Answer:
Step-by-step explanation:
The ratio of fiction books to non-fiction books is 5:2, which means that for every 5 fiction books in the library, there are 2 non-fiction books.
We know that the total number of books in the library is 1421. To figure out how many of those books are fiction, we need to divide the total by the sum of the parts in the ratio (5 + 2 = 7), and then multiply the result by the number of parts that represent fiction books (5).
So, the number of fiction books in the library is:
5/7 x 1421 = 1015
To find out how many non-fiction books there are, we can subtract the number of fiction books from the total:
1421 - 1015 = 406
Finally, to figure out how many more fiction books there are than non-fiction books, we can subtract the number of non-fiction books from the number of fiction books:
1015 - 406 = 609
Therefore, there are 609 more fiction books than non-fiction books in the library.
Need help!!
An individual borrowed $95,000 at an APR of 5%.
which will be paid off with monthly payments of $ 450 for 25 years.
Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?
Percentage of amount paid towards principal = 70.37%
Percentage of amount paid towards interest = 29.63%
What is APR?APR is abbreviation Annual Percentage Rate. APR is estimate cost over a year of borrowing, It is expressed in percentage of the money borrowed. The higher it is, the more expensive to borrow. The lower it is, the cheaper it'll be to borrow.
Given,
Principal amount (P) = $95000
APR (R) = 5% = 0.05
Time (T)= 25 years
Amount paid monthly $450 for 25 years
There are 12 payments every year for 25 years
No. of payments,
12 × 25 = 300.
Total amount paid
3000 × $450 = $135000.
Amount paid toward Principal = $95,000
In percentage
= (95000/135000)×100
= 70.37%
Toward Interest = $135000 - $95000 = $40000
In percentage
= (95000/135000)×100
= 29.63%
Hence, 70.37% of amount is paid toward principal and 29.63% is paid for interest.
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Answer:
Step-by-step explanation:
To determine what percentage of the total amount paid is applied towards the principal and interest, we first need to calculate the total amount paid over the 25-year term.
The monthly payment can be calculated using the formula for a loan payment:
P = (r(PV)) / (1 - (1+r)^(-n))
where P is the monthly payment, r is the monthly interest rate (APR / 12), PV is the present value of the loan (or the amount borrowed), and n is the total number of payments (25 years * 12 months/year = 300).
Plugging in the given values, we get:
P = (0.05/12 * $95,000) / (1 - (1+0.05/12)^(-300)) = $536.82
This means that the total amount paid over the 25-year term is:
Total amount paid = 300 * $536.82 = $161,046
The amount borrowed (or the principal) is $95,000. Therefore, the amount of interest paid over the 25-year term is:
Total interest paid = $161,046 - $95,000 = $66,046
To find the percentage of the total amount paid that is applied towards the principal, we can divide the principal by the total amount paid and multiply by 100:
Percentage of total amount paid towards principal = ($95,000 / $161,046) x 100% = 59.03%
To find the percentage of the total amount paid that is applied towards interest, we can divide the interest paid by the total amount paid and multiply by 100:
Percentage of total amount paid towards interest = ($66,046)
Case 1. ABY is the accounting expert for a firm that has many small clients that need monthly accounting services. ABY has been asked by the partner in charge to analyze the asset section of firms’ statements of financial positions which follow below:
2017
2018
Cash
$2,500
$3,900
Accounts receivable, net
35,000
40,000
Inventory
85,000
122,000
Other current assets
3,400
4,110
Total current assets
125,900
170,010
Property, plant & equipment, net
180,000
230,000
Other assets
15,000
26,000
Total assets
$320,900
$426,010
Required:
Prepare a Horizontal analysis of the assets section of the project statement of financial position for 2017 & 2018.and interpret any significant change in assets values. Round all percentage answers to one decimal place.
The analysis shows that the company experienced significant growth in assets from 2017 to 2018, which could be a positive sign for investors and stakeholders.
What is the Horizontal analysis of the assets section?Horizontal analysis is used to examine a company's financial statements over time. It is typically represented as a percentage increase over the same line item in the base year. Horizontal analysis enables users of financial statements to quickly identify trends and growth patterns.
