The concept of best-, worst-, and average-case analyses extends beyond algorithms to other counting problems in mathematics. Recall that the height of a binary tree is the number of edges in the longest path from the root to a leaf. Find the best-case height of a binary tree with seven nodes.

The number of terms  - 2.

Here we assume that [tex]a_{n}[/tex] > 0 or all n, the terms are monotone decreasing and [tex]\lim_{n \to \infty} a_n[/tex] =0. This guarantees the convergence of the series. Now, if we choose a finite value N, and approximate the series by Σ [tex](-1)^{n}[/tex][tex]a_{n}[/tex] , the error in the approximation of the infinite series by this finite sum is bounded by [tex]a_{N + 1}[/tex] .

We are given the infinite alternating series

                      n=4,              ∑ [tex]\frac{(-1)^{n+1} }{n^{4} }[/tex]

and wish to approximate the sum with an error of less than 0.001.

Define [tex]a_{n}[/tex] = [tex]\frac{1}{n^{4} }[/tex] . Then we will solve the inequality [tex]a_{n}[/tex] < 0.001 :

                     [tex]\frac{1}{n^{4} }[/tex] < 0.001

                     [tex]n^{4}[/tex] > 1000

                     n > [tex]\sqrt[4]{1000}[/tex]

                        ≈ 5.62

Therefore, if we stop at n=5, the error will be less than 0.001. Since the series starts at n=4, we need only use 2 terms.

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The most effective study design was "a totally random structure. Randomly choose three stores for each of the nine permutations of the price level as well as packaging type."

Based on information provided by the market research firm

27 shoppers with comparable characteristics in total were included in the study.

There are nine combinations in total.

3 levels are the total amount of price tiers.

Three different package types total.

Total sales time period: 7 weeks

According to the completely randomised design, just one key component needs to be studied in order to determine its impacts.

For each type and level for each combination, we must here employ a completely random design.

Consequently, the appropriate claim is "a totally random structure. Randomly choose three stores for each of the nine permutations of price level but also packaging type."

Since the stated question isn't complete, I've generally answered it.

The complete question is :

A market research firm is studying the effects of price and type of packaging on sales of a particular product. Twenty-seven stores with shoppers of similar characteristics will be used in the study. The nine combinations of three price levels and three packaging types are the treatments of interest. Total sales of the product over a seven-week period will be recorded. Which of the following describes the best design to use for the study?

a. А A completely randomized design Randomly assign the nine combinations of price level and packaging type that three stores use each combination

b. A completely randomized design. Randomly assign the three price levels so that nine stores use each price level

c. A completely randomized design. Randomly assign the three packaging types so that nine stores use each type of packaging

d. A randomized block design Use packaging as a block. Randomly assign the nine combinations of three price levels and three packaging types so that three stores use each combination

e. A randomized block design. Use packaging as a block Randomly assign nine stores to each packaging type, then randomly assign price level to three stores within each block.

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Answer:

  A, B, C

Step-by-step explanation:

You want to know the correct descriptors of the given graph.

The solution to a system of equations is the set of points that satisfy all of the equations at once. On a graph, it will be the set of points where the graphs of the equations intersect.

Here the two lines cross at one point, hence there is one solution.

The point where the lines cross is approximately (3, -0.5). That makes (3, -0.5) a reasonable estimate of the solution of the system.

The ordered pair for the vertices after the transformation will be:

Q' = (3, 5)

R' = (5, -1)

S'= (2, 0)

T' = (0, 3)

A geometric transformation is a function that maps points in a plane or space to other points in the same plane or space. Geometric transformations can be used to change the size, shape, orientation, or position of an object or image.

Given:  (Ry-axis T(2, 0))(QRST). That means we have a translation T(2, 0). This implies (x,y) → (x + 2, y + 0). Thus, the ordered pair for the vertices will be:

Q (x = 1, y = 5)

Q' = Q(x+2, y + 0) = (1+2, 5+0) = (3, 5)

R (x = 3, y = -1)

R' = R(x+2, y + 0) = (3+2, -1+0) = (5, -1)

S (x = 0, y = 0)

S' = S(x+2, y + 0) = (0+2, 0+0) = (2, 0)

T (x = -2, y = 3)

T' = T(x+2, y + 0) = (-2+2, 3+0) = (0, 3)

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The polar coordinates of the points are: A(√29,68.1°),B(√45,-63.4°),C(√97,66.0°),D(√65,7.12°)

consider A=(2,5)

