-3s(s - 10) + 7(-2s -1)​

The percentage length increase of the new road compared to the old road is 92.8%.

The term "percentage" was adapted from the Latin word "per centum", which means "by the hundred". Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of whole is always taken as 100.

A road builder changed the grade (slope) of the road from 27% to 14%.

Maximum grade range of 12%-15%.

Height = 600 feet

Slope of the road = Height / Length

Let the length of the original road be l and the length of the new road be l'.

For the original road, slope = 27% = 0.27

⇒ 0.27 = 600 / l

⇒ l = 600/0.27 = 2222.22 feet

For the new road, slope = 14% = 0.14

⇒ 0.14 = 600/ l'

⇒ l' = 600/0.14 = 4285.71

Now, the percentage length increase of the new road compared to the old road:

% increase = (l' - l/l )×100

∴ % increase = (4285.71 - 2222.22/2222.22 )×100

= 92.8 %

Thus, the percentage length increase of the new road compared to the old road is 92.8%.

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The MP curve initially rises to its maximum value because of the specialized nature of the fixed capital, where each additional worker's productivity rises due to the marginal product of the fixed capital.

Production Function: q = f(L,K) = 20L + 25K + 5KL - 0.03L² - 0.02K²

Given, K = 5, i.e., capital is fixed. Therefore, the total product of labor, average product of labor, and marginal product of labor are:

TPL = f(L, K = 5) = 20L + 25 × 5 + 5L × 5 - 0.03L² - 0.02(5)²

= 20L + 125 + 25L - 0.03L² - 5

= -0.03L² + 45L + 120

APL = TPL / L, or APL = 20 + 125/L + 5K - 0.03L - 0.02K² / L

= 20 + 25 + 5 × 5 - 0.03L - 0.02(5)² / L

= 50 - 0.03L - 0.5 / L

= 49.5 - 0.03L / L

MP = ∂TPL / ∂L

= 20 + 25 - 0.06L - 0.02K²

= 45 - 0.06L

The following diagram illustrates the TP, MP, and AP curves:

Figure: Total Product (TP), Marginal Product (MP), and Average Product (AP) curves

The production function demonstrates increasing marginal returns due to specialization when L is low enough, i.e., when L ≤ 750. The marginal product curve initially increases and reaches a maximum value of 45 units of output when L = 416.67 units. When L > 416.67, MP decreases, and when L = 750 units, MP becomes zero.

The MP curve's initial increase demonstrates that the production function displays increasing marginal returns due to specialization when L is low enough. This is because when the capital is fixed, an additional unit of labor will benefit from the fixed capital and will increase production more than the previous one.

In other words, Because of the specialised nature of the fixed capital, the MP curve first climbs to its maximum value, where each additional worker's productivity rises due to the marginal product of the fixed capital.

The APL curve initially rises due to the MP curve's increase and then decreases when MP falls because of the diminishing marginal returns.

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If a bank receives a new deposit of $15,000, the bank can lend out $13,785.

The required reserve ratio is the fraction of deposits that banks must hold as reserves. If the current required reserve ratio is 8.1% and a bank receives a new deposit of $15,000, they can lend out $13,785.

The bank can lend out the amount equal to the deposit minus the required reserve amount. In this case, the new deposit is $15,000 and the required reserve ratio is 8.1%, so the calculation is as follows:

Required reserve amount = Deposit × Required reserve ratio

Required reserve amount = $15,000 × 0.081

Required reserve amount = $1,215

The bank must hold $1,215 as required reserves and can lend out the remaining amount:Amount available for lending = Deposit − Required reserve amount

Amount available for lending = $15,000 − $1,215

Amount available for lending = $13,785

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The quotient from the synthetic division (9a^4-31a^3-21a^2+6a-13)/(a-4) is 9a⁴ - 22a³ - a² + 5a - 8/a -4

Synthetic division can be defined as a mathematical method of dividing a polynomial by a  binomial x - c

Such that, c is a constant.

The steps to take in synthetic division;

Given the polynomial;

(9a^4-31a^3-21a^2+6a-13)/(a-4)

\(\sqrt[a -4]{9a^4 -31a^3 +6a -13}\)

c of divisor x-c

                4         coefficients of dividend

                           9     -31     -21      6     -13

                          _____9__-22__-1___ 5_______

                          9       -22     -1      5       -8

The quotient is the;

9a⁴ - 22a³ - a² + 5a - 8/a-4

Hence, the expression is  9a⁴ - 22a³ - a² + 5a - 8/a-4

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The balance of the account after 7 years would be approximately $247.95.