To perform a horizontal analysis, we need to compare the changes in the values of assets between two years (2017 and 2018) as a percentage of the base year (2017). The analysis is as follows:
Assets 2017 2018 Change % Change
Cash $2,500 $3,900 $1,400 56%
Accounts receivable, net $35,000 $40,000 $5,000 14%
Inventory $85,000 $122,000 $37,000 44%
Other current assets $3,400 $4,110 $710 21%
Total current assets $125,900 $170,010 $44,110 35%
PPE, net $180,000 $230,000 $50,000 28%
Other assets $15,000 $26,000 $11,000 73%
Total assets $320,900 $426,010 $105,110 33%
Interpretation
The analysis shows that the total assets of the company increased by 33% from 2017 to 2018. The most significant change occurred in the other assets category, which increased by 73%, followed by inventory, which increased by 44%. The increase in other assets could be due to investments made by the company or acquisitions of other companies. The increase in inventory could indicate an increase in sales or production. The increase in property, plant & equipment, net by 28% could indicate that the company invested in new equipment or facilities to increase productivity or efficiency.Read more about Horizontal analysis
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A television manufacturer produces x sets per week so the total cost of production is given by relation C(x)=x²-195x² +66000x+15000 find how many television sets must be manufacturer per week to minimize the total cost.
We require x = 170 televisions to minimize total cost
What is the minimum of a function?The minimum of a function is the lowest value of that function.
How to find how many television sets must be manufacturer per week to minimize the total cost.?Given that a television manufacturer produces x sets per week so the total cost of production is given by relation C(x) = x² - 195x² + 66000x + 15000.
To find the minimum value, we differentiate C(x) with respect to x and equate to zero.
So, C(x) = x² - 195x² + 66000x + 15000
dC(x)/dx = d(x² - 195x² + 66000x + 15000)/dx
= dx²/dx - d195x²/dx + d66000x/dx + d15000/dx
= 2x - 195(2)x + 66000 + 0
= 2x - 390x + 66000
= -388x + 66000
Equating to zero, we have
dC(x)/dx = 0
-388x + 66000 = 0
-388x = -66000
x = -66000/-388
x = 170.1
x ≅ 170
So, we require x = 170 televisions to minimize total cost
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Myles writes down the distance readings from his car at the start and end of a journey.
Start of journey 12468
End of journey. 12845
Myles knows that the cost of petrol for this journey is 13p per mile.
Work out the total cost of the petrol used for this journey.
Give your answer in pounds.
Distance reading at the start of journey = 12468
Distance reading at the end of the journey = 12845
Distance traveled in the journey = 12845 - 12468 = 377 miles
Cost of petrol per mile = 13p
Cost of petrol for the journey = 13 × 377 = 4901p
Since one pound is one hundred pence, 4901p in pounds will be 4901/100 = 49.01 pounds
Cost of petrol used in the journey is 49.01 pounds
In the year 2020, there were 14.02 billion cell phones in use worldwide. In 2022, the number
increased to 15.96 billion worldwide.
a. What is the average rate of change in the number of worldwide cell phones?
b. Using 14.02 as the initial amount, write a linear equation that models the number of
worldwide cell phones. Make sure to define the variables.
C.If the rate stays the same, predict the number of cell phones that will be in use worldwide
in the year 2027.
Answer:
Step-by-step explanation:
a. The average rate of change in the number of worldwide cell phones can be calculated as:
Average rate of change = (change in number of cell phones) / (change in time)
The change in number of cell phones is 15.96 billion - 14.02 billion = 1.94 billion, and the change in time is 2 years. Therefore,
Average rate of change = 1.94 billion / 2 years = 0.97 billion/year
So, the average rate of change in the number of worldwide cell phones is 0.97 billion per year.
b. We can use the point-slope form of a linear equation to model the number of worldwide cell phones. Let t be the time in years since 2020, and C(t) be the number of worldwide cell phones in billions. Then the equation can be written as:
C(t) - 14.02 = 0.97t
Simplifying, we get:
C(t) = 0.97t + 14.02
So, the linear equation that models the number of worldwide cell phones is C(t) = 0.97t + 14.02.
c. To predict the number of cell phones that will be in use worldwide in the year 2027, we need to find the value of C(2027 - 2020) = C(7) using the linear equation we derived in part (b).
C(7) = 0.97(7) + 14.02 = 20.83 billion
Therefore, if the rate stays the same, we can predict that there will be 20.83 billion cell phones in use worldwide in the year 2027.