To find the polar coordinates we have the formula:

[tex]r=\sqrt{x^2+y^2} and tan^{-1} (\frac{y}{x} )----------(1)[/tex]

Assume that x=2,y=5 and substitute in equation(1)

r=√2^2+5^2 and tan^-1(5/2)

r=√4+25 and tan^-1(2.5)

r=(√29,68.1°)

For point B =(3,-6)

Assume that x=3,y=-6 and substitute in equation(1)

r=√3^3+(-6)^2 and tan^-1(-6/2)

r=√9+36 and tan^-1(-2)

r=(√45,-63.9°)

For point C=(-4,9)

Assume that x=-4,y=9 and substitute in equation(1)

r=√(-4)^2+9^2 and tan^-1(9/-4)

r=√16+81 and tan^-1(2.25)

r=(√97,66.0°)

For the point D=(-8,-1)

Assume that x=-8,y=-1 and substitute in equation(1)

r=√(-8)^2+(-1)^2 and tan^-1(-1/-8)

r=√64+1 ,7.12°

r=(√65,7.12°)

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A stock price will rise if demand for stock is greater than supply. So, the correct answer is option (d).

The stock price or share price is the amount of money it costs to buy shares in a company. Stock prices are not fixed and fluctuate based on market conditions. It is likely to go up if the company is viewed as good, and it is likely to go down if the company is not performing as expected. If there are more people who want to buy a demand than sell (supply ) it, the stock price will go up. Conversely, if more people want to sell than buy stocks, there will be more supply than demand and prices will fall. Understanding supply and demand is easy.

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Complete question:

A Stock Price Will Rise If:

a) Supply Of Stock Is Greater Than Demand

b)The Price-Earnings Ratio Is 10 Or Greater

c)Stock Yield Is Greater Than 8%

d) Demand For Stock is Greater Than Supply

e) None Of These.

Step-by-step explanation:

so, we have 1 position with 2 options (0 or 1).

and 6 positions with 10 options (0 to 9).

so, we have

2×10×10×10×10×10×10 = 2×10⁶ = 2,000,000

different identification numbers possible.

Letss try using Pythagoras Theorem with

[tex]a+b+c=180\\21+28+c=180\\c=180-21-28\\c=131[/tex]

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Answer:

the nth term is 2n

Step-by-step explanation:

notice how for each number of tiles, 2, 4, 6, 8, 10, they are all multiples of 2, so like ok 2 is definitely in the term, next check how n can fit. Well, since they are multiples, you multiply n by 2, now check to see if you dont need to add any values by the following method:

first number = 2,  then 2(1) = 2 if n = 1

second = 4, then (2)(2) = 4 if n = 2

its all the same for the rest. Each new diagram or tile structures represents n, so if n =1, then there are 2 tiles, if n = 4 there are 8 tiles and so on, which explains us why the nth term is 2n

The nth term formula for the number of square tiles in the nth figure is aₙ=2n.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is aₙ=a+(n-1)d.

The given sequence is 2, 4, 6, 8, 10,.....

Here, a=2 and d=4-2=2

Substitute a=2 and d=2 in aₙ=a+(n-1)d, we get

aₙ=2+(n-1)×2

aₙ=2+2n-2

aₙ=2n

Therefore, the nth term formula for the number of square tiles in the nth figure is aₙ=2n.

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Answer:

x = 6

Step-by-step explanation:

let x = the width

let x + 8 = the length

Area = w times l

84 = 14 x 6

width = 6

length = 6+8

           = 14

We get the following answers:

A) The least square regression line is:

yi = 88.73 - 2.827(xi)

B) The slope  is β₁ = -2.827 and The intercept is β₀ = 88.73.

C) e*₆ = -0.6964, final grade is below average grade.

E) It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

we have Xi = No of absences

Yi = Final grade

The regression model is

Yi = β₀ +  β₁Xi + i

β₀ = y -  β₁x

we have n = 10, x bar = 4.5 , y bar = 76.01

cov(x,y) = -23.325 and var(x) = 9.1667

therefore,  β₀ = 88.73 and  β₁ = -2.827

A) Least square regression line is given by:

yi =  β₀+ β₁Xi

yi = 88.73 - 2.827(xi)

B) The slope  β₁ = -2.827 which means when no of absence is increased by 1 duty then the final grade will decrease by 2.827

The intercept  β₀ = 88.73 when there are 0 days absence the average grade is 88.73

C) Predicted graph for student who misses five class periods is

x = 5

y*5 = 88.73 - 2.827(5) = 74.5964

Hence for corresponding residual is:

e*₆ = 73.9 - 74.5964

e*₆ = -0.6964, final grade is below average grade.

