suppose a number is chosen at random from the set {0,1,2,3,...,501}. what is the probability that the number is a perfect cube? the probability of choosing a perfect cube is

Answers

Answer 1

The probability of choosing a perfect cube is [tex]\frac{7}{502}[/tex] .

According to the question,

Suppose a number is chosen at random from the set {0,1,2,3,...,501}.

Cube of 1=1

Cube of 2=8

Cube of 3=27

Cube of 4=64

Cube of 5=125

Cube of 6 = 216

Cube of 7 = 343

Cube of 8 = 512

So in a set of members {0,1,2,3,... 501}, only 7 numbers are a cube of a natural number: 1,8,27,64,125,216,343.

The probability of selecting cubes in a set of members {0,1,2,3,... 501} is

= [tex]\frac{7}{502}[/tex]

So, the probability is [tex]\frac{7}{502}[/tex] .

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Related Questions

Write an equation of the parabola that satisfies the conditions.
Vertex: (3, 3); y-intercept: (0, -6)

Answers

The equation of the parabola with the given vertex and y-intercept is:

y = -(x - 3)² + 3

How to Write an Equation of a Parabola with a Given Vertex and Y-intercept?

The equation of a parabola in vertex form is given by:

y = a(x - h)² + k

Where (h, k) is the vertex of the parabola, and a is a nonzero constant. To find the equation of the parabola that satisfies the given conditions, we can use the vertex and the y-intercept to find the values of a, h, and k.

The vertex of the parabola is (3, 3), so h = 3 and k = 3. The y-intercept of the parabola is (0, -6), which means that when x = 0, y = -6. Substituting these values into the equation of the parabola, we get:

y = a(x - 3)² + 3

When x = 0, y = -6. Plugging in the value of x and y, we get

-6 = a(0 - 3)² + 3

-6 = 9a + 3

-9 = 9a

a = -1

Therefore, the equation of the parabola that satisfies the given conditions is:

y = -(x - 3)² + 3

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I NEED THE ANSWER ASAP plssss-Solve the following multiplying polynomials question:Cindy wants to buy flooring and baseboards for her office. She needs to know how much to buy. What is the area and perimeter of her office?

Answers

The perimeter of a 500-square-foot square is roughly 89.44 feet.

To calculate the perimeter, we must assume the room is square. We take the square root of the area to calculate the length of one side of a square:

√500 = 22.36 feet

As a result, each side of the square is roughly 22.36 feet long. 

To get the perimeter, multiply the length by four: 

22.36 feet × 4 = 89.44 feet.

This dimension is critical for establishing the quantity of baseboard and flooring required. To make the computation procedure easier, round the measurements to the closest foot. Cindy will be able to evaluate the cost and make an informed buying decision with the aid of this information.

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The question is -

Solve the following multiplying polynomials question: Cindy wants to buy flooring and baseboards for her office. She needs to know how much to buy. What is the perimeter of 500 square feet?

Question

During this same time, the digital print manager tracked the number of visits to the website's

homepage. He found that before launching the new marketing plan, there were 4,800 visits. Over the

course of the next 5 weeks, the number of site visits increased by a factor of 1. 5 each week.

Write an equation to model the relationship between the number of weeks, x, and the number of site

visits, f(x).

Enter the correct answer in the box by replacing the values of a and b.

TT

a а в

sin cos tan sin-'costan-

9

+

o

2 Δ Ο

Σ

U OD

A

yo

>



1

5

2

CSC sec cotlog log in

|

4800(0. 081)

Answers

f(x) = 4800 * 1.5^x is the equation to model the relationship between the number of weeks, x, and the number of site visits.

It is said that the number of visits increased by a factor of 1.5 each week, which means it multiplied by 1.5 every week.

So the equation can be modeled as:

f(x) = 4800 * 1.5^x

Where x is the number of weeks and f(x) is the number of site visits.

Note that this equation is only valid for the number of weeks after the new marketing plan has been launched, since before that the number of visits was 4,800.

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A large container holds 8 gallons of water. It begins leaking at a constant rate. After 32 minutes the container has 6 gallons left. At what rate is the water leaking. Express answer as a positive value. ​

Answers

Answer:

1/16 gallons per minute

Step-by-step explanation:

The water level drops from 8 gallons to 6 gallons in 32 minutes

The volume of water that has leaked is 8 - 6 = 2 gallons

Since this volume of water has leaked in 32 minutes, rate of leak

+ 2/32 = 1/16 gallons per minute

A
Solve for x.
x =
10
x = 4
x = 5
x = 2
10
4
2
E
B
X

Answers

The value for the following image is

X=5

Find the missing length of the figure.






x=
mm

Answers

The measure of the missing length in the figure, found using Pythagorean Theorem is; x = 37 mm

What is Pythagorean Theorem?

