Problem 1 Denote by 9 (t) is the position at time t of an object moving on a line. The function q need not be a position, q may be any differentiable function. The derivative, g, of a need not be a velocity, j is just the derivative of q. Assume that q is differentiable, so that its derivative, 9 = d', is the velocity, u: v (t) = (t) = ' (t) (1) Position and velocity are given, or measured, at three times, to, tı, and t2, with to 01 = v(tı) > 03 = v(t2) 20 (3) 059(to) = % <91 = q (ti) < 42 = 9 (t2) Assume also that the position increases as the velocity decreases on the interval of time [to, ta]. The problem is to establish a procedure to estimate a time t, between to and 1, when the position 4. = q (1.) is exactly halfway between qo and 4: 4. = 9(t.) = 40 +91 Assume that v is affine: for some constanta, v (t) = 10 + (t-to). (6) (1.1) Calculate a in terms of to, tı, to and v1. (5) (1.2) Find a formula for q (t) for every t in terms of t. to. 11, 90. 91.00, 01. (1.3) Then solve Equation (5) fort, in terms of to, +1.90:01. Vo, and 0. (1.4) Calculate the velocity when the position is halfway, v (t.)

Answer:

Eliminate redundant parentheses

(−108−14)−128

(-10x^{8}-14)-12x^{8}(−10x8−14)−12x8

−108−14−128

-10x^{8}-14-12x^{8}−10x8−14−12x8

2

Combine like terms

−108−14−128

−228−14

Solution

−228−14

Answer: 2n-4

Step-by-step explanation:

Cross multiply and add!

n*n=2n

Answer:  6 months

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Answer: B: The correlation is most likely due to a lurking variable.

I took this test and used the review to see the right answer, hope this helps you

Answer:

Cost of each blank shirt is less than or equal to $ 5.5

Step-by-step explanation:

Let x denotes cost of each blank shirt.

Total number fo shirts bought by Tyina = 12

Amount charged for each shirt to have the club logo = $2.75

So,

Amount charged for 12 shirts to have the club logo = [tex]12(2.75)=\$33[/tex]

As Tyina cannot spend more than $99,

[tex]12x+33\leq 99[/tex]

Now solve the inequality.

[tex]12x+33\leq 99\\12x\leq 99-33\\12x\leq 66\\x\leq \frac{66}{12}\\ x\leq 5.5[/tex]

So,

Cost of each blank shirt is less than or equal to $ 5.5

Answer:follow the snippit on ther

Step-by-step explanation:

Answer: WOW 2 yrs

Step-by-step explanation:

The equation you provided represents the IS (Investment-Saving) relation, which relates the equilibrium level of income (Y) to the components of aggregate demand.

Let's break down the equation:

Y = C(Y - T) + I(i) + G

Y represents the equilibrium level of income or output.

C(Y - T) represents consumption, which is a function of disposable income (Y - T). It assumes that consumption depends on the level of income after taxes (Y) minus taxes (T). The function is represented as C(Y - T) = co + ₂ x (Y - T), where co is the autonomous consumption and ₂ is the marginal propensity to consume (MPC).

I(i) represents investment, which is a function of the interest rate (i). It assumes that investment depends on the interest rate. The function is represented as I(i) = ao - ai, where ao is the autonomous investment and ai is the marginal propensity to invest.

G represents government spending.

To solve for the equilibrium level of income (Y), we need to set Y equal to the components of aggregate demand and solve for Y. The equilibrium occurs when aggregate demand equals aggregate supply.

Y = C(Y - T) + I(i) + G

Substituting the expressions for C(Y - T) and I(i) into the equation, we get:

Y = (co + ₂ x (Y - T)) + (ao - ai) + G

Simplifying the equation, we have:

Y = co + ₂Y - ₂T + ao - ai + G

Rearranging the terms with Y on one side, we get:

Y - ₂Y = co - ₂T + ao - ai + G

Combining like terms, we have:

Y = co - ₂T + ao - ai + G

Finally, multiplying both sides by -1, we obtain:

Y = -co + ₂T - ao + ai - G

Therefore, the equilibrium level of income (Y) is determined by the values of autonomous consumption (co), the marginal propensity to consume (₂), taxes (T), autonomous investment (ao), the marginal propensity to invest (ai), and government spending (G).

