in each of problems 1 through 4, express the given complex number inpolarform r(cosθ isinθ) = reiθ.

Answers

Answer 1

For each of the problems, we will start by identifying the values of r and θ from the given complex number in rectangular form (a + bi).

1) (1 + i)
r = sqrt(1^2 + 1^2) = sqrt(2)
θ = tan^-1(1/1) = π/4
Therefore, the polar form of (1 + i) is:
sqrt(2) * (cos(π/4) + i sin(π/4)) = sqrt(2) * e^(iπ/4)
2) (-3 + 3i)
r = sqrt((-3)^2 + 3^2) = 3sqrt(2)
θ = tan^-1(3/-3) = -π/4 or 7π/4
Note that we have two possible values for θ because the point (-3, 3) falls in the second and fourth quadrants. We will use the value 7π/4 because it is the standard angle in the fourth quadrant.
Therefore, the polar form of (-3 + 3i) is:
3sqrt(2) * (cos(7π/4) + i sin(7π/4)) = -3sqrt(2) * e^(i7π/4)
3) (-2 - 2i)
r = sqrt((-2)^2 + (-2)^2) = 2sqrt(2)
θ = tan^-1(-2/-2) = π/4
Therefore, the polar form of (-2 - 2i) is:
2sqrt(2) * (cos(π/4) - i sin(π/4)) = 2sqrt(2) * e^(-iπ/4)
4) (4 - 4i)
r = sqrt(4^2 + (-4)^2) = 4sqrt(2)
θ = tan^-1(-4/4) = -π/4 or 7π/4
Again, we have two possible values for θ. We will use 7π/4 because it is the standard angle in the fourth quadrant.
Therefore, the polar form of (4 - 4i) is:
4sqrt(2) * (cos(7π/4) - i sin(7π/4)) = -4sqrt(2) * e^(i7π/4).

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Related Questions

The interior angles of a polygon are; (3x + 30), x, 2x, (x + 20) and 3x. find the value of x

Answers

Answer: 49

Step-by-step explanation:

This polygon has 5 sides, meaning its interior angles add to [tex]180(5-2)=540^{\circ}[/tex].

[tex]3x+30+x+2x+x+20+3x=540\\\\10x+50=540\\\\10x=490\\\\x=49[/tex]

State the transformations being applied to each quadratic function.
a) y = -1/2(x+2)^2+4
b) y= -(x-1)^2-2
c) y=(4x)^2
d) y= 4x^2

Answers

The function transformations are:

The function (a) y = -1/2(x + 2)^2 + 4 is translated to the left by 2 units, reflected across the x-axis, compressed vertically by a factor of 1/2 and translated up by 4 unitsThe function (b) y = -(x - 1)^2 - 2 is translated right by 1 unit, reflected across the x-axis, and translated down by 2 unitsThe function (c) y = (4x)^2 is stretched horizontally by a factor of 1/4The function (d) y = 4x^2 is stretched vertically by a factor of 4

What are transformations?

Transformations involve translating, reflecting, rotating and dilating a function across the coordinate plane

How to determine the transformations?

The parent function of a quadratic function is represented as:

y = x^2

When the function is stretched horizontally by a factor of k, where k is between 0 and 1, we have:

y = (x/k)^2

Assume k = 1/4. we have:

y = (4x)^2

This means that the function (c) y = (4x)^2 is stretched horizontally by a factor of 1/4

When the function is stretched vertically by a factor of k, where k is greater than 1, we have:

y = k(x)^2

Assume k = 4. we have:

y = 4x^2

This means that the function (d) y = 4x^2 is stretched vertically by a factor of 4

Translating the function left is represented as:

y = (x + k)^2

Assume k = 2. we have:

y = (x + 2)^2

Reflecting the function across the x-axis is represented as

y = -(x + 2)^2

When the function is compressed vertically by a factor of k, where k is between 0 and 1, we have:

y = -k(x + 2)^2

Assume k = 1/2. we have:

y = -1/2(x + 2)^2

Translating the function up is represented as:

y = -1/2(x + 2)^2 + k

Assume k = 4. we have:

