**100 POINTS**
Written Assignment 2. The Selfridge-Conway Method
Attached find a document with a couple questions. Please be specific about answers, detailed feedback is most appreciated

The area οf the actual bridge deck in square feet is 1,280 square feet.

Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.

The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).

The dimensiοns οf the scaled bridge deck in feet are:

24 inches = 2 feet

4 and 4/5 inches = 0.4 feet

Sο, the area οf the scaled bridge deck in square feet is:

2 feet x 0.4 feet = 0.8 square feet

Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:

Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet

Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.

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Answer:

Step-by-step explanation:

The scale factor indicates the actual bridge is 40 times larger than the drawing.

Increase the scale dimensions by the factor of 40.

24 times 40 = 960"

4.8 times 40 = 192" (I changed 4 4/5 to 4.8)

Area = length times width

960 times 192 = 184320 sq inches actual bridge deck in square inches

Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet

It would be two numbers left from 0.

|----------------|-------------------|-----------------|-------------------|

-2                -1                    0                   1                    2

Answer:

\(\angle C \cong \angle F\)

Step-by-step explanation:

Given

\(\angle A \cong \angle D\)

\(AB \cong DE\)

See attachment

Required

What proves \(\triangle ABC \cong \triangle DE F\) by AAS

We have:

\(\angle A \cong \angle D\) --- Angle

\(AB \cong DE\) --- Side

We need to prove that one more angle are congruent

\(\angle B \cong \angle E\)

The above angles are congruent; however, it will prove \(\triangle ABC \cong \triangle DE F\) by ASA

So, we make use of:

\(\angle C \cong \angle F\) because it completes the proof by AAS

Answer:

6.25 minutes or 375 seconds

Step-by-step explanation:

We can solve the following problem through the Proportion method.

Here,

we may take the time taken by the machine as x

\(96 : 2 : : 300 : x\\96x= 2 *300\\96x=600\\x=600/96\\x=6.25\ minutes\)

Answer:

Anthony T. answered • 03/17/21

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First, let's ask ourselves what do we want to know? We want to know how many cups of small and large lemonades were sold. Let's let S = # of small cups, and L the # of large cups.

It says she sold a total of 155 cups; that means S + L = 155. So this is one equation.

Next it says she made a total of $265. The small cups sold for $1.25 each, so she made $1.25S amount of money on these. It also says she sold large cups for $2.50 each, so she made $2.50L on these.

So, if we add up the money she made from each size, we can say 1.25S + 2.50L = 265.

Now we have two equations with 2 unknowns, and we can solve by either elimination or substitution. Let's solve it by substitution.

As S + L =155, L = 155 - S. Put this expression for L into the second equation.

1.25S + 2.50(155-S) = 265. Now solve this for S.

You should get S = 98 small cups. So, from the equation S + L = 155, solve for L which gives

L = 57 large cups. You can prove this by substituting these numbers in the second equation.

The same principles apply to other problems of this type.

A graph of the given piecewise-defined function is shown in the image below.

In Mathematics and Geometry, a piecewise-defined function simply refers to a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of this piecewise-defined function, we can reasonably infer and logically deduce that it is constant over several intervals or domains such as x > 2 and x < -2.

In conclusion, this piecewise-defined function has a removable discontinuity.

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Answer:

x = 4

Step-by-step explanation:

Because we know both figures have the same perimeter, we can set them equal to each other.

3x + 4 + 5x + 1 + 2x + 5 = x + 13 + x + 13 + 2x + 2x

10x + 10 = 6x + 26 (Added like terms.)

4x + 10 = 26 (Subtracted 6x on both sides.)

4x = 16 (Subtracted 10 on both sides.)

x = 4 (Divided 4 on both sides.)

Answer:

C

Step-by-step explanation:

the scale factor is the ratio of corresponding sides, image to original, so

scale factor = \(\frac{EF}{BC}\) = \(\frac{11}{66}\) = \(\frac{1}{6}\)

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Answer:Therefore, the equation of the line with a slope of 9/7 and containing the midpoint of the line segment with endpoints (2, -3) and (-6, 5) is:

y = (9/7)x + 25/7.

