what is the exact value of cos 105°

Answers

Answer 1

The exact value of cos 105 degrees is (√3-1) / 2√2 .

What is Trigonometric Function ?

Trigonometric functions also are referred to as circular features can be really described as the capabilities of an angle of a triangle. It method that the relationship among the angles and facets of a triangle are given by using these trig capabilities. The fundamental trigonometric features are sine, cosine, tangent, cotangent, secant and cosecant.

So,

we know that ,

cos(A+B) = cosA cosB - sinA sinB

So,

cos(105) can be written as

cos(60+45 ) = cos60 cos 45  - sin60 sin45

= 1/2  *  1/√ 2  - √ 3 / 2 * 1/√2

=1/√2  *  (√3 - 1) / 2

=(√3-1) / 2√2 .

so the value of cos105 is (√3-1) / 2√2 .

Therefore , The exact value of cos 105 degrees is (√3-1) / 2√2 .

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Related Questions

What percent is represented by the region that is shaded? Exact
answers only (no rounding).

Answers

I jus sayin the park with the woods on the woods at the mall

Answer:

64 percent

Step-by-step explanation:

because there is 24 sq and 100 divided by 24 is 4, 4 times 16 is 64

Lines m and n are parallel Line m is described by the equation y = 40 +2. Line n contains the point (1, -3). Which of the following is an equation for linen?
A Oy-3= (2+1)
B. Oy+ 3 = 4(x - 1)
M
cOy-3 = 4(2+1)
DOy+3 = (- 1)

Answers

Answer:

B)Oy+ 3 = 4(x - 1)

Equation of the straight line   y +3 = 4( x-1)

Step-by-step explanation:

Explanation:-

Step(i):-

Given that the equation   y = 4x +2

and given that the point (1,-3)

The equation of the parallel line to the given line

                       ax +by +k=0

                       4x-y +k=0

This line is passing through the point (1,-3)

                  ⇒ 4(1) -(-3) +k=0

                  ⇒   4+3 +k=0

                          7 +k=0

                             k =-7

The equation of the Parallel line  4x-y -7 = 0

Step(ii):-

Given that the slope m = 4 and the point (1,-3)

Equation of the straight line

             y - y₁ = m(x-x₁)

             y -(-3) = 4( x-1)

            y +3 = 4( x-1)

20 PTS !!!!!!
HELP PLEASE

Answers

It is 53...... BODMAS

geometry need help asap

Answers

The value of angle LAF in the intersecting chords is determined as  104⁰.

What is the value of angle LAF?

The value of angle LAF is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

m∠LAF = ¹/₂ (arc LF + arc YS)

From the diagram, we have arc LF = 160⁰ and YS = 48⁰

m∠LAF = ¹/₂ (160 + 48)

m∠LAF = 104⁰

Thus, the value of angle LAF is calculated by applying intersecting chord theorem.

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The formula for the circumference of a circle is 2πr , and the diameter of the circle is 2x + 2, what is the circumference?

Answers

The circumference of the circle whose diameter is 2x + 2 is (44x + 44)/7

The formula for the circumference of a circle is 2πr

r = radius of the circle

Diameter of circle = radius  of circle × 2

The radius of the circle = ( diameter of the circle ) / 2

The radius of circle = (2x+2)/2

Taking 2 commons from 2x + 2

we get 2( x + 1 )

The radius of circle = 2(x+1)/2

The radius of the circle = x + 1

Circumference =  2 × 22/7 × (x+1)

Circumference = 44(x+1)/7

Circumference = (44x + 44)/7

Or in the form of π circumference can be written as (2x + 2)π

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(a) The area of a rectangular garden is 7371 m².
If the width of the garden is 81 m, what is its length?
What is the Length of the garden:

Answers

Answer:

length = 91 m

Step-by-step explanation:

area = length * width

so,

7371 = length * 81

cancel out 81 by dividing on both sides

91 = length

Which of the following is the best estimate of the number of centimeters (cm) in 1 yard? (Note: 1 yard-3 feet; 1 foot-12 inches; 1 inch -2.54 cm)
..
36 cm
72 cm
90 cm
180 cm
CONTINUE