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Answer:

What's the question, it's bloked on my computer

Step-by-step explanation:

Answer:

30208^2

Step-by-step explanation:

hope this helps

Answer:

y = 12x + 8

Step-by-step explanation:

1. 3x - 1/4y = -2

Subtract 3x from both sides

2. -1/4y = -2 - 3x

The equation is in standard form.

3. -1/4y = -3x - 3

Multiply both sides by -4

4. Check photo for step 4

Divide by -1/4 = -0.25 undoes the multiplication -1/4 = -0.25

5. y = (-3x-2) / (-1/4)

Divide -2 - 3x by -1/4 = -0.25 by multiplying -2 - 3x by the reciprocal of -1/4 = -0.25

y = 12x + 8

The probability that fewer than 1690 blocks meet the specification in three or more of the six lots is  0.0000428%.

1. Let's calculate the probability of a single block meeting specification:

p(block meets spec) = 0.85

p(block doesn't meet spec) = 1 - 0.85

= 0.15

The number of blocks that meet the specification follows a binomial distribution with n = 2000 and p = 0.85.

Let X be the number of blocks that meet the specification.

Therefore, P(X < 1690) can be calculated using the binomial cumulative distribution function.Using a calculator or a software, we get:

P(X < 1690)

= 0.0006 (rounded to four decimal places)

Therefore, the probability that, in a given lot, fewer than 1690 blocks meet the specification is 0.0006 or 0.06%.

2. The number of blocks that meet the specification follows a binomial distribution with n = 2000 and p = 0.85.

We need to find the number of blocks k, such that

P(X < k) = 0.70

Using a calculator or a software, we get:

k = 1743

Therefore, the 70th percentile of the number of blocks that meet the specification is 1743.3.

The number of blocks that meet the specification in each lot follows a binomial distribution with n = 2000 and p = 0.85.

The probability that fewer than 1690 blocks meet the specification in a given lot is:

P(X < 1690) = 0.0006

From part 1, we know that the probability that fewer than 1690 blocks meet the specification in a given lot is 0.0006. Let Y be the number of lots with fewer than 1690 blocks meeting the specification.

Therefore, Y follows a binomial distribution with n = 6 and p = 0.0006.

We need to find P(Y ≥ 3).

Using a calculator or a software, we get:

[tex]P(Y ≥ 3) = 4.28 x 10^(-7)[/tex] (rounded to nine decimal places)

Therefore, the probability that fewer than 1690 blocks meet the specification in three or more of the six lots is 4.28 x [tex]10^(-7)[/tex] or 0.0000428%.

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a. In these equations, n represents the number of citizens who participate in the revolution. The baseline payoff for both cases is 50. Participants receive an additional 5 units of payoff for each additional citizen who joins the revolution, while non-participants receive an additional 3 units of payoff for each additional participant.

b. The NE values of n would be the point where the two payoff functions intersect.

c. The minimum number of citizens, k, that would ensure all remaining citizens would participate in the revolution in a NE is 8.

(a) The graphical representation of the payoff functions for participating and not participating in the revolution can be depicted as follows:

Participating in the revolution:

Payoff = 50 + 5(n - 1)

Not participating in the revolution:

Payoff = 75 + 3n

In these equations, n represents the number of citizens who participate in the revolution. The baseline payoff for both cases is 50. Participants receive an additional 5 units of payoff for each additional citizen who joins the revolution, while non-participants receive an additional 3 units of payoff for each additional participant.

(b) To find the Nash Equilibrium (NE) values of n, we need to identify the values where no citizen has an incentive to unilaterally deviate from their chosen strategy. In this case, we need to find the values of n for which the participants and non-participants have equal payoffs.

Setting the two payoff functions equal to each other, we have:

50 + 5(n - 1) = 75 + 3n

Simplifying the equation, we get:

2n = 20

n = 10

Therefore, the NE values of n are 10.

In the graphical representation, the NE values of n would be the point where the two payoff functions intersect.

(c) The socially optimal number of revolution participants can be determined by maximizing the total payoff of all citizens. To find this, we need to consider the sum of the payoff functions for participating and not participating citizens:

Total Payoff = 1000 * (50 + 5(n - 1)) + (1000 - n) * (75 + 3n)

By maximizing this equation, we can find the socially optimal number of revolution participants. However, it is important to note that the socially optimal number of participants may not necessarily correspond to a Nash Equilibrium.

