What is the probability that both events B and C will occur?

The inverse of the given function is f -1(x) = \[\frac{x+2}{3}\], where x is greater than or equal to -2/3.

Consider the function, f(x) = 3x - 2. To find the inverse of the function, follow the steps given below:

Step 1: Replace f(x) with y. y = 3x - 2

Step 2: Interchange x and y. x = 3y - 2

Step 3: Solve for y. Add 2 to both sides. x + 2 = 3y Divide both sides by 3. \[\frac{x+2}{3}=y\]

Step 4: Replace y with f -1(x).

Hence, f -1(x) = \[\frac{x+2}{3}\] The resulting function can be written as f -1(x) = \[\frac{x+2}{3}\], where x is greater than or equal to -2/3.

Note that the domain of f(x) is all real numbers, which means that the range of f -1(x) is also all real numbers.

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The correct matches are as follows:

15% of 30 ➔ 4.5

30% of 45 ➔ 13.5

60% of 72 ➔ 43.2

3% of 201 ➔ 6.03

Here is the correct matching of the percent amounts to their respective values:

15% of 30 ➔ 4.5

30% of 45 ➔ 13.5

60% of 72 ➔ 43.2

3% of 201 ➔ 6.03

To determine the values, we multiply the given percent amounts by their corresponding numbers.

For example, to find 15% of 30, we multiply 0.15 (which is the decimal form of 15%) by 30. The result is 4.5.

Similarly, 30% of 45 is obtained by multiplying 0.30 by 45, resulting in 13.5.

60% of 72 is calculated by multiplying 0.60 by 72, giving us 43.2.

Finally, 3% of 201 is obtained by multiplying 0.03 by 201, resulting in 6.03.

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Answer:

AA Postulate

Step-by-step explanation:

To prove that two triangles are similar in problem 6-7, we would use the Angle-Angle (AA) postulate. This postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

Answer:

y = 3[tex]\sqrt{5}[/tex]

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × (whole hypotenuse)

y² = 3 × (3 + 12) = 3 × 15 = 45 ( take square root of both sides )

y = [tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]

Answer:5 drops

Step-by-step explanation:

Every 100 nanograms is 0.1 microgram so 500 nanograms + 0.5 micrograms so 5 drops because everydrop is 100 nanograms

Answer:

$16,453.80

Step-by-step explanation:

5 × 12 months = 60 months (the time she payed the monthly payments in months)

219.23 × 60 = 13, 153.8

13,153.8+3,300= $16,453.80.

You would expect to pay $90 each month for electricity based on an average usage of 120 KWHs per month.

To calculate the monthly cost of electricity, you can multiply the average number of kilowatt-hours (KWH) used per month by the cost per KWH.

Given:

Cost per KWH: $0.75

Average monthly usage: 120 KWHs

To find the monthly cost, you can multiply the cost per KWH by the average monthly usage:

Monthly Cost = Cost per KWH * Average monthly usage

Plugging in the values, we have:

Monthly Cost = $0.75/KWH * 120 KWHs

Calculating the result:

Monthly Cost = $90

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The division between the functions f(x) = ∛(4 · x) and g(x) = 2 · x + 3 is equal to (f / g) (x) = ∛(4 · x) / (2 · x + 3), x ≠ - 3 / 2. (Correct choice: D)

In this problem we find two functions, with which we must perform a division between two functions, whose definition is shown below:

(f / g) (x) = f(x) / g(x)

If we know that f(x) = ∛(4 · x) and g(x) = 2 · x + 3, then the division between the two functions is:

(f / g) (x) = ∛(4 · x) / (2 · x + 3)

The restrictions on the domain is represented by every x when 2 · x + 3 = 0:

2 · x + 3 = 0

2 · x = - 3

x = - 3 / 2

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Answer:

[tex]37in^2[/tex]

Step-by-step explanation:

We can break up this figure into two bits, the longer rectangle at the top, and the smaller square at the bottom.

To find area if a rectangle, you do length x width. You can do this with the square, too. For the area of the square, you would do:

[tex]3 * 3=9in^2[/tex]

For the area of the bigger rectangle, we know the length of it (7 at the top), so we now have to find the width. The only width number that is available to us is the 7 at the right, and the 3 at the left side of the square.

