In order to cover the entire land area of United States with dollar bills, it would cost 9 × 10¹⁴ dollars.
What is a conversion factor?A conversion factor can be defined as a number that is typically used to convert (change) a number in one (1) set of units to another, either by dividing or multiplying.
Generally speaking, an appropriate conversion factor to an equal value must be used when it is necessary to perform any mathematical conversion.
Conversion:
1 mile = 160934 cm
Length of contiguous land = 160934 × 3000 miles = 482,802,000 cm.
Width of contiguous land = 160934 × 1000 miles = 160,934,000 cm.
Mathematically, the area of a rectangle can be calculated by using this formula;
Area of rectangle = length × width
Area of contiguous land = 482,802,000 × 160,934,000
Area of contiguous land = 77,699,257,068,000,000 cm²
Next, we would determine the area of Alaska:
Area of Alaska = 1/5 × 77,699,257,068,000,000
Area of Alaska = 15,539,851,413,600,000 cm²
Total area = Area of Alaska + Area of contiguous land
Total area = 15,539,851,413,600,000 + 77,699,257,068,000,000
Total area = 93,239,108,481,600,000 cm²
Also, the area of a dollar bill is given by:
Area of dollar bill = 6.5 × 15.5
Area of dollar bill = 100.75 cm²
Now, we can determine the cost:
Cost = Total area/Area of dollar bill
Cost = 93,239,108,481,600,000/100.75
Cost = 9 × 10¹⁴ dollars.
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Complete Question:
How much would it cost to cover the entire land area of United States with dollar bills? To answer this question, you may find the following information useful:
The contiguous United States (all of the states minus Alaska and Hawaii) can be approximated as a rectangle that measures 1000 miles north to south and 3000 miles east to west, while Alaska has about one-fifth the area of the contiguous states and Hawaii is small enough to be ignored for this rough calculation. Also, note that a dollar bill measures around 6.5cm × 15.5cm. Express your answer to one significant figure!
To make a small vase, Elisa uses no more than 4.5 ounces of clay. To make a large vase, she uses at least 12 ounces of clay. Which compound inequality represents the number of ounces of clay, c, that Elisa uses to make one vase of either size? 4.5 < c < 12 4.5 ≤ c ≤ 12 c < 4.5 or c > 12 c ≤ 4.5 or c ≥ 12
The compound inequality that represents the number of ounces of clay, "c", Elisa uses to make one vase of either size is [(c ≤ 4.5) or (c ≥ 12)].
As per the question statement, Elisa uses no more than 4.5 ounces of clay to make a small vase and at least 12 ounces of clay to make a large vase.
We are required to find out the compound inequality that represents the number of ounces of clay, that she uses to make one vase of either size.
Let the number of ounces of clay, that Elisa uses to make one vase of either size be denoted by "c".
Since, Elisa uses no more than 4.5 ounces of clay to make a small vase, The words "no more than" implies maximum, i.e., "either less than or equals to" and hence, for a small vase, "c" must be less than or equal to 4.5 oz, which gives [tex](c \leq 4.5)[/tex] ...(1)
On the other hand, to make a large vase, she uses at least 12 ounces of clay where the words "at least" means minimum, i.e, "either more than or equals to" and hence, for a large vase,
Thus "c" is more than or equal to 12 oz, which gives [tex](c \geq 12)[/tex]...(2)
Now, combining (1) and (2), we get [(c ≤ 4.5) or (c ≥ 12)] which is option "d".
compound inequality: In mathematics, a compound inequality is an inequality that combines or "compounds" two simple inequalities.To know more about compound inequality, click on the link below.
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raise 6 to the 7th power, then multiply j by the results
Answer:
279936j
Step-by-step explanation:
When Isabel began her book-selling business, she stored her inventory in her garage. Now that her business has grown, she wants to rent warehouse space. Lisa owns a large warehouse nearby and can rent space to Isabel. The area of the warehouse is 8,100 square feet. Lisa is willing to rent Isabel as little as 100 square feet of the space or up to as much as the entire warehouse. Her only requirement is that all spaces must be square.
The total length of each row of bookshelves will be 45 of the length of the storage space.
