Random numbers are useful for_____ real words situations that involve chance.
A.being
B.selling
C.modeling
D.creating

f'(x) = 0 * x^(-2) + (-2/x^3) = -2/x^3.

So, the derivative of f(x) = 2/x^2 is f'(x) = -2/x^3.

To find f'(x) for the function f(x) = x + 2, we can use the power rule for derivatives.

The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).

In this case, the function f(x) = x + 2 can be written as f(x) = x^1 + 2.

Applying the power rule, we differentiate each term separately:

f'(x) = d/dx (x^1) + d/dx (2)

The derivative of x^1 is 1x^(1-1) = 1x^0 = 1.

The derivative of a constant term like 2 is 0, as the derivative of a constant is always 0.

Therefore, f'(x) = 1 + 0 = 1.

So, the derivative of f(x) = x + 2 is f'(x) = 1.

To find f'(x) for the function f(x) = 2/x^2, we can use the power rule and the constant multiple rule.

The power rule states that if we have a function of the form f(x) = x^n, then the derivative is given by f'(x) = n*x^(n-1).

The constant multiple rule states that if we have a function of the form f(x) = cg(x), where c is a constant, then the derivative is given by f'(x) = cg'(x), where g'(x) is the derivative of g(x).

In this case, the function f(x) = 2/x^2 can be written as f(x) = 2 * x^(-2).

Applying the power rule and the constant multiple rule, we differentiate each term separately:

f'(x) = d/dx (2 * x^(-2))

Applying the constant multiple rule, the derivative of 2 is 0, as it is a constant term.

Applying the power rule, the derivative of x^(-2) is (-2) * x^(-2-1) = (-2) * x^(-3) = -2/x^3.

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Answer:

x = 90

Step-by-step explanation:

The given diagram shows a circle with intersecting chords, KM and JL.

To find the value of x, we can use the Angles of Intersecting Chords Theorem.

According to the Angles of Intersecting Chords Theorem, if two chords intersect within a circle, the angle formed at the intersection point is equal to half the sum of the measures of the arcs intercepted by the angle and its corresponding vertical angle.

Let the point of intersection of chords KM and JL be point P.

As the chords are straight lines, angle x° forms a linear pair with angle JPM.

Note: We cannot use the Angles of Intersecting Chords Theorem to find the value of x directly, since we have not been given the measures of the arcs KJ and ML. Therefore, we need to use the theorem to find m∠JPM first.

From inspection of the given diagram:

Using the Angles of Intersecting Chords Theorem, we can calculate the measure of angle JPM (shown in orange on the attached diagram):

[tex]\begin{aligned}m \angle JPM &=\dfrac{1}{2}\left(m\overset\frown{JM}+m\overset\frown{LK}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+(2x-30)^{\circ}\right)\\\\&=\dfrac{1}{2}\left(30^{\circ}+2x^{\circ}-30^{\circ}\right)\\\\&=\dfrac{1}{2}\left(2x^{\circ}\right)\\\\&=x^{\circ}\end{aligned}[/tex]

As angle JPM forms a linear pair with angle x°, the sum of the two angles equals 180°:

[tex]\begin{aligned}m \angle JPM+x^{\circ}&=180^{\circ}\\\\x^{\circ}+x^{\circ}&=180^{\circ}\\\\2x^{\circ}&=180^{\circ}\\\\\dfrac{2x^{\circ}}{2}&=\dfrac{180^{\circ}}{2}\\\\x^{\circ}&=90^{\circ}\\\\x&=90\end{aligned}[/tex]

Therefore, the value of x is 90, which means that the two chords intersect at right angles.

Answer:

a) [tex]\frac{x^2-4}{(x + 7)(x - 4)(x+2)}[/tex]

b)[tex]\frac{x^2-4x}{(x + 7)(x + 2)(x-4)}[/tex]

Step-by-step explanation:

x² + 3x - 28

= x² + 7x - 4x -28

= x(x + 7) - 4(x + 7)

=

= x² + 7x + 2x + 14

= x(x + 7) + 2(x + 7)

= (x + 7)(x + 2)

LCM of x² + 3x - 28 and x² + 9x + 14 is

(x + 7)(x - 4)(x + 2)

We can write:

