Aristotle was the first to draw the conclusion that the Earth is round from actual data.
The first people to reach the empirically supported conclusion that the Earth was spherical were the ancient Greeks. In the sixth century BCE, Pythagoras originally put out the notion of a spherical Earth, which was further expanded by his disciples Parmenides and Plato. Yet in the fourth century BCE, the Greek philosopher Aristotle offered the strongest factual support for a spherical Earth.
Aristotle noted that the Moon experiences a bent shadow from the Earth during lunar eclipses. He understood that the Earth would have to be a sphere for this to happen. Aristotle also observed that the North Star's height fluctuates as one moves north or south, which could only be justified if the Earth were curved. Aristotle came to the conclusion that the Earth was a spherical based on these and other observations, which was a commonly held belief in the ancient world and has subsequently been supported by a wealth of data.
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3sintheta=sintheta+1
To solve for theta in the equation 3sin(theta) = sin(theta) + 1:
First, we can simplify the equation by subtracting sin(theta) from both sides:
2sin(theta) = 1
Then, we can isolate sin(theta) by dividing both sides by 2:
sin(theta) = 1/2
Using the unit circle or a calculator, we can find the two possible solutions for theta:
theta = pi/6 + 2npi or theta = 5pi/6 + 2npi, where n is an integer.
How to convert 95 confidence z score?
The z-score associated with a 95% confidence level is approximately 1.96.
The z-score associated with a 95% confidence level is the value of the standard normal distribution that corresponds to an area of 0.95 to the left of the z-score.
Using a standard normal distribution table or calculator, we can find that the z-score associated with a 95% confidence level is approximately 1.96.
Therefore, if we want to calculate the z-score for a 95% confidence level, we can use the formula
z = invNorm(1 - α/2)
where α is the significance level (α = 0.05 for a 95% confidence level), and inv Norm is the inverse normal cumulative distribution function. Using this formula, we can calculate the z-score as:
z = inv Norm(1 - 0.05/2)
= inv Norm(0.975) ≈ 1.96
Therefore, the z-score is 1.96
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1) At a pet store, the ratio of female birds to male birds was 5:3. Write a sentence explaining what this means.
This statement simply means there are more female birds in the pet store than there are male birds. It also means for every 5 female birds in the pet store there are 3 male birds
Ratio: Writing the meaning of a sentenceFrom the question, we are to write a sentence that explains what the given sentence means.
From the given information, the given sentence is
"At a pet store, the ratio of female birds to male birds was 5:3"
This statement simply means there are more female birds in the pet store than there are male birds; or there are less male birds in the pet store than there are female birds. It also means for every 5 female birds in the pet store there are 3 male birds; or for every 3 male birds in the pet store, there are 5 female birds.
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Which theorem or postulate proves that â–³ABC and â–³DEF are similar?Select from the drop-down menu to correctly complete the statement.The two triangles are similar by the ________.A. AA Similarity PostulateB. SSS Similarity TheoremC. SAS Similarity Theorem
The postulate that can be used to prove that triangles ABC and DEF are similar triangles is A. AA Similarity Postulate.
What is the AA Similarity Postulate?According to the AA triangle similarity criterion, two triangles are considered similar if their three angles are identical to one another. Equi-angular triangles are comparable in a nutshell. As just two pairs of angles must be equal in order for the third pair to be automatically equal thanks to the angle sum property of triangles, the proper term for this criterion would then be the AAA(Angle-Angle-Angle) criterion. However, we refer to it as the AA criterion instead.
We have, triangles ABC and DEF with:
two pairs of congruent angles - ∠B ≅ ∠E and ∠C ≅ ∠F.
Therefore, the postulate that has been used to prove that the triangles ABC and DEF are similar triangles is AA Similarity Postulate.
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The complete question is:
Which theorem or postulate proves that â–³ABC and â–³DEF are similar?Select from the drop-down menu to correctly complete the statement. The two triangles are similar by the ________. A. AA Similarity Postulate B. SSS Similarity Theorem C. SAS Similarity Theorem
unit 5 systems of equations and inequalities homework 4 solving systems by elimination day 2
To solve this system of equations by elimination, we need to eliminate one of the variables (either x or y) by adding or subtracting the equations.