Pythagorean Theorem states the relationship between the lengths of the sides of a right triangle. According to Pythagorean Theorem, the sum of the squares of the leg lengths of a right triangle is equivalent to the square of the length of the hypotenuse side.

Please find attached a possible figure in the question, obtained from a similar question posted on the website.

The 13 mm side hypotenuse length of the right triangle on the left  indicates a other leg length of the right triangle can be found using Pythagorean Theorem as follows;

Square of the length of the hypotenuse side = Sum of the square of the length of the other two sides

13² = 5² + (second leg length)²

The second leg length of the right triangle on the left = √(13² - 5²) = 12

The 12 mm leg length of the right triangle on the left indicates that the leg length of the right triangle on the right which correspond with the 12 mm leg length on the left is 12 mm

The length of the hypotenuse of the right triangle on the right, which is the missing length, x is therefore;

x² = 12² + 35² = 1369

The measure of the missing length x is therefore;

x = √(1369) = 37

The missing length in the figure is; x = 37 mm

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A right rectangular prism measures 12 cm tall, 8 cm long, and 5 cm wide.

A manufacturer would like to double the surface area of this prism. What should be the height of the new prism so that its surface area is doubled?

Enter your answer, to the nearest tenth, in the box.


cm

Answers

Answer:

24

Step-by-step explanation:

12*8*5 =480 current surface

double = 960

so make the 12 into 24 height.

done

of 4
Workers in an office of 40 staff were asked their favourite type of take-away.
The results are summarised in the table.
Take-away
Pizza
Curry
Fish & chips
Kebab
Other
What fraction of a person is one degree?
Give your answer in its simplest form.
Frequency
4
4
8
5
19
Angle
a
b
C
d
e

Answers

Workers in an office of 40 staff were asked their favourite type of take- away.1/9 bit of a person is one degree.

What's Fraction?

An element of a total is a bit. The number is represented mathematically as a quotient, where the numerator and denominator are resolve. Both are integers in a simple bit. A bit appears in the numerator or denominator of a complex bit. The numerator of a proper bit is lower than the denominator.

The magnitude of an angle is measured using a unit of dimension. In magnitude, 1 degree is original to1/360 of a full gyration.

Degree 1 – direct.

Degree 2 – quadratic.

Degree 3 – boxy.

Degree 4 – quartic( or, if all terms have indeed degree, biquadratic)

Given that;

total workers = 40

Bit of a person = 1 degree

we know that 360 ° = 40 person

so for 1 degree = 40/360 = 1/9

Hence,1/9 bit of a person is one degree.

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nine percent of americans have rh-negative o blood type. in a random sample of 200 americans, what is the probability that the sample proportion with rh-negative o blood types will be less than 12% (round off to second decimal place)?

Answers

The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.

According to the question,

91 pts nine percent of Americans have rh-negative o blood type.

In a random sample of 200 Americans, what is the probability that the sample proportion with rh-negative o blood types will be less than 12% = ?

by Using central limit theorem,

P(p cap < p) = P(Z<p cap-p/√p(1-p)/n)

so,

P(p cap < 0.12) = P(Z<0.12-0.09/√(0.09×0.91/200)

= P(Z<1.4825)

= 0.9309 (from Z table)

= 0.93 (Rounded to second decimal place)

so, The probability that the sample proportion with rh-negative o blood types will be less than 12% is 0.93.

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Question 9 (2 points)

Lily threw a ball. The balls equation that demonstrated its height and velocity is:


h(x) = -16x² + 3x + 35


What was the initial height that she threw the ball from?

Answers

The initial height of the ball is the y-intercept of the function. The initial height she threw the ball from was 35.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient, and 'c' is called the absolute term of f (x).

The function is as follows:

h(x) = -16x² + 3x + 35

Substitute the value of x = 0.

So, we have:

h(0) = -16(0)² + 3(0) + 35

Evaluate the exponent

h(0) = -16(0) + 3(0) + 35

Evaluate the products

h(0) = 0 + 0 + 35

Evaluate the sum

h(0) = 35

Hence, the initial height she threw the ball from was 35.

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Write two expressions (with at least two terms each) that when added together have a sum of -4n + 6.


