A cone and a pyramid have the same height and same volume. If the radius of the base of the cone is r, what is the side length of the square base of the pyramid?

Answers

Answer 1

let Vc : cone's volume, Vp : pyramid's Volume, r radius, h height. w width and l length.

Vc=πr²h/3

Vp=(lwh)/3

make it equal to each other and cancel out the 3.

πr²h = lwh

heights will cancel out

πr²=lw

l=(πr²)/w

Answer 2

To find the side length of the square base of a pyramid with the same volume and height as a cone with radius r, one can use the volume formulas V = (1/3)πr²h for a cone and V = (1/3)a²h for a pyramid. Setting them equal and solving for a yields a = r√π, indicating that the pyramid's base side length is the cone's radius times the square root of π.

The student is asking for the relationship between the dimensions of a cone and a pyramid that have the same volume and height. Specifically, if we have a cone with a radius r, and we want to find the side length of a square base of a pyramid that also has the same volume and height as the cone.

The volume of a cone is given by the formula [tex]V = (\frac{1}{3}) \pi r^2h[/tex], where radius of the cone's base is denoted by 'r' and the height is denoted by 'h'. For a pyramid with a square base, the volume formula is [tex]V = (\frac{1}{3} )a^2h[/tex], where a is the side length of the square base and h is again the height.

Given that both volumes are equal, we can set the formulas equal to each other and solve for a: [tex](\frac{1}{3} )\pi r^2h = (\frac{1}{3} )a^2h[/tex]. The heights cancel out, and we can simplify the equation to solve for the side length a: a = r√π. Therefore, the side length of the square base of the pyramid is the radius of the cone's base times the square root of π.

Related Questions

A runner is participating in a 10.3 mile race. If the runner stopped at a water station that is twice as far from the starting line as from the finish line, how far is the runner from the finish line?

Answers

We have the representation of this problem in the figure below. As we have a 10.3 mile race, then the equation is fulfilled as:

[tex]d = 10.3mi = d_{1}+ d_{2}[/tex]

We know that there is a water station that is twice as far from the starting line as from the finish line, then:

[tex]d_{2}=2d_{1}[/tex]

So:

[tex]d_{1} +2d_{1}=10.3[/tex]
∴ [tex]d_{1}=3.43mi[/tex]

and [tex]d_{2}=2(3.43)=6.86mi[/tex]

Finally, the distance of the runner from the finish line is:

[tex]6.86mi[/tex]

Answer:

6.86

Step-by-step explanation:

Find the sum of this problem

Options:
52
26
13
32

Answers

[tex]\displaystyle\sum_{i=3}^{10}(2i-9)=2\sum_{i=3}^{10}i-9\sum_{i=3}^{10}1[/tex]
[tex]\displaystyle=2\left(\sum_{i=1}^{10}i-\sum_{i=1}^2i\right)-9\left(\sum_{i=1}^{10}-\sum_{i=1}^21\right)[/tex]

Recall that

[tex]\displaystyle\sum_{i=1}^ni=\frac{n(n+1)}2[/tex]
[tex]\displaystyle\sum_{i=1}^n1=n[/tex]

so the above reduces to

[tex]2\left(\dfrac{10\cdot11}2-\dfrac{2\cdot3}2\right)-9\left(10-2\right)=32[/tex]

Paul, Colin and Brian are waiters.
One night the restaurant earns tips totalling £77.40.
They share the tips in the ratio 1:3:5.
How much more does Brian get over Paul?

Answers

You have to add the ratio, which is 1:3:5 and 1+3+5= 9. Then you must do £77.40 divided by 9. This gives you £8.6. So 1 part is £8.60, also how much Paul got. To find out Brian, you must do 5 multiplied by £8.60 which gives you £43. Then, to get the difference, you must do £43 take away £8.60, giving you £34.40. Your final answer will be £34.40. I hope this helped!

He probability of choosing a vowel (a, e, i, o, or u) from a deck of cards containing the 26 letters of the alphabet is shown below. what is the probability of choosing the letters a and e one after the other without replacement?

Answers

Small. very small.

Out of 26 cards, you must choose one of them -- an "a". That's 1/26.

There are 25 cards left and again you must choose one of them. That's one out of 25. or 1/25.

The probability can only be 1/26 * 1/25 = 1/650

Put another way, if you played this game 650 times, you would only choose an a first and an e second once.