In this case, we can eliminate x by multiplying the first equation by 2 and subtracting it from the second equation:
2x - 6y = 12 (original second equation)
-2(x - 3y = 7) (original first equation multiplied by -2)
-----------------
0x - 12y = -2
Now we have a new equation, 0x - 12y = -2, that relates only to y. Solving for y, we get:
0x - 12y = -2
-12y = -2
y = 1/6
Substituting this value of y back into either of the original equations, we can solve for x:
x - 3y = 7
x - 3(1/6) = 7
x - 1/2 = 7
x = 7 + 1/2
x = 15/2
Therefore, the solution to the system of equations is x = 15/2 and y = 1/6.
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Answer: (-4,-8)
Step-by-step explanation:
Use the figure below to answer the following question.
The figure is not drawn to scale, From top to bottom, the lines are labeled, t, q, r, s. From top to bottom, the measures read, 93 degrees, 93 degrees, 87 degrees.
The figure represents the four angles of a quadrilateral.
What is angle?Angel is a geometric figure that can be described as the amount of rotation between two straight line or planes and angles is measured in degree with the full circle being 360°.
The angles are labeled t, q, r and s. The measure of angle t and q is 93 degrees, while the measure of angle r and s is 87 degrees. This means that the quadrilateral is a parallelogram since opposite angles of a parallelogram are equal. The measure of each of the remaining angles is 180 degrees minus the measure of the known angles, which means that angle t and q are 87 degrees and angle r and s are 93 degrees. The sum of the angles of a parallelogram is 360 degrees, which further confirms that the figure is a parallelogram.
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2 checks for $90. 50 each
$45. 00
$150. 00
How much is the deposit?
To calculate the deposit, we need to add up the amounts of the two checks and the cash: $90.50 + $90.50 + $45.00 + $150.00 = $376.00. Therefore, the deposit is $376.00.
The problem asks us to calculate the deposit amount for two checks of $90.50 each, and cash of $45.00 and $150.00. To solve the problem, we simply add up the amounts of the checks and cash to find the total deposit amount. Adding $90.50 and $90.50 gives us $181.00, and adding this to the cash amounts of $45.00 and $150.00 gives us a total of $376.00. Therefore, the deposit amount is $376.00. This is the total amount of money that will be added to the account when the checks and cash are deposited.
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7.4.2. what values of x satisfy the following equations? (a) p(−x ≤ t22 ≤ x) = 0.98
The values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.
The expression p(- x ≤ t22 ≤ x) represents the probability of a t-distribution with 22 degrees of freedom lying between - x and x.
We want to find the values of x such that this probability is 0.98.
We can use a table of t-distribution probabilities or a calculator to find the value of t for which the probability of a t-distribution with 22 degrees of freedom lying between −t and t is 0.98.
This value is , 2.518.
Therefore, we need to solve the inequalities:
-2.518 ≤ -x ≤ 2.518
Solving for x, we get:
-2.518 ≤ -x x ≤ 2.518
Therefore, the values of x that satisfy the equation p(−x ≤ t22 ≤ x) = 0.98 are all values between -2.518 and 2.518, inclusive.
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the six sigma dmaic approach is the best way to attack all problems and should be employed whenever possible. true or false?
False. The Six Sigma DMAIC approach is one of many problem-solving methods that can be used, and is most appropriate when the problem is complex and the potential solutions are not immediately evident.
Six Sigma DMAIC (define, measure, analyze, improve, control) is a strategy used to improve processes and products. It is designed to help companies identify and eliminate defects and reduce variability in their processes. It is not the best way to attack all problems, as there are many other problem-solving methods, such as Design Thinking and Lean, that may be more suitable solution depending on the complexity of the problem.
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Make a graph to show the relationship between distance and time for a bicycle that travels
10 miles every hour.
Answer:
answer is in the graph
Step-by-step explanation:
label your y axis miles (horizontal axis) with intervals of 10
label your x axis hours (right to left axis) with intervals of 1
for every 1 hour (x axis) your graph increases by 10 miles (y axis)
so your points are
(1, 10) and (2, 20) and (3, 30) and so on
your equation for the line is y=10x
see attached graph
What is the conversion of 500000 yen to usd?