(d) To ensure that all remaining citizens would participate in the revolution in a NE, the remaining citizens should have a higher payoff from participating compared to not participating. In this case, we can set up the following inequality:

75 + 3(1000 - k) > 50 + 5(k - 1)

Simplifying the inequality, we have:

3k - 25 < 0

k < 8.33

Therefore, the minimum number of citizens, k, that would ensure all remaining citizens would participate in the revolution in a NE is 8.

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The geometric mean of 4 and 8 is 5.7.

The geometric mean is a type of average that is calculated by taking the product of the given numbers and then finding the square root of that product. In this case, we have to find the geometric mean of 4 and 8.

To calculate the geometric mean, we multiply the given numbers: 4 * 8 = 32.

Next, we take the square root of the product: √32 ≈ 5.7.

Therefore, the geometric mean of 4 and 8 is approximately 5.7.

The geometric mean is often used to find an average when dealing with quantities that multiply together or have an exponential relationship. It is particularly useful when analyzing growth rates, ratios, or values that are inherently multiplicative. In this case, the geometric mean helps find a value that represents the "middle" or "average" of 4 and 8 in terms of their multiplication. The resulting value of 5.7 represents the common ratio between 4 and 8 that, when multiplied repeatedly, gives the same final result as directly multiplying 4 and 8 together.

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Answer:

3/2x is the slope and -9 is the y-intercept

Step-by-step explanation:

Answer:

x-intercept= ( 6,0)

y-intercept=(0,-9)

Step-by-step explanation:

Answer:

[tex] \frac{ {x}^{2} - 3x - 10 }{2x - 10} = \frac{(x - 5)(x + 2)}{2(x - 5)} = \frac{x + 2}{2} [/tex]

At x = 5, the limit is 7/2, or 3.5.

Answer:

z-3.2>16

Step-by-step explanation:

it is

Answer:

1800(5/6)^t

Step-by-step explanation:

Restricted stock refers to shares of stock given to a person subject to certain restrictions. It is an efficient method for attracting and retaining key employees because it incentivizes them to stay with the organization by giving them a financial interest in the company's success.

Restricted stock may be valued based on the current market price of the underlying stock at the time it is awarded. In this case, Novak Corporation issues 2,400 shares of restricted stock to its executives on January 1,2020 (the date of grant). The fair value of these shares is $111,000, and their par value is $12,000.The entries for Jan 1, 2020 are as follows: Restricted Stock ($99,000) Share Capital (Par Value) ($12,000) Additional Paid-In Capital ($87,000)These journal entries display the following information:

The corporation acknowledges the delivery of 2,400 shares of restricted stock worth $111,000 to its executives on January 1,2020.The par value of the shares is $12,000, meaning that each share has a par value of $5. As a result, the share capital account should be credited for the total par value of the shares, which is $12,000.

The remaining $99,000 ($111,000 - $12,000) represents the fair value of the shares given to the executives. The corporation must credit additional paid-in capital, an equity account, for this amount, as it is paid-in capital contributed to the corporation by investors.The entries for Dec 31, 2020 are as follows:

Compensation Expense ($33,000) Restricted Stock ($33,000)These journal entries display the following information: $33,000 is the yearly compensation cost (i.e., expense) related to the restricted shares granted to executives (one-third of the fair value). The compensation cost is debited to compensation expense, an income statement account. The balance in the restricted stock account ($99,000) is reduced by $33,000 to reflect the quantity of restricted stock given to the executives that have been earned for services delivered during the year. Restricted stock is credited for $33,000.

In the year 2020, the entries for the issuance of restricted stock to its executives on January 1 and the compensation expense and the related reduction in restricted stock at December 31 are provided in this solution.

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7.1  The null space of A is spanned by the vector [1, 3, 0, 0].

7.2 A basis for the column space is formed by the vectors [0, 1, 2]⁺ and [2, -1, 3]⁺.

7.3 The nullity of A is equal to the number of free variables in the parametric form of the nullspace solution, which is 2.

7.4 A subset that forms a basis for the space spanned by the given vectors is {v₁, v₃}.

For the given matrix A, we will find the basis for the nullspace and column space, determine the rank and nullity of A, and find a subset of vectors that forms a basis for the space spanned by those vectors. We will also determine the row equivalent matrices B and D.