We can subtract these two numbers to get 4 for the width. We just have to multiply our length (7) by our width (4):

[tex]7*4=28in^2[/tex]

Now that we have our areas of our smaller figures, we just need to add them together:

[tex]9in^2 + 28in^2 = 37in^2[/tex]

The area of the figure is [tex]37in^2[/tex]

Answer:

x = 1/2

Step-by-step explanation:

-3x + 1 + 10x = x + 4

7x + 1 = x + 4

6x + 1 = 4

6x = 3

x = 3/6

x = 1/2

Answer:

the solution to the equation is x = 1/2.

Step-by-step explanation:

To solve the equation -3x + 1 + 10x = x + 4, we can start by simplifying both sides of the equation:

Combine like terms on the left side:

(-3x + 10x) + 1 = x + 4

7x + 1 = x + 4

Next, we want to isolate the x term on one side of the equation. We can do this by subtracting x from both sides and subtracting 1 from both sides:

7x - x + 1 - 1 = x - x + 4 - 1

6x = 3

Finally, to solve for x, we divide both sides of the equation by 6:

6x/6 = 3/6

x = 1/2

So, the solution to the equation is x = 1/2.

Since the probability of success is 0.74, the probability of failure is 1 - 0.74 = 0.26. This means that there is a 26% chance of failure in the given binomial trial. Option C

In a binomial trial, the probability of success, denoted by "p," represents the likelihood of the desired outcome occurring. The probability of failure, denoted by "q," represents the complement of the probability of success, i.e., the likelihood of the desired outcome not occurring.

In this case, the probability of success is given as 0.74. To find the probability of failure, we subtract the probability of success from 1, since the sum of the probabilities of success and failure must equal 1.

Probability of failure = 1 - Probability of success

Therefore, the probability of failure = 1 - 0.74 = 0.26.

Hence, the correct answer is C. 0.26.

It's important to understand that in a binomial distribution, there are only two possible outcomes: success and failure. The probabilities of these outcomes must add up to 1. Therefore, if the probability of success is known, the probability of failure can be obtained by subtracting the probability of success from 1.

Option C

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The ratio of 6/5 and 8/7 is 21/20

A ratio is a relationship between two things when it is expressed in numbers or amounts.

For example if the ratio of boys to girls In a class is 4: 5 , this means that there are 4 boys to 5 girls in the class , i.e for every 4 boys there are 5 girls.

For example if two boys are to share 10 mangoes in the ratio 1:4 , this means one will take 2 and the other will take 8

2:4 can also be expressed as 2/4 = 1/2

Similarly, 6/5 : 8/7

= 6/5)/8/7

= 6/5 × 7/8

= 42/40

= 21/20

Therefore the ratio of 6/5 : 8/7 is 21/20

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The best description of the graph is option B) It is a line which intersects the y-axis at (2, 2). This is because the line has a y-intercept of 2 and intersects the y-axis at the point (0, 2). Option B

To determine the best description of the graph of the equation x + y = 2, we can rearrange the equation into slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Rearranging the equation, we have:

y = -x + 2

From this equation, we can see that the slope is -1, meaning that for every unit increase in x, y decreases by 1. The y-intercept is 2, indicating that the line intersects the y-axis at the point (0, 2).

Therefore, the best description of the graph is option B) It is a line which intersects the y-axis at (2, 2). This is because the line has a y-intercept of 2 and intersects the y-axis at the point (0, 2).

Option A) It is a line which intersects the x-axis at (2, 2) is incorrect because the line intersects the x-axis at the point (2, 0), not (2, 2).

Option C) It is a line joining the points whose x- and y-coordinates add up to 2 is incorrect because the equation represents a line and not a set of points.

Option D) It is a line joining the points whose x- and y-coordinates add up to 4 is incorrect because the equation represents a line where the x- and y-coordinates add up to 2, not 4.

