A country can use all its resources to produce Product A and Product B. If you know the opportunity cost of
producing Product A in terms of Product B, how can you quickly determine the cost of Product B in terms of
product A? Explain in one to two sentences, using an example.

Answer:

a=9

Step-by-step explanation:

a^3 = 729

Taking the cube root of each side

a^3 ^(1/3) = 729^ (1/3)

a = 9

The smallest possible number of members of the committee is 5005.

Let \($v_i$\) be the number of votes received by the i th candidate, and let \($p_i$\)be the percentage of votes received by the i th candidate. We know that\($p_i = \frac{v_i}{m} \times 100$\), where m$is the total number of committee members.

We are given that\($p_i + 1 \leq v_i$\), which can be rewritten as  \($\frac{v_i}{m} \geq \frac{101}{100} \times \frac{1}{27}$\)

Since\($\sum_{i=1}^{27} \frac{1}{27} = 1$\), it follows that \($\sum_{i=1}^{27} \frac{v_i}{m} \geq \frac{27 \times 101}{100 \times 27} = \frac{101}{100}$\). Therefore, the total number of votes received by the candidates is at least \($\frac{101m}{100}$\). Since each committee member gave exactly one vote, it follows that \($m \geq \frac{101m}{100}$\), which implies that\($m \geq 5005$.\)

To show that 5005 committee members is indeed possible, we can let\($v_1 = 2777$\),\($v_2 = 1389$, $v_3 = 693$,\) and \($v_i = 0$\) for\($4 \leq i \leq 27$\). Then the percentage of votes received by the $i$th candidate is \($\frac{v_i}{m} \approx 0.01960784$\), which is less than 1% away from \($1.960784 \d = \frac{1}{27} \times 100%$\).

Moreover, \($v_1 + v_2 + v_3 = 4859$\), which is 1 less than 4858, so each percentage is at least 2% less than the corresponding number of votes. Therefore, the smallest possible number of committee members is 5005.

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The reason that best supports Statement 4 in the

given proof is option A. Addition Property of Equality

The statement 4, "4x + 18 = 78," is an equation that is being derived from the previous statements in the proof. The left side of the equation (4x + 18) represents the value of m/X, which was given as 4x + 18 in statement 2.

The right side of the equation (78) represents the value of m2Y, which was given as 78° in statement 3.

Therefore, statement 4 is derived by substituting the known values of m/X and m2Y into the equation m/X = m2Y, which was given as statement 1.

The reason for this substitution is the Addition Property of Equality, which states that if you add the same value to both sides of an equation, the two sides remain equal.

In this case, the same value (4x + 18) is being added to both sides of the equation m/X = m2Y, resulting in the equation 4x + 18 = 78.

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The quotient of the rational expressions shown above is given by, Answer: option (C) 7x²/6x-10

To simplify the expression 7x² / 3x-5 / 2x+6 / x+3

We need to perform the following steps:

Invert the divisor.

Change the division to multiplication.

Factor the numerator and denominator.

First, divide the first term in the numerator (7\(x^2\)) by the first term in the denominator (2x) to get 3.

Then multiply (2x + 6) by 3 to get 6x + 18 Subtract this from the numerator.

2x + 6 | 7\(x^2\) + 3x - 5

- (6x + 18)

_______

-3x - 23

Then subtract the following term from the numerator: -3x.

Dividing -3x by 2x gives -3/2.

Multiply (2x + 6) by -3/2. The result is -3x - 9.

Subtract this from the previous result.

3 - (3/2)x

_________

2x + 6 | - 14

The result of polynomial long division is -14.

Therefore, the quotient of the rational expression is (7\(x^2\) + 3x - 5) / (2x + 6) -14.

So the correct answer is option D: -14.

Cancel out any common factors.

Multiply the remaining terms to get the answer.

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Answer:

48

Step-by-step explanation:

6 x 8 = 48. Simple as that. She made enough to send 6 cookies to 8 different groups.

Answer:

x=20

Step-by-step explanation:

Substitute 15 for y

it will be 2/3 multiplied by 15 then you get 10

you add 10 to 30 getting 40

then you divide 40 by 1/2 getting 20

:)))

Answer:

x = 80

Step-by-step explanation:

First, plug the 15 into the y.

\(1/2x - 2/3(15) = 30\)

Use PEMDAS to solve the parentheses, 2/3 of 15 is 10.

\(1/2x - 10 = 30\)

Add 10 to both sides of the equation.

