2 points Save Answer Question 6 Solution of the following LP Problem. Maximize z = 2x + 6y subject to -x + y S 12x + y S2, and *20. y 20 is a 4/3 b. 1/3 c26/3 d. no feasible region

Answer:

B

Step-by-step explanation:

a² + 14a - 51 = 0 ( add 51 to both sides )

a² + 14a = 51

to complete the square

add ( half the coefficient of  the x- term )² to both sides

a² + 2(7)a + 49 = 51 + 49

(a + 7)² = 100 ( take square root of both sides )

a + 7 = ± \(\sqrt{100}\) = ± 10 ( subtract 7 from both sides )

a = - 7 ± 10

then

a = - 7 + 10 = 3

a = - 7 - 10 = - 17

Answer:

I would say that by the 20th figure, there would be more than 400 small triangles by the 20th figure.

Step-by-step explanation:

Based on figure 1 and 2, I'm guessing the ratio is 2.

Figure 4: 32

Figure 5: 64

Figure 6: 128

Figure 7: 256

Figure 8: 512

Figure 9: 1,024

To find a 95% confidence interval for the population mean salary, we can use the t-distribution since the population standard deviation is unknown.

The formula for the confidence interval is: CI = sample mean ± t * (sample standard deviation/sqrt (n)) where t represents the critical value for the desired confidence level and n is the sample size. Since the sample size is small (n = 41), we use the t-distribution instead of the standard normal distribution. The critical value for a 95% confidence level with 40 degrees of freedom (n - 1) is approximately 2.021. Plugging in the values, the confidence interval is:

CI = $22,045 ± 2.021 * ($1,255 / sqrt(41))

To find a 99% confidence interval for the population mean salary, we follow the same formula but use the appropriate critical value for a 99% confidence level. With 40 degrees of freedom, the critical value is approximately 2.704. Substituting the values into the formula, the confidence interval is: CI = $22,045 ± 2.704 * ($1,255 / sqrt(41))

The difference in the results between parts (a) and (b) lies in the choice of confidence level and the associated critical values. A higher confidence level, such as 99%, requires a larger critical value, which increases the margin of error and widens the confidence interval. As a result, the 99% confidence interval will be wider than the 95% confidence interval. This wider interval provides a greater degree of certainty (confidence) that the true population mean salary falls within the interval but sacrifices precision by allowing for more variability in the estimates.

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Answer:

Let ac=ab=5

With this, bc= 5√2

Step-by-step explanation:

So to find ad, Let ad be x

5√2=(2)(x)

(5√2/2)= x

This proves that bc=2ad

The value of sin(A + B) = 72/85 if sin A = − 24/25 with 270° ≤ A ≤ 360° and cos B = − 15/17 with 90° ≤ B ≤ 180°.

To find sin(A + B), we will use the formula:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

First, we need to find sin(A) and cos(A). Since sin A = −24/25 with 270° ≤ A ≤ 360°, we know that A is in the fourth quadrant where sin A is negative and cos A is positive. Using the Pythagorean identity, we can find cos A:

cos² A + sin² A = 1
cos² A + (-24/25)² = 1
cos² A = 1 - (-24/25)²
cos A = √(1 - 576/625) = √49/625 = 7/25 (positive because A is in the fourth quadrant)

Therefore, sin A = -24/25 and cos A = 7/25.

Next, we need to find sin(B) and cos(B). Since cos B = −15/17 with 90° ≤ B ≤ 180°, we know that B is in the second quadrant where sin B and cos B are both negative. Using the Pythagorean identity, we can find sin B:

sin² B + cos² B = 1
sin² B + (-15/17)² = 1
sin² B = 1 - (-15/17)²
sin B = -√(1 - 225/289) = -√64/289 = -8/17 (negative because B is in the second quadrant)

Therefore, sin B = -8/17 and cos B = -15/17.

Now, we can substitute these values into the formula for sin(A + B):

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)
= (-24/25)(-15/17) + (7/25)(-8/17)
= 360/425
= 72/85

Therefore, sin(A + B) = 72/85.

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The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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We are given 2 statements.

We translate them to algebraic statements.

Let

smaller integer be s, and

larger integer be l

"The larger of two integers is 4 more than 9 times the smaller."

We can write this as:

Then, we are given sum of 2 integers is greater than or equal to 26, we can write:

We put 1st equation in 2nd:

The next integer value (smallest of them all) of s is "3".

Now, if s is 3, l would be:

l = 9s + 4

l = 9(3) + 4

l = 27 + 4

l = 31

smaller of the both integers:

Smaller Number: 3

Larger Number: 31

The statements that are true when there exists a constant rate of change between x and y are:

1. The graph of the relationship between x and y is a straight line.
2. The slope of the line represents the constant rate of change between x and y.
3. The value of the slope is the same for any two points on the line.
4. The equation that represents the relationship between x and y can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
5. The value of the y-intercept is the y-coordinate of the point where the line crosses the y-axis.

Let's break down each statement:

1. The graph of the relationship between x and y is a straight line:
When there is a constant rate of change between x and y, the graph will be a straight line. This means that the points representing the relationship between x and y will lie on a straight line when plotted on a graph.