[tex]\frac{x-2}{x^2 + 3x - 28}\\ \\= \frac{x-2}{(x + 7)(x - 4)}\\\\= \frac{x-2}{(x + 7)(x - 4)} *\frac{x+2}{x+2} \\\\=\frac{(x-2)(x+2)}{(x + 7)(x - 4)(x+2)} \\\\=\frac{x^2-2^2}{(x + 7)(x - 4)(x+2)} \\\\=\frac{x^2-4}{(x + 7)(x - 4)(x+2)}[/tex]

and

[tex]\frac{x}{x^2 + 9x + 14 }\\ \\= \frac{x}{(x + 7)(x + 2)}\\\\= \frac{x}{(x + 7)(x + 2)} *\frac{x-4}{x-4} \\\\= \frac{x(x-4)}{(x + 7)(x + 2)(x-4)} \\\\= \frac{x^2-4x}{(x + 7)(x + 2)(x-4)}[/tex]

Answer:

Step-by-step explanation:

To find the ratio of correct to incorrect answers on the test, we need to determine the number of correct and incorrect answers.

If you got 95% of the questions correct, it means you got 95% of 140 questions correct.

Number of correct answers = 95% of 140 = (95/100) * 140 = 133

To find the number of incorrect answers, subtract the number of correct answers from the total number of questions:

Number of incorrect answers = Total number of questions - Number of correct answers = 140 - 133 = 7

Therefore, the ratio of correct to incorrect answers on the test is 133:7, which is already in its lowest terms and cannot be simplified further.

Final result:

Of the 140 questions, you properly answered 133 of them, while 7 of them were incorrect. You have a 133:7 chance of winning because you provided the right answers.

Explanation:

We need to know how many questions were correctly and wrongly answered before we can fix this issue. You correctly answered 140 out of 140 questions, or 95 percent of them, giving you a total of 133 valid answers.

Thus, 133 correct answers out of 140 total questions equals 7 incorrect answers. As a result, the ratio of correct to incorrect answers is already very low at 133:7.

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Answer:

It looks to be -4, -2, 1, and 3

The probability of the four events are: Event 1: 1/84Event 2: 3/14Event 3: 15/28 Event 4: 5/21

The total number of drinks = 9The number of sweet teas = 3The number of unsweetened teas = 6If you select 3 drinks at random, the following events can take place:

Event 1: All three drinks are sweet teas. The probability of event 1 = (Number of ways in which all three drinks can be sweet teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be sweet teas = 3C3 = 1 (because all three sweet teas are already fixed)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 1 = 1/84 = 1/84

Event 2: Exactly two drinks are sweet teas. The probability of event 2 = (Number of ways in which two drinks are sweet teas and one is an unsweetened tea) / (Number of ways to select 3 drinks)The number of ways in which two drinks are sweet teas and one is an unsweetened tea = (3C2 × 6C1) = 18 (because you can choose 2 sweet teas from 3 and 1 unsweetened tea from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 2 = 18/84 = 3/14

Event 3: Exactly one drink is a sweet tea. The probability of event 3 = (Number of ways in which one drink is a sweet tea and the other two are unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which one drink is a sweet tea and the other two are unsweetened teas = (3C1 × 6C2) = 45 (because you can choose 1 sweet tea from 3 and 2 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84Therefore, the probability of event 3 = 45/84 = 15/28

Event 4: All three drinks are unsweetened teas. The probability of event 4 = (Number of ways in which all three drinks can be unsweetened teas) / (Number of ways to select 3 drinks)The number of ways in which all three drinks can be unsweetened teas = 6C3 = 20 (because you can choose 3 unsweetened teas from 6)The number of ways to select 3 drinks = 9C3 = (9 × 8 × 7)/(3 × 2 × 1) = 84 Therefore, the probability of event 4 = 20/84 = 5/21

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Answer:the space is 7 in the text below

Step-by-step explanation:

Answer:

  (c)  31 units

Step-by-step explanation:

Given quadrilateral ABCD has AD║BC, with AD=3x+7 and BC=5x-9, you want to know the length of AD for the quadrilateral to be a parallelogram.

Opposite sides of a parallelogram are congruent, so for ABCD to be a parallelogram, we must have ...

  BC = AD

  5x -9 = 3x +7

  2x = 16

  x = 8

  AD = 3x +7 = 3(8) +7 = 31

The length of AD must be 31 units if ABCD is to be a parallelogram.

<95141404393>

According to the information we can infer that the period of the graph is 8.

To determine the period of the graph we have to consider that the period of a grah is the distance between rigdes. So, in this case we have to count what is the difference between each rigde.

In this case, the distance between rigdes is 8 units because the first is located in the line 1 an the second is located in the line 9. So we can conclude that the period of the graph is 8.

