Answer: [tex]1.83\text{ feet}[/tex]
Step-by-step explanation:
Given : If a line of one billion people standing shoulder to shoulder stretches 346,439 miles long.
We know that 1 mile =5280 feet
Then, the length of line=[tex]346439\times5280=1829197920[/tex] feet
We know that 1 billion can be written as :
[tex]1,000,000,000=10^9[/tex]
Now, the average shoulder width of the people in the line :-
[tex]\dfrac{1829197920}{1000000000}=1.8291979\approx1.83\text{ feet}[/tex]
Hence, the average shoulder width of the people in the line is about [tex]1.83\text{ feet}[/tex]
Last year, Amanda had
$10,000
to invest. She invested some of it in an account that paid
6%
simple interest per year, and she invested the rest in an account that paid
10%
simple interest per year. After one year, she received a total of
$760
in interest. How much did she invest in each account?
A train travels 50 kilometers in 4 hours, and then 77 kilometers in 3 hours. What is its average speed?
7 • (–5) • (–3) • (–8)
The length of a rectangle is 4 centimeters more than twice its width. If the perimeter of the rectangle is 86 centimeters , find the dimensions of the rectangle
- 1/2 (-3/2x + 6x +1) -3
Let w(s,t)=f(u(s,t),v(s,t)) where u(1,0)=−6,∂u∂s(1,0)=5,∂u∂1(1,0)=7 v(1,0)=−8,∂v∂s(1,0)=−8,∂v∂t(1,0)=6 ∂f∂u(−6,−8)=−1,∂f∂v(−6,−8)=2
Each side of a square is lengthened by 2 inches. the area of the new, larger square is 121 square inches. find the length of a side of the original square.
The length of the original square is 9 inches
What is a square?A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.
Area of square = x * x
where x is the side of the square
According to the question,
The area of the new square is 121 square inches.
Let the side of the original square is = x inches
Then the side of the new square is = x + 2 inches
Area of the new square = ( x + 2 )²
121 = ( x + 2 )²
11 = x + 2
x = 9 inches
Therefore, The length of the original square is 9 inches.
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the temperature on the earth's surface is about 5500 degrees Celsius .scientist believe that the temperature of the center of the sun is 270 times hotter. what is the temperature oof the center of the Sun?
Two negative integers are five minutes apart on the number line, and their product is 126. What is the sum of the two integers?
In an American Sign Language (A.S.L) class of 26 students, 15 are hearing impaired. What fraction of the students are hearing impaired?
The 15/26 fraction of the students is hearing impaired if in an American Sign Language (A.S.L) class of 26 students, 15 are hearing impaired.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
In an American Sign Language (A.S.L) class of 26 students, 15 are hearing impaired.
The fraction:
= 15/26
We can convert the above value in the percentage as follows:
The best method for obtaining this answer is to divide 15 by 26 to obtain the number 0.5769, multiply that number by 100 to obtain the number 57.69; and then round it to the closest full number if necessary.
15/26 in percentage will be 57.69
Thus, the 15/26 fraction of the students is hearing impaired if in an American Sign Language (A.S.L) class of 26 students, 15 are hearing impaired.
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Earth is about 4.5 billion years old and written human history extends back about 10,000 years. Suppose the entire history of Earth is represented with a 1000-meter-long timeline, with the birth of Earth on one end and today at the other end.
2 billion years is represented by how many meters of the timeline?
Celine's Cereal Company is launching a new brand of cereal and she is considering two different sizes for the base of the boxes. Box 1: The length is 3 times the width. Box 2: The length is 1 less than 4 times the width. The dimensions of the base of Box 1 are: width: x; length: 3 width: x; length: x + 3 width: x; length: x – 3 width: x; length: 3x
Answer:
D. Width = x and Length = 3x
Step-by-step explanation:
We are given that,
The length of Box 1 is 3 times the width of Box 1. ..................(1)
Let the width of Box 1 = x
So, from (1), we have,
Length of Box 1 = 3 × Width of Box 1
i.e. Length of Box 1 = 3x
Thus, the dimensions of Box 1 are : Width = x and Length = 3x
Hence, option D is correct.