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

Hence, the function (a) y = -1/2(x + 2)^2 + 4 is translated to the left by 2 units, reflected across the x-axis, compressed vertically by a factor of 1/2 and translated up by 4 units

Translating the function right is represented as:

y = (x - k)^2

Assume k = 1. we have:

y = (x - 1)^2

Reflecting the function across the x-axis is represented as

y = -(x - 1)^2

Translating the function down is represented as:

y = -(x - 1)^2 - k

Assume k = 2. we have:

y = -(x - 1)^2 - 2

Hence, the function (b) y = -(x - 1)^2 - 2 is translated right by 1 unit, reflected across the x-axis, and translated down by 2 units

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Annual starting salaries for college graduates with degrees in business administration are generally expected to be between and . Assume that a confidence interval estimate of the population mean annual starting salary is desired. a. What is the planning value for the population standard deviation

Answers

The planning value for the population standard deviation is 4330.

Given the confidence interval 20000 and 35000.

We have to find the planning value of standard deviation.

Standard deviation is measuring dispersion of data. Uniform probability distribution has two bounds a and b. The standard deviation is given by :

s=[tex]\sqrt{(b-a)^{2}/12 }[/tex].

Annual starting salaries for college graduates be between 20000 and 35000.

It is uniform in the interval so, a=20000, b=35000.

Now we have to just put the values of a and b in the above formula to get the value of standard deviation.

s=[tex]\sqrt{(35000-20000)^{2} /12}[/tex]

=[tex]\sqrt{(15000)^{2} /12}[/tex]

=[tex]\sqrt{225000000/12}[/tex]

=[tex]\sqrt{18750000}[/tex]

=4330

Hence the planning values for the population standard deviation is 4330.

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Question is incomplete as it should includes the confidence interval of $20000 and $35000.

The volume, V, of a cylinder is V=r²h, where r is the
radius of the cylinder and h is the height. Using rounding
to the nearest whole number, which of the following is an
estimate of the volume of a cylinder with a radius of
3.75 inches and height of 6.21 inches?

Answers

Answer:

~87.33 in³

Step-by-step explanation:

All you have to to is pkug the numbers in the formula. You start by doing 3.75 as the r² and you get around 14.06. Then you multiply that by the height (6.21) which gets you around 87.33. I hope this helps!

What is the parameter of interest to compare the proportions from two populations?.

Answers

Answer:

also known as the population parameter of interest the parameter of interest is a practical value that gives you more information about the research sample or population being studied in other words these parameter define the describe the search population

what is parameter answer is given above

The likelihood that a patient with a heart attack dies of the attack is 0.04 (i.e., 4 of 100 die of the attack). Suppose we have 50 patients who suffer a heart attack. What is the probability that all will survive

Answers

The probability solved by binomial distribution that all will survive is 0.8154.

What is Binomial distribution?

When each trial has the same probability of achieving a given value, the number of trials or observations is summarized using the binomial distribution. The likelihood of observing a specific number of successful outcomes in a specific number of trials is determined by the binomial distribution.

Computation of probability of all survived people from heart attack;

A heart attack patient has a 0.04 percent chance of dying from the attack (i.e., 4 of 100 die of the attack).

What is the likelihood that each of the five patients who experience a heart attack will survive?

We'll refer to a victory in this scenario as a heart attack (p = 0.04). In other words, we are interested in the likelihood that none of our n=5 patients will die (0 successes).

Each attack has a chance of being fatal or not, with a probability of 4 percent for all patients, and each patient's result is independent.

Assume for the purposes of this example that the five individuals being examined are unrelated, of the same age, and free of any concomitant disorders.