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Answer:

Step-by-step explanation:

First find the slope using m = (y2-y1)/(x2-x1)

m = (-1-7)/(-5-3)

   =  -8/-8

   =  1

y = mx + b

find the y-intercept

use 1 of the 2 points

Let's try (3,7)

7 = 1(3) + b

b = 4

Equation of the line is y = x + 4

The equation is:

Work/explanation:

First, we will use the slope formula and determine the slope:

[tex]\sf{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where m = slope.

Plug in the data

[tex]\sf{m=\dfrac{-1-7}{-5-3}}\\\\\\\sf{m=\dfrac{-8}{-8}}\\\\\\\sf{m=1}[/tex]

The slope is 1; the equation so far is y = 1x + b or y = x + b.

Plug in the point:

[tex]\sf{7=3+b}[/tex]

[tex]\sf{3+b=7}[/tex]

Solve for b

[tex]\sf{b+3=7}[/tex]

[tex]\sf{b=4}[/tex]

So the y-intercept is 4; we plug that in and see that the equation is y = x + 4.

The required answer is: 9.61

Rounding the answer to two decimal places gives the best estimate for the mean percentage of underweight children as 9.61%.

To find the best estimate for the mean percentage of underweight children,

we need to calculate the midpoint of each interval and multiply it by the number of countries in that interval, then add the products and divide by the total number of countries.Below is the table that shows the midpoint of each interval and the corresponding calculations.

MidpointNumber of CountriesProducts16.73 (16 + 21.45) / 22383.29 (21.45 + 26.9) / 33253.13 (26.9 + 32.35) / 97194.08 (32.35 + 37.8) / 61411.025 (37.8 + 43.25) / 6 246.3 (43.25 + 48.7) / 2.

Total471Calculating the average of the above data giv

es:\[\frac{471}{23 + 3 + 9 + 6 + 6 + 2} = 471 / 49 = 9.6122\].

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Answer:

Pamela is 30 years old.

Step-by-step explanation:

First equation:  

Since Pamela is 3 times older than Jakob, our first equation is given by:

P = 3J

Second Equation:

Since Pamela will be twice as old as Jakob in 10 years, our second equation is given by:

P = 2J + 10

Method to solve:  Substitution:

We can solve with substitution by isolating J in the second equation.  This will allow us to substitute it for J in the second equation and find P, Pamela's age:

Isolating J:

Step 1:  Divide both sides by 3

(P = 3J) / 3

P/3 = J

Substituting P/3 = J for J in P = 2J + 10:

P = 2(P/3) + 10

Step 1:  Distribute the 2 to P/3:

P = 2/3P + 10

Step 2:  Multiply both sides by 3 to clear the fraction:

(P = 2/3P + 10) * 3

3P = 2P + 30

Step 3:  Subtract 2P from both sides:

(3P = 2P + 30) - 2P

P = 30

Step 4:  Divide both sides by 2 to find P, Pamela's age:

(2P = 30) / 2

P = 30

Thus, Pamela is 30 years old.

Optional Steps to check the validity of our answer:

Plugging in 30 for P in P = 3J:

Step 1:  Divide both sides by 3:

(30 = 3J) / 3

10 = J

Thus, Jakob is 10 years old.

Checking the validity of answers with verbal statements:

Since 30 (i.e., Pamela's age) is indeed 3 times 10 (i.e., Jakob's age), this satisfies the first statement.

In 10 years, Pamela will be 40 as 30 + 10 = 40.

In 10 years, Jacob will be 20 as 10 + 10 = 20.

Since 40 (i.e., Pamela's age in 10 years) is indeed twice 20 (i.e., Jakob's age in 10 years), this satisfies the second statement.

Thus, our answer for Pamela's age is correct.

[tex]\begin{gathered} \; \color{pink}{\frak{\qquad \: x - \dfrac{x - 1}{2} = 1 - \dfrac{x - 2}{3}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{(2 \times x) - x - 1}{2} = \dfrac{(3 \times 1) - x - 2}{3}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{2x - x - 1}{2} = \dfrac{3 - x - 2}{3}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{\dfrac{x - 1}{2} = \dfrac{1 - x}{3}}} \\ \end{gathered}[/tex]

Cross Multiplying,,

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3(x - 1) = 2(1 - x)}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x - 3 = 2 - 2x}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{3x + 2x = 2 + 3}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{5x = 5}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{pink}{\hookrightarrow \: \frak{x = \dfrac{\cancel{ \: 5}}{\cancel{ \: 5}}}} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \; \color{cyan}{\hookrightarrow \: \underline{\boxed{\frak{x = 1}}}} \: \pmb{\bigstar} \\ \\ \end{gathered}[/tex]

[tex]\begin{gathered} \qquad{\qquad{\pmb{━━━━━ღ◆ღ━━━━━}}} \end{gathered}[/tex]

Answer:

45

Step-by-step explanation:

Do the operation in parentheses first.

