2. Suppose the market demand for a new brand of Tex-Mex burritos is as Q d
​
=40−5∗P. And the market supply for burritos is given by Q s
​
=10∗P−20, where P= price ( $ per burrito). What is the value of equilibrium price and equilibrium quantity? What would happen to total revenue if the seller sets price at $6, instead of selling the burritos at market equilibrium level? Note: Total revenue − price ∗ the units sold −P∗Q d
​
, with the price given.

Answer:

y^2 + 5y = 0

y(y + 5) = 0

y = 0, -5

The answer is y = 0 and y = -5.

The given question :

Despite having written more than 30 works, Stowe's best-selling anti-slavery classic Uncle Tom's Cabin is what made her famous around the world and cemented her legacy.

With Uncle Tom's Cabin, Stowe aimed to persuade her sizable Northern readership of the importance of putting an end to slavery. The Fugitive Slave Act of 1850, which made it unlawful to help a runaway slave, was the primary cause for which the book was written.

Therefore, She later recalled how the loss of her child had made her feel extremely sympathetic with enslaved mothers who had their children sold away.

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To determine the sign of the sum of two integers when one integer is positive and the other is negative, we can follow a simple rule based on their magnitudes.

If the magnitude of the positive integer is greater than the magnitude of the negative integer, the sum will be positive. This is because the positive integer outweighs the negative integer, resulting in a positive value.

On the other hand, if the magnitude of the negative integer is greater than the magnitude of the positive integer, the sum will be negative. In this case, the negative integer dominates and determines the sign of the sum.

In both scenarios, the sign of the larger magnitude integer takes precedence and determines the sign of the sum. It is important to note that the sum will always have the sign of the integer with the larger magnitude, regardless of the specific values of the integers involved.

By considering the magnitudes of the integers, we can easily determine the sign of their sum when one integer is positive and the other is negative.

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The letter M has reflectional symmetry, but it does not have rotational symmetry.

The other image has a rotational symmetry.

The axis of symmetry is an imaginary straight line that divides a shape into two identical parts, thereby creating one part as the mirror image of the other part.

The axis of symmetry for the letter M is the vertical line that divides it into two mirrored halves. When the letter is reflected across this axis, the left half becomes the right half, and vice versa.

There is no angle of rotation for the letter M that would allow it to be rotated and look the same as the original letter.

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Answer:

(For question 5)

Step-by-step explanation:

It is rotational and reflectional.

The Laplace transform of the given function is,

L{f(t)} = (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

Given function is f(t) = {8 12 1 Jo, 0 ≤ t < 3/2, 3/2 ≤ t < 2, 2 ≤ t < ∞ respectively.

We have to find Laplace transform of the given function.

For first interval 0 ≤ t < 3/2,

f(t) = 8u(t) - 8u(t-3/2)

For second interval 3/2 ≤ t < 2,

f(t) = 12u(t-3/2) - 12u(t-2)

For third interval 2 ≤ t < ∞,

f(t) = Jo(u(t-2))

Hence, we can write the Laplace transform of the given function as,

L{f(t)} = L{8u(t) - 8u(t-3/2)} + L{12u(t-3/2) - 12u(t-2)} + L{Jo(u(t-2))}

Where, L is Laplace transform.

Let's calculate each Laplace transform stepwise,

1. L{8u(t) - 8u(t-3/2)}L{8u(t)} = 8/L{u(t)}L{u(t)}

= 1/sL{u(t-3/2)}

= e^{-3s/2}/s

Therefore,

L{8u(t) - 8u(t-3/2)} = 8[1/s - e^{-3s/2}/s]

2. L{12u(t-3/2) - 12u(t-2)}L{12u(t-3/2)}

= 12e^{-3s/2}/sL{12u(t-2)}

= 12e^{-2s}/s

Therefore,

L{12u(t-3/2) - 12u(t-2)} = 12[e^{-3s/2}/s - e^{-2s}/s]