By binomial distribution,

[tex]\begin{gathered}P(0 \text { successes })=\frac{5 !}{0 !(5-0) !} 0.04^{0}(1-0.04)^{5-0} \\P(0 \text { successes })=\frac{5 !}{5 !}(1)(0.96)^{5}=(1)(1)(0.8154)=0.8154\end{gathered}[/tex]

Therefore, with a 4 % chance that anyone will die, there is an 81.54% chance that every patient will survive the onslaught. The outcomes in this example could be 0, 1, 2, 3, 4 or 5 successes (fatalities).

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I need help on this please!

Answers

Answer:

Step-by-step explanation:

Part A:  

CIRCLE A : Circumference is (pi)(diameter) so if they give you the circumference (21.98), divide it by 7 which gives you 3.14.

CIRCLE B: 18.84/6 = 3.14

Part B:

CIRCLE A: Area is (pi)(radius^2) so if they give you the area (38.465), divide it by radius^2 (7/2 = 3.5^2 = 12.25) = 3.14

CIRCLE B: 28.26/(3^2) = 3.14

Part C:

The value of pi stays the same for circle A and B.

Hope this helps :)

I need help!!! I don't get it.

Answers

The ship's horizontal distance from the lighthouse is 1930.59 feet. Using trigonometric ratio 'tanθ' the distance is calculated.

What are trigonometric ratios?

The trigonometric ratios are used for determining the lengths of the right-angled triangle. There are six basic trigonometric ratios. they are:

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

sec θ = hypotenuse/adjacent

cosec θ = hypotenuse/opposite

cot θ = adjacent/opposite

Calculation:

It is given that,

The height of the bacon-light is 135 feet above the water

Consider the horizontal distance between the boat and the lighthouse = x feet

The angle of elevation is given as 4°

Constructing a model as below in the figure.

From the trigonometric ratios, we have

tan θ = 135/x

⇒ tan 4° = 135/x

⇒ x = 135/tan 4°

∴ x = 1930.589 feet ≅ 1930.59 feet (rounding to the nearest hundredth of a foot)

Therefore, the ship's horizontal distance from the lighthouse is 1930.59 feet.

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URGENT WILL GIVE BRAINLIEST

Answers

Answer:

626.7 [tex]cm^{2}[/tex]

Step-by-step explanation:

Consider the figure as a circle with radius 7.5 and a rectangle with width 30 and length 15.

CIRCLE

A = pi*r*r = pi*7.5*7.5 = 56.25pi =176.7

RECTANGLE

A = l*w = 15*30 = 450

176.7 + 450 = 626.7 [tex]cm^{2}[/tex]

Answer: 626.7cm^2

Step-by-step explanation:

30 * 15 = 450

area of circle = πr^2

r = 15/2 = 7.5

[tex]7.5^2=56.25*pi=176.7[/tex]

450+176.7 = 626.7

Which type of function describes f(x)?
Exponential
Logarithmic
Rational
Polynomial

Answers

Rational, It isn't logarithmic or exponential, because those lines look totally different

A 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 2 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 3 feet from the wall

Answers

Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.                      

Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.

Pythagoras theorem, [tex]x^{2} + y^{2} = (12)^{2}[/tex]       --->(1)

Given,[tex]\frac{dx}{dt}= 2feet/second[/tex]   at x=3

Put x=3 in Pythagoras theorem equation (1)

[tex](3)^{2} + y^{2} = 144[/tex]

         [tex]y^{2} = 144 - 9[/tex]

        [tex]y^{2}[/tex]  =  135

        y = 11.61

Derive equation (1) w.r.t to 't'

[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0[/tex]                ---->(2)

substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall

[tex]2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0[/tex]

12 + 23.22 [tex]\frac{dy}{dt}[/tex]  = 0

                  [tex]\frac{dy}{dt}= \frac{-12}{23.22}[/tex]

                  [tex]\frac{dy}{dt} = -0.518[/tex]

Hence,  using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.  