\(1/2x = 40\)

Divide each side by 1/2 (or multiply by it's reciprocal, which is 2)

That will get you your answer of x = 80

Answer:

slope = 2 , y- intercept = -8

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

- 4x + 2y = - 16 ( add 4x to both sides )

2y = 4x - 16 ( divide both sides by 2 )

y = 2x - 8 ← in slope- intercept form

with slope m = 2 and y- intercept c = - 8

Answer:

the slope is 2 and y-intercept is (0,-8)

Step-by-step explanation:

Step 1: is to subtract 2y from both sides, -4x+2y-2y=-16-2y

Step 2: Simplify, -4= -16-2y

Step 3: Divide both sides by -4, -4x/4=-16/-4-2y/-4

4x/4=x=1

the series ex2 converges for all real values of x.

The general term of the series ex2 = 1 + x^2 + x^4/2! + x^6/3! + x^8/4! + ... is given by:

an = xn/(n!) for n ≥ 0, where n is an even integer.

Here, xn represents the term with exponent n in the series.

Therefore, the range of values for the index n is all even non-negative integers starting from 0.

Note that n! (n factorial) in the denominator of the general term ensures that each term after the first term (which is 1) is smaller than the preceding term, as n increases.

what is integer?

An integer is a whole number that can be positive, negative, or zero. It does not include fractions or decimals. Examples of integers include -3, -2, -1, 0, 1, 2, 3, and so on. The set of integers is denoted by the symbol Z.

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The z-score when x = 7 is approximately -3.75. This means that 7 is 3.75 standard deviations to the left of the mean.

To find the z-score when x = 7, we can use the formula:

z = (x - μ) / σ

where x is the value (7 in this case), μ is the mean (22 in this case), and σ is the standard deviation (4 in this case).

Substituting the given values:

z = (7 - 22) / 4

z ≈ -3.75

So, the z-score when x = 7 is approximately -3.75. This means that 7 is 3.75 standard deviations to the left of the mean.

Please note that the mean is 22, as stated in the problem.

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Answer:

The first table

Step-by-step explanation:

A function can only have one corresponding y coordinate per x coordinate

The distance between functions \(f(x) = x\)  \(g(x) = e^(^-^x^)\) can be calculated  \(d(f, g) = \sqrt{((1/3) - 2(-e^(^-^x^) + x * e^(^-^x^)) + (-1/2) * e^(^-^2^x^))}\) using the given inner product, and the "angle" between f and g can be found  \(\theta = \arccos ((f.g) / (||f|| * ||g||))\) by evaluating the inner product and dividing it by the product of their magnitudes.

a) The distance between functions \(f(x) = x\) and \(g(x) = e^(^-^x^)\) can be calculated using the inner product defined as \((f.g) = \int{f(x)g(x)} \, dx\) over the interval [-1, 1].

To find the distance, we can compute the square root of the inner product of f and g:

\(d(f,g) = \sqrt{((f.f) - 2(f.g) + (g.g))}\)

Plugging in the functions f(x) = x and g(x) = e^(-x), we have:

\(d(f,g) = \sqrt{(\int{x^2} \, dx - 2\int {xe^-^x^} \, dx+ \int {e^-^2^x^} \, dx)}\)

Evaluating the integrals, we get:

\(d(f,g) = \sqrt{((1/3) - 2(-e^-^x^ + x * e^-^x) + (-1/2) * e^-^2^x)}\)

Simplifying further, we obtain the distance between f and g.

b) The "angle" between functions f and g can be determined using the inner product and the concept of orthogonality. Two functions are orthogonal if their inner product is zero.

To find the angle, we can calculate the inner product (f.g) and normalize it by dividing by the product of their magnitudes:

\(\theta = \arccos((f.g) / (||f|| * ||g||))\)

Substituting the given functions and their norms, we can find the angle between f and g.

In conclusion, the distance between functions \(f(x) = x\) and \(g(x) = e^(^-^x^)\) can be calculated using the inner product, while the "angle" between the two functions can be determined using the inner product and the concept of orthogonality.

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Answer:This is 69

Step by step explanation:67 +2 is 69

Every morning, Mr. Cross bakes 80 strawberry frosted donuts unless there is a special order. Each donut costs $3 to make, and it is sold for $5. Unsold donuts are given away to a charity at the end of the day, at a discounted price of $1.50. What will be Mr. Cross’s total earnings if he sells all 80 donuts?

