How much greater is the area of a circle with a radius of 7.6 inches than the area of a square with a side length of 5 inches?

Answer:

75x² + 10x - 2

Step-by-step explanation:

Substitute x = 5x into f(x), that is

f(5x) = 3(5x)² + 2(5x) - 2

       = 3(25x²) + 10x - 2

       = 75x² + 10x - 2

Zork's algorithm guarantees that it always gets within a factor of 2 of the optimal solution because of the way that it combines the solutions from the left half and the right half. Zork's algorithm is an algorithm that is used to solve optimization problems.

Zork's algorithm always gets within a factor of 2 of the optimal solution. Zork's algorithm works by dividing the problem into two halves and then recursively solving each half. In each step, the algorithm decides whether the optimal solution lies in the left half, the right half, or across the middle.

If the optimal solution is in the left half, the algorithm recursively solves the left half. If the optimal solution is in the right half, the algorithm recursively solves the right half. I

f the optimal solution is across the middle, the algorithm takes the best solution that it found in the left half and the best solution that it found in the right half and combines them. The algorithm stops when it has solved the problem to the desired accuracy.

Suppose that the optimal solution is across the middle and that the solution in the left half is l and the solution in the right half is r. Without loss of generality, suppose that l ≤ r. Then the combined solution is at most r.

But r is at most twice the optimal solution, because r is in the right half and the optimal solution is across the middle. Therefore, the combined solution is at most twice the optimal solution.

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Answer:

mica should have added 2 to 3 instead of 1

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

use pythagoras first

x² + x² = (12√2)²

expand & simplify the squares

2x² = 144(2)

x² = 144

root both sides to get x

x = 12

Answer:

2.10?????????????

Answer:

$18 per ticket

Step-by-step explanation:

you have to find the cost of one ticket so you divide 306 by 17 and you get $18

Marcos has a total of 78 toy cars, and he wants to arrange them into 6 equal groups.

To determine the number of toy cars in each group, we divide the total number of toy cars by the number of groups: 78 ÷ 6 = 13. Therefore, there will be 13 toy cars in each group.

This can be represented as 78 divided by 6 equals 13. By dividing the total number of toy cars by the number of groups, Marcos ensures that each group has an equal distribution of toys.

This allows for a fair and balanced arrangement of the toy cars, making it easier for Marcos to organize and manage them.

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Answer:

58 - (3d) = c

Step-by-step explanation:

3 per day, so if she does it for two days it would be 58 - 6 which would say how much she has left.

Since both terms are perfect cubes, factor using the sum of cubes formula, a³ + b³ = (a + b) (a² - ab + b²) where a = x and b = 3y.

2 (x + 3y) (x² - 3xy + 9y²)

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

Answer:

Infinite

Step-by-step explanation:

infinite because it will be never ending. hope this helps.

Answer:

5 hours

Step-by-step explanation:

1in per hour ×5=5 hours

Answer: 5 inches

Step-by-step explanation:

If the snail travels an inch {1} an hour the five inches should be 5 hours

The dimensions of the box that minimize the cost are a length of 10 inches and a height of 4 inches.

In order to minimize the cost of the decorative jewelry box, the dimensions of the box need to be determined. The box has a square base and requires a volume of 400 cubic inches.

The four sides and the base bottom will be made with wood costing 50 cents per square inch and the top will be made of glass costing $1 (100 cents) per square inch.

The first step to solving the problem is to determine the dimensions of the box that will satisfy the requirements for volume.

Let x represent the length of the base of the box and y represent the height.

Then the area of the base will be x^2 and the volume of the box will be x^2y.

Since the box needs to have a volume of 400 cubic inches, we have:

x^2y = 400 y = 400/x^2

Now we can use the area of the sides of the box to determine the cost. There are four sides and a bottom that will be made of wood, so the cost will be 5xy for the wood.

The top will be made of glass, so the cost will be 100x^2.

