Marshall and oliver went to an arcade where the machines took tokens. marshall played 10 games of skee ball and 8 games of pinball, using a total of 44 tokens. at the same time, oliver played 3 games of skee ball and 8 games of pinball, using up 30 tokens. how many tokens does each game require?

The dimensions that maximize the enclosed area are L = 41.665 feet and W = 41.665 feet for each corral and the maximum area is 10868.09 square feet.

To find the dimensions that maximize the enclosed area, we need to use optimization techniques. Let's denote the length of each rectangular corral by L and the width by W. We can write the total enclosed area as A = 6LW.

The perimeter of each corral is given by P = 2L + 2W, and we have a total of 6 corrals, so the total length of fencing required is 6P = 12L + 12W.

We are given that we have 1,000 feet of fencing, so we can write 12L + 12W = 1000, or equivalently, L + W = 83.33 (rounded to two decimal places).

We can now use this equation to express one of the variables (say, W) in terms of the other: W = 83.33 - L.

Substituting this expression for W into the formula for the enclosed area, we get A = 6L(83.33 - L) = 499.98L - 6L^2.

To find the value of L that maximizes the area, we need to take the derivative of A with respect to L and set it equal to zero: dA/dL = 499.98 - 12L = 0. Solving for L, we get L = 41.665 (rounded to three decimal places).

Substituting this value back into the expression for W, we get W = 83.33 - L = 41.665.

The maximum area is A = 6LW = 10868.09 square feet (rounded to two decimal places).

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Answer:

permutations: order matters

combinations: order doesn't matter

Answer:

A combination doesn't need to be in a specific order, unlike permutation which needs to go in order.

Step-by-step explanation:

Answer:

y = 2/5x + 18.

Step-by-step explanation:

The line will have the same slope of 2/5.

Using the point-slope form of a line:

y - 12 = 2/5(x - -15)

y - 12 = 2/5(x + 15)

y = 2/5x + 6 + 12

y = 2/5x + 18.

Answer:

y  = (2/5)*x + 18

Step-by-step explanation:

Because the line is parallel to the line y = 2/5 x + 17, the slope of the new line has to be the same as well. So far, we have y = (2/5)*x .

Now what we can do is plug in -15 for x and see what we get for y. Because we get -6, we need 18 more to make it 12. Because of that, the y-intercept is 18 to make the equation of the line y  = (2/5)*x + 18.

Answer:

the first one

Step-by-step explanation:

the other 3 are correct if you was to convert them into fractions

Yellow = 8/17

Orange = 3/17

Red = 6/17

2nd statement: Y > R which is correct

3rd statement: R = 2×O which is correct

4th statement: 1/2×R=O which is correct

Answer: It is likely that the pinnies will be orange

Step-by-step explanation:

Because there are a total of 17 pinnies and only 3 of them are orange so there is a 3/17 chance you get the orange. which is the least likely to happen

1. The number of quarters you could receive for a $5,000 payment is 47.73 quarters. Therefore, the correct option is C.

2. The amount you receive every month for 6 years is 3,910.04. Therefore, the correct option is B.

1. The formula to determine the number of quarters we will use the present value formula which is given as:

PV * (1 + r / n)^(n * t) = FV

PV = $200,000

r = 2.0% = 0.02

n = 4 (quarterly payment)

FV = $5,000

Using the formula:

200,000(1 + 0.02 / 4)^(4q) = 5000 (divided both sides by 200,000 and log to base 1.005 on both sides to isolate for 'q')

q = log(0.025 / -4log(1.005)) ≈ 47.73 quarters (rounded to two decimal places)

Thus, the correct option is C) 47.73 quarters

2. The formula to determine the monthly payment is given as:

PMT = (P * r) / (1 - (1 + r)^(-n))

P = $200,000

r = 1.0% / 100 = 0.01

n = 6 * 12 = 72

Using the formula:

PMT = (200,000 * 0.01) / (1 - (1 + 0.01)^(-72))≈ $3,910.04

Thus, the correct option is B) $3,910.04

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Check the picture below.