(45)(4 - 3) = (45)(1) = 45

Answer:

Step-by-step explanation:

The answer is 45.

Given,

[tex](45)(4-3)\\=(45)(1)\\=45[/tex]Using subtraction and multiplication rule.

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Answer:To determine the range is the same as to determine which numbers appear as the second number (the y-value) in an ordered pair that is part of the graph. Here are some examples: y ≥ x2 + 3. graph {y >= x^2+3 [-11.6, 13.72, 0.15, 12.81]} Although it is not 100% certain from just the graph, this graph does get wider and wider.

Step-by-step explanation:

Answer:

i dont know

Step-by-step explanation:

give proper diagram please

Answer:

Step-by-step explanation:

I think there is a typo in the question

Qn : let p(n) be  [tex]\sum\limits^n_{i = 1}{i2^i} = 2 + (n-1)2^{n+1} \;\;\;\;\;\;:n\geq 1[/tex]

When n = 1:

LHS: 1(2¹) = 2

RHS: 2 + (1 - 1)(2¹ ⁺ ¹) = 2

LHS = RHS

⇒ p(n) holds for n = 1

Let us assume that the proof holds for p(n): n = x

ie.

[tex]p(x): \sum\limits^x_{i = 1}{i2^i} = 2 + (x-1)2^{x+1}[/tex]

To prove that the proof holds for n = x+1

ie   [tex]p(x+1): \sum\limits^{x+1}_{i = 1}{i2^i} = 2 + (x)2^{x+2}[/tex]

Consider LHS

[tex]\sum\limits^{x+1}_{i = 1}{i2^i}\\\\= \sum\limits^{x}_{i = 1}{i2^i}+\sum\limits^{x+1}_{i = x+1}{i2^i}\\\\= p(x) + (x+1)2^{x+1}\\\\= 2 + (x-1)2^{x+1} + (x+1)2^{x+1}\\\\= 2 + 2^{x+1} (x-1 + x+1)\\\\= 2 + 2^{x+1} (2x)\\\\= 2 + (x)2^{x+2}\\\\= RHS[/tex]

By finding the point where the graphs intercept, we will see that the solution of the system of equations is the point (0, 2).

The solutions of a system of equations are the points where the graphs of the different equations intercept when graphed.

Below you can see the graph of the system:

There you can see that we have only one intersection point at x = 0, y = 2, then we can conclude that our system has only one solution, and the solution is the point (0, 2).

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Answer:

Step-by-step explanation:

[tex]\lim_{x\to 1} \frac{x^3-1}{x-1} \\= \lim_{x \to 1} \frac{(x-1)(x^2+x+1)}{(x-1)} \\= \lim_{x \to 1} (x^2+x+1)\\=(1)^1+1+1\\=1+1+1\\=3[/tex]

The sum of the geometric sequence in this problem is given as follows:

5.77.

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number, which is called the common ratio q.

The first term, the common ratio and the number of terms for this problem are given as follows:

[tex]a_1 = 10, q = -\frac{2}{3}, k = 8[/tex]

The formula for the sum of the first n terms is given as follows:

[tex]S_n = a_1\frac{1 - r^n}{1 - r}[/tex]

Hence the sum for this problem is given as follows:

[tex]S_8 = 10 \times \frac{1 - \left(-\frac{2}{3}\right)^8}{1 + \frac{2}{3}}[/tex]

[tex]S_8 = 5.77[/tex]

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Answer:

Area = 7.065 square miles

Step-by-step explanation:

The diameter of a circle is the distance across the circle passing through its centre, and it is equal to twice the radius. Therefore, if the diameter of a circle is 3 miles, then the radius is 1.5 miles.

The formula for the area of a circle is [tex]A = \pi r^2[/tex] ([tex]A = \pi \times r^{2}[/tex])

Substituting the value of the radius into this formula, we get:

Therefore, the area of the circle is approximately 7.065 square miles.

________________________________________________________

The answer is:

A = 7.069 miles²

Work/explanation:

We have the diameter, but we need to find the radius. We can do that by diving the diameter by 2:

radius = diameter ÷ 2 = 3 ÷ 2 = 1.5 miles

Now we move on to the next step - the formula.