[tex]|\Omega|=26\cdot25=650\\ |A|=1\\\\ P(A)=\dfrac{1}{650}\approx0.15\%[/tex]

Which describes a cost that fluctuates depending on the number of units produced?

Answers

Variable cost describes a cost that fluctuates depending on the number of units produced. It is defined as a cost that varies in line with the output produced. It increases or decreases based on the volume of the production of the company; they increase as production rises and decreases as production fall.

Answer: Variable Cost APEX

Please help please please

Answers

[tex]\Omega=\{1;\ 2;\ 3;\ 4;\ 5;\ 6;\ 7;\ 8;\ 9;\ 10\}\\\\|\Omega|=10\\\\A=\{1;\ 3;\ 6;\ 7\};\ B=\{2;\ 3\}\\\\A\ \cup\ B=\{1;\ 2;\ 3;\ 6;\ 7\}\\\\|A\ \cup\ B|=5\\\\P(A\ \cup\ B)=\dfrac{|A\ \cup\ B|}{|\Omega|}\to P(A\ \cup\ B)=\dfrac{5}{10}=\dfrac{1}{2}=0.5=0.50[/tex]

\Omega=\{1;\ 2;\ 3;\ 4;\ 5;\ 6;\ 7;\ 8;\ 9;\ 10\}\\\\|\Omega|=10\\\\A=\{1;\ 3;\ 6;\ 7\};\ B=\{2;\ 3\}\\\\A\ \cup\ B=\{1;\ 2;\ 3;\ 6;\ 7\}\\\\|A\ \cup\ B|=5\\\\P(A\ \cup\ B)=\dfrac{|A\ \cup\ B|}{|\Omega|}\to P(A\ \cup\ B)=\dfrac{5}{10}=\dfrac{1}{2}=0.5=0.50

A fire truck has a ladder that can extend to 60 feet in length. the ladder can be safely raised to a maximum angle of 75o with the horizontal. disregarding the height of the fire truck itself, which is closest to the maximum height that the ladder can safely reach?

Answers

see the attached figure to better understand the problem

we know that
in the right triangle ABC

sin 75°=BC/AB-------> BC=AB*sin 75°----> BC=60*sin 75°----> BC=57.96 ft

the answer is
57.96 ft

A bookstore marks up the cost of a book from $6 to $10. What was the percent increase?

Answers

Final answer:

To find the percent increase from $6 to $10, subtract the initial cost from the final cost, divide by the initial cost, and multiply by 100. The percent increase is 66.67%.

Explanation:

To find the percent increase, you need to calculate the difference between the final cost and the initial cost, and then divide that difference by the initial cost. Finally, multiply by 100 to get the percentage.

Given that the initial cost is $6 and the final cost is $10, the difference is $10 - $6 = $4.

To find the percent increase, divide $4 by $6: $4/$6 = 0.6667 (rounded to four decimal places).

Multiply by 100 to get the percentage: 0.6667 * 100 = 66.67% (rounded to two decimal places).

How many numbers between 50 and 250 (inclusive) are not perfect squares?

Answers

64, 81, 100, 121, 144, 169, 196, 225
are perfect square
So 201-8=193

Helppp!! I need help with this question. Can anyone help me?

Answers

find the height of a residentail floor:

22-15 = 7 floors
76.4 -54 = 22.4 meters

22.4 / 7 = 3.2 meters ( each residential floor )

now find height of ground floor:

floor 8 - 1 = 7 floors

7 floors x 3.2 meters = 22.4 meters total

31.6 meters - 22.4 meters = 9.2 meters

the ground floor = 9.2 meters

Therefore, the height of the ground floor is 9.2 meters above the ground.

The pattern observed in the data is that the difference in height between consecutive floors remains constant. To find this constant difference, we can subtract the height of one floor from the height of the next floor.

For example:

Height of floor 1 (15th floor) - Height of ground floor (8th floor) = 54 m - 31.6 m = 22.4 m

Height of floor 2 (22nd floor) - Height of floor 1 (15th floor) = 76.4 m - 54 m = 22.4 m

The constant difference is 22.4 meters. This represents the height between each residential floor. To find the height of the ground floor (floor 0), we can subtract this constant difference from the height of the first residential floor.

Ground floor height = Height of floor 1 - Constant difference

Ground floor height = 31.6 m - 22.4 m = 9.2 meters.