7.1 To find the basis for the null space of A, we need to solve the equation Ax = 0, where x is a vector. By row reducing A to its echelon form, we obtain the matrix B. The solutions of Bx = 0 can be written in a parametric form as x₁ = t and x₂ = 3t, where t is a scalar. Thus, the null space of A is spanned by the vector [1, 3, 0, 0].

7.2 To find the basis for the column space of A, we observe that the column vectors of A that correspond to the pivot columns of B form a basis for the column space. From B, we can see that the pivot columns are the first and third columns of A. Therefore, a basis for the column space is formed by the vectors [0, 1, 2]⁺ and [2, -1, 3]⁺.

7.3 The rank of A is equal to the number of pivot columns in the row reduced echelon form B, which is 2. The nullity of A is equal to the number of free variables in the parametric form of the nullspace solution, which is 2.

7.4 To find a subset of the given vectors that forms a basis for the space spanned by those vectors, we observe that the vectors v₁ and v₃ are linearly independent, while v₂ can be expressed as a linear combination of v₁ and v₃. Therefore, a subset that forms a basis for the space spanned by the given vectors is {v₁, v₃}.

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1) To find the optimum quantities of X and Y that the consumer will purchase, we need to consider two conditions: the budget constraint and the utility maximization. The budget constraint can be expressed as Px*X + Py*Y = Income. Given that Px = 1, Py = 2, and Income = 300, the budget constraint becomes X + 2Y = 300. To maximize utility, we need to find the combination of X and Y that maximizes the utility function U = X*Y^2  Taking the derivative of U with respect to X and Y, we get dU/dX = Y^2 and dU/dY = 2XY. Setting dU/dX equal to the marginal rate of substitution (MRS), which is the ratio of prices (MRS = Px/Py), we have Y^2 = 1/2. Rearranging, we get Y = 1/sqrt(2). Setting dU/dY equal to the MRS, we have 2XY = 1/2. Substituting Y = 1/sqrt(2), we get X*(1/sqrt(2)) = 1/2. Solving for X, we find X = sqrt(2)/2. Therefore, the optimum quantities of X and Y that the consumer will purchase are X = sqrt(2)/2 and Y = 1/sqrt(2). 2) This combination of X and Y is an equilibrium in the sense that it maximizes the consumer's utility given the budget constraint and the prices of the goods. It represents the point where the consumer allocates their income between X and Y in a way that maximizes their overall satisfaction, taking into account the relative prices of the goods.

3) To find the maximum satisfaction, we substitute the optimum quantities of X and Y into the utility function. The maximum satisfaction is given by U = X*Y^2 = (sqrt(2)/2) * (1/sqrt(2))^2 = 1/2. Therefore, the maximum satisfaction that this utility-maximizing consumer can achieve is 1/2. 4) On the diagram, we can plot X on the x-axis and Y on the y-axis. The budget constraint can be represented by the line X + 2Y = 300. The optimum combination of X and Y, given by X = sqrt(2)/2 and Y = 1/sqrt(2), can be shown as a point on the diagram. Note: Unfortunately, as a text-based AI, I am unable to provide a visual diagram.

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Answer:

D

Step-by-step explanation:

First, you must solve this equation

6x+14=3(2x+5)

distribute 3 on the right side

6x+14=6x+15

subtract 6x on both sides

14=15

Since there are no values of x that will make this true, the answer is equal to no solutions, so it's D

Answer:

160 quarters, I believe.

Step-by-step explanation:

.25 (an individual quarter) multiplied by 160 equals 40 (the amount of dollars).

Answer:

Relationship between Josiah's pay and Tillery's pay  is not proportional

Step-by-step explanation:

Amount paid to Josiah per hour = $14

Amount paid to Tillery per hour = $7

Ratio of amount paid to Josiah to amount paid to Tillary = [tex]14:7=2:1[/tex]

In the next year,

Amount paid to Josiah per hour = 14 + 2 = $16

Amount paid to Tillery per hour = 7 + 2 = $9

Ratio of amount paid to Josiah to amount paid to Tillary = [tex]16:9[/tex]

As [tex]2:1\neq 16:9[/tex],  relationship between Josiah's pay and Tillery's pay  is not proportional

For k = ±7/4, every member of the family of functions y = A sin(kt) + B cos(kt) is indeed a solution to the differential equation 16y'' - 49y = 0.