By using the current exchange rate for converting "Japanese Yen" to "US Dollar" , 500000 Yen is = 3729.12 USD .
To convert the amount of 500000 YEN to USD, we use the current exchange rate between the currencies "Japanese Yen" and the "US Dollar" .
The exchange rate varies constantly due to fluctuations in the global financial markets ,
The current exchange rate of 1 US Dollar = 134.08 Japanese Yen ,
We have to convert the amount 500000 yen to USD by dividing 500000 by 134.08 ;
⇒ 500000/134.08 = 3729.1169 USD ;
≈ 3729.12 USD .
Therefore, 500000 Japanese yen is approximately equal to 3792.12 US Dollars .
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what is 1000 hours in days?
1000 hours in day can be converted in to by a formula dividing the the 1000 hours by 24 is 41.66 days.
Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.
As 1 Hour is equal to 0.0416666666667 Days, you must multiply 1000 by 0.041666666666667 to convert hours to days. The outcome is as follows:
1000 hr × 0.041666666666667 = 41.667 d
1000 hr = 41.667 d
We come to the conclusion that one thousand thousand hours is equal to 41.7667 days:
41.667 days are equivalent to 1000 hours.
Hence, using the conversion method above, you can figure out how many days there are in 1000 hours.
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what is 10 pm military time
The time 10 pm can be expressed in military time as 2200 hours .
In military time, the hours of the day are expressed in a 24-hour format,
The time starts from 0000 (midnight) hours and goes up to 2359 (11:59 PM) hours.
To convert a time from the standard 12-hour clock to military time, we add 12 hours to any time in the afternoon or evening .
In this case , to convert 10 PM to military time, we add 12 hours to the time ;
⇒ 10 PM + 12 hours = 22:00 hours or 2200 hours ;
Therefore, 10 PM in military time is 2200 hours.
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−3.6−1.9t+1.2+5.1t does any body know? I’m new at this and don’t know it well.
Answer: 3.2t − 2.4
Step-by-step explanation:
Add −3.6 and 1.2
Then, add −1.9t and 5.1t
3.2t − 2.4
what is definition of sampling error
Sampling error refers to the difference between the results of a sample and the true characteristics of the population from which the sample was drawn.
In statistics, sampling error is a measure of the degree of uncertainty that arises when estimating the characteristics of a population based on a sample of that population. This error occurs due to the fact that it is not feasible to collect data from every individual in a population, so researchers must rely on samples.
Sampling error can arise from various sources, including biases in the sample selection process, variability in the characteristics of the population, and random chance. Understanding and quantifying sampling errors are important in order to assess the validity and reliability of statistical estimates and to draw accurate conclusions from data.
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If the 2nd term is 2 and the 5th term is 432, find the 3rd term of the geometric sequence.
The 3rd term of the geometric sequence is 6.
Describe Equation.In mathematics, an equation is a statement that two expressions are equal. It usually contains one or more variables, which are unknown quantities that can take on different values. Equations are used to represent relationships between quantities, and they can be used to solve problems by finding the values of the variables that make the equation true.
An equation typically consists of two sides, separated by an equal sign. Each side can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. For example, the equation:
2x + 3 = 7
contains the variable x, as well as constants 2, 3, and 7, and mathematical operations of addition and multiplication.
Equations can be solved by applying algebraic techniques to isolate the variable on one side of the equation. For example, to solve the above equation for x, we can first subtract 3 from both sides to get:
2x = 4
Then, we can divide both sides by 2 to get
x = 2
This is the solution to the equation, which means that x must be equal to 2 in order to make the equation true.
Equations are used in many areas of mathematics, including algebra, calculus, geometry, and trigonometry. They are also used in physics, engineering, and other sciences to model physical phenomena and solve problems related to them.
Let's call the first term of the geometric sequence "a" and the common ratio "r".
The formula for the nth term of a geometric sequence is:
an = a *[tex]r^(n-1)[/tex]
We are given that the 2nd term is 2, so we know that:
a * r = 2 --(1)
We are also given that the 5th term is 432, so we know that:
a * [tex]r^4[/tex] = 432 --(2)
Now we need to solve for "a" and "r" in order to find the 3rd term.