Step-by-step explanation:Step 1: Find the midpoint of the line segment.

The midpoint formula is given by:

Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)

Given the endpoints of the line segment as (2, -3) and (-6, 5), we can find the midpoint as follows:

Midpoint = ((2 + (-6)) / 2, (-3 + 5) / 2)

Midpoint = (-4 / 2, 2 / 2)

Midpoint = (-2, 1)

So, the midpoint of the line segment is (-2, 1).

Step 2: Write the equation of the line using the slope-intercept form.

The slope-intercept form of a line is given by:

y = mx + b

where m is the slope and b is the y-intercept.

Given the slope as 9/7, we have:

y = (9/7)x + b

Step 3: Substitute the coordinates of the midpoint to find the value of b.

Using the coordinates of the midpoint (-2, 1), we can substitute these values into the equation:

1 = (9/7)(-2) + b

1 = -18/7 + b

To find the value of b, we can solve this equation:

1 + 18/7 = b

25/7 = b

Step 4: Write the final equation of the line.

Using the value of b, the equation becomes:

y = (9/7)x + 25/7

The domain of the function or relation is {6, 9, -4 and 2}

The function is represented by the set of relation or ordered pairs

The ordered pairs in the relation are:

(x, y)  = (6, -3), (9, -3), (-4, 1) and (2, 1)

Remove the y values in the above domain

x = 6, 9, -4 and 2

The x values represent the domain of the function

Hence, the domain of the function or relation is {6, 9, -4 and 2}

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The number of men and women in the group will be 18 and 26 respectively.

Given is that there are eight more women than men in a theater group. The group has a total of 44 members.

Let the number of men in the group be {x}. Then, the number of women will be (x + 8). We can write -

x + (x + 8) = 44

2x = 36

x = 18

Number of women : x + 8 = 26

The number of women in the group will be 26.

Therefore, the number of men and women in the group will be 18 and 26 respectively.

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1. The probability of selecting a 3 of Diamonds is 1/52.

2. The probability of selecting a Club or Diamond is 1/2.

3. The probability of selecting a number smaller than 9 is 9/13.

1. The probability of selecting a 3 of Diamonds:

There is only one 3 of Diamonds in the deck, and the total number of cards in the deck is 52. Therefore, the probability of selecting a 3 of Diamonds is 1/52.

2. The probability of selecting a Club or Diamond:

There are 13 Clubs and 13 Diamonds in the deck, making a total of 26 cards. The probability of selecting a Club or Diamond is the ratio of the number of favorable outcomes (Club or Diamond) to the total number of possible outcomes (52 cards). Therefore, the probability is 26/52, which simplifies to 1/2.

3. The probability of selecting a number smaller than 9:

There are four suits in the deck (Clubs, Diamonds, Hearts, and Spades), and each suit has cards numbered 2 to 10. So, there are 4 suits * 9 cards per suit = 36 cards that are numbered smaller than 9.

The probability of selecting a number smaller than 9 is the ratio of the number of favorable outcomes (36 cards) to the total number of possible outcomes (52 cards). Therefore, the probability is 36/52, which simplifies to 9/13.

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The length of the rectangle is twice its width. If its perimeter is 7 1/3 cm, its length will be 22/9 cm, and the width is 11/9 cm.

Let's assume the width of the rectangle is "b" cm.

According to the given information, the length of the rectangle is twice its width, so the length would be "2b" cm.

The formula for the perimeter of a rectangle is given by:

Perimeter = 2 * (length + width)

Substituting the given perimeter value, we have:

7 1/3 cm = 2 * (2b + b)

To simplify the calculation, let's convert 7 1/3 to an improper fraction:

7 1/3 = (3*7 + 1)/3 = 22/3

Rewriting the equation:

22/3 = 2 * (3b)

Simplifying further:

22/3 = 6b

To solve for "b," we can divide both sides by 6:

b = (22/3) / 6 = 22/18 = 11/9 cm

Therefore, the width of the rectangle is 11/9 cm.

To find the length, we can substitute the width back into the equation:

Length = 2b = 2 * (11/9) = 22/9 cm

So, the length of the rectangle is 22/9 cm, and the width is 11/9 cm.

