Fay has a lemonade stand.
She spends £28 on ingredients.
She sells each glass of lemonade for £1.30.
If she sells 50 glasses of lemonade, what is her total profit?

Answer:

Step-by-step explanation:

If im understanding the question correctly

3 days: 36 pages

5 days: 60 pages

15 days: 180 pages

12 days: 144 pages

102 days: 1224 pages

Answer:

4x - 9

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define

5(2x - 1) - 2(3x + 2)

Step 2: Solve for x

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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The amount of volleyballs that the coach can buy is given as follows:

19 volleyballs.

The total spending can be modeled by a linear function in slope-intercept format, as follows:

y = mx + b.

The coefficients of the linear function are given as follows:

She buys 4 volleyball nets for $28 each, hence the intercept is given as follows:

b = 4 x 28 = 112.

Volleyballs cost $7 each, hence the slope is given as follows:

m = 7.

Then the cost function is defined as follows:

C(x) = 7x + 112.

The coach has $250 to spend on volleyball equipment, hence:

C(x) = 250.

Thus the amount of volleyballs that can be purchased is obtained as follows:

7x + 112 = 250

7x = 138

x = 138/7

x = 19.7.

The amount is rounded down, as there would not be enough money remaining for the 20th ball.

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2 If we were to deposit money for nine years, the answer may change as compounding frequency would have a greater effect over a longer time period.

3 The future value of a loan of $1000 would be $1,238.36, while at Trusty Bank it would be $1,169.81.

3 it takes approximately 11.55 years for the money to triple at Trusty Bank with monthly compounding.

When comparing the two banks, it is important to note that Happy Bank is offering semiannual compounding while Trusty Bank is offering monthly compounding. To compare the two rates on an equal basis, we need to convert them into their equivalent annual rates with continuous compounding, which takes into account compounding frequency.

The formula for the continuous compounding rate is e^(r/n)-1, where r is the nominal rate and n is the compounding frequency. For Happy Bank, the continuous compounding rate would be e^(0.06/2)-1 = 0.0294, or 2.94%. For Trusty Bank, the continuous compounding rate would be e^(0.06/12)-1 = 0.0049, or 0.49%.

Using these rates, we can calculate the future value of $1000 over three years. At Happy Bank, the future value would be $1,238.36, while at Trusty Bank it would be $1,169.81. Therefore, Happy Bank is the better deal for a three-year deposit.

If we were to deposit money for nine years, the answer may change as compounding frequency would have a greater effect over a longer time period. However, without additional information about compounding frequency and rates, we cannot determine which bank would be the better deal.

If we were to borrow money for three years, the calculations would be similar but the direction would be reversed. At Happy Bank, the future value of a loan of $1000 would be $1,238.36, while at Trusty Bank it would be $1,169.81. Therefore, Trusty Bank would be the better option for a three-year loan.

To determine how long it takes for the money to triple at Trusty Bank, we can use the formula FV = PV * e^(rt). If we start with $1000 and want to find when it will triple, we can set FV = $3000 and solve for t. This gives t = ln(3)/0.06 = 11.55 years. Therefore, it takes approximately 11.55 years for the money to triple at Trusty Bank with monthly compounding.

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The transition matrix A is \(\left[\begin{array}{ccc}0&13&-2/3\\0&2&1\\0&0&1/2\end{array}\right]\) .

To find the transition matrix from vector b to vector b', we can set up a linear system of equations and solve for the coefficients of the matrix.

Let's denote the transition matrix as A. We want to find A such that b' = A * b.

b = (4, 1, -6), (3, 1, -6), (9, 3, -16)

b' = (5, 8, 6), (2, 4, 3), (2, 4, 4)

Let's write the equation for the first row:

(5, 8, 6) = A * (4, 1, -6)

This can be expanded into three equations:

5 = 4\(a_{11\) + 1\(a_{21\) - 6\(a_{31\)

8 = 4\(a_{12\) + 1\(a_{22\) - 6\(a_{32\)

6 = 4\(a_{13\) + 1\(a_{23\) - 6\(a_{33\)

Similarly, we can write equations for the second and third rows:

(2, 4, 3) = A * (3, 1, -6)

(2, 4, 4) = A * (9, 3, -16)

Expanding these equations, we have:

2 = 3\(a_{11\) + 1\(a_{21\) - 6\(a_{31\)

4 = 3\(a_{12\) + 1\(a_{22\) - 6\(a_{32\)

3 = 3\(a_{13\) + 1\(a_{23\) - 6\(a_{33\)

2 = 9\(a_{11\) + 3\(a_{21\) - 16\(a_{31\)

4 = 9\(a_{12\) + 3\(a_{22\) - 16\(a_{32\)

4 = 9\(a_{13\) + 3\(a_{23\) - 16\(a_{33\)

Now, we have a system of linear equations. We can solve this system to find the coefficients of matrix A.

