For the function f(x) = 9/x-4, find f^(-1)(x).

70 different divisions are possible when eight children are divided into two teams each containing 4 children to play a game against each other

so this is what's known as a combination. a combination is a group where the order does not matter. to solve a combination, you use this equation:

n! / (r! *(n-r)!)

n is the total number of objects being sorted (8)

r is the group you need to sort them into (4)

(i know it's 2 groups of 4 but if you solve this for 1 group, the other group is automatically made of the remaining kids)

definition of !:

a number with a ! means 1*2*3...*that number (so that number multiplied by every number smaller than it all the way to one)

so we put 8 and 4 in this equation:

8! / (4! *(8-4)!)

simplify:

8! / *(4! 4!)

multiply out:

(8*7*6*5*4*3*2*1) / (4*3*2*1 * 4*3*2*1)

and put that in your calculator

you will get 70 different divisions are possible

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The value of x in the expression 1 - (2/x²) = - x - 1 is  ± √2, 4.

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zero then it is confirmed that x - a = 0 is a factor.

Given, An expression 1 - (2/x²) = - x - 1.

- (2/x²) + x = 2.

Multiplying each term by x².

- 2 + x³ = 2x².

x³ - 2x² = 2.

x²(x - 2) = 2.

x² = 2 ⇒ x = ± √2 Or x - 2 = 2 ⇒ x = 4.

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Answer:

C

Step-by-step explanation:

807 is equal to 800 + 7, and 24 is equal to 20 + 4. Using the distributive property, we get 20(800) + 4(800) + 20(7) + 20(7)

Answer:

C

Step-by-step explanation:

Because 24*807 in distributive property is C

Answer:

398.32

Step-by-step explanation:

647.82 - 249.50 = 398.32

======================================================

Explanation:

Check out the diagram below.

I've defined the following points:

Now focus on triangle ACF. This is an isosceles right triangle with legs of 0.5x each. The hypotenuse is the radius of the circle. Let R be that unknown radius.

The area of the circle is given to us. It is 56 square cm. Use this to find the value of R.

[tex]A = \pi*(\text{radius})^2\\\\56 = \pi*R^2\\\\R^2 = 56/\pi\\\\R = \sqrt{56/\pi}\\\\R = 4.22200825\\\\[/tex]

This value is approximate. I used the calculator's stored version of pi to get the most accuracy possible.

------------

We now know the hypotenuse of triangle ACF.

Use Pythagoras (aka Pythagorean Theorem) to have the following steps:

[tex]a^2+b^2 = c^2\\\\(0.5\text{x})^2+(0.5\text{x})^2 = 4.22200825^2\\\\0.25\text{x}^2+0.25\text{x}^2 = 17.82535366\\\\0.5\text{x}^2 = 17.82535366\\\\\text{x}^2 = 17.82535366/0.5\\\\\text{x}^2 = 35.65070732\\\\\text{x} = \sqrt{35.65070732}\\\\\text{x} = 5.97082132708726\\\\\text{x} = 5.97\\\\[/tex]

With the exception of 0.5 and 0.25, each decimal value mentioned is approximate.

Keep in mind that rounding to 3 sig figs means that we're rounding to 2 decimal places. The units digit is 1 sig fig, and the 2 decimal places give a total of 1+2 = 3 sig figs.

In short, we're rounding to the nearest hundredth.

--------------------

Check:

x = 5.97 is the square's side length.

It divides in half to get x/2 = 5.97/2 = 2.985 which gives each leg of triangle ACF.

Use a = 2.985 and b = 2.985 in the Pythagorean Theorem to find that c = 4.22142748 approximately. This is the approximate radius of the circle.

Use that radius to find the area of the circle.

A = pi*r^2

A = pi*(4.22142748)^2

A = 55.984594705958

A = 56.0

I'm rounding the area to 3 sig figs to keep consistent with the rounding done to x. We arrive at the circle area of 56 square cm, which helps confirm the answer is correct.

The fourth co-ordinate of the rectangle is D (-2, -1). The equation of the line that passes through the points B and D is 3y = 2x + 3.

The given points are:

A(−2,3), B(4,3), C(4,−1)

When we plot these points on the graph we can easily estimate the fourth point which will be equidistant from A as the point C is from B and from the point C as the point A is from B.

Therefore, the diagonal points are B(4, 3) and D(-2, -1).

The equation of the line between these two points is:

(y - y1) = ((y2 - y1)/(x2 - x1)) (x - x1)

(y - 3) = ((-1 -3)/(-2 - 4)) ( x - 4)

y - 3 = (2/3) (x - 4)

3y - 9 = 2x - 8

3y = 2x + 1

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Here are three different sequences starting with 1, 2, and 4, where the terms are generated by a simple rule:

1, 2, 4, 8, 16, 32, ...