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AE= 17.4 to nearest tenth

Step-by-step explanation:

Opposite + hypotenuse = SOH / sin

Sin 31 = 6/h

xh, then ÷ sin31

H= 6/sin31

H= 11.649....(a or b & 6 being a or b)

a^2 + b^2 = c^2

c = 13.1

Actually it's not a right-angle triangle

180 - 13+31 (or 44) = 136 degrees

Cosine rule: a^2=b^2+c^2 - 2bc cosA

AE = root 11.649...^2 + 7^2 - 2x11.649...x7xcos136

= 17.3791......

AE= 17.4 to nearest tenth

Hope this helps!

Answer:

abigail

Step-by-step explanation:

abigail is correct because she has 30 dimes a dime is worth 30 cents and if 30 times ten equals 300 it would be 3 dollars so all together they have 6 dollars so now all they need is 3 dollars

I hope that made it easier for you good luck

Answer:

A. 90.24 divided by 6.3

Step-by-step explanation:

We take each option one by one and solve for it

A. 90.24 divided by 6.3

Divisor = 90.24

Dividend = 6.3

if the divisor and dividend were rounded to the nearest whole number?

= 90÷ 6

= 15

Answer:

A, I got it right on edge.

Step-by-step explanation:

The original square has one verticles at the origin, which is at (0,0), and the opposite corner at (4,4), we draw the square show below:

The transformation is moving each verticles 2 unit left and 3 units down.

The tranformation rulw can be written as:

\(x = x - 2 \\ y = - 3\)

From the graph shown above, we write the 4 cordinate pairs:

(0,0)

(4,0)

(4,4)

(0,4)

Aplying the transformation rule, we subtract 2 from x cordinate and subtract 3 from each y cordinate.

The new transformed cordinate are:

(0,0) >>>>>> (0-2, 0-3) >>>>>>> (-2, -3)

(4,0) >>>>>> (4-2, 0-3) >>>>>>> (2, -3)

(4,4) >>>>>> (4-2, 4-3) >>>>>>> (2, 1)

(0,4) >>>>>> (0-2, 4-3) >>>>>>> (-2, 1)

We name the first four cordinates A,B,C and D, respectively.

The graph ia shown below:

Answer:

There are a total of 20 presents, and 3 of them contain gems. Therefore, there are 20 - 3 = 17 presents that do not contain gems.

The probability of randomly selecting a present that does not contain a gem is 17/20 = 0.85 or 85%.

hope it helps you...

The measure of the minor arc m∡rv = 111°

Recall that according to the principle of angle of intersecting secants, (a-b)/2 = c

Where a = ∡RV
b = ∡SU = 37°:

and c = ∠T (the angle between intersecting secants.

Thus, if (a-b)/2 = c, and b = c = 37 degrees, then we can substitute these values into the equation to get:

(a - 37) / 2 = 37

Multiplying both sides by 2 gives:

a - 37 = 74

Adding 37 to both sides gives:

a = 111

Therefore, a is equal to  m∡rv = 111°.

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The system A has no solution.

The system B has the solution y=( 3-x )/3

What is the solution to an equation?

In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

System A:

x+3y=9..........(1)

-x-3y=9 ..........(2)

(1) => x=9-3y........(3)

Substitute (3) into (2)

(2) = >  - ( 9-3y ) - 3y = 9

          -9 + 3y - 3y = 9

          -9 =9

This is false.

So, the system has no solution.

System B:

-x-3y=-3..........(1)

x+3y=3..........(2)

(2) => x=3-3y........(3)

Substitute (3) into (1)

-(3-3y)-3y=-3

-3+3y-3y= -3

-3=-3

This is true,

So, the solution is:

x=3-3y

=> 3y= 3-x

=> y=( 3-x )/3

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Given that the diameter of a circle is 8.4 inches.

