multiply and simplify (7ab+3c)(7ab-3c)

Answer:

22%

Step-by-step explanation:

change/years since 2000

2.2/10

multiply by 100

22

Answer:

22%

Step-by-step explanation:

We can writey + dy = 2x1x2 / (x1+x2) + 2x1Δx2/ (x1+x2) + 2x2Δx1/(x1+x2)+ 2Δx1Δx2/ (x1+x2)On subtracting y from both sides, we getdy = 2x1Δx2/ (x1+x2) + 2x2Δx1/ (x1+x2) + 2Δx1Δx2/ (x1+x2)

Given y= x1/(x1+x2)  we need to find the total differential of y.It is given that, y= x1/(x1+x2)Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we get + dy = (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)We know that dy = y - (x1 + Δx1)/ (x1 + Δx1 + x2 + Δx2)

On further simplification, we get,dy = (Δx1(x2+Δx2))/(x1+Δx1+x2+Δx2)²-(Δx1x2)/((x1+Δx1+x2+Δx2)²)Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y= x1/(x1+x2) is given by dy = (-x1x2/(x1+x2)²) dx1 + (x1²/(x1+x2)²) dx2. Note: x1 and x2 are independent variables.

Therefore, dx1 and dx2 are their differentials.Given y=2x1x2 /(x1+x2) Let us assume, x1 = x1+Δx1, x2 = x2+Δx2. On substituting these values, we gety + dy = 2(x1 + Δx1)(x2 + Δx2)/ (x1 + Δx1 + x2 + Δx2)On simplifying, we gety + dy = (2x1x2+2x1Δx2+2x2Δx1+2Δx1Δx2)/(x1+Δx1+x2+Δx2)

Since Δx1 and Δx2 are very small, we can neglect their squares and products, i.e., Δx1², Δx2², and Δx1.Δx2

Hence the total differential of y=2x1x2 /(x1+x2) is given by dy = (2x2/(x1+x2)²) dx1 + (2x1/(x1+x2)²) dx2.

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(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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Answer:

x = 5

Step-by-step explanation:

substitute the y  equation into -2x +3y =8 and you will get 5 as the solution :)

Therefore, the volume of liquid needed to fill a sphere of radius r to height h = r/3 is (92/81)πr^3.

To find the volume of liquid needed to fill a sphere of radius r to a height h = r/3, we first need to find the volume of the spherical cap that makes up the top portion of the sphere.

The volume of a spherical cap is given by the formula:

V = (1/3)πh^2(3r - h)

where h is the height of the spherical cap and r is the radius of the sphere.

Substituting h = r/3, we get:

V = (1/3)π(r/3)^2(3r - r/3)

= (1/3)π(r^2/9)(8r/3)

= (8/27)πr^3

This is the volume of the spherical cap that makes up the top portion of the sphere. To find the volume of liquid needed to fill the sphere to the given height h, we need to subtract this volume from the total volume of the sphere.

The total volume of the sphere is given by the formula:

V = (4/3)πr^3

Substituting the value of V for the spherical cap, we get:

V = (4/3)πr^3 - (8/27)πr^3

= (92/81)πr^3

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The probability that a woman is having one child of each sex is 0.2548.

The probability of having two children of the same gender (either both girls or both boys) can be calculated by multiplying the probability of having a girl or a boy is (which is 1/2 or 0.5) by itself twice, as each child is independent of the other:

0.5 × 0.5 = 0.25 (probability of having either two girls or two boys)

Since the total probability of having two girls or two boys is 0.5048 as given in the question, the probability of having one child of each sex is: 0.5048 - 0.25 = 0.2548.

Therefore, the probability that a woman with two children has one child of each sex is 0.2548

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The probability of having 3 or fewer Hispanics on the 15-member union executive committee, chosen at random from all the workers, can be calculated using the binomial probability formula.

The situation can be modeled as a binomial distribution, where we have n = 15 trials (the number of members on the executive committee) and a probability of success (selecting a Hispanic worker) p = 0.30 (the proportion of Hispanic workers among all the workers). We are interested in finding the probability of having 3 or fewer successes (Hispanic members) in these 15 trials.

To calculate this probability, we can use the binomial probability formula:

P(X ≤ 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)

Where P(X = k) represents the probability of exactly k successes in the 15 trials.

Using this formula, we can substitute the values into the formula and calculate the probability.

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Third pair of triangles is congruent by SAS.

In geometry, two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.

If any two sides and angle included between the sides of one triangle are equivalent to the corresponding two sides and the angle between the sides of the second triangle, then the two triangles are said to be congruent by SAS rule.

In the third pair, this rule is visible. Two pair of sides are equal to each other and the angles formed at the common vertex of the two sides are equal. Hence, the two triangles are congruent by SAS.

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Answer:

Not sure, is there a problem or only the rant? lol. I'd appreciate my first brainliest though.

Step-by-step explanation:

Answer:

5 and -5

This is because these 2 spots are exactly 5 spaces from 0.

Answer:

8n+7

Step-by-step explanation:

Answer:

C'(1, 2 )

Step-by-step explanation:

The translation (x + 3, y - 2 ) means add 3 to the original x- coordinate and subtract 2 from the original y- coordinate, thus

C(- 2, 4 ) → C'(- 2 + 3, 4 - 2 ) → C'(1, 2 )

The x-intercepts of the graph of the equation indicates the initial position of the golf ball and the final point it landed after the flop shot.

The golf ball would land 5 meters away.

