothesis test is 2.576. As the judges' opinions in rating ice-skating competitors is required, therefore, we have to apply the hypothesis testing method.

Since the sample size is less than 30, the hypothesis test is done using a t-distribution. The hypotheses are:H0: μd = 0; the judges do have similar opinions in rating ice-skating competitors HA: μd ≠ 0; the judges do not have similar opinions in rating ice-skating competitors The level of significance is α = 0.01. The rejection point condition for the hypothesis test is given by t = ±2.576 (for a two-tailed test), where α/2 = 0.01/2 = 0.005 and the degree of freedom is 15 - 1 = 14. Therefore, the rejection point condition for the hypothesis test is 2.576.

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