(Please answer immediately, worth 25 points and i'll mark brainliest)

Answers

The two expressions that add to get a sum of - n + 6 are

A. (-6n) + (6 + 2n) and

B. (- 10n + 2) + (6n + 4)

Now, According to the question:

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

The expression is :

-4n + 6

Now the expression as

A. (-6n) + (6 + 2n)

After adding, we have;

(-6n) + (6 + 2n) = -6n + 6 + 2n

= - 4n + 6

B. (- 10n + 2) + (6n + 4)

After adding we have;

(- 10n + 2) + (6n + 4) = - 10n + 2 + 6n + 4

= - 4n + 6

Hence, The two expressions that add to get a sum of - n + 6 are A. (-6n) + (6 + 2n) and B. (- 10n + 2) + (6n + 4)

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What do i put in the boxes ?…

Answers

The quotient of the expression 76 ÷ 6 is, 4

What is Division method?

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

⇒ 76 ÷ 6

Now, By using division calculation, we get;

   | 10     | 2   |

   |         |       |  4

6  | 60   | 16   |

   _________

Thus, We get;

The quotient of the expression 76 ÷ 6 is, 4

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PLEASE HELP!!!
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
A pyramid has a regular hexagonal base with side lengths of 4 and a slant height of 6. Find the total area of the pyramid.
T. A. =

Answers

The total area of the pyramid is (24√3 + 72) square units or 113.57 square units.

What is a hexagonal pyramid?

A hexagonal pyramid is a 3D design in which the base is hexagonal and the faces or sides are isosceles triangles, which come together to form the hexagonal pyramid at the summit of the pyramid. A hexagonal pyramid has six sides on the base and six isosceles triangles on the sides.

Given a hexagonal pyramid,

base length = 4

slant height = 6

area of pyramid = sum of the area of the base to the lateral area

area of pyramid = A(base) + A(lateral)

Area of base = 3√3/2*(a²)

a = base length = 4

Area of base = 3√3/2*(4²)

Area of base = 24√3 square units

now lateral area or area of triangular faces,

lateral area = 6*1/2*b*h

h = height of triangle = 6

b = base of triangle = 4

lateral area = 6*1/2*4*6

lateral area = 72 square units

total area =  A(base) + A(lateral)

total area = (24√3 + 72) square units

Total area = 113.57 square units.

Hence the area of the pyramid is (24√3 + 72) square units or 113.57 square units.

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How is solving a compound inequality in compact form similar to solving a simple inequality? How is it different?

Answers

The similarity between solving a compound inequality in a compact form and solving a simple inequality is that the same basic ways of resolving an algebra are followed in both cases. The difference is that any manipulation on one side of the equation must be repeated on all three sides of the compound inequality.

What are the similarities and differences?

The similarity between solving a compound inequality and a simple one is that they both follow the same basic principles of solving an algebra.

However, there is a slight difference because any change that is applied in one part of the expression must be spread to other parts of the expression.  If we are dividing or multiplying in compound inequalities, the same must apply to all sides.

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A heat source generates heat at a rate of 70. 0 W (1 W = 1J/s). How much entropy does this produce per hour in the

surroundings at 28. 5 °C? Assume the heat transfer is reversible.

Answers

The entropy produced by the heat source is 2.17 J/K per hour.

In order to calculate the amount of entropy produced by a heat source, we need to use the formula for entropy change: ΔS = Q/T,

where Q is the amount of heat transferred and T is the temperature of the surroundings in kelvins.

To convert the temperature to Kelvin, we add 273.15 to the temperature in degrees Celsius.

In this case, the heat source generates 70.0 W of heat and the temperature of the surroundings is 28.5 °C.

So, to find the entropy change per hour, we need to multiply the power generated by the time:

ΔS = (70.0 W) * (3600 s/h) / (28.5+273.15)

This calculation results in approximately 2.17 J/K * h or 2.17 J/K per hour.

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Can someone help me asap please?

Answers

By Interception of a point f(x) = 3.75b + 25 and this we get the Value 3.75.

How do you find the interception of a point?A line's x-intercept and y-intercept are the points at which the x- and y-axes cross, respectively.In order to locate the point or points of intersection, we must solve the equation f(x) = g. (x). We shall learn the x value(s) of the intersection point(s) from the solution of this equation. Once we have determined the value for x, we may use it to solve one of the original equations to determine the value of y.

Examples :

f(x) = 3.75b + 25

Axis interception points of 3.75b + 25:

X intercepts:(-20 / 3,0),

Y intercepts : (0.25)

Slope of 3.75b + 25: 3.75.