D) please see graph

E) when student miss 15 class periods the final grade will be

X = 5

y* = 88.73 - 2.827(15)

= 46

It would not be reasonable since no of absence increases the score decreases, it works well for small no of absences but will not work for large number of absences since it may give absurd final grade.

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if the null hypothesis is not rejected at the 5% level of significance, it 1 , 2 will always be rejected at the 1% level, 4 may be rejected or not rejected at the 1% level.

The null hypothesis is a statement of a general population parameter that is assumed to be true. It is typically tested using a statistical test, such as an independent t-test or ANOVA. If the null hypothesis is not rejected at the 5% level of significance, it does not necessarily mean that it will also not be rejected at the 1% level. This is because the 1% level of significance is a stricter level of significance, meaning that the sample data must be even more extreme in order to reject the null hypothesis. Thus, the null hypothesis may be rejected or not rejected at the 1% level, depending on how extreme the data are.

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The function f{ g(2) } is equivalent to for the functions f(x) = 2x² + 1 and g(x) = 3x - 5 is 3.

Given is that f(x) = 2x² + 1 and g(x) = 3x - 5.

We have to find -

f{g(2)}

Now -

g(2) = g(2) = 3 x 2 - 5 = 6 - 5 = 1

g(2) = 1

f{g(2)} = 2x² + 1 = 2 x 1 x 1 + 1

f{ g(2) } = 3

Therefore, the function f{ g(2) } is equivalent to for the functions f(x) = 2x² + 1 and g(x) = 3x - 5 is 3.

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Number of people that use blogs to make a purchase are 24.75= 25 and number of people that never buy anything without reading a review first are 60.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given, 33% of millennials rely on blogs before making a purchase.

Eight out of 10 millennials never buy anything without reading a review first.

That means,

8 out of 10 is 80%.

In a sample size of 75 millennials:

To find the number of people that never buy anything without reading a review first:

80% of 75

80 x 75 / 100

= 6000/ 100

= 60

To find the number of people that use blogs to make a purchase:

33% of 75

33 x 75 / 100

= 2475/ 100

= 24.75

Therefore, the number of people are 24.75 and 60.

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Answer: b. The radius is the same as a cylinder with a volume of 500(3) and the same height.

Step-by-step explanation:

The volume of a cylinder is 3 times that of a cone (assuming they have the same perpendicular height and radius).

If her current wealth is $100 and f 0.25, then she bets $25 and either gains or loses that amount then the probability is 0.139.

It is given that Xj is the amount she has immediately after the j the bet is settled.

In the J+1 the bet, she bets fXj of her welath, which has a probability of win of P and probability  of loss of 1-p.

Thus:

Xj+1 = Xj + fpXj - f(1-p)Xj

Xj+1 = Xj (1+fp-f(1-p))

Xj+! = Xj(1+2fp-f)

Taking expected values on both sides

E(Xj+1) = E9Xj)(1+2fp-f)

we can write:

E(Xₙ) = E(Xₙ₋₁)(1+2fp-f)

E(Xₙ) = E(Xₙ₋₂)(1+2fp - f)²

E(Xₙ) = E(Xₙ₋₃)(1+2fp - f)³

Hence we get the required answer.

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An ellipse's equation has its origin at its center, its foci on the y-axis, and its major axis at x2/16+y2/144, which is three times longer than its minor axis.

In mathematics, an ellipse is a planar curve with two focal points, where the total of the two distances from any point on the curve to the focal points is a constant.

It generalizes the shape of a circle, a unique variety of ellipse in which the two focus points coincide.

The eccentricity of an ellipse,  , which ranges from 0 (the limiting case of a circle) to 1 (the length of the ellipse), is used to determine how long it is (the limiting case of infinite elongation, no longer an ellipse but a parabola).

The area of an ellipse has a straightforward algebraic solution, while the perimeter (also known as circumference), for which integration is necessary to arrive at a precise answer, only has approximations.

