Solve the quadratic equation x2+8x−30=0 by completing the square.
What are the solutions to the quadratic equation, if any?

x=4±46−−√
This equation has no real solutions.
x=4±34−−√
x=±46−−√

Answers

Answer 1

Answer:

               [tex]\bold{x=-4\pm\sqrt{46}}[/tex]

Step-by-step explanation:

[tex](a+b)^2=a^2+2ab+b^2\\\\\\x^2+8x-30=0\\\\\underbrace{x^2+2\cdot x\cdot 4+4^2}-4^2-30=0\\\\{}\qquad(x+4)^2\,-\,16-30=0\\\\{}\qquad\ \ (x+4)^2=46\\\\ {}\qquad\ \ x+4=\pm\sqrt{46}\\\\ {}\qquad\ \ x=-4\pm\sqrt{46}[/tex]

Answer 2

The solution to the quadratic equation by completing the square will be

x = -4 ± √46. The correct option is A.

What is a quadratic equation?

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The given equation will be solved as below:-

x² + 8x − 30 = 0

Completing the square for the above equation.

( x + 4 )² - 16 - 30 = 0

( x + 4 )² = 46

x + 4 = ±√46

x = ±√46 - 4

Therefore, the solution to the quadratic equation by completing the square will be x = -4 ± √46. The correct option is A.

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Related Questions

Does this graph show a function?

Answers

Answer:

I think that is is C

Step-by-step explanation:

The Vertical Line Test determines whether or not a curve on the graph is a function. This one passes the vertical line test because no vertical line can intersect the curve more than once. I hope that helps!

Which of the sets of ordered pairs represents a function?

A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}

B = {(4, 2), (3, −2), (9, 4), (11, −3)}

Only A
Only B
Both A and B
Neither A nor B

Answers

Answer:

Both A and B

Step-by-step explanation:

A set of ordered pairs is not a function if there is a repeating output (Y value.)

Y values of A= 5, 2, -2, -5.

Y values of B= 2, -2, 4, -3.

There are no repeating outputs.

A music website claims the mean length of their songs is 3.75 minutes. Suppose the length of songs from this website follows a Normal distribution with standard deviation 0.5 minutes. If 7 songs from this website are randomly selected, then there is about a 90% probability that the sample mean will fall in which interval

Answers

The confidence interval is from 3.44 to 4.06 minutes.

According to the statement

we have given that the mean length of songs is 3.75 minutes and standard deviation 0.5 minutes and the sample size n is 7. and the confidence interval is 90%

and we have to find the mean interval.

So, We know that the

A confidence interval is defined as the range of values that we observe in our sample and for which we expect to find the value that accurately reflects the population.

And A margin of error is a statistical measurement that accounts for the difference between actual and projected results in a random survey sample.

We know that the z value for 90% confidence interval is 1.64.

so, The formula to calculate margin of error is

MOE = Z*standard deviation/ (n)^1/2

put the values in it

MOE = Z*standard deviation/ (n)^1/2

MOE = 1.64*0.5/ (7)^1/2

MOE = 1.64*0.189

MOE = 0.310

And to find the interval the formula is

Confidence interval = sample mean ± margin of error

Confidence interval = 3.75 ± 0.310

Confidence interval = (4.06,3.44)

So, The confidence interval is from 3.44 to 4.06 minutes.

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if the coordinate of p and t are -6 and 4 respectively, what it the length of segment pt?

Answers

The length of the segment [tex]pt[/tex]is [tex]10[/tex] if the coordinates of [tex]p[/tex] and [tex]t[/tex] is [tex](-6 )and( 4)[/tex]

How can find the length of the segment ?

The coordinate of [tex]p=-6[/tex]

The coordinate of [tex]t=4[/tex]

We can assume only [tex]x[/tex] coordinates given and [tex]y[/tex] coordinates is [tex]0[/tex]

so coordinate of [tex]p=(-6,0)\\[/tex]

And coordinate of [tex]t=(4,0)[/tex]

So the length of the segment

[tex]pt=x_{2} -x_{1} \\pt=4-(-6)\\pt=4+6\\pt=10[/tex]

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lines L, R, and S are coplanar. Suppose L is perpendicular to R and R is perpendicular to S. Is L perpendicular to S? Explain.