Answers

The best estimate of the number of centimeters (cm) in 1 yard is; Yard ⇒ feet ⇒ inches ⇒ centimeters

If we have to determine the number of centimeters in 1 yard, the best way is;

Here we convert  yard to feet = 1 yard = 3 ft

Then, we convert ft to inches = 1 ft = 12 inches

                                                  3 ft = 3 × 12 = 36 inches

Now, we convert inches to centimeters = 1 inch = 2.54 cm

                                            36 inches = 36 × 2.54 = 91.44 cm

Therefore, the best path is Yard to feet to inches to centimeters

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The volume of a cube, in cubic centimeters, is given by the function V(x) = x3, where x is the side length of the cube in centimeters. Write a new function for the volume of the cube in cubic millimeters.

Answers

I think we can all agree that 1 centimeter=10millimeters.

And if x is the side in centimeters then 10x will be the side in millimeters.

We just need to rewrite x^3 into (10x)^3.

Because you need to do the exponent to all part of the ( )...

(10x)^3=1000x^3

V(x)=1000x^3 cubic millimeters is the answer

Hence, a new function for the volume of the cube in cubic millimeters is [tex]V(x)=1000x^3[/tex].

What is the volume of cube?

The volume of a cube is defined as the total number of cubic units occupied by the cube completely.

A cube is a three-dimensional solid figure, having six square faces. Volume is nothing but the total space occupied by an object.

Here given that,

The volume of a cube, in cubic centimeters, is given by the function [tex]V(x) = x^3[/tex], where [tex]x[/tex] is the side length of the cube in centimeters.

As, [tex]1[/tex] centimeter=[tex]10[/tex]millimeters.

If the side is [tex]x[/tex] then the side in millimeter is [tex]10x[/tex].

So, we have [tex]x^3[/tex] which would be [tex](10x)^3[/tex]

[tex](10x)^3=1000x^3[/tex]

Then,

[tex]V(x)=1000x^3[/tex] cubic millimeters.

Hence, a new function for the volume of the cube in cubic millimeters is [tex]V(x)=1000x^3[/tex].

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Plz help. One winter day, the temperature in Houston is 12 degrees Celsius. Find the temperatures in these other cities.
A) In Minneapolis, it is 30 degrees colder than it is in Houston.

B) In Fairbanks, it is 9 degrees colder than it is in Minneapolis

C) Write an addition equation that represents the relationship between the temperature in Houston and the temperature in Fairbanks. (Hint: Equation means it must be solved; so it has an equal symbol)

Answers

A= -18
B= -27
12-39=-27
These should be the answers

Tanner had $42.80 and spent 20% of his money on a book including tax. If he paid with a $10 bill, how much change did Tanner get back?

A. $7.28
B. $6.24
C. $1.44
D. $17.54

Answers

C.
42.8 x 0.2 = 8.56
10 - 8.56 = 1.44

Help please!!!

The finance charge on your credit card was supposed to be $12.22. Instead you were charged $19.54.
Find the absolute error and the relative error in the finance charge

Answers

Taxes and federal made you get charged like that but you can divide it

Answer:The absolute error is that they said that the finance charge will be $12.22 but the charge ends up being $19.54 . As for the relative error is that they said that the charge will be $12.22 but the charge was $19.54 which means they were unsure what the charge was and failed to check what it actually was.

Step-by-step explanation:

Consider the following figure

Answers

The arrangement of the side length of the triangles from the least to the greatest is DF <  DE < EG <  EF <  GF.

What is the arrangement of lengths of the triangle?

The arrangement of the lengths of the triangle from the least to the greatest is determined as follows;

The size of the length of a triangle increases as the size of the angle opposite to the length increases.

That is the greater the size of the angle opposite the side length of a triangle, the greater the size of the side length of the triangle.

From the given diagram, we can arrange the size of the side length of the triangle as follows;

angle D = 180 - (57 + 58 )

angle D = 65⁰ (this is opposite to length EF)

So the arrangement of the side length of the triangles are;

length DF < Length DE < length EG < length EF < length GF

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what are integra in algebra ​

Answers

Answer:

this is what i found for ya:3

Step-by-step explanation:

In mathematics, specifically abstract algebra, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero. ... Noncommutative integral domains are sometimes admitted.