In Mathematics and Geometry, the x-intercept simply refers to the zeros or roots of any quadratic function and it can be defined as the point where the line of a graph passes through the x-axis (x-coordinate) as shown in the image attached above.

Next, we would determine the x-intercept of the given quadratic function as follows;

y = -x² + 5x

Where:

x represents the horizontal distance (in yards).

0 = -x² + 5x

0 = -x(x - 5)

x = 0 or x = 5

Next, the distance is given by;

Distance = 5 - 0

Distance = 5 meters.

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The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.

To find P(A | B), we use the formula:

P(A | B) = P(A ∩ B) / P(B)

In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.

Plugging these values into the formula, we get

P(A | B) = 0.45 / 0.60 = 0.750.

To find P(B | A), we use the formula:

P(B | A) = P(A ∩ B) / P(A)

Here, P(A ∩ B) = 0.45 and P(A) = 0.50.

Substituting the values, we find

P(B | A) = 0.45 / 0.50 = 0.900.

A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.

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Answer: b

Step-by-step explanation:

Just took the test

The value of y is 12√3

From the diagram given, we are to find the value of "y"

First, we need to get the length of TU

TU² = 6² - 3²

TU² = 36 - 9

TU = √27

Next is to get the value of y

y² = (√27)² + 9²

y² = 27 +81

y = √108

y = 12√3

Hence the value of y is 12√3

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Answer:

B

Step-by-step explanation:

;)

Answer:

The volume of the box is 1630.72

Step-by-step explanation:

11.2x11.2x13= 1630.72

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Let's say that the cost of each postcard is "p".

We can write the equation as follows:

7p + 15.89 = 19.32

If we solve for "p", we get:

7p = 19.32 - 15.89

p = 3.43 / 7

p = $<<3.43/7=0.49>>0.49

Therefore, each postcard costs $0.49.

Answer:

Step-by-step explanation:

8 ÷ 2 4/9

36/11 or 3 3/11 or 3.27

Answer:

In exact form it is 36/11. In decimal form it is 3.277777 going on forever. And last is mixed number form 3 3 11.

Step-by-step explanation:

The solutions to \((x+5)^(3/2) = (x-1)^3\)are x ≈ -4.65 and x ≈ 0.51, obtained by graphing the functions in Desmos.

To solve \((x+5)^(3/2) = (x-1)^3\) by graphing, we can plot both sides of the equation on the same graph using a tool like Desmos. The solution will be where the two curves intersect.

First, we can simplify the equation by cubing both sides:

\((x+5)^3 = (x-1)^6\)

Next, we can plot \(y1 = (x+5)^3 and y2 = (x-1)^6\) on the same graph in Desmos. The intersection of the two curves will give us the solutions to the equation.

By examining the graph, we can see that there are two real solutions: x ≈ -4.65 and x ≈ 0.51.

Therefore, the solutions to the equation \((x+5)^(3/2) = (x-1)^3\) are x ≈ -4.65 and x ≈ 0.51.

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Answer:

g(x) = [x/6]

Step-by-step explanation:

The given graph is f(x)=[x]

On stretching the function f(x) by a factor of 6, the new function g(x) is

g(x) = f(x/6)

So, g(x) = [x/6]

Hence, on stretching the f(x) by a factor of 6, the new function g(x)=[x/6].

Note that none of the given options matched.

Answer:

A) $547 + 140($1.50 - $0.59)=x

Step-by-step explanation:

you would have $547 dollars to start them you would multiply 140 by the amount you sell the bars for subtracted by the amount you paid for them because you dont get to keep that money

The best interpretation for the function notation a(s) is: D. A square with sides 2 units long has an area of 4 square units.

If we are given that a function, f(x), it means that the value of the output f(x) is dependent on the value of the input that is given as x. f(x) is a function of x. f(x) changes depending on the changes that occurs to x.

We have that, the area of a square is a function of the length of its sides, and it is expressed in function notation as a(s), where:

a(s) if the area of the square.

s represents the length of the side of the square.

This means that, the side length of the square determines what the area of the square is, based on the function notation that is given as a(s).

Therefore, the interpretation that is best given to a(s) = 4, means that, if a square has a side length of 2 units, it would give an area of 4 square units.

Therefore, the correct interpretation of a(2) is: D. A square with sides 2 units long has an area of 4 square units.

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Answer:

0.75=n

Step-by-step explanation:

10=4n+7

-7        -7

3=4n

divide by four

0.75=n

your welcome :)

Answer:

C. f(x) = x + 4

Step-by-step explanation:

Answer:

is it from a textbook

Step-by-step explanation:

The volume of an ice cube produced by this machine is of:

Volume ice cube = 1 inch³

  A volume is the physical space that an object occupies in space, although it is also defined as the capacity of space that a hollow object may have.

If this machine produces ice that has a cube shape with a side of 1 inch, then to know the value of the volume of these cubes we will use the following equation:

Volume cube = side x side x side

Volume cube = side³

side = 1 inch

Volume ice cube = 1 inch³

As the side is 1 the volume and area will be 1 but with corresponding unit

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The Mean of the data is 87 secs. The Median is 99 secs.

The Range is 56 secs.

Given the data set for the number of secs that Braden ran in the 200-meter dash as: 56 sec, 99 sec, 112 sec, 56 sec, and 112 sec, first, order the data from lowest to highest.

56, 56, 99, 112, 112

Mean = sum of all data / number of data set = 435/5 = 87 secs.

Median = the middle data value which is 99 secs.

Mode = most appeared data value, thus, there is none that appeared the most. It means there is no mode.

Range = highest data value - lowest data value

= 56 secs.

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