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65. Find the perimeter & area:
13 cm
5 cm
12 cm
66.

Answers

Given, that the sides of a triangle are [tex]$5 \mathrm{~cm}, 12 \mathrm{~cm}$[/tex] and [tex]$13 \mathrm{~cm}$[/tex] semi-perimeter [tex]$=\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}}{2}$[/tex]

[tex]$$\begin{aligned}&\mathrm{s}=\frac{(5+12+13)}{2} \\&\mathrm{~s}=\frac{30}{2} \\&\mathrm{~s}=15 \mathrm{~cm}\end{aligned}$$[/tex]

Area of the triangle (according to Heron's Formula)

[tex]$$\begin{aligned}&=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})} \\&=\sqrt{15(15-5)(15-12)(15-13)} \\&=\sqrt{15(10)(3)(2)} \\&=\sqrt{900} \\&=30 \mathrm{~cm}^{2}\end{aligned}$$[/tex]

What is  Heron's Formula?

Heron's formula was first given by Heron of Alexandria. It is used to calculate the area of various triangles such as equilateral, isosceles, and scalene triangles or quadrilaterals. When we know the sides of a triangle, we can use Heron's formula to find its area. Using Heron's formula, we find the area of a triangle by taking its semi-perimeter and side lengths.Heron's formula is used to calculate the area of triangles given the lengths of all their sides, as well as the area of quadrilaterals. It's also known as Hero's formula. This formula for calculating the area does not rely on the angles of a triangle. It is solely determined by the lengths of all triangle sides. It contains the term "s," which stands for semi-perimeter, which is obtained by halving a triangle's perimeter. Similarly, the concept of determining the area is extended to determine the area of quadrilaterals.

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A pattern has 77 yellow triangles to every 33 green triangles. What is the ratios of green triangles to yellow triangles?

Answers

For every 33 green triangles, we have 77 yellow triangles.
So using the original ratio 33:77 we can simplify this by dividing both sides by 11 so that we get the ratio 3:7 so for every 3 green triangles we have 7 yellow triangles.

uan recently hired a roofer to do some necessary work. On the final bill, Juan was charged a total of $1131.5. $450 was listed for parts and the rest for labor. If the hourly rate for labor was $47, how many hours of labor was needed to complete the job?

Answers

Based on the total cost that Juan incurred to hire the roofer including the charge for parts and labor, the number of hours that was needed to complete the job was 14.50 hours.

How many hours did the roofer use?

The first thing to do is to find out the amount that went to labor:

= Final bill - cost of materials

= 1,131.5 - 450

= $681.50

Now that you have the cost of labor, you can find out the number of labor hours that were used based on the hourly rate:

= Cost of labor / Hourly rate

Solving gives:

= 681.50 / 47

= 14.5 hours

In conclusion, the number of labor hours that the roofer used to complete the work, based on the total amount charged to Juan is 14.50 hours.

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Which of the following are like terms?
3x and 5x²
4xy and 2x²y
6x and -3x
7x and 7y

Answers

The like terms are 6x and -3x

Quick algebra 1 question for 50 points!

Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!

Answers

Answer:

y is equal to 24

Step-by-step explanation:

If y is directly proportional to x when x is equal to 5 and y is 12, then when you multiply 5 by 2 which is 10, y will be proportional to that when you multiply 12 by 2 which is 24

Answer:

b: 25

Step-by-step explanation:

The previous answer wowwubbzy13 uploaded is absolutely correct!

I'll set up a proportion.

If y = 12, then x = 5

--> 12:5

We want to find the y when x is 10

--> y:10

12:5 = y:10

5y = 120

y = 25

So B: 25 is the correct answer!

What is the value of the discriminant for the quadratic equation zero equals 2x^2+x-3

Answers

Discriminant for the quadratic equation  [tex]2x^2+x-3=0[/tex] is [tex]d=25[/tex]

How to find the d Discriminant of the quadratic equation ?