3. L{Jo(u(t-2))}L{Jo(u(t-2))} = ∫_{0}^{∞}δ(t-2)e^{-st}dtL{Jo(u(t-2))}

= e^{-2s}

Hence, the Laplace transform of the given function is,

L{f(t)} = 8[1/s - e^{-3s/2}/s] + 12[e^{-3s/2}/s - e^{-2s}/s] + e^{-2s}

= (8/s) - 4e^{-3s/2}/s - 6e^{-2s}/s

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The compound inequality for the given situation is $2.75x + $4.25y ≥ $65 and $2.75x + $4.25y ≤ $75, where x represents the number of daylight cameras and y represents the number of flash cameras.

To solve this compound inequality, we need to find the values of x and y that satisfy both conditions. The inequality $2.75x + $4.25y ≥ $65 represents the lower bound, ensuring that the total cost of the cameras is at least $65. The inequality $2.75x + $4.25y ≤ $75 represents the upper bound, making sure that the total cost does not exceed $75.

To list the solutions involving whole numbers of cameras, we need to consider integer values for x and y. We can start by finding the values of x and y that satisfy the lower bound inequality and then check if they also satisfy the upper bound inequality. By trying different combinations, we can determine the possible solutions that meet these criteria.

After solving the compound inequality, we find that the solutions involving whole numbers of cameras are as follows:

(x, y) = (10, 10), (11, 8), (12, 6), (13, 4), (14, 2), (15, 0), (16, 0), (17, 0), (18, 0), (19, 0), (20, 0).

These solutions represent the combinations of daylight and flash cameras that fulfill the requirements of buying exactly 20 cameras and spending between $65 and $75.

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Answer:

(-2.5,1)

Step-by-step explanation:

Let the point be (m, n). Using section formula we have

m=(5*(-1)+3*(-5))/(5+3)=-20/8=-2.5

n=(5*(7)+3*(-9))/(5+3)=1

The given line is 5x - 3y = 0. It is required to write the equation of a line that is perpendicular to this line and passes through the point (-2,-1).We know that if two lines are perpendicular, then the product of their slopes is equal to -1.Therefore, the slope of the line 5x - 3y = 0 is given by:5x - 3y = 0-3y = -5x + 03y = 5x y = (5/3) x

The slope of the required line is negative reciprocal of the slope of this line: m = -3/5The point (-2,-1) lies on the required line and the slope of the line is -3/5.Therefore, the equation of the line in the slope-intercept form is given by:

y - y1 = m(x - x1),

where (x1,y1) = (-2,-1)

Substituting the values, we get:

y - (-1) = -3/5(x - (-2))y + 1 = -3/5(x + 2)y + 1 = (-3/5)x - 6/5y = (-3/5)x - 6/5 - 1y = (-3/5)x - 11/5

Thus, the equation of the required line in slope-intercept form is y = (-3/5)x - 11/5. The slope-intercept form of a linear equation is y = mx + b where m represents the slope and b represents the y-intercept. To find the equation of a line that passes through a given point and is perpendicular to a given line, we need to use the properties of perpendicular lines.In order for two lines to be perpendicular, their slopes must have opposite signs and be reciprocals of each other. We can find the slope of the given line by rearranging it in slope-intercept form as follows:

5x - 3y = 0-3y = -5x + 0y = (5/3)x

So the slope of the given line is 5/3. Since the slope of the perpendicular line must be the negative reciprocal of 5/3, we have:m = -1/(5/3) = -3/5Now we can use the point-slope form of the equation of a line to find the equation of the line passing through the point (-2,-1) with slope -3/5:

y - y1 = m(x - x1)y - (-1) = (-3/5)(x - (-2))y + 1 = (-3/5)(x + 2)y + 1 = (-3/5)x - 6/5y = (-3/5)x - 6/5 - 1y = (-3/5)x - 11/5

So the equation of the line that passes through (-2,-1) and is perpendicular to 5x - 3y = 0 is y = (-3/5)x - 11/5.