In this exercise we have to identify which of the alternatives best represents the equation, like this:
Letter D
So we have that it is the area of a box, where we have:
The length of box is 3 times widthThe width of the box is XSo is the same as:
[tex]L= 3W\\W=X\\L=3X[/tex]
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What is the image of G for a dilation with center (0,0) and a scale factor of 1?
Students were surveyed about their favorite colors one fourth of the students perfered red , one eighth of the students perferred blue, and three fifth of the remaining students perferred green . if 15 students perferred green , how many students were surveyed
"sam's furniture was destroyed by a fire. the furniture cost $1200 when it was purchased, but similar new furniture now costs $1800. assuming the furniture was 50 percent depreciated, what is the actual cash value of sam's loss?"
The actual cash value of Sam's furniture loss is $600.
To calculate the actual cash value of Sam's furniture loss, we first determine the amount of depreciation applied to the original purchase price. Since the furniture was 50 percent depreciated, we calculate this amount to be 50% of $1200, which is $600. This means the depreciated value of the furniture is $1200 - $600 = $600. However, because the replacement cost of new, similar furniture is now $1800, this does not affect the actual cash value of the lost furniture, which remains at the depreciated value of $600. So the actual cash value of Sam's loss is $600.
Eight members of a chess club are having a tournament. In the first round every player will play a chess game against every other player. How many games will be in the first tournament
About 11/12 of a golf course is in the fairways, 1/11 in the greens, and the rest in the trees. What part of the golf course is in the trees?
[tex]\frac{1}{132}[/tex] part of the golf course is in the trees.
To find out what part of the golf course is in the trees, we need to add the fractions of the golf course that are in the fairways and the greens, and then subtract that sum from 1 (which represents the whole golf course).
First, we add the fractions of the golf course that are in the fairways and greens:
Fairways: [tex]\frac{11}{12}[/tex]Greens: [tex]\frac{1}{11}[/tex]To add these fractions, we must first find a common denominator. The denominators are 12 and 11, so the common denominator is 12 x 11 = 132.
Convert each fraction to have this common denominator:
[tex]\frac{11}{12}[/tex] = [tex]\frac{121}{132}[/tex][tex]\frac{1}{11}[/tex] = [tex]\frac{12}{132}[/tex]Now, add these converted fractions together:
[tex]\frac{121}{132}[/tex] + [tex]\frac{12}{132}[/tex] = [tex]\frac{133}{132}[/tex]
Since the sum [tex]\frac{133}{132}[/tex] is greater than 1, we convert it to a whole number plus a fraction. [tex]\frac{133}{132}[/tex] = 1 + [tex]\frac{1}{132}[/tex].
Now, to find the part of the golf course in the trees, subtract this sum from the whole golf course:
1 - 1 + [tex]\frac{1}{132}[/tex] = [tex]\frac{1}{132}[/tex]
So, [tex]\frac{1}{132}[/tex] of the golf course is in the trees.
Complete question:
About [tex]\frac{11}{12}[/tex] of a golf course is in the fairways, [tex]\frac{1}{11}[/tex] in the greens, and the rest in the trees. What part of the golf course is in the trees?
10 11/12 + 7 1/4 =
A. 3 8/12
B. 3 2/3
C. 17 1/4
D. 18 1/6
You purchase three packs of batteries at $11.99/pack. You have a coupon for 10% off and the sale tax is 7% how much is the total cost of your purchase?
The answer is 34.64. C.
The entire purchase of the three items cost about $34.
How to determine the total cost?The given parameters are:
The cost of one packs of batteries is $11.99/pack.
Coupon = 10% off
The total cost is then calculated using:
Total = (three packs of batteries) * (1 - Coupon)
So, we have:
Total = (11.99 + 11.99 + 11.99 ) * (1 - 10%)
Evaluate,
Total = 34.47
Approximate
Total = 34
Hence, the entire purchase of the three items cost about $34.
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The volume of a rectangular prism is given by the formula V = lwh, where l is the length of the prism, w is the width, and h is the height. Suppose a box in the shape of a rectangular prism has length (2a + 11), width (5a – 12), and height (a + 6). Which expression represents the volume of the box? v=(2a+11)(5a-12)(a+6) v=(10a^2-24a+55a-132)(a+6) v=(10a^3+60a^2-24a^2-144a+55a^2+330a-132a-792 v=10a^3+60a^2-24a^2+55a^2-144a+330a-132a-792 v=10^3+91a^2+54a-792
All of the given expressions for v are various stages in the process of "simplifying" the product of length, width, and height. Each and every one of them represents the volume of the box.
