Can you prove this statement using properties of logarithms? Assume all expressions exist
and are well-defined
3 log y z^9= log y z^27

Answers

Answer 1

Answer:

see below

Step-by-step explanation:

what 3 logy z^9 means you need to break it into two pieces, one log y z^9 means to find the exponent of y, and you can think z^9 as a number, and then if we multiple it with 3, which means three logs are summed,(the property of multiplication:3*2 means 2+2+2), thus log + log

has the property that the y is same z^9*z^9*z^9=z^(9+9+9)=z^27


Related Questions

Dr. Dominic Estores has written a prescription for a patient to take a preoperative medication at 2200 on the evening before his scheduled surgery. Using the standard time system, what time should you tell the patient to take his medication?

Answers

Using the conversion from the 24-hour system to the AM/PM system, the patient should take the medicine at 10 PM.

How to convert from 24 hours to AM/PM?

If the hour is between 0 and 11:59, the hour is kept with AM.If the hour is 12, it is PM.If the hour is between 13 and 23:59, the hour the remainder of the division of the hour and 12, PM.

22 divided by 12 has remainder 10, hence 22 is equivalent to 10 PM.

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QUESTION IS DOWN BELOW!

Answers

Answer:

The ratio of the widths is 3:16, the ratio of the volumes is 27:4096, and the ratio of the surface areas is 9:256.

Step-by-step explanation:

In Geometry, you'll learn that when the scale factor of similar figures is a:b, then the ratio of the perimeter is a:b, the ratio of the area is a*a:b*b and the ratio of volume is a*a*a:b*b*b.

Which expression is equivalent to (2x²y) ³?
O 2x¹y4
2x¹2y3
8x¹ y
O 8x¹2y³

Answers

Answer: [tex]8x^6 y^3[/tex]

Step-by-step explanation:

See attached image.

The expression which is equivalent to (2x²y)³ is 8x⁶y³

What is Expression?

An expression is combination of variables, numbers and operators.

The given expression is (2x²y)³

Two times of x square times of y whole to the power of three

We have to find the equivalent expression of the given expression.

Equivalent expressions are expressions that work the same even though they look different.

We have a property that [tex](a^m)^n=a^m^n[/tex]

So (2x²y)³ = 2³x⁶y³

=8x⁶y³

Hence, the expression which is equivalent to (2x²y)³ is 8x⁶y³

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When we graph a line using slope and y-intercept, the first point that you graph is
ALWAYS on_____, and you use _____ to get to the next point.

Answers

Answer:

y=mx+b is the formula starting with b say it is 4 you put a dot on 4  on the y axis m is 1/2 you go up 1 right 2 on the 4 points then do the same on the next point you get then you get your line. hope this helps  

The graph of f(x) was vertically translated down by a value of k to get the function g(x) = 5x + k. What is the value of k?

Answers

The value of k in g(x) = 5^x + k is -7

How to determine the value of k?

The complete question is added as attachment

The functions are given as:

f(x) = 5^x

g(x) = 5^x + k

From the attached graph, we can see that:

f(x) is shifted down by 7 units to form g(x)

This means that:

g(x)= f(x) - 7

This gives

g(x) = 5^x - 7

Substitute g(x) = 5^x - 7 in g(x) = 5^x + k

5^x + k = 5^x - 7

This gives

k = -7

Hence, the value of k in -7

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You are planning a trip to Bermuda but have heard stories of people getting "lost" in the area that forms what is known as the Bermuda Triangle. You are
curious just how big the area that forms the triangle actually is and decide to investigate. You discover that one side length of the triangle is 900 miles and
another sides is 930 miles and the angle between them is 56 degrees. What is the area that the plane can fly and be in the zone known as the Bermuda
Triangle? Round your answer to the nearest mile.

Answers

The area that the plane can fly and be in the zone known as the Bermuda is; 346952 mile²

How to use the area rule to find the area of a triangle?

The area rule states that the area of any triangle is equal to half the product of the lengths of the two sides of the triangle multiplied by the sine of the angle included by the two sides.

Now, from the question, we are give;

Side 1 = 900 miles

Side 2 = 930 miles

Angle between two sides = 56°.

