which of the following is an arithmetic sequence with common difference 2
A. 1, -3, 5, -7, 9
B. 2, 4, 8, 16, 32
C. 10, 8, 6, 4, 2
D. 13, 15, 17, 19, 21

An equilibrium phase diagram can be used to determine phase transitions, phase presence, and phase compositions at different conditions.

An equilibrium phase diagram can be used to determine the below mentioned parameters:

A) It can determine where phase transitions will occur. Phase transitions refer to changes in the state or phase of a substance, such as solid to liquid (melting) or liquid to gas (vaporization). The phase diagram provides information about the conditions at which these transitions take place, such as temperature and pressure.

B) It can determine what phases will be present for each condition of chemistry and temperature. The phase diagram shows the different phases or states of a substance (such as solid, liquid, or gas) under different combinations of temperature and pressure. It provides a visual representation of the stability regions for each phase, indicating which phase(s) will be present at a given temperature and pressure.

C) It can determine the chemistry and amount of each phase present at any condition. The phase diagram gives information about the composition (chemistry) and proportions (amount) of different phases present under specific conditions. It helps identify the coexistence regions of multiple phases and provides insight into the equilibrium compositions of each phase at various temperature and pressure conditions.

In summary, an equilibrium phase diagram is a valuable tool in understanding the behavior of substances and can provide information about phase transitions, phase stability, and the chemistry and amounts of phases present at different conditions.

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Answer:

The probability of choosing a 2 first and a 3 second is 1/9

.

P(2 1st and 3 2nd) = P(2 1st ) * P(3 2nd)

= 1/3 * 1/3

= 1/9

.

Answer:

y+1=-5(x-4)

Step-by-step explanation:

YOUR WELCOME

Lines 'a' and 'c' are parallel lines.

We have to given that,

There are three lines are shown in image.

We know that,

In a parallel line,

If two angles are alternate angles then both are equal to each other.

And, If two angles are corresponding angles then both are equal to each other.

Now, From the given figure,

In lines a and c,

Corresponding angles are 65 degree.

Hence, We can say that,

Lines a and c are parallel lines.

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Answer:

(-7,-3)

Step-by-step explanation:

Answer:

If you move the point (-8,-5) to the right one, then you would be left with (-7,-5), and then to move it down 5, you get (-7,-10)

Answer:

\(\frac{85}{800}\) or \(\frac{17}{160}\) simplified

Step-by-step explanation:

In order to find the probability of this sequence of events happening we first need to find the probability of each event happening seperately and then multiply them together.

If there are 40 slip-joint pliers and only 5 are 6-inch then the probability of picking a 6-inch plier is 5/40. If there are a total of 20 rubber malets and only 3 are small then the probability of picking a non-small rubber mallet would be 17/20... Now we simply multiply these two probabilities together...

\(\frac{5 *17}{40 * 20}\) = \(\frac{85}{800}\) or \(\frac{17}{160}\) simplified

Answer:

Grade can make 55 bracelets

Step-by-step explanation:

2640/48 = 55

Answer:

55

Step-by-step explanation:

2640 divided by 48

the answer is 55

Answer:

62.17 days

Step-by-step explanation:

The computation of the number of days  is shown below:

Given that

A(t)=10 × 0.5^(t ÷ 18.72)

1 = 10 × 0.5 ^ (t ÷ 18.72)

0.1 = 0.5 ^ (t ÷ 18.72)

Now consider the log in both sides

ln(0.1) = ln(0.5)^ (t ÷ 18.72)

ln(0.1)  ÷  ln(0.5) = (t ÷ 18.72)

3.321928095  = (t ÷ 18.72)

So, t = 62.17 days

With the help of log, we can easily compute it

The scale factor used in the scale drawing which has the scale of 6 centimeters = 7 meters is 116.667

Scale factors are used to increase or decrease image. The situation of increment is usually called magnifying.

For the scale drawing with a scale of scale of 6 centimeters = 7 meters

the units are converted to be same, using the conversion unit of

100 cm = 1 m

x cm  = 7 meters'

solving for x

x = 700 cm

hence the scale of the drawing is 6 cm = 700 cm, we solve for the scale factor

6 cm = 700 cm

1 cm = scale factor

solving for the scale factor

scale factor = 700 / 6

= 350 / 3

the factor is 116.667

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The evaluation of the segment formed by the parallel lines using Thales Theorem also known as the triangle proportionality theorem are;

8. \(\overline {ST}\) is parallel to \(\overline{PR}\)

9. \(\overline{ST}\) is parallel to \(\overline{PR}\)

10. \(\overline{ST}\) is not parallel to \(\overline{PR}\)

11. x = 57.6

12. x = 25.8

13. x = 11

14. x = 10

15. x = 5

16. x = 17

Thales Theorem also known as the triangle proportionality theorem states that a parallel line to a side of a triangle that intersects the other two sides of the triangle, divides the two sides in the same proportion.

