Joaquin wants to make his famous chocolate chip cookies to bring to his friend's birthday party. the original recipe serves 5 people and requires one quarter of a cup of butter, but he needs it to serve 28 people. how many cups of butter will he need? 2 and one fourth cups 1 and one fifth cups 1 and two fifths cups 1 and one fourth cups

The estimate from direct proportionality is higher than the prediction from KLEIBER's law.

a. For a 180 kilogram lion, we can use KLEIBER's law: R = 73.3*(180^0.75) = 6136.5 Calories per day. For an 80 kilogram human, we can use the same formula: R = 73.3*(80^0.75) = 1537.6 Calories per day.

b. If metabolic rate and mass were directly proportional, we could use the ratio of the masses to find the basal metabolic rate for an 80 kilogram human.

The ratio of the masses is 80/180 = 0.44. We can multiply this by the basal metabolic rate for the lion to get an estimate for the human: 0.44*6136.5 = 2701.26 Calories per day.

This estimate is higher than the prediction from Kleiber's law for an 80 kilogram human (1537.6 Calories per day). KLEIBER's law indicates that smaller organisms have a higher metabolic rate per kilogram of mass than do larger organisms.

Therefore, the estimate from direct proportionality is higher than the prediction from KLEIBER's law.

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The probability that the selected person will be a freshman or a female is 34/43.

A probability is a numerical representation of the likelihood or chance that a specific event will take place.

Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

So, we know that:

Male freshman = 21

Female Freshman = 7

Male Sophomores = 9

Female Sophomores = 6

So, the probability formula is:

P(E) = Favourable events/Total events

Now, insert the values as follows:

P(E) = Favourable events/Total events

P(E) = 21+7+6/43

P(E) = 34/43

Therefore, the probability that the selected person will be a freshman or a female is 34/43.

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Answer: $7.50

Step-by-step explanation:

Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

Answer: X

Step-by-step explanation: Because look at the chart

Answer:

It’s b

Step-by-step explanation:

ANSWER

EXPLANATION

The reef grows 0.18m every week

hence,

after 9weeks, it grows:

A function that is positive in the entire interval [-3, -2] is -x² - 5x - 5.

calculating the positive and negative gaps from a graph sketch. Drawing a rough sketch of a polynomial's graph based on the polynomial's end behaviour and the multiplicities of its zeros is another method for determining the periods over which it is positive or negative.

f(x) = -2x - 1 will be our first function to examine.

f(-3) = -2(-3) - 1 = 5

f(-2) = -2(-2) - 1 = 3

Now, let's try the second function, g(x) = x² - 2x - 3.

g(-3) = (-3)² - 2(-3) - 3 = 9 + 6 - 3 = 12

g(-2) = (-2)² - 2(-2) - 3 = 4 + 4 - 3 = 5

Finally, let's try the third function, h(x) = x³ - 4x² + 5x - 2.

h(-3) = (-3)³ - 4(-3)² + 5(-3) - 2 = -27 - 36 - 15 - 2 = -80

h(-2) = (-2)³ - 4(-2)² + 5(-2) - 2 = -8 - 16 - 10 - 2 = -36

We cannot conclude that this function is positive for the full range [-3, -2] because h(-3) and h(-2) are both negative.

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Answer:

\(r = -\dfrac{2}{5}\\\\\textrm{or, in decimal, r = -0.4}\)

Step-by-step explanation:

The sum of a geometric sequence

\(S_n \textrm{ as } n \rightarrow \infty\\\\\) is given by the formula

\(S_{\infty} = \dfrac{a_1}{1-r}\)

where
\(\textrm{$a_1$ = the first term}\\\textrm}{r = common ratio}\)

Given
\(S_{\infty} = 250\\\\a_1 = 350\\\\250 = \dfrac{350}{1-r}\\\\\)

\(\Rightarrow 1- r = \dfrac{350}{250}\\\\\Rightarrow 1-r = \dfrac{7}{5}\\\\r = 1 - \dfrac{7}{5}\\\\r = -\dfrac{2}{5}\\\\\textrm{or, in decimal, r = -0.4}\)

The dual for the given linear programming problems are as follows:

(i) Minimize Z' = 10a + 12b Subject to: a + 7b ≥ 3 2a + 3b ≥ 4 a + 9b ≥ 5 a, b ≥ 0.