100 POINTS WILL MARK BRAINLIEST PLEASE HELPPPP
Answer: B. 3300
Step-by-step explanation: Answers in the 5000 range would be Expenses, and 2000 would be Liabilities, which are both opposite of capital. "S.E." in accounting typically stands for "Shareholder Equity" or "Stockholder's Equity" and would be one type of capital.
Si una pelota más un bate cuesta 1.10 dólares el precio del bate es 1 dólar más que la pelota
Answer:
Step-by-step explanation:
If a ball plus a bat costs 1.10 dollars and the price of the bat is 1 dollar more than the ball, what is the cost of the bat?
If we represent the price of the ball as "p", then the price of the bat will be "p + 1", since the problem tells us that the price of the bat is 1 dollar more than the price of the ball.
We also know that the sum of the price of the ball and the bat is 1.10 dollars. We can write this as an equation:
p + (p + 1) = 1.10
Simplifying and solving for p, we get:
2p + 1 = 1.10
2p = 0.10
p = 0.05
Therefore, the price of the ball is 0.05 dollars. To calculate the price of the bat, we can add 1 dollar to the price of the ball:
p + 1 = 0.05 + 1 = 1.05
So, the price of the bat is 1.05 dollars.
help with maths problem please
The area of the shaded region is 73.5 cm square.
How to find the area of a region?Supposing that there is no direct formula available for deriving the area, we can derive the area of that region by dividing it into smaller pieces, whose area can be known directly. Then summing all those pieces' area gives us the area of the main big region.
We are given the dimension of the shaded region.
Length = 15 cm
Breadth = 7 cm
The area of the trapezium is
Area = 1/2(sum of non parallel sides)height
Area = 1/2 (12 + 9) 7
Area = 1/2 x 21 x 7
Area = 73.5
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Point P is inside ΔABC and is equidistant from points A and B. On which of the following segments must P be located? A. AB B. The perpendicular bisector of AB C. The midsegment opposite AB D. The perpendicular bisector of AC
Answer:
Step-by-step explanation:
ASQASSA
This is about Linear equations, please help.
Answer:
Step-by-step explanation:
line a is 5ft
Which of the following expressions are written in standard form? Choose ALL that apply.
Answer:
[tex]A. \;x^2 -7x + 1[/tex]
[tex]B.\;5x^2 + 2x[/tex]
Step-by-step explanation:
Standard Form of Polynomial
Standard form of a polynomial is written in the descending order of the power of the variable.
The standard form of polynomial is given by
[tex]f(x) = a_nx^n + a_{n-1}x^{n-1}+....... + a_1x + a_0[/tex]
where [tex]x[/tex] is the variable and [tex]a_i,\; i = 0...n[/tex] are coefficients.
The only two expressions in standard form are
[tex]A. \;x^2 -7x + 1[/tex]
and
[tex]B.\;5x^2 + 2x[/tex] (here the constant a₀ is 0)
in exercises 9 and 10, (a) for what values of h is v3 in span fv1; v2g, and (b) for what values of h is fv1; v2; v3g linearly dependent? justify each answer.
The values of h is v3 in span fv1; v2g and h is fv1; v2; v3g is 4.
How to find the vector component?If we have given a vector v of initial point A and terminal point B
v = ai + bj
then the components form as;
AB = xi + yj
Here, xi and yj are the components of the vector.
We are given that;
v1 and v2 are not scalar multiples to each other
So, they are not linearly dependent
Now,
1(10h -42) -3(-14 +3h) +2 (18-20) =0
10h -9h-4 =0
h = 4
Therefore, by vectors the answer will be 4 so that the vector v3 is in {v1,v2}.
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The rectangle shown has a length of 0.9 centimeters and a width of 0.4 centimeters. A circle is drawn inside that touches the rectangle at two points. Which is closest to the area of the shaded region of the rectangle? Responses 0.14 cm2 0.23 cm2 0.28 cm2 0.49 cm2
The area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.
What are complex figures?The combined shapes of one or more simple polygons and circles make up the area of the composite shapes. We can add or subtract the areas of all the fundamental shapes together to determine the area of the composite shapes. Simply calculate the area of each individual form to obtain the area of composite shapes.
The length of the rectangle is 0.9 cm.