8. The ratio of the sides the segment \(\overline{ST}\) divides the sides QR and QP of the triangle ΔPQR into are; 7/11.2 = 10/16 = 0.625

Therefore; according to the Thales theorem, \(\overline{ST}\) ║ \(\overline{PR}\)

9. The ratio of the sides the parallel side to the base divides the other two sides are;

33/41.8 = 15/19

45/(102 - 45) = 45/57 = 15/19

Therefore, \(\overline{ST}\) and \(\overline{PR}\) bisects \(\overline{QP}\) and \(\overline{QR}\) into equal proportions and therefore, \(\overline{ST}\) ║ \(\overline{PR}\)

10. The ratio of the sides the segment \(\overline{ST}\)  bisects the other two sides are;

24/57 and 19/38

24/57 ≠ 19/38, therefore \(\overline{ST}\) ∦ \(\overline{PR}\)

Second part; To solve for x

11. x/30 = 48/25

x = (48/25) × 30 = 57.6

x = 57.6

12. x/34.4 = (49 - 28)/28

x = 34.4 × (49 - 28)/28 = 25.8

x = 25.8

13. (2·x + 6)/52.5 = 32/60

(2·x + 6) = 52.5 × (32/60)

x = (52.5 × (32/60)) - 6)/2 = 11

x = 11

14. (x - 3)/21 = (x - 1)/27

27·x - 27 × 3 = 21·x - 21

27·x - 81 = 21·x - 21

6·x = 60

x = 60 ÷ 6 = 10

x = 10

15. (35 - 20)/20 = (4·x - 2)/(7·x - 11)

15/20 = (4·x - 2)/(7·x - 11)

15 × (7·x - 11) = 20 × (4·x - 2)

105·x - 165 = 80·x - 40

105·x - 80·x = 165 - 40 = 125

25·x = 125

x = 125/25 = 5

x = 5

16. (x - 3)/35 = 4/(x - 7)

(x - 3) × (x - 7) = 35 × 4 = 140

x² - 10·x + 21 = 140

x² - 10·x - 119 = 0

(x - 17) × (x + 7) = 0

x = 17 or x = -7

Therefore, the possible value of x is 17

x = 17

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The Distance between the given parallel planes is 8.84.

According to the statement

we have given that the two parallel planes and we have to find the distance between them.

So, For this purpose, we know that the

First let us find a point on one plane. For this in plane 9z +3x - 3y = 2

assume x = 0 and y = 0 then and hence (0,0,2/9) on this plane.

Now we find the distance between point (0,0,2/9) and plane 6z -2y + 2x =0

So,

As distance from a point to plane is

\(D= \frac{|ax_1+by_1+cz_1+d|}{\sqrt{ (a^2+b^2+c^2)}}\)

And

now substitute the values in then

\(D= \frac{|2*0+ (-2)0+6*2/9+0|}{\sqrt{ 36 +4+4)}}\)

Then the value becomes

\(D= \frac{4/3}{\sqrt{ (44)}}\)

\(D= \frac{4\sqrt{44} }{3}\)

Then solve it

\(D= \frac{26.52}{3}\)

then

D = 8.84

So, The Distance between the given parallel planes is 8.84.

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Answer:

-6x+19

Step-by-step explanation:

-6(x-4) = -6x+24

-6x+24-5 = -6x +19

Answer:

The quotient of 4 and 9 raised to the power of r.

Step-by-step explanation:

The verbal translation of  \(r^{\frac{4}{9} }\)  is r to the power four-tenths.

Given,

\(r^{\frac{4}{9} }\)

We have a number r with power 4 / 9.

we need to translate it into verbal form.

If a number is expressed in this form - \(A^{B}\)

A = base and B = exponents.

We can say that a number has base A with exponents B.

There are many ways to verbally express a given number.

Example:

3 / 2 = 3 divide by 2.

\(6^{2}\) = six to the power two.

3 x ( 3 + 2 ) = three multiplied with the addition of three and two.

7 x \(8^{3}\) =  seven multiplied by 8 to the power three.

\(3^{\frac{1}{7} }\) = three to the power of one-tenths.

We are given,

     \(r^{\frac{4}{9} }\)

We can say that the base is r and the exponent is 4/9.

or

we can also say r to the power four-tenths.

Thus the verbal translation of  \(r^{\frac{4}{9} }\)  is r to the power four-tenths.