We may use the compound interest calculation to determine the account balance after seven years:

\(A = P(1 + r/n)^{(nt)\)

Where:

A = the final amount (balance) in the account

P = the principal amount (initial deposit)

r = annual interest rate (as a decimal)

n = number of times the interest is compounded per year

t = number of years

In this case, P = $150, r = 7.4% = 0.074 (as a decimal), n = 4 (quarterly compounding), and t = 7.

Plugging in these values into the formula, we get:

\(A = 150(1 + 0.074/4)^{(4\times7)\)

Calculating this expression, we find:

A ≈ $247.95

Therefore, the balance of the account after 7 years would be approximately $247.95.

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Answer: The answer is 226.2 feet.

Step-by-step explanation: The formula to find the total surface area of a cylinder is 2\(\pi\) x radius squared x height. If you use the formula you will get 226.19 feet as your answer and I rounded that to 226.2 feet.

UR MOM

P(X = 7), λ = 6: The Poisson probability of X = 7, with a parameter (λ) value of 6, is 0.1446. P(X = 11), λ = 12: The Poisson probability of X = 11, with a parameter (λ) value of 12, is 0.0946. P(X = 6), λ = 8: The Poisson probability of X = 6, with a parameter (λ) value of 8, is 0.1206.

The Poisson probability is used to calculate the probability of a certain number of events occurring in a fixed interval of time or space, given the average rate of occurrence (parameter λ). The formula for Poisson probability is P(X = k) = (e^-λ * λ^k) / k!, where X is the random variable representing the number of events and k is the desired number of events.

To calculate the Poisson probabilities in this case, we substitute the given values of λ and k into the formula. For example, for the first case (a), we have λ = 6 and k = 7: P(X = 7) = (e^-6 * 6^7) / 7!

Using a calculator, we can evaluate this expression to find that the probability is approximately 0.1446. Similarly, for case (b) with λ = 12 and k = 11, and for case (c) with λ = 8 and k = 6, we can apply the same formula to find the respective Poisson probabilities.

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Answer:

$13.20

Step-by-step explanation:

A dozen consists of 12 items. If you have 3 you must multiply the current amount by 4 to get 12. Therefore you must also multiply the price by 4.

3.30*4=13.20

The Upper Control Limit (UCL) and Lower Control Limit (LCL) are calculated for different data sets, as specified in the given values.

The UCL and LCL are statistical control limits used in process control to determine if a process is in a stable and predictable state. These limits define the range within which data points should fall if the process is under control.

In each case provided (A, B, C, D, E), the UCL and LCL values are given. These values represent the calculated control limits for the respective data sets.

To calculate the control limits, a specific statistical method such as the ± 3σ (sigma) method may have been used. This method sets the UCL and LCL at three standard deviations above and below the mean.

The UCL represents the upper threshold or upper boundary, while the LCL represents the lower threshold or lower boundary. These limits help identify any potential deviations or out-of-control situations in the data.

By applying the given values, the corresponding UCL and LCL for each data set can be calculated. These limits are important for quality control and process monitoring, ensuring that the data falls within acceptable ranges.

To calculate the UCL and LCL using ±3σ limits, we use the following formulas:

UCL = Mean + 3σ
LCL = Mean - 3σ

Here, σ represents the standard deviation of the data set. The ±3σ limits provide a range that encompasses most of the data points in a normal distribution, with approximately 99.7% of the data falling within this range.
A) For data set A:
UCL = 7.437
LCL = -2.237

B) For data set B:
UCL = 7.82
LCL = 0

C) For data set C:
UCL = 8.382
LCL = 0

D) For data set D:
UCL = 7.82
LCL = -2.22

E) For data set E:
UCL = 9.112
LCL = 0

The ±3σ limits are derived from the standard deviation (σ) of the data set. Unfortunately, the standard deviation is not provided in the given information. If you have the standard deviation available, we can proceed to calculate the UCL and LCL using the formulas UCL = Mean + 3σ and LCL = Mean - 3σ.

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Question - What are the upper control limit (UCL) and lower control limit (LCL) using a ±3σ limit for the given data sets?