The rule for this sequence is to multiply the previous term by 2.

1, 2, 4, 7, 11, 16, 22, ...

The rule for this sequence is to add the previous two terms.

1, 2, 4, 8, 14, 24, ...

The rule for this sequence is to multiply the previous term by 2 and then subtract it from the previous term.

Note that there is an infinite number of different sequences that can be generated by simple rules.

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The maximum area of the rectangle is determined by the distance between the two points on the graph and the -axis.

A rectangle is a four-sided shape with four right angles and two pairs of parallel sides. It is one of the most common shapes in the world, found in everything from building designs to artwork. Rectangles are also used in math, specifically to measure area and perimeter. Rectangles can also be classified according to their sides, with squares being a special type of rectangle with four equal sides.

To calculate the maximum possible area of the rectangle, we can use the formula A = (x2 - x1)(y2 - y1).

In this case, the two points on the graph have the same -coordinate, so the x2 - x1 part of the equation is zero. This means that the y2 - y1 part of the equation gives the maximum possible area of the rectangle. To calculate this, we need to take the difference between the two points on the graph.

For example, if the two points on the graph were (2,4) and (2,6), the maximum area of the rectangle would be (6 - 4) = 2.

Therefore, the maximum possible area of the rectangle is equal to the difference between the two points on the graph.

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Answer:

D)

That is the only one we can be certain with.

1st option is obviously incorrect

2nd option is wrong as it can also be two are negative one is positive

3rd option is wrong as it can also be one is negative two are positive

4th option is correct as u can't get negative values without a negative numberl.

Using the tangent side from trigonometric ratio, the angle of depression is 86.6 degrees

The angle created between the line of sight to a location below the horizontal line and the horizontal line of sight is known as the angle of depression.

The angle of depression that the balloon makes with the launch pad can be calculated using the trigonometric ratio.

Data;

Since we have the opposite and adjacent side, we can use the tangent of the angle to find the angle of depression.

tanθ = opposite / adjacent

substituting the values into the formula

tan θ = 10000 / 600

tan θ = 100 / 6

tan θ = 16.666

θ = tan⁻¹(16.666)

θ = 86.6°

The angle of depression is 86.6°

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On solving the provided question, we can say that  10% condition is met,

There are two separate random samples available.

selected at random (purely random, unpredictable). Every member of the population being polled ought to have an equal probability of getting chosen. She randomly selected 25 names from a pool of 250 employees as an example of a simple random sample. Since there are 250 of her employees in total, and each one has an equal probability of being chosen, the sample in this instance is random. Using simple random sampling, which is a form of probability sampling, researchers choose individuals at random from a population. There is an equal opportunity for selection for every person in the population.

There are two separate random samples available.

The 10% requirement is satisfied.

For both samples, 24, 26, 29, and 31 triumphs and failures are anticipated.

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The probability is 1/10.

The equation x(x+5) = -n can be rewritten as x^2 + 5x + n = 0. To find the solutions of this equation, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a, where a = 1, b = 5, and c = n.

For there to be no real solutions, the discriminant (b^2 - 4ac) must be negative. The discriminant is 5^2 - 4(1)(n) = 25 - 4n. So for there to be no real solutions, 25 - 4n < 0, or n > 6.25.

Since the integer n is between 1 and 10 inclusive, the only value that would not have a real solution is n = 7. Therefore, the probability that for the randomly chosen n there exist no real solutions is 1/10.

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Answer: all are congruent

Step-by-step explanation:

a. The pair of triangles are not congruent.

b. It is impossible to tell about congruency.

c. The pair of triangles are congruent.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

These triangles can be slides, rotated, flipped and turned to be looked identical.

a. The given triangles are not congruent.

The triangle has same measures but the side lengths are different.

So the pair of triangles are not congruent.

b. The given pair of triangles are might be congruent if they have side lengths same.

But in the given triangles the side lengths are not measured.

So it is impossible to tell.

c. The given pair of triangles have same measures and same side lengths.

By AAS rule the pair of triangles are congruent.

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The different percentages of the distance is 100%, 25% & 125%.

The Latin word "per centum," which means "by the hundred," served as the basis for the English word "percentage." Percentages are fractions with the denominator 100. In other words, it is the relationship between a part and a whole in which the value of the whole is always assumed to be 100.

A percentage is a fraction or ratio in which the whole value is always 100. For instance, Sam would have received 30 out of a possible 100 points if he had received 30% on his math test. It is expressed as 30/100 in fractional form and 30:100 in ratio form.