Total revenue if all 80 donuts are soldRevenue = Total units sold × Selling price per unitSince there are 80 donuts and each donut costs $5,Total revenue if all 80 donuts are sold = 80 × 5 = $400Total cost if all 80 donuts are soldTotal cost of making all 80 donuts = Cost of one donut × Total units madeSince each donut costs $3,Total cost of making all 80 donuts = 3 × 80 = $240Total profitTotal profit = Total revenue - Total cost

Since revenue is $400 and the total cost is $240,Total profit = 400 - 240 = $160At the end of the day, unsold donuts are given away to charity at a discounted price of $1.50 each. Therefore, Mr. Cross’s total earnings would be $160 if he sold all 80 donuts.

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According to the information provided, statistics A seems to be an unbiased estimator of the population parameter.

Statistic A is the objective estimator of the population parameter, it should be emphasized. This is as a result of its 75 population parameter being its focal point. Statistic A would provide a more accurate estimate of the population parameter. This is due to the sample mean being 75, which is also the population mean. Given that statistic D is equal to the population means, it would serve as a more accurate estimate of the population parameter. The final point to make is that statistic C has no distribution shape.

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The dimensions of the cylindrical mailing tube of greatest volume that may be mailed using the US Postal Service are approximately:

Diameter: 3.45 inches

Length: 18.7 inches
Volume: 123.8 cubic inches.

To find the dimensions of the cylindrical mailing tube of greatest volume that may be mailed using the US Postal Service, we need to consider the dimensional restrictions set by the Postal Service. According to their regulations, the length and girth (circumference plus the diameter) of a package must not exceed 108 inches combined.

Let's assume that the tube has a diameter of "d" and a length of "L". The girth of the package is the sum of the circumference of the circular ends and the diameter of the tube, so we have:

Girth = 2π(d/2) + d = πd + d

The length and girth must satisfy the inequality:

L + Girth ≤ 108

Substituting the expression for Girth, we get:

L + πd + d ≤ 108

Solving for L in terms of d, we get:

L ≤ 108 - (π + 1)d

Now, let's consider the volume of the cylindrical tube, which is given by:

V = πr²L = (πd²/4) L

Substituting the expression for L, we get:

V = (πd²/4) (108 - (π + 1)d)

To find the maximum volume, we can take the derivative of V with respect to d, set it equal to zero, and solve for d:

dV/dd = 0

d[πd²/4 (108 - (π + 1)d)]/dd = 0

πd/2 - 3π²d/4 - π/4 + 27/4 = 0

Solving for d, we get:

d = 27/(4π - 6π²)

Substituting this value of d back into the expression for L and the equation for the maximum volume, we get:

L = 108 - (π + 1)d ≈ 18.7 inches

V = (πd²/4) (108 - (π + 1)d) ≈ 123.8 cubic inches

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Answer:247.74

Step-by-step explanation:

use a calculator

Using the absolute value function, linear functions and translations, we have that:

9. Vertex (2, 0), Range: {y | 0 ≤ y < ∞}

10. The equation is f(x) = -5x + 100.

11. The correct option is: The slope of f(x) is greater than the slope of g(x).

12. h(-5) = 10.

13. The equation is f(x) = 2x + 5.

14. The graph of y = f(x) will shift right 9 units.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0, and has vertex(turning point) at (0,0). The range is from the y-coordinate of the vertex to positive infinity.

In item 9, from the table, the turning point is at (2,0), hence:

Vertex (2, 0), Range: {y | 0 ≤ y < ∞}

A linear function is modeled by the following rule:

y = mx + b

In which:

For item 10, we have that:

Then:

The equation is f(x) = -5x + 100.

For item 11, the slope is given by change in y divided by change in x, hence:

Hence:

The correct option is: The slope of f(x) is greater than the slope of g(x).

For item 12, we have that:

h(x) = -4x - 10.

Hence, when x = -5:

h(-5) = -4(-5) - 10 = 20 - 10 = 10.

Hence:

h(-5) = 10.

For item 13, we have that when x changes by 4, y changes by 8, hence the slope is:

m = 8/4 = 2.

When x = 1, y = 7, hence, considering the slope, when x = 0, y = 5, and:

The equation is f(x) = 2x + 5.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x). Examples are shift left, shift right, shift down, shift up, vertical stretching, horizontal stretching, vertical compression, horizontal compression, reflection over the x-axis, reflection over the y-axis, and rotations by a determined amount(in degrees). All these translations have predetermined rules that we apply to the figures.

For this problem, the rule is given by:

y = f(x - 9).

The translation is x -> x - 9, hence:

The graph of y = f(x) will shift right 9 units.

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Answer:

(For number 9) Range {y/0<y<infinity} Vertex (2,0)

Step-by-step explanation:

I took test

I hope I helped for that part of it.

