this is a super hard one

Answers

Answer 1

Notice that in the given sequence the difference between the first two terms is 7 so the solution must be in terms of multiples of 7 plus a constant. The only two options that have this characteristic are first and last ones, for the sum to consider the first term the sum must start for r=0.

Answer: last option.


Related Questions

PLEASE HELP NO LINKS OKAY!!

PLEASE HELP NO LINKS OKAY!!

Answers

I’m sorry dude I really don’t know I keep on getting links to

Point (∃xP(x)∧Q(x))≡∃x(P(x)∧Q(x)) Q6 1 Point Which rule of ND justifies P(0) from ∀xP(x) ? There is no rule of ND that justifies this. (∀E) (∀I) (∃E) (∃I)

Answers

The (∃E) rule is used to infer P(0) from ∀xP(x), and this conclusion is supported by the existence of an object that satisfies the predicate.

The rule of natural deduction that justifies P(0) from ∀xP(x) is the existential elimination (∃E) rule. This rule allows us to infer a particular instance of an existential quantification based on the existence of an object that satisfies the predicate. In this case, since we have the universal quantification ∀xP(x), we can use (∃E) to conclude P(0) by substituting 0 for x. By doing so, we have shown that there exists an object, namely 0, that satisfies the predicate P(x). Therefore, (∃E) justifies the statement P(0) from the given universal quantification.

To know more about existence, visit:

https://brainly.com/question/31869763

#SPJ11

What are range, index of qualitative variation (IQV), interquartile range (IQR), standard deviation, and variance

Answers

Answer:

To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

Step-by-step explanation:

Tina make 480 sandwiches she only makes tuna sandwiches beef sandwiches and ham sandwiches amd cheese sandwiches 3/8 of the sandwiches are tuna 35% of the sandwiches are beef the ratio of the number of ham sandwhiches to the number of cheese sanwiches is 5:6 work out the number of ham sandwhiches that tina makes

Answers

= 5x = 5(12) = 60 sandwiches, the number of ham sandwiches. Tina makes 60 ham sandwiches.

First, we need to find the total number of each type of sandwich that Tina makes:

3/8 of the sandwiches are tuna, so the number of tuna sandwiches

= 3/8 x 480

= 180 sandwiches

35% of the sandwiches are beef, so the number of beef sandwiches

= 35% x 480

= 0.35 x 480

= 168 sandwiches

The remaining sandwiches must be ham and cheese sandwiches. Let's call the number of ham sandwiches "h" and the number of cheese sandwiches "c". We know that h:c = 5:6, which means that h = 5x and c = 6x for some common factor x. The total number of sandwiches is 480, so:

h + c = 480 - 180 - 168

h + c = 132

Substituting h = 5x and c = 6x, we get:

5x + 6x = 132                              

11x = 132

x = 12

Therefore, the number of ham sandwiches = 5x = 5(12) = 60 sandwiches. Tina makes 60 ham sandwiches.

                               

To learn more about common factor click here

brainly.com/question/11221202

#SPJ4

NEED HELP FOR A TEST, PLEASE :) (30 POINTS)
Match each condition to the number of triangles that can be constructed to fit the condition.

condition A: one side
measuring 4 inches,
another side measuring
8 inches, and a third
side measuring 10 inches

condition B: one angle
measuring 60°, another
angle measuring 40°, and
a third angle measuring 90°

condition C: one side
measuring 4 inches,
another side measuring
8 inches, and the angle
between them measuring 70°

condition D: one side
measuring 5 inches,
another side measuring
7 inches, and a third
side measuring 12 inches

condition E: one angle
measuring 30°, another
angle measuring 80°,
and the length of the
included side measuring
8 inches

condition F: one angle
measuring 40°, another
angle measuring 80°, and
a third angle measuring 60°

-no triangles
-one triangles
-many triangles

Answers

Answer:

Hey!

Your Answer Is,

No Triangles: A, C

One Triangle, F, D

Many Triangles: B,E

I hope this helps you!

Step-by-step explanation:

A certain paint is to be mixed with 3 parts yellow to 2 parts blue. What is the ratio of yellow paint to the total amount of mixed paint

Answers

The ratio of yellow paint to mixed paint is 3/5.