Answer:

That's the meaning of of integers in math and algebra: Whole numbers. No fractions allowed! Integers are counting numbers, and they include 0. ... In other words, integers can be negative, but they can't be fractional. Any number with a fraction – and that includes decimal fractions – is not an integer.

Step-by-step explanation:

Kl and CaCl₂ particle diagram

Answers

Answer:

CaCL2 + KL → KCL + CaL2

Step-by-step explanation:

To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. The balanced equation will appear above.

Use uppercase for the first character in the element and lowercase for the second character. Examples: Fe, Au, Co, Br, C, O, N, F.

Ionic charges are not yet supported and will be ignored.

Replace immutable groups in compounds to avoid ambiguity. For example, C6H5C2H5 + O2 = C6H5OH + CO2 + H2O will not be balanced, but XC2H5 + O2 = XOH + CO2 + H2O will.

Compound states [like (s) (aq) or (g)] are not required.

You can use parenthesis () or brackets [].Li + Ag = Li + Ag

KOH + KMnO4 + H2SO4 = KOH + KMnO4 + H2SO4

C6H6O + KOH = C6H7KO2

CUO + HNO3 = CU(NO3)2 + H2O

C4H6O4 + KOH = C2K2O4 + C2H6O2

Zn + Sr(OH)2 = Sr + Zn(OH)2

Al + Pb(No3)2 = Al(No3)3 + Pb

HNO3 + Zn = Zn(NO3)2 + H2

ZnO + CH3COOH + H2O + Al2O3 = Zn(CH3COO)2*2H2O + Al2O3

BeO + Zn(OH)2 = Be(OH)2 + ZnO

CH3COOK + CH3Br = CH3COOCH3 + KBr

Pb(NO3)2 + HBr = PbBr2 + NHO3

Find the value of x. Round
To the nearest tenth .

Answers

Answer:

x = 5.7

Step-by-step explanation:

Use the pythagorean theorem, which says a^2+b^2 = c^2 where c is the hypotenuse (longest side of a right triangle, always opposite the 90 degree right angle).

7^2 + x^2 = 9^2

49 + x^2 = 81

x^2 = 32

now take the square root of both sides

x = 5.65685424949

Round to the nearest tenth.

x = 5.7

Answer:

5.7

Step-by-step explanation:

x^2 + 7^2 = 9^2

x^2 + 49 = 81

x^2 = 81 - 49

x^2 = 32

x = the square root of 32

x = 5.657

round to the nearest tenth

x = 5.7

The continent of North America has an area of approximately 9.4x10^(6) square miles. The area of Asia is approximately 1.74x10^(7) square miles. Approximately how many square miles larger is Asia than North America

Answers

Asia is larger than North America by approximately 8.0 x 10⁶ square miles.

What is the difference between the areas of the two countries?

The difference in area between Asia and North America is calculated as follows;

Difference in area = Area of Asia - Area of North America

Difference in area  = 1.74 x 10⁷ mi² - 9.4 x 10⁶ mi²

The difference in the area between Asia and North America is calculated as

= 1.74 x 10⁷ mi² - 9.4 x 10⁶ mi²

= 8.0 x 10⁶ mi²

Thus, The difference in area between Asia and North America is 8.0 x 10⁶ mi².

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Please help me anwser this

Answers

The values are given as:

a. Mean = 19

Median = 20

Mode = 22

Standard deviation = 7.2

Range  = 24

b. Mean = 75

Median  =  80

Mode  = 90

Standard deviation  = 16

Range = 100

What the measures of central tendency?