\(~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-5}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) ~\hfill AB=\sqrt{[ -1- (-5)]^2 + [ 6- 2]^2} \\\\\\ ~\hfill \boxed{\sqrt{32}} \\\\\\ B(\stackrel{x_1}{-1}~,~\stackrel{y_1}{6})\qquad C(\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) ~\hfill BC=\sqrt{[ 3- (-1)]^2 + [ 2- 6]^2} \\\\\\ ~\hfill \boxed{\sqrt{32}}\)

\(C(\stackrel{x_1}{3}~,~\stackrel{y_1}{2})\qquad D(\stackrel{x_2}{-1}~,~\stackrel{y_2}{-2}) ~\hfill CD=\sqrt{[ -1- 3]^2 + [ -2- 2]^2} \\\\\\ ~\hfill \boxed{\sqrt{32}} \\\\\\ D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-5}~,~\stackrel{y_2}{2}) ~\hfill DA=\sqrt{[ -5- (-1)]^2 + [ 2- (-2)]^2} \\\\\\ ~\hfill \boxed{\sqrt{32}}\)

\(~\dotfill\\\\ \sqrt{32}\implies \sqrt{16\cdot 2}\implies \sqrt{4^2\cdot 2}\implies 4\sqrt{2}\implies \stackrel{\textit{four times that much}}{4(4\sqrt{2})\implies \blacksquare~~ 16\sqrt{2} ~~\blacksquare}\)

It's a rhoumbus as AC and BD both diagonals are perpendicular to each other .

Find one side

AD

So

Perimeter

Labor content (labor dollar per unit) is the total cost of labor required to produce one unit of a product. It can be calculated by dividing the total labor cost by the number of units produced.

In this scenario, we are given that an employee produces 17 parts during an 8-hour shift and earns $109 per shift.

To calculate the labor content, we first determine the labor cost per hour. This is done by dividing the total amount earned in the 8-hour shift by 8.

Labor cost per hour = $109 ÷ 8 = $13 per hour

Next, we calculate the number of parts produced per hour by dividing the total number of parts produced (17) by the duration of the shift (8 hours).

Parts produced per hour = 17 ÷ 8 = 2.125 parts per hour

Finally, we calculate the labor cost per part by dividing the labor cost per hour by the number of parts produced per hour.

Labor cost per part = $13 ÷ 2.125 = $6.12 per part

Therefore, the labor content (labor dollar per unit) of the product is $6.12 per part.

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Answer:

x = 10

Step-by-step explanation:

Sum of all the angle of triangle = 180

71 + 50 + 6x - 1 = 180

71 + 50 -1 + 6x = 180

    120  + 6x   = 180

            6x = 180 - 120

           6x = 60

             x = 60/6

x = 10

Answer:

4 1/4

Step-by-step explanation:

Using ratios, the sentences are completes as follows:

The ratio between two amounts a and b is given by the division of a by b, as follows:

r = a/b.

Between two amounts b and a, the ratio is given by the division of b by a, as follows:

r = b/a.

This means that the ratio between two amounts is not commutative, meaning that the order of the amounts matters.

A ladybug with 2 eyes and 6 spots, hence the first sentence is given as follows:

There are 6 spots for every 2 eyes. (ratio is the number of eyes for 6 spots).

The number of spots per eye is the ratio of the number of spots and the number of eyes, as follows:

Spots per eye = 6 spots/2 eyes = 3 spots per 1 eye.

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The total number of students in the school is calculated as; 600 students

Usually, some figures are expressed as a fraction of a whole as depicted in this case. Thus, when we are given a fraction of a whole to be equal to a particular figure, we will just cross multiply to get the total number.

We are told that;

Number of students that play a team sport at Lincoln high school = 225

Now, we are told that the number above represents a fraction of 3/8 of the total students in that school.

Thus, if the total number of students in the school is x, then we can say that;

(3/8)x = 225

Multiply both sides by 8 to get;

3x = 1800

x = 1800/3

x = 600 students

Thus, we can conclude that if two hundred and twenty five students play a team sport at Lincoln high school and these students represent 3/8 of the total, then we can say that the total number of students in the school is 600 students.

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The amount of simple interest on a $1250 loan at 6.5% simple interest for 3 years would be $243.75.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

From the given information, P = $1250, r = 6.5 and t = 3.

Therefore, SI = (1250×6.5×3)/100.

SI = 12.5×6.5×3.

SI = $243.75

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Answer:

ray walks 3/8th of a mile

Step-by-step explanation:

1/4 multiplyed by 2/3 and you will get 3/8

Answer:

Solve x2 − 24x = −80 by completing the square. what is the solution set of the equation?

The Answer Is X = 20 or x = 4

Answer: A

Step-by-step explanation: M= -28

The estimate speed at which the absolute maximum gasoline mileage is obtained is at 60 mph, 65 mph, and 70 mph, we get an estimated maximum fuel economy of around 30 mpg. Trying speeds of 80 mph, 85 mph, and 90 mph, we get an estimated minimum fuel economy of around 15 mpg. The mileage obtained at 10 mph is relatively high, possibly around the maximum value of the fuel economy function.

To estimate the speed at which the absolute maximum gasoline mileage is obtained, we need to find the maximum point of the fuel economy function. Since we know that fuel economy decreases rapidly for speeds over 70 mph, we can assume that the maximum occurs at or below this speed.