What are ratio and proportion?

A ratio is a comparison or relationship between two amounts of the same quantity to determine how much larger one number is than the other. Where b is not equal to zero, it is written as a/b or a: b. An equality of two ratios is a proportion. In order to write equivalent ratios, proportions are used, which aids in resolving the unknown quantities. As an illustration, a proportion is written as a: b = c: d.

Solution:-

Given,

Amount of yellow paint=3

Amount of blue paint=2

Ratio=yellow paint/total mixed paint

Ratio=3/(3+2)

Ratio=3/5

To know more about proportion visit:-

brainly.com/question/29774220

#SPJ4

Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
551. 340,000

Answers

Answer:

Hence, 3,40,000 can be expressed as \($$3.4\times10^5$$\)

Step-by-step explanation:

Step 1 of 1

Consider 3,40,000

3.4

So, 3.4 lies between 1 & 10

Now, Decimal has moved 5 places to left.

\($3.4=10^{5}$\)

So, 3,40,000=\(3.4 \times 10^{5}$\)

The expected return on MSFT next year is 12% with a standard deviation of 20%. The expected return on AAPL next year is 24% with a standard deviation of 30%. If James makes equal investments in MSFT and AAPL, what is the expected return on his portfolio. 3. Siebling Manufacturing Company's common stock has a beta of .8. If the expected risk-free return is 2% and the market offers a premium of 8% over the risk-free rate, what is the expected return on Siebling's common stock

Answers

The expected return on James's portfolio is 18%.

The expected return on Siebling Manufacturing Company's common stock is 8.4%.

To calculate the expected return on James's portfolio, we need to take the weighted average of the expected returns of MSFT and AAPL based on their respective investments.

Let's assume James invests x% in MSFT and (100 - x)% in AAPL.

The expected return on James's portfolio can be calculated as:

Expected Return = (x * Expected Return of MSFT) + ((100 - x) * Expected Return of AAPL)

Substituting the given values:

Expected Return = (x * 12%) + ((100 - x) * 24%)

To find the value of x that makes James's investments equal, we set the weights equal:

x = 100 - x

Solving this equation gives us x = 50.

Now we can substitute this value back into the expected return equation:

Expected Return = (50% * 12%) + (50% * 24%)

Expected Return = 6% + 12%

Expected Return = 18%

Therefore, the expected return on James's portfolio is 18%.

To calculate the expected return on Siebling Manufacturing Company's common stock, we can use the Capital Asset Pricing Model (CAPM).

The CAPM formula is:

Expected Return = Risk-Free Rate + Beta * Market Premium

Risk-Free Rate = 2%

Market Premium = 8%

Beta = 0.8

Expected Return = 2% + 0.8 * 8%

Expected Return = 2% + 6.4%

Expected Return = 8.4%

Therefore, the expected return on Siebling Manufacturing Company's common stock is 8.4%.

Learn more about Capital Asset Pricing Model here:

https://brainly.com/question/32230922

#SPJ11

derive the first-order (one-step) adams-moulton formula and verify that it is equivalent to the trapezoid rule.

Answers

The first-order Adams-Moulton formula derived as: y(t+h) ≈ y(t) + h/2 * [f(t, y(t)) + f(t+h, y(t+h))].

The first-order Adams-Moulton formula is equivalent to the trapezoid rule for approximating the integral in ordinary differential equations.

How to verify the first-order Adams-Moulton formula using trapezoid rule?

The first-order Adams-Moulton formula is derived by approximating the integral in the ordinary differential equation (ODE) using the trapezoid rule.

To derive the formula, we start with the integral form of the ODE:

∫[t, t+h] y'(t) dt = ∫[t, t+h] f(t, y(t)) dt

Approximating the integral using the trapezoid rule, we have:

h/2 * [f(t, y(t)) + f(t+h, y(t+h))] ≈ ∫[t, t+h] f(t, y(t)) dt

Rearranging the equation, we get:

y(t+h) ≈ y(t) + h/2 * [f(t, y(t)) + f(t+h, y(t+h))]

This is the first-order Adams-Moulton formula.

