Given the triangular prism find the following

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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The number of polynomials that can be formed with -2 and 5 as zeroes are more than 1.

What is a polynomial?

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.x² -3x - 7 is an illustration of a polynomial with a single indeterminate x.

Given that the zeros of a polynomial are -2 and 5.

The polynomial that has a and b as zeors is p(x) = k[x² + (a+b)x + ab].

where k is a real number.

The polynomial that has -2 and 5 zeros is

p(x) = k[x² + (-2 + 5)x + (-2)×5]

p(x) = k[x² + 3x - 10]

Where k is a real number.

The number of real numbers is infinity.

The number of polynomials is infinity.

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(a) The statement 0 < Sn => 1 for all n in N is false.

(b) The statement Sn+1 < Sn for all n in N is false.

(c) The limit limₙ→∞ Sn does not exist.

a) To show that 0 < Sn ≤ 1 for all n ∈ N, we need to prove two conditions:

1) Show that Sn ≥ 0 for all n ∈ N.

2) Show that Sn ≤ 1 for all n ∈ N.

Let's prove these conditions one by one:

1) Sn ≥ 0 for all n ∈ N:

We have Sn = ∑(i=1 to n) (1/log(i)).

Since the natural logarithm (ln) of any number greater than 1 is positive, we can conclude that 1/log(i) > 0 for all i ∈ N.

Therefore, the sum of positive terms (Sn) will also be positive for all n ∈ N.

2) Sn ≤ 1 for all n ∈ N:

Let's prove this by induction.

Base case (n = 1):

S1 = 1/log(1) = 1/0 (undefined).

However, since the sum starts from i = 1, we can consider Sn as the limit of the partial sums as n approaches infinity.

So, for the base case, we can say that S1 = lim(n→∞) Sn = 1/log(1) = 1/0 → ∞.

Therefore, S1 is less than 1.

Inductive step:

Assume Sn ≤ 1 for some k ∈ N (inductive hypothesis).

We need to show that Sn+1 ≤ 1.

Let's consider Sn+1:

Sn+1 = Sn + (1/log(n+1)).

Since Sn ≤ 1 (inductive hypothesis) and 1/log(n+1) > 0, we can conclude that Sn+1 ≤ 1 + 1/log(n+1).

We need to prove that 1 + 1/log(n+1) ≤ 1.

To do this, we need to show that 1/log(n+1) ≤ 0.

This is true because log(n+1) > 1 for all n ∈ N (as n+1 > 2 for n ≥ 1).

So, 1/log(n+1) ≤ 1/1 = 1.

Therefore, Sn+1 ≤ 1 + 1/log(n+1) ≤ 1 + 1 = 2.

Since Sn+1 ≤ 2, we can conclude that Sn+1 ≤ 1.

By induction, we have shown that Sn+1 ≤ Sn for all n ∈ N.

b) We have already shown in part a) that Sn+1 ≤ Sn for all n ∈ N.

c) To show that the limit lim(n→∞) Sn exists, we need to prove that the sequence {Sn} is both bounded above and bounded below.

From part a), we know that 0 < Sn ≤ 1 for all n ∈ N. Therefore, Sn is bounded below by 0.

Now, we need to show that Sn is bounded above. Let's consider Sn = ∑(i=1 to n) (1/log(i)).

We can observe that 1/log(i) > 1 for all i > e (where e is Euler's number, approximately 2.71828). This is because the natural logarithm is a strictly increasing function for positive values, and for i > e, log(i) > 1.

Therefore, for n > e, we have Sn = ∑(i=1 to n) (1/log(i)) ≤ ∑(i=1 to n) 1 = n.

Since n is finite, we can conclude that Sn is bounded above.

Since Sn is bounded both above and below, the limit lim(n→∞) Sn exists.

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Answer:

10 : 9

Step-by-step explanation:

Given that a retailer sold a vacuum cleaner for 40% below its marked price.

Let the marked price = P

40% below = (100 - 40)P/100

Sale price = 60P/100

Sale price = 0.6P

The sale price was 50% above the cost to the retailer.

That is, cost price = (100 + 50)0.6P/100

Cost price = (150)0.6P/100

Cost price = 1.5 × 0.6P

Cost price = 0.9P

What is the ratio of marked price to cost?