Therefore, the equation of the required line in slope-intercept form is y = (-3/5)x - 11/5.

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Answer:

Perimeter= 20 inches

Step-by-step explanation:

since the perimeter of a plane figure is distance round the shape, we add all the sides in order to get 20inches.

Perimeter= 4+5+4+4+3= 20incjes. That's for the perimeter.

Then area, we divide the shape into two portions sides A and B.

We find the area of side A which is a rectangle so, the are = Length×Breadth..

= 4×5 = 29cm².Side B is a triangle so it's area will be

Answer:

Total Perimeter = 30 in

Total Area: 30 in²

Step-by-step explanation:

First, do the perimeter of the triangle.

Equation: side+side+base = 3 + 4 + 5 = 12

Next is the perimeter of the rectangle.

Equation: 2(length + width) = 2·(5 + 4) = 18

Then, add the two perimeters:

12 + 18 = 30 in (Total Perimeter = 30 in)

Next, do the area of the triangle.

Equation: height • base/2 = 4 · 5/2 = 10

Finally, the area of the rectangle.

Equation: width • length = 4 · 5 = 20

Then, add the two areas:

10 + 20 = 30 (Total Area: 30 in²)

Answer:11486.34

Step-by-step explanation:

p is semiperimeter

p=(a+b+c)/2

p=(174+138+188)/2

For Heron equation,

S=\(\sqrt{p*(p-a)*(p-b)*p-c}\)

so, it is 11487.34

Answer:

  11,486.3 square units

Step-by-step explanation:

You want the area of the triangle with side lengths a=174, b=138, c=188.

The area of a triangle can be found from the lengths of the three sides using Heron's formula:

  A = √(s(s -a)(s -b)(s -c)) . . . . . . . where s = (a+b+c)/2, the "semiperimeter"

The calculation is shown in the second attachment.

  s = (174 +138 +188)/2 = 500/2 = 250

  A = √(250(250 -174)(250 -138)(250 -188)) = √(250(76)(112)(62))

  A = √131936000 ≈ 11486.3

The area of the triangle is about 11486.3 square units.

__

Additional comment

An effectively equivalent way to find the area is to use the Law of Cosines to find an angle, then use the trig formula for the area.

  C = arccos((a²+b²-c²)/(2ab)) = arccos(13976/48024) ≈ 73.080899°

  Area = 1/2(ab·sin(C)) = 1/2(24012·0.9567166) ≈ 11486.3

We say this is "effectively equivalent" not only because it gives the same area, but because using the relation between cos(C) and sin(C), you can demonstrate that this formula gives Heron's formula for the area.

Answer:

hope this helps

Step-by-step explanation:

my parents are the same way so if you listen to classical music then things will stick in you head and you can draw things to remind you what they mean like if you had a definitions then draw what they mean

After considering the given data we conclude that the answer for the sub questions are
a) Jeff consumes 33.33 units of good x.
b) the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c) The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.