Therefore, the total cost will be:

C(x) = 5xy + 100x^2

Substitute y = 400/x^2 into the equation for C(x) to obtain:

C(x) = 5x(400/x^2) + 100x^2

Simplify the expression for C(x):

C(x) = 2000/x + 100x^2

Differentiate C(x) with respect to x to find the critical values of C(x):

C'(x) = -2000/x^2 + 200x

Setting C'(x) = 0 and solving for x, we obtain:

x = 10 or x = 2.82

Since x represents the length of the base of the box, it cannot be negative, so we must choose x = 10.

Therefore, the length of the base is 10 inches, and the height of the box is:y = 400/x^2 = 4 inches.

The cost of the box is:C(10) = 5xy + 100x^2 = 5(10)(4) + 100(10^2) = $1500.

Therefore, the dimensions of the box that minimize the cost are a length of 10 inches and a height of 4 inches.

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The probability of getting 0 lemons in the sample is 0.8836, the probability of getting 1 lemon in the sample is 0.1060, and the probability of getting 2 lemons in the sample is 0.0564.

The probability distribution of x can be calculated as follows:

Given that 6% of all cars produced at a large auto company are lemons. This means that out of every 100 cars manufactured at the company, 6 of them are lemons.Let x denote the number of lemons in this sample. Then, x can take the values 0, 1, or 2. To find the probability of each value of x, we use the binomial probability formula, which is:

P(x) = (nCx) * p^x * (1-p)^(n-x)

where n is the sample size, p is the probability of success, and x is the number of successes.

The sample size is 2 because we are selecting two cars at random from the production line. The probability of success (getting a lemon) is 0.06. Using the binomial probability formula, we get:

P(0) = (2C0) * 0.06^0 * (1-0.06)^(2-0) = 0.8836

P(1) = (2C1) * 0.06^1 * (1-0.06)^(2-1) = 0.1060

P(2) = (2C2) * 0.06^2 * (1-0.06)^(2-2) = 0.0564

Therefore, the probability distribution of x is:X P(x) 0. 0.8836 1. 0.1060 2. 0.0564

In conclusion, the probability of getting 0 lemons in the sample is 0.8836, the probability of getting 1 lemon in the sample is 0.1060, and the probability of getting 2 lemons in the sample is 0.0564.

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Answer:

Angle JC is 63.

Angle AJ is 117

Angle BC is 117

Angle DH is 63

Angle HF is 117

Angle FE is 63

Angle DE is 117

In Question 10, the functions f(x) = sin(x) and g(x) = cos(x) are considered, and W is defined as the span of f and g. The problem requires demonstrating the linear independence of f and g using the Wronskian. Additionally, for any real number a, new functions fi(x) = sin(x + a) and gi(x) = cos(x + a) are introduced, and it needs to be shown that f₁.91 ∈ W. Finally, it is required to prove that the set {f₁,91} is linearly independent.

10.1 To show that f and g are linearly independent, we can use the Wronskian. The Wronskian of two functions f(x) and g(x) is defined as the determinant of the matrix [f(x), g(x)] and its derivative [f'(x), g'(x)]. In this case, the Wronskian of f(x) = sin(x) and g(x) = cos(x) is:
W(f, g) = |sin(x) cos(x)|
|cos(x) -sin(x)|
Calculating the determinant, we get W(f, g) = sin^2(x) + cos^2(x) = 1. Since the Wronskian is nonzero (1 ≠ 0), f and g are linearly independent.
10.2 To show that f₁.91 ∈ W, we consider the function f₁.91(x) = sin(x + a). Since sin(x + a) can be rewritten as sin(x)cos(a) + cos(x)sin(a), we can express f₁.91 as a linear combination of f and g:
f₁.91(x) = sin(x)cos(a) + cos(x)sin(a) = cos(a)sin(x) + sin(a)cos(x) = g(x)cos(a) + f(x)sin(a).
Thus, f₁.91 is a linear combination of f and g, indicating that it belongs to the span W.
10.3 To show that {f₁,91} is linearly independent, we need to demonstrate that the only linear combination of f₁.91 that equals the zero function is the trivial combination where all coefficients are zero. Suppose we have c₁f₁.91(x) = 0 for some scalar c₁. Expanding this expression, we get c₁(sin(x + a)) = 0. Since sin(x + a) ≠ 0 for any x, this implies that c₁ must be zero. Therefore, the set {f₁,91} is linearly independent.
Overall, using the Wronskian, we established the linear independence of f and g, showed that f₁.91 belongs to the span W, and proved that {f₁,91} is linearly independent.

