Which equation has infinitely many solutions?
1/3(6x - 12) = 2(x-2)
1/2(4x+8)=2x+8
3(2x-7)= 6(x-4)-3
5 (2+1)= 3x + 2(x+1)+4

If one her 4 numbers come up, she wins $40 (and gets to keep her bet!). Alyssa can expect to lose 47 cents per bet over the long run.

The expected value of a game is the average amount that a player can expect to win or lose per bet, taking into account both the probabilities and the payouts of each possible outcome. To find the expected value, we multiply the probability of each outcome by the amount won or lost for that outcome, and then sum up these products.

In this case, Alyssa bets $5 on a block of 4 numbers, which gives her a probability of winning of 4/38, or approximately 0.1053. If one of her 4 numbers comes up, she wins $40, for a net gain of $35 (since she gets to keep her $5 bet as well). If none of her 4 numbers comes up, she loses her $5 bet.

Therefore, the expected value for each bet is:

(0.1053 × $35) + (0.8947 × -$5) = -$0.47

So if she plays many times, she can expect to lose money overall. It's important to keep in mind that expected value is not a guarantee of what will happen on any particular bet, but rather a long-term average based on probabilities.

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The percentage increase of the gas would be 2.5%.

We can calculate the value of the percentage increase by the following formula,

percentage increase = (final value - initial value) / initial value × 100%

As per the given question, we have

initial value = $2.81 , and final value = $2.88

Substitute the values in the above formula, and we get

percentage increase= (2.88 - 2.81 ) / 2.81 × 100%

percentage increase = (0.07) / 2.81× 100%

percentage increase = 0.0249 × 100%

Apply the multiplication operation, and we get

percentage increase = 2.49%

Thus, the percentage increase of an item would be 2.5%.

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The measure of ∠A is 53.

The measure of ∠B is 37.

An expression contains one variable or more than one variable with addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

∠A and ∠B are complementary.

This means,

∠A + ∠B = 90

Now,

∠A = 7x + 4

∠B = 4x + 9

7x + 4 + 4x + 9 = 90

11x + 13 = 90

11x = 90 - 13

11x = 77

x = 7

Now,

∠A = 7x + 4 = 7 x 7 + 4 = 49 + 4 = 53

∠B = 4x + 9 = 4 x 7 + 9 = 28 + 9 = 37

Thus,

∠A = 53

∠B = 37

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Answer:

The distance to the nearest exit door is at most 100 feet can be written as an inequality as:

d ≤ 100

Answer:

9 cups

Step-by-step explanation:

1 cup is 8 ounces

72/8 is 9

The explicit formula and recursive formula of the geometric sequence is  Aₙ = 12(R)ⁿ⁻¹ where n is an integer.

It is given that in a geometric sequence, the second term and the common ratio are 6 and /2 respectively.

Now, we have to write the standard formula that can be further formulated as the explicit formula and recursive formula of the geometric sequence, The formula goes as,

Aₙ = A₁(R)ⁿ⁻¹

Here,

Aₙ is the nth term of the sequence. So, if we want the first term then will put n = 1, n= 2 for second term and so on.

Now, putting n = 2,

A₂ = A₁(R)²⁻¹

A₂ = A₁(R)

6 = A₁(1/2)

A₁ = 12

So, the explicit and recursive formula will be Aₙ = 12(R)ⁿ⁻¹.

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the equation of the straight line will be y = 10x+10.

What is equation straight line?

Y = mx + c is the general equation for a straight line, where m denotes the line's slope and c the y-intercept. It is the version of the equation for a straight line that is used most frequently in geometry. There are numerous ways to express the equation of a straight line, including point-slope form, slope-intercept form, general form, standard form, etc. A straight line is a geometric object with two dimensions and infinite lengths at both ends. The formulas for the equation of a straight line that are most frequently employed are y = mx + c and axe + by = c. Other versions include point-slope, slope-intercept, standard, general, and others.

The initial value 10

slope m = 30-20/2-1

m = 10/1=10

So the equation of the straight line will be y = 10x+10.

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Answer:

27,5%

Step-by-step explanation:

To find the percent decrease, we need to calculate the difference between the original number and the new number and then divide it by the original number and multiply by 100%.

The difference is 40 - 29 = 11.

The percent decrease is (11/40) * 100% = 27.5%

So the percent decrease in staff is 27.5%

The radius of the curved part of the track will be 37.3m.

Solution:

Given that

The length of straight parts = 80m each

The total length of the track = is 400m

So, the total length of curved parts = 400 - (80*2) = 240m

Therefore, the radius of the curved parts =

[tex]2\pi r = 240\\r = 240/2\pi \\[/tex]

Hence, r = 37.3m.

