in a state lottery, a player must choose 8 of the numbers from 1 to 40. the lottery commission then performs an experiment that selects 8 of these 40 numbers. assuming the choice of the lottery commission is equally likely to be any of the

The limit does exist for lim x→49 (x^2 - 7x - 49) and it approaches value of 2009.

The limit can be found using algebraic manipulation. First we will try plug in the value and see if we can determine the limit. We have:

lim x→49 (x^2 - 7x - 49) = 49^2 - 7×49 - 49 = 2009

So limit exist at x^2 - 7x - 49 and it can be found out by simple substitution.

So, as x approaches 49, the expression x^2 - 7x - 49 approaches 2009.

Therefore, lim x→49 x^2 - 7x - 49 = 343.

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Answer: The numeric coefficient is 3.

Step-by-step explanation:

Answer:

q is independent var, r is dependent

Step-by-step explanation:

Answer:

matt needs to use more than 2% mixture for his aquarium

Step-by-step explanation:

The maturity date of the loan is July 31st.

To find the maturity date, you first need to find the number of days between May 11th and the maturity date. The loan was taken out for 82 days, so you add 82 days to May 11th to find the maturity date.

For example, if May 11th is day 1, then day 82 would be July 31st. Therefore, the maturity date of the loan is July 31st.

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Answer: -21

Step-by-step explanation: first you multiply 4 x -5 or 4(-5) - 1 4 x -5 would give you -20 and -20 - 1, since both are negative we add to get a total of -21 hope this helps.

The total number of twenty questions prepared by Josh can be find by using the expression k = 20 * P(getting a question right) / (1 + 20 * 0.08 / 0.92), where, k = total question prepared by Josh

Let's call the number of questions Josh was prepared for as "k".

The probability of Josh getting a question right given that he knew the answer is 0.92,

So the probability of him getting a question right by guessing is

1 - 0.92 = 0.08.

The overall probability of Josh getting a question right is the sum of the probability of him getting it right given that he was prepared and the probability of him getting it right by guessing:

P(getting a question right) = P(getting a question right | prepared) * P(prepared) + P(getting a question right | guessed) * P(guessed)

Since each question is either prepared or guessed, the sum of P(prepared) and P(guessed) is 1:

P(getting a question right) = 0.92 * P(prepared) + 0.08 * (1 - P(prepared))

Simplifying the expression:

P(getting a question right) = 0.92 * P(prepared) + 0.08

Since the overall probability of Josh getting a question right is the same for every question,

it must be the same for all twenty questions:

So, we can write it as:

0.92 * P(prepared) + 0.08

= 0.92 * k/20 + 0.08 * (20-k)/20

Dividing both sides by 0.92:

P(prepared) = k/20 = (0.92 * k + 0.08 * 20 - 0.08) / 0.92

Isolating k:

k = 20 * P(prepared) / (1 + 20 * 0.08 / 0.92)

Plugging in the overall probability of Josh getting a question right, we have:

k = 20 * P(getting a question right) / (1 + 20 * 0.08 / 0.92)

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Multiply the mass in kilogrammes by 2.2046226218 to convert 50 kg to pounds.

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On the right side, we can just simplify the expression to 1+tanθ+cotθ

Yes, this is true.

The left side of the equation can be simplified to 1, which is equal to the right side.

Left side:

(cotθ/1-tanθ)+(tanθ/1-cotθ)

= (cotθ + tanθ)/(1 - tanθ - cotθ)

= (tanθ + cotθ)/(1 - tanθ - cotθ)

= 1/(1 - tanθ - cotθ)

= 1

Right side:

1 + tanθ + cotθ = 1

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Answer:

See proof below

Step-by-step explanation:

(Please excuse any typos and point them out to me. It is a pain typing in LateX)

We are asked to prove:

[tex]\dfrac{\cot\theta}{1-\text{\ensuremath{\tan\theta}}}+\dfrac{\tan\theta}{1-\cot\theta}=1+\tan\theta+\cot\theta[/tex]

Since
[tex]\tan\theta =\dfrac {\sin\theta}{\cos\theta}\\\\\cot\theta = \dfrac {\cos\theta}{\sin\theta}\\\\[/tex]

the left side becomes

[tex]\dfrac{\cos\theta/\sin\theta}{1-\sin\theta/\cos\theta}+ \dfrac{{\sin\theta/\cos\theta}}{1-\cos\theta/\sin\theta} \cdots \cdots \cdots(1)[/tex]

For ease of expressing this let

[tex]a = \sin\theta\\b = \cos\theta\\[/tex]

Substituting the above in expression (1) gets us
[tex]\dfrac{b/a}{1- a/b} + \dfrac{a/b}{1-b/a}[/tex]