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a) The minimum cost of producing exactly 10 goods for the production function f(K, L) = 1/2 min{K, L} can be graphically determined.

b) The minimum cost of producing exactly 10 goods for the production function f(K, L) = 5K^1/2 L^1/2 can be graphically determined.

For the production function f(K, L) = 1/2 min{K, L}, the firm aims to produce exactly 10 goods. The function 1/2 min{K, L} represents a diminishing returns to scale production, where the output is determined by the minimum of the two inputs (K and L).

In order to minimize costs and produce exactly 10 goods, the firm needs to find the combination of inputs (K, L) that achieves this output level while minimizing the total cost.

To graphically determine the minimum cost, we plot the isoquant curve representing the output level of 10 goods on a graph with the two inputs, K and L. The isoquant curve is the locus of all input combinations that produce the same output level. The firm's goal is to find the input combination on this curve that minimizes the total cost.

Now, assuming that the cost of labor falls, the isoquant curve for f(K, L) = 1/2 min{K, L} remains the same because the production function itself is not affected by changes in input prices.

However, with the lower cost of labor, the firm can now achieve the desired output level of 10 goods by employing more labor relative to capital. Consequently, the firm will choose an input combination with a higher labor input and a lower capital input, resulting in a lower total cost.

In the case of the production function f(K, L) = 5K^1/2 L^1/2, the firm also aims to produce exactly 10 goods. This production function represents constant returns to scale, where the output is proportional to the square root of both capital (K) and labor (L). To minimize costs and produce exactly 10 goods, the firm needs to find the input combination that achieves this output level while minimizing the total cost.

Similarly, for this production function, we plot the isoquant curve representing the output level of 10 goods on a graph with K and L as inputs. The firm's objective is to locate the input combination on this curve that minimizes the total cost.

With the assumption of falling labor costs, the isoquant curve for f(K, L) = 5K^1/2 L^1/2 remains the same. However, due to the lower cost of labor, the firm can now achieve the desired output level by employing more labor relative to capital. Therefore, the firm will choose an input combination with a higher labor input and a lower capital input, resulting in a lower total cost.

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Answer:

Terms: 4

Degree: 3

Leading coeff: 7

Step-by-step explanation:

a term is either a single number or variable, or numbers and variables multiplied together. Terms are separated by + or − signs, or sometimes by division. 7x³+5x²-3x+1 would have 4 terms: 7x³, 5x², -3x, and 1

You already have the degree which is the highest power in a polynomial

The leading coefficent is the coefficient in the term with the highest power, in this case being 7.

hope this helps!

Answer:

128

26 +26 is 52.

Total sum of the angles has to be 180.

180-52=128

Answer:

x = 128 degrees

Step-by-step explanation:

This is an isosceles triangle, so that means that both base angles equal 26 degrees.

The sum of a triangle is 180 degrees, so we can use that to solve for x.

x + 26 + 26 = 180

x + 52 = 180

x = 128

Hope this helps!

Accounts receivable (Art) $1,078Sales Discount    $22Cash $1,100

Journal entry is a process of recording every transaction in a business in the order they take place. In the case of Cabela's, the following merchandising transactions were recorded:1. Purchased merchandise from Boden Company for $6,000 under credit terms of 1/15, n/30, FOB shipping point, invoice dated July 1The cost of merchandise purchased from Boden Company is debited while Accounts payable (Boden Company) is credited. The cost of merchandise is calculated as $6,000 * (1-1%) = $5,940 while the remaining $60 is the discount received.