To verify its equivalence to the trapezoid rule, we can substitute the derivative approximation from the trapezoid rule into the Adams-Moulton formula. Doing so yields:

y(t+h) ≈ y(t) + h/2 * [y'(t) + y'(t+h)]

Since y'(t) = f(t, y(t)), we can replace it in the equation:

y(t+h) ≈ y(t) + h/2 * [f(t, y(t)) + f(t+h, y(t+h))]

This is equivalent to the trapezoid rule for approximating the integral. Therefore, the first-order Adams-Moulton formula is indeed equivalent to the trapezoid rule.

Learn more about first-order Adams-Moulton formula on:

https://brainly.com/question/30401353

#SPJ4

Work out x^2- 2x
when x =4

Answers

Answer:

8

Step-by-step explanation:

\(x^2-2x \\x=4\\(4)^2-2(4)\\16-8\\8\)

A runner runs 160 metres in 20 seconds what is his average speed

Answers

Answer:

8 metres per second (8m/s)

Step-by-step explanation:

160 metres divided by 20 = 8.

this is because he runs x metres each second so X must be 8

Answer:

8m/s or 8 metres per second

Step-by-step explanation:

To find the average speed you must divide 160 metres by 20 seconds:

160÷20=8

After dividing you get the answer of 8(metres per second).

Don't forget to use terms of measurements in your answer if needed!

Let f be the function from {a,b,c} to {1,2,3} such that f(a) = 2 , f(b) = 3, and f(c) = 1. Which of the following is f^-1

Answers

f^-1 is the inverse function of f, which means it maps the range of f back to its domain. In other words, if f maps a to 2, b to 3, and c to 1, then f^-1 maps 1 to c, 2 to a, and 3 to b.

^-1 is defined as follows: For any y in the range of f, f^-1(y) is the set of all x's in the domain of f such that f(x) = y. In this case, the range of f is {1,2,3}, so we need to find f^-1(1), f^-1(2), and f^-1(3).

Since f(a) = 2, we have f^-1(2) = {a}. Similarly, f^-1(3) = {b} and f^-1(1) = {c}. Therefore, f^-1 is the function that maps 1 to c, 2 to a, and 3 to b.

Learn more about inverse function: https://brainly.com/question/29141206

#SPJ11

The line plot represents data collected from a used bookstore.

Which of the following describes the spread and distribution of the data represented?

The data is almost symmetric, with a range of 9. This might happen because the bookstore offers a sale price for all books over $6.
The data is skewed, with a range of 9. This might happen because the bookstore gives away a free tote bag when you buy a book over $7.
The data is bimodal, with a range of 4. This might happen because the bookstore sells most books for either $3 or $6.
The data is symmetric, with a range of 4. This might happen because the most popular price of a book at this store is $4.

The line plot represents data collected from a used bookstore.Which of the following describes the spread

Answers

The information that describes the line plot is

The data is symmetric, with a range of 4. This might happen because the most popular price of a book at this store is $4.

When is a line plot said to be symmetric

A line plot is said to be symmetric when the data points on one side of the center line (usually the median) mirror the data points on the other side. In other words, if you fold the line plot in half at the center line, the two halves would overlap perfectly.

Symmetry can be determined visually by looking at the line plot and assessing whether the data points appear to be evenly distributed on either side of the center line.

If the line plot is symmetric, it suggests that the data is evenly distributed around the center, and there are no significant outliers or biases in the data. If the line plot is not symmetric, it suggests that there may be some skewness or asymmetry in the data, and further analysis may be needed to understand the underlying patterns and trends.

Learn more about symmetric data at

https://brainly.com/question/30888145

#SPJ1

HELP ME OUT!!!!!!!!!!

HELP ME OUT!!!!!!!!!!

Answers

Answer: it costs 1/3 or 0.333... for one orange

X represents number of oranges

Y represents the cost

HELP ME OUT!!!!!!!!!!

** h(x) = 2f(x).g(x)
Find the value of h’(1), if f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1.

** h(x) = 2f(x).g(x)Find the value of h(1), if f(1) = 3, g(1) = 2, f(1) = 4, g(1) = 1.

Answers

The value of  h’(1) is = 22

How may the chain rule example be used?