Thus, by the area rule we have;

Area = (1/2) * 900 * 930 * sin 56°

Area = 346952 mile²

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Let v = leftanglebracket 3, negative 2 rightanglebracket. what is the approximate direction angle of v?

Answers

The approximate direction angle of v is 326°

Definition of Direction Angle

A vector's direction angle is the angle formed by the positive x-axis and the vector v. The arctangent of the ratio between the vertical and horizontal components of the vector, v=xi+yj, can be used to determine the direction angle, θ.

What is the direction angle of v?

Let θ be the direction angle of v or the angle mad by v with the horizontal line.

It is given that,

[tex]v = < 3, -2 >[/tex]

We know that,

θ = tan⁻¹([tex]\frac{y}{x}[/tex])

Here, we have y = -2 and x = 3. Hence, we get,

∴ θ = tan⁻¹[tex](\frac{-2}{3})[/tex]

⇒θ = tan⁻¹(0.66)

Hence the direction angle of v = 360 - tan⁻¹(0.66)

≈ 326°

Thus, the approximate direction angle of v is 326°.

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Roller Coaster Crew
Ray and Kelsey have summer internships at an engineering firm. As part of their internship, they get to assist in the planning of a brand new roller coaster. For this assignment, you help Ray and Kelsey as they tackle the math behind some simple curves in the coaster's track.

Part A
The first part of Ray and Kelsey's roller coaster is a curved pattern that can be represented by a polynomial function.
1. Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only. Is there a way for the both of them to be correct? Explain your answer.

2. Kelsey has a list of possible functions. Pick one of the g(x) functions below and then describe to Kelsey the key features of g(x), including the end behavior, y-intercept, and zeros.
g(x) = (x + 2)(x − 1)(x − 2)
g(x) = (x + 3)(x + 2)(x − 3)
g(x) = (x + 2)(x − 2)(x − 3)
g(x) = (x + 5)(x + 2)(x − 5)
g(x) = (x + 7)(x + 1)(x − 1)

3. Create a graph of the polynomial function you selected from Question 2.

Part B
The second part of the new coaster is a parabola.

4. Ray needs help creating the second part of the coaster. Create a unique parabola in the pattern f(x) = (x − a)(x − b). Describe the direction of the parabola and determine the y-intercept and zeros.
5. Create a graph of the polynomial function you created in Question 4.

Part C
6. Now that the curve pieces are determined, use those pieces as sections of a complete coaster. By hand or by using a drawing program, sketch a design of Ray and Kelsey's coaster that includes the shape of the g(x) and f(x) functions that you chose in the Parts A and B. You do not have to include the coordinate plane. You may arrange the functions in any order you choose, but label each section of the graph with the corresponding function for your instructor to view.

Answers

The key features of the function g(x) = (x + 3)(x + 2)(x − 3) are; Maximum Point at g(x) = 6.065; Minimum Point at g(x) = -0.879; 2.593 is the point of inflection

How to identify the features of a Polynomial?

1) The Fundamental Theorem of Algebra states that a polynomial of degree "n" has at most "n" number of complex roots.

Since Kelsey argues the function can have as many as three zeros only, then we can say that Kelsey is correct.

2) The g(x) function that I will choose is;

g(x) = (x + 3)(x + 2)(x − 3)

Expanding this gives us;

g(x) = x³ - x² - 4x + 4

To find the key features which are critical points (maximum, minimum, point of Inflection), we will differentiate g(x) with respect to x to get;

g'(x) = 3x² - 2x - 4 = 0  

Using quadratic formula gives;

x = 1.535  and  Minimum Point; x = -0.869

Thus;

g(1.535)  = -0.879  minimum point

g(-0.869) = 6.065  maximum point

Thus;

Maximum Point occurs at g(x) = 6.065

Minimum Point occurs at g(x) = -0.879

g"(x) = 6x -2

At g"(x) = 0, we will have the point of inflection which is at;

x = 1/3

g(1/3) = 2.593 which is the point of inflection

3) The graph of the Polynomial of the function g(x) = (x + 3)(x + 2)(x − 3) is as attached.