Let's take the individual terms and simplify each
[tex]\dfrac{b/a}{1- a/b} = \dfrac{b}{a}\cdot \dfrac{1}{1-\dfrac{a}{b}}[/tex]

[tex]\dfrac{1}{1-\dfrac{a}{b}}= \dfrac{1}{\dfrac{b-a}{b}}=\dfrac{b}{b-a}[/tex]

Therefore

[tex]\dfrac{b}{a}\cdot\dfrac{b}{b-a} = \dfrac{b^2}{a(b-a)}[/tex]

For the second term we get

[tex]\dfrac{a/b}{1-b/a} = \dfrac{a^2}{b(a-b)}[/tex]

Noting that (a - b) = - (b - a)

the entire expression becomes

[tex]\dfrac{b^2}{a(b-a)} = - \dfrac{a^2}{b(b-a)}[/tex]

Multiply this expression throughout by the LCM which is
[tex]ab(b-a)[/tex]

[tex]\dfrac{b^2 \cdot b - {a^2}\cdot a}{ab(b-a)}\\\\= \dfrac{b^3 - a^3}{ab(b-a)}\cdots\cdots(2)\\[/tex]

(b -a) cancels in numerator and denominator on both sides giving

For the numerator we have the identity
[tex]b^3 - a^3 = (b-a)(b^2 + ab + b^2)[/tex]

So the expression in (2) becomes
[tex]\dfrac{(b-a)(b^2 + ab + a^2)}{ab(b-a)}\\\\\textrm{(b-a) cancels from the numerator and denominator}\\\\[/tex]

This leaves us with:

[tex]\dfrac{(b^2 + ab + a^2)}{ab}[/tex]

Substituting for a = sinθ and b = cosθ we get

[tex]\dfrac{\cos^2\theta + \sin^2\theta+ \cos\theta\sin\theta}{\sin\theta\cos\theta}[/tex]

Divide each term in the numerator by [tex]\sin\theta \cos\theta[/tex]

==> [tex]\dfrac{cos^2\theta}{\sin\theta\cos\theta} + \dfrac{\sin^2\theta}{\sin\theta\cos\theta}+ \dfrac{\sin\theta\cos\theta}{\sin\theta\cos\theta}}[/tex]

==> [tex]\dfrac{\cos\theta}{\sin\theta} + \dfrac{\sin\theta}{\cos\theta} + 1[/tex]

[tex]\cot\theta + \tan\theta + 1\\== > 1 + \tan\theta + \cot\theta[/tex]

Hence PROVED

The antiderivative of f(x) = tan(eˣ + π/2) on 0≤x≤ln(π/2) is:

⇒  ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex]

Now, For the antiderivative of f(x) = tan(eˣ + π/2) on the interval 0≤x≤ln(π/2), we need to integrate the given function.

Now, using the substitution u = eˣ + π/2.

Then, we have:

du/dx = eˣ

dx = du / eˣ

Using this substitution, we can rewrite the original function as:

f(x) = tan(eˣ + π/2) dx = tan(u) du / eˣ

Now let's integrate this function:

∫tan(u) du / eˣ = - ln |cosec(u)| / eˣ + C

Substituting back u = eˣ+π/2:

ln |cosec(eˣ + π/2)| / eˣ + C

= - ln |cosec(eˣ + π/2)| / eˣ + C

Now we need to evaluate this expression at the limits of integration x = 0 and x = ln(π/2):

F(ln(π/2)) - F(0)

= - ln |cosec([tex]e^{\pi /2 } + \frac{\pi }{2}[/tex])| / [tex]e^{\pi /2}[/tex] + C - (- ln |cos(0)| / [tex]e^{\pi /2}[/tex] + C)

= - ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex] + ln |cos(0)| / [tex]e^{\pi /2}[/tex]

= - ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex] + ln(1) / [tex]e^{\pi /2}[/tex]

=  ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex]

So, the antiderivative of f(x) = tan(eˣ + π/2) on 0≤x≤ln(π/2) is:

⇒  ln |sec([tex]e^{\pi /2}[/tex])| / [tex]e^{\pi /2}[/tex]

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Answer:The number of dollar bills, d, is the independent variable.

The quarters, q, is the dependent variable.

Step-by-step explanation:

The number of dollar bills, d, is the independent variable.

The quarters, q, is the dependent variable.

Answer:

Step-by-step explanation:

dependent then independent because i passes the lesson.

The inequality is equivalent to the given inequality? -4(x+7)< 3(x-2) is x>-22/7

Inequality is a mathematical statement which shsow that two quantities are not the same or that they are not equal.

The given inequality is -4(x+7) < 3(x-2)

Opening the brackets to have

-4x-28<3x-6

Collecting like terms to have

-4x-3x<-6+28

This shows that -7x<22

Making x the subject of the relation we have

x>-22/7

The inequality that satisfies the given inequality is x>-22/7

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The probability of exactly 2 couples dancing together is 100/45 = 20/9.