(ii) Maximize Z' = 5a + 6b + 2c Subject to: 3a + 2b + c ≤ 1 4a + 6b + c ≤ 2 a + b ≤ 0 a, b, c ≥ 0.

In the first problem, we have a maximization problem with three variables (x, y, z) and two constraints. The dual formulation involves minimizing a new objective function with two variables (a, b) and four constraints. The coefficients of the variables and the constraints are transformed according to the rules of duality.

The primal problem is:

Maximize Z = 3x + 4y + 5z

Subject to:

x + 2y + z ≤ 10

7x + 3y + 9z ≤ 12

x, y, z ≥ 0

To find the dual, we introduce the dual variables a and b for the constraints:

Minimize Z' = 10a + 12b

Subject to:

a + 7b ≥ 3

2a + 3b ≥ 4

a + 9b ≥ 5

a, b ≥ 0

In the second problem, we have a minimization problem with two variables (y1, y2) and three constraints. The dual formulation requires maximizing a new objective function with three variables (a, b, c) and four constraints. Again, the coefficients and constraints are transformed accordingly.

The primal problem is:

Minimize Z = y1 + 2y2

Subject to:

3y1 + 4y2 > 5

2y1 + 6y2 ≥ 6

y1 + y2 ≥ 2

To find the dual, we introduce the dual variables a, b, and c for the constraints:

Maximize Z' = 5a + 6b + 2c

Subject to:

3a + 2b + c ≤ 1

4a + 6b + c ≤ 2

a + b ≤ 0

a, b, c ≥ 0

The duality principle in linear programming allows us to find a lower bound (for maximization) or an upper bound (for minimization) on the optimal objective value by solving the dual problem. It provides useful insights into the relationships between the primal and dual variables, as well as the economic interpretation of the problem.

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Answer:

£2.18

Step-by-step explanation:

£19=500

£2.176=1088

rounded to 2dp =2.18

Answer:

-7

Step-by-step explanation:

p mark brainliest please

Answer:

-7

Step-by-step explanation:

0 subtract 7 is negative 7

Answer:

176 cm

Step-by-step explanation:

Area of a triangle = h b/2

8 * 11 ÷ 2 = 44 cm

Area of a rectangle = l * w

12 * 11 = 132 cm

Add both areas together

44 + 132 = 176 cm

Answer:

Proportional

Step-by-step explanation:

Search up the definition of proportional.

Answer:

proportional

Step-by-step explanation:

Alphonso signed a contract with the martial arts training studio called "Champions Ta-Kwon-Do" that contained a liability waiver clause.

The clause stated that the studio would not be held responsible for any injuries or damages suffered by the participants. Alphonso agreed to the contract by signing it, despite his initial reluctance.

However, Alphonso experienced an injury while participating in a sparring session at the studio due to a water spill on the floor, which was the fault of Champions Ta-Kwon-Do. Alphonso now wishes to sue the studio for his injuries.

The enforceability of the liability waiver clause in the contract depends on several factors, including the jurisdiction's laws and regulations governing such waivers, as well as the specific circumstances surrounding the contract's formation.

In general, liability waivers are not always absolute and can be subject to scrutiny by courts.

While Alphonso did sign the contract, it may be argued that the waiver clause is unconscionable or against public policy if it seeks to absolve Champions Ta-Kwon-Do from liability for their own negligence or intentional wrongdoing.

Courts may consider factors such as the bargaining power between the parties, any undue influence exerted by the studio, the clarity of the waiver language, and the nature of the injury suffered.

Additionally, the court may assess whether the waiver provision was prominently displayed and whether Alphonso had a reasonable opportunity to negotiate or seek legal advice before signing.

It is advisable for Alphonso to consult with a qualified attorney who specializes in personal injury law. The attorney can evaluate the specific laws applicable in the jurisdiction and the facts of the case to provide accurate legal advice regarding Alphonso's chances of pursuing a lawsuit against Champions Ta-Kwon-Do despite the signed contract.

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The three lengths 8, 9 and 10 form a triangle.

In Euclidean geometry stating that any two triangle sides added together must be greater than or equal to the third side; represented by the symbols a + b ≥c. The basic tenet of the theorem is that a straight line connects any two places.

Given:

Sides: 8, 9, 10

As from Triangle Inequality the sum of two sides are greater than the third side of triangle.

So, 8 + 9 > 10

9 + 10 > 8

10+ 8> 9

Since the triangle inequality satisfied.