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Can someone please help me with this please please thank you

Answers

Answer: Keith on top, Patricia below Keith, Jim below Patricia, and Sara at the bottom.

1/2x + 3 = 4
What does x equal?

Answers

1/2x + 3 = 4|-3
1/2x = 1|•2
x = 2

determine the value of the f(-3) for the function

Answers

Answer: Undefined

Step-by-step explanation:

[tex]\displaystyle\\x=-3\ \ \ \ \Rightarrow\\\\f(x)=\frac{3x+9}{x^3+4x^2+x-6} \\\\\\f(-3)=\frac{3(-3)+9}{(-3)^3+4(-3)^2+(-3)-6}\\\\\\f(-3)=\frac{-9+9}{-27+4(9)-3-6} \\\\\\f(-3)=\frac{0}{-36+36} \\\\\\f(-3)=\frac{0}{0}\\\\\\\\[/tex]

write an equation:

an addition equation with one variable that has a solution of 3

Answers

Answer:

x + 5 = 8

Step-by-step explanation:

x + 5 = 8

Subtract 5 from both sides.

x + 5 - 5 = 8 - 3

x = 3

Answer: x+5=8

Step-by-step explanation:

Given V=4ti-6tj find the Integral of the magnitude over the bounds [-2,2]?​

Answers

The integral of the magnitude of a given vector is 0.

What is vector ?

Vector can be defined as the object  in which it has both magnitude and direction.

Given

vector ,  V=4t i-6t j

we have to find the Integral of the magnitude over the bounds [-2,2]

So, Lets integrate the given vector

we get,

-[tex]\int\limits^2_2 { v dt } \, dx[/tex]    =

|v| =   √4t^2 + (-6t)^2

=  √16t^2 + 36t^2

= √52t^2

=  2√13 t

-[tex]\int\limits^2_2 {2\sqrt{13}t } \, dt[/tex]  =   2√13 t^2 / 2

when we integrate t , we get t = t^2 / 2

= √13 t^2  

=√13 (2^2 - (-2)^2 )

=√13 (4 - 4 )

= 0

Hence, The integral of the magnitude of a given vector is 0.

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David knows a phone call to a friend costs 25 cents for the first 3 minutes and 10 cents for additional minute. Write a liner equation and calculate how long does he make a phone call if he spends $10


PLEASE HELP

Answers

If David spends $10, he may call for 50 minutes.

As per the data given in the above question are as bellow,

Let x represent the duration of David's phone calls.

The following linear equation can be used to express the call's cost:

Price = x + (x - 3) (0.10)

By setting the equation's value to 10 and finding the value of x, we can determine how long David will talk on the phone if he spends $10:

10 = 0.25x + (x-3)(0.10) (0.10)

The right side of the equation is first made simpler:

10 = 0.25x + 0.10x - 0.30

Next, we may combine related words as follows: 10 = 0.35x - 0.30

10 plus 0.30 equals 0.35x when applied to both sides.

Consequently, x = 50. David talks on the phone for 50 minutes.

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simplify. 1.4x−5x+4−x+3 Enter your answer by filling in the boxes. Use decimal form when necessary.

Answers

1.4x-5x+4-x+3= -4.6x+7

is the system linear or non-linear? you need to justify your answer. b) is the system time-varying or time-invariant? you need to justify your answer. c) is the system causal or not causal? you need to justify your answer. d) find the impulse response function of the system

Answers

The given system is :

a) Linear

b) Time-invariant

c) Casual

d) Impulse response function is h(n) = 2δ(n-1) + δ(n-2).

a) Linear: A system is considered linear if it satisfies the superposition principle, meaning that if the inputs x1(n) and x2(n) produce outputs y1(n) and y2(n), respectively, then the output of the system to a weighted sum of inputs is equal to the weighted sum of the outputs. In this system, 2x(n-1) and x(2n) are both linear operations, and the sum of two linear operations is also a linear operation. Therefore, this system is linear.

b) Time-invariant: A system is considered time-invariant if the output is not dependent on the current time, but only on the input and its previous values. In this system, the coefficients 2 and 1 do not change with time, and the system does not depend on the current time. Therefore, this system is time-invariant.

c) Causal: A system is considered causal if the output only depends on the present and past inputs, and not on future inputs. In this system, x(2n) only depends on the past and present inputs, and x(n-1) only depends on past inputs. Therefore, this system is causal.

d) Impulse response function: The impulse response function of the system can be found by taking the unit impulse as the input, solving for the output and normalizing it.

h(n) = 2δ(n-1) + δ(n-2)

where δ(n) is the unit impulse function and h(n) is the impulse response function of the system.