First, let's solve equation (1) for "a":
a = 2 / r
Now we can substitute this expression for "a" into equation (2):
(2/r) *[tex]r^4[/tex]= 432
Simplifying, we get:
[tex]r^3[/tex]= 54
Taking the cube root of both sides, we get:
r = 3
Now we can substitute this value for "r" back into equation (1) to solve for "a":
a * 3 = 2
a = 2/3
So the first term of the sequence is 2/3 and the common ratio is 3.
Now we can use the formula for the 3rd term of a geometric sequence:
a3 = a * [tex]r^(3-1)[/tex]
a3 = (2/3) *[tex]3^2[/tex]
a3 = (2/3) * 9
a3 = 6
Therefore, the 3rd term of the geometric sequence is 6.
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Vanessa invested $2,500 into account that will increase in value by 3.5% each year. Write an exponential function to model this situation, then find the value of the investment after 20 years
(i) An exponential function to model this situation, [tex]A=2500(1.035)^n[/tex].
(ii) The value of the investment after 20 years A =$ 4,974.47 .
What is Exponential function ?When the input variable x appears as an exponent in the formula f(x) = ax, an exponential function is indicated. Both the exponential function and the value of x have an impact on the exponential curve.
An essential mathematical function is the exponential function, which has the following formula:
f(x) = ax
When a>0 and a=1 are not true.
x can be any real number.
The exponential function is given as :
[tex]A=P(1+r)^n[/tex]
Where :
A = amount
P = principal
r = rate %
n = number of years
the situation can be modelled using an exponential function by substituting.
[tex]A=2500(1+0.035)^n\\\\A=2500(1.035)^n[/tex]
(ii) when n = 20 , the Amount,
[tex]A=2500(1.035)^{20}[/tex]
A =$ 4,974.47
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Which inequality
represents the values of x
for y ≤-6(x-18)-2
when y=46?
The inequality that represents the value of x is x ≥ -10.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
y ≤ -6 (x - 18) - 2
Substitute y = 46
So,
46 ≤ - 6 (x - 18) - 2
46 ≤ - 6x + 108 - 2
46 ≤ 6x + 106
46 - 106 ≤ 6x
-60 ≤ 6x
-10 ≤ x
Thus,
The inequality of x is x ≥ -10.
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Question 3(Multiple Choice Worth 2 points)
(Effects of Changes in Data MC)
The shoe sizes of a group of middle school girls are shown.
5.5 6 7 8.5 6.5
6.5 8 7.5 8 5
If a shoe size of 7 is added to the data, how does the IQR change?
The IQR becomes a 2.5.
The IQR becomes a 1.5.
The IQR remains a 3.
The IQR remains a 2.
If a shoe size of 7 is added to the data the IQR remains the same 2. Option D is the correct answer.
What is IQR?The interquartile range (IQR) in descriptive statistics is a measurement of statistical dispersion, or the spread of the data. The IQR is also known as the middle 50%, the fourth spread, or the H-spread. The difference between the data's 75th and 25th percentiles is how it is defined.
By using linear interpolation, the data set is separated into quartiles, or four rank-ordered even sections, to determine the IQR.
The shoe size in increasing order are written as:
5,5.5,6,6.5,6.5,7,7.5,8,8.5
The median of the data is:
Median = 5th value
Median = 6.5
The IQR of the data is given as:
IQR = Q2 - Q1
IQR = (7.5 + 8)/ 2 - (5.5 + 6) / 2
IQR = 2
When 7 is added to the data, the new order is:
5,5.5,6,6.5,6.5,7,7,7.5,8,8.5
The median of the new data is:
Median = 5th + 6th value/ 2
Median = (6.5 + 7)/2 = 6.75
The IQR of the data is given as:
IQR = Q2 - Q1
IQR = (7.5 + 8)/ 2 - (5.5 + 6) / 2
IQR = 2
Hence, if a shoe size of 7 is added to the data the IQR remains the same 2. Option D is the correct answer.