The augmented matrix for this system is:

[4 1 -6 | 5]

[3 1 -6 | 8]

[9 3 -16 | 6]

[3 1 -6 | 2]

[9 3 -16 | 4]

[9 3 -16 | 4]

We can perform row operations to reduce the matrix to row-echelon form. I'll perform these row operations:

[\(R_2\) - (3/4)\(R_1\) => \(R_2\)]

[\(R_3\) - (9/4)\(R_1\) => \(R_3\)]

[\(R_4\) - (1/3)\(R_1\) => \(R_4\)]

[\(R_5\) - (3/9)\(R_1\) => \(R_5\)]

[\(R_6\) - (9/9)\(R_1\) => \(R_6\)]

The new augmented matrix is:

[4 1 -6 | 5]

[0 1 0 | 2]

[0 0 0 | -3]

[0 0 0 | -2]

[0 0 0 | -2]

[0 0 0 | 1]

Now, we can back-substitute to solve for the variables:

From row 6, we have -2\(a_{33\) = 1, so \(a_{33\) = -1/2

From row 5, we have -2\(a_{32\) = -2, so \(a_{32\) = 1

From row 4, we have -3\(a_{31\) = -2, so \(a_{31\) = 2/3

From row 2, we have \(a_{22\) = 2

From row 1, we have 4\(a_{11\) + \(a_{21\) - 6\(a_{31\) = 5. Plugging in the values we found so far, we get 4\(a_{11\)+ \(a_{21\) - 6(2/3) = 5. Simplifying, we have 4\(a_{11\) + \(a_{21\) = 13. Since we have one equation and two variables, we can choose \(a_{11\) and \(a_{21\) freely. Let's set \(a_{11\) = 0 and \(a_{21\) = 13.

Therefore, the transition matrix A is:

A = \(\left[\begin{array}{ccc}0&13&-2/3\\0&2&1\\0&0&1/2\end{array}\right]\)

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Answer:

well if you would put the question or at least a picture i dont think anyone can help. Try the number 7

Step-by-step explanation:

9514 1404 393

Answer:

  yes; $25/hour

Step-by-step explanation:

The ratio between cost and hours is 25 for each table entry. This tells you the relationship is proportional, which is a linear relationship. It also tells you the rate of change is 25 (dollars per hour).

Answer:

A, A and A

Step-by-step explanation:

Given

y = ax² + bx + c

• If a > 0 then minimum vertex

• If a < 0 then maximum vertex

Here the vertex is a maximum, thus a < 0 , that is negative → A

The value of c is the y- intercept

The graph crosses the y- axis below the y- axis, thus c is negative → A

The solutions to ax² + bx + c = 0 are the values of x on the x- axis where the graph crosses the x- axis.

The graph crosses the x- axis to the left of the y- axis , thus

Both solutions are negative → A

Answer:

h = -1.25

Step-by-step explanation:

isolate the variable by dividing each side by factors that don't contain the variable.

Integer values of x in the interval [-4, 2] that satisfy the following Inequality: 4x + 5 < -6 are -4 and -3.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

A sign of inequality can be used to show that one of the two variables is larger than, more than or equal to, less than, or equal to another value.

Income gap, gender inequality, access to health care, and social class are some of the most prominent instances of social inequality.

Given the inequality:

4x + 5 < -6

Therefore the all values of x which satisfy the given inequality on the interval [-4,2].

So, x= -4 and x= -3

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Answer:

-60

Step-by-step explanation:

Im smart

The likelihood that the number will be higher than 4 is 1/3, and the likelihood that the two numbers will both be higher than 2 is 4/9.

The probability is calculated by dividing the total number of outcomes by the total number of possible possibilities for an event. The concepts of probability and odds are distinct. Odds are calculated by dividing the possibility of an event occurring by the likelihood that it won't.

So, formula for probability P(E) = Positive Events/Total Events.

The likelihood that the quantity will be higher than 4;

P(E) stands for Positive Events/Total Events.

P(E) = 2/6

P(E) = 1/3

The likelihood that the two numbers will both exceed 2:

P(E) = Favorite Events / All Events

P(E) = 4/6 P(E) = 2/3

2 digits: 2/3 x 2/3 = 4/9.

The likelihood that the number will be higher than 4 is thus 1/3, and the likelihood that the two numbers will be higher than 2 is 4/9.

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According to the given information, (yn) is convergent.

What is the convergence and divergence of the sequence?

Convergence: A sequence approaches a fixed number as the number of terms increases.

Divergence: A sequence does not approach a fixed number as the number of terms increases.

Yes, (yn) is convergent.

Since (xn) is a convergent sequence, it has a limit L, which means that for any ε > 0, there exists an N such that |xn - L| < ε for all n ≥ N.