To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.

The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.

So the probability of exactly 2 couples dancing together is 100/45 = 20/9.

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The probability of exactly 2 couples dancing together is 100/45 = 20/9.

To find the probability of the total number of ways to form pairs of 5 couples is C(10, 2) = 45, because there are 10 people and we need to choose 2 at a time.

The number of ways to form exactly 2 couples dancing together is C(5, 2) * C(5, 2) = 10 * 10 = 100. This is because we first choose 2 couples out of the 5 couples and then pair the males and females within each chosen couple.

So the probability of exactly 2 couples dancing together is 100/45 = 20/9.

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By using permutations and combinations, We can arrange 12 people into 3 teams of 4 in 5775 different ways.

Here, we will use the concept of permutations and combinations to solve the question.

We have to arrange 12 people into 3 teams of 4.

We know that ⁿCr = n! / [(n - r)! × r!]

No. of ways to select the first 4 people in the first group = ¹²C₄

                                                                                         = 12! / [(12 - 4)! × 4!]

                                                                                             = 12! / [(8! × 4!)]

                                                                                             = 495

No. of ways to select 4 people from the remaining 8 for the second group = ⁸C₄   = 8! / [(8 - 4)! × 4!] = 8! / [(4! × 4!)] = 70

No. of ways to select 4 people from 4 for third group = ⁴C₄  = 4! / [(4 - 4)!] × 4!] = 4! / [(0! ×4!)] = 1

Total no. of ways to select people for group = (495 x 70 x 1) / 3! = 34650 /6 = 5775

Hence, we can split 12 people into 3 teams of 4 in 5775 different ways.

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(f ◦ g)(x) = -2x^2 + 11.

What is Composition of two functions ?

The new function obtained by performing f first and then g is the combination of two functions g and f.

The composition of two functions f and g, denoted by (f ◦ g)(x), is defined as the function that maps x to f(g(x)).

Given the functions f(x) = 2x + 3 and g(x) = -x^2 + 5, the composition of these two functions is:

(f ◦ g)(x) = f(g(x)) = f(-x^2 + 5) = 2(-x^2 + 5) + 3 = -2x^2 + 11

So, (f ◦ g)(x) = -2x^2 + 11.

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By using the properties of similar triangles, the values of x and y are respectively, 15 & 7

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

Side lengths of triangle 1,  y + 9, x, x -2

Side lengths of triangle 2,  30, 26, 5y - 3

Both the triangles are similar,

So, we can write

(x - 2)/x = 26/30

After solving it, x = 15

Similarly,

(y + 9)/x = (5y - 3)/30

y = 7

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The kind of data we have is Categorical data. Data that can be broken down into groups or categories is known as categorical data.

There are three categories in this case: eggs, cereal, and no breakfast These groups include the 10 students who ate cereal, 5 students who ate eggs, and 3 students who did not eat breakfast at all.

A categorical variable is a variable in statistics that can have one of a limited, typically fixed number of possible values and assign each observational unit to a specific group or nominal category based on some qualitative property.

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Triangle ABC is similar to triangle DEF because their corresponding angles, ∠A and ∠D, and ∠B and ∠E, are equal.

The AAA similarity is a theorem of a triangle which means "angle-angle-angle", that is, two triangles are similar to each other if they both have three corresponding angles that are congruent to each other.

The line BC divides the line AD and AE, we can state that the two triangles are similar by the Angle-Angle-Angle (AAA) Similarity Theorem.

The AAA Similarity Theorem states that if the three angles of one triangle are equal to the three angles of another triangle, then the two triangles are similar.

Here is an example similarity statement based on the Angle-Angle-Angle (AAA) Similarity Theorem: "Triangle ABC is similar to triangle DEF because they both have equal corresponding angles, ∠A and ∠D, ∠B and ∠E, and ∠C and ∠F, and because the line BC divides the line AD and AE."

Hence, Triangle ABC is similar to triangle DEF because their corresponding angles, ∠A and ∠D, and ∠B and ∠E, are equal.

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The actual weight of a pound is 0.45359237 kilos.

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For the given function; Domain: -4 ≤ x ≤ 4, Range: 0 ≤ y ≤ 3, Relative max: x = 0, y=3, and Relative min: x = -2, y=0 and x = 2, y =0.

The range of values that we are permitted to enter into our function is known as the domain of a function.

The x values for a function like f make up this set (x).

A function's range is the collection of values it can take as input. The values in this set

Hence, once we input an x value, the function returns. The y values are those.