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Answer:

x = 12; m<ABC = 76

Step-by-step explanation:

The two angles whose measures are given form a linear pair. Therefore, they are supplementary angles, and their measures add up to 180 degrees.

8x - 20 + 116 - x = 180

7x + 96 = 180

7x = 84

x = 12

The angle with measure 8x - 20 and angle ABC are vertical angles. That means that their measures are equal.

m<ABC = 8x - 20 = 8(12) - 20 = 96 - 20 = 76

Answer: x = 12; m<ABC = 76

Answer:

it needed your to focus on school work , homework and work hard to make yourself feel ready

Answer:

21/2 or 10.5

Step-by-step explanation:

5x - 3y

5(5/2) - 3(2/3)

25/2 - 2

25/2 - 4/2

21/2

Use the given recursion and starting value of \(x_0 = 2.4\) to find \(x_1\) :

\(x_1 = \dfrac{x_0 + \frac6{x_0}}2 = \dfrac{2.4 + \frac{6}{2.4}}2 = 2.45\)

Do the same for \(x_2\) and \(x_3\) :

\(x_2 = \dfrac{x_1 + \frac6{x_1}}2 = \dfrac{2.45 + \frac6{2.45}}2 \approx 2.44949\)

\(x_3 = \dfrac{x_2+\frac6{x_2}}2 \approx \dfrac{2.44949 + \frac6{2.44949}}2 \approx \boxed{2.44949}\)

(That's not a mistake. This just tells you that the 2nd and 3rd iterates are very close together and have at least the same first 5 digits after the decimal.)

If 5 guests are randomly selected from 17 guest and all 5 prizes are identical, there are 89107200 ways in which the prizes can be awarded.

It is given to us that -

17 guests are in attendance at a baby shower

5 of them are randomly selected for a prize

All the 5 prizes are identical

We have to find out the number of ways in which the prizes can be awarded.

In this case, we have to use the combination formula to find the required answer.

We know that the combinations of n number of objects taken r at a time can be represented by the formula as -

\(C(n,r) = r!\frac{n!}{(n-r)!}\)   ------ (1)

where,

n = total objects in the given set

r = total chosen objects from the given set

According to the given information, we have -

n = 17

r = 5

Substituting these values in equation (1), we have

\(C(n,r) = r!\frac{n!}{(n-r)!}\\= > C(n,r) = 5!*\frac{17!}{(17-5)!}\\= > C(n,r) = 5!*\frac{17!}{12!}\\= > C(n,r) = 89107200\)

Therefore, if 5 guests are randomly selected from 17 guest and all 5 prizes are identical, there are 89107200 ways in which the prizes can be awarded.

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Answer:

-1 or -1/1

Step-by-step explanation:

Looked it up, found an answer that said

"X+Y = 6

change into slope intercept form y=mx+b

y= -x +6

the number infront of X is the slope...so....-1/1 would be your slope

Parallel lines have the same slope, so the answer is -1 or -1/1"

Hope this is correct, and good luck

Lex will need approximately 18.96 units of tile to surround his pool. The perimeter of the quadrilateral is the sum of these lengths.

To find the number of units of tile Lex will need to surround his pool, we can calculate the perimeter of the quadrilateral ABCD.
Given the coordinates of the vertices on the coordinate plane, we can calculate the lengths of the sides:
AB = \(\sqrt((3-0)^2 + (5-4)^2) = \sqrt(9+1) = \sqrt(10)\) = 3.16 units (rounded to the nearest hundredth)
BC = \(\sqrt((5-3)^2 + (-1-5)^2) = \sqrt(4+36) = \sqrt(40)\) = 6.32 units (rounded to the nearest hundredth)
CD = \(\sqrt((2-5)^2 + (-2+1)^2) = \sqrt(9+1) = \sqrt(10)\) = 3.16 units (rounded to the nearest hundredth)
DA = \(\sqrt((2-0)^2 + (-2-4)^2) = \sqrt(4+36) = \sqrt(40)\) = 6.32 units (rounded to the nearest hundredth)
The perimeter of the quadrilateral is the sum of these lengths:
Perimeter = AB + BC + CD + DA = 3.16 + 6.32 + 3.16 + 6.32 = 18.96 units (rounded to the nearest hundredth)
Therefore, Lex will need approximately 18.96 units of tile to surround his pool.

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Lex will need approximately 20.46 units of tile to surround his pool. To find the number of units of tile needed to surround the pool, we need to calculate the perimeter of the pool.

Given the coordinates of the four vertices of the pool:
    A(0, 4)
    B(3, 5)
    C(5, -1)
    D(2, -2)

We can find the length of segment AB using the distance formula:
    \(AB = \sqrt{(3-0)^2 + (5-4)^2} = \sqrt{9 + 1} = \sqrt{10} = 3.16\)units (rounded to the nearest hundredth).