The width of the rectangle is 0.4 cm.
The diameter of the circle us 0.4 cm, thus the radius = 0.4/2 = 0.2 cm.
The area of the rectangle is:
A = (l)(b)
Substituting the values:
A = (0.9)(0.4)
A = 0.36 sq. cm.
The area of the circle is:
A = πr²
A = (3.14)(0.2)²
A = 0.1256 sq. cm.
The area of the shaded portion is:
Area of shaded portion = area of rectangle - area of circle
Area of shaded portion = 0.36 - 0.1256 = 0.2344 sq. cm
Hence, the area of the shaded region of the rectangle is 0.23 cm², and option 2 is the correct answer.
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PLS HELP!! I don’t understand
The points are as selected on the graph.
How to select points on the graph?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
Since f(x) = -9. What this means is that the value of f(x) will always be -9 irrespective of the value of x. That is:
x f(x)
-2 -9
0 -9
2 -9
7 -9
9 -9
Check the attached image for the points on the graph
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i dont understand at all
The equation is given by 5n + 100n = 210
Peggy has 8 quarters and 2 nickels
Let's call q the number of quarters and n the number of nickels.
If Peggy has four times as many quarters as nickels, we can write the following equation:
q = 4n
Then, each quarter has a value of 0.25 dollars and each nickel has a value of 0.05 dollars, so
0.25q + 0.05n = 2.10
Because she had $2.10. Now, we can replace the first equation on the second one
0.25(4n) + 0.05n = 2.10
1n + 0.05n = 2.10
Finally, we can multiply both sides by 100, so
100n + 0.05(100)n + 2.10(100)
100n + 5n = 210
Therefore, the equation that can be used to solve the problem is
5n + 100n = 210
Now, we can solve the equation for n
105n = 210
105n/105 = 210/105
n = 2
Then, q is equal to
q = 4n
q = 4(2)
q = 8
It means that Peggy has 8 quarters and 2 nickels.
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complete question is listed below:
Peggy had four times as many quarters as nickels. She had $2.10 in all. How many nickels and how many quarters did she have?
Which of the following equations could be used to solve the problem?
On+4 n=210
5 n+100 n=210
n+4 n=2.10
5n+100 n=2.10.
b. 3 and b= b- Let A= Show that the equation Axb does not have a solution for some choices of b, and describe the set of all b for which Ax b does have a solution. -6 -2 How can it be shown that the equation Ax=b does not have a solution for some choices f b? O A. Row reduce the matrix A to demonstrate that A has a pivot position in every row. O B. Find a vector b for which the solution to Ax b is the identity vector. O C. Row reduce the matrix A to demonstrate that A does not have a pivot position in every row. O D. Find a vector x for which Ax b is the identity vector. O E. Row reduce the augmented matrix o demonstrate that A bhas a pivot position in every row. A b Describe the set of all b for which Ax b does have a solution. b does have a solution is the set of solutions to the equation 0=2b, +b2. The set of all b for which Ax (Type an integer or a decimal.)
The way it can be shown that the equation Ax=b does not have a solution for some choices is A. Row reduce the matrix A to demonstrate that A has a pivot position in every row
How to solve thisA us 2 x 2 matrix, then Ax =b will not have a solution fot some B if rank(A) <2
This implies A does not have pivot position in every row in its reduced row echelon form.
This shows that option A is correct.
The augmented matrix [A b] is
[tex]\left[\begin{array}{ccc}1&4&b1\\3&-12&b2\end{array}\right][/tex]
Perform R2 = R2 +3 R1
[tex]\left[\begin{array}{ccc}-1&4&b1\\0&0&b2 = 3b1\end{array}\right][/tex]
New solutions exist if [tex]b_2 + 3b_i = 0[/tex]
0 = [tex]3b_1 + b_2[/tex]
Thus, the equation Ax = b have the solution if rank(A) = rank([A b])
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Find the number of positive integers that satisfy both the following conditions:
Each digit is a 1 or a 2
The sum of the digits is 3
Answer:
12
Step-by-step explanation:
1+2=3 and 12 satisfied all the conditions
The uniform distribution of a random variable
is given in the figure below.
From the figure, what is P (X < 1.48) or P (X > .2)
?