Two parallel lines are intersected by a transversal. Two parallel lines are intersected by a transversal. One of the angles formed measures 88°

Answers

I put the transversal line and the 2 parallel lines.
Also I added what the other angle right next to it.

Final answer:

Two parallel lines intersected by a transversal create angles that are congruent or supplementary. The given 88° angle determines the measures of all other angles, which can either be 88° or supplementary to it, totaling 180°.

Explanation:

When two parallel lines are intersected by a transversal, several angles are formed. These angles have special relationships with each other. Since one of the angles is given as 88°, we can determine the measures of all other angles formed by using the properties of parallel lines and a transversal.

There are corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles (also known as same-side interior angles). Corresponding angles and alternate angles are equal, while consecutive interior angles are supplementary, meaning they add up to 180°.

Given that one of the angles measures 88°, its corresponding angle also measures 88°. The alternate exterior and alternate interior angles relative to the 88° angle would also measure 88°. The consecutive interior angles to the given angle would measure 92° (180° - 88° = 92°).

In a situation where mirrors are placed at an angle relative to each other, the same principle of angle measurement applies. For example, if two mirrors are inclined at an angle of 60°, the reflections would follow geometry consistent with angle relationships.

square root of 75 plus square root of 3

Answers

Your answer is: 10.3923048

Answer:
6√3

Explanation:
Before we begin, remember the following:
[tex] \sqrt{a*b} = \sqrt{a} * \sqrt{b} [/tex]
[tex]m \sqrt{a} + n \sqrt{a} = (m+n) \sqrt{a} [/tex]

Now, for the given:
75 can be written as 25*3
This means that:
[tex] \sqrt{75} = \sqrt{25*3} [/tex]
Applying the above concept, we can find that:
[tex] \sqrt{75} = \sqrt{25*3} = \sqrt{25} * \sqrt{3} [/tex]
Now, we know that:
√25 = 5 (we ignored the negative value)

This means that:
√75 = 5√3

Finally, we can compute the needed sum as follows:
√75 + √3 = 5√3 + √3 = 6√3

Hope this helps :)

What is the surface area of a cone, to the nearest whole number?

a.221 cm^2
b.240 cm^2
c.304 cm^2
d.620cm^2

Answers

the answer is 240cm^2, so B.
Surface Areas of Pyramids and Cones Practice: connexus
1) B, 448cm^2
2) D, 209pi cm^2
3) D, 351m^2
4) B, 240cm^2
5) C, 561.1pi cm^2
Just took it so they are all correct! your welcome

The surface area of a cone is b. 240 cm^2.

What is surface area of a cone?

The surface area of a cone is equal to the curved surface area plus the area of the base: π r^2 + π L r .

where r denotes the radius of the base of the cone, and L denotes the slant height of the cone.

Here, we have,

from the given figure,

we get,

L= 12.5 cm

r=9/2

=4.5cm

by using the formula, we get,

the surface area of a cone is = 240.33 cm^2

Hence, the surface area of a cone is b. 240 cm^2.

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Two forest fire stations, P and Q, are 20.0 km apart. A

ranger at station Q sees a fire 15.0 km away. If the angle

between the line PQ and the line from P to the fire is

how far, to the nearest tenth of a kilometre, is

station P from the fire?

Answers

Station P is approximately 15.0 km away from the fire.

Given that:

A right triangle with sides PQ: 20.0 km

And QF: 15.0 km

Where F is the location of the fire.

To find how far station P is from the fire, use trigonometry.

Let's call the distance from station P to the fire x km.

The angle between PQ and PF is given.

Using the trigonometric tangent function:

tan(angle) = opposite/adjacent

In this case, the opposite side is QF , and the adjacent side is PQ.

tan(angle) = 15.0 km / 20.0 km

Now, let's find the value of the angle:

angle = arctan(15.0 km / 20.0 km)

Using a calculator to get,

angle ≈ 36.87 degrees

Now, use trigonometry again to find x:

tan(36.87 degrees) = x / 20.0 km

x ≈ 20.0 km * tan(36.87 degrees)

x ≈ 20.0 km * 0.75

x ≈ 15.0 km

So, station P is approximately 15.0 km away from the fire.

Learn more about Trigonometry here:

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Final answer:

The distance from station P to the fire is approximately 21.23 km.

Explanation:

To find the distance from station P to the fire, we can use trigonometry. Since the ranger at station Q sees the fire at an angle between the line PQ and the line from P to the fire, we can consider the triangle created by station P, station Q, and the fire.