The length of diagonal BD can also be found using the distance formula:
    \(BD = \sqrt{(2-3)^2 + (-2-5)^2} = \sqrt{1 + 49} = \sqrt{50} = 7.07\) units (rounded to the nearest hundredth).

Since angles A and C are right angles, we know that the opposite sides AB and CD are parallel. Similarly, the opposite sides AD and BC are parallel.

The perimeter of the pool is the sum of the lengths of all four sides:
    Perimeter = AB + BC + CD + AD
                      = 3.16 + BD + 3.16 + BD
                      = 6.32 + 7.07 + 7.07
                      = 20.46 units (rounded to the nearest hundredth).

Therefore, Lex will need approximately 20.46 units of tile to surround his pool.

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p-value of the test.

To answer this question, we can use the KS Test. The KS Test is used to compare two empirical cumulative distribution functions. In this case, we can use the KS Test to compare the ECDFs of stores with above-median prices and those with below-median prices in the carseats dataset. To do this, we use the `ks.test()` function, which has two parameters - `x` and `y`. The `x` parameter represents the data from stores with above-median prices, and the `y` parameter represents the data from stores with below-median prices. The function will then return the p-value of the test.

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Step-by-step explanation:

Let's solve your equation step-by-step.

3(2x+1)+4=10

Step 1: Simplify both sides of the equation.

3(2x+1)+4=10

(3)(2x)+(3)(1)+4=10(Distribute)

6x+3+4=10

(6x)+(3+4)=10(Combine Like Terms)

6x+7=10

6x+7=10

Step 2: Subtract 7 from both sides.

6x+7−7=10−7

6x=3

Step 3: Divide both sides by 6.

6x/6=3/6

x=1/2

Answer:

x=1/2

Answer:

x = 1/2

Step-by-step explanation:

3(2x + 1) + 4 = 10

open the parenthesis

3 * 2x + 3 * 1 + 4 = 10

6x + 3 +4 = 10

6x + 7 = 10

subtract 7 from both sides of the equation

6x + 7 - 7 = 10 - 7

6x = 10 - 7

6x = 3

divide both sides of the equation by 6

6x/6 = 3/6

x = 3/6

simplify the fraction

x = 1/2

Based on the data in the table, if a cow is randomly selected from farm B, the probability that its feed includes seaweed is 0.597 (Option D) and without is 0.57

Note that the total number of feed with sea weed is 74.
And the total number of cows on the farm B is 124.

Thus, the cows whose feed includes seaweed is 74/124

= 0.59677419354

≈ 0.597

The Probability of those whose feed is without sea weed is

Note that the total number of feed without sea weed is 40.
And the total number of cows on the farm B is 76.

Thus, the probability is 40/70
= 0.5714285714

≈ 0.571

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The correct answer is B) The maximum acceptable cost of the new bridge is $2,183,180.

To determine the maximum acceptable cost (X) of the new bridge, we need to compare the costs of the new bridge and the refurbished bridge over a 20-year period, taking into account the maintenance costs, toll revenue, and MARR (Minimum Acceptable Rate of Return) of 12% per year.

For the new bridge:

Initial cost: $X

Annual maintenance cost: $23,000

Toll revenue per year: 390,000 cars * $0.27 per car = $105,300

Cost of collecting tolls (salaries): 5 collectors * $10,000 per collector = $50,000 per year

For the refurbished bridge:

Initial refurbishing cost: $1,800,000

Additional refurbishing costs every 5 years: $65,000

Regular annual maintenance cost: $19,000

To find the maximum acceptable cost (X) of the new bridge, we need to calculate the present worth (PW) of costs and benefits for both options over the 20-year period, considering the MARR of 12% per year. The option with the higher PW would be the maximum acceptable cost.

Calculating the present worth for the new bridge:

PW of costs = X + (Annual maintenance cost + Cost of collecting tolls) * Present Worth Factor (PWF) at 12% for 20 years

PW of benefits = Toll revenue per year * PWF at 12% for 20 years

Calculating the present worth for the refurbished bridge:

PW of costs = Initial refurbishing cost + (Additional refurbishing costs + Regular annual maintenance cost) * PWF at 12% for 20 years

Comparing the PW of costs and benefits for both options, the maximum acceptable cost (X) of the new bridge is the value that makes the PW of costs for the new bridge equal to the PW of costs for the refurbished bridge.

By performing the calculations using the interest and annuity table for discrete compounding at 12%, we find that the maximum acceptable cost (X) of the new bridge is $2,183,180.

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