Cost of merchandise   $5,940Accounts payable (Boden)     $5,9402. Sold merchandise to Creek Company for $900 under credit terms of 2/10, n/60, FOB shipping point, invoice dated July 2.The sales revenue is credited while the cost of goods sold is debited with the cost of the merchandise. This is because the cost of merchandise sold is an expense and expenses are debited.

Sales revenue $900Cost of goods sold $500Merchandise inventory $5003. Paid $125 cash for freight charges on the purchase of July 1The Freight Out expense is debited while Cash is credited.

Freight out expense $125Cash $1254. Sold merchandise that had cost $1,300 for $1,700 cashThe cash received for the sale is debited while the cost of goods sold is credited with the cost of the merchandise. This is because the cost of merchandise sold is an expense and expenses are debited.

Cash $1,700Cost of goods sold $1,300Merchandise inventory $1,3005. Purchased merchandise from Leight Company for $2,200 under credit terms of 2/15, n/60, FOB destination, invoice dated July 9The cost of merchandise purchased is debited while Accounts payable (Leight Company) is credited. The cost of merchandise is calculated as $2,200 * (1-2%) = $2,156 while the remaining $44 is the discount received.

Cost of merchandise   $2,156Accounts payable (Leight)     $2,1566. Returned $200 of merchandise purchased on July 9 from Leight Company and debited its account payable for that amount.The Accounts payable is debited with the amount of merchandise returned while the Merchandise inventory account is credited with the cost of the returned merchandise.Accounts payable (Leight)   $200Merchandise inventory $2007. Received the balance due from Creek Company for the invoice dated July 2, net of the discountThe accounts receivable account is debited with the net amount received while the sales discount account is credited with the discount received.

Accounts receivable (Creek) $882Sales discount     $18Cash $9008. Sold merchandise that cost $800 to Art Company for $1,200 under credit terms of 2/15, n/60, FOB shipping point, invoice dated July 19The sales revenue is credited while the cost of goods sold is debited with the cost of the merchandise.

This is because the cost of merchandise sold is an expense and expenses are debited.Sales revenue $1,200Cost of goods sold $800Merchandise inventory $8009. Gave a price reduction (allowance) of $100 to Art Company for merchandise sold on July 19 and credited Art's accounts receivable for that amount.

The allowance account is debited while Accounts receivable (Art Company) is credited.Allowance    $100Accounts receivable (Art) $10010. Paid Leight Company the balance due, net of discountAccounts payable (Leight) is debited with the net amount paid while Cash is credited.Accounts payable (Leight)   $2,128Cash $2,12811.

Received the balance due from Art Company for the invoice dated July 19, net of discount The accounts receivable account is debited with the net amount received while the sales discount account is credited with the discount received.

Accounts receivable (Art) $1,078Sales discount    $22Cash $1,100

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The triangle, such as an angle measurement or the length of side AC, please provide it, and I will be able to assist you in calculating the area.

The area of triangle ABC, we can use the formula for the area of a triangle:

A = (1/2) × base × height.

We are given the lengths of two sides of the triangle, AB = 12 cm and BC = 10 cm.

We don't have the height or the length of the base.

To proceed, we need to obtain additional information.

Without the height or the length of the base, we cannot accurately calculate the area of the triangle.

One possible approach to find the missing information is to use trigonometry.

If we have an angle measurement within the triangle, we can apply trigonometric functions such as sine, cosine, or tangent to find the height or other missing lengths.

Alternatively, if we know the length of side AC, we can use the Pythagorean to the height.

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The rate of return of approximately 17.95% in the third year would produce a cumulative gain of 7% after two consecutive years of 6% losses.


To solve the problem completely, let's calculate the rate of return required in the third year to achieve a cumulative gain of 7% after two consecutive years of 6% losses.