Now, let ε > 0 be given. Then, there exists an M such that |xn - yn| < ε for all n ≥ M.

Combining these two inequalities, we have:

|yn - L| = |yn - xn + xn - L|

≤ |yn - xn| + |xn - L|

< ε + ε (for all n ≥ M)

Therefore, we have shown that for any ε > 0, there exists an M such that |yn - L| < 2ε for all n ≥ M.

Since 2ε can be made arbitrarily small by choosing ε small enough, this implies that (yn) converges to L, the limit of (xn).

Hence, (yn) is also convergent.

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\(7 > -2\\7 -7 > -2-7\\0 > -9\)

Hope that helped!

If a circle has a radius of r, then its area is equal to π times the square of r.

In the statement, "The area of a circle is πr²," we have the formula for calculating the area of a circle, which is A = πr².

To convert it into if-then form, we need to establish a condition. Let's consider the condition as "If a circle has a radius of r."

The consequence of the condition is the area of the circle, which is "its area is equal to π times the square of r."

Combining the condition and the consequence, we can form the if-then statement: "If a circle has a radius of r, then its area is equal to π times the square of r."

This statement expresses that the area of a circle depends on the radius, and it can be calculated using the formula A = πr².

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Random permutations and a random variable X are defined on this probability space such as X = 1 when the product XYZ is even and X = 0 when that product is odd. \(E[X] = \[\frac{53}{63}\]\)

To determine the expected value of the random variable X given the permutation of 10 decimal digits, we will find the probability of the random variable X being odd or even. If the product XYZ is odd, then X is odd, otherwise, X is even.

Consider A be the event that x is odd, B be the event that y is odd and C be the event that z is odd. The probability of A occurring is:

\(P(A) = \[\frac{5}{9}\]\)

since there are 5 odd digits out of the 9 remaining after any digit is chosen as the first digit in x.

, \(P(B) = \[\frac{4}{7}\]\)

since there are 4 odd digits out of the 7 remaining after any digit is chosen as the first digit in y.

Also, \(P(C) = \[\frac{3}{6}\]\)

Since there are 3 odd digits out of the 6 remaining after any digit is chosen as the first digit in z.

Therefore, P(A ∩ B ∩ C) is the probability of the product being odd which is given as:

P(A ∩ B ∩ C) = P(A) × P(B) × P(C)

\(= \[\frac{5}{9}\] \times \[\frac{4}{7}\] \times \[\frac{3}{6}\]\)

= 10/63

Thus, the probability of the product being even

P(A ∩ B ∩ C)¯ = 1 − P(A ∩ B ∩ C) = 1 − 10/63= 53/63

Therefore, the expected value of X is given as:

\(E[X] = (0 \times \[\frac{10}{63}\]) + (1 \times\[\frac{53}{63}\])\)

= 53/63

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Answer:

b. interaction effect

Step-by-step explanation:

In a regression model, the interaction effect is present when a predictor variable changes the effect of another predictor variable on the outcome.

In a regression model, the interaction effect exists when one predictor variable impacts the outcome of another predictor variable differently than when examined individually. It refers to the interaction between two or more predictor variables and their influencers on an outcome or response variable. For example, in a regression model, studying and having a quiet place may individually contribute to a better score on a test, but perhaps studying in a quiet place provides a significantly better effect than the sum of those two effects separately. This would be considered an interaction effect.

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In the given table

at x=-1, the value of f(x) = 1 and g(x)=1

which satisify the condition of our question i.e. f(x)=g(x)

thus,

Answer : (a). x = -1

Answer:

sqrt(37) = arpox 6.1

Step-by-step explanation:

sqrt(1^2+6^2) = sqrt(37)

Answer:

s is not inversely proportional to t

Step-by-step explanation:

s is not inversely proportional to t.  I had responded that they were, based on the fact that as s went up, t went down.  But the question was not simply is there an inverse relationship, but are they inversely proportional.

The term proportional means that the relationship between s and t is a constant.  That is:

                                        t = s*(1/x)

Let's rewrite that to y*x = k and then check the numbers.  See the attached spreadsheet.  If the relationship were inversel proportioanl, thaen the product of t*s would be a contant for the series.  The third set is different from the first two.  The data has an is inverse relationship, but it is NOT proportional.

The probability that we need at most 3 rolls to see the number four appear is 7/8.

we can analyze the possible outcomes. In the first roll, there are 6 equally likely outcomes since each face of the die has an equal chance of appearing. Out of these 6 outcomes, only one outcome results in seeing the number four, while the other 5 outcomes require additional rolls. Therefore, the probability of needing exactly one roll is 1/6.

In the second roll, there are two possibilities: either we see the number four (with a probability of 1/6) or we don't (with a probability of 5/6). If we don't see the number four in the second roll, we proceed to the third roll.