Let x be the area of the space that Isabel rents and f(x) represent the total length of a row of bookshelves. How would you find the length of a row of bookshelves? (3 points)
Answer:
f(x) = 4 ÷ 5√x
The area is mentioned to be square, so its length will be the square root of x. 4-fifths of that same length are the length of 1 row of the bookshelves, therefore, this is your answer.
➲ Hope it helps!
Answer: 90 feet
Step-by-step explanation:
The function that expresses length f(x) feet, in terms of area x square feet can be written as:
f(x) = sqrt(x)
So, when x = 100 square feet, f(x) = 10 feet,
when x = 121 square feet, f(x) = 11 feet,
when x = 8100 square feet, f(x) = 90 feet
i did what i could do
Alex is buying a sweater that originally costs $35 and a pair of jeans that originally cost $28. If the sweater is marked down 30% and the jeans are marked down 15%, find the total cost, including 8% sales tax.
Answer: $67.28
Step-by-step explanation:
I also do need help on this one, Simplify the Radical. Thank you.
The simplified form of the radical is expressed as 6xz²∛4
Simplifying radical expressionsGiven the radical function below expressed as:
2(108x²z⁴)^1/3
Expand to have:
2(108x^2/3z^4/3)
Simplify to have:
2(∛108x^2/3z^4/3) = 6(x)
2(3)(∛4)*x^2/3 * z^4/3
6∛4 * x^2/3 * z^4/3
6xz²∛4
Hence the simplified form of the radical is expressed as 6xz²∛4
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In November 2010 the average cost of 5 gallons of regular unleaded gasoline in the U,S. was $14,46. What was the average cost for 16 galions
The average cost for 16 gallons is $46.272
How to calculate the cost of 16 gallons ?The first step is to calculate the price of one gallon
5= 14.46
1= x
cross multiply
5x= 14.46
x= 14.46/5
x= 2.892
The price of 16 gallons can be calculated as follows
= 16 × 2.892
= 46.272
Hence the price of 16 gallons is $46.272
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Matthew bought a scale model toy version of the
space ship in his favorite science fiction television
show. If the tov is constructed with the scale
1 inch
= 12 feet and the toy is 1 foot 4 Inches
long, how long is the ship in the television show?
A. 192 feet
B.168 feet
C.60 feet
D. 49 feet
Answer: A. 192 feet
Step-by-step explanation:
1 foot 4 inches=
1 foot+4 inches=
12 inches+4 inches=
16 inches
Hence,
16*12=
16*(10+2)=
(16)(10)+(16)(2)=
160+32
192 feet
Determine whether the statement is true or false if x=8, y=2 , and z=3 .
2 x=3 y z
Given that x = 8, y = 2, and z = 3, the equation 2x = 3yz is false.
An expression is a number, variable or the combination of both put together by operation symbols while an equation is a statement that shows that two expressions are equal and is separated by an equal sign "=".
To check if the equation 2x = 3yz is true when x = 8, y = 2, and z = 3, plug in or substitute the value of each variable to the equation and evaluate.
2x = 3yz
2(8) = 3(2)(3)
16 ≠ 18
Since 16 is not equal to 18, the given values do not satisfy the equation, then the statement is not true.
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negative 3 and 4 over 5 minus 5 and 2 over 3.
Answer:
-6.53333333333 (-6.53)
Step-by-step explanation:
Hope this helps! <3
Hello! :) Pls help me with this math question :)) I want 5 halves of a cupcake for myself, 2 halves for my friend and 1 half for our other friend, FrostingTower would be great. Pls help!!! Ty :>
The total cupcakes that are needed will be 9 1/2.
How to calculate the fraction?The fraction needed for yourself = 5 1/2
The fraction needed for your friend = 2 1/2
The fraction needed for your other friend = 1 1/2
The total fraction needed will be:
= 5 1/2 + 2 1/2 + 1 1/2
= 9 1/2
Therefore, the cupcakes that are needed will be 9 1/2.
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I want 5 halves of a cupcake for myself, 2 halves for my friend and 1 half for our other friend. What is the total needed?
Use the figure to the right to find the value of PT. T is the midpoint of PQ
PT=5x+7 and TQ=9x-9
======================================================
Explanation:
Since T is the midpoint of PQ, this means the smaller pieces PT and TQ must be equal. In other words, T divides PQ in half.