According to our question-

M(X0|Y)   M(0|0)

(X-X0)^2/a^2 +(Y-Y0)^2/b^2=1

x2/a2+x2b2=1

a=4 b=3 .a=12

x2/16+y2/144

Hence, An ellipse's equation has its origin at its center, its foci on the y-axis, and its major axis at x2/16+y2/144, which is three times longer than its minor axis.

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Answer: Brazil and Alaska

Step-by-step explanation

Take away Brazil's temperature from Alaska's to get your answer

81 - 23 = 58'F

The ordered pair that is NOT a solution to the equation y = 2x is (3, 8)

From the question, we have the following parameters that can be used in our computation:

y = 2x

From the graph (see attachment), we have the following points:

A = (1, 2)

B = (2, 4)

C = (3, 8)

D = (5, 10)

The equation y = 2x means that

y is twice of x

In C = (3, 8), 8 is not twice of 3

Hence, the ordered pair that is NOT a solution is C = (3, 8)

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Answer:

See below

Step-by-step explanation:

If I make x the scope of mix and y the quarts of water, my equation would be y = .125x

I can find the constant of Proportionally by y/x

Using points (4,.5) and (12,1.5)

(.5/4) = 0.125

(1.5/12) = 0.125

The equation would then be:

y = 0.125x

C see the graph provided from Desmos (a free graphing calculator).  as x Increases by 1, y increases by 0.125

y = 0.125x

y =.0125(20)

y = 2.5

For 20 scoops, I would need 2.5 quarts of water.

You can also see from the graph as 8 scoops, I would need 1 quart of water.

When you determine the number of months it takes to pay off a credit card and you get 24.35, payments, you have to round up.

You should understand that rounding up numbers or decimals involves writing it as a whole number

The question is given in months and we are not asked to state the weekly fractions.

24.35 is 24 months + .35*30=10 weeks

Now 24.35 in months is 24 months 10 weeks and 5 days

Hence payment is in months it should be 24 months only.

In conclusion you should not round it up.

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Answer:

A. x = -6

Step-by-step explanation:

-1/6x - 5 = 2/3x

add 1/6x to both sides:

-1/6x - 5 + 1/6x = 2/3x + 1/6x

-5 = 2/3x + 1/6x

common denominator on right side:

-5 = 4/6x + 1/6x

combine right side:

-5 = 5/6x

multiply both sides by 6/5:

(-5)(6/5) = (5/6x)(6/5)

-30/5 = x

reduce left side:

-6 = x

x = -6 (option a)

Answer: A) x=-6

Step by step explanation:

[tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x }}[/tex]

We calculate the multiplication expression.

    [tex]\boldsymbol{\sf{\dfrac{-1}{6}x-5=\dfrac{2}{3}x \iff \ -\dfrac{x}{6}-5=\dfrac{2}{3} x \iff -\dfrac{x}{6}-5=\dfrac{2x}{3} }}[/tex]

Eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

     [tex]\boldsymbol{\sf{ -\dfrac{x}{6}-5=\dfrac{2x}{3} \iff \ -x-30=4x}}[/tex]

The variable is moved to the left and the symbol is changed.

    [tex]\boldsymbol{\sf{-x-30=4x \iff -x-30-4x=0}}[/tex]

We move the constant to the right side and change the sign.

    [tex]\boldsymbol{\sf{-x-30-4x=0 \iff -x-4x=30}}[/tex]

 [tex]\boldsymbol{\sf{-x-4x=30 \ < == We \ organize \ the \ equation== > \ -5x=30 }}[/tex]

             [tex]\bf{\underline{Change \ the \ sign \ on \ both \ sides \ of \ the \ equation.}}[/tex]

  [tex]\boldsymbol{\sf{-5x=30 \iff \ 5x=-30 \ < ==Split== > \ x=-\dfrac{30}{5}=\boxed{\boxed{\boldsymbol{\sf{-6}}}} }}[/tex]

Answer:

7

Step-by-step explanation:

the circle is the midpoint

the midpoint is at (1,0)

And we have to find the 2 edges

(-6,0) and (8,0)

To find the distance we just subtract the x values since y is 0

8-1=7

1-(-6)

1+6=7

The radius is 7

Hopes this helps

To write the equation in exponential form we must follow certain rules:

1. Logarithm product rule -            log b ( x ∙ y) = log b ( x) + log b ( y)

2. Logarithm quotient rule -           log b ( x / y) = log b ( x) - log b ( y)

3. Logarithm power rule -               log b ( x y) = y ∙ log b ( x)

4. Logarithm base switch rule -     log b ( c) = 1 / log c ( b)

1. ㏒z(w) = p

Here all constants are taken to be positive and not equal to 1

z = base of the logarithmic function

z^p = w --------> (1)