Solution: Since f′(x)=ex, the exponential function with base e's derivative is simply the function itself. G′(x)=4 is the derivative of g. The chain rule states that h′(x)=f′(g(x))g′(x)=f′(4x)4=4e4x. It was crucial that we assessed f's derivative at 4x in this example.

Given that :

h(x) = 2f(x).g(x)

f(1) = 3, g(1) = 2, f’(1) = 4, g’(1) = 1

h’(x) = 2 f'(x)g(x) + g'(x)f(x) by chain rule

h’(1) = 2 f'(1)g(1) + g'(1)f(1)

= 2 * (4 * 2 + 1 * 3)

= 2* (11)

= 22

Learn more about chain rule

https://brainly.com/question/28350594

#SPJ1

Slope fields are not usually useful for ODEs of second order or higher, as we need to know the first derivative of our desired function in order to draw the slope field. True or false

Answers

Slope fields are not usually useful for ODEs of second order or higher, as we need to know the first derivative of our desired function in order to draw the slope field. This staetment is True

True.

Slope fields are a graphical tool that can be used to visualize the behavior of solutions to first-order ordinary differential equations (ODEs). They involve drawing short line segments at various points on the x-y plane to indicate the slope of the solution curve at those points, based on the value of the first derivative at each point.

For ODEs of second order or higher, we need to know the values of higher-order derivatives of the solution function in order to draw a slope field. However, slope fields are not typically used for these types of ODEs, since the solutions can become more complicated and difficult to visualize in higher dimensions. Other methods, such as numerical methods or phase portraits, may be more appropriate for analyzing and visualizing solutions to ODEs of higher order.

To learn more about complicated visit:

https://brainly.com/question/5116762

#SPJ11

Can someone divide these two? I forgot how to over quarantine and it’s my sisters homework

Can someone divide these two? I forgot how to over quarantine and its my sisters homework

Answers

Answer:

Step-by-step explanation:

Can someone divide these two? I forgot how to over quarantine and its my sisters homework
Can someone divide these two? I forgot how to over quarantine and its my sisters homework

use a linear approximation (or differentials) to estimate the given number. (1.999)5

Answers

The approximate value of  \((1.999)^5\) is 31.92.

Describe linear approximation :

A linear approximations in maths is the use of a linear function to estimate a generic function. They are frequently used to create first order methods for solving or approximating equation solution in the method of finite difference.

To estimate \((1.999)^5\)

we’ll find the linearization of f(x) = \(x^5\)

at a = 2. Since

f′(x) = 5\(x^4\)

, f(2) = 32, and

f′(2) = 80,

we have L(x) = 32+80(x−2). Thus,

\(x^5\) ≈ 32 + 80(x − 2) when x is near 2,

so (1.999)5 ≈ 32 + 80(1.999 − 2) =

32 − 0.080 = 31.92.

To know more about linear approximation click below:

https://brainly.com/question/1621850#

#SPJ4

Four times the greatest of three consecutive odd
integers exceeds three times the least by 31.
What is the greatest of the three consecutive
odd integers?

Answers

Answer:

The largest is 25.

Step-by-step explanation:

If the first integer is x, the second is x+1 and the third is x+2.

When you multiply the largest by 4: (x+2)*4

It is 31 more than 3 times the smallest: (x+2)*4 = (x)*3+31

When you simplify you get : 4x+8 = 3x+31

Which means: x = 23

But since you want the largest you get: 23+2 = 25

The greatest of the three consecutive odd integers will be  \(19\).

What are integers ?

Integers are whole numbers that can be positive, negative and zero.

We have,

Let first integer \(= x\)

Second integer \(= x+2\)

Third integer  \(= x+4\)

Now,

According to the question,

\(4(x+4) = 3(x)+31\)

Simplifying;

\(4x+16=3x+31\)

Taking \(x\) variable on one side and constant on the other;

\(4x-3x=31-16\)

\(x=15\)

So,

Now substitute the value of \(x\)  in every integer's equation,

i.e.

First integer \(= 15\)

Second integer \(= 17\)

Third integer  \(= 19\)

So, the greatest of the three consecutive odd integers is \(19\).