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Joy is going to a sub shop for a sandwich. At the restaurant, she can choose either a roll (R), bread (B), or a wrap (W). There are two meat choices, ham (H) and turkey (T), and 2 kinds of cheese, Swiss (S) and American (A). Before she goes, Joy wants to make a list of her choices. If she chooses one item from each selection, which will be part of her list?

Answers

Answer:

so their are three kinds of breed 2 kinds of meet and 2 kinds of cheese here the list

roll, ham,swiss

roll, turkey,american

roll,ham,american

roll, turkey,swiss

bread, ham,swiss

bread, turkey,american

bread,ham,american

bread, turkey,swiss

wrap, ham,swiss

wrap, turkey,american

wrap,ham,american

wrap, turkey,swiss

Hope This Helps!!!

(a) The coefficient of variation for males is _%
(b) The coefficient of variation for females is _%


(c) Compare the variability of grade point averages of males and females. Choose the correct answer below.
A.
The grade point averages of females and males have the same variation.
B.
The grade point averages of females and males do not vary.
C.
The grade point averages of males are more variable than females.
D.
The grade point averages of females are more variable than males.

Answers

The coefficients of variation shows that D. The grade point averages of females are more variable than males.

How to illustrate the information?

From the complete information, the coefficients of variation for male is 21.3% and the coefficient of variation for female is 25.1%.

In this case, the coefficients of variation shows that the grade point averages of females are more variable than males.

In conclusion, the correct option is D.

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What is the equation of the function represented by this graph?

Answers

Answer:

[tex]\displaystyle g(x) = -(x + 2)(x - 4)[/tex]

Step-by-step explanation:

First, look at the graph to determine whether it opens down or up, which in this case is down, so you insert a negative in front of the expression. Next, locate your x-intercepts [zeros (where the graph insects the x-axis)]. You will see that the graph intersects [tex]\displaystyle [-2, 0][/tex] and [tex]\displaystyle [4, 0],[/tex] so what you do is insert the zeros' OPPOCITES into the equation because according to the vertex equation, [tex]\displaystyle y = A[x - h]^2 + k,[/tex] that negative in front of [tex]\displaystyle h[/tex] gives you the OPPOCITE outcome, so be careful.

I am joyous to assist you at any time.

y = -2 f(3(x - 4)) - 1 Describe this transformation

The graph y = x^3 is compressed vertically by a factor of 1⁄2 , translated 4 units to the right, and translated 5 units upward.
Write the equation of the transformed function.

Answers

The equation of the transformed function is y = 1/2(x - 4)^3 + 5

How to describe the transformation?

The parent function is given as:

y = x^3

When the function is vertically compressed by 1/2, the rule is:

(x, y) ⇒ (x, 1/2y)

So, we have

y = 1/2x^3

When translated 4 units right, we have:

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

When translated 5 units up, we have:

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

Hence, the equation of the transformed function is y = 1/2(x - 4)^3 + 5

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20 people show up to the party and robert decides to give them

Answers

Answer:

This question looks and sounds like a "personal opinion question" to me.

so from my opinion Robert give them a Smack in their ases .

Hope this helps .

Good luck ✅.

The plane 15x − 12y + 20z = 60 is represented by which graph below? Notice the z-axis.

Answers

Answer:

b

Step-by-step explanation:

I did it

0. In 1996 Jabu decides to invest in the Stock Exchange. He buys 1200 shares in a company at R6.75 per share. How much did he pay for the shares?​

Answers

Answer:

[tex]1200\times6.75=R8100[/tex]

gym help

when doing any weighted exercises that involve using all or little of my body weight do i count my body weight and the added weight as my “actual weight lifted”? for example i weigh 150lbs and let’s say i did a single rep of weighted overhand chin ups with a single 20lbs weight wrapped around me and i wanted to track how much “actual weight” i just lifted would i write down and track just the 20lbs or my body weight 150lbs plus the weight 20lbs?

Answers

You should write down and track only the 20lbs weight during your weighted exercise while ignoring your body weight.

What is actual weight?

Actual weight is also referred to as gross weight and it can be defined as the exact (original) weight of an object, as measured using an appropriate weighing scale.

This ultimately implies that, you would write down and track only the 20lbs weight during your weighted exercise such as a single rep of weighted overhand chin ups.