A) For data set A, the UCL is 7.437 and the LCL is -2.237.
B) For data set B, the UCL is 7.82 and the LCL is 0.
C) For data set C, the UCL is 8.382 and the LCL is 0.
D) For data set D, the UCL is 7.82 and the LCL is -2.22.
E) For data set E, the UCL is 9.112 and the LCL is 0.

13=9+m, 7-m=3 and im not sure about the third answer

The smallest number a such that A + BB is regular for all B > a can be determined by finding the eigenvalues of the matrix A. The value of a will be greater than or equal to the largest eigenvalue of A.

A matrix A is regular if it is non-singular, meaning it has a non-zero determinant. We can consider the expression A + BB as a sum of two matrices. To ensure A + BB is regular for all B > a, we need to find the smallest value of a such that A + BB remains non-singular. One way to check for singularity is by examining the eigenvalues of the matrix A. If the eigenvalues of A are all positive, it means that A is positive definite and A + BB will remain non-singular for all B. In this case, the smallest number a can be taken as zero. However, if A has negative eigenvalues, we need to choose a value of a greater than or equal to the absolute value of the largest eigenvalue of A. This ensures that A + BB remains non-singular for all B > a.

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Answer:

3/5

Step-by-step explanation:

First add all of the balls together to know the total.

2 + 2 + 1 = 5

Probability of Green: 2/5

Probability of Red: 2/5

Probability of Blue: 1/5

Add red and blue together

2/5 + 1/5 = 3/5

3/5

Brainliest would be appreciated. :)

Answer:

X=11 not so sure about y

Step-by-step explanation:

Since this is a square, x and 11 sides are the same. So, x would have to be 11. Sorry I can’t help on y but I hope this helps.

Answer:

10/39   0.256

Step-by-step explanation:

5 girls and boys each from kenilworth.

total is 39

The given vector equation represents a twisted tube or helix in three-dimensional space. The given vector equation r(s, t) = s sin(5t), s², s cos(5t) represents a parametric surface in three-dimensional space.

To identify the surface, let's analyze the components of the vector equation:

x = s sin(5t)

y = s²

z = s cos(5t)

From the equation, we can observe that the variable s appears in all three components. This suggests that the surface is radial, meaning it extends outward from the origin (0, 0, 0) or contracts towards it.

The trigonometric functions sin(5t) and cos(5t) indicate periodic behavior along the t direction. These functions oscillate between -1 and 1 as t varies.

The component s² indicates that the surface extends or contracts based on the square of s. When s > 0, the surface expands outward, and when s < 0, it contracts towards the origin.

Considering these observations, we can identify the surface as a twisted tube or a helix that extends or contracts radially while twisting in a periodic manner along the t direction.

In summary, the given vector equation represents a twisted tube or helix in three-dimensional space.

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Answer:

D- 5hrs

Step-by-step explanation:

If the family can hike 3 miles per hour,
for 15 miles: 15/3 = 5 hours.

Every hour they cover 3 miles per hour, so to cover 15 miles, they will take 5 hours

Answer:

D. 5 hours

Step-by-step explanation:

3 miles per 1 hour so 3/1

15 miles per x hours so 15/x

3/1 = 15/x or 3 = 15/x

get x by itself so

3 divided by 3 and 15 divided by 3

x = 5 hours

No, the function f(x) = x² - 25x + 5 is not continuous at x = 1. In the summary, we state that the function is not continuous at x = 1.

To explain further, we observe that a function is continuous at a particular point if three conditions are met: the function is defined at that point, the limit of the function exists as x approaches that point, and the limit value is equal to the function value at that point.

In this case, we evaluate the function at x = 1 and find that f(1) = 1² - 25(1) + 5 = -19. However, to determine if the function is continuous at x = 1, we need to examine the behavior of the function as x approaches 1 from both the left and right sides.

By calculating the left-hand limit (lim(x→1-) f(x)) and the right-hand limit (lim(x→1+) f(x)), we find that they are not equal. Therefore, the function fails to satisfy the condition of having the limit equal to the function value at x = 1, indicating that it is not continuous at that point. Thus, the answer is No.

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One large bucket of popcorn costs $6 and one box of candy costs $3.75.

Let's call the cost of one large bucket of popcorn as "p" and the cost of one box of candy as "c". We can set up two equations based on the information given in the problem :

Equation 1: 4p + 5c = 42.75 (first group's purchase)

Equation 2: 3p + 2c = 25.50 (second group's purchase)

We can use any method to solve these equations, such as substitution or elimination.