We can use trial and error to estimate the maximum speed by plugging in different values of speed and finding the corresponding fuel economy. For example, we can start by trying speeds of 60 mph, 65 mph, and 70 mph. The speed that gives the highest fuel economy is the estimated speed at which the absolute maximum gasoline mileage is obtained.

Similarly, to estimate the speed at which the absolute minimum gasoline mileage is obtained, we need to find the minimum point of the fuel economy function. Since we know that fuel economy decreases rapidly for speeds over 70 mph, we can assume that the minimum occurs at or above this speed.

We can use trial and error to estimate the minimum speed by plugging in different values of speed and finding the corresponding fuel economy. For example, we can start by trying speeds of 80 mph, 85 mph, and 90 mph. The speed that gives the lowest fuel economy is the estimated speed at which the absolute minimum gasoline mileage is obtained.

The question asks for the mileage obtained at 10 mph. Since we don't have a specific fuel economy function, we cannot give an exact answer. However, based on the given information, we can assume that the fuel economy is relatively high at low speeds, and decreases rapidly for speeds over 70 mph.

Therefore, we can estimate that the mileage obtained at 10 mph is relatively high, possibly around the maximum value of the fuel economy function.

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Solution

We will consider each and every statement and the translate what it mean appropriately

Horizontally translate 4 units left

That means

The option to choose is

Vertically translate 2 units down

That basically mean is to subtract 2

That is

Shrunk vertically by one half

That is

The image below shows what to select

The mean absolute deviation (MAD) of the 16 values we had is 6.172. It means that the average absolute distance between each data value and the mean of the data set is 6.172.

The formula to calculate the mean absolute deviation (MAD) is

MAD = ∑(|x - x⁻|)/ n

where x⁻ is the mean of the data and

n is the total number of values in the data set

The mean is calculated by

x⁻ = (18 + 19 + 33 + 38 + 39 + 35 + 31 + 22 + 20 + 32 + 27 + 32 + 30 + 20 + 18 + 28)/ 16

x⁻ = 27.625

Now ∑(|x - x⁻|) = 9.625 + 8.625 + 5.375 + 10.375 + 11.375 + 7.375 + 3.375 + 5.625 + 7.625 + 4.375 + 0.625 + 4.375 + 2.375 + 7.625 + 9.625 + 0.375 = 98.75

Therefore, the mean absolute deviation is

MAD = ∑(|x - x⁻|)/ n

MAD = 98.75/ 16

MAD ≈ 6.172

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Answer:4200

Step-by-step explanation:

Using a system of equations, the quantity of Type A coffee that Trey's Coffee Shop blended with Type B coffee was 78 pounds.

A system of equations or simultaneous equations is two or more equations solved concurrently, simultaneously, or at the same time.

Unit Cost Per Pound:

Type A coffee = $5.80

Type B coffee = $4.25

The total quantity of pounds of the blend = 142 pounds

The total cost of 142 pounds = $724.40

Let the number of Type A coffee = x

Let the number of Type B coffee = y

x + y = 142 ... Equation 1

5.8x + 4.25y = 724.40 ... Equation 2

Multiply Equation 1 by 4.25:

4.25x + 4.25y = 603.5 ... Equation 3

Subtract Equation 3 from Equation 2:

5.8x + 4.25y = 724.40

-

4.25x + 4.25y = 603.5

1.55x = 120.9

x = 78

Substitute x = 78 in either equation:

x + y = 142

78 + y = 142

y = 64

Thus, 78 pounds of Type A coffee was used for the mixture.

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Answer:

9 m/s

Step-by-step explanation:

To calculate the change in the tram's elevation each second, you must divide the given figures which is now the given formula of \(\frac{meters}{seconds}\);

\(54\) ÷ \(6 =\)

\(\frac{54}{6} = 9\)

Therefore, the change in the tram's elevation is 9 each second.

Answer:

-9

Step-by-step explanation:

I say this because, the change in this problem is a negative one. Meaning you change the 54 into a negative number then divide by 6. So, -54 divided by 6 = -9. And remember, if there is one negative number and one positive it will be negative. If two negative it will be positive.

I hope I helped! Sorry if I'm wrong!

The original recipe had 0.9 cups of bananas.

Using only fresh ingredients, strawberry banana smoothie is a simple, nutritious dish. It is creamy, sweet, nutritious, and dairy- or dairy-free can be used to make it. The ideal summertime smoothie. Putting the strawberries, frozen banana, milk, and yoghurt in a blender and mixing until smooth and creamy is all that is required to make it.

Cups of strawberries = 1.75

No. of cups added of banana = 1/2

                                            = 0.5

No. of cups of banana smoothie have = 14.