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The voyage of the Mayflower took 8 months and 11 days. Convert the time to days.

Answers

Answer:

If i did it correctly the answer should be 255 days

Step-by-step explanation:

please mark brainliest

Simplify the following expression, and combine like terms: 15x²y - 4(-2xy² - 9xy) + 12xy² - 8xy - 9x ​

Answers

Answer:

15x^2y+20xy^2+28xy-9x

Step-by-step explanation:

15x²y - 4(-2xy² - 9xy) + 12xy² - 8xy - 9x ​

First distribute the -4 to all the terms in the parentheses

15x²y +8xy² + 36xy + 12xy² - 8xy - 9x ​

Now combine like terms

15x²y       +8xy²  + 12xy²      + 36xy - 8xy     - 9x ​

15x^2y+20xy^2+28xy-9x

A coach in a train can seat exactly 72 people for a trip. The train has 12 such coaches. If the train made 156 trips in full capacity this year, how many people has it carried in that time. I will give brain to the first person who answers this question correctly.

Answers

Answer:

134,784 people

Step-by-step explanation:

Hello!

Let's first find the number of people it can carry on 1 trip. We can do this by multiplying the number of people per coach, by the number of coaches.

72 x 12864

The train carries 864 people per trip. We can find the number of people in 156 trips by multiplying 864 by 156.

864 x 156134,784

The train, in full capacity, will carry 134,784 people in 156 trips.

Suppose the theoretical probability of winning a prize at a carnival game is 0.18. Based on this probability how many more customers would you have expected to win a prize

Answers

Answer:

Could you please provide more context to the problem

Step-by-step explanation:

There is not much context provided for us on this problem, but you can set the decimal to a percentage: 18% of customers win a prize. Now to properly solve this question we need to know either the number of people or the percentage of kids and adults.

Whats the correct answer answer asap

Answers

Answer: Temperature
Explanation: There are very dry places in India and some humid too.

A line passes through the point (-2, 8) and has a slope of-5/2.
Write an equation in slope-intercept form for this line.

Answers

Answer:

[tex]y = -\frac{5}{2} x + 3[/tex]

Step-by-step explanation:

We are given that a line passes through (-2, 8) and has a slope of -5/2.

We want to write the equation of this line in slope-intercept form.

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y-intercept.

Since we are already given the slope of this line, we can immediately plug it into the equation.

Replace m with -5/2.

[tex]y = -\frac{5}{2} x+ b[/tex]

Now we need to find b.

As the equation passes through the point (-2, 8), we can use its values to help solve for b.

Substitute -2 as x and 8 as y.

[tex]8 = -\frac{5}{2} (-2) +b[/tex]

Multiply.

8 = 5 + b

Subtract 5 from both sides.

3 = b

Replace b with 3 in the equation.

[tex]y = -\frac{5}{2} x + 3[/tex]

Topic: finding the equation of the line (slope-intercept form)

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Consider a convex hexagon in which all pairs of opposite sides are parallel. Prove that if one pair of opposite sides have equal length, then the other two pairs of opposite sides also have equal length.

Answers

A pair of the opposite sides of a hexagon has equal length and this is proved below.

How to illustrate the hexagon?

It should be noted that a hexagon is a polygon that has six sides.

In this case, it has 6 sides.

The total angles will be:

= (n - 2) × 180

= (6 - 2) × 180

= 720°

Each angle will hence be:

= 720°/6

= 120°

Each angle are equal and this illustrates that the parallel sides are equal.

A diagram is attached to illustrate the pair of parallel sides.

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The auto parts department of an automotive dealership sends out a mean of 4.2 special orders daily. What is the probability that, for any day, the number of special orders sent out will be exactly 3? Round your answer to four decimal places.

Answers

The probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.

What are some of the properties of Poisson distribution?

The Poisson distribution is a discrete probability distribution that describes the likelihood of a specific number of events occurring in a specified span of time or space, if these events occur at a constant mean rate and regardless of the time since the last occurrence.