Answers

Answer:

No, L and S are parallel.

Step-by-step explanation:

Perpendicular lines go directly opposite from each other, making a + looking arrangement. While parallel lines go in the exact same direction, making a = looking arrangement. The only way both S and L can both be perpendicular to R is if they are both parallel to each other. An illustration by yours truly is placed below to represent it visually.

                    L                                              |

_______________________________|_____

                                                                    |

                                                                    |

                                                                    |   R

                                                                    |

_______________________________|_____

                     S                                             |  

                                                                    |

Now, if this were on the outside of a sphere, then it would be totally possible to have three lines all be parallel, because they can curve with the sides of the sphere and create a triangle with all right angles.

A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters.

Answers

The area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].

What is an area of a triangle?

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h. As a result, in order to calculate the area of a triangular polygon, we must first determine its base (b) and height (h).

To find the area of the plate covered by the napkin:

Given :

A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate.The napkin has a perimeter of 38 centimeters.

The following steps can be used in order to determine the area of the plate covered by the napkin:

Step 1 - The formula of the perimeter of a triangle is given below:

P = a + b + c   --- (1)

where a, b, and c are the length of the sides of the triangle.

Step 2 - According to the given data, the triangle is isosceles.

Therefore, the two sides are similar and the length of the base is 8 cm.

Step 3 - Now, substitute the values of the known terms in the above formula.

38 = 2L + 8

38 - 8 = 2L

L = 15 cm

Step 4 - The area of the plate covered by the napkin is given below:

[tex]A=\frac{1}{2} * 15 * 15 *Sin30[/tex]

Step 5 - Simplify the above expression.

[tex]A=56.25cm^{2}[/tex]

Rounding off to the nearest whole number, which is [tex]56cm^{2}[/tex].

Therefore, the area of the plate covered by the napkin is (C) [tex]56cm^{2}[/tex].

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The question you are looking for is here:

A napkin is folded into an isosceles triangle, triangle ABC, and placed on a plate, as shown. The napkin has a perimeter of 38 centimeters. To the nearest square centimeter, how many square centimeters of the plate is covered by the napkin?

(A) 16 square centimeters

(B) 30 square centimeters

(C) 56 square centimeters

(D) 60 square centimeters

A bookmark has an area of 18 cm the perimeter is 22 cm what are the dimensions of the bookmark

Answers

Answer:369

Step-by-step explanation:

all you have to do is multiply 18 and 22 its easy

18 x 22 = 369.

Give the perimeter and the area of a square with sides that measure 9 cm.

Answers

Answer:

Perimeter = 36

Area = 81

Step-by-step explanation:

Perimeter of a square is side length * 4.

9*4 = 36

Area of a square is L*L,

9*9 = 81

What is the domain of the quadratic function graphed below?

Answers

The domain of the graph is the set of all real values

How to determine the domain?

The domain is the set of x values of the graph

From the graph, the x values extend in both directions without end

This means that the x values can accommodate all real values

Hence, the domain of the graph is the set of all real values

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A helicopter is flying from Hong Kong to Jakarta. The latitude of Jakarta is -6.20°, and its longitude is 106.80°. The latitude of Hong Kong is 22.27°, and its longitude is 114.15°. What is the helicopter’s net change in latitude and longitude as it travels from Hong Kong to Jakarta?

Answers

The net Change in latitude and longitude of the helicopter are; 28.47 and 7.35 respectively.

What is the net Change in latitude and longitude of the helicopter?

The net change in latitude of the helicopter can be evaluated as follows;

x = |-6.20° - 22.27°| = |-28.47°|

x = 28.47°

The net change in longitude of the helicopter can be evaluated similarly as follows;

y = |106.80° - 114.15°| = |-7.35°|

x= 7.35°

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If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?

Answers

Haven worked on an externship in a prosecutor’s office, the legal support position which you would be best suited for is: paralegal.