Thus, the triangle can form using sides 8, 9, 10.

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Answer:

1= b to the second power, 2=a to the second power, 3=b to the fourth power, 4=a to the fourth

Step-by-step explanation: your welcome

Answer: 2)b^2+a^2

Step-by-step explanation:

x and y would have to be the same value since y(sin) and x(cos) of x and y on the unit circle is the same meaning it's the same point. Thus, cos(x-y) = cos(0) = 1. b^2+a^2=cos^2(x)+sin^2(x)= 1.

Answer: To find the total amount of sugar required to make the banana pudding, we need to add the amount of sugar needed for the flour mixture to the amount of sugar needed for the meringue topping.

The recipe calls for 2/3 of a cup of sugar for the flour mixture and 1/4 of a cup of sugar for the meringue topping. To add these two fractions, we need to find a common denominator. The least common multiple of 3 and 4 is 12, so we can convert these fractions to twelfths:

2/3 = 8/12

1/4 = 3/12

Now we can add these two fractions:

8/12 + 3/12 = 11/12

So the total amount of sugar required to make the banana pudding is 11/12 of a cup.

The equation of the line passing through the points (0,0) and (7,4) is option 3, y = 4/7 x.

What is equation of line?

To find the equation of the line passing through two given points, we need to use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where (x1, y1) is one of the given points and m is the slope of the line.

First, let's find the slope of the line passing through the points (0,0) and (7,4). The slope formula is:

m = (y2 - y1)/(x2 - x1)

Substituting the values, we get:

m = (4 - 0)/(7 - 0) = 4/7

Now, we can use the point-slope form with either of the two given points. Let's use (0,0):

y - 0 = (4/7)(x - 0)

Simplifying, we get:

y = 4/7 x

Therefore, the equation of the line passing through the points (0,0) and (7,4) is option 3, y = 4/7 x.

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In a piece-rate pay system, an employee's gross pay is calculated by multiplying the number of units produced by the rate per unit. This type of pay system is often used in manufacturing, agriculture, and other industries where employees are paid based on their productivity.

Piece-rate pay system is a compensation system in which employees are paid a fixed amount for each unit they produce. The rate per unit is set by the employer and can vary depending on the industry and type of work being performed. For example, a factory worker might be paid a certain amount for every item they assemble, while a farm worker might be paid based on the number of baskets of fruit they harvest.

To calculate an employee's gross pay in a piece-rate system, the employer simply multiplies the number of units produced by the rate per unit. For example, if a factory worker produces 100 units and the rate per unit is $1.50, their gross pay would be $150. Piece-rate pay can be beneficial for both employers and employees, as it incentivizes productivity and allows employees to earn more money if they work efficiently. However, it can also lead to exploitation if the rate per unit is set too low or if employees are forced to work long hours to meet production targets.

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Answer:

A = 47 degrees

Step-by-step explanation:

cosineA = adjacent/hypotenuse

cosineA =  34/50

cosineA = 0.68

reverse cosine

A = 47 (rounded to the nearest whole number)

The value of f(-1, 2, 0, -1) is \(-e^2 - 1.\)

To calculate f(-1, 2, 0, -1), we need to substitute these values in the given expression for f(x, y, z, w) as follows:

\(f(-1, 2, 0, -1) = (-1)(2)^2(0) - (-1)(-1)^2 - e^2(-1)^2 - (2)^2 - (0)^2 + 2\times (-1)^2\)

Simplifying the expression, we get:

\(f(-1, 2, 0, -1) = 0 + 1 - e^2 - 4 + 0 + 2\\f(-1, 2, 0, -1) = -e^2 - 1\)

Therefore, the value of f(-1, 2, 0, -1) is \(-e^2 - 1.\)

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Answer:

the answer is C

Step-by-step explanation:

Answer:

x = 6.928

Step-by-step explanation:

Since we don't know the hypotenuse, we will use tan

tanΘ = opposite/adjacent     (Θ = theta, which is basically the variable for an angle)

tan30° = x/12

to find x, multiply 12 to the other side

12tan30° = x            (plug this into a calculator)

x = 6.928

Answer:

Step-by-step explanation:

that is incorrect.

if it were to be equal, one side should equal each other when multiplied to make the ratio equal.