Hence, we can say that the greatest of the three consecutive odd integers will be  \(19\).

To know more about integer click here

https://brainly.com/question/15276410

#SPJ2

at what rate percent compound interest wil Rs2000 amount to Rs2420 in 2 years.​

Answers

The Compound Interest of Principle 2000 will become 2420 within 2 years when the rate of interest is 21%

Compound interest = P(1 + R ÷ 100) to the power of n,

where P = Principle

           R = Rate of Interest

           n = no. of years

According to the given question,

Principle(P) =Rs2000

Rate of interest (R) =?

no. of years(n) = 2 years

given CI (Compound Interest) = Rs2420

CI = 2000(1 + R ÷ 100)² = 2420

    = 20(100 +R) = 2420

    = 100 + R = 2420 ÷ 20

    = 100 + R = 121

    = R = 121 - 100

    = R = 21%

Refer to the link below to know more about Compound Interest,

https://brainly.com/question/14295570?referrer=searchResults

 

Solve 6x
12y = 18 for x

Answers

12y = 18x
4y = 6x

Because 18 divided by 3 gives 6
And therefore 12 divided by 3 gives the answer

use the graph to determine wither the function is even, oddPlease check photo

use the graph to determine wither the function is even, oddPlease check photo

Answers

EXPLANATION:

Given;

We are given a graph of a function.

Required;

We are required to determine from the graph if the function is even, odd or neither even nor odd.

Solution:

To determine this from a graph, we should note that a function which is symmetrical with the y-axis is an even function. The graph which is symmetrical with the origin after a 180 degree rotation is an odd function.

Observe that if this graph is flipped from left to right (across the y-axis), it would not retain its original shape.

However, if the graph is rotated 180 degrees about the origin, it would retain its original shape.

Therefore, the graph depicted is an odd function

ANSWER:

The function is an ODD function

an airline pilot is flying at 10,000 feet in the air and sees his airport at angle of depression of 12 degrees. To the nearest foot how far is the pilot from the airport ? the pilot is ______ feet from the airport.

Answers

Using the sine function:

\(\begin{gathered} \sin (\theta)=\frac{opposite}{hypotenuse} \\ \sin (12)=\frac{10000}{x} \\ solve= \\ x=\frac{10000}{\sin (12)} \\ x=48097ft \end{gathered}\)

an airline pilot is flying at 10,000 feet in the air and sees his airport at angle of depression of 12

What percent of 40.4 is 50.5?​

Answers

I use key words to set up as an equation and solve. What percent is your variable. I’ll use x
Of means multiply and is means equals.

So. X times 40.4 =50.5
Written algebraically: 40.4x =50.5
Divide both sides by 40.4
I get 1.25 but I need to convert to percent so multiply by 100

125%
Answer:
40.4 is 80% of 50.5
Sorry if wrong! Plz mark brainiest if correct :D Have a great day luv <3
-Bee

Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.


Outcome Frequency
Green 4
Black 6
Orange 5

Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67

Answers

The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

What is probability?

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

When Denine went to the pizza palace to order pizza for her party her friend Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza. If there were 35 pepperoni pizzas ordered how many total pizza were ordered? While waiting on the pizza something went wrong with the oven and 2 out of every 25 pizzas were burned. How many pizzas were burned? If 360 pizzas were ordered how many cheese and how many mushroom pizzas were ordered?

Answers

Using proportions, it is found that:

If there were 35 pepperoni pizzas ordered, 150 total pizzas were ordered.12 pizzas were burned.120 cheese pizzas and 96 mushroom pizzas were ordered out of 360 pizzas.

What is a proportion?

A proportion is a fraction of a total amount, and the measures in the context of a problem are found using basic arithmetic operations such as multiplication and division.

One application of proportions is for ratio problems, as fractions are built from the ratios to find the equivalent amounts.

Caleb noticed that for every 10 orders of cheese pizza there were 7 orders of pepperoni pizza, 5 orders of sausage pizza and 8 orders of mushroom pizza, hence the fraction of Pepperoni pizzas out of the total is given by:

Pepperoni = 7/(10 + 7 + 5 + 8) = 7/30 of the total.