The domain of the function is the input values, that is the x-coordinates thus,

Domain: -4 ≤ x ≤ 4

Range of the function is the output values, that is the y-coordinate thus,

Range: 0 ≤ y ≤ 3

Relative max is a point where the function changes from increasing to decreasing thus,

Relative max: x = 0, y=3

Relative min is a point where the function changes from decreasing to increasing, thus,

Relative min: x = -2, y=0 and x = 2, y =0

Hence, the Domain: -4 ≤ x ≤ 4, Range: 0 ≤ y ≤ 3, Relative max: x = 0, y=3, and Relative min: x = -2, y=0 and x = 2, y =0.

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A statement which best explains if the graph correctly represents the proportional relationship y = −2x include the following: D. Yes, the points shown on the line would be part of y = −2x.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios, a straight line, and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Generally speaking, the graph of any proportional relationship such as the linear equation (y = -2x) is characterized by a straight line as shown in the image attached below, with the following ordered pairs (0, 0), (1, -2),(2, -4), and (-1, 2).

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The slope of line D and line E will be congruent. Then the lines are parallel to each other.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equations are given below.

Line D: y = (3/8)x +3

Line E: y = (3/8)x + 8/3

The slope of line D and line E will be congruent. Then the lines are parallel to each other.

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Let P be the principal Vanilla Ice borrowed. The interest charge is calculated as P * 10.3% * 240/365.

So, 330 = P * 10.3% * 240/365

Solving for P, we get:

P = 330 / (10.3% * 240/365) = $3,116.71

Therefore, Vanilla Ice borrowed a principal of $3,116.71.

Simple Interest (SI) is calculated based on the principal amount only, and the interest rate stays constant throughout the tenure. The formula for Simple Interest is:

SI = P * R * T

Where:

P = Principal amount

R = Interest rate

T = Time (in years)

Compound Interest (CI) is calculated based on the principal amount and the interest earned on it in previous periods. The interest earned in each period is added to the principal, and the new amount becomes the principal for the next period. This leads to an exponential growth of the invested amount. The formula for Compound Interest is:

CI = P * (1 + R/n)^(nt)

Where:

P = Principal amount

R = Interest rate

n = Number of compounding periods per year

t = Time (in years)

In summary, the main difference between simple and compound interest is that simple interest is calculated only on the principal amount, whereas compound interest is calculated on the principal amount and the accumulated interest.

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Answer: 0.56

Step-by-step explanation: convert from fraction to decimal

EF is parallel to GH by using the slope formula. Both the slope is equal to -4/5.

Given that the information below:

E(2,5), F(7,1), G(2.-3) and H(-8,5) is EF parallel to line GH.

By using slope formula method we can compare the slopes of line EF & line GH.

Where m = (y2 - y1 ) / (x2 - x1) slope of segment become (x1,y1) & (x2,y2)

EF Slope = (1-5)/(7-2) = -4/5

GH Slope = (5-(-3)/(-8-2) = 8/-10 = -4/5

By using slope formula method EF  slope is -4/5 & GH slope is -4/5. Both the slopes of the equation is equal. In this way we can prove that the EF is parallel to GH.

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Answer: 1.5

Step-by-step explanation:

The time taken by Edson to complete his workout routine is 13 t

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here:  Edson exercises in sets that are each t minutes long. He does 6 sets of push-ups, 3 sets of pull-ups, and 4 sets of sit-ups

Now Edson does 6 sets of pushups time taken to finish the sets are

Time ( pushups)=6t

similarly, the time it takes to complete the other exercises are

Time(pull ups)=3t

Time(sit ups)=4t

Thus total time taken is equal to 3t+4t+6t=13t

Hence, The time taken by Edson to complete his workout routine is 13 t

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Step-by-step explanation:

The slope of a line can be calculated as the difference of the y-coordinates divided by the difference of the x-coordinates of two points on that line. In this case, we have two points: (10,23) and (20,36).

So, the slope of the line would be:

(36 - 23) / (20 - 10) = 13 / 10 = 1.3.

Therefore, the slope of the line that has the coordinates of (10,23) and (20,36) is 1.3

The average of the 3-day simple moving averages for these five days to the nearest $0.01 is $105.99, $107.19 and $110.40.

What is a Simple Moving Average?

By dividing the number of periods inside the range by the average of the range of prices, simple moving averages are used.

We are given closing prices of a stock over a 5-day period.

So, 3-day simple moving averages are

For Monday - $104.67

For Tuesday - $103.95

For Wednesday - ($104.67 + $103.95 + $109.35)/3 = $105.99

For Thursday - ($103.95 + $109.35 +$108.27)/3 = $107.19

For Friday - ($113.58 + $109.35 +$108.27)/3 = $110.4

Hence, the average of the 3-day simple moving averages for these five days to the nearest $0.01 is $105.99, $107.19 and $110.40.

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