Option B

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The ratio of the length of the shortest diagonal to the length of the longest diagonal in a regular hexagon is [tex]$\sqrt{3}/2$[/tex]. This can also be written as [tex]$\frac{\sqrt{3}}{2}$[/tex].

A hexagon is a six-sided polygon with all angles equal to 120 degrees. In a regular hexagon, all sides are equal in length and all angles are equal. The diagonals of a hexagon are line segments that connect non-adjacent vertices of the hexagon.

A regular hexagon has nine diagonals. The shortest diagonal of a regular hexagon is the one that connects opposite vertices and is equal to the length of a side of the hexagon. The longest diagonal of a regular hexagon is the one that connects opposite vertices and passes through the center of the hexagon.

To find the ratio of the length of the shortest diagonal to the length of the longest diagonal, we need to find the length of the longest diagonal in terms of the length of the shortest diagonal. We know that the length of the shortest diagonal is equal to the length of a side of the hexagon.

We can draw the longest diagonal and form an equilateral triangle by connecting the center of the hexagon to the two endpoints of the longest diagonal. The length of the side of this equilateral triangle is equal to the length of the longest diagonal of the hexagon.

The ratio of the length of the shortest diagonal to the length of the longest diagonal is then equal to the ratio of the side length of this equilateral triangle to the length of the side of the hexagon, which is [tex]$\frac{\sqrt{3}}{2}$[/tex].
Therefore, the ratio of the length of the shortest diagonal to the length of the longest diagonal in a regular hexagon is $\sqrt{3}/2$. This can also be written as [tex]$\frac{\sqrt{3}}{2}$[/tex].

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Answer:

2997 cm²

Step-by-step explanation:

If the scale factor of linear dimensions of 2 figures is k, then the scale factor of the surface areas is k².

The linear scale factor of the figures is 9.

k = 9

k² = 9² = 81

The area of the big pot is 81 times the area of the small pot.

37 cm² × 81 = 2997 cm²

  Hence, The Surface Area of the Larger Pot is:   2997 cm^2

MAKE A PLAN:

We need to find the Ratio of the Surface Areas of the TWO POTS, based on the given Height Ratio, And then, Calculate the Surface Area of the Larger Pot:

1) - The Height Ratio is Given as ( 9:1 ), So, the Linear Ratio is ( 9 )

2) - The Ratio of Surface Areas is the Square of the Linear Ratio:

      9^2   =   81

3) - Calculate the Surface Area of the LARGER POT:

      h1 / h2  =  1/9

      S1 / S2  =  1/81

      S2  = 37  *  81  =  2997 cm^2

      37 cm^2  *  81   =   2997 cm^2

Hence,  The Surface Area of the Larger Pot is:   2997 cm^2

I hope this helps you!

Answer:

204

Step-by-step explanation:

Sum: 816

Count: 4

Median: 199

Geometric Mean: 202.92942642991

Largest: 238

Smallest: 180

Range: 58

The inequality shown by the graph is m ≤ 1. This means that the values of m are less than or equal to 1. Any value of m that is equal to or smaller than 1 satisfies the inequality. However, any value of m that is greater than 1 does not satisfy the inequality.

Inequalities can be represented graphically using number lines.

The inequality m ≤ 1 means that all values of m that are less than or equal to 1 are solutions to the inequality.

The solution set is represented by a closed circle on the number line at the point where m = 1, and a line segment extending to the left of this point.
If we choose a value of m from the shaded region on the graph, such as m = 0, the inequality m ≤ 1 is satisfied because 0 is less than 1.

If we choose a value of m from the unshaded region, such as m = 2, the inequality is not satisfied because 2 is greater than 1. Therefore, the inequality shown by the graph is m ≤ 1.

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135 as a product of its prime factors is written as  3 × 3 x 3 x 5

The prime factors are those prime digits that can divide a particular digit evenly and without leaving any remainder. To put it differently, these are the main digits that, when multiplied with one another, result in the initial number.

In mathematics and number theory, prime factors hold significant value as they enhance comprehension of number properties and interconnections. In addition, they are utilized in a range of mathematical calculations and algorithms.