The probability that X falls inside this range according to the uniform distribution of a random variable is 0.38, or 38%.
what is probability ?The risk that an event will occur or maybe even a claim will now be true is measured by quantum mechanics, a mathematics field. The probability of an occurrence is a value between 0 and 1 and 1, where about range from 0 how likely the event is to occur and value of 1 indicates certainty. A probability is a numerical illustration of something like the possibility that a specific thing will take place. Probabilities can also be expressed using percentages ranging from 0% to 100% or from 0 to 1. the percentage of the number of outcomes to the proportion of occurrences in a full set of equally likely opportunities that lead to a particular occurrence.
given
As the boundaries are 0 and 2, a = 0 and b = 2
The likelihood that X falls between 0.68 and 1.44 is given by the formula P(0.68X1.44) = 1.44- 0.68 / 2-0
= 0.38
The probability that X falls inside this range according to the uniform distribution of a random variable is 0.38, or 38%.
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6. Suppose 2 more pieces of rope are cut to
be 2 feet. Would the value that occurred
most often change? Explain your
reasoning.
450
Topic 10 Assessment Practice
Answer:6
Step-by-step explanation: because the 2 feet already has four pieces and if you add two more pieces to it there will be six in total.
six numbers have a median of 9, all of the numbers are even, the range is 8 and the mode is 6
Answer:
Step-by-step explanation:
Let's start by finding the six even numbers. We know that the median is 9, so the middle two numbers in the set must be 9. Since all of the numbers are even, these two numbers must be 8 and 10.
So we have four numbers remaining, and we know that they are even. We also know that the range is 8, which means that the largest number in the set minus the smallest number in the set is 8. Since the largest number is 10, the smallest number must be 2.
So far, we have the following numbers in the set:
2, 8, 9, 9, 10
Now we need to find one more even number to make a set of six. We are given that the mode is 6, which means that one of the numbers in the set must be 6. However, we cannot add 6 to the set because it is odd. Therefore, the other number in the set that is closest to 6 must appear twice in the set, making it the mode. The number closest to 6 is 8, so we can add one more 8 to the set.
The final set of six even numbers that satisfy the given conditions is:
2, 8, 8, 9, 9, 10
A circular grassy plot of land of diameter 42 metre has a path wide 3.5 m running around it on outside find the cost of gravelling the path ₹ 4 per square metre
Answer:
₹ 2,001.20
Step-by-step explanation:
We can consider the grassy plot as a circle with radius = 42/2 = 21 m
The grassy plot and the path together form another circle with radius = 21 + 3.5 = 24.5 m
Area of a circle = πr² where r is the radius
Area of grassy plot = π x 21² = 441π m²
Area of outer circle (grassy plot + path) = π x (24.5)² = 600.25π m²
Area of the outer path alone = 600.25π - 441π = 159.25π = 500.30 sq meters
Cost of paving 1 square meter = ₹ 4
Cost of paving 500.3 sq m = 500.3 x 4 = ₹ 2,001.20
calculate the following using the long division method 8328÷ 24
Answer:
347
Step-by-step explanation:
Im not sure if that helps but thats the answer I got.
By using the long division method, The value of expression 8328 ÷ 24 after divide is,
⇒ 8328 ÷ 24
= 347
What is mean by Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.
For example, To dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The mathematical expression for divide is,
⇒ 8328 ÷ 24
Now, We can formulate;
We can use the long division method for the expression as;
⇒ 8328 ÷ 24
⇒ 8328 / 24
24 ) 8328 ( 347
- 72
-----
112
- 96
------
168
- 168
--------
0
Therefore, We get the correct answer,
By using the long division method,
The value of expression 8328 ÷ 24 after divide is,
⇒ 8328 ÷ 24
= 347
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Number of strike outs after 20 hours
Answer:
According to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.
Step-by-step explanation:
The equation given is:
y = 20x + 0
where y represents the number of strikeouts and x represents the number of hours of practice. To find the number of strikeouts after 20 hours of practice, we substitute x = 20 into the equation and solve for y:
y = 20(20) + 0
y = 400
Therefore, according to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.
let X be a random variable with support {1,2,3,5,15,25,50}, each point of which has the same probability 1/7. Argue that c = 5 is the value that minimizes h(c) = E( | X - c | ). Compare c with the value of b that minimized g(b) = E[( X - b )^2]
To minimize h(c) = E( | X - c | ), we need to find the value of c that makes the difference between X and c as small as possible.