What is paralegal?

Paralegal can be defined as a person who has been trained in subsidiary legal matters (issues), but not fully qualified to act as an attorney or lawyer.

In this context, we can infer and logically deduce that paralegal is a legal support position which you would be best suited for a person who has worked on an externship in a prosecutor’s office.

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Complete Question:

If you had worked on an externship in a prosecutor’s office, and then you moved to another state, which of these legal support positions would be best suited for?

mediator

paralegal

legal secretary

court reporter

I need helppppp for this question

Answers

Answer:

too small

Step-by-step explanation:

PLEASE HELP HURRY!!!!!
Jerry makes coffee tables to sell in a furniture shop. The length of each table is n+8 and the width is 1/2n - 4 inches. If n=42, what are the measurements of the length and width of each coffee table?

Answers

Answer:

Length= 50

Width=17

Step-by-step explanation:

length= n+8

Since n= 42, Just plug it in. So it would be 42+8 which is 50 for the length

Widith: 1/2n-4

basically since N is given for 42, you do 1/2 multipied by 42 which is 21.

Since you also have to subtract 4 inches it would be 17 for the length

Mamadou drove 168 miles in 8 hours. If he continued at the same rate, how long
would it take to travel 126 miles?

Answers

With the given rate Mamadou will take 6 hours to travel 126 miles.

What is Unitary method ?

In order to solve a problem for two different values of a quantity, its unit value is first derived. This method is known as unitary method.

Given that,

The distance travelled in 8 hours is 168 miles.

In order to calculate time for 126 miles, unitary method can be used as,

The time for 168 miles is 8 hours.

Then, the time for 1 mile is 8/168 hours.

Thus, the time for 126 mile is 8/168 × 126 = 6 hours.

Hence, the time taken by Mamadou to travel 126 miles is 6 hours.

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Each edge of a graph is colored with one of the four colors red, blue, yellow, or green. How could you represent the edges in this graph using a variation of the adjacency matrix structure

Answers

G is the matrix representation of the four colored graph.

According to the statement

we have given that a graph is colored with one of the four colors red, blue, yellow, or green.

And we have to represent the edges of this graph using a variation of the adjacency matrix structure

So, Adjacency Matrix Structure is a way of representing a graph as a matrix of booleans (0's and 1's). A finite graph can be represented in the form of a square matrix on a computer, where the boolean value of the matrix indicates if there is a direct path between two vertices.

And in this graph representation the Adjacency Matrix Structure denoted by a matrix G.

so, there are a four colors used that's why there are 4 into 4 matrix is formed to represent the edges.

G =  [tex]\left[\begin{array}{cccc}1&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{array}\right][/tex]

And this is the matrix representation of the graph which is colored with four graphs.

So, G is the matrix representation of the four colored graph.

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WILL MAKE BRAINLIEST!!! Find the correct angle measure for angle b in each figure.

_1. 52°

_2. 27°

_3. 32°

_4. 98°

Answers

Answer:

98, 27

Step-by-step explanation:

In the first figure, the two angles are supplementary, meaning that their sum would equal 180 degrees, giving the equation: b+82 = 180 --> b=98

In the second figure, the two angles are complementary, meaning that they add up to 90 degrees, giving the equation: b+63 = 90 --> b=27

Find the equivalent expression of 20a + 28b.

Answers

Answer:

4 (5a + 7b)

Don't worry I helped my brother with this.

The standard deviation of the sampling distribution of the sample mean is also called?

Answers

The standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.

For the given question,

Standard error is a mathematical tool used in statistics to measure variability. The standard error of the mean (SEM) measures how much discrepancy is likely in a sample's mean compared with the population mean.The SEM takes the SD and divides it by the square root of the sample size. The SEM will always be smaller than the SD.

The standard error of the mean indicates how different the population mean is likely to be from a sample mean. You can decrease the standard error by increasing the sample size.

Standard error of the mean and standard deviation are both measures of variability used to summarize sets of data.  It helps you estimate how well your sample data represents the whole population by measuring the accuracy with which the sample data represents a population using standard deviation.

Hence we can conclude that the standard deviation of the sampling distribution of the sample mean is also called standard error of the mean.

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8. For circle A, the circumference is 31.4 ft. What is the area? Use 3.14 for pi

314 ft²

15.7ft²

78.5 ft²

9.9 ft²

Answers

Answer:

[tex]\huge\boxed{\sf A = 78.5\ ft\²}[/tex]

Step-by-step explanation:

Circumference = C = 31.4 ft

We know that,

C = 2πr

Where, r is the radius

31.4 = 2(3.14)r

31.4 = 6.28(r)

Divide 6.28 to both sides

31.4/6.28 = r

5 ft. = r

r = 5 ft.

Now,

Finding area:

A = πr²

A = (3.14)(5)²

A = (3.14)(25)

A = 78.5 ft²

[tex]\rule[225]{225}{2}[/tex]

To solve this problem, you need to find a radius... Circumference=2(3.14)(r)

2(3.14)=6.28

31.4/6.28=5=radius

A=(3.14)(r^2)

A=(3.14)(5^2)=78.5

Area= 78.5 ft^2

Nozomi works as a waiter and earns $16/h. She also receives 8% of the gratuities earned by all the staff. In one week, she worked 20 hours and the gratuities totalled $1,267.28. What was Nozomi’s gross pay?

Answers

Her gross pay is $421.38

What was Nozomi’s gross pay?

First, we know that she gets $16 per hour, and she worked 20 hours, then she gets:

20*$16 = $320

Now we also know that she receives a percentage of 8% of the gratuities, and the gratuities totaled $1,267.28

The 8% of $1,267.28 is:

$1,267.28*(8%/100%) = $1,267.28*0.08 = $101.38

Her gross pay is:

P = $101.38 + $320 = $421.38

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2. Un auto viaja a 60 km/h y se detiene a los 2 segundos. qué distancia recorrió en el
frenado? ¿qué aceleración adquirió? ¿Si la aceleración es positiva o negativa, explica
por qué?

Answers

Se calcula que la aceleración es - 8,35 m/s.

¿Qué es la aceleración?

Ahora sabemos lo siguiente de la pregunta;

Velocidad inicial (u) = 60 km/h o 16,7 m/s

Tiempo empleado (t) = 2 s

Dado que;

v = tu + en

v = 0 m/s porque el carro se detenía

tu = -en

a = -(u/t)

 a= -1(6,7 m/s/2 s)

a =- 8,35 m/s

La aceleración es negativa porque la velocidad disminuye con el tiempo.

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If 1 skip equals 4 hops, and 1 jump equals 3 skips, what is the total number of hops in a hop, a skip and a jump

Answers

There are 17 hops in a hop, a skip, and a jump.

How to perform changes of units?

We have the relations:

1 skip = 4 hops.1 jump = 3 skips.

How many hops are in a hop, a skip and a jump?

So we have:

1 hop + 1 skip + 1 jump.

First, using the second relation we rewrite:

1 hop + 1 skip + 3 skips = 1 hop + 4 skips.

Now, using the first relation:

1 hop + 4 skips = 1 hop + 4*(4 hops) = 1 hop + 16 hops = 17 hops.

There are 17 hops in a hop, a skip, and a jump.

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The two dot plots below compare the forearm lengths of two groups of schoolchildren: Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group X and the title for the bottom plot is Forearm Length, Group Y. Below the line for each dot plot is written Length in inches. There are markings from 10 to 13 on each line at intervals of one. For the top line there are 4 dots above the first mark, 4 dots above the second mark, and 2 dots above the third mark. For the bottom line there are 2 dots above the second mark, 2 dots above the third mark, and 6 dots above the fourth mark. Based on the visual inspection of the dot plots, which group appears to have the longer average forearm length? Group X, because no child in the group has a forearm length longer than 12 inches. Group X, because four children in the group have the least forearm length of 10 inches. Group Y, because a child in the group has the least forearm length of 10 inches. Group Y, because six children have a forearm length longer than 12 inches.

Answers

The group that have the longer average forearm length is group Y, because six children have a forearm length longer than 12 inches.

Which group has a longer forearm length?

A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.

In group X, the highest arm length is 12 while in group Y, it is 13. This means that group Y would have longer arm lengths.

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The cost in collars, CCC, from an airplane flight given that the average cost of a first class seat is fff dollars and the average cost of an economy seat is eee dollars is given by the equation above if all seats are sold. What is the best interpretation of 88e88e88, e as shown in the above equation

Answers

88e interprets the total cost for all the economy class seats, as all seats are sold, where 88 is the number of economy class seats and e dollars is the cost of each economy class seat.

In the question, we are given an equation, C = 24f + 88e, and are informed that the cost, C, in dollars from an airplane flight given that the average cost of a first class seat is f dollars and the average cost of an economy seat is e dollars is given by the equation above if all seats are sold.

We are asked for the interpretation about the 88e as shown in the equation.

The equation given to us is a cost equation.

A cost equation comprises of two parts:

Per unit priceNumber of units.

In the given equation, we have two types of quantities:

First class seatsEconomy seats

Thus, both these quantities must be having a per unit price, multiplied by the number of units sold.

Now, we are informed that e dollars is the per unit price for an economy class seat.

Thus, 88e interprets the total cost for all the economy class seats, as all seats are sold, where 88 is the number of economy class seats and e dollars is the cost of each economy class seat.

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For complete question, refer to the attachment.

At which angle is sin theta=1

Answers

Answer: pi/2; aka 90degrees

Answer:

second option : π/2 or pi/2

Step-by-step explanation:

sinθ = 1 = 90


π = 180

π/2 = 90

https://www.mathsisfun.com/geometry/radians.html

URGENT ASAP Please answer the option b

Answers

The solution to the system of inequalities x < 2y + 3 and -2x < y + 1 is the darker region shown in the graph.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Inequality is an expression that shows the non equal comparison of two or more numbers and variables.

The solution to the system of inequalities x < 2y + 3 and -2x < y + 1 is the darker region shown in the graph.

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The system of inequalities x > 2 · y + 3 and - 2 · x < y + 1 includes the point (x, y) = (10, 0).

How to change signs of the inequalities to contain a given point.

The solution area of the two inequalities given in the statement does not contain the point (x, y) = (10, 0) as we can see in the first figure.

But if we change the sign "<" for ">" in the first inequality, then the solution area includes the point mentioned above. Please see the second figure for further details.

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Solve the equation algebraically. Calculus section 1.5 of textbook
2^x + 2^-x = 5

Answers

The value of x from the given expression is [tex]\frac{5+\sqrt{29}}{2log2} \\[/tex]

Solving quadratic expression

Given the algebraic expression below;

2^x + 2^-x = 5

This can also be expressed as:

1/2^x+ 1/2^x = 5

Let P = 2^x, such that;

P + 1/P = 5

P²-1/P = 5

P²-1 = 5P

P²-5P-1=0

On factrorizing, then;

P = [tex]\frac{5+\sqrt{29}}{2} \\[/tex]

Since 2^x = P, then;

[tex]2^x=\frac{5+\sqrt{29}}{2} \\\\xlog2=\frac{5+\sqrt{29}}{2} \\\\x=\frac{5+\sqrt{29}}{2log2} \\[/tex]

Hence the value of x from the given expression is [tex]\frac{5+\sqrt{29}}{2log2} \\[/tex]

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Jeremy rides a Ferris wheel. The graph shows h, Jeremy’s height above the ground at any time during the ride.


Which inequality represents the heights shown on the graph?

Answers

The inequality that represents the height that is displayed by the graph is: 10 ≤ h ≥ 50.

How to Identify the Inequality of a Graph?

In an inequality graph, we the small circle at any end is shaded or full, the inequality sign used is either "less than or equal to" or "greater than or equal to" ("≤" or "≥"). If the circle is empty or not shaded, we use "less than" or "greater than" ("<" or ">").

In the graph showing Jeremy’s height above the ground at any time during the ride, we have a full circle (shaded) starting from 10, and another on the right at 50.