From the information given, we have the value as;

135

The prime factors are  3 × 3 x 3 x 5

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Answer:

$71.95

Step-by-step explanation:

$29.95- 200 copies

$14- 100 copies

$14- 100 copies

$14- 25 copies

so 14[3] + 29.95 = $71.95

The function f(x) in standard form is 3x³ - 12x² + 16x -2

A function is an expression that shows the relationship between the independent variable and the dependent variable.  A function is usually denoted by letters such as f, g, etc.

We have:

The function = f(x)

dividend = (x-1)

quotient = 3x²-9x+7

remainder = 5

Thus, the function f(x) in standard form will be:

f(x) = (x - 1)(3x² - 9x + 7) + 5

Expand the left-hand side:

f(x) = (3x³ - 9x² + 7x - 3x² + 9x - 7) + 5

f(x) = 3x³ - 12x² + 16x -7 + 5

f(x) = 3x³ - 12x² + 16x -2

Therefore, the function f(x) in standard form is 3x³ - 12x² + 16x -2.

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The system has infinitely many solutions, and they can be expressed in the form (x, y) = (x, x - 27), where x can take on any real value.

The given system of equations is:

x - 27 - 8 = 0

x - 27 = 8

To solve this system, let's start by simplifying the second equation:

x - 27 = 8

Adding 27 to both sides, we get:

x = 35

Now we can substitute the value of x into the first equation

x - 27 - 8 = 0

35 - 27 - 8 = 0

8 - 8 = 0

0 = 0

We see that the equation is satisfied, which means that the system is consistent. However, the system is not unique because it has infinitely many solutions. This is because when we simplified the second equation, we obtained a value for x (x = 35) that satisfies both equations.

The system can be represented by the equation y = x - 27. Since x can take on any value, y will also vary accordingly. Therefore, the solutions to the system can be written as (x, y) = (x, x - 27), where x is any real number.

In summary, the system has infinitely many solutions, and they can be expressed in the form (x, y) = (x, x - 27), where x can take on any real value.

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A rectangular tank measuring 40 cm long, 30 cm wide and 35 cm high was filled with water to a hight of 15 cm. 4800 cm3 of water were poured into water ,The new height of the water in the tank is approximately 19.83 cm.

To find the new height of water in the tank after pouring in 4800 cm³ of water, we can use the concept of ratios.

First, let's calculate the initial volume of water in the tank before pouring in the additional water. The initial volume can be calculated as the product of the length, width, and initial height:

Initial volume = 40 cm * 30 cm * 15 cm = 18,000 cm³

Next, we add the volume of the water poured in:

Total volume = Initial volume + Volume poured in = 18,000 cm³ + 4800 cm³ = 23,800 cm³

To find the new height, we divide the total volume by the base area of the tank (length * width):

New height = Total volume / (Length * Width) = 23,800 cm³ / (40 cm * 30 cm) = 19.83 cm (rounded to two decimal places)

As a result, the tank's new water level is roughly 19.83 centimetres high.

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Answer:

y = -2x+10

Step-by-step explanation:

Slope-intercept form of the equation for a line is

y = mx+b  where m is the slope and b is the y intercept

We know the slope is -2

y = -2x+b

Substituting the point in for x and y and solving for b.

8 = -2(1) + b

8 = -2+b

10 =b

Now

y = -2x+10

Answer:

y = - 2x + 10

Step-by-step explanation:

The equation of a line in slope-intercept form is given by:

y = m x + c

Here,

m → slope of the line

c →  y-intercept

Using the point-slope form of a line, we have:

( y - y₁ ) = m ( x - x₁ )

Substituting the coordinates ( x₁, y₁ ) = ( 1, 8 ), and the slope m = -2:

( y - 8 ) = - 2 ( x - 1 )

Expanding and rearranging the equation:

y - 8 = - 2x + 2

Adding 8 to both sides:

y = - 2x + 10

Answer:

45,54,63,72

Step-by-step explanation:

d=9

36+9

45+9

54+9

Answer: 45, 54, 63, 72

Step-by-step explanation

just look at each number and go up in the tens and down in the ones and once you get to 0 you start at 9 again