The three measures of central tendency include;

MeanModeMedian

The measures of dispersions are;

Rangeinterquartile range standard deviation

From the information given, if 4 is added to all the measures, we get;

Mean = 15 + 4 = 19

Median = 16 + 4 = 20

Mode = 18 + 4 = 22

Standard deviation = 3.2 + 4 = 7.2

Range = 20 + 4 = 24

If the values are multiplied by 5

Mean = 15(5) = 75

Median = 16(5) =  80

Mode = 18(5) = 90

Standard deviation = 3.2(5) = 16

Range = 20(5) = 100

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Question 4(8 points)
Ralph receives money from his family members for his high school graduation. He
decides he wants to spend no more than $120.00 on movies to bring with him to
college. Each DVD is $10.00, and each Blu-Ray is $15.00. He wants to purchase at least
8 movies. Determine the following,
You are given this inequality to represent "he wants to purchase at least 8
movies": x+y 28
BLANK 1: Would this be the correct way to write this (yes or no)?
BLANK 2-4: Fill in the blanks for the second inequality (all three answers are whole
numbers):
ys
x+
BLANK 5 AND 6:
What label would go on the x-axis, if you graphed this?
What label would go on the y-axis, if you graphed this?
BLANK 7 AND 8:
If Ralph were to JUST purchase DVDs, what is the maximum amount he could buy?
If Ralph were to JUST purchase Blu-Rays, what is the maximum amount he could buy?

Answers

what is your name? Jan kskskksk ksksmskksnsns nsksmms a ksmsms

Find the percent of change

1970's: $0.79
2010's: $3.72

Answers

Answer:

471%

Step-by-step explanation:

If you divide 3.72 by .79 you get 4.7088...

Multiply by 100 to get your percentage is 470.88...

Rounded to nearest percentage is 471

hope this helps

Three angles in a triangle measure x°, (4x+12)° and (3x+16)°. What is the measure of the largest angle in this triangle?

Answers

Answer:

Step-by-step explanation:

90°

Now look at the 5-year performance of Amazon. What do you think explains the general upward trend of the stock price?

Answers

Answer:

expansion

Step-by-step explanation:

I believe that the biggest reason for the general upward trend in the stock price is expansion. Amazon has expanded their company immensely over the last 5 years. They have also expanded into different markets such as drones, gaming, cloud streaming, video streaming, etc. All of these expansions and acquisitions have been incredibly profitable for Amazon and therefore reflect on the stock price. This also gives investors faith that the future of the company will continue growing which causes them to buy more stocks and therefore increase the price.

Answer:

Step-by-step explanation:

Given the regression line Ŷ = –6 + 0.41(X), make predictions for each of the following:
a. X = 25
b. X = 50
c. X = 75

Answers

For the "regression-line",  Ŷ = -6 + 0.41(X), the predicted value,

(a) when X=25 is 4.25,

(b) when X=50 is 14.50,

(c) when X=75 is 24.75.

The "Regression-Line", is Ŷ = -6 + 0.41(X), we can make predictions for the value of Y (the dependent variable) for different values of X (the independent variable).

(a) To predict the value of "Y" when X = 25, we substitute 25 into the regression line equation:

Ŷ = -6 + 0.41(25)

Ŷ = -6 + 10.25

Ŷ = 4.25

So, the predicted value of Y when X = 25 is 4.25.

(b) To predict the value of Y when X = 50, we substitute 50 into the regression line equation:

Ŷ = -6 + 0.41(50)

Ŷ = -6 + 20.50

Ŷ = 14.50

So, the predicted value of Y when X = 50 is 14.50.

(c) To predict the value of Y when X = 75, we substitute 75 into the regression line equation:

Ŷ = -6 + 0.41(75)

Ŷ = -6 + 30.75

Ŷ = 24.75

So, the "predicted-value" of Y when X = 75 is 24.75.

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help me plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Answers

The first option, as it positively supports the claim stated.

Answer:

"Playing video games has been shown to enhance memory and even increase brain volume"

Step-by-step explanation:

The claim is approves the usage of video games.

The first piece of evidence supports the usage, citing how video games can "enhance memory" which is positive.

The second piece of evidence does the opposite and disapproves video games, citing them as an "addiction" which is negative.

A system of linear equations is shown on the graph.
-12 -11 -10 -9 -8 -7
-5
There is no solution.
What is the solution to the system of equations?
There are infinitely many solutions.
O There is one unique solution (-5, 9).
There is one unique solution (0,8).

Answers

The lines intersect at only one specific point (-5, 9)

The correct answer is: There is one unique solution (-5, 9).