The ratio will be = P/0.9P

Multiply both the numerator and denominator by 10

Ratio = 10 : 9

a. Based on the sample data, the mean price in dollars for a gallon of unleaded gasoline in San Francisco is $3.72.

b. The sample standard deviation in dollars is $0.3589.

Standard deviation,

Mean (the simple average of the numbers

Data and Calculations:

Average price of a gallon of unleaded gasoline in U.S. = $3.28

Number of gasoline and convenience stores for the U.S. average price = 90,000

Sample of San Francisco gasoline and convenience stores = 20

Prices of a gallon of gasoline in 20 San Francisco stores are as follows:

S/N.     Prices Difference in Mean  Difference Squared

1.          $3.59             -$0.13                     0.0169

2.           3.39                -0.33                     0.1089

3.           4.79                 1.07                      1.1449

4.           3.56               -0.16                      0.0256

5.           3.35              -0.37                      0.1369

6.           3.71               -0.01                     0.0001

7.           3.85              0.13                     0.0169

8.           3.40              -0.32                     0.1024

9.           3.55              -0.17                      0.0289

10.         3.76             0.04                      0.0016

11.          3.77             0.05                        0.0025

12.         3.39             -0.33                      0.1089

13.         3.75              0.03                       0.0009

14.         3.79              0.07                      0.0049

15.         4.19              0.47                       0.2209

16.        4.15             0.43                      0.1849

17.        3.66              -0.06                      0.0036

18.        3.93              0.21                       0.0441

19.        3.41              -0.31                       0.0961

20.      3.57              -0.15                       0.0225

Total $74.40                                          2.5765

Mean = $3.72 ($74.40/20)                 $0.12885 ($2.27394/20)

Standard deviation = square root of $0.12885

= $0.3589

Thus, in San Francisco, the price per gallon of unleaded gasoline is $0.03589 .

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To find the average price of unleaded gasoline in San Francisco, add up all the given prices and divide by the total number of prices. The standard deviation, indicating spread around this average price, is computed by finding the square root of the average of the squared deviations from the mean.

To estimate the mean price of a gallon of unleaded gasoline in San Francisco, you need to add up all the 20 given prices, then divide by the number of terms (20) in this case. The mean gives us the average value of the data set.

The standard deviation is a measure of how spread out the prices are from the mean. It is calculated by finding the square root of the variance, which is the average of the squared differences from the mean.

Remember, these calculations provide estimates, as the sample might not represent the entire population of gasoline prices in San Francisco. It's also important to note that external factors, such as changes in crude oil prices or regional taxes, can impact the cost of unleaded gasoline in diverse regions.

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your answer would be A. 122/27

The piece of cardboard needed will be 44 by 44 inches.

The volume of a square box can be defined as the space occupied by the square box or the cube, It is equal to the cube of the length of the side of the square box.

The formula for the volume is V = s³

The volume will be L*W*H

We are cutting 3 inches from each corner, so the length and width will each be x-6.

The height will be 4.

4332 = 4* (x - 6)* (x - 6)

1444= (x - 6)²

38 = x-6

x=44 inches.

The piece of cardboard needed will be 44 by 44 inches.

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Answer: 6x

Step-by-step explanation:

so consider x as the number,

twice of x= 2x

2x tripled= 2x*3

               = (2*3)x

               = 6x

The expression that represents the expected population next year is C. 0.93p. To calculate the expected population, you need to multiply the current population (p) by the percentage decrease (93% or 0.93 as a decimal): p x 0.93 = 0.93p. Therefore, the expected population next year is 0.93 times the current population.
Since the population is expected to decrease by 93% next year, we will need to find the remaining percentage of the population.

1. Calculate the remaining population percentage: 100% - 93% = 7%

2. Convert this percentage to a decimal: 7% = 0.07

3. Multiply this decimal by the current population (p) to find the expected population next year: 0.07 * p

The expression representing the expected population next year is 0.07p. Therefore, the correct answer is E. 0.07p.

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Answer: 90 is a number which has 9 as the sum of its digits, 9+0=9 and if the digits are reversed, 09 is 81 less than 90.