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Answer: no. it is not in standard form

We cannot find the x-intercept of this  equation by substituting 0 for y and solving for the x.

Step-by-step explanation:

Answer:

If the height of the triangle is 11 cm greater than its corresponding base, we can represent the base as b and the height as h = b + 11.

Using the formula for the area of a triangle, A = (1/2) bh, we can substitute the values of b and h:

A = (1/2) (b)(b + 11)

A = (1/2) b^2 + (1/2) 11b

If the base of the triangle is 10 cm, then we can substitute b = 10 into the equation:

A = (1/2) (10^2) + (1/2) 11 * 10

A = 50 + 55

A = 105 cm^2

So, the area of the triangle is 105 cm^2.

Step-by-step explanation:

The amount of money Jamar will make in his 18th year working at this job is = $107,500

A salary is a form of periodic payment from an employer to an employee, which may be specified in an employment contract. It is contrasted with piece wages, where each job, hour or other unit is paid separately, rather than on a periodic basis.

here, we have,

Calculation of yearly salary outcome

The amount of money Jamar made in his first year= $48,000

The salary rise per year = $3,500

The amount of money he will make for the extra 17 years is

= 17 × $3,500

= $59,500

Therefore the amount he will receive as his salary in the 18th year working at this job = $48,000 + $59,500

= $107,500

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In circle M, m/NMO = 144º, and the area of the shaded sector = 107. then the length of MN is 23.19 units.

What is the sector of the circle?

That the portion (or part) of the circular region enclosed by two radii and the corresponding arc is called a sector of the circle.

The area of the shaded sector of circle M can be represented as follows:

Area of sector = (m/NMO / 360) * π * r²

We know that m/NMO = 144° and the area of the sector is 107, so we can substitute these values into the equation and solve for the radius:

107 = (144 / 360) * π * r²

Multiplying both sides of the equation by 360 / 144 gives:

360 * 107 / 144 = π * r²

Dividing both sides of the equation by pi gives:

r² = 360 * 107 / (144 * π)

Taking the square root of both sides of the equation gives:

r = √(360 * 107 / (144 * π))

Now that we know the radius, we can use it to find the length of MN.

The length of the minor arc MN is equal to the length of the central angle NMO in radians times the radius:

MN = m/NMO * π * r / 180

Substituting in the values for m/NMO and r gives:

MN = 144 * π * √(360 * 107 / (144 * π)) / 180

Hence, In circle M, m/NMO = 144º, and the area of the shaded sector = 107. then the length of MN is 23.19 units.

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Answer:

Radius is 2√3 units

Center is (8,-4)

Step-by-step explanation:

Compared to the standard form equation of a circle, [tex](x-h)^2+(y-k)^2=r^2[/tex], then the radius would be [tex]r=\sqrt{12}=2\sqrt{3}[/tex] and the center would be [tex](h,k)\rightarrow(8,-4)[/tex].

Answer:

Step-by-step explanation:

From a hot-air balloon, Violet measures a 24

∘

∘

 angle of depression to a landmark that’s 806 feet away, measuring horizontally. What’s the balloon’s vertical distance above the ground? Round your answer to the nearest tenth of a foot if necessary.

Answer:

Area = 200ft²

Step-by-step explanation:

Perimeter of a rectangle = 2(length+width)

Area of a rectangle = length * width

Then:

g = 2w           Eq. 1

60 = 2(g+w)   Eq. 2

g = length

w = width

From Eq. 2

60 = 2g + 2w

60 - 2g = 2w      Eq. 3

matching Eq. 1 and Eq. 3

g = 60 - 2g

g + 2g = 60

3g = 60

g = 60/3

g = 20 ft

From Eq. 1

g = 2w

20 = 2w

20/2 = w

w = 10 ft

Area

area = length * width

area = 20ft * 10 ft

area = 200ft²

Answer:

it could be either 1, 2 or 7

Step-by-step explanation:

1×14=14

2×7=14

7×2=14

There are 4,431,621,036,503,680 different ways to seat the 60 students in 62 seats.

If there are 60 students and 62 seats, then there will be 2 empty seats in the classroom. We need to find out the number of ways to seat the 60 students in these 62 seats.

To solve this problem, we can use the permutation formula:

nPr = n! / (n - r)!

where n is the total number of objects and r is the number of objects we want to arrange.

In this case, we want to arrange 60 students in 62 seats, so we can use the formula as follows:

62P60 = 62! / (62 - 60)!

= 62! / 2!