The original recipe had = 1.4 - 0.5

                                   = 0.9

Hence, the original recipe had 0.9 cups of bananas.

Correct Question :

to make a strawberry banana smoothie, a recipe calls for 1.75 cups of strawberries and some bananas. to make the recipe taste more like banana, 1/2 cup more banana was added to the blender. the smoothie now has 1.4 cups of bananas. how many cups of bananas were in the original recipe?

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Answer: 14

Step-by-step explanation:

to find the answer we must figure out what half of 35 points is because Andrew scored 2/5 of 35.

we can write the equation like this:

2/5 of 35 = Andrew's points

2/5 of 35 = 14

therefore 2/5 of 35 is 14

therefore Andrew scored 14 points.

Answer: He needs 6 baskets

Step-by-step explanation: Its division 24 divided by 4 equals 6

Approximately 5.6 x 10¹⁴ grains of wheat in scientific notation.

A geometric series is a sequence of numbers in which each term is obtained by multiplying the previous term by a fixed constant. This constant is called the common ratio, and it is denoted by the letter "r".

The formula for the sum of the first n terms of a geometric series is:

S_n = a(1 - rⁿ)/(1 - r)

where S_n is the sum of the first n terms, a is the first term of the sequence, r is the common ratio, and n is the number of terms in the series.

The number of grains of wheat on each square of the board can be found by raising 2 to the power of the square number minus 1. For example, the number of grains of wheat on the first square is 2⁰ = 1, the number on the second square is 2¹ = 2, the number on the third square is 2² = 4, and so on.

So, the total number of grains of wheat on the board is the sum of 2⁰ + 2¹ + 2² + ... + 2⁴⁸. This is a geometric series with first term 1 and common ratio 2. Using the formula for the sum of a geometric series, the total number of grains of wheat is:

2⁰ + 2¹ + 2² + ... + 2⁴⁸ = (2⁴⁹ - 1)/(2 - 1) = 2⁴⁹ - 1

This is approximately 5.6 x 10¹⁴ grains of wheat in scientific notation.

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If Shen produced and Manuel consumed one additional bottle of water, total surplus would be $2

The law of supply and demand combines two fundamental economic ideas that describe how changes in the price of a resource, commodity, or product affect its supply and demand.

Supply grows as the price rises, but demand drops. In contrast, as the price falls, supply is constrained and demand is increased.

Demand and supply levels for different prices can be displayed as curves on a graph. The intersection of these curves symbolizes the process of price discovery in the marketplace, as it indicates the balance, or market-clearing price, at which demand equals supply.

According to the law of demand, demand for a good or resource will decrease as its price increases and increase as its price decreases.

How to solve?

Price ------ Quantity Supplied ----- Quantity Demanded

2 --------------------- 1 ------------------------- 3

4 --------------------- 2 ------------------------ 2

6 --------------------- 3 ------------------------ 1

4 (quantity supplied = quantity demanded = 2)

4 ($7>$4 and $5>$4, $3<$4<$5, area above price line but under curve if price line was at $4, $7-$4=$3, $5-$4=$1, $3+$1=$4); 4 ($1<$4 and $3<$4, $3<$4<$5, area below price line and under curve if price line at $4, $4-$1=$3, $4-$3=$1, $3+$1=$4); 8 ($4 from consumer surplus + $4 from producer surplus)

fall (equilibrium = 2, 2-1=1, Shen: quantity supplied = 1 -> $2, Manuel: quantity demanded = 1 -> $6, total surplus = producer surplus + consumer surplus = ($4-$1)+($7-$4)=$6, $8>$6)

rise (equilibrium = 2, 2+1=3, Manuel: quantity demanded = 3 -> $2, Shen: quantity supplied = 3 -> $6, total surplus = consumer surplus + producer surplus = ($3-$2)+($7-$6)=$2, $8>$2, $6>$2)

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Answer:

b. 6x2 - 17x + 12

Step-by-step explanation:

hope this helps. have a great time :)

The number of prime factors of 3×5×7+7 is 3.

To find the number of prime factors, we need to calculate the given expression:

3×5×7+7 = 105+7 = 112.

The number 112 can be factored as 2^4 × 7.

In the first step, we factor out the common prime factor of 7 from both terms in the expression. This gives us 7(3×5+1). Next, we simplify the expression within the parentheses to get 7(15+1). This further simplifies to 7×16 = 112.

So, the prime factorization of 112 is 2^4 × 7. The prime factors are 2 and 7. Therefore, the number of prime factors of 3×5×7+7 is 3.

In summary, the expression 3×5×7+7 simplifies to 112, which has three prime factors: 2, 2, and 7. The factor of 2 appears four times in the prime factorization, but we count each unique prime factor only once. Thus, the number of prime factors is 3.

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