Step-by-step explanation: Since the number must be a 2-digit number, it seems that 90 is the only number that qualifies.

If you need some equations, here is a way to set up a system to solve:

x+y= 9 rewrite to get a value for y to substitute:

y = 9-x

10x +y = 10y + x + 81 rewrite by moving (subtracting variable terms from both sides)

10x -x + y-10y = 81 combine like terms

9x - 9y = 81

Substitute for y and solve for x

9x - 9(9-x)= 81 distribute.

9x - 81 + 9x = 81

18x = 162. 162/18 = 9

x = 9

Substitute in the original equation to solve for y

9 + y = 9

y = 0

10(9) + 0 = 10(0) + 9 +81

90 - 81 = 09

The total pressure of a mixture of two gases is the finalized value of the summation of the total pressure of each of the gases.

The total pressure of a mixture of two gases can be expressed in the form of an equation, as below,

Total Pressure = Pressure of Gas 1 + Pressure of Gas 2

It is noteworthy to be mentioned that the partial pressure of an individual gas is completely in contrast to that of the individual pressure of a gas. It can be expressed in the form of an equation, as below,

Partial Pressure = Total Pressure of Gas x Mole Fraction of Gas

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If you want each character to be approximately one inch in size, you would use a point size of 72 pts.

Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.

Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.

Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.

Therefore the correct answer is option b.) 72 pts.

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The total number of students in year 6, considering the bar chart, is of:

48 students.

A bar chart shows that number of times that each measure appears in the data-set, which are also called absolute frequencies of each observation.

From the bar chart given by the image at the end of the answer, the absolute frequencies of each observation are given as follows:

The total number of students is obtained by the sum of these numbers of students, hence:

14 + 10 + 16 + 5 + 3 = 48 students.

The bar chart is shown by the image at the end of the answer.

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Answer:  a) bus b)shown below c)2 d) 52

Step-by-step explanation:

The given proof follows the symmetric property of angle congruence. Therefore, option C is the correct answer.

Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.

Given that,

       Statements            Reasons

1. ∠ABC≅∠DEF           1. Given

2. m∠ABC=m∠DEF     2. Definition of congruent angles

3. m∠DEF=m∠ABC     3. Symmetric property of equality

4. ∠DEF≅∠ABC          4. Definition of congruent angles

The symmetric property says that if one geometric shape is congruent to another, than the second shape is also congruent to the first. The symmetric property of congruence says that for any angles A and B, if ∠A≅∠B then ∠B≅∠A.

Therefore, option C is the correct answer.

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Answer:

17

Step-by-step explanation:

The value of the function at x  = 5 will be equal to f(5) = -3.

The expression that established the relationship between the dependent variable and independent variable is referred to as a function.

In the function as the value of the independent variable varies the value of the dependent variable also varies.

From the given graph the equation of the curve or function is  f(x) = -2x + 7.

We need to find the value of f(5).

Calculate this by replacing x with 5

The value of the function at x=5 will be calculated as,

f(5) = -2(5) + 7.

f(5) = -10 + 7.

f(5) = -3.

Therefore, the value of the function at x  = 5 will be equal to f(5) = -3.

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Answer: 18 is 45% of 40

18/40 =.45

.45 x 100 = 45%

The correct answer is option 3: 2250. To calculate the number of different clients that can be identified with a coding system we need to multiply the number of options for each component.

For the two-letter component, there are five options (A, D, R, S, U) that can be chosen for each letter. Since repetition is allowed, there are 5 choices for the first letter and 5 choices for the second letter. Therefore, there are 5 x 5 = 25 possible combinations of two letters.

For the two-digit component, there are 10 options (0-9) for the first digit. Since no digit can be repeated, there are 9 options for the second digit (one less than the available options). Therefore, there are 10 x 9 = 90 possible combinations of two digits.

To calculate the total number of different clients that can be identified, we multiply the number of options for the two-letter component (25) by the number of options for the two-digit component (90). This gives us a total of 25 x 90 = 2250 different clients that can be identified with the coding system.