Using the tangent function, we can determine this distance:

tan(angle) = opposite / adjacent

Let x be the distance from station P to the fire:

tan(angle) = x / 15

Solving for x, we get:

x = 15 * tan(angle)

Now, we need to find the angle between the lines PQ and the line from P to the fire. Since the triangle created by station P, station Q, and the fire is a right triangle, we can use the inverse tangent function to find the angle:

angle = arctan(opposite / adjacent) = arctan(20 / 15)

Using a calculator, we find that the angle is approximately 53.13 degrees.

Substituting this angle into the equation for x, we have:

x = 15 * tan(53.13)

Solving for x, we get:

x ≈ 21.23 km

Given the equation of two lines how can I distinguish if these lines are parallel, perpendicular, or neither?

Answers

If they are perpendicular, they form a right angle. For example, this is perpendicular:

I_

If likes are parallel, they run along each other, never meeting. For example, these two lines are parallel:

___
___

Hope this helps!

Choose the correct answer. two cars leave phoenix and travel along roads 90 degrees apart. if car 1 leaves 30 minutes earlier than car 2 and averages 42 mph and if car 2 averages 50 mph, how far apart will they be after car 1 has traveled 3.5 hours? miles.

Answers

The equation of movement for each car is given by:
Car 1:
d1 = v1 * t1
Substituting values:
d1 = 42 * 3.5
d1 = 147 miles
Car 2:
d2 = v2 * t2
d2 = v2 * (t1 + 0.5)
Substituting values:
d2 = 50 * (3.5 + 0.5)
d2 = 200 miles
The distance between the cars is:
d = root ((d1) ^ 2 + (d2) ^ 2)
d = root ((147) ^ 2 + (200) ^ 2)
d = 248.2 miles
Answer:
They will be 248.2 miles far.

The answer is 210 miles.

The reciprocal of two more than a number is three times the reciprocal of the number. find the number

Answers

let the number be x
reciprocal=1/x
2 more the reciprocal=1/2+x
but 1/2+x=3(1/x)
1/2+x=3/x
x=6+3x
x=-2

virgil is traveling around a circular island. if he travels a 1000 mile course keeping a constant distance of 200 miles from the center of the island, through what angle does he travel?

Answers

we know that
circumference of a circle=2*pi*r
for r=200 miles
circumference of a circle=2*pi*200-----> 1256 miles

if 360° (full circle) has a length of------------------> 1256 miles
X°----------------> 1000 miles
x=1000*360/1256------> x=286.62°

the answer is
286.62 degrees

What is the area of the figure? The diagram is not drawn to scale.
A. 1,190 in^2
B. 595 in^^2
C. 1,435 in^2
D. 1,394 in^2

Answers

the picture in the attached figure

we know that
the figure is a parallelogram
the area of parallelogram=base*height
in this problem
base=34 in
height=35 in
so
area=34*35----> area=1190 in²

the answer is
A. 1,190 in^2

Given the following functions f(x) and g(x), solve fraction f over g ( 3) and select the correct answer below. f(x) = 2x2 – 8 g(x) = x – 5

Answers

(f/g)(x) = (2x² - 8)/(x - 5)
(f/g)(3) = (2(3)² - 8)/(3 - 5)
      = (18 - 8)/(-2)
      = 10/-2
      = -5

select the values of r, below, that represent a low or no correlation

0.8

0.3

0.1

-0.2

-0.5

1

-0.001

Answers

0.3, 0.1, -0.2, -0.001 are all little to no correlation.

The closer our values get to 1 or -1, the stronger the correlation. Anything below 0.5 is not a strong correlation.

Which situation is represented by the equation? 9x + 90 = 6x + 120

A) Jake has $90 and Mike has $120. Jake saves $6 per week and Mike saves $9 per week. How long will it be before Jake has more money than Mike?

B) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake has more money than Mike?

C) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Mike has more money than Jake?

D) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake and Mike have the same amount of money?

Answers

The answer is D . Because it make them equally to each other which means they are trying to have the same amount

Answer:

D) Jake has $90 and Mike has $120. Jake saves $9 per week and Mike saves $6 per week. How long will it be before Jake and Mike have the same amount of money?