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what is 5 8 as a decimal
The number 5/8 as a decimal is 0.625
As we divide a whole into smaller parts, we get decimals. Hence, there are two parts to a decimal number: a whole number part and a fractional part. The whole component of a decimal number has the same decimal place value system as the complete number. After the decimal point, however, when we proceed to the right, we obtain the fractional portion of the decimal number.
An informal way to read a decimal is to first read the whole number as you would any whole number, then the decimal point as "point," and finally each individual digit of the rational part.
the decimal of 5/8 is
5÷8 = 0.625
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You and your friends decide to rent some studio time to make a CD. Big Notes Studio rents for $100 plus $60 per hour. Great Sounds Studio rents for $25 plus $80 per hour. Determine the number of hours for which the cost of 1 Step renting the studios is the same. Work needs to be showed btw
The solution is found by slope of the graph and the solution is 2,200.
Let x the amount of money per hour and y the total amount of money.
Studio A:-
Rents for 100 dollars plus 50 dollars per hour.
[tex]y= 100 + 50x[/tex]
So the slope is 50 and the y intercept is 100.
Studio B:-
rents for 50 dollars plus 75 dollars per hour.
[tex]y= 50 + 75x[/tex]
So the slope is 75 and the y intercept is 50.
ThrTh solution is 2200 , see the gragraphph.
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Complete question:- You and your friends decide to rent some studio time to make a CD. Big Notes Studio rents for $100 plus $50 per hour. Great Sounds Studio rents for $50 plus $75 per hour. Solve the system by graphic method.
Write each expression with fewer terms.
`10x-2x`
18x-(7+4x)
Step-by-step explanation:
10x - 2x = 8x
18x - (7 + 4x) = 18x - 7 - 4x = 14x - 7
= 7(2x - 1)
please pick whatever you think your teacher prefers.
The mean and the median are closely related concepts. The median is the numerical value separating the higher half of your data from the lower half. You can find the median by arranging all of the observations from lowest value to highest value and picking the middle value​ (assuming you have an odd number of​ observations). Although the mean and median are closely​ related, the difference between the mean and the median is sometimes of interest.
Suppose Country A has five families. Their incomes are $9000, $21,000, $29,000, $39,000, and $50,000.
Country A's median income is _______, and its mean income is ______.
Suppose country B also has five familities. Their incomes are $9000, 21000, 29000, 39000, and 151000.
Country B's median income is _____ and its mean income is ____.
Country _____ has a greater income inequality
Based on your answers to this​ question, would you expect the ratio of the mean income in the United States to the median income has risen or​ fallen? Explain.
A.
​Fallen, because means change less with standard deviation.
B.
​Risen, because means change more with extreme values.
C.
​Risen, because means increase but medians decrease with income.
D.
​Risen, because medians increase with variance but means do not.
Mean of country A is $29600 and median $29000. Mean of country B is $49800 and median is $29000. Country B has greater income inequality. So option B is the correct answer.
Mean of incomes in country A = (9000+ 21000+ 29000 + 39000+ 50000)/5 = $29600
Median income of country A = (5+1)/2 th term = 3rd term = $29000
Mean to median ratio = 29600/ 26000= 1.02
Mean income of country B = ( 9000+ 21000+ 29000+ 39000+ 151000)/5 = $ 49800
Median income = (n+1)/2 th term = (5+1)/2 = 3rd term = 29000
Mean to median ratio of country B = 49800/29000 = 1.71
Since mean and median are closer to each other, standard deviation is less. The mean to median ratio is greater for country B. So country B has greater income inequality.
If the income inequality has been increasing, then the mean-median ratio will increase, due to the extreme values, mean will increase. So option B is the correct answer.
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1. Alden took out a mortgage on his home for $275,000 for 30 years at an annual interest rate of 4%. In January, Alden paid $495 toward the principal and the rest of his mortgage payment was the interest on
the loan. How much did Aiden pay in interest for the month of January? Use the monthly mortgage payment table below.
Show your work.
A) $859.92
B) $817.91
C) $759.96
D) $805.42
So, in response to the above question, we can state that As a result, equation Alden paid interest of $816.75 for the month of January.