PT = TQ
5x+7 = 9x-9
5x-9x = -9-7
-4x = -16
x = -16/(-4)
x = 4
Use this to find each segment length.
PT = 5x+7 = 5(4)+7 = 20+7 = 27TQ = 9x-9 = 9(4)-9 = 36-9 = 27Both pieces are 27 units long, which confirms the answer.
Given m || n, find the value of x and y.
5. Which equation's line is steeper and explain how you know
A. y = 3x + 7
B. y=x+9
Answer:
Step-by-step explanation:
A, because the slope 3 is larger than a slope of 1.
Equation A's line is steeper than equation B's line because it has a higher slope.
To determine which equation's line is steeper, we need to compare their slopes. In both equations, the coefficients of the x term represent the slope of the line.
Let's first rewrite both equations in slope-intercept form, which is of the form y = mx + b, where "m" is the slope and "b" is the y-intercept:
A. y = 3x + 7
B. y = x + 9
In equation A, the coefficient of x is 3, which means the slope of the line is 3.
In equation B, the coefficient of x is 1, which means the slope of the line is 1.
Now, to compare the slopes, we can see that the slope of equation A (3) is greater than the slope of equation B (1).
This means that the line represented by equation A is steeper than the line represented by equation B.
Hence, equation A's line is steeper than equation B's line because it has a higher slope.
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Which expression has a value of 8?
. 21 - 3 × 5
. (28 ÷ 4) + (10 × 2)
. (16 ÷ 4) + 3 × 2
. 4 × 5 - 6 × 2
Answer:
Hi, it's D.
Step-by-step explanation:
[tex]4\times \:5\\= 20\\6\times \:2\\= 12\\20-12\\= 8[/tex]
a student performed the following steps to find the solution to the equation . where did the student go wrong? step 1. factor the polynomial into (x 8) and (x – 6) step 2. x 8
The student is wrong in the steps of the factorization.
What do you mean by factorization in polynomial?Factorization of polynomials, also known as polynomial factorization, is a mathematical and computer algebraic technique that combines irreducible factors with coefficients in the same domain to produce a polynomial with coefficients in a particular field or in integers. A polynomial with coefficients in a certain field or in integers is expressed as the product of irreducible factors with coefficients in the same domain in mathematics and computer algebra, which is known as polynomial factorization. A polynomial can be expressed as the product of its factors, where the components must have a degree that is less than or equal to the original polynomial.
The equation is given as:
x^2 + 2 x - 48 = 0
Expand the equation
x^2 + 8x - 6x - 48 = 0
Factorize the equation
x(x + 8)- 6(x + 8)
Factor out x + 2
(x + 8)(x - 6) = 0
The above means that the factored equation of x^2 + 2x - 48 = 0 is (x + 8)(x - 6) = 0
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Please help! I need help hurry please
Answer:
Step-by-step explanation:
f(x)=x^2+1
f(x^2+1)
f(x^2+1):x^4+2x^2+2
f(f(x))=x^4+2x^2+2
2nd answer
Hope this helps!^^
A central angle has the center as its vertex and its sides contain two radii of the circle.
Answer: A central angle is an angle with its vertex at the center of the circle and its two sides are radii. The sum of all central angles in a circle 360 degrees. The degree of the arc formed by the endpoints of a central angle is equal to the degree of the central angle.
Step-by-step explanation:
the percent of the observations that are classified as outliers by the 1.5 × iqr rule is the same in any normal distribution. what is this percent? show your method clearly.
In any normal distribution, about 0.7 percent (0.7%) of the data are outliers.
What is an outlier?An outlier is also referred to as anomalous data and it can be defined as a numerical value that is either unusually too small or large (big) in comparison with the overall pattern of the numerical values contained in a data set.
What is an interquartile range?IQR is an abbreviation for interquartile range and it can be defined as a measure of the middle 50% of data values when they are ordered from lowest to highest.
Mathematically, interquartile range (IQR) is the difference between quartile 1 (Q₁) and quartile 3 (Q₃):
IQR = Q₃ - Q₁ = 75th percentile - 25th percentile.