Correct Question :

y(n) = 2x(n-1) + x(2n). is the system linear or non-linear? you need to justify your answer. b) is the system time-varying or time-invariant? you need to justify your answer. c) is the system causal or not causal? you need to justify your answer. d) find the impulse response function of the system

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Please help me with my math homework! It’s due soon!

Answers

Answer:

The slope of the line is -2.

Step-by-step explanation:

Rise/Run

you have 2 points on the graph since this is a negative slope you start on the top point

you count straight down up to your next point and you should get 8.

then you count to the right to your next point and should get 4.

that would give you 8/4 as your slope.

8/4 simplified is 2.

The slope is 2

Determine the domain of the graph

Answers

Answer:

x [tex]\geq[/tex] -2

Step-by-step explanation:

The domain is all the possible numbers that x can be.

A rectangular pyramid has a length of 7 cm and a width of 9 cm. Its volume is 231 cubic centimeters. Use the formula for the volume of a pyramid to calculate the height of this pyramid. Show all your work. (PLEASE HELP ME)

Answers

Answer:

h = 11cm

Step-by-step explanation:

Rectangular pyramid formula:

[tex] \frac{lwh}{3} [/tex]

therefore

[tex]\frac{7 \times 9 \times h}{3} = 231[/tex]

simplify 7x9=63, then multiply the equation by 3

[tex]63h = 693[/tex]

now divide by 63

[tex]h = 11cm[/tex]

h=11cm

This question has two parts. First, answer Part A. Then, answer Part B.
Part A
Select the correct choices to complete the sentence.
TICKETS Jamal has $40 to buy tickets to a performance for himself and his friends. If he buys a $10 membership, he can buy tickets for $5 each. How many tickets can he buy while remaining within his budget?

Part A

If x represents the number tickets Jamal purchases, write an inequality that represents the situation.

, 1 of 4.
Select Choice
+, 2 of 4.
Select Choice
x , 3 of 4.
Select Choice
, 4 of 4.
Select Choice

Part B
Select the correct choices to complete the sentence.
Part B

Solve the inequality.

x , 1 of 2.
Select Choice
, 2 of 2.
Select Choice

Answers

Within his budget, he can still purchase 6 tickets. The inequality is 40 < 5x + 10.

Unitary method: what is it?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

In light of the query

With his $40, Jamal may get tickets for himself, his friends, and a show.

If he spends $10 to join a membership,

Money remaining = $40 - $10 = $30

Now he may purchase the ticket at $5 apiece.

Now, tickets that he may purchase while staying within his budget found using utilizing the unitary technique.

Tickets= $30 / $5

Tickets = 6

As a result, he may purchase the remaining 6 tickets for his budget.

A:

Number of tickets = x

Hence, the inequality is 40 < 5x + 10.

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The equation represents length Y of Ben and jada's hair in inches after X months which ordered pair (0,0) (4,7) or (4,8)is a solution to the system will their hair ever be the same length explained

Answers

(4, 7) is a solution to the system, will their hair ever be the same length.

What is linear equation?

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

The equation represents length y of Ben and Jada's hair in inches after x months.

And we have equations,

Ben : y = 3/4(x) + 4

Jada : y = 1/4(x) + 6.

Substituting the values of ordered pair,

when x = 0 then y = 0

we get,

Ben : y =  4

Jada : y = 6.

But not equals to y = 0.

When x = 4 then y = 8

we get,

Ben : y =  7

Jada : y = 7.

But not equals to y = 8.

When x = 4 then y = 7

we get,

Ben : y =  7

Jada : y = 7.

This is required solution.

Therefore, (4,7) is a solution.

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Help Me Please!!!!!
Homework!

Answers

A graph of the solution of this inequality w ≤ 200 is shown in the image attached below.

How to graph the inequality?

In this exercise, we would solve the given inequality by making w the subject of formula as follows;

w/-10 ≤ -20

By multiplying both sides of the inequality by -10, we have the following:

-10 × w/-10 ≤ -20 × -10

w ≤ 200

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle on the number line (graph) is closed because of the less than or equal to (≤) symbol.