48 = 100% of 48

12 = 25% of 48

60 = 125% of 48

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Answer:

Step-by-step explanation:

the sum of the interior angles in a triangle is 180°, take away the know angle and divide by 2, it's an isosceles triangle so 2 side and 2 equal angles

(180 - 134) : 2 =                         (remember PEMDAS)

46 : 2 =

23°

----------------------------

23 + 23 + 134 = 180°

As per the given matrix, the stable distribution for the regular stochastic matrix is [tex]\begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}0.40 \\0.10\end{bmatrix}[/tex]

The term matrix is defined as  a set of numbers arranged in rows and columns so as to form a rectangular array.

Here we have given that the matrix is written as

[tex]\begin{bmatrix}0.5 & 0.2 \\0.5 & 0.8\end{bmatrix}[/tex]

In order to find the  stable distribution for the regular stochastic matrix, we must know what does it means in matrix.

The term  stable distribution for the regular stochastic matrix in math is defined as a square matrix whose columns are probability vectors. And the  probability vector is a numerical vector whose entries are real numbers between 0 and 1 whose sum is 1.

Here in order to find the solution, we have to equate the value with x and y and then we have to cross multiply the terms, then we get,

=> [tex]\begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}0.5\times0.8 \\0.2\times0.5\end{bmatrix}[/tex]

When we simplify this we get the solution as,

[tex]= > \begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}0.40 \\0.10\end{bmatrix}[/tex]

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The profit of the insurance company is -20x, where x is the monthly premium.

Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating them. It is used to describe and analyze the relationship between numbers, variables, and operations. Algebra is used to solve equations and simplify expressions, and it is useful in a wide range of applications such as engineering, economics, and science. Algebra also helps us understand and explore abstract concepts such as equations, functions, and graphs. Algebraic thinking is a valuable skill that can help us to make sense of the world around us.

Let x = monthly premium

The insurance company's profit = (500,000 - 20x) - 500,000 = -20x

Therefore, the profit of the insurance company is -20x, where x is the monthly premium.

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A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other

What is an equivalent ratios?

A ratio compares two quantities named as antecedent and consequent, by the means of division. For example, when we cook food, then each ingredient has to be added in a ratio. Thus, we can say, a ratio is used to express one quantity as a fraction of another quantity.

Two ratios are equivalent to each other if one of them can be expressed as the multiple of the other. Hence, to get the equivalent ratio of another ratio, we have to multiply the two quantities (antecedent and consequent) by the same number.

Given ratios are 2:1 and 3:1

we can write it as 2/1 and 3/1.

The lcm of 2 and 3 is 6.

Multiply denominator of both ratio with 6, we get

2/6 and 3/6 And we can see both the ratios are not equal.

Hence, there are not equivalent ratios.

4:1 and 8:3 are equivalent ratios -----> is false, because 4:1 is equivalent to 8:2

11:2 and 2:11 are equivalent ratios------> is false (because, are reciprocal ratios, not equivalent ratios)

3:1 and 9:3 are equivalent ratios ------> is true

because 3:1 multiply both sides by 3 -----> 3*3:1*3=9:3

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On solving the provided question we can say that there are 7!/(7-5)! potential sequences if 0 appears 0 or 1 times in the sequence.

A collection of numbers, or "terms," is referred to as a sequence. Examples of terms are 2, 5, and 8. Some sequences can be made endlessly lengthy by taking advantage of a particular pattern they follow. Use the example of 2,5,8 and add 3 to continue the sequence. There are formulas that demonstrate where to look for words within a sequence. A collection of objects that are in some order is known as a sequence in mathematics (or events). It resembles a set in that it contains pieces (also called elements or terms). The entire, perhaps infinite number of ordered objects are referred to as the sequence's length. the act of placing two or more items in a logical order. Chronological.

N/10 has a value of 372.

The letters can be selected from the words "AIME" or "2007."

The only number that can be repeated twice is 0; there are seven different characters that can be chosen.

There are 7!/(7-5)! potential sequences if 0 appears 0 or 1 times in the sequence.

There are 2520 possible sequences if 0 appears 0 or 1 times in the sequence.

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The property of square depicted is not common for all regular polygon

If a polygon's sides and angles are equal, it is said to be regular. As a result, an equilateral triangle is a regular triangle, and a regular quadrilateral is a square.

The property showed how the square was merged with every two sides fully overlapping to form a bigger square

The trapezium which can also be a regular polygon (quadrilateral) lacks such property of arranging four trapeziums side by side, making overlaps that will form a bigger trapezium.

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On solving the provided question we can say that the equation gives us  101.77 mi S; 63.59 mi W and S 39.4° W; 131.7 nautical miles

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence.

The ship will have traveled 120 nautical miles in the six hours between noon and six o'clock using the formula distance = speed time distance (20 nm/h) (6 h).

The location of the ship will be in (S, W) coordinates.

[tex]120(cos(32), sin(32)) ≈ 120(0.848048, 0.529919) ≈ (101.77, 63.59)[/tex]

The ship will have traveled 101.77 miles south and 63.59 miles west.