Step-by-step explanation:

The answer is D, because it make them equal

Simplify this radical.Which ordered pair makes both inequalities true? y > –3x + 3 y > 2x – 2 (1,0) (–1,1) (2,2) (0,3)

Answers

First, split this inequality then try each answer.

y>-3x+3y>2x-2
split this into two and simplify each,
y > -3x + 3y -3x+3y > 2x - 2
y - 3y > -3x 3y>2x+3x - 2
-2y > -3x 3y>5x -2
2y<3x

Substituting all the 3 ordered pairs, none of them makes the inequalities true.

(a.) Find an angle between 0 and 2[tex] \pi [/tex] that is coterminal with 27[tex] \pi [/tex] /10

(b) Find an angle between 0°and 360° that is coterminal with 1015°

*give exact values for your answers*

Answers

To find a positive and a negative angle coterminal with a given angle, you can add and subtract 2π (360°).
[tex](a)\ \dfrac{27\pi}{10}-2\pi=\dfrac{27\pi}{10}-\dfrac{20\pi}{10}=\dfrac{7\pi}{10}[/tex]
[tex](b)\ 1015^o-2\cdot360^o=295^o[/tex]

Please help asap 2 questions 55 pts

Answers

2x-2 must be zero or greater, since we cannot have a negative quantity under the radical sign (unless we allow for imaginary roots).

Solving 2x-2≥0, we get x-1≥0, or x≥1. x must be equal to or greater than 1.

16 - 16, so the answer to the 2nd problem is the fourth one: x=4.

BRAINLIEST ELP NOW if i flip a coin 200 times and it lands on heads up every time what is the probability it will on heads the next flip

Answers

the answer is 50/50 because the country only has 2 sides like a said before

A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs
20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in
pounds can be represented by f x( ) = 20x + 4.

What is the range of the function for this situation?

Please explain.

Answers

The range of the function is the distance from the maximum of the function to the minimum of the function. The minimum amount of pairs of plates that you can add to the bar (x) is 0, meaning you add no plates. The maximum amount of plates that you can add to the bar is 6, because this is how many plates come in one weight set. The range of the function is y values, and 0 and 6 are x values, so we must plug these values into the function to find the range values.

f(x) = 20x + 4 = 20(0) + 4 = 0 + 4 = 4

f(x) = 20x + 4 = 20(6) + 4 = 120 + 4 = 124

Therefore, the range of the function is 120 pounds, or from [4, 124].

Hope this helps!

The range of a function is the possible output values of the function. The range of [tex]f(x) =20x + 4[/tex] is [4,124]

Given that:

[tex]f(x) =20x + 4[/tex]

To determine the range of the function, we simply determine the value of f(x) using the input values

When no pair is added (this means x = 0).

So, we have:

[tex]f(0) =20 \times 0 + 4[/tex]

[tex]f(0) = 0 + 4[/tex]

[tex]f(0) = 4[/tex]

When 4 pairs are added (this means x = 4).

So, we have:

[tex]f(4) = 20 \times 4 + 4[/tex]

[tex]f(4) = 84[/tex]

When 6 pairs are added (this means x = 6).

So, we have:

[tex]f(6) = 20 \times 6 + 4[/tex]

[tex]f(6) = 124[/tex]

f(6) is greater than f(4).

i.e. [tex]124 > 84[/tex]

So, the range of the function is: [0,124] or [tex]4 \le x \le 124[/tex]

Answers

Step 1. Check if both terms of your expression have a common factor.
Notice that both 28x and 4 are divisible by 4, so the common factor of your expression is 4.

Step 2. Take out the common factor by dividing each one of the terms by the common factor and grouping the results inside a parenthesis:
[tex] \frac{28x}{4}=7x [/tex] and [tex] \frac{4}{4} =1[/tex]
[tex]28x-4=4(7x-1)[/tex]

We can conclude that the factored form of [tex]28x-4[/tex] is [tex]4(7x-1)[/tex].

Text messages cost $.15 each. You can spend no more than $10. How many text messages can you send? Show Working

Answers

10 divided by 0.15.
You can send 66 Text messages.
Whenever a situation like this comes up try dividing :D

Could you please give me brainliest?

Final answer:

If each text message costs $.15, and you have $10, you can send a maximum of 66 text messages after rounding down.

Explanation:

To figure out how many text messages you can send with $10, given that each text message costs $.15, we need to divide the total amount of money ($10.00) by the cost of each text message ($.15).

It's a simple division problem: $10.00 ÷ $.15 = 66.67.