The radius (r) of the circle can be found by dividing the diameter by 2:

r = d/2 = 8.4/2 = 4.2 inches

The area (A) of a circle can be found using the formula:

A = πr^2

Substituting the value of r, we get:

A = 3.14 x 4.2^2 = 55.3896 ≈ 55.39 square inches

The circumference (C) of a circle can be found using the formula:

C = 2πr

Substituting the value of r, we get:

C = 2 x 3.14 x 4.2 = 26.3896 ≈ 26.39 inches

Therefore, the area of the circle is approximately 55.39 square inches and the circumference of the circle is approximately 26.39 inches.

We know that the area of a circle is given by the formula A = π×r²

Given the diameter of the circle = 8.4 in

Therefore radius of the circle = 8.4/2 = 4.2 in    (diameter/2 = radius)

Now Area of the circle = π × 4.2²

                                     = 3.14 × 17.64
                                     = 55.3896

                                     = 55.39   (round up to the nearest hundredth)

Circumference of the circle = 2 × π × r

                                              = 2 × 3.14 × 4

                                              = 26.376

                                              = 26.38 (round up to the nearest hundredth)

Therefore the area of the circle is 55.39 in² and the circumference is 26.38 in.

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The area of the triangle is 52.32 square units

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

The triangle (see attachment)

The base of the triangle is calculated as

base = 12 * tan(36)

The area of the triangle is then calculated as

Area = 1/2 * base * height

Where

height = 12

So, we have

Area = 1/2 * base * height

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 12 * tan(36) * 12

Evaluate

Area = 52.32

Hence, the area of the triangle is 52.32 square units

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Differentiate both sides implicitly:

\(\dfrac{\mathrm d}{\mathrm dt}[e^y+x^3y^2+\ln x]=\dfrac{\mathrm d[1]}{\mathrm dt}\)

\(e^y\dfrac{\mathrm dy}{\mathrm dt}+3x^2y^2\dfrac{\mathrm dx}{\mathrm dt}+2x^3y\dfrac{\mathrm dy}{\mathrm dt}+\dfrac1x\dfrac{\mathrm dx}{\mathrm dt}=0\)

Solve for \(\frac{\mathrm dx}{\mathrm dt}\):

\(\left(3x^2y^2+\dfrac1x\right)\dfrac{\mathrm dx}{\mathrm dt}=-(e^y+2x^3y)\dfrac{\mathrm dy}{\mathrm dt}\)

\(\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{e^y+2x^3y}{3x^2y^2+\frac1x}\dfrac{\mathrm dy}{\mathrm dt}\)

\(\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac{xe^y+2x^4y}{3x^3y^2+1}\dfrac{\mathrm dy}{\mathrm dt}\)

Plug in \(x=1\), \(y=0\), and \(\frac{\mathrm dy}{\mathrm dt}=2\):

\(\dfrac{\mathrm dx}{\mathrm dt}=\boxed{-2}\)

Answer:

Step-by-step explanation:

slope of AB = (-3 - (-2)) / (-3 -(-7) = -1/4

slope of BC = (-3 - (-7)) / (-3 -(-4) =  4/1

As the slopes of AB and BC are negative reciprocals of each other, they are perpendicular and therefore triangle ABC is a right triangle.

Answer:

a. x1,x2,x3,x4

b. 20x1 + 24x2 + 28x3

c. x1 +x2 ≥ 25

Step-by-step explanation:

At a time that spans from 1 to 5pm, we have timing as follows:

1pm - 2pm = x1

2pm - 3pm = x2

3pm - 4pm = x3

4pm - 5pm = x4

a. The decision variables are x1, x2, x3, x4 and these are the number of people for each shift.

b. The objective function is the minimum cost which is

20x1 + 24x2 + 28x3

c. The constraints for each has been listed

1 - 2pm, x1 ≥ 20 workers

2 - 3pm, x1 + x2 ≥ 25

3 - 4pm, x2 + x3 ≥ 25

4 - 5pm, x3 ≥ 30

The question asked us to write the one for 2-3pm, which is x1 + x2 ≥ 25

The calculated price per video game for store A is $1.79 per game

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

The price per video game for store A is calculated as

Price per video game = Total price/Number of games

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

Price per video game = 8.95/5

Evaluate the quotient

So, we have

Price per video game = 1.79

Hence, the price per video game for store A is $1.79 per game

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