Answer:

4x²=2(x-4)

2x²=x-4

2x²-x+4=0​

x=1+√31​/ 4, 1-√31​/4

Step-by-step explanation:

1. Cancel log on both sides

2. Divide both sides by 2

3. Move all terms to one side

4. Use the quadratic formula

Answer:

2.4 yd

Step-by-step explanation:

Let the width of the walkway = x.

total length = x + 7.5

total width = x + 4.5

total area = (x + 7.5)(x + 4.5)

total area = 68.31 yd²

(x + 7.5)(x + 4.5) = 68.31

x² + 4.5x + 7.5x + 33.75 - 68.31 = 0

x² + 12x - 34.56 = 0

x = [-12 ± √(12² - 4(1)(-34.56)]/(2 × 1)

x = [-12 ± √(144 + 138.24)]/(2 × 1)

x = [-12 ± 16.8]/2

x = 2.4 or x = -14.4

Answer: 2.4 yd

a. The value of y when x = 4 is 13.

b. The correct point using part a is point B.

The graph is represented with x and y axis. If y = x² - 3  let's find the value of y when x = 4.

Therefore,

a.

y = x² - 3

y = 4² - 3

y = 16 - 3

y = 13

b

Some point on the graph of y = x² - 3 have been plotted. Using the part a answer, the point B is the correct point of the equation.

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The distance between points C and D is given as follows:

5 units.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates for this problem are given as follows:

(-4, -6) and (1, -6).

Hence the distance is given as follows:

[tex]D = \sqrt{(-4 - 1)^2 + (-6 - (-6))^2}[/tex]

D = 5 units.

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The cost of the labor per hour is $105. the equation can be used to determine x. The cost of labor per hour is $105. the total amount paid by Casho was $627 - $102 (the cost of the parts) = $525. The technician charged her $105 per hour for his labor.

Given, The technician at the store worked on the computer for 5 hours and charged her 102$ for parts a total 627.

Since Casho needed to get her computer fixed, she took it to the repair store. Therefore, the cost of labor per hour can be calculated.

To find the cost of labor per hour, we can use the following formula; Total Cost = Cost of Parts + Labor Cost * Hours Worked Given, Total Cost = 627Cost of Parts = $102 Labor Cost = x (unknown)Hours Worked = 5Thus, the equation can be written as;

Total Cost = Cost of Parts + Labor Cost * Hours Worked$627 = $102 + x * 5Solving the above equation for x; Let's first subtract $102 from both sides,$627 - $102 = x * 5$525 = x * 5Then, divide both sides by 5 to isolate x,$\frac{525}{5} = x$105 =

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Let's start by using variables to represent the salaries of Saima and Atika. Let S be Saima's salary, and A be Atika's salary. Then, we can write:

We know that their total salary is Rs. 35,000, so we can write an equation:

S + 3S + 9S = 35,000

Simplifying the left side, we get:

13S = 35,000

Dividing both sides by 13, we get:

S = 2,692.31 (rounded to two decimal places)

Now that we know Saima's salary, we can find Farheen's salary:

Farheen's salary = 3S = 3 × 2,692.31 ≈ Rs. 8,076.92

Therefore, the closest answer choice is A. 10,000, which is not the exact value but is the closest option to the calculated value.

In this math problem, using the given ratios and total salary, we find Saima's salary is Rs. 5000. As Farheen's salary is three times Saima's, Farheen earns Rs.15,000.

According to the problem, Farheen's salary is three times Saima's salary, and Saima's is one-third of Atika's. Let's denote Saima's salary as 'x'. Hence, Farheen's salary is '3x' and Atika's salary is '3x'. All their salaries add up to Rs.35,000 as per the question. Therefore, the equation becomes as follows:

x + 3x + 3x = 35000. This reduces to 7x = 35000 after adding the like terms on the left hand side of the equation. Dividing each side by 7, we find 'x = 5000', which is Saima's salary.

Therefore, Farheen's salary is three times Saima's, so it equals '3 * 5000 = 15000', which matches with option C from the list. So, Farheen's salary is Rs. 15,000.

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