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Other Questions
does sound travel faster in warm air or in cold air? in humid air or dry air? which of the following was not associated with the earthquakes in japan in 2011 and chile 1960? responses the earthquakes caused tsunamis that traveled across the pacific ocean. the earthquakes caused tsunamis that traveled across the pacific ocean. the earthquakes caused property damage and loss of life. the earthquakes caused property damage and loss of life. the earthquake waves went through earth's interior the earthquake waves went through earth's interior all of the above are true and associated with these two earthquakes Type the correct answer in each box. Lmk! what are examples of potential security breaches that would need to be referred to the local spec territory office? a. loss of computer containing personally identifiable information (pii) b. loss of computer bag containing tax returns c. loss of taxpayer information d. all of the above Question 3Which of the following questions collect nominal qualitative data? Select all that apply.O Did anyone recommend our restaurant to you today?O How likely are you to recommend this restaurant to a friend?O Is this your first time dining at this restaurant?O Have you heard of our frequent diner program? Organisms are classified today using the Linnaean system, and the following table shows the taxonomic classification of two marine organisms living along the Pacific Coast. Taxonomic Classification, Common dolphin, Killer whale, Animalia, Animalia, Chordata, Chordata, Vertebrata, Vertebrata, Mammalia, Mammalia, Cetacea, Cetacea, Delphinidae, Delphinidae, Delphinus, Orcinus, delphis, orca, Taxonomic classification is important to marine biologists because it provides a way to - if i have all as for my mid year report, can i get in regular decision after getting deferred from gt? 8. If you had to choose between defending the statement: "adaptations are given to organisms", or the statement: "adaptations are earned by organisms", which one would you choose to defend and why? listen to exam instructions you have just purchased a used laptop, and you want to configure it to hibernate when you press the power button. you edit the power options settings and enable hibernation. then you configure the power button to trigger hibernation. everything works fine for several weeks. one day, when you press the power button, the laptop does not hibernate. which of the following will best resolve this issue? a client with dementia is admitted with a fractured hip after a fall at home. four hours after admission, the client's blood pressure increases to a moderately severe hypertensive level and the client pulls on the bedclothes continuously. which inference would the nurse make as the basis for an intervention? a bullet is fired straight up and takes 14.8 s to reach its peak. determine how high the bullet goes and its initial velocity (magnitude In within-subject experiments, each subject's performance is compared with his or her performance during a ______. 2. Which statement correctly applies the theory of natural selection to giraffes?Giraffes wrap their bodies around their offspring, ultimately resulting in their limbs growing longer, and they pass along that trait to offspring.Giraffes born with longer necks can get more food, survive longer, and reproduce, and they pass along that trait to offspring.Giraffes born with longer necks more easily attract a mate, resulting in them reproducing and passing along their traits to offspring.Giraffes constantly lift their heads to reach leaves on trees, ultimately resulting in their necks growing, and they pass along that trait to offspring. The dominant allele for dimples is D. What genetic condition does an individual with the alleles dd have? Classify each function as a power function, root function, polynomial (state its degree), rational function, algebraic function, trigonometric function, exponential function, or logarithmic function:y = (pie)x Power Functiony = xy Exponential Functiony = x2(2-x3) Polynomial (degree of 2)y = tan t cos t Trigonometricy = s / 1+s Algebraic Functiony = sqrt(x3 1) / 1+ 3sqrt(x) Root FunctionNot sure on these. Thanks! Question 3 (2 points)Lauren deposited $300 to start her savings account. After one year, she had $312 inher account. If she did not deposit or withdraw any money that year, how muchinterest did she earn?A 6. Insert < >, or = to make the sentence true. (1 point)3/4 ? 4/7O>O flor in English? what is that word? Imagine you are a team leader at a mid-sized communications company. One of your fellow team leaders is considering setting up a cloud computing system for their team to store and share files. They have begun to question the wisdom of this move, as someone has told them that security might be an issue. Security concerns aside, what would you say in order to convince them that cloud computing is a good idea? Mention at least three advantages that would benefit their team 1. Based on the Data Table, what mass of magnesium is contained in your compound? Show all calculations.31.634 31.064 = 0.572. Based on the Data Table, what mass of oxygen is contained in your compound? Show all calculations.3. Compare the mass of the Mg ribbon with the mass of the magnesium oxide. How can you account for the change in mass between the two?4. Now that you have the mass of magnesium and oxygen in your compound, you can find moles of each element in the compound and you can determine your experimental empirical formula. Show all calculations and your empirical formula below.5. What is the known formula for magnesium oxide? Compare the known formula to the empirical formula you determined in question 4. Are they the same or no?