We know that the standard quadratic equation

[tex]ax^2+bx+c=0[/tex]

Discriminant of the equation is [tex]d=b^2-4ac[/tex]

Equation given in the question is

[tex]2x^2+x-3=0[/tex]

So we can find the values of [tex]a,b,c[/tex]

[tex]a=2\\b=1\\c=-3[/tex]

Substitute the values

[tex]d=1^2-4*2*(-3)\\d=1+24\\d=25[/tex]

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The diameter of a varicocele measures more than _____ millimeters (mm). * 5 points 5 3 4 2

Answers

Answer:

A varicocele measures more than 2 mm in diameter.

Step-by-step explanation:

pampiniform plexus veins measuring more than. 2 mm in diameter at rest and which increased in diameter by 1 mm, and subjective color Doppler.

The graph of the function f(x)=x2+12 is shown which stamen te describe the graph Check all that apply

Answers

I am sorry but I don’t know

Points A and B are 200 miles apart. A cyclist starting at point A and a motorcyclist starting at point B move toward each other. The speed of the cyclist is 17 mph and the speed of the motorcyclist is 83 mph. what distance from point A will they meet.

Answers

Answer:

34 miles from A

Step-by-step explanation:

Find time to cover 200 miles at ( 17 + 83 mph) = 200/100 = 2hours

 cyclist will be at   2 * 17 = 34 miles from A

The combination for opening a safe is a four-digit number made up of different digits. How many different comninations can you make, using only add digits?

Answers

There are 625 different 4-digit codes only made with odd numbers.

How many different combinations can you make?

To find the total number of combinations, we need to find the number of options for each one of the digits.

There are 4 digits, such that each digit can only be an odd number.

For the first digit, there are 5 options {1, 3, 5, 7, 9}For the second digit, there are 5 options {1, 3, 5, 7, 9}For the third digit, there are 5 options {1, 3, 5, 7, 9}For the fourth digit, there are 5 options {1, 3, 5, 7, 9}

The total number of different combinations is given by the product between the numbers of options, so we have:

C = 5*5*5*5 = 625.

There are 625 different 4-digit codes only made with odd numbers.

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A combination lock uses three integers in the combination, and the dial is numbered with the integers 0, 1, 2 and 3. If adjacent numbers in the combination cannot be the same, how many possible combinations are there

Answers

There can be 36 combinations.

How to find the total number of combinations?

The total number of combinations of the dial can be found by using permutations without any number repeating.

There are four integers on the dial. They are 0, 1, 2, and 3.

It is also given that the numbers shouldn't repeat on the adjacent dial.

Therefore, we can say that there are 4 possible numbers on the first.

Similarly, on the second dial, only 3 numbers are possible since no two adjacent dials can have the same.

This is also the case for the third dial. It can also have 3 possible numbers.

Therefore, the total number of combinations is given by 4*3*3 = 36 combinations.

Therefore, we have found that there can be 36 combinations.

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which whole number is equal to the fraction 42/6

Answers

Answer:

7.

Step-by-step explanation:

Think of 42/6 as a division question.

42 ÷ 6.

The answer to this equation is 7.

James and Simon have a reading assignment to complete. James has read r
rr pages, and Simon has read 75 pages. Together they have read a total of 200 pages. Select the equation that matches this situation.
Choose 1 answer:

Answers

Answer:

Step-by-step explanation:

125 I think

Total book=y
rrr+200=y

A bookstore sells books for $2, $3, $5, and $10. Let random variable X = "amount of
money for one book."
Look at the relative-frequency table below representing the amount of money spent on
one item and the relative frequencies with which customers purchase them
If the expected amount of money spent by a customer is $3.23 what is the standard deviation?

Answers

The value of the standard deviation is σ = 2.20. Using probability distribution, the required standard deviation is calculated.