When two straight-line equations intersect at a point, it means that there is one unique solution to the system of equations. In this case, the point of intersection is (-5, 9), which indicates that the system has a single solution. This means that there is a unique set of values for the variables that satisfy both equations simultaneously.

If the system had no solution, it would mean that the two lines are parallel and will never intersect. However, since the lines in the given system intersect at (-5, 9), it implies that there is a solution.

Alternatively, if the system had infinitely many solutions, it would mean that the two equations represent the same line. In this case, the lines intersect at every point along their entire length, resulting in an infinite number of solutions. However, the fact that the lines intersect at only one specific point (-5, 9) indicates that there is one unique solution to the system of equations.

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3. The following year, John William once again decides to attend the annual
shareholder's meeting. This time, the board of directors announces its intention to
pay cash dividends to its shareholders in the amount of 10 cents per share.
a. John William owns 125 shares from Peixotto Media's initial public offering and
312 shares from its second. What dividend will he receive? (2 points)
b. Peixotto Media's stock price is currently at $7.25 per share. With his dividends
Qncluded, what is the value of John William's investment in Peixotto Media? (3
points)

Answers

John William will receive a total dividend of $43.70.

The value of John William's investment in Peixotto Media, including dividends, is $3,216.95.

a. John William owns a total of 125 + 312 = 437 shares in Peixotto Media. If the company is paying a cash dividend of 10 cents per share, then John William's total dividend income will be:

437 shares x $0.10 per share = $43.70

Therefore, John William will receive a total dividend of $43.70.

b. If John William owns 437 shares in Peixotto Media and the current stock price is $7.25 per share, then the value of his investment in the company (excluding dividends) is:

437 shares x $7.25 per share = $3,173.25

If we add the dividend income of $43.70 to this value, then the total value of John William's investment in Peixotto Media is:

$3,173.25 + $43.70 = $3,216.95

Therefore, the value of John William's investment in Peixotto Media, including dividends, is $3,216.95.

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James had 42 dollars. He bought his sister a gift that cost x dollars. Write an expression representing how much money James has now.

Answers

Answer:

42 dollars -x......................


What is the value of f(-5)?

Answers

u have to plug in -5 as x in the function/equation

Answer:

None

Step-by-step explanation:

Cant solve it without an X value

Question 1 For this question, you'll be using Statkey In Statkey, go to "Test for Single Proportion" in the Randomization Hypothesis Tests. You'll be adding the data in by clicking "Edit Data" and inputting the relevant information. Situation: A sample of 50 U.S. adults were asked if they wear a helmet when they go for a bike ride. 35 of the adults in the sample said "yes" they wore a helmet. Does this provide evidence to suggest that a majority of U.S adults wear a helmet when they ride their bike?

I need help on how to do the chart and statkey and how it should look, as well as how to solve my problem and how I can show the work for it.​

Answers

Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.

How to explain the information

The randomization distribution will show the proportion of people who wear helmets in each of the 1000 samples.

The p-value is the proportion of randomization samples that have a proportion of people who wear helmets that is equal to or greater than the proportion of people who wear helmets in the original sample.

In this case, the p-value is 0.04. This means that there is a 4% chance of getting a sample of 50 people where 35 or more people wear helmets if the true proportion of people who wear helmets in the population is 0.5.

Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.

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Sadie swam x laps in the pool. Eric swam 3/5 more than that. Write an expression for the number of laps Eric swam

Answers

Answer:

y = 3/5 + x

'y' = # laps Eric swam

Step-by-step explanation:

Answer:

                                                             .

Step-by-step explanation:

                                                                  .

If you answer these questions i will give you free point's. (Answer all of them pls)


1. I am 50% of a quarter of 32.
2. I am two thirds of 60.
3. I am exactly half-way between 25% of 80 cm and 40% of 120cm.
4. I am one-quarter of 50% of 88kg.
5. I am 3% of half of 600 pounds.
6. I am exactly halfway between one fifth of 25cm and 2% of 300 cm.
7. I am greater that 0.6 kg, less than one-third of 6 kg, and equal to four times 10% of 3kg.

Answers

Answer:

1. 4

2.40

3. 28

4.11

5.12

6. 1

7. 1200

Step-by-step explanation:

I used • instead of x to show you multiply.