If 35 pepperoni pizzas were ordered, the total number is found as follows:

7x/30 = 35

7x = 30 x 35

x = 30 x 5

x = 150 pizzas.

2 out of every 25 pizzas were burned, hence the number of burned pizzas is given by:

2/25 x 150 = 2 x 6 = 12 pizzas.

The cheese fraction is given by:

10/30.

Hence, out of 360 pizzas, the number is given by:

10/30 x 360 = 10 x 12 = 120 cheese pizzas

The mushroom fraction is given by:

8/30.

Hence, out of 360 pizzas, the number is given by:

8/30 x 360 = 8 x 12 = 96 mushroom pizzas

Learn more about proportions at https://brainly.com/question/24372153

#SPJ1

use the distributive property 15(4n-2)=​

Answers

Answer:

60n-30

Step-by-step explanation:

you would do 15 * 4n

that would give you 60. since 15 *4 is 60 and then you would just put the n

15*2 equals 30. You would make it a negative 30 since it is a negative 2.

then you would combine them and get the answer

60n-30

Hope this helps!

Answer: 60n-30 also i didn't copy frank because i forgot the hope this helps and if you report me you'll regret it really bad. Have a great day! :>  Step-by-step explanation: you would do 15 * 4n  that would give you 60. since 15 *4 is 60 and then you would just put the n  15*2 equals 30. You would make it a negative 30 since it is a negative 2. then you would combine them and get the answer 60n-30

What is the mean number of points scored by these players?

What is the mean number of points scored by these players?

Answers

The answer is 6... hope this helps.......

hello pleASE I need helppppppp​

hello pleASE I need helppppppp

Answers

I can help you with that problem i just did that on my own.

If your heart rate is 120 beats per minute during strenuous exercise, what is the period of a single heart beat in units of seconds

Answers

0.5 s/beat

I hope this helps (:
Other Questions
What country will soon become the first large industrial economy powered primarily by renewable energy? Tengo dolor de ________________. ciruga doctor estmago fiebre A. Mt. Kilimanjaro is 19,341 feet above sea level. The sea of galilee in Israel is 646 feet below sea level. Draw and label a diagram comparing the difference between these two elevations. Let zero represent sea level on your drawing.B. what is the difference in feet between these two elevations? please help work this out Autozone is selling 3 cans of fix-a-flat (250ml) for $2.01. o'reily's auto parts is selling 5 cans of fix-a-flat (300ml) for $4.77. who has the best price? what is a terminal illness? A.) a way of honoring memories of dead loved ones B.) a series of stages that people go through when dealing with death C.) a condition for which there is no recovery D.) a program that provides care for dying people A cone has a radius of 3.8 m and a slant height of 8.8 m. Which would decrease the cone's surface area less, halving the radius or halving the slant height? The roots of unity (1) may be calculated from the equation x3-1=0. What are they? Companies who reward only success are often innovativesucessfully.Group of answer choicesTrueFalse what angle of incidence is going to get you the most light being transmitted into the water of the pool? 1.In which sentence is the underlined verb in the active voice?A. Before we arrived at home, dinner had been cooked.B. When we got home, dinner was ready.C. As soon as we sat down at the table, dinner was served. What are 4 common themes?. A rigid tank contains 2 kg of an ideal gas at 4 atm and 40C. Now a valve is opened, and half of mass of the gas is allowed to escape. If the final pressure in the tank is 2.2 atm, the final temperature in the tank isA. 44CB. 172CC. 20CD. 71CE. -100C Umbridge Purses Unlimited sells purses with a sales price of $35 each. Each purse costs the company $20 to produce, and the store incurs a total of $300,000 in fixed costs each year. What is the yearly breakeven point in units best answer gets brainliest the uniform resource locator (url) is the address of content placed on the web. T/F If you have a 1000-element balanced binary search tree, what is the maximum number of comparisons that may be needed to find an element in the tree? How is modern democracy different from ancient democracy? What are 3 ways an author develops a theme?. hank is a project manager for the nhy project. his project has a very tight budget with little room for project overruns on costs. he needs to control costs and reduce expenses as much as possible to make the project successful in the organization. on the nhy project, hank is using many contractors that are integrated into the project team. what can hank do to keep project costs down in this scenario?