In the third roll, the only remaining possibility is seeing the number four, as we must stop rolling after this point. The probability of seeing the number four in the third roll is 1/6.

To find the probability of needing at most 3 rolls, we sum up the probabilities of these three independent events: 1/6 + (5/6)(1/6) + (5/6)(5/6)(1/6) = 7/8. Hence, the probability that we need at most 3 rolls is 7/8.

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Answer: 49.5 dollars

Step-by-step explanation: the original price is 330, but the sale takes 15 percent off

so we turn 15% into a decimal so we can multiply 330 and 15%

we get 0.15 × 330 = 49.5

the formula for the equation of the line is ,

y-y1 = m (x-x1 )

2)

for point .( -5,-6), and slope m = 2

put x1 = -5 and y1 = -6

the equation of the line is,

y - (-6) = 2 (x -(-5) )

y +6 = 2(x + 5)

thus, the answer is point slope equation is y + 6 = 2(x + 5)

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3)

for point .( -7,2), and slope m = 3

put x1 = -7 and y1 = 2 and m = 3

the equation of the line is,

y - 2 = 3 (x -(-7) )

y - 2 = 3(x + 7)

thus, the answer is point slope equation is y - 2 = 3(x + 7)

Answer:

(4,-2)

Step-by-step explanation:

Start off by doing everything in the parenthesis which is everyone of them so 2x-1=-2 , your problem then should look like this:

-2(3x2-5x+2) carry the 2 over so multiply the 2 to everything so

(-6x-4+10x+2) add like numbers

10x+-6=4

-4+2=-2

(4,-2)

Answer:

A

I believe because p→q

q→p

The correct option is: D) 0.005 < p < 0.01  which defines the p - value.

To determine the p-value for a chi-square test of homogeneity, we need to compare the computed chi-square statistic (χ²) with the chi-square distribution with appropriate degrees of freedom.

The p-value represents the probability of observing a chi-square statistic as extreme or more extreme than the computed value, assuming the null hypothesis is true.

In this case, the null hypothesis assumes that there is no difference in the proportions of the categorical variable across the three populations.

Since the chi-square statistic obtained is χ² = 9.375, we need to determine the corresponding p-value. This requires knowing the degrees of freedom associated with the test.

For a test of homogeneity with two categories and three populations, the degrees of freedom can be calculated as (number of categories - 1) × (number of populations - 1) = (2 - 1) × (3 - 1) = 2.

Using a chi-square distribution table or statistical software, we can find that the p-value for χ² = 9.375 with 2 degrees of freedom is approximately 0.009.

Therefore, the correct option is:

D) 0.005 < p < 0.01

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Answer:

3,250

Step-by-step explanation:

Let's go from left to right, using multiple of 12 times a power of 10 in the process.

What is the closest multiple of 12,000 (12 * 10^3) to 39,000 without going over? That's 3 (36,000). That's the thousands digit in this answer.

12,000 * 3 = 36000

39000 - 36000 = 3000

What's the closest multiple of 1,200 (12 * 10^2) to 3,000 without going over? That's 2 (2,400). That's the hundreds digit.

1,200 * 2 = 2,400

3,000 - 2,400 = 600

What is the multiple of 120 (12 * 10) closest to 600 without going over? That's 5 (600, it's even!). That's the tens digit. Since it goes evenly, 0 is the ones digit.

120 * 5 = 600

600 - 600 = 0.

The answer to 39,000 over 12 is 3,250.

The required expressions in summation and product notations are: ∏(n = 1 to 7) [(n + 1)²] / (2 × 4 × 8 × 16 × 32 × 64 × 128) and ∑ (n = 0 to 5) n + (n + 5) / (n + 2)

The given expression is 1/2 × 4/4 × 9/8 × 16/16 × 25/32 × 36/64 × 49/128

To express the given expression using product notation, let's consider the numerators and the denominators separately.

Product of the numerators = 1 × 4 × 9 × 16 × 25 × 36 × 49

Product of the denominators = 2 × 4 × 8 × 16 × 32 × 64 × 128

Therefore, the given expression in the product notation is:

∏(n = 1 to 7) [(n + 1)²] / (2 × 4 × 8 × 16 × 32 × 64 × 128)

Now, let's consider the second expression.

The given expression is: 4 + 5/2! + 6/3! + 7/4! + 8/5! + 9/6!

To express this given expression in the summation notation, we can write it as:

∑ (n = 0 to 5) n + (n + 5) / (n + 2)!

Therefore, the required expressions in summation and product notations are:

∏(n = 1 to 7) [(n + 1)²] / (2 × 4 × 8 × 16 × 32 × 64 × 128) and ∑ (n = 0 to 5) n + (n + 5) / (n + 2)

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