However, you can't send a fraction of a message, so we need to round down to the nearest whole number. So, you can send a total of 66 text messages for $10.

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why am i so bad at math ;w;

Joshua was surveying students about their use of the new biology lab in a school. Which question in the survey is a statistical question?

Where is the biology lab located in the school?

How qualified is the trainer at the biology lab?

What is the number of learning stations at the biology lab?

How many familiar specimens did you observe at the biology lab?

Answers

D might be the answer I am pretty sure it is D if not then sorry

The answer is D... :)

Other Questions

HELPAn individual having difficulty with high blood pressure may be experiencing an imbalance in all of the following hormones except __________. A. growth hormone (GH) B. estrogen C. norepinephrine D. cortisol 1 n Blake's to spring the speaker portrays the season as a?shy guest who refuses to remain with his host strong man who storms across the landscapepowerful man who desires to destroy earthyouth who is reunited with his beloved Farmer toby's chickens and pigs have a total of 30 heads and 84 legs. a chicken has 2 legs, a pig has 4 legs, and each animal has 1 head. how many of each type of animal does toby have Which type of tax places a heavier burden on low-income people? The acceptable macronutrient distribution range (amdr) for carbohydrates is ____ percent of daily energy intake. ((Sociology))What is meant by the phrase "the graying of America"? A.Life expectancy has increased in the United States. B.The size of the average American family has decreased. C.The cost of medical care in the United States has remained constant. D.Americans are having children at an older age. The lawyers worked all night on their computers to prepare a brief for their upcoming court case. Based on the context clues, which definition of brief is used in the sentence? short in time or length an outline of a legal argument short pants or underpants to give essential information to I need help... i don't really understand this...In 2000, the circulation of a local newspaper was 3,250. In 2001, its circulation was 3,640. In 2002, the circulation was 4,100. a. Find the percent of increase in the newspapers circulation from 2000 to 2001 and from 2001 to 2002. b. Which period had a higher percent of increase, 2000 to 2001, or 2001 to 2002? Which of the following statements best describes how endemic diseases impact a nations population? A. Endemic diseases can result in decreasing population numbers: many people die from diseases, and others move away from or avoid moving to places where diseases are rampant. B. Endemic diseases can result in increasing population numbers: people living in areas where certain diseases are prevalent tend to have more children because there is a risk that some will die. C. Endemic diseases can result in decreasing population numbers: people living in areas where certain diseases are prevalent tend to have fewer children. D. Endemic diseases can result in increasing population numbers: areas where certain diseases are prevalent attract more medical professional and researchers who move to these areas for jobs. Write a 10 line bio poem for a character in a raisin in the sun How have physical features affected the human geography of the eastern mediterranean? Before the arrival of Europeans in New Zealand, the Maori _____.A.were made up of many groupsB.lived in peace with other nationsC.had few traditional customsD.considered themselves a nation (gradpoint) A system of writing in which pictorial symbols represented sounds, syllables, or concepts, and was used for official and monumental inscriptions in ancient egypt, is called: during the editing phase of the writing process, a dictionary or thesaurus can be helpful with.A.grammar checks.B.topic sentences.C.paragraphing.D.word choice The slope of a line in a blueprint must be . A line is drawn that contains the points 5/6 < | m | In 1990, Saddam Hussein sent Iraqi troops to invade and occupy Kuwait, a country with huge oil reserves. Both the United Nations and NATO authorized the use of force against Iraq to free Kuwait. The Persian Gulf War began and ended in 1991. President George H. W. Bush worked hard to create an unusual coalition to fight Iraq which included forces from Which of the following quotes speak to the freedoms America identifies itself with? Select all that apply. "And by virtue of the power, and for the purpose aforesaid, I do order and declare that all persons held as slaves within said designated States, and parts of States, are, and henceforward shall be free" "One hundred years later, the life of the Negro is still sadly crippled by the manacles of segregation and the chains of discrimination." "The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of sex." "Fourscore and seven years ago our fathers brought forth upon this continent a new nation, conceived in liberty, and dedicated to the proposition that all men are created equal..." "To the memory of the man, first in war, first in peace, and first in the hearts of his countrymen." What are some of the changes the Gorbachev made to the soviet economy Amines and amides are derivatives of:1. nitrogen gas2. ammonia3. nitrous oxide4. aldehyde In close comparisons, external fertilization often yields more offspring than does internal fertilization. however, internal fertilization typically offers the advantage that _____.