2. The slope of the line represents the constant rate of change between x and y:
The slope of a line is a measure of how steep or flat the line is. In this case, when there is a constant rate of change between x and y, the slope of the line will be the same for any two points on the line. It represents the rate at which y changes for every unit change in x.

3. The value of the slope is the same for any two points on the line:
As mentioned earlier, the slope represents the constant rate of change between x and y. Regardless of which two points we choose on the line, the ratio of the change in y to the change in x will always be the same.

4. The equation that represents the relationship between x and y can be written in the form y = mx + b, where m is the slope and b is the y-intercept:
When there is a constant rate of change between x and y, we can express their relationship using an equation in the form y = mx + b. The slope, represented by the variable m, will be the coefficient of x, and the y-intercept, represented by the variable b, will be the value of y when x is equal to 0.

5. The value of the y-intercept is the y-coordinate of the point where the line crosses the y-axis:
The y-intercept is the point where the line representing the relationship between x and y crosses the y-axis. It represents the value of y when x is equal to 0.

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Answer:

Step-by-step explanation:

(a+2,b)=(4,5)

Since the points are equal we can equate them to find a

Comparing a + 2 to 4

We have

a + 2 = 4

Send 2 to the right side of the equation

a = 4 - 2

We have the final answer as

Hope this helps you

Step-by-step explanation:

Here,

according to the question,

(a+2, b)=(4,5)

since, they are equal, equating with their corresponding elements we get,

(a+2)=4

or, a= 4-2

Therefore, the value of a is 2.

Also you can find value of b in same way,

b=5.

Therefore, the value of a abd b are 2 and 5 respectively.

Hope it helps...

The vendor sold 172 sodas and 58 hotdogs at the hockey game.

An equation of degree one is known as a linear equation.

A linear equation of two variables can be represented by ax + by = c.

let, the number of soda cans be 'x' and the number of hot dogs be 'y'.

So, From the given information x = 3y and the vendor sold a total of 232.

Therefore, x + y = 232.

3y + y = 232.

4y = 232.

y = 232/4.

y = 58.

So, He sold 58 hot dogs and 3×58 = 172 soda cans.

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Answer:

w = \(\frac{p -2l}{2}\)

Step-by-step explanation:

p = 2l + 2w  Subtract 2l from both sides of the equation

p - 2l = 2p  Divide both sides by 2

\(\frac{p -2l}{2}\) = w

Step-by-step explanation:

For the given problem:

Let the number = x

Two less than the quotient of a number and 8 is 1/4

so, we can write the following expression:

Now, solve the equation to find (x)

Multiplying by (8) to eliminate the denominators:

Add (6) to both sides:

So, the answer will be the number is 18

Given, Height of the cliff = 20 m Distance of the car from the foot of the cliff = 10 m.

The time taken by the car to fall from the cliff can be found using the formula:

\(`h = (1/2) g t^2`\)

Where h is the height of the cliff, g is the acceleration due to gravity and t is the time taken by the car to fall from the cliff.

Substituting the given values,`20 = (1/2) × 9.8 × t^2`

Solving for t, `t = sqrt(20/4.9)` = 2.02 s

Let the initial velocity of the car be V0 and the time taken for the car to come to rest after applying brakes be t1.

Distance covered by the car before coming to rest can be found using the formula: `\(s = V0t1 + (1/2) (-5) t1^2\)`

Where s is the distance covered by the car before coming to rest.

Simplifying the above equation,\(`2.5 = V0 t1 - (5/2) t1^2`\)

Substituting the given values,`5 = V0 - 5 t1`

Solving the above two equations,\(`V0 = 32.5/2 t1`\)

Simplifying the above equation,`V0 = 16.25 t1`

Substituting the value o\(f t1,`V0 = 16.25 × 2` = 32.5 m/s\)

Therefore, the speed of the car before the start of braking is 32.5 m/s.

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The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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Answer: x = -1 , y = 5

Step-by-step explanation:

chuck the equations into desmos com

Answer:

x = - 1 , y = 5

Step-by-step explanation:

y = 7x + 12 → (1)

y = - 3x + 2 → (2)

substitute y = 7x + 12 into (2)

7x + 12 = - 3x + 2 ( add 3x to both sides )

10x + 12 = 2 (subtract 12 from both sides )

10x = - 10 ( divide both sides by 10 )

x = - 1

substitute x = - 1 into either of the 2 equations and solve for y

substituting into (1)

y = 7(- 1) + 12 = - 7 + 12 = 5

then x = - 1 and y = 5

Answer:

Step-by-step explanation:

 nn, ,b,,566666666666666666665

The estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

To estimate the monthly average daily radiation on a horizontal surface H in June in Amman, we can use the following equation:

\([H = S \times H_s \times \frac{\sin(\phi)\sin(\delta)+\cos(\phi)\cos(\delta)\cos(H_a)}{\pi}]\)

where:

S is the solar constant, which is approximately equal to 1367 W/m(^2);

\(H(_s)\) is the average number of sunshine hours per day in Amman in June, which is given as 10 hours;

(\(\phi\)) is the latitude of the location, which for Amman is approximately 31.9 degrees North;

(\(\delta\)) is the solar declination angle, which is a function of the day of the year and can be calculated using various methods such as the one given in the answer to Q1;

\(H(_a)\) is the hour angle, which is the difference between the local solar time and solar noon, and can also be calculated using various methods such as the one given in the answer to Q1.