= 62 x 61 x 60 x ... x 3 x 2 x 1

= 4,431,621,036,503,680

Therefore, there are 4,431,621,036,503,680 different ways to seat the 60 students in 62 seats.

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Answer:

The solution is (x = 6, y = -3)

Step-by-step explanation:

[tex]\sf \frac{x}{y + 1} = - 3 \: \: ........(1) \\ \\ \sf \frac{y}{x - 3} = - 1 \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \sf x + 3y = - 3 \: ........(1) \\ \\ \sf x + y = 3 \: \: \: \: \: \: ........(2) \\ \\ - - - - - - - - - \\ \\ \: \: \: \sf x + 3y = - 3 \: \: \: \: \: | \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \sf x + y = 3 \: \: \: \:\: \: \: \: | \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

The possible height of Natasha's little brother is less than or equal to 4.5 feet. We can write the final inequality as: b ≤ 4.5

Let's denote the height of Natasha as "n" and the height of her little brother as "b".

We know that Natasha is one foot taller than her little brother, so we can write:

n = b + 1

We also know that Natasha's height is no more than 5-1/2 feet, so we can write:

n ≤ 5.5

Now we can substitute the first equation into the second equation and get:

b + 1 ≤ 5.5

Simplifying this inequality, we get:

b ≤ 4.5

Therefore, the possible height of Natasha's little brother is less than or equal to 4.5 feet. We can write the final inequality as:

b ≤ 4.5

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The correct equations are:8x^3 * (3x^2) = 24x^5, 6b^3 * (-2b^3) = -12b^6, 3a^3 * (-3a^4) = -9a^7. The equations are correct because they follow the rules of algebra. The equation 4x^3 * (6x^2) = 24x^5 is not correct.

The distributive property of multiplication over addition allows us to multiply a factor by each term inside a set of parentheses. In the equation 8x^3 * (3x^2), we can use the distributive property to multiply 8x^3 by each term inside the parentheses, giving us 24x^5.

Similarly, the product of two negative numbers is positive, which explains why the equation 6b^3 * (-2b^3) equals -12b^6.

Finally, multiplying two terms with the same base means we add the exponents, so in the equation 3a^3 * (-3a^4), we get -9a^7.

Therefore, these equations are correct and follow the rules of algebra.

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The required, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.

Given: ABCD is a parallelogram. To prove: mZA + mZB + mZC + mZD = 360 degrees

A parallelogram is a quadrilateral consisting of pairs of parallel sides.

Here,
The proof you provided is correct! Here's a step-by-step explanation of the proof:

By the definition of a parallelogram, AD // BC and AB/DC.

Using AD as a transversal, ZA and ZD are same-side interior angles, so they are supplementary (meaning their measures add up to 180 degrees).

Using side AB as a transversal, ZB and ZC are same-side interior angles, so they are supplementary as well.

By the definition of supplementary angles, mZA + mZD = 180 degrees and mZB + mZC = 180 degrees.
Adding the two equations together, we get:

mZA + mZD + mZB + mZC = 180 degrees + 180 degrees

Simplifying the right side of the equation, we get:

mZA + mZB + mZC + mZD = 360 degrees

Therefore, we have proven that the sum of the measures of the angles in parallelogram ABCD is 360 degrees.

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Answer:

5(x – 3) = x + 13 with x = 6 substituted: 5(6 – 3) = 6 + 13

Simplifying both sides: 5(3) = 6 + 13

15 = 19

x = 6 is not a solution to the equation because when you substitute it, the left side of the equation (15) does not equal the right side of the equation (19).

To find a value of x that is a solution to the equation, we can start by solving for x:

5(x – 3) = x + 13

5x – 15 = x + 13

4x = 28

x = 7

So, x = 7 is a solution to the equation 5(x – 3) = x + 13. To find this solution, we first substituted x = 7 into the equation and simplified both sides to see if they were equal.

Step-by-step explanation:

The linear equation that describes the problem is: 2x + y = 300.

A linear equation can be defined in standard form as Ax + By = C, where:

A, B, and C are integers

x and y are variables.

From the information given, we have the following:

number of games = x

rent for a pair of shoes for any number of games = y

total earnings goal for that day = 300

Therefore, the linear equation would be: 2x + y = 300

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A chairman and vice chairman are to be selected from a committee of eight people in such a way that no one treasurer individual can hold more than one position. The permutation of 8 different objects, chosen two at a time, results in the number of possible chairman selections in this situation.