a. To find Jeff's demand function for good x, we can use the following equation:
\(\frac{\partial U}{\partial x}=\frac{1}{x}=\frac{p_x}{p_y}=\frac{1}{2}\)
Solving for x, we get:
\(x=\frac{1}{2}y\)
Substituting the given values, we get:
\(x=\frac{1}{2}(200/3)=33.33\)
Therefore, Jeff consumes 33.33 units of good x.
b. If Px increases to 2, the new demand function for good x is:
\(x'=\frac{1}{2}y'\)where y'  is the amount of good y consumed at the new prices and income. To find the compensating variation, we need to find the amount of income Jeff would need at the original prices to achieve the same level of utility as he does at the new prices. We can use the following equation:
\(W'=W+CV\) where W is the original income, W' is the new income, and CV is the compensating variation.
Substituting the given values, we get:
\(8.51=\ln(33.33)+\ln(66.67)8.51=ln(33.33)+ln(66.67)\)
\(y'=\frac{W'}{2}\)
\(x'=\frac{1}{2}y'\) Solving for y', we get:
y'=100
Solving for x', we get:
x'=50
Therefore, the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c. To calculate the total effect, substitution effect, and income effect of the price change, we can use the following equations:
\(TE=\frac{\Delta U}{U_0}\)
\(SE=\frac{\Delta x_s}{x_0}\)
\(IE=\frac{\Delta x_i}{x_0}\)where \(\Delta U\)is the change in utility, \(U_0\) is the initial utility,\(\Delta x_s\) is the change in consumption due to the substitution effect, \(x_0\) is the initial consumption, and \(\Delta x_i\) is the change in consumption due to the income effect.
The change in consumption due to the price change can be calculated as:
as:
\(\Delta x=x'-x_0=\frac{1}{2}y'-\frac{1}{2}y_0\)
where \(y_0=2x_0\) and \(y'=2x'\)
Substituting the given values, we get:
\(\Delta x=x'-x_0=50-33.33=16.67\)
The substitution effect can be calculated as:
\(SE=\frac{\Delta x_s}{x_0}=\frac{x_s'-x_0}{x_0}=\frac{1}{2}\frac{y_0-y_s'}{x_0}=\frac{1}{2}\frac{p_x}{p_y}\frac{y_0}{x_0}\)
Substituting the given values, we get:
\(SE=\frac{1}{2}\frac{1}{2}\frac{2x_0}{4x_0}=\frac{1}{4}\)
The income effect can be calculated as:
\(IE=\frac{\Delta x_i}{x_0}=\frac{\Delta W}{W_0}=\frac{CV}{W_0}\)
Substituting the given values, we get:
\(IE=\frac{-100}{200}=-0.5\)
The total effect can be calculated as:
\(TE=SE+IE=\frac{1}{4}-0.5=-0.25\)
Therefore, the total effect of the price change is negative, indicating that Jeff will consume less of good x as a result of the price increase. The substitution effect is positive, indicating that Jeff will consume more of good x due to the relative price change. The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
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Answer:

96 cm^2

Step-by-step explanation:

The triangle can be split into 2 6-8-10 triangles, each with area 24. The bottom parallelogram area is base times height, or 8 * 6, so 48. 24 + 24 + 48 is 96.

As per the median, the set of data that fulfilling Marjane's requirement is 24, 25, 25, 25, 26, 26 (option c).

In statistics, data is a collection of numbers or values that represent a particular phenomenon. One way to measure central tendency, or the typical or representative value of the data, is through the median and the mode.

The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently.

The third set of data is 24, 25, 25, 25, 26, 26.

The median is the middle value, which is also (25+25)/2 = 25.

The mode is the value that appears most frequently, which is 25.

Therefore, the mode and median are the same, fulfilling Marjane's requirement.

Therefore, the correct option is (c).

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Answer:

-2p + 3

Step-by-step explanation:

Answer:

= -2p+3

Step-by-step explanation:

combine like terms, which gives you -2p (-4p+2p). since the three isn't alike to the other term, you cant add them.

i hope this helps :)

Answer: #1

Step-by-step explanation: if you look closely at the purple line you will see it falls into (y <3) and yeah

Answer:

3 2/3 square feet.

Step-by-step explanation:

You just need to multiply 6 and 4 2/3. To do this you have to change both of them into improper fractions so 6 would be 21/3 and 4 2/3 would be 14/3. If you cross cancel the 21/3 will become 7/3 and the 14/3 will become 14/1. Now you have to multiply across and you should get 98/3. To change the improper fraction into a mixed number you have to divide 98 and 3 so you can get 3 2/3. Therefore, the answer to the area of the quilt is 3 2/3 square feet.