83.59). The distance from port will be ...

[tex]d = √(101.77^2 +83.59^2) = 131.7\\ arctan(83.59/101.77) ≈ 39.4[/tex]

The bearing and distance are ...

S 39.4° W

131.7 nautical miles

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Answer:

Total hours = (total time in seconds) / (3600 seconds in an hour)

Note: Remember to convert the result from seconds to hours.

It's important to mention that you need to know the value of t and y to be able to calculate the total time and the total hours.

If you have the values, you can substitute them in the equations above and get the answer.

Answer:

x = 5

Step-by-step explanation:

You are solving for a x that can, when plugged in, equate both given expressions. To do so, set each given expression equal to each other:

4x - 4 = 8x - 24

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

PEMDAS is the order of operations, and stands for:

Parenthesis

Exponents (& roots)

Multiplications

Divisions

Additions

Subtractions

~

First, subtract 8x and add 4 to both sides of the equation:

4x (-8x) - 4 (+4) = 8x (-8x) - 24 (+4)

4x - 8x = -24 + 4

-4x = -20

Next, divide -4 from both sides of the equation:

(-4x)/-4 = (-20)/-4

x = -20/-4

x = 5

5 is your answer.

Check:

Plug in 5 for x in both given expressions:

4x - 4

4(5) - 4

= 20 - 4

= 16

-

8x - 24

8(5) - 24

= 40 - 24

= 16

~

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Answer:

A. Even

Step-by-step explanation:

Even Function

A function is "even" when:

[tex]f(x) = f(-x) \;for\; all\; x\\\\[/tex]

Stated in other terms, the function graph is symmetric about the vertical(y-axis). The right part of the function graph about the y-axis is a reflection of the left part of the function graph  about the y-axis

Looking at the function graph, we see it is indeed symmetric about the y-axis

Hence an even function

Answer: Let's call the hourly rate of the first mechanic "r1" and the hourly rate of the second mechanic "r2".

We know that the total time they worked is 20 hours + 5 hours = 25 hours.

We also know that the sum of their hourly rates is $95 per hour, so:

r1 + r2 = $95

We can use this information along with the total amount they charged, $1150, to find out how much each mechanic charged. We know that the total amount charged is the product of the number of hours worked and the hourly rate. So we can use the following equation:

(20 hours * r1) + (5 hours * r2) = $1150

Now we can substitute the equation r1 + r2 = $95 into the above equation and solve for r1:

(20 hours * r1) + (5 hours * (95 - r1)) = $1150

20r1 + 475 - 5r1 = 1150

15r1 = 675

r1 = $45/hour

To find out the hourly rate of the second mechanic, we can use the equation r1 + r2 = $95

r2 = $95 - r1

r2 = $95 - $45

r2 = $50/hour

So the first mechanic charges $45 per hour and the second mechanic charges $50 per hour.

Step-by-step explanation:

Answer: (0, -1/3)

Step-by-step explanation: The answer is: (0, -1/3)

y=mx+b

Slope being "m"
And the y intercept being "b"

I think it's (0, -1/3)

......

..

Answer: X = [tex]\frac{1}{\sqrt{2} }[/tex]

Step-by-step explanation: Because the two angles are equal (You circled them, also 45 degs), and there is a right triangle, which means that the 90-degree angle's adjacent sides are equal, in this case, both sides equal to X.

Using the special triangle ratio ( 1, 1, [tex]\sqrt{2}[/tex]), in this case, the "2" is equal to [tex]\sqrt{2}[/tex] times [tex]\sqrt{2}[/tex], so you have to divide the "1" (X) by [tex]\sqrt{2}[/tex], you simply get [tex]\frac{1}{\sqrt{2} }[/tex].

Sorry for my bad english

The interpretation of the value, 29,864, in the quadratic regression equation is the initial loss incurred by the company. The correct option is therefore;

A quadratic regression equation is the equation of the parabola that corresponds of best fits the points of the dataset on the coordinate plane.

The points on the graph of the question, obtained from a similar question, posted online are;

Number of units [tex]{}[/tex]           Profits ($)

500 [tex]{}[/tex]                         -10000

1200  [tex]{}[/tex]                   3000

2500  [tex]{}[/tex]                   27000

3200  [tex]{}[/tex]                   40000

3600  [tex]{}[/tex]                   45000

4300  [tex]{}[/tex]                   47000

5000  [tex]{}[/tex]                   45000

6750  [tex]{}[/tex]                   20000

The polynomial regression equation that corresponds to the points in the above table, obtained with MS Excel is presented as follows;

y = -0.004·x² + 34.637·x - 29864

Where;

y = The profit made

x = Number of units

When the company produces 0 units, x = 0, we get;

The 29864 is therefore the loss of $29864, of the company when the company produces zero units.

The correct option is therefore;

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