20-5x=40-10x (when multiplied by 2 on each side)

It CANNOT equal 50, if it were there would not be -10x

20-5x=100-25x

DIVIDE BY 2 to get 50 WOULD GIVE:

20-5x=50-17.5x

Answer:

Yes

Step-by-step explanation:

solve the equation for x , then evaluate and compare both sides

20 - 5x = 50 - 10x ( add 10x to both sides )

20 + 5x = 50 ( subtract 20 from both sides )

5x = 30 ( divide both sides by 5 )

x = 6

then

left side = 20 - 5x = 20 - 5(6) = 20 - 30 = - 10

right side = 50 - 10x = 50 - 10(6) = 50 - 60 = - 10

since both sides are equal then

20 - 5x = 50 - 10x is true

The price of $285,000 for a 1,465-square-foot home is likely above the average for a home of this size.

The average price of homes can vary depending on various factors such as location, market conditions, amenities, and overall demand. However, based on typical market trends, a home with 1,465 square feet selling for $285,000 is likely to be above the average price for a property of that size.

There could be several reasons for the higher price of this particular home. Location plays a crucial role in determining property prices, and if the home is situated in a desirable neighborhood or a sought-after area with good schools, amenities, or proximity to major attractions, it could command a premium. Additionally, the home may have undergone significant renovations or upgrades that justify the higher price.

Features like modern appliances, updated fixtures, renovated bathrooms or kitchens, energy-efficient systems, or high-quality finishes can contribute to the increased value. Other factors like a larger lot size, attractive landscaping, or special architectural design may also influence the price. Furthermore, market conditions and demand-supply dynamics can impact the pricing, as high demand and limited inventory can lead to higher prices in certain areas.

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Answer:

A) The percentage of the bacteria increasing each hour is 15% per hour

B) When t=0 the population of bacteria is 3000 bacteria

C) After 24 hours the a sensible degree of accuracy in population is about 85875 (since only whole numbers count)

Step-by-step explanation:

A) To find the percentage of the bacteria increasing each hour the growth rate needs to be determined. To find it you need to subtract 1.15 by since the formula for exponential growth is a(1+r)^t one is added to the rate so to inverse it 1.15 needs to be subtractied by one to get 0.15. At this point you found the decimal rate to find the percentage you multiply 0.15 by 100 to make it a whole number and it results in 15%

B) To determine the size if the population when t=0 you substitute the variables t for 0 to get 3000×1.15^0 to get 3000 (remember anything times 0 is 0). Another way is to keep in mind that 3000 is the initial amount because that's the number with no variable with it.

C) To find the population after 24 hours substitute t for 24. After substituting t and multiplying 3000×1.15^24 the exact answer is 85875.52857. To find the answer in a sensible degree of accuracy you would round it to the nearest whole number which is 85876 since the dight in the tenths place is 5 or greater than the answer is rounded up by one.

Answer:

any integer in between 29,30,31,32,33,34 will work.

The CLV for transactors is $37.5, for revolvers it is $208.33, and for dormants, it is $2,000,000.

Customer Lifetime Value (CLV) is a financial analysis of the total revenue an organization can reasonably anticipate from a single customer over the course of their relationship. It is the net present value of the cash flows attributed to the relationship with a customer.

This metric is widely used in business to determine how valuable a customer is to the company.

The formula for CLV is:

CLV = (Average Value of a Sale) X (Number of Repeat Transactions) X (Average Retention Time in Months or Years)

There are three sub-segments of the credit card product: transactors, revolvers, and dormants.

The transactors are customers who pay off their credit card balance every month.

Revolvers are customers who carry a balance from month to month.

Dormants are customers who no longer use their credit card.

Each sub-segment will have a different CLV.

Here is how to calculate CLV for each sub-segment:

Transactors:

CLV = (Annual Fee) X (1/Churn Rate)

CLV = (450) X (1/12)

CLV = 37.5 dollars

Revolvers:

CLV = (Annual Interest Paid) X (Average Customer Lifespan)

CLV = (5000) X (1/24)

CLV = 208.33 dollars

Dormants:

CLV = (Number of Dormant Customers) X (Average Annual Spend per Customer) X (Profit Margin)

CLV = (10,000) X (1000) X (0.2)

CLV = 2,000,000 dollars

Therefore, the CLV for transactors is $37.5, for revolvers it is $208.33, and for dormants, it is $2,000,000.

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(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.

(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.

(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.

(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.

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