Using Venn diagram, if a student is chosen randomly, (a) the probability that he or she is not in any of the language classes is 0.5, (b) the probability that he or she is taking exactly one language class is 0.32, and (c) if 2 students are chosen randomly, the probability that at least 1 is taking a language class is 0.753.

Venn diagram is a diagram used to present the relationship between sets in a logical form. (See attached image)

Let A = students in the Spanish class = 28

B = students in the French class = 26

C = students in the German class = 16

Hence, the probability of each class is:

P(A) = 28/100 = 0.28

P(B) = 26/100 = 0.26

P(C) = 16/100 = 0.16

P(A ∩ B) = 12/100 = 0.12

P(B ∩ C) = 6/100 = 0.06

P(A ∩ C) = 4/100 = 0.04

P(A ∩ B ∩ C) = 2/100 = 0.02

(a) P(not A, B, C) = 1 - P(A ∪ B ∪ C)

P(not A, B, C) = 1 - [P(A) + P(B) + P(C) - P(A ∩ B) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]

P(not A, B, C) = 1 - (0.28 + 0.26 + 0.16 - 0.12 - 0.06 - 0.04 + 0.02)

P(not A, B, C) = 1 - 0.5

P(not A, B, C) = 0.5

(b) P(A, B, C only) = P(A only) + P(B only) + P(c only)

P(A, B, C only) = [P(A) - P(A ∩ B) - P(A ∩ C) + P(A ∩ B ∩ C)] + [P(B) - P(A ∩ B) - P(B ∩ C) + P(A ∩ B ∩ C)] + [P(C) - P(B ∩ C) - P(A ∩ C) + P(A ∩ B ∩ C)]

P(A, B, C only) = (0.28 - 0.12 - 0.04 + 0.02) + (0.26 - 0.12 - 0.06 + 0.02) + (0.16 - 0.06 - 0.04 + 0.02)

P(A, B, C only) = 0.14 + 0.10 + 0.08

P(A, B, C only) = 0.32

(c) P = 1 - (50/100 x 49/99)

P = 1 - (49/198)

P = 149/198

P = 0.753

To complete the problem, here are the questions:

(a) If a student is chosen randomly, what is the probability that he or she is not in any of the language classes?

(b) If a student is chosen randomly, what is the probability that he or she is taking exactly one language class?

(c) If 2 students are chosen randomly, what is the probability that at least 1 is taking a language class?

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SOLUTION

Step 1:

A store pays $ 127. 53 for a Jedi outfit.

Assuming the store marks up the price 15 %.

We are asked to find the amount of mark-up? ( nearest hundredth)

Step 2 :

The amount of the mark - up ( to the nearest hundredth ) = $ 19. 13

Answer:

55

Step-by-step explanation:

6(10)-5

60-5

55

Hope it helps! :): ^-^ ^_^

The solution for the variable w in the equation s = a + lw is w = (s - a)/l.

Given the equation in the question:

s = a + lw

w = ?

To solve the equation s = a + lw for the variable w, we have to isolate w on one side of the equation.

s = a + lw

Subtract a from both sides:

s - a = a + lw - a

s - a = a - a + lw

s - a = lw

Reorder the equation:

lw = s - a

Divide both sides by the coefficient of w:

lw/l = ( s - a )/l

Simplifying, we get:

w = ( s - a )/l

Therefore, the variable w equals ( s - a )/l.

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The probability that their hospital stay is greater than 6 days is approximately 0.6985.

(a) To find the probability that their hospital stay is from 5 to 6 days, we need to calculate the z-scores for both values using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For 5 days: z = (5 - 7.37) / 2.60 = -0.9
For 6 days: z = (6 - 7.37) / 2.60 = -0.52

Next, we need to find the corresponding probabilities using a z-table or a calculator. From the z-table, we find that the probability of z being less than -0.9 is 0.1841, and the probability of z being less than -0.52 is 0.3015.