The 75th percentile is equal to x when z has a p-value of 0.75, therefore, z is equal to 0.675. Similarly, the 25th percentile is equal to x when z has a p-value of 0.25, therefore, z is equal to -0.675.
Based on the 1.5 × IQR rule for outliers, the lower and upper z-scores are given by:
Zl = -0.675 -1.5(IQR)
Zl = -0.675 -1.5(0.675 + 0.675)
Zl = -0.675 -1.5(1.35)
Zl = -0.675 - 2.025
Zl = -2.7
Zu = 0.675 + 1.5(IQR)
Zu = 0.675 + 1.5(0.675 + 0.675)
Zu = 0.675 + 1.5(1.35)
Zu = 0.675 + 2.025
Zu = 2.7
For the p-value, we have:
P(z<2.7) = 1 - 0.9965
P(z<2.7) = 0.0035.
For the percentage of outliers, we have:
Outliers = 2 × 0.0035 × 100
Outliers = 0.0070 × 100
Outliers = 0.7%.
In this context, we can reasonably infer and logically deduce that about 0.7 percent (0.7%) of the data are outliers in any normal distribution.
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the solution set of a linear system involving variables x1; : : : ; xn is a list of numbers.s1; : : : ; sn/that makes each equation in the system a true statement when the values s1; : : : ; sn are substituted for x1; : : : ; xn, respectively.
The given statement is False, because the description only applies to one solution. The solution set contains all conceivable solutions.
What is a linear number pattern?A linear number pattern is a succession of numbers with the same difference between each term. As an example, consider the numbers 1, 3, 5, 7, 9,... Every phrase differs by a factor of two. These are also known as linear numbers. Another example would be 7, 17, 27, 37,...
What is the nonlinear sequence formula?A formula can be found for linear sequences, that is, sequences in which the difference between succeeding terms is always the same. would have resulted in the formula un = 3n + 35. produces the formula un = 3n - 10, where c is either positive or negative.
To obtain the remaining phrases, you simply keep using the addition of 1 method.
Here are a few further illustrations of linear number patterns:
Beginning with three points and a two-point difference:
3, 5, 7, 9, … Starting with five and a three-point difference:
5, 8, 11, 14, …
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Which of the following is not equivalent to -2/5
-2/5
2/-5
-2/-5
Answer:
-2/-5
Step-by-step explanation:
your welcome<3<3<3<3<<3
giving away points and marking brainliest
what is 500-60
Thanksss for ur kindness :)
hopefully brainly would not take it down
Answer:440
Step-by-step explanation:
y is directly proportional to x.
When y = 30, x = 6
a) Work out an equation connecting y and x.
b) Work out the value of y when x = 12.
Answer: Our required equation would be
Step-by-step explanation:
Since we have given that
y=30, when x = 6.
As there is direct proportion between x and y.
so, it becomes,
So, the equation connecting y and x would be
When we put the value of k, we get that
Hence, our required equation would be y=5x
some aspects of the spline smoothing approach to non-parametric regression curve fitting (with discussion).
Regression without parameters using smoothing splines A scatterplot's data is smoothed by fitting a smooth curve to it. Will initially concentrate on two variable issues: OneX Yand Will eventually include more than two predictors. Our example: Where "1; "1;::: "are independent from me," yi=f(xi) + I.
What is a non-parametric regression?The appealing, adaptable, and widely-used method of non-parametric regression uses cubic splines for curve estimation. Although the fundamental concept was developed many years ago, the approach is maybe not as well recognized or used as it could be. This paper's topics and examples are meant to increase comprehension and broaden the applicability of the spline smoothing technology. The fundamentals of the method, its relationship with moving averages and other smoothing techniques, the automatic selection of the degree of smoothing, and the use of residuals for model adaption and diagnostic testing are just a few of the specific topics covered. A finite-dimensional Bayesian framework is used to address the issue of offering inference areas for curves and for pertinent curve attributes.
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a campus performance series features plays, music groups, dance troops, and stand-up comedy. the committee responsible for selecting the performance groups includes three students chosen at random from a pool of volunteers. this year the volunteers came from a variety of majors. however, the three students for the committee were all music majors. does this fact indicate there was bias in the selection process and that the selection process was not random? explain.
