A barn is an atomic unit of area equal to 10–28 m2. what is the surface area of the earth expressed in units of barn? assume the earth is a sphere with a radius of km. (the surface area of a sphere is 4πr2.)
Answers
we know that
surface area of a sphere=4*pi*r²
for r=6380 km------->r=6380 x 10^3 m
surface area of of the earth=4*pi*(6380 x 10^3)²-----> 511506576035121,52 m²
if 1 barn is equal to-------------> 10^(-28) m²
x barn----------------------> 511506576035121,5
x=511506576035121,5/(10^(-28))------> x=5.12 x 10^42 barn
the answer is
5.12 x 10^42 barn
Related Questions
The probability of event A is .43, the probability of event B is .32, and the probability of event C is .66. What is the probability of all three events occurring at the same time?
Answers
= 0.43*0.32*0.66 = 0.0908 Answer
Final answer:
The probability of independent events A, B, and C all occurring together is found by multiplying their individual probabilities: P(A AND B AND C) = P(A) × P(B) × P(C) = 0.090528.
Explanation:
The question involves calculating the probability of all three independent events happening simultaneously. To find the combined probability of independent events A, B, and C occurring at the same time, we use the multiplication rule of probability.
This rule states that if the events are independent, the probability of all events occurring is the product of their individual probabilities.
Here are the probabilities for each event:
Probability of event A (P(A)) = 0.43
Probability of event B (P(B)) = 0.32
Probability of event C (P(C)) = 0.66
The probability of events A, B, and C all occurring together is:
P(A AND B AND C) = P(A) × P(B) × P(C) = (0.43) × (0.32) × (0.66) = 0.090528
Use addition to solve the linear system of equations. Include all of your work in your final answer.
x - y = 4
x+ 2y = 4
Answers
x - y = 4-------> multiply by -1-----> -x+y=-4-----> equation 1
x+ 2y = 4------> equation 2
add equation 1 and equation 2
-x+y=-4
x+2y=4
-----------------
0+3y=0-----> y=0
x+2y=4------> x+0=4------>x=4
the solution is the point (4,0)
Algebra question ( Matrices and Determinants ) 20 points
Answers
You must multiply each term of the matrix by the scalar 4.
Since it is a multiplication by a scalar, the dimension of the matrix must be the same.
Answer:
option B
See attached image.
Hexagon DEFGHI is translated 6 units down and 6 units to the right. If the coordinates of the pre-image of the point F are (-9,2) what are the coordinates of F
Answers
Hexagon DEFGHI is translated 6 units down and 6 units to the right. If the coordinates of the pre-image of the point F are (-9,2) what are the coordinates of F'?
we know that
the transformation has the following rule
(x,y)--------> (x+6,y-6)
so
(-9,2)-----> (-9+6,2-6)------> (-3,-4)
the answer is
(-3,-4)
Answer:
-6,-6
Step-by-step explanation:
(-9,2) + (-8,3) = (-6,-6)
correct on the test :)
How does the volume of an oblique cylinder change if the radius is reduced to 2/9 of its original size and the height is quadrupled?
A. V=2/81pir^2h
B. V=16/81pir^2h
C. V=4/9pir^2h
D. V=16/9pir^2h
Answers
[the volume of an oblique cylinder]=pi*r²*h
if the radius is reduced to 2/9 of its original size and the height is quadrupled
then
[the new volume of an oblique cylinder]=pi*[(2/9)*r]²*[4*h]---> (16/81)*pi*r²*h
the answer is
the option B. V=16/81pir^2h
Consider the arithmetic series:
1 + 9 + 17 + 25 + ...
Write a formula for the sum of the first n terms in this series.
A) 4n2 - 3n
B) 6n2 - 7n
C) 8n2 - 5n
Answers
[tex] S_{n}= \frac{n}{2}(2a_{1}(n-1)*d) [/tex]
where,
d = Common Difference = Difference of any two consecutive terms.
So,
d = 8
a1 = First term = 1
Using the values, we get:
[tex] S_{n}= \frac{n}{2}(2*1+(n-1)*8) \\ \\ S_{n}= \frac{n}{2} (2+8n-8) \\ \\ S_{n}= \frac{n}{2}(8n-6) \\ \\ S_{n}=n(4n-3) \\ \\ S_{n}==4n^{2}-3n [/tex]
The above equation gives the formula for n terms of an Arithmetic Series.
So, option A is the correct answer
what is the solution of the equation?
please help!!
Answers
[tex] \sqrt{2x+8}-6=4 \\ \\ \sqrt{2x+8}=10 \\ \\ 2x+8=(10)^{2} \\ \\ 2x+8=100 \\ \\ 2x=92 \\ \\ x= 46 [/tex]
Suppose that an individual has a body fat percentage of 12.8% and weighs 131 pounds. how many pounds of his weight is made up of fat? round your answer to the nearest tenth.
Answers
16.76 pounds of fat so
17pounds or 16.7
sin^{2} theta +cos theta = 2
Use the pythagorem identity sin^{2} theta +cos^{2} theta =1 to replace sin^{2} theta in the given equation
Answers
Applying Pythagorean Identity, the original equation sin² theta +cos theta = 2 can be altered by substituting sin² theta with 1 - cos² theta. This forms a quadratic equation: cos² theta - cos theta - 1 = 0, which can be solved using the quadratic formula to find the possible values of cos theta.
Explanation:To solve the equation sin² theta +cos theta = 2 by using the Pythagorean identity sin² theta +cos² theta =1, we can substitute sin² theta in the original equation with 1 - cos² theta.
Step-by-step solution:
We start by replacing sin² theta in the equation with 1 - cos² theta. So, the equation becomes 1 - cos² theta + cos theta - 2 = 0.This can be rearranged to form a quadratic equation as cos² theta - cos theta - 1 = 0.We can solve this quadratic equation using the quadratic formula cos theta = [- (-1) ± √{(-1)²-4(1)(-1)} ] /2(1).Computing the values, we get the two possible values of cos theta.Learn more about Pythagorean Identity here:https://brainly.com/question/24287773
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You draw a single card from a standard deck of cards. what is the probability of drawing a diamond?
Answers
13/52=25
25%
QS is the perpendicular bisector of PR solve for x
Answers
3x=90
so the answer is x=30
2x - 20 = 70 - x
3x - 20 = 70
3x = 90
x = 30
In a weekly lottery, ten ping-pong balls numbered 0 to 9 are placed in each of six containers, and one ping-pong ball is drawn from each container. To win the prize, a participant must correctly identify the ping-pong ball that is drawn from each of the six containers. If Juan played the lottery last week and didn’t win, what is the probability that he will win this week?
Answers
The probability that he will win this week is 0.0001%.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Ten ping-pong balls numbered 0 to 9 are placed in each of six containers.
It will not effect the outcome if Juan didn't win last week.
So, the probability that he will win this week
= [tex](1/10)^6[/tex]
= 1/1,000,000
= 0.000001
= 0.0001%
Hence, the probability that he will win this week is 0.0001%.
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trignometry help what's the answer?
Answers
See attached picture for solution:
Tell whether each set of ordered pairs representd a function. Justify your answers.
a. (0,0), (1,1), (2,2), (3,3), (4,4)
b. (0,8), (1,6), (2,4), (3,2), (4,0)
c. (3,0), (3,1), (3,2), (3,3), (3,4)
Answers
a. (0,0), (1,1), (2,2), (3,3), (4,4) - We do not see repeating values of x, so it is a function
b. (0,8), (1,6), (2,4), (3,2), (4,0)- We do not see repeating values of x, so it is a function
c. (3,0), (3,1), (3,2), (3,3), (3,4) - We see repeating value of x, that means that one value of x corresponds many values of y , so it is not a function.
Which additional information is needed to solve this problem?
John wants to buy a new game for his computer. He can save $12 a week if he mows his neighbor's lawn and $10 a week if he babysits his nephew. How many weeks will it take John to save enough money to buy the computer game?
A.
total amount John can save in 1 week
B.
the cost of the game
C.
amount John earns per hour babysitting
Answers
The answer is B.
the cost of the game.
We need to know the cost of the game in order to find out how many weeks John has to save money. If we don't know this price, we'll never know whether John has saved enough money.
We can find out the total amount of money John can save in 1 week (so A. is not the answer). The amount of money John earns per hour doesn't matter to answer the question (so C. is wrong).
~ Hope this helps you!
A survey of 80 students found that 24 students both play in the band and play a sport. But 22 students are not in band and do not play a sport. There are 48 students in the band. If being in band is the row variable and playing sports is the column variable, fill in the labels in the table. tables Which of the following correctly represents the given data in the problem?
Answers
D) a = 24, c = 48, e = 22, i = 80
The line plot represents the heights of students in a second-grade classroom. Which statement is true?
A. The median is less than the mode.
B. The median height is 42 inches, and the mode height is 36 inches.
C. Most of the students in the class are shorter in height.
D. The mode is less than the median.
Answers
Answer:
B. The median is less than the mode
Step-by-step explanation:
During a family vacation, Ms. Walker drove 918 miles on 3 tanks of gasoline. Her daughter, Amani, wants to create an equation in the form em equals square tee, to represent the total number of miles, m, her mom can drive on t tanks of gasoline. What number should Amani put in the square to complete her equation?
Answers
Rate=(miles)/(number of tanks)
thus the rate will be:
miles=918 mile
tanks=3 tanks
thus
rate=918/3=306 miles/tank
Ajuda eu !!!!!!!!!!!!!!!!
Answers
Ms.kellsons storage closet is 3ft long,3ft wide,and 7 ft high.can she fit 67 boxes that each have a volume of 1 cubic foot in her closet
Answers
67 x 1 ft³ = 67 ft³
Answer: No, she does not have enough to fit 67 boxes of 1 ft³ each.
|-x-2y| for x =-3 and y=3
Answers
simplify radical (1-cos0)(1+cos0)/ cos^2 0
HELP ME PLS!! ASAP
Answers
(1-cos)(1+cos)=1-cos² which equals to sin²
√sin²/cos²= sin/cos which equals to tan
Need help with math thank u
Answers
2,-4
These are two answers
It is infinitely many solutions
match the following situation with one of the linear systems. Lewis wants to acquire at most 12 packages of baseball cards. Some packages have 4 rookie cards and some have only 3. In all, there are at most 38 rookie cards.
A.
B.
C.
D.
Answers
The correct linear system for the student's question is D. x + 3y \<= 38, x + y \<= 12, which matches the conditions of Lewis's situation for acquiring baseball cards.
The student is looking to match a situation with a linear system. The situation is that Lewis wants at most 12 packages of baseball cards, some containing 4 rookie cards and others 3 rookie cards, with a total of 38 rookie cards at most.
To match the situation with the correct linear system, we must set up two inequalities: one for the number of packages and another for the number of rookie cards.
Let x represent the number of packages with 4 rookie cards and y represent the number of packages with 3 rookie cards.
The first condition is that Lewis can have at most 12 packages, which gives us the inequality x + y \<= 12. The second condition is that the total number of rookie cards is at most 38, which gives us the inequality 4x + 3y \<= 38.
Considering these conditions, the correct answer is: D. x + 3y \<= 38, x + y \<= 12.
Vanessa is opening a clothing store. She plans to start by selling gym shorts. If it costs her $4 for each pair of shorts, $3 for the ink per pair of shorts, and $0.20 a bag, what is her unit cost per pair of shorts?
Answers
cost of shorts=$4
Number of pairs=1
thus
unit cost=4/1=4 dollars per pair
Answer: 4 dollars per pair
Answer:
its $7.20 on APEX
Step-by-step explanation:
A poll was conducted in states A, B, and C to determine which candidate voters would most likely vote for. The results are displayed in the table below:
What is P(conservative | State B)?
State A State B State C Total
Liberal 17 20 12 49
Conservative 23 15 13 51
Total 40 35 25 100
Answers
Answer:
15/35 = 3/7 = 0.428571
Explanation:
We are asked to find the probability that a given voter is conservative given they are in State B.
Going to the State B column, we see that there are 15 conservatives. This is out of a total of 35 voters in state B; this makes the probability 15/35.
Probability helps us to know the chances of an event occurring. The probability that a voter from State B is supporting Conservative is 0.4285.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
We're supposed to figure out how likely it is that a specific voter in State B is a conservative.
There are 15 conservatives in State B, according to the column. This is based on a total of 35 voters in state B, resulting in a 15/35 probability. Therefore,
P(conservative | State B) = 15/35 = 3/7 = 0.4285
Hence, the probability that a voter from State B is supporting Conservative is 0.4285.
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This is a question about inverse/transcendental functions. Can anyone confirm that the answer is D? The question is asking which statement is FALSE, and I'm bouncing back and forth a bit.
Answers
It is NOT true that [tex]\dfrac{d}{dx} \left( f^{-1}(x) \right) \ge 0[/tex]
The perimeter of the base of a pentagonal prism is 25 inches and one of its lateral edges is 4 inches. The lateral area of the prism is ________ square inches.
Answers
Answer:
Lateral area=100 square inches
Step-by-step explanation:
It is given that the perimeter of the base of a pentagonal prism is 25 inches, therefore each sides of the pentagon will be of 5 inches.
Also, one of its lateral edge is 4 inches, therefore each lateral face has area which will be equal to=[tex]5{\times}4[/tex]=[tex]20[/tex]square inches.
Since, there are 5 lateral faces of the pentagonal prism, therefore the lateral area of the prism will be: [tex]5{\times}20[/tex]
= [tex]100[/tex]square inches.
Which expression is equivalent to 4 sqrt 16x^11y^8/81x^7y^6
Answers
The given expression 4 sqrt(16x^11y^8/81x^7y^6) simplifies to (4/9) * x^2 * y by taking the square root of each term separately and then simplifying the powers of x and y.
Explanation:The expression given is 4 sqrt(16x^11y^8/81x^7y^6). To simplify this expression, we need to apply the square root to both the numerator and the denominator separately and simplify any like terms, as well as using the property of exponents to simplify the powers of x and y.
We start by simplifying the square root of each component:
Square root of 16 is 4.x^11 under the square root becomes x^(11/2).Similarly, y^8 under the square root becomes y^(8/2), which is y^4.The square root of 81 is 9.x^7 under the square root becomes x^(7/2).y^6 under the square root becomes y^(6/2), which is y^3.Now, divide and simplify:
(4 * x^(11/2) * y^4) / (9 * x^(7/2) * y^3) = (4/9) * x^((11/2) - (7/2)) * y^(4 - 3)
Therefore, we get:
(4/9) * x^2 * y
A trapezoid with an area of 166.75 in has bases that measure 21 in and 8 in find the height of the trapezoid
Answers
The required height of the trapezoid is 11.5 inches.
What is simplification?Simplification involves applying rules of arithmetic and algebra to remove unnecessary terms, factors, or operations from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve.
Here,
The formula for the area of a trapezoid is:
A = (b₁ + b₂) * h / 2
where A is the area, b1 and b2 are the lengths of the two bases, and h is the height.
We are given that the area of the trapezoid is 166.75 in² and the lengths of the two bases are 21 in and 8 in. So we can plug these values into the formula and solve for h:
166.75 = (21 + 8) * h / 2
Simplifying the expression on the right side:
166.75 = 29 * h / 2
Multiplying both sides by 2:
333.5 = 29 * h
Dividing both sides by 29:
h = 11.5
So the height of the trapezoid is 11.5 inches.
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Final answer:
To find the height of a trapezoid given its area (166.75 sq in) and bases (21 in and 8 in), you use the formula-
[tex]A = \frac{1}{2} h(b_1 + b_2)[/tex]
By rearranging to solve for h, you find that the height is 11.5 inches.
Explanation:
The question asks to find the height of a trapezoid given its area and bases. The area of a trapezoid is calculated using the formula A = [tex]\(\frac{1}{2}\)h(b_1 + b_2)[/tex], where A represents the area, h the height, and [tex]b_1[/tex] and [tex]b_2[/tex] the lengths of the two bases. In this case, the area is 166.75 square inches, and the bases measure 21 inches and 8 inches.
To find the height, we can rearrange the formula to-
h = [tex]\(\frac{2A}{b1 + b2}\)[/tex]
Plugging in the given values gives us-
h = [tex]\(\frac{2 \times 166.75}{21 + 8}\)[/tex]
which simplifies to-
h = [tex]\(\frac{333.5}{29}\)[/tex]
Therefore, the height of the trapezoid is 11.5 inches.