Al-Fatihah is an Islamic prayer recited during the five daily prayers. Comparing radio and television in reading Al-Fatihah from its beginning requires an analysis of how each medium conveys the prayer to its audience. Radio precedes television in reading Al-Fatihah from its beginning.

This is because radio broadcasting began in the early 1900s while television broadcasting began in the late 1940s.

This delay can range from a few seconds to a few minutes depending on several factors such as the geographical location of the audience, the strength of the signal, and the quality of the receiver. Therefore, the time difference between radio and television in reading Al-Fatihah can vary depending on the factors mentioned above.

Mathematically, the time difference between radio and television can be calculated using the formula: d = s / tWhere d is the distance between the transmitter and the receiver, s is the speed of the signal, and t is the time it takes for the signal to reach the receiver.

In this case, d is the distance between the broadcasting station and the audience, s is the speed of the signal which is constant (i.e., the speed of light), and t is the time it takes for the signal to reach the audience. Since the speed of light is approximately 299,792,458 m/s, the time it takes for the signal to reach the audience can be calculated using the following formula:t = d / s

Therefore, the time difference between radio and television in reading Al-Fatihah can be calculated by subtracting the time it takes for the radio signal to reach its audience from the time it takes for the television signal to reach its audience. This difference can range from a few milliseconds to a few minutes depending on the factors mentioned above.

In network concepts, the time difference between radio and television in reading Al-Fatihah can be affected by the bandwidth of the network. The bandwidth is the amount of data that can be transmitted over a network in a given time. If the bandwidth is low, it can cause a delay in the transmission of the signal which can affect the time difference between radio and television.

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By calculation, your grade in the class now is 78.7

From the question, we have the following parameters that can be used in our computation:

Score of 47.2 in 60

Represent the score in 100% with x

So, we have the following equation

47.2/60 = x/100

Multiply both sides of the equation by 100

So, we have

100 * 47.2/60 = x/100 * 100

This gives

100 * 47.2/60 = x

So, we have

x = 100 * 47.2/60

Evaluate

x = 78.7

Hence, your grade in the class now is 78.7

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Answer:

I think 13 cm. You add the numbers 5,5,3 together to get 13

Step-by-step explanation:

Answer:

25 cm

Step-by-step explanation:

Answer: A

Hope this helps :)

Answer: A

Step-by-step explanation:

Answer: The slope is -1.

Twenty-five more tickets were sold to the Sunday shows than to the Saturday shows. The correct answer is option c.

The practise or science of organising and interpreting numerical data in big quantities, particularly for the objective of concluding proportions in a whole from those in an expected sample.

The table is given as:-

Time       Saturday      Sunday

12 pm      178               211

4 pm       204              212

8 pm       212               196

Total    -------------------------------

              594              619

The difference between the two shows on Sunday and Saturday is:-

Difference = 619  -  594  =  25 tickets

Therefore twenty-five more tickets were sold to the Sunday shows than to the Saturday shows. The correct answer is option c.

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Answer:

C. Twenty-five more tickets were sold to the Sunday shows than to the Saturday shows.

Step-by-step explanation:

Edge 2023

Answer:

Of the 52 cards, 4 are fives.

So the probability that a 5-card hand has no fives is:

(48/52)(47/51)(46/50)(45/49)(44/48) =

.658842 = 65.8842%

Answer:

Step-by-step explanation: hope u like that cus i sike that C?

Answer:

B looks like a 180 degree angle cause its js a straight line and isnt curved or bent. Brainliest plz?

Step-by-step explanation:

Answer:

$10.83

Step-by-step explanation:

Answer:

7:12

Step-by-step explanation:

Total no of animals in the field = 7 + 5 = 12

Ratio of cows 2 all d animals in the field =

\( \frac{no \: of \: cows}{total \: no \: of \: animals \: on \: the \: field} \)

Ratio = 7/12 = 7:12

The probability of drawing a queen first and then a heart second without replacement is 1/51.

In this case, the probability of drawing a queen first and then a heart second is:

P(Queen and Heart) = P(Queen) * P(Heart | Queen)

The probability of drawing a queen first is 4/52, since there are 4 queens in a standard deck of 52 cards. The probability of drawing a heart second, given that a queen has already been drawn, is 13/51, since there are 13 hearts in the deck and now only 51 cards remaining after the first draw.

Therefore, the probability of drawing a queen first and then a heart second without replacement is:

P(Queen and Heart) = (4/52) * (13/51) = 52/2652 = 1/51

So the probability of drawing a queen first and then a heart second without replacement is 1/51.

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