Let's use the elimination method by multiplying both sides of Equation 1 by 2 and both sides of Equation 2 by -5 to eliminate "c" and get an equation in terms of "p":

8p + 10c = 85.50 (multiplying Equation 1 by 2)

-15p - 10c = -127.50 (multiplying Equation 2 by -5)

Adding the two equations, we get :

-7p = -42

p = 6

Now we can substitute the value of "p" into either Equation 1 or Equation 2 to solve for "c". Let's use Equation 1:

4(6) + 5c = 42.75

24 + 5c = 42.75

5c = 18.75

c = 3.75

Therefore, one large bucket of popcorn costs $6 and one box of candy costs $3.75.

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The minimum number of pizzas must they sell in order to have at least $300 is 44.

What is the profit?

The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product. In other words, the profit is a gain obtained from any business activities.

The student council needs to raise $300 - $235 = $65 to reach their goal.

They make a profit of $1.50 for each pizza they sell.

so they need to sell $65 / $1.50 = 43.333 pizzas to reach their goal.

As you cannot sell a fractional number of pizzas, they need to sell at least 44 pizzas to raise enough money for the field trip.

Hence, the minimum number of pizzas must they sell in order to have at least $300 is 44.

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Option C, \((x - 7)^2 + (y + 24)^2 = 625\), is the correct equation for the circle.

To identify the equation of the circle, we can use the general equation of a circle:

\((x - h)^2 + (y - k)^2 = r^2\)

where (h, k) represents the center of the circle and r represents the radius.

In this case, the center of the circle is (7, -24), and it passes through the origin (0, 0). Therefore, the radius is the distance between the center and the origin, which can be calculated using the distance formula:

\(r = sqrt((7 - 0)^2 + (-24 - 0)^2)\)

=\(sqrt(49 + 576)\)

= \(sqrt(625)\)

= 25

Now we can substitute the values into the equation:

\((x - 7)^2 + (y + 24)^2 = 25^2\)

Simplifying further, we have:

\((x - 7)^2 + (y + 24)^2 = 625\)

Therefore, the equation of the circle that has its center at (7, -24) and passes through the origin is:

\((x - 7)^2 + (y + 24)^2 = 625\)

Option C, \((x - 7)^2 + (y + 24)^2 = 625\), is the correct equation for the circle.

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In hypothesis testing, the null hypothesis (H0) is a statement that there is no significant difference between two groups, or that a certain parameter is equal to a specified value. In this case, the null hypothesis is that the mean difference is 0, meaning there is no significant difference between the two groups being compared.

The alternative hypothesis (Ha), on the other hand, is a statement that contradicts the null hypothesis. It can be one-tailed (directional), indicating that the mean difference is greater than or less than 0, or two-tailed (non-directional), indicating that the mean difference is not equal to 0. So, to determine the null and alternative hypotheses in this case, we know that the null hypothesis is that the mean difference is 0. The alternative hypothesis can be either one of the following:
- Ha: The mean difference is not equal to 0 (two-tailed)
- Ha: The mean difference is greater than 0 (one-tailed)
- Ha: The mean difference is less than 0 (one-tailed)

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The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

We have,

To arrange the length of the sides of the quadrilateral from longest to shortest, we need to calculate the length of each side of the quadrilateral using the distance formula:

Distance Formula:

If (x1, y1) and (x2, y2) are two points in a plane, then the distance between them is given by:

d = √((x2 - x1)² + (y2 - y1)²)

Using the distance formula, we can calculate the length of each side of the quadrilateral as follows:

AB = √((4 - (-5))² + (5 - 5)²) = 9

BC = √((2 - 4)² + (0 - 5)²) = √(29)

CD = √((-5 - 2)² + (-2 - 0)²) = √(74)

DA = √((-5 - (-5))² + (5 - (-2))²) = 7

Therefore,

The sides of the quadrilateral arranged from longest to shortest are CD, AB, DA, and BC.

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The solution to the equation 2(n-6) = -4(2n-1) is n = 8/5.

The greatest common factor is the largest common factor of the given numbers.