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 + 40t + 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0.2 s and 2.7 s. Which solution can be eliminated and why?
Answer:
Its -0.2 Because time cannot be a negative value.
Step-by-step explanation:
The correct value would be the 2.7 sec. one.
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Here, Indicated when h(t) = 0, we are to find for the time where the football has reached a certain height.
⇒ - 16t² + 40t + 7 = 0
Then, the values of t would be -0.2 and 2.7.
Since, we are to look for the time, it is impossible for us to have an answer that has a negative value.
So based from our answer, the solution that we will eliminate is the -0.2 one. Since its value is negative.
Thus, the correct value would be the 2.7 sec. one.
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Given that the points (-1, 10), (2, 10), (2, -2), and (-1, -2) are vertices of a rectangle, what is the ratio of the rectangle's length to its width?
Convert 604,800 seconds to weeks using Dimensional analysis
Is 25/99 a terminating or repeating decimal
a square has the side measurment of s = 2 3 over 2 using the formula 1= s^2 find the area of the square
30 + (.0825 x 30) + (15% x 30) =
What is the place value of the 4 in the number 5,679.04
Sections of pre-fabricated fencing are each 4 1/3feet long how long are 6 1/2 sections placed end to end
Sin(x2 + y2) da r , where r is the region in the first quadrant between the circles with center the origin and radii 2 and 5
A double integral of Sin(x^2 + y^2) over a region between two circles with radii 2 and 5 is transformed into polar coordinates for simplification. The limits of the polar coordinates correspond to this region, and the integral becomes ∫ ∫ rSin(r^2) dr dθ, with r ranging from 2 to 5, and θ from 0 to π/2.
Explanation:The student asked about the calculation of a double integral over a region between two circles, presented in polar coordinates, where the function is Sin(x^2 + y^2). For simplification, we can change to polar coordinates. In polar coordinates, x = rcosθ and y = rsinθ. Thus, x^2 + y^2 becomes r^2, and the function becomes Sin(r^2).
For a region between two circles of radii 2 and 5 in the first quadrant, we can describe the limits of the polar coordinates. r will range from 2 to 5, and θ from 0 to π/2. Thus, the integral will be ∫(from 0 to π/2) ∫(from 2 to 5) rSin(r^2) dr dθ. Evaluation of the integral will require techniques of polar integration.
It's important to note that this is a theoretical discussion and the actual integration may have complex results depending on the function to integrate.
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We need solve the given integral, convert coordinates to polar form and integrate step by step. First we will solve the inner integral from 2 to 5 and then the outer integral from 0 to π/2
We need to evaluate the double integral of Sin(x² + y²) over the region between the circles with radii 2 and 5.
In polar coordinates, where x = r cos(θ) and y = r sin(θ), this integral becomes:
∫(from 0 to π/2) ∫(from 2 to 5) sin(r²) r dr dθ
Let's solve the inner integral first, with respect to r:
Firstly, set up the integral: ∫(from 2 to 5) sin(r²) r dr.
Then Use the substitution u = r², then du = 2r dr.
Now Rewriting the integral: (1/2) ∫(from 4 to 25) sin(u) du = (1/2) [-cos(u)] (from 4 to 25).
and evaluating this: (1/2) [-cos(25) + cos(4)].
Next, integrate the result with respect to θ:
Set up the outer integral: (1/2) ∫(from 0 to π/2) [-cos(25) + cos(4)] dθ.
Now since [-cos(25) + cos(4)] is constant, the integral is straightforward: (1/2) [-cos(25) + cos(4)] * (π/2).
Hence the final answer: (π/4) [-cos(25) + cos(4)].
Therefore, the integral evaluates to (π/4) [-cos(25) + cos(4)].
EDITED QUESTION
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Find the double integral Sin(x² + y²) over the region between the circles with radii 2 and 5.
The price of 6 pretzels is $5.10. Simon and Sofia bought 8 pretzels and shared the cost equally. How much did each person pay?