1. 1/4 (one quarter) of 32 = 8.
50% of 8 = 4

2. 2/3• 60 = 120/3 = 40

3. 25% = 0.25, 40% = 0.40
So 0.25 • 80= 20
0.40 • 120 = 48
Then subtract: 48-20 = 28. Half of 28 is 14. Add that 14 to 20, and your answer is 34. It will probably be helpful to either write that on a number line, or picture it on a number line.

4. 50% of 88kg is half of that, which is 44. One quarter = 1/4, so 44/4 = 11

5. Half of 600 pounds is 300 pounds. 3% = 3/100 = 0.03. Multiply that by 300 to get your answer. 300 • 0.03 = 9

6. 1/5 of 25cm = 25/5= 5
2% of 300 = 300• 0.02= 6
What is exactly halfway between 5 and 6? 5.5

7. Start this one with the last statement. 10% (0.10) of 3kg = 3•0.10= 0.3. Four times that = 4•0.3= 1.2

Then check: is that greater than 0.6? Yes.

One third of 6kg = 6/3= 2

Is 1.2 less than 2? Yes.
Other Questions
Besides HEV and EVmotor systems themselves what other systems may use high voltage? determine the force exerted by the bicep muscle, assuming that the hand is holding a ball with a mass of 5.00kg. Assume that the mass of the forearm is 8.50kg with the center of the mass located 20.0cm away from the elbow joint. Assume also that the center of the mass of the ball in the hand is 30.0 cm away from the elbow joint. Can somebody help me on this? How is workplace stress related to work outcomes?a - Higher levels of stress diminish organizational commitmentb - Lower levels of stress are related to increases in employee turnoverc - There is a U-shaped relationship that very high and very low levels of stress improve performanced - Increases in alcohol and illicit drug use are typically associated with lower levels of stress How do genre and point of view contribute to the power of Holocaust literature? Use evidence from your chosen text to support your answer. What are the six reasons in A Modest Proposal? which tough battle in the pacific led to the american military to think about using the atomic bomb?a. Pacific Battlesb. Battle of Okinawac. The Pacific Ward. a and c What is the equation of a circle with a radius of 4 and a center located at (2,3) 6.8.3 Configure a Cable Internet ConnectionYou work at a computer repair store and are on-site at a customer's office. They have signed up for cable internet access. The cable company has installed the line into their office. Brandon wants to use the Distributive Property to figure this problem out. What should be his next step?8 (10 + 7) Which of the following are the solution to the equation 2x 5x 3 0?(i) x = 3 (ii) x= 2(iii) x=-1/2 (iv) x=-1/3 Which of the following does not happen as the temperature of a gas increases? a. Molecules move faster. b. Molecules have more collisions. c. Kinetic energy increases. d. Kinetic energy decreases. Ahmed is making jelly. He needs the jelly to set in time for his party. He has two dishes that he can use to cool the jelly in. Dish A has a width of 30cm and a length of 45cm. Dish B has a width of 15cm and a length of 40cm. To get his jelly cooled faster which dish should Ahmed use? In Australia, for example (where our study was performed), many of the birds can fly great distances, sometimes across the whole of Australia, often because of unpredictable weather. Birds in other parts of the world where the weather is more predictable, such as England and America, do not have to fly such long distances.1. Observation2. Question3. Hypothesis4. Collect Evidence What does it mean when displacement is zero? As the _____was called in, they mounted their horses and descended into the valley to confront the enemy.A: QuellB: CalvaryC: ManifestD: Plight To prepare for a half-marathon, Colleen recently had 3 training runs. The table shows how far she ran in each session and how long it took. LIMITED TIME!!!!!! HELP!!!!!!!!In the Galapagos Islands, species of tortoises have been found ondifferent islands that cannot interbreed. They came from the sametortoise ancestor, but over time they became separate speciesbecause they were on different islands. Today there are a total of 9different Galapagos tortoise species. Which type of isolation isthis?Select one:A, episodic isolationB, geographic isolationC, temporal isolationD, behavioral isolation 5x^2+14x=x+6HURRYY SOLVE BY FACTORING EXPLAIN AND SHOW EVER STEP Which feed is mostly eaten by birds?