#A company uses a coding system to identify its clients. Each code is made up of two letters and a sequence of digits, for example AD108 or RR45789 The letters are chosen from A;D; R; S and U. Letters may be repeated in the code. The digits 0 to 9 are used, but NO digit may be repeated in the code. The number of different clients that can be identified with a coding system that is made up of TWO letters and TWO digits is: 1. 2230 2. 2240 3. 2250 4. 2210 22

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Solving a system of equations we can see that each pair of pants costs €82.94 and each coat costs €26.37

Let's define the variables:

x = cost of a pant

y = cost of a coat.

First, we know that:

3x + 2y = 245

And then there are discounts of 20% and 5%, and the cost of one of each is 100.75, then:

0.8x + 0.95y = 100.75

Then we have a system of equations:

3x + 2y = 245

0.8x + 0.95y = 100.75

We can isolate x on the second equation to get:

x = (100.75 - 0.96y)/0.8

x = 125.9 - 1.2y

Replace that in the other equation:

3*(125.9 - 1.2y) + 2y = 245

Solving for y:

3*125.9 - 3*1.2y + 2y = 245

y*(2 - 3*1.2) = 245 - 3*125.9

y = (245 - 3*125.9)/(2 - 3*1.2)

y = 82.94

Then the value of x is:

x = 125.9 - 1.2*82.94

x = 26.37

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Answer:

so d = 43

and the answer to the question is divide

Answer:

x+23+80=4x+17

x+103=4x+17

103-17=4x-x

86/3=x

x=28.66

Step-by-step explanation:

The 95 percent confidence interval that the true mean lead level of crows in the region is between 4.4157 and 5.3843.

What is a confidence interval?

An estimated range for an unknown parameter is known as a confidence interval. The 95% confidence level is the most popular, however other levels, such as 90% or 99%, are occasionally used when computing confidence intervals.

Here, we have

Given:  the mean lead level of the 23 crows in the sample was 4.90 ppm and the standard deviation was 1.12 ppm.

= x ± t×s/√n

= 4.90 ± (2.074)×1.12/√23

= (4.4157, 5.3843)

Hence, the 95 percent confidence interval that the true mean lead level of crows in the region is between 4.4157 and 5.3843.

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Answer:

The 90% confidence interval

(74.71, 82.63)

Step-by-step explanation:

Confidence Interval Formula is given as:

Confidence Interval = μ ± z (σ/√n)

Where

μ = mean score

z = z score

N = number of the population

σ = standard deviation

The mean is calculated as = The average of their scores

N = 6 students

(71.6 + 81.0 + 88.9 + 80.4 + 78.1 + 72.0 )/ 6

Mean score = 472/6

= 78.666666667

≈ 78.67

We are given a confidence interval of 90% therefore the

z score = 1.645

Standard Deviation for the scores =

s=(x -σ)²/ n - 1 =(71.6 - 78.67)²+(81.0 - 78.67)²+(88.9 - 78.67)² + (80.4 - 78.67)²+ (78.1 - 78.67)²+( 72.0 - 78.67)2/ 6 - 1

= 5.886047531

= 5.89

The confidence interval is calculated as

= μ ± z (σ/√N)

= 78.67 ± 1.645(5.89/√6)

= 78.67 ± 3.9555380987

The 90% confidence interval

is :

78.67 + 3.9555380987 = 82.625538099

78.67 - 3.9555380987 = 74.714619013

Therefore, the confidence interval is approximately between

(74.71, 82.63)

Answer:

43cm²

Step-by-step explanation:

let's first consider the area of a square.

the area is L² which means all sides are equal so we take the length times the breadth which is both equal because like we said all sides are equal.

so to find the side of the square using the area, we take the square root of both of the area.

\( \sqrt{25} = 5\)

and also

\( \sqrt{18} = 4.2\)

so we have the height of the triangle as 5cm and the base is 4.2cm.

now, from the triangle, since we have two sides and it's a right-angled, we can use Pythagoras' formula.

\( \sqrt{ {5}^{2} + {4.2}^{2} } = 6.53cm\)

so the side 6.53cm is also the same side as the largest triangle. Since it's a square, all sides are equal. So we find the area of the largest triangle by using the formula

Area = L²

Area = 6.53²

Area = 42.6cm

the nearest cm square

Area = 43cm²

Check the picture below.

Answer:

118.0 in^3

Step-by-step explanation: