The chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.
There are two types of proportions.
1) Direct Proportion - shows the direct relationship between two quantities. It can be represented by the equation y = kx. As one quantity increases, the other quantity also increase.
2) Inverse Proportion - describes the indirect relationship between two quantities. It can be represented by the equation y = k/x. As one quantity increases, the other quantity decreases.
According to the problem, a body’s weight varies inversely with the square of its distance from the center of the earth.
y = k/x
let y = a body's weight
x = square of its distance from the center of the earth
Solving for the proportionality constant, k.
y = k/x
12 = k / (5000^2)
k = 12 x 25, 000, 000
k = 300, 000, 000
The equation for the relationship in the problem can now be represented by:
y = 300,000,000/x
where
y = a body's weight
x = square of its distance from the center of the earth
Evaluating the new equation where x = square of 10,000:
y = 300,000,000/x
y = 300,000,00/(100,000,000)
y = 3
Hence, the chicken will weigh 3 pounds when it is 10,000 miles from the earth's center.
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PLEASE HELP!!!! IMPORTANT!!!!
A, B, C and D are junctions on a motorway.
A B C D
distance CD= 3 x distance AB
distance BC= 25 miles
Salma drives from A to C.
She drives for 30 minutes at an average speed of 62 miles per hour.
Work out the distance AD.
Not drawn
accurately
The distance AD is 49 miles.
As per the given values of speed and time, we will calculate the distance AC. Firstly equalising the units.
As per the known fact, 60 minutes = 1 hour
30 minutes = (1/60)×30
30 minutes = 0.5 hour
Now, speed, distance and time are related as -
Speed = distance ÷ time
Distance = speed × time
Distance = 62 × 0.5
Distance = 31 miles
So, AC = 31 miles and BC = 25 miles.
Therefore, AB = AC - BC
AB = 31 - 25
AB = 6 miles
The distance AD = AC + CD
AD = 31 + 3 × AB
AD = 31 + 3 × 6
AD = 31 + 18
AD = 49 miles
Therefore, the distance between AD is 49 miles.
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The complete question is attached.
The plan for a concrete birdbath is shown
below. The bowl is a cylinder with a depth
of 10 cm. If the bowl has a diameter of
30 cm, what is the exposed surface area
of the birdbath, including the pillar and
pedestal?
Answer:
Step-by-step explanation
10 cm
Answer: unknwon
Step-by-step explanation:
because height of pillar not given
2p=47−17 please help with explinations
We calculate the right side of the equation : 47 - 17 = 30
2p = 30
Divide both side by 2, we have : p/2 = 30/2 -> p = 15.
Answer:
P=15
Step-by-step explanation:
2p = 47-17
2p = 30
Divide both sides by the coefficient of p which is 30
[tex]\frac{2p}{2} =\frac{30}{2}[/tex]
P= 15
In the figure, m∠AOD=105. If m∠AOB=8x, m∠BOC=7x and m∠COD=6x, what is the value of x?
Answer:
x = 5
Step-by-step explanation:
from the diagram
∠ AOB + ∠ BOC + ∠ COD = ∠ AOD ( substitute values )
8x + 7x + 6x = 105
21x = 105 ( divide both sides by 21 )
x = 5
Answer:
5
Step-by-step explanation:
AOB+BOC+COD=AOD
6x+8x+7x=105
21x=105
x=105÷21
x=5
what is the value of 8 4/3 ?
[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf= 9.\bar{33}[/tex]
Step-by-step explanation:[tex] \bf{8 \frac{4}{3} = \frac{3 \times 8 + 4}{3} = \frac{24 + 4}{3} = \frac{28}{3} = 9. \bar{{33 }}}[/tex]
What number is equal to √9?
Answer:
3
Step-by-step explanation:
x =√9
x= 9½
Multiply both sides by the power of 2
x²=9½*²
x²= 9
x²=3²
x=3
Alisa has $2.00 in change. If she has 7 quarters, what is the maximum number of dimes she can have?
Caroline is driving to a concert and needs to pay for parking. there is an automatic fee of $5 just to enter the parking lot, and when she leaves the lot, she will have to pay an additional $2 for every hour she had her car in the lot. how much total money would caroline have to pay for parking if she left her car in the lot for 3 hours? how much would caroline have to pay if she left her car in the lot for t hours?
The total money Caroline would have to pay for parking if she left her car in the lot for 3 hours is $11
For t hours the Caroline would pay 5+2t
What is algebraic expression?
Algebraic expression is a mathematical statement which points to when operations such as addition, subtraction, multiplication as well as division, are used for variables and constants, in essence, using algebraic expression, we can derive the equation that gives the total cost of Caroline driving and using the parking lot at the concert
There is a fixed charge of $5, there is also an additional $2 for every spent, if represent hours spent by t, then she would pay 2t in total for using the parking lot.
Total cost=5+2t
when t=3 hours
total cost=5+(2*3)
total cost=$11
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966500 in scientific notation
9.665 x 10^5
966500.0
Move the dot to the right 5 times
Emma bought a salad for $4.75 and a drink for $1.65. She had $18.35 left. How much money did she have before she bought the salad and drink
Answer: The amount she started with is $24.75
is 7.69 x 24^8 in scientific notation
Reason:
The 24 needs to be changed to a 10 for it to be in scientific notation.
The template for scientific notation is [tex]a * 10^b[/tex] where [tex]0 \le |a| < 10[/tex]
So for example, [tex]1.23 \times 10^4[/tex] is in scientific notation.
in mrs. middleton's math class, there are 7 more boys than girls. if there are 29 total students in the class, how many boys are there?
Answer:
18
Step-by-step explanation:
Answer:
18
Step-by-step explanation:
18 boys + 11 girls = 29 students
18-11=7
Can anyone answer these for me?
Answer:
x=12 y=10 z=-12
Step-by-step explanation:
Which segment (s) are perpendicular to AB?
Answer:
B) Segment CD onlyStep-by-step explanation:
In the plane, there is exactly one perpendicular line to a line from a particular point.
We can see CD is marked as perpendicular segment and there are no more such possible segments.
Correct choice is B.
Answer:
b) Segment CD only
Step-by-step explanation:
Now we have to,
→ find the segment perpendicular to AB.
The segment will be,
→ CD (only)
* As it is 90° from the segment AB, we can say that it is perpendicular to AB.
Hence, option (b) is correct answer.
consider measurements of the width w and length l of a piece of paper used to calculated the area of the paper using a
The area of the piece of paper is;
Area = length x width
⇒ a = l w unit square.
Here,
Given that;
The width of piece of paper = w
The length of piece of paper = l
We have to find the area of piece of paper by using a.
What is Area of rectangle?
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
Now,
Consider the shape of piece of paper is rectangular.
The width of piece of paper = w
The length of piece of paper = l
Since, we know that;
Area of rectangle = length x width
Then, The Area of piece of paper 'a' = length x width
⇒ a = l * w
Where, a = Area of rectangle, l = length of piece of paper and
w = width of rectangle.
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Sep 16, 1:21:38 AM
(3x-26)°, then find the measure of
The measurement or the value of x in the given equation [tex](3x-26)degrees = 180degrees[/tex] is [tex]x=68.67[/tex]°
As per the question statement, we are supposed to find the measure of angle x in the given equation, [tex](3x-26)= 180[/tex]
Before solving this question, we should know that this question is an example of solving a linear equation in one variable.
[tex](3x-26)= 180\\3x=206\\x=\frac{206}{3} \\x=68.67[/tex]
Hence the measure of the angle x is x=68.67°
This question is a good example of solving a linear equation in one variable.
Linear Equation: It is an equation which when plotted on a graph forms a straight line and we solve for an unknown number called as variable.
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There are 55 stickers in each box how many stickers are in seven boxes
Answer: 385 stickers
Step-by-step explanation:
7 boxes * 55 stickers/1 box=
7 * 55/1=
7*55=385 stickers
An airplane that can travel 450 mph in still air, encounters a 30-mph headwind. How long will it take the plane to travel 1050 miles into the wind?
The time plane will take to travel 1050 miles into the wind is 2.5 hours.
What is speed?Speed is defined as the rate of change of position in unit time.
Mathematically,
Speed = Distance/Time
Now given that,
Speed of airplane in still air = 450 mph
Speed of wind = 30 mph
Distance to travel = 1050 miles
So, Actual speed of wind = 450 mph - 30 mph
⇒ Actual speed of wind = 420 mph
So, since Speed = Distance/Time
⇒ Time = Distance/Speed
⇒ Time = 1050/420
⇒ Time = 2.5 hours
Thus, the time plane will take to travel 1050 miles into the wind is 2.5 hours.
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a game arcade consists of a balloon that is inflated little-by-little during each round of play. The player wins when the balloon pops. The amount of air that is needed to make the balloon pop can be modeled bya. uniform distribution on the interval from 25 to 35 cubic inches of air.
help it due in 4 mins please
Answer:
Step-by-step explanation:
draw an open circle on point -11 and a line going towards the left. Because it is less than -11 and not equal.
Point ( open circle ) on 0 going to the right because it is greater and does not including 0.
X
-3
1
O
y =
= 2x+2
q
-2
b
2
C
व
use the table to work out!
a, b, c,d when
Y=2x+2
Answer:
y and x = 4 if wanted a dinner equation in one hand over least common multiple
A 3.5 ft child casts a 60 inch shadow, the child is next to a telephone pole that casts a 50 ft shadow how tall is the telephone pole
The telephone pole is 35ft tall .
What is height?The height of any object is define as the distance measurement of that object from the top to its base. In geometry it is also called as altitude.
Height can be measured in various quantities such as feet, inches, centimeters etc.
Some of measurements are as below.
feet to inches1 feet = 12 inches
feet to centimeters1 feet = 30.48 cm
inches to centimeters1 inch = 2.54 cm
meters to feet1 feet = 3.28 feet
In the given question,
Convert 60 inches to feet ,
60 inches = 60/12 feet = 5 feet
Given, pole shadow = 50ft
child height =3.5ft
now, Set up proportion between the ratios of the child and his shadow and the telephone pole and its shadow.
[tex]\frac{child \ height}{child \ shadow \ length} =\frac{pole \ height}{pole \ shadow \ length}[/tex]
Let, x be pole height
=> [tex]\frac{3.5}{5} =\frac{x}{50}[/tex]
now solve the equation,
3.5 ×50 = x × 5
x = 35
Thus, the pole is 35 feet tall.
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Simplify the following expression in Scientific Notation. (1.8x10⁹) (6.7 x 10¹²)
a x 10^b
a=?
b=?
the following expression i.e. (1.8x10⁹) (6.7 x 10¹²) in Scientific Notation is 120.6×[tex]10^{20}[/tex] and a=120.6 and b=20
Scientific notation:
Scientific notation is a method of presenting very large or very small numbers in a more simplified format. We know that whole numbers can be extended indefinitely, but such large numbers cannot be written on a piece of paper. Furthermore, the numbers found after the decimal point needed to be represented in a more straightforward manner.
(1.8x10⁹) (6.7 x 10¹²) = 120.6×[tex]10^{20}[/tex]
Given (1.8x10⁹) (6.7 x 10¹²) =a x [tex]10^{b}[/tex]
a x [tex]10^{b}[/tex]= 120.6×[tex]10^{20}[/tex]
a=120.6 and b=20
Therefore,the following expression i.e. (1.8x10⁹) (6.7 x 10¹²) in Scientific Notation is 120.6×[tex]10^{20}[/tex] and a=120.6 and b=20
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Ken and Hamid run around a track.
It takes ken 80 seconds to complete one lap
It takes Hamid 60 Seconds to complete one lap
Ken and Hamid start running at the same time from the start line
How may laps will they each run when they next meet on the start line?
It is found that Ken will have run 3 laps and Hamid will have run 4 around a track.
What is prime factorization?Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities. Prime factorization is when all those factors are prime numbers.Thus, prime factorization expresses an integer in terms of multiples of prime numbers.
Prime factorization is unique for each integer.
To determine the number of seconds that will have passed when they meet again. We will use the LCM, or least common multiple, for this.
Thus the prime factorization of each number:
80 = 10(8)
10 = 5(2)
8 = 2(4)
4 = 2(2)
80 = 2(2)(2)(5)(2)
60 = 10(6)
10 = 5(2)
6 = 2(3)
60 = 2(2)(3)(5)
For the LCM,
2(2)(5)(2)(2)(3) = 240
This means every 240 sec; they will both be at the start line.
Since Ken completes a lap in 80 seconds, then he will completes
240/80 = 3 laps in 240 seconds.
Since Hamid completes a lap in 60 seconds, then he will completes 240/60 = 4 laps in 240 seconds.
Hence, It is found that Ken will have run 3 laps and Hamid will have run 4.
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4x-18=x-3 will give ten points for answer asap
Answer: x=5
Good luck :)
a boy throws a baseball across a field. the ball reaches its maximum height, 18 meters, after 1 second. after approximately 2.3 seconds, the ball lands on the ground. the ball’s motion can be modeled using the function f(x)
The height of the ball after 1.5 seconds is 15.5 meters so option (C) will be correct.
What is a function?A certain kind of relationship called a function binds inputs to essentially one output.
A function can be regarded as a computer, which is helpful.
The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.
Given the function as the height of ball f(x) and time x
f(x) = -10x² + 20x + 8
At x = 1.5
f(1.5) = -10(1.5)² + 20(1.5) + 8
f(1.5) = 15.5
Hence "The height of the ball after 1.5 seconds is 15.5 meters".
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Given question is incomplete complete question is attached below image ;
a rectangle has a perimeter of 10 meters. choose ,begin emphasis,all,end emphasis, the possible dimensions of the rectangle.
The possible dimensions of the rectangle having a perimeter 10 are
1)length= 4 and bredth= 1
2)length= 3 and bredth= 2
The perimeter of rectangle=2( length of rectangle + breadth of rectangle)
Given that the perimeter of rectangle=10
10=2( length of rectangle + breadth of rectangle)
5=length of rectangle + breadth of rectangle
For a rectangle, length must be always greater than the breadth
The possible values of length of rectangle= 4 and 3
As a result,the Breadth of the rectangle will be 1 if length =4
As a result,the Breadth of rectangle will be 3 if length =2
Therefore, The possible dimensions of the rectangle having a perimeter 10 are
1)length= 4 and bredth= 1
2)length= 3 and bredth= 2
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mcgraw hill determine whether each relation is a function
How many two-ninths are in eight-ninths?
Answer:
4
Step-by-step explanation:
2/9 + 2/9 + 2/9 + 2/9 = 8/9