[tex]^{8} P_{2} =[/tex][tex]8/8-2=8/6=8*7*6/6=8*7=56[/tex]

Cash and liquidity management, risk management, and corporate finance are among the important basic responsibilities of a corporate treasurer. The division in charge of a nation's finances, economy, and revenue is known as the treasury. Although in certain nations the treasury answers to a Secretary of the Treasury or Chancellor of the Exchequer, the treasurer is often in charge of the department. After the Prime Minister and Deputy Prime Minister, the Treasurer is a senior minister in Australia and frequently the second or third most significant member of the cabinet. Additionally, each Australian state and autonomous territory has its own treasurer.

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Answer:

400 calories

Step-by-step explanation:

Let's call the number of calories in the loaded baked potato as P. Then the coleslaw had P-50 calories and the steak had 2P calories.

So the equation for the total number of calories in the meal is:

P + (P-50) + 2P = 1550

4P = 1600

P = 400

Therefore, the loaded baked potato had 400 calories.

Answer:

Below

Step-by-step explanation:

c oleslaw =   p - 50

p = potato

s = 2 p       Summed these = 1550

p-50     + p    + 2p   =  1550      Gather 'like' terms

4p - 50 = 1550                           add 50 to both sides of the equation

4p = 1600                                  divide both sides by 4

p = 400 calories

The probability that the dictionary is selected is 0.417, 3 novels and 2 books of poems are selected is 0.707. The probability that 4 novels are selected is 0.354.

The probability that the dictionary is selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select the dictionary and 4 other books.

The total number of ways to select 5 books from the shelf is:

C(12,5) = 12! / (5! * 7!) = 792

The number of ways to select the dictionary and 4 other books is:

C(1,1) * C(11,4) = 11! / (4! * 7!) = 330

Therefore, the probability that the dictionary is selected is:

P(dictionary) = 330/792 = 0.417

The probability that 3 novels and 2 books of poems are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 3 novels and 2 books of poems.

The total number of ways to select 5 books from the shelf is:

C(12,5) = 12! / (5! * 7!) = 792

The number of ways to select 3 novels and 2 books of poems is:

C(8,3) * C(3,2) = (8! / (3! * 5!)) * (3! / (2! * 1!)) = 560

Therefore, the probability that 3 novels and 2 books of poems are selected is:

P(3 novels, 2 books of poems) = 560/792 = 0.707

The probability that 4 novels are selected, we need to determine the total number of ways to select 5 books from the shelf, as well as the number of ways to select 4 novels and 1 other book.

The total number of ways to select 5 books from the shelf is:

C(12,5) = 12! / (5! * 7!) = 792

The number of ways to select 4 novels and 1 other book is:

C(8,4) * C(4,1) = (8! / (4! * 4!)) * (4! / (1! * 3!)) = 280

Therefore, the probability that 4 novels are selected is:

P(4 novels) = 280/792 = 0.354

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_____ The given question is incomplete, the complete question is given below:

If 5 books are picked at random from a shelf containing 8 novels, 3 books of poems, and a dictionary, what is the probability that a. the dictionary is selected? b. 3 novels and 2 books of poems are selected? c. 4 novels are selected?

Answer:

See below

Step-by-step explanation:

Sum of 18 and 6 = 24

1/4 of the sum of 18 and 6 is asking you what is the result of dividing 24 by 4

In  a way you can think of it as a fractional question but the answer is a whole number

[tex]\dfrac{1}{4} \cdot (18 + 6) = \dfrac{1}{4} \cdot 24 = \dfrac{24}{4} = 6\\[/tex]

Answer: x = 4, y = -8

Step-by-step explanation:

Because 2 is a multiple of four, multiply the first equation by two to eliminate the x value and effectively isolate y.

4x - 4y = 48

4x + 7x = -40

If we were to subtract the x values, that gives us -11y = 88, or y = -8.

Then, just plug y into your equation of choice.

2x - 2(-8) = 24

2x + 16 = 24

2x = 8

x = 4

One way you can check whether the values is right is plug the y value into the other equation and see if you receive the same answer.

4x + 7(-8) = -40

4x = -40 + 56

4x = 16

x = 4

The time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.

What is the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value.

Let W be the total work to be done, which is installing a new deck.

Given Ted alone can complete the work W  in 15 hours.

Using unitary method,

So in one hour, work done by Ted = W/15

Also given Jimmy alone can complete the work W in 16 hours.

So in one hour, work done by Jimmy = W/16

Using unitary method,

In one hour the work done by Jimmy and Ted together = W/15 + W/16 = 31W/240

ie 31W/240 = 1 hour

 So W = 240/31 = 7.7 hours

Therefore the time taken to complete the work when Ted and Jimmy work together is found using the unitary method and it is 7.7 hours.

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