This z^p = w is the exponential form of ㏒z(w) = p

2. ㏒(s) = r

Here all constants are taken to be positive and not equal to 1

e = base of the logarithmic function

e^r = s --------> (2)

This e^r = s is the exponential form of ㏒(s) = r

3. 7m = a

Here we have to write the equation in logarithmic form

㏒(7m) = log r

log(7m) - log r = 0

We know quotient rule :-

log b ( x / y) = log b ( x) - log b ( y)  --------(A)

Applying that same principle to our question by using this equation we have:

log (7m/r)

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Answer:

Step-by-step explanation:

-7-9=-16

The solutions of the given system of equations are, (-2, 11) and (-1, 6).

What is system of equations?

A group of equations involving one or more variables is known as a system of equations. The variable mappings that satisfy each component equation, or the points where all of these equations intersect, are the solutions to systems of equations.

Consider, the given system of equations

y = x^2 - 2x + 3            ..(2)

y = -5x + 1                    ..(1)

Plug value of y in equation (1).

⇒ -5x + 1 = x^2 - 2x + 3

x^2 - 2x + 3 + 5x - 1 = 0

x^2 + 3x +2 = 0

x^2 + 2x + x + 2 = 0

x(x + 2) + 1(x + 2) = 0

(x + 2)(x + 1) = 0

(x + 2) = 0,      (x + 1) = 0

       x = -2,             x = -1

Now to find the value of y for each value of x.

Plug x = -2 in equation (2)

y = -5(-2) + 1 = 10 + 1 = 11

Plug x = -1 in equation (2)

y = -5(-1) + 1 = 5 + 1 = 6

Hence, the solutions of the given system of equations are, (-2, 11) and

(-1, 6).

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The factorized expression of  5x³ + 40y⁶ is  5 ((x + 2y²) (x² - 2xy² + 4y⁴))

Factorisation of an algebraic expression means writing the given expression as a product of its factors. These factors can be numbers, variables, or an algebraic expression.

To the factor, a number means to break it up into numbers that can be multiplied to get the original number

According to the question,

We have to factorize the expression

5x³ + 40y⁶

Taking a Common factor 5 out ,

5 (x³ + 8y⁶)

Factoring the expression within the parenthesis we have:

5 ((x + 2y²) (x² - 2xy² + 4y⁴))

Now, we cant do further factor

Hence ,  The factored expression is given by:  5 ((x + 2y²) (x² - 2xy² + 4y⁴))

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In a normal distribution, a data value located 1.1 standard deviations below the mean has Standard Score: z = -1.1

What is standard deviation?

In statistics, the quality deviation could be a live of the quantity of variation or dispersion of a group of values. an occasional variance indicates that the values tend to be about to the mean of the set, whereas a high variance indicates that the values area unit opened up over a wider vary

Main body:

The z score tells us the distance, in terms of standard deviation, the raw score is from the mean. Negative z values are below the mean, while positive ones are above the mean.

Something like z = 2.5 indicates we're 2.5 standard deviation units above the mean.

Something like z = -1.1 indicates we're 1.1 standard deviation units below the mean.

The value z = 0 itself is the center of the standard normal distribution (it's the mean mu).

The sigma value for the standard normal Z distribution is sigma = 1

sigma = population standard deviation

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If the circumference of ABDE is 30 cm, then the length of the line DE is 6 cm.

The answer to the query is

ABDE's perimeter is 30 cm.

AB length is 12 cm.

Let DE ne length be "x"

Since DE and AB are parallel, the alternate interior angles theorem states that

∠ABE = ∠DEB and ∠BAD = ∠ADE.

Since AD is the angle that bisects ∠A,

∠DAB = ∠EAD

BE is the angle bisector of B, therefore

∠EBD = ∠ABE.

∠EAD = ∠ADE and ∠EBD = ∠BED as a result.

If AE = ED and ED = DB, the triangles ADE and EDB are therefore isosceles. AE = DE = DB = x, then.

Given that ABDE's perimeter is 30 cm,

therefore 12 + 3x = 30,

By finding the x,

=> 3x = 30 -12

=> 3x = 18

=> x = 6 cm.

Consequently, DE has a length of 6 cm.

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