To find the probability of the hospital stay being between 5 and 6 days, we subtract the probability of z being less than -0.9 from the probability of z being less than -0.52:
P(5 ≤ X ≤ 6) = P(X ≤ 6) - P(X ≤ 5)

= 0.3015 - 0.1841

= 0.1174
Therefore, the probability that their hospital stay is from 5 to 6 days is approximately 0.1174.

(b) To find the probability that their hospital stay is greater than 6 days, we need to find the probability of z being greater than -0.52.

From the z-table, we find that the probability of z being less than -0.52 is 0.3015.

Therefore, the probability that their hospital stay is greater than 6 days is approximately

1 - 0.3015 = 0.6985,

rounded to five decimal places.

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False. very few tools are available to assist system analysts and end users in analyzing data.

There are many tools available to assist system analysts and end users in analyzing data. Some commonly used tools include spreadsheets (such as Microsoft Excel), data visualization software (such as Tableau or Power BI), statistical analysis software (such as R or SPSS), and business intelligence software (such as SAP or Oracle).

These tools allow analysts and end users to process, manipulate, and visualize large volumes of data, as well as to perform complex statistical analyses and modeling. Additionally, with the advent of big data technologies, such as Hadoop and Spark, analysts and end users can now analyze vast amounts of data in real-time, using distributed computing systems.

In summary, there are many tools available to assist system analysts and end users in analyzing data, and these tools continue to evolve and improve over time.

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Answer:

Commutative property of addition

Prove that :

\( \sf \: { |\vec{A} + \vec{B}| }^{2} - { |\vec{A} - \vec{B}| }^{2} = 4 \: \vec{A} \: . \: \vec{B}\)

\( \green{\large\underline{\sf{Solution-}}}\)

Consider, LHS

\(\rm :\longmapsto\: { |\vec{A} + \vec{B}| }^{2} - { |\vec{A} - \vec{B}| }^{2} \)

We know,

\(\rm :\longmapsto\:\boxed{\tt{ |\vec{x}| ^{2} = \vec{x}.\vec{x}}}\)

So, using this, we get

\(\rm \:  =  \: (\vec{A} + \vec{B}).(\vec{A} + \vec{B}) - (\vec{A} - \vec{B}).(\vec{A} - \vec{B})\)

\(\rm \:  =  \:[ \vec{A}.\vec{A} + \vec{A}.\vec{B} + \vec{B}.\vec{A} + \vec{B}.\vec{B}] - [\vec{A}.\vec{A} - \vec{A}.\vec{B} - \vec{B}.\vec{A} + \vec{B}.\vec{B}]\)

\(\rm \:  =  \: [ { |\vec{A}| }^{2} + \vec{A}.\vec{B} + \vec{A}.\vec{B} + { |\vec{B}| }^{2}] - [ { |\vec{A}| }^{2} - \vec{A}.\vec{B} - \vec{A}.\vec{B} + { |\vec{B}| }^{2}]\)

\(\red{ \bigg\{  \sf \: \because \: \vec{A}.\vec{B} = \vec{B}.\vec{A} \bigg\}}\)

\(\rm \:  =  \: [ { |\vec{A}| }^{2} + 2\vec{A}.\vec{B} + { |\vec{B}| }^{2}] - [ { |\vec{A}| }^{2} -2 \vec{A}.\vec{B} + { |\vec{B}| }^{2}]\)

\(\rm \:  =  \: { |\vec{A}| }^{2} + 2\vec{A}.\vec{B} + { |\vec{B}| }^{2}- [{ |\vec{A}| }^{2} + 2 \vec{A}.\vec{B} - { |\vec{B}| }^{2}\)

\(\rm \:  =  \: 4 \: \vec{A}.\vec{B}\)

Hence,

\( \sf \:\boxed{\tt{ \: \: { |\vec{A} + \vec{B}| }^{2} - { |\vec{A} - \vec{B}| }^{2} = 4 \: \vec{A} \: . \: \vec{B} \: \: }}\)