First, let's simplify both sides of the equation by multiplying out the brackets:

2n - 12 = -8n + 4

Next, we can add 8n to both sides of the equation to get all the n terms on one side:

10n - 12 = 4

Then, we can add 12 to both sides of the equation to isolate n:

10n = 16

Finally, we can divide both sides of the equation by 10 to get the value of n:

n = 16/10

This can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:

n = 8/5

Therefore, the solution to the equation 2(n-6) = -4(2n-1) is n = 8/5.

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Answer:

k = - 5/√3 = - (5√3)/3

Step-by-step explanation:

5x + ky = 20

y = (- 5/k) * x + (20/k)

Line equation: y = mx + b     m: slope   m = - 5/k

60° with x-axis (suppose it's positive x axis): slope m = tan 60° = √3

- 5/k = √3

k = - 5/√3 = - (5√3)/3

To determine the missing amounts in each situation, let's analyze the given information.Situation a: Supplies available-prior year end: $3,578

Supplies purchased during the current year: $675

Total supplies available: $4,725

To find the missing amount, we can subtract the known values from the total supplies available:

Missing amount (Situation a) = Total supplies available - (Supplies available-prior year end + Supplies purchased during current year)

                           = $4,725 - ($3,578 + $675)

                           = $4,725 - $4,253

                           = $472

Therefore, the missing amount in Situation a is $472.

Situation b:

The missing amount is already provided in the question as $12,165.

Situation c:

Supplies available-current year-end: $3,041

Supplies expense for the current year: (unknown)

To find the missing amount, we need to determine the supplies expense for the current year. However, based on the given information, there is no direct indication of the supplies expense. It is not possible to determine the missing amount in this situation without additional information.

Situation d:

Supplies available-current year-end: $5,400

Supplies expense for the current year: $24,257

To find the missing amount, we can subtract the known supplies expense from the supplies available at the current year-end:

Missing amount (Situation d) = Supplies available-current year-end - Supplies expense for the current year

                           = $5,400 - $24,257

                           = -$18,857 (negative value indicates a loss)

Therefore, the missing amount in Situation d is -$18,857 (indicating a loss of $18,857).

In summary, we were able to determine the missing amounts in Situations a and d, while Situations b and c already provided the missing amounts in the question.

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The number 2 is the first even counting number,4 is the second even number, 6 is the third even number, and so forth. the sum of the first 25th even counting numbers is 650.

Since we are given that the first even counting number is 2 and each subsequent even counting number can be obtained by adding 2 to the previous one. so  by using the formula for finding the 25th term of an arithmetic series  which :

an=a+(n-1)d, where the nth term d is a common difference and a is the first term so, the  25th term is 2 + (25-1)*2 = 2 + 48 = 50. Now for finding the sum of the first 25 even counting numbers, we use the formula which is Sn = n /2 * (a1 + an),  where Sn is the sum of the first n terms of the series, a1 is the first term, and an is the nth term. since in this  n=25, a1=2 and an=50, so  after substituting the  values we get  S25 = 25/2 * (2 + 50) = 25/2 * 52 = 650

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At least 15/16 or 15 out of 16 numbers in the data set must lie within 4 standard deviations from the mean.

Chebyshev's Theorem states that for any set of numbers, the fraction that will lie within k standard deviations of the mean is at least\(1 - 1/k^2\).

In this case, we are interested in finding the fraction of numbers that must lie within 4 standard deviations from the mean. Therefore, k = 4.

Using the formula from Chebyshev's Theorem, we can calculate the fraction:

\(1 - 1/k^2 = 1 - 1/4^2 = 1 - 1/16 = 15/16.\)

Hence, at least 15/16 or 15 out of 16 numbers in the data set must lie within 4 standard deviations from the mean.

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Question

Chebyshev's Theorem states that for any set of numbers, the fraction that will lie within k standard deviations of the mean is at least 1 - 1/k2. Use this theorem to find the fraction of all the numbers of a data set that must lie within 4 standard deviations from the mean. At least of all numbers must lie within 4 standard deviations from the mean. (Type an integer or a fraction.)

The required Poisson distribution used to model the elapsed time between the occurrence of successive events for a poisson random variable

We have to find distribution model used to model elapse the time between the occurrence of successive events for Poisson random variable.

we know that, Poisson distribution

P(x=x) = e^-λ(λ)^x/x!

Time between succeess,

P(y>x) = e^-λy

and, P(y<x) = 1- e^-λy

They are exponential distribution.

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