How to calculate the standard deviation?

The formula for the standard deviation of the given probability distribution is

σ = √∑([tex]x_i^2[/tex] × [tex]P(X_i)[/tex]) - μₓ²

Where the mean μₓ = ∑[[tex]x_i[/tex] × [tex]P(X_i)[/tex]]

Calculation:

It is given that,

x: $2, $3, $5, $10

P(X=x): 0.55, 0.26, 0.11, 0.08

Step 1: Calculating the mean:

we have μₓ = ∑[[tex]x_i[/tex] × [tex]P(X_i)[/tex]]

⇒ μₓ = 2 × 0.55 + 3 × 0.26 + 5 × 0.11 + 10 × 0.08

∴ μₓ = 3.23

Step 2: Calculating the standard deviation:

x: 2, 3, 5, 10

x²: 4, 9, 25, 100

P(X=x): 0.55, 0.26, 0.11, 0.08

([tex]x_i^2[/tex]) × [tex]P(X_i)[/tex]: 4 × 0.55 = 2.2; 9 × 0.26 = 2.34; 25 × 0.11 = 2.75; 100 × 0.08 =8

∑[([tex]x_i^2[/tex]) × [tex]P(X_i)[/tex]]: 2.2 + 2.34 + 2.75 + 8 = 15.29

Therefore,

The standard deviation, σ = √∑([tex]x_i^2[/tex] × [tex]P(X_i)[/tex]) - μₓ²

⇒ σ = [tex]\sqrt{15.29-(3.23)^2}[/tex]

      = [tex]\sqrt{15.29-10.43}[/tex]

σ = 2.20

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Quick algebra 1 question for 50 points!

Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the

Answers

Answer:

10 points

Step-by-step explanation:

From the passage, we know:

1. Jay earned 15 points after spending $60

2. We want to know the number of points he can earn if he spends $40

We can set this up into proportions.

60:15 = 40:x

The x is the number of points he will get after spending $40.

15(40) = 60x

600 = 60x

x = 10

Jay will earn 10 points if he uses $40.


[tex] \color{red} \sf Solve \: for \: x : \\ \sf \: \: 4x + 2 = -8?[/tex]





Thank uh !​

Answers

Answer:

x = -5/2

Step-by-step explanation:

4x+2 = -8

We are solving for x

The first step in isolating x is to subtract 2 from each side

4x+2-2 = -8-2

4x = -10

Divide each side by 4

4x/4 = -10/4

x = -10/4

Simplify the fraction

x = -5/2

Answer:

x= -5/2

Step-by-step explanation:

4x+2 = -8

4x = -10

4x/4 = -10/4

x = -5/2

Which geometric solids would model the tent?

cone and sphere
cylinder and cone
pyramid and rectangular prism
triangular prism and rectangular prism

Answers

Triangular prism and rectangular prism

A marble has a mass of 5 grams. juan has 17 marbles in his bag.
what is the total mass of the marbles?
o a. 22 grams
o b. 55 grams
o c. 57 grams
o d. 85 grams

Answers

Answer:

85 grams

Step-by-step explanation:

Marble:  5 g/marble

17 marbles in a bag:  (17 marbles)*(5 g/marble) = 85 grams/bag of 17 marbles

A knight is placed at the origin of the cartesian plane it moves in an L shape what is the expected distance from the origin after 2016 moves

Answers

Answer:

Below in bold.

Step-by-step explanation:

Using the Pythagoras theorem:

Distance from the origin after  1 move = √(1^2 + 2^2) = √5.

So after 2016 distance is 2016√5 units.