To verify which values of k satisfy the differential equation 16y'' - 49y = 0, we substitute the function y = cos(kt) into the differential equation and see if it holds true for any value of k.

First, let's find the derivatives of y = cos(kt)

y' = -k sin(kt) y'' = -k² cos(kt)

Substituting these derivatives into the differential equation, we get

16(-k² cos(kt)) - 49(cos(kt)) = 0

Simplifying, we have

(-16k² - 49) cos(kt) = 0

For this equation to hold true for all x, the coefficient of cos(kt) must be zero. Therefore, we have

-16k² - 49 = 0

Solving this equation, we find

k² = -49/16

Since the square of a real number cannot be negative, there are no real values of k that satisfy the differential equation 16y'' - 49y = 0.

Now, let's verify that every member of the family of functions y = A sin(kt) + B cos(kt) is also a solution.

Taking the derivatives of y = A sin(kt) + B cos(kt), we have

y' = Ak cos(kt) - Bk sin(kt) y'' = -Ak² sin(kt) - Bk² cos(kt)

Substituting these derivatives into the differential equation 16y'' - 49y = 0, we get

16(-Ak² sin(kt) - Bk² cos(kt)) - 49(A sin(kt) + B cos(kt)) = 0

Simplifying, we have

(-16Ak² - 49A) sin(kt) + (-16Bk² - 49B) cos(kt) = 0

For this equation to hold true for all x, the coefficients of sin(kt) and cos(kt) must be zero. Therefore, we have

-16Ak² - 49A = 0 -16Bk² - 49B = 0

Solving these equations, we find

k = ±√(49/16) = ±7/4

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Answer: Ray's car wash receives more money per car wash

Step-by-step explanation:

The class limits for the class with the highest Frequency are 35 up to 45.

The given distribution table is related to cost of textbooks, frequency, and class limits. To find out the class limits for the class with the highest frequency, we need to determine the class interval with the highest frequency. From the given distribution table, it can be observed that the class interval with the highest frequency is 35 up to 45. The frequency of this interval is 20.

The class limit for this interval will be 35 up to 45, which is Option D. The class limit is the lowest and the highest possible value that can be included in a class interval. For example, if we take the class interval 35 up to 45, the lower class limit is 35 and the upper class limit is 45.

The steps to find the class limits for the class with the highest frequency are given below:

Step 1: Determine the class interval with the highest frequency from the given distribution table, we can determine the class interval with the highest frequency, which is 35 up to 45. This class interval has a frequency of 20.

Step 2: Find the class limits for this intervalThe class limits for the class interval 35 up to 45 will be 35 up to 45, which is Option D. The class limits refer to the smallest and largest values that can be included in a class interval.

Thus, the class limits for the class with the highest frequency are 35 up to 45.

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The probability of having a boy or girl during birth is an independent event, which means the result of one event has no impact on the outcome of another event.

Let p be the probability of having a boy, then q (1-p) will be the probability of having a girl. According to the binomial probability distribution, the probability of having r boys in a family of n children is given by;

P(X=r) = (nCr)p^r(1-p)^(n-r)

Where, nCr is the binomial coefficient. It is given by;

nCr = (n!)/(r!(n-r)!)

Here, n = 4 and p = 1/2.
Expected Value of the number of boys in a family of four children:
The expected value (µ) of the number of boys in a family of four children is given by;
µ = np = 4(1/2) = 2
In a four-child family, the probability distribution of the number of boys is as follows;
Number of Boys, X     0       1       2       3       4
Probability, P(X)       1/16  4/16  6/16  4/16  1/16
The probability of having 0 boys is 1/16, the probability of having one boy is 4/16, the probability of having two boys is 6/16, the probability of having three boys is 4/16, and the probability of having 4 boys is 1/16.
We can also calculate the variance (σ^2) and standard deviation (σ) of the number of boys in a family of four children using the following formulas;
σ^2 = np(1-p) = 4(1/2)(1/2) = 1
σ = sqrt(σ^2) = sqrt(1) = 1

The expected number of boys in a family of four children is 2. Also, the probability distribution of the number of boys in such a family is 1/16 for 0 boys, 4/16 for 1 boy, 6/16 for 2 boys, 4/16 for 3 boys, and 1/16 for 4 boys. The variance and standard deviation of the number of boys in a family of four children are 1 and 1 respectively.

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