This implies that the range of height is from 10 to 50. Since the circle is full (shaded), then we would use "less than or equal to" and "greater than or equal to" ("≤" and "≥") in writing the inequality that represents the height.

Thus, where h is the height, the inequality would be: 10 ≤ h ≥ 50.

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Find the distance between the two points.
(-1,1)
(4,-3)
✓ [?]
Enter the number that
goes beneath the
radical symbol.

Answers

Answer: square root (41)
by using the formula
square root [(x2 - x1)^2 + (y2 - y1)^2]

What are the coordinates of the midpoint of the segment whose endpoints are C(−7, −10) and D(3, 9) ?


(−2, −0.5)


(−4, −1)


(−5, −9.5)


(−8.5, 3)

Answers

Answer:

(-2, -0.5)

Step-by-step explanation:

1. add the x-coordinates and then either divide by 2 or multiply by 1/2

2. add the y-coordinates and then either divide by 2 or multiply by 1/2

(-7+3)/2 = -2

(-10+9)/2 = -0.5

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find the period of the following functions. g ( x ) = cos ( x 4 ) All of the following elements are included in the transactional communication model introduced in Chapter One except A. Message B. Environment C. Channel D. Control a risk avoider would want zero safety stock. Completa la oracin con la opcin correcta.Una persona que lee mucho es ______.poderosavasijaestudiosaguerrera Which statement best describes the relationship that exists among proteins, DNA, and cells?A. Proteins combine to produce cells, which produce DNA.B. Proteins are made up of DNA, which determines the cells that are produced.C. DNA is made up of proteins, which tell a cell how to function.D. Cells contain DNA, which controls the production of proteins. Create two views to display the same object shown below. The view on the left is perspective with an FOV 0.4 and a front clip distance 0.01. It is located at (0,0,1) looking at (0,0,0) with the positive y-axis as its up direction. The other view is parallel located at (1,1,1) looking at (0,0,0) with the positive x-axis as its up direction. What is the HHI for the following industry . Firm 1 has a market share of 40% Firm 2 has a market share of 20% Firm 3 has a market share of 15% Firm 4 has a market share of 10% Firm 5 has a market share of 10% Firm 6 has a market share of 5% Caterpillars of the same species on a large leaf each chew as much leaf as they can. This is an example ofA. amensalism.B. interference competition.C. exploitation competition.D. commensalism.E. interspecific competition. A bookshelf has 24 books, which include 10 books that are graphic novels and 11 books that contain animal characters. Of these books, 7 are graphic novels that contain animal characters. What is the probability that a book contains animal characters given that it is a graphic novel? 10/7 11/24 7/24 7/10 Please choose the correct answer for the Coriolis force O A. The higher the latitude, the larger the Coriolis force O B. Coriolis force doesn't depend on the latitude O C. The higher the latitude, the smaller the Coriolis force Using the given data, calculate the rate constant of this reaction.A+B ----> C+DTrial [A](M) [B](M) Rate(M/s)1 0.340 0.200 0.01422 0.340 0.520 0.09603 0.476 0.200 0.0199k=_____ safety: when using an aluminum heating block with an electric hot plate it is important to (more than one answer could be correct) 5. How many meters of fencing will beneeded to enclose this dog pen?4 m175 cm what is the molar solubility of caf2 in a solution containing 0.100 m naf? Labor unions can lower wages for everyone through costly work stoppages. True or False. E = 160 GPa and I = 39.9(10-6) m4. Determine the maximum deflection of the simply supported beam. I need an explanation as to how and why this is right. Which of the following describes the change in the nucleus of an atom that undergoes B decay? A The number of nucleons decreases by 1. B The number of protons increases by 1, and the number of neutrons decreases by 1. The number of neutrons increases by 1, and the number of protons remains the same. D.There is no change. identify and discuss business situations or problems that can be solved using linear programming. provide specific examples. What famous guitarist wrote and performed hits like "Maybelline, "Johnny B. Goode", and "Run, Run, Rudolph"? Which geometric term describes TAG ? in math