NO , this fact does not indicate that there was bias in the selection process and that the selection process was not random.
This fact does not indicate that there was bias in the selection process and that the selection process was not random unless we know the number of different subject majors among the thirty volunteers.
It is possible that out of 30 volunteers , 20 can be from music majors and the rest 10 are majors from other subjects.
so in this case it is possibility for the process to be random and for the three students in the committee to all end up being music majors.
Therefore , by the given information it can be said that the selection process was random and unbiased.
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What is the slope of the line that passes through the points (7,-4)
and (11,-4)? Write your answer in simplest form.
Slope of line=0
Slope of line=[tex]\frac{y2-y1}{x2-x1}[/tex]
=[tex]\frac{-4+4}{11-7}[/tex] =[tex]\frac{0}{4}[/tex] =0
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. The letter m is frequently used to represent slope; the reason for this usage is unclear, but it can be found in O'Brien's (1844) and Todhunter's (1888) formulations of the equation for a straight line as "y = mx + b" and "y = mx + c," respectively.
The ratio of the "vertical change" to the "horizontal change" between (any) two unique points on a line is used to compute the slope.A declining line has a negative "rise." The line might be useful, as determined by a road surveyor, or it might appear in a diagram that represents a road or a roof as a description or a design.
The slope's absolute value serves as a gauge for a line's steepness, incline, or grade. A steeper line is indicated by a slope with a higher absolute value. A line can be drawn in one of four directions: upward, downward, horizontal, or vertical.
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a youth chorus has 30 members. there are 14 boys in the chorus. what is the ratio of boys to girls in simplest form? 715 7 over 15 87 8 over 7 815 8 over 15 78
The ratio of boys to girls in Simplest form is [tex]\frac{7}{8}[/tex] or 7:8 .
Ratio is defined as the term that is used to compare two or more numbers.
It is denoted by a:b and ":" is read as "is to" .
For Example , In a mixture of 10liter there 9 liter of milk and 1 liter of water ,
So the ratio of milk to water in the mixture will be 9:1 or [tex]\frac{9}{1}[/tex].
In the given question
Total members = 30
Number of Boys =14
Number of Girls = 30-14=16
The ratio of boys to girls =[tex]\frac{14}{16} =\frac{7}{8}[/tex] or 7:8 .
Therefore , the ratio of boys to girls in simplest form is 7:8.
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What is the density? Mass= 42.63g Volume= 49ml. Please put in the ml and g at the end.
The shape is a rectangle.
Step-by-step explanation:
49ml
43.63g
the answer is 29ml
The cost of a ticket to the circus is $23.00 for children and $47.00 for adults. on a certain day, attendance at the circus was 500 and the total gate revenue was $18,700. how many children and how many adults bought tickets?
Answer:
200 children and 300 adults
Step-by-step explanation:
No. of children = c
No. of adults = a
EQUATION 1: a + c = 500
EQUATION 2 : 23c + 47a = 18700
a = 500 - c
23c + 47(500 - c) = 18700
23c + 23500 - 47c = 18700
-24c = 18700 - 23500
-24c = -4800
-4800/-24 = c
c = 200
a = 500 - 200
a = 300
Need help with this….
-(v+4)+5=4v+1-5v
Answer:
All real numbers
Step-by-step explanation:
We can first factor the negative onto the parentheses to get [tex]-v-4+5=4v+1-5v[/tex]. Now we can combine like terms, getting [tex]-v+1=-v+1[/tex] . Since both sides are equal, the answer is "all real numbers," which can be represented with this symbol: [tex]\mathbb{R}[/tex]. (an R but with an extra vertical line in front)
a climate change program surveyed 1263 adults in a recent month and asked them about their attitudes on global climate change. a display of the percentages of respondents choosing each of the major alternatives offered is provided. list the errors in this display.
The error are;
1) The percentages do not sum to 100%
2) Showing the pie chart on a slant violates the area principle.
What are the errors?A pie chart is used to show the relationship between variables. We can use the bar chart to categorize the relationship that exists between different variables. In this case, we are looking at the responses to a climate change survey.
We can see that there are the following errors in the chart;
1) The percentages do not sum to 100%
2) Showing the pie chart on a slant violates the area principle.
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