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

\(\boxed{\tt{ \vec{A}.\vec{B} = \vec{B}.\vec{A}}}\)

\(\boxed{\tt{ \vec{A}.\vec{A} = { |\vec{A}| }^{2} }}\)

\(\boxed{\tt{ \vec{A} \times \vec{B} = - \vec{B} \times \vec{A}}}\)

\(\boxed{\tt{ \vec{A} \times \vec{A} = 0}}\)

\(\boxed{\tt{ \vec{A}.\vec{B} = 0 \: \rm\implies \:\vec{A} \: \perp \: \vec{B}}}\)

\(\boxed{\tt{ \vec{A} \times \vec{B} = 0 \: \rm\implies \:\vec{A} \: \parallel \: \vec{B}}}\)

Answer:

Step-by-step explanation:

Yes, there is a proportional relationship between the original price of an item and its price after sales tax.

In general, a proportional relationship between two variables means that the ratio of one variable to the other is constant. In this case, the ratio of the original price of an item to its price after sales tax is constant, as long as the sales tax rate remains the same.

For example, if the original price of an item is x, and the sales tax rate is 8%, then the price after sales tax is x * 1.08. The ratio of the original price to the price after sales tax is x / (x * 1.08) = 1 / 1.08 = 0.93, which is a constant value. This means that the original price and the price after sales tax are in a proportional relationship.

I hope this helps! Let me know if you have any questions.

Answer:

6

Step-by-step explanation:

Don't quote me on this bc I'm not 100% sure I'm sorry

3. In a shipment of 360 dozen bolts, approximately 108 bolts can be expected to be defective, based on an average defect rate of 2.5%.

4. In a batch of 12000 batteries, there is a percentage of 0.125% defective batteries, which amounts to approximately 15 defective batteries.

3. To find the number of bolts that can be expected to be defective in a shipment of 360 dozen, we first need to determine the total number of bolts in the shipment.

One dozen is equal to 12, so 360 dozen would be 360 * 12 = 4320 bolts in total.

Since the average percentage of defective bolts is 2.5% or 0.025, we can calculate the expected number of defective bolts by multiplying the total number of bolts by the defective percentage:

Number of defective bolts = 4320 * 0.025 = 108 bolts

Therefore, it can be expected that 108 bolts will be defective in a shipment of 360 dozen.

4. To calculate the percentage of defective batteries, we divide the number of defective batteries by the total number of batteries in the batch and then multiply by 100 to express it as a percentage.

Percentage of defective batteries = (Number of defective batteries / Total number of batteries) * 100

Given that there are 15 defective batteries in a batch of 12000, we can substitute these values into the formula:

Percentage of defective batteries = (15 / 12000) * 100

Calculating this expression gives us:

Percentage of defective batteries = 0.00125 * 100 = 0.125%

Therefore, the percentage of defective batteries in the batch is 0.125%.

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The solutions to the differential equations depend on the equation itself. Depending on the equation, there could be a variety of solutions, including linear solutions, constant solutions, polynomial solutions, exponential solutions, and trigonometric solutions.
Linear solution: A linear solution is of the form\(y=mx+b\). This is the solution to a first-order linear differential equation.
Constant solution: A constant solution is when the differential equation has a solution of the form y=c, where c is a constant.
Polynomial solution: A polynomial solution is when the differential equation has a solution of the form

\(y=a_nx^n+a_(n-1)x^(n-1)+…+a_0,\)

where a_n, a_(n-1),…,a_0 are constants.
Exponential solution: An exponential solution is when the differential equation has a solution of the form\(y=Ae^(kx),\)where A and k are constants.
Trigonometric solution: A trigonometric solution is when the differential equation has a solution of the form \(y=a_ncos(nx)+b_nsin(nx),\) where a_n and b_n are constants.
Therefore, it is important to carefully analyze the equation in order to determine the type of solution needed.

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