This = 4507.9 units to the nearest tenth,

Other Questions
you drive for 30min at 100kmh and then stop for 15 min you then drive for 45 min at 80 kmh your average speed for the entrie trip was Experiments suggest that practicing parts of a discrete task in isolation _______.a. transfer a great deal to the whole taskb. transfers very little to the whole taskc. improves performance on a transfer test of the whole taskd. improves performance on a retention test of the whole task age-associated cognitive changes may relate to alterations in the brain areas that are most responsible for memory, particularly the As recently as a few hundred years ago, most Westerners thought the earth was about how many years old?a.60,000,000b.6,000,000c.60,000d.6,000 part of an exon at a locus has the dna sequence aaagcgtttagc. what mrna would be transcripted from this? tttcgcaaatcg aaagcgtttagc uuucgcaaaucg uuucccaaagcu Predict what would occur if the soil around a legume lacked Rhizobium. Multiple Choice Useable nitrogen would be much less available to the plant. The plant would be free of disease. Water would be less available to the plant. The growth rate of the plant would increase. An electron in a bohr model hydrogen atom jumps from the 2nd energy level to the 4th level. calculate the wavelength of the photon such a jump produces. (e) based on the data, the student claims that the catalyzed reaction has zeroth-order kinetics. do you agree with the students claim? justify your answer. In each of the following situations, explain what is wrong and why.a. The null hypothesis H0: 3 = 0 in a multiple regression involving three explanatory variables implies there is no linear association between x3 and y. TRUE OR FALSE americans with disabilities act (ada) and occupational safety and health administration (osha) regulations are the responsibility of a safety engineer and not a concern of a technology installer. Dot plot 1 is the top plot. Dot plot 2 is the bottom plot.According to the dot plots, which statement is true?ResponsesA. The mode of the data in dot plot 1 is less than the mode of the data in dot plot 2.B. The range of the data in dot plot 1 is less than the range of the data in dot plot 2.C. The median of the data in dot plot 1 is greater than the median of the data in dot plot 2.D. The mean of the data in dot plot 1 is greater than the mean of the data in data plot 2. The earth is approximately spherical, with a diameter of 1.27 x 10 mn. It takes 24.0 hours for the earth to complete one revolution. Part A What is the tangential speed of a point on the surface of the earth, at the equator? Express your answer with the appropriate units. Value Units Submit Request Answer Part B What is the radial acceleration of a point on the surface of the earth, at the equator? Express your answer with the appropriate units. HAR OO? Value Units Qurad = A researcher collated data on Americans leisure time activities. She found the mean number of hours spent watching television each weekday to be 2. 7 hours with a standard deviation of 0. 2 hours. Jonathan believes that his football team buddies watch less television than the average American. He gathered data from 40 football teammates and found the mean to be 2. 3. Which of the following are the correct null and alternate hypotheses? H0: Mu = 2. 7; Ha: Mu less-than 2. 7 H0: Mu not-equals 2. 7; Ha: Mu = 2. 3 H0: Mu = 2. 7; Ha: Mu not-equals 2. 7 H0: Mu = 2. 7; Ha: Mu greater-than-or-equal-to 2. 3. your patient presents with chf and has a potassium level of 5.8. which diuretic do you anticipate being ordered by the provider 1)Find f(23)?(4) for the Taylor series for f(x) centered at 4 iff(x) = \sum_{n=0}^{Infinity}(n+3)(x-4^n)/(n+1)!2)Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that Rn(x) ? 0.]f(x)=\frac{8}{x} a = -2 (THE GREAT GATSBY) "The first pages of chapter one establish contradictions in Nick's point of view. He describeshimself as tolerant and nonjudgmental, he also views himself as morally privileged, having a better senseof "decencies" than most other people" (Sparknotes). Do you agree or disagree with Nick'sHow does the characterization of Nick change in the course of the book?self-characterization? Does anyone know the answer? Mathematics question: A school dedicated 20% of the courtyard area for students to start a garden. The students want to know how much of the 950-square-foot space they will be able to use. a quasi-legislative administrative process of writing regulations is called true or false the filtrate from the glomerulus enters into the distal convoluted tubule. if you were working in the feild of psychoneyroimmuniology, you would be studying