1. Calculate the total loss over the two years:

  Total loss = (1 - 0.06) * (1 - 0.06) = 0.9416

2. Calculate the target cumulative gain:

  Cumulative gain = 1 + 0.07 = 1.07

3. Set up the equation to solve for the rate of return:

  1 + Rate of return = Cumulative gain / (1 - Total loss)

4. Substitute the values into the equation:

  1 + Rate of return = 1.07 / (1 - 0.9416)

  1 + Rate of return = 1.07 / 0.0584

5. Solve for the rate of return:

  Rate of return = (1.07 / 0.0584) - 1

  Rate of return ≈ 17.95%

Therefore, a rate of return of approximately 17.95% in the third year would be needed to achieve a cumulative gain of 7% after two consecutive years of 6% losses.

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Area of the room = 5.4m × 4.2 m

Thus area = 22.6 [tex]{m}^{2}[/tex]

Number of square tiles = 1575

Thus The area of each tile:

[tex] = \dfrac{22.6}{1575} {m}^{2} [/tex]

[tex] \bold{\red{= 0.0144 {m}^{2}}} [/tex]

Now the dimensions of square tile will be:

[tex] = \sqrt{0.0144} m[/tex]

[tex] \bold{\red{= 0.12m}}[/tex]

Answer:

Measure of each angle is 90, 45, 45 degrees

Step-by-step explanation:

We know a right angle automatically is 90 degrees. An entire triangle is 180 degrees. Lets make our problem.

90 + 2x = 180

Subtract 90 from both sides: 2x = 90

Divide each side by 2: x = 45

I hope this helped, please mark Brainliest, thank you!

Answer:

$76.72

(135.62-58.90=76.72)

Answer:

x=27

Step-by-step explanation:

m<AOB = 180

36+90+2x=180

x=27 degrees

[tex]5x+7=2x-2\\5x+7-2x+2=0\\3x+9=0\\3x=-9\\x=\frac{-9}{3} \\x=-3[/tex]

Thus, x = -3

[ Check ]

Substitute x = -3 in the equation

[tex]5(-3)+7=2(-3)-2\\-15+7=-6-2\\-8=-8[/tex]

The equation is true so the answer is x = -3 #

Answer:

move 2x over the equal sign do the same for seven so that the equation reads 5x - 2x = -2 - 7 so it will be 3x = -9 divide both sides by 3 x= -3

Answer:

Mean = 78.2

Standard deviation = 5.8

Step-by-step explanation:

Mathematically z-score;

= (x-mean)/SD

From the question;

12% of test scores were above 85

Thus;

P( x > 85) = 12%

P(x > 85) = 0.12

Now let’s get the z-score that has a probability of 0.12

This can be obtained from the standard normal distribution table and it is = 1.175

Thus;

1.175 = (85 - mean)/SD

let’s call the mean a and the SD b

1.175 = (85-a)/b

1.175b = 85 - a

a = 85 - 1.175b ••••••••(i)

Secondly 8% of scores were below 70

Let’s find the z-score corresponding to this proportion;

We use the standard normal distribution table as usual;

P( x < 70) = 0.08

z-score = -1.405

Thus;

-1.405 =( 70-a)/b

-1.405b = 70-a

a = 70 + 1.405b ••••••(ii)

Equate the two a

70 + 1.405b = 85 - 1.175b

85 -70 = 1.405b + 1.175b

15 = 2.58b

b = 15/2.58

b = 5.81

a = 70 + 1.405b

a = 70 + 1.405(5.81)

a = 78.16

So mean = 78.2 and Standard deviation is 5.8

Answer:

£3575

Step-by-step explanation:

If Trevor bought the car for £5000, he wants to make a 10% profit on it.

His profit will be 10% of £5000 which is (10/100) x 5000 = £500.

So, his total cost for the car and profit will be £5000 + £500 = £5500.

Since Trevor is holding a sale, he is offering a 35% discount on the car. Therefore, the discounted price of the car will be:

Discount = 35/100 x £5500 = £1925

The price at which Trevor should advertise the car is the original price minus the discount:

Advertised price = £5500 - £1925 = £3575

Therefore, Trevor should advertise the car for £3575.