Let X ~ Pois(λ)

Then we have:

E(X) = λ = Var(X)

Since standard deviation is the square root (positive) of variance,

Thus,

The standard deviation of X = [tex]\sqrt{\lambda}[/tex]

Its probability function is given by

[tex]f(k; λ) = Pr(X = k) = \dfrac{\lambda^{k}e^{-\lambda}}{k!}[/tex]

Given the mean is 4.2.

We have to find the probability that on any day, the number of special orders sent out will be exactly 3. Therefore, the value of x will be 5.

Using the Poisson distribution,

[tex]P(x) = \dfrac{e^{-\lambda}\lambda ^x}{x!}\\\\P(5) =\dfrac{e^{-4.2}(4.2)^5}{5!}\\\\P(5) = 0.1633[/tex]

Hence, the probability that, for any day, the number of special orders sent out will be exactly 3 is 0.1633.

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6 in.
10 in.
15 in.
V = [?] in.³
area of base
Volume of Prism B.h

Answers

Answer:

300

Step-by-step explanation:

A pyramid with a triangle-shaped base whose three triangular faces meet at the ap/ex. The triangular pyramid formula included both the volume and surface area of the pyramid. The triangular pyramid volume formula calculates the base area and the height whereas the surface area of the triangular pyramid calculates the base area, perimeter,, and slant height. Formulas for volume and surface area of the triangular pyramid are given below that are used in the triangular pyramid formula: 

Volume= 1/3 × Base area × Height

Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your
finding to state whether or not the given r represents a significant linear correlation. Use a significance level of
0.05.
r = 0.543, n = 25
A) Critical values: r = +0.487, no significant linear correlation
B) Critical values: r = +0.396, no significant linear correlation
C) Critical values: r = +0.487, significant linear correlation
D) Critical values: r = +0.396, significant linear correlation

Answers

The critical value of r is mathematically given as r = +0.487, with no significant linear correlation. Option A.

What are the critical values of r?

Question Parameters

r = -0.868

n = 5

df = 5 - 2

df = 3

[tex]\alpha / 2 =0.025[/tex]

Critical values [tex]r= \pm 0.878[/tex]

Generally, there exists no linear correlation between the Critical values

as r=0.878

In conclusion,  Critical values: r = +0.487, no significant linear correlation

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Which of the following is not in the domain of tan(x)? Select all correct answers.

Answers

The Domain and Range of tan(x) are mathematically given as

Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]

Range: all Real numbers

What is The Domain and Range of tan(x)?

All real numbers are in the domain of the function "y=tan (x)," with the exception of the value "[tex]\pi/2+\pi n[/tex]" for all integers n, which is the case when cos(x) = 0.

It follows that "[tex]\frac{-3 \pi }{2}[/tex]" is not in the domain of "tan (x)" among the possible values.

In conclusion,

Domain [tex]:{x/x \neq.....\frac{-3\pi}{2}, \frac{-\pi}{2},....}[/tex]

Range: all Real numbers

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Type the correct answer in the box.
The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below.
V = r²h
Write the formula to calculate the height, h.

Answers

Answer:

Cone: h =  [tex]3\frac{V}{\pi r^{2} }[/tex]

Cylinder: h = [tex]\frac{V}{\pi r^{2} }[/tex]

Step-by-step explanation:

- the formula you described is not the formula for the volume of a cone as it is V = [tex]\pi rx^{2} \frac{h}{3}[/tex]

- to find the height you simply rearrange the formula, so the formula to calculate the height of the cone is:

- h =  [tex]3\frac{V}{\pi r^{2} }[/tex]

- based on the formula you described, it is closer to a cylinder and the formula for the volume of a cylinder is: V = [tex]\pi r^{2} h[/tex]

- once again, to find the height you simply rearrange the formula, so the formula to calculate the height of the cone is:

- h = [tex]\frac{V}{\pi r^{2} }[/tex]

hope this helps :)

AM and AN are tangent to circle C. If AM measures 2.5 cm, what is the measure of AN?
M
2.0 cm
O 5.0 cm
O 1.5 cm
2.5 cm
C
A
N

Answers

The measure of AN form the given figure is 2. 5cm. Option D

How to determine the length

It is important to note that if from one external point, two tangents are drawn to a circle then they have equal tangent segments.