Substituting the given values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(\delta)+\cos(31.9)\cos(\delta)\cos(H_a)}{\pi}]\)

Since we are only interested in the monthly average daily radiation, we can assume an average value for the solar declination angle and the hour angle over the month of June. For simplicity, we can assume that the solar declination angle (\(\delta\)) is constant at the value it has on June 21, which is approximately 23.5 degrees North. We can also assume that the hour angle \(H(_a)\) varies linearly from -15 degrees at sunrise to +15 degrees at sunset, with an average value of 0 degrees over the day.

Substituting these values, we get:

\([H = 1367 \times 10 \times \frac{\sin(31.9)\sin(23.5)+\cos(31.9)\cos(23.5)\cos(0)}{\pi}]\)

Simplifying the equation, we get:

\([H \approx 7.35 \text{ kWh/m}^2\text{/day}]\)

Therefore, the estimated monthly average daily radiation on a horizontal surface in June in Amman is approximately 7.35 kWh/m(^2)/day.

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Answer:

Step-by-step explanation:

horizontal line: y=9

vertical line: x = -1

Answer:

Answer in picture with working

Step-by-step explanation:

Answer:

\(\boxed {\boxed {\sf D. \ 30 \ feet}}\)

Step-by-step explanation:

The area of a square is found by multiplying the base and the height, but since all the sides are equal, it is equal to multiplying a side by another side.

\(a=s*s\)

\(a=s^2\)

We know the square garden has an area of 900 square feet. We can substitute this value in for a.

\(900 \ ft^2=s^2\)

Since we are solving for the side, we have to isolate the variable s. It is being squared. The inverse of a square is the square root, so we take the square root of both sides.

\(\sqrt {900 \ ft^2}= \sqrt{s^2}\)

\(\sqrt {900 \ ft^2}=s \\\)

\(30 \ ft=s\)

One side of the garden is equal to 30 feet and choice D is correct.

Step-by-step explanation:

Area of square garden=a^2

ATQ

➝a^2=900 sq.feet

➝a=√900

➝a=30feets

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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The number of bits transferred or received per unit of time is referred to as the "bit rate."

The term "bit rate" refers to the rate at which bits of data are transferred or received in a given unit of time. It measures the speed or capacity of a digital communication channel to transmit information.

Bit rate is typically expressed in bits per second (bps) or multiples thereof, such as kilobits per second (Kbps) or megabits per second (Mbps). It represents the amount of data that can be transmitted or received in a specific timeframe.

For example, a bit rate of 1 Mbps means that one million bits can be transferred or received in one second. Higher bit rates indicate a faster data transmission or reception capability.

Bandwidth, on the other hand, refers to the capacity of a communication channel to carry data and is typically measured in hertz (Hz). It represents the range of frequencies that can be transmitted through the channel.

Wireless fidelity (Wi-Fi) is a technology standard that enables wireless local area networking. While Wi-Fi can be used to transmit data wirelessly, the specific term for the rate at which data is transferred or received is still referred to as the "bit rate."

In summary, the term "bit rate" accurately describes the number of bits transferred or received per unit of time in a digital communication system.

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Answer:

2,100 $28 tickets were sold, and 3,900 $40 tickets were sold!

Step-by-step explanation:

So, we need to write two equations in order to solve this:

We will think of 28 dollar tickets as x, 40 dollar tickets as y.

Now lets make those equations:

\(x + y = 6,000\)

             and

\(28x+40y = 193,200\)

Now, to solve for x and y, lets set a value for x or y. In this case I will set the value of y:

I will do this by taking \(x + y = 6,000\), and subtracting x to the other side, to get y alone:

\(y = 6,000 - x\)

Now lets plug in y to our second equation:

\(28x + 40(6,000-x) = 193,2000\)

=

\(28x+240,000-40x = 193,200\)

Now combining like terms and solving for x we get:

\(-12x + 240,000 = 193,200\)

=

\(-12x = -46,800\)

=

\(x=3,900\)

Now that we know x, lets solve for y by plugging into our first equation!

\(3,900 + y = 6,000\)

=

\(y = 2,100\)

So now we know that our answer is:

2,100 $28 tickets were sold, and 3,900 $40 tickets were sold!

Hope this helps! :3

Answer:

2/3*3/3

Step-by-step explanation:

I mean its just doing 2/3 * 1 which i mean, 3/3 is still a fraction so i did it (TBH cant think of anything else

Answer: 2/3 x 1 = 2/3

technically everything 1 one will equal itself hope it helps.

Answer:

The answer is

\(4+ x\)

Using the definition of linear equation,

\(y = 4 + x\)

Is the answer.