The formula is:

[tex]\sf{A=\pi r^2}[/tex]

where:

diagram

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\small 1.5\ miles}\end{picture}[/tex]

Plug in the data

[tex]\sf{A=\pi \times 1.5^2}[/tex]

[tex]\sf{A=\pi\times2.25}[/tex]

[tex]\sf{A=7.069~miles^2}[/tex]

Answer:

y = [tex]\frac{-5}{4}[/tex]x - 30

Step-by-step explanation:

we will use the x = -40 and the y = 20 from the point given (-40,20).  The perpendicular slope would be the opposite reciprocal from the slope given.  The slope given is 4/5.  The reciprocal is 5/4 and the opposite would be -5/4

y = mx + b  Plug in what we know and solve for b

20 = [tex]\frac{-5}{4}[/tex] ( -40) + b

20 = [tex]\frac{-5}{4}[/tex] ·[tex]\frac{-40}{1}[/tex] + b

20 = [tex]\frac{200}{4}[/tex] + b

20 = 50 + b  Subtract 50 from both sides

20 - 50 = 50 - 50 + b

-30 = b

To write the equation we need the slope (m) ([tex]\frac{-5}{4}[/tex]) and the y-intercept (b) (-30)

y = mx + b

y = [tex]\frac{-5}{4}[/tex]x - 30

Helping in the name of Jesus.

Step-by-step explanation:

To convert all pulse rates of women to z-scores, we use the formula:

z = (x - μ) / σ

where x is the pulse rate, μ is the mean, and σ is the standard deviation.

Substituting the given values, we get:

z = (x - 77.5) / 11.6

Therefore, after converting all pulse rates of women to z-scores, the mean will be 0 and the standard deviation will be 1.

Answer:

-12

Step-by-step explanation:

3/5 * (1 + sqrt(16))^2 - (5 - 2)^3 =

= 3/5 * (1 + 4)^2 - (3)^3

= 3/5 * (5)^2 - 27

= 3/5 * 25 - 27

= 15 - 27

= -12

Answer:

(2n - 3) + 5 is a correct expression.

Answer: D

Step-by-step explanation:

we will multiply

4/7* 1/8

we will get 1/14

Answer:

Step-by-step explanation:
After reducing 4/7 of 1/8 to the lowest terms we get 1/14. Thus, option C is the answer.

For reducing a number to its lowest terms, first, we need to simplify the numbers to a more significant number, i.e. 4/7 of 1/8 means 4/7*1/8=4/56.

Now we know that 56 is a multiple of 4 when multiplied by 14. Hence, when we get it in the lowest term we would get 1/14

Answer:

136 [tex]ft^{2}[/tex]

Step-by-step explanation:

Find the area of the wall and subtract out the area of the window

16 x 9 = 144

4 x 2 = 8

144 - 8 = 136

Helping in the name of Jesus.

Answer:

A

Step-by-step explanation:

the x- axis is a horizontal line. A line perpendicular to it will be a vertical line, parallel to the y- axis with equation

x = c ( c is the value of the x- coordinates the line passes through )

the only equation fitting this description from the list is

x = 3

Answer:

1711

Step-by-step explanation:

[tex]4\cdot(14+8)^2-9\cdot(9-4)^2\\=4\cdot(22)^2-9\cdot(5)^2\\=4(484)-9(25)\\=1936-225\\=1711[/tex]

Make sure to follow order of operations!

The amount of carpet needed for the living room is three times greater than the amount of carpet needed for the bedroom.

To calculate the amount of carpet needed for each room, we need to consider the dimensions of the rooms. Let's assume the length of the bedroom is x units.
Since the living room is two times as long as the bedroom, its length will be 2x units.
Similarly, the width of the living room is one and a half times as wide as the bedroom. So, the width of the living room will be 1.5x units.
To find the area of each room, we multiply the length by the width.
The area of the bedroom is x units * x units = x^2 square units.
The area of the living room is 2x units * 1.5x units = 3x^2 square units.
The amount of carpet needed is directly proportional to the area of the room. Therefore, the amount of carpet needed for the living room is 3x^2 square units, while the amount needed for the bedroom is x^2 square units.
To find the difference, we divide the area of the living room by the area of the bedroom: 3x^2 / x^2 = 3.
Thus, the amount of carpet needed for the living room is three times greater than the amount needed for the bedroom.

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