We have that,

AM ≅ AN

so, if AM  measures 2. 5cm

AN measures 2. 5cm

Thus, the measure of AN form the given figure is 2. 5cm. Option D

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giving brainliest :)

Answers

Answer:

The last one - 256 people

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As you move from your outline to your draft, make sure that you have done the following things. Check allof the boxes that apply to you.My outline is complete.I am ready to write about what makes each editorial effective.I have a thesis that indicates my viewpoint on what makes the arguments effective.I am prepared to compare and contrast the editorials.I understand the components of a solid argument.DONEOIntro In this line from Thomas pained rights of man what element denotes that it is from the revolutionary era Jenny started a dog walking business at the start of the summer. She spent $10 to make signs for her service and posted them all over her neighborhood. She spent $60 for a leash and a pooper-scooper. She charged $10 per dog and walked 5 dogs per day for 3 months (assume 30 days per month). What was Jenny's profit for her summer gig? If f(n) = n-n, then f(-4) Please help ill give whoever answers the best the brainliest answer :))) Which of the following equations results in infinitely many solutions?9x80 = 8(x + 10)9x + 10- 1x = 8(x + 10)9x + 80 1x = 8(x + 10)9x + 80 1x = 9(x + 10) Hakim walked into his house one summer day and discovered that the air conditioning was not working. He did not get upset because the last time this happened, he found a great repair company that was fast and affordable; he also had a couple of fans that he used to keep cool until the AC was restored. Hakim did not experience excessive stress because Group of answer choices he has a Type A personality. he had a plan in place due to his last experience with the repair company. he has low self-esteem and knew he could not fix the AC himself. his appraisal of the stressor told him he could cope with it. A group of men and women are asked if they prefer summer or winter. The resulting two-way frequency table is shown below. Use the data in the table to find each probability. a. P(woman) b. P(woman or summer) c. P(woman and summer) d. P(woman | summer)women: summer 85 Winter 32Men: summer 70 winter 51 What is the error if I want to assign a value to that same index? i.e. var_str[5] = rPLEASE QUICK Who was the effective politician who compromised to successfully unite Italy and ended up being the new country's first prime minister? Giuseppe Garibaldi Camillo Cavour Giuseppe Mazzini Victor Emmanuel II Please help! Which is the solution set of the following inequality? The due date of a baby isO A calculated guess.Always a fact.O Always accurateO A calculated fact. At the end of paragraph 6, Krakauer mentions the belt fashioned from a strip of blanket. This detail serves to...Select one:a. illustrate how poorly equipped McCandless was for the Alaskan wilderness.b. describe how many personal possessions were left in the bus after McCandless death.c. remind the reader of what McCandless physical condition must have been like before his death.d. contribute to the readers understanding of Krakauers uneasy feeling while in the bus. According to the Theory of Continental Drift, South America and Africa once formed part of a single larger continent called Pangaea that eventually broke apart. Today, the average distance between matching shorelines of South America and Africa is about 8000 km. Measurements indicate that the continents are drifting apart at a speed of about 4.0 cm/year. a. According to these measurements, how long ago did these continents separate? b. What assumptions did you make in order to answer (a)? what are the advantages and disadvantages of being famous? Sometimes, researchers will administer a(n) ________ to participants in the control group to control for the effects that participant expectation might have on the experiment. Why were mortality rates of slaves so high on the slave ships during the "Middle Passage?"Illness-- The conditions on the ships were not suitable for the number of people aboard or their bodily functions.Disease ran rampant among all on board the slave ships of the "Middle Passage."Illness- The mental health of the crew often deteriorated during a long voyage. Hallucinations would occur thatwould lead to mass executions of slaves on board during the "Middle Passage."Illness-- The Africans were not immune to European diseases and would contract the disease when first makingcontact with European slavers at the trade ports in Africa. The disease would manifest itself weeks later duringthe "Middle Passage."OIllness-- The mental health of people locked to a boat for weeks on end often deteriorated and they would jumpoverboard during the "Middle Passage." A comprehensive weight-control program should include a balanced, reduced-kcal diet and _________. Use the table to find the products of the two polynomials. Write your answer indescending order. B) (x2 + x 2)(4x2 8x) Can someone help with these geometry fill in blank questions? Just 9, 10, 11, 12.. its urgent