What is equation?A mathematical equation links two statements and utilises the equals sign (=) to indicate equality. In algebra, an equation is a mathematical assertion that proves the equality of two mathematical. For examples, in the equation 3x + 5 = 14, because equal sign separates the numbers by a gap. A mathematical formula may be used to determine how the two sentences on either side of a letter relate to one another. The emblem and the particular piece of software are usually identical. like, for instance, 2x - 4 = 2.
We must first estimate the monthly mortgage payment using the monthly mortgage payment table in order to compute the amount of interest paid for the month of January.
The table shows that the monthly payment per $1,000 borrowed for a 30-year loan at 4% interest is $4.77. So, the following formula may be used to determine Alden's mortgage payment each month:
$275,000 / $1,000 = 275
$275 x $4.77 = $1,311.75 (monthly mortgage payment) (monthly mortgage payment)
Alden's January mortgage payment included $495 towards the principle, with the balance going to interest. The amount of interest paid can be determined as follows:
$1,311.75 - $495 = $816.75
As a result, Alden paid interest of $816.75 for the month of January.
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How to multiply Matrices 3x3 matrix by 3x3 matrix ?
Multiply each row of the first matrices of 3 x 3 order by the column of another matrix of 3 x 3 order, then add the result.
To multiply the two matrices the number of column of the first matrices should be equal to the number of rows of the second matrices.Multiply each row of the first matrices to the each column of the second matrices .Now add the result of the multiplication for each input.Order of the resultant matrix is always equals to same number of rows of first matrix and number of the columns of the second matrix.In the given 3 x 3 order matrices number of columns of the first matrix is same as the number of columns of the second matrix.Resultant matrix is also of the order 3 x 3 order.Therefore, to multiply 3 x 3 order matrices multiply each row of first matrix with each column of the second matrix.
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Please look at the screenshot and help with the problem. Will be giving 15 points.
Answer:-1
Step-by-step explanation:
When you multiply exponents that have the same bases you add the exponent. You subtract the exponents when you divide.
x^9=x^y*x^10 the blank box is -1.
Marieme wants to build a rectangular garden whose area is
24
2424 square meters.
1. Write an equation that represents the garden's length in meters (
l
ll) based on its width in meters (
w
ww).
The equation representing the length of the garden in meters
is length = 24/width.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
Given, A rectangular garden has an area of 24 square meters.
We know, Area = length×width.
Therefore, 24 = length×width.
Now, An equation that represents the garden's length in meters is,
24 = length×width.
length = 24/width (meters).
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The dot plot shows the number of chess games won by each of the 20 students in a competition.
:
1
2
The mean is 20.
Number of Chess Games Won
:
What statement about the data is true?
The mean is 5.35.
The mean is 91.
3
The mean is 4.55.
6
7
8
9 10
Answer:25
Step-by-step explanation:
pls explain how to do this!!!
The explanation is in the picture
find the ordered pairs in f(x)=x^2-2x+3 and f(x)=-2x+19
The ordered pairs in f(x)=x^2-2x+3 and f(x)=-2x+19 are (√21, 24 - 2√21) and (-√21, 24 + 2√21)
How to find the ordered pairTo find the ordered pairs of the two functions, we need to solve the system of equations:
f(x) = x^2 - 2x + 3
f(x) = -2x + 19
We can set the two expressions for f(x) equal to each other:
x^2 - 2x + 3 = -2x + 19
Simplifying and rearranging, we get:
x^2 = 21
Taking the square root of both sides, we get:
x = ± √21
Therefore, there are two ordered pairs that satisfy both equations:
(√21, f(√21)) and (-√21, f(-√21))
To find the values of f(√21) and f(-√21), we can substitute the values of x into either equation. Let's use the first equation:
f(√21) = (√21)^2 - 2(√21) + 3 = 21 - 2√21 + 3 = 24 - 2√21
f(-√21) = (-√21)^2 - 2(-√21) + 3 = 21 + 2√21 + 3 = 24 + 2√21
Therefore, the two ordered pairs are:
(√21, 24 - 2√21) and (-√21, 24 + 2√21)
Learn more about ordered pairs at: https://brainly.com/question/11139505
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