One way to do this is to find the median of the support set. The median is the middle value when the values are arranged in ascending order.
In this case, the median is 5, so c = 5 is the value that minimizes h(c).
To compare c with the value of b that minimized g(b) = E[( X - b )^2], we need to find the value of b that makes the difference between X and b as small as possible squared. One way to do this is to find the mean of the support set.
The mean is the sum of the values divided by the number of values. In this case, the mean is (1 + 2 + 3 + 5 + 15 + 25 + 50) / 7 = 14.57, so b = 14.57 is the value that minimizes g(b).
Comparing c and b, we can see that c = 5 is closer to the median of the support set, while b = 14.57 is closer to the mean of the support set. This is because the median is a measure of central tendency that is less affected by extreme values, while the mean is a measure of central tendency that is more affected by extreme values.
Therefore, c = 5 is the value that minimizes h(c) = E( | X - c | ), while b = 14.57 is the value that minimizes g(b) = E[( X - b )^2].
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When will the graph meet the line y=5 ? Explain how you know.
By solving the logarithmic equation for x when y = 5, we determined that the graph would meet the line y = 5 when x = 10^5
Solving logarithmic equationFrom the question, we are to determine when the graph will meet the line y = 5
From the given information,
The given function is
y = log10 (x)
To determine when the graph would meet the line y = 5, we will determine the value of x when y = 5 in the function
y = log10 (x)
5 = log10 (x)
Applying the exponent law of logarithm, we get
10^5 = (x)
Therefore, x = 10^5
Hence, the graph would meet the line y = 5 when x = 10^5
The point (100, 2) is on the graph because, x = 100, y = 2 is true for the function
That is,
y = log10 (x)
2= log10 (100)
Applying the exponent law
10^2 = 100
100 = 100
This shows why the point (100, 2) is on the graph
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Use this table to answer the question. Round to 2 decimal places.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total are made up of Yellow Trains?
Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.
It's unclear what the percentages mean.A percentage that corresponds to one tenth of an amount. One percent, represented by the symbol 1%, is equivalent to one hundredth of something; hence, 100 percent represents the complete object, and 200 percent represents twice the amount given.
According to the table:
The total number of Yellow Trains is 450.
The total number of all modes of transportation is 4730.
To calculate the percentage of the total that Yellow Trains make up, we can use the following formula:
percentage = (part/whole) x 100
Substituting the values we have:
percentage = (450/4730) x 100
percentage = 0.095 x 100
percentage = 9.5%
Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.
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13. The table below gives air pressures in kPa at selected altitudes above sea level measured in
kilometers.
X
y
Altitude (km)
0
1
Air Pressure (kPa) 101 90
2
79
3
70
durma
4
62
5
54
Write an exponential regression equation that models these data rounding all values to the nearest
thousandth.
Use this equation to algebraically determine the altitude, to the nearest hundredth of a kilometer,
when the air pressure is 29 kPa.
Answer:
I don't know yet bye
Step-by-step explanation:
The exponential regression equation that models the data is y = 101 × (0.899)ˣ and when the air pressure is 29 kPa, the altitude is 6.09 km.
To find an exponential regression equation that models the given data, we can use the general form:
y = abˣ
where y is the air pressure and x is the altitude.
Using the provided data, we can substitute the values of x and y into the equation to obtain a system of equations:
When x = 0, y = 101:
101 = ab⁰
101 = a
When x = 1, y = 90:
90 = ab¹
90 = ab
90=101b
Divide both sides by 101:
b=90/101
b= 0.899
Therefore, the exponential regression equation that models the data is:
y = 101 × (0.899)ˣ
To determine the altitude when the air pressure is 29 kPa, we can substitute y = 29 into the equation and solve for x:
29 = 101 × (0.899)ˣ
Dividing both sides by 101:
0.287 = (0.899)ˣ
log(0.287) = log((0.899)ˣ)
log(0.287) = x × log(0.899)
x = log(0.287) / log(0.899)
x = 6.093.
Hence, when the air pressure is 29 kPa, the altitude is 6.09 km.
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The table below gives air pressures in kPa at selected altitudes above sea level measured in
kilometers.
x Altitude 0 1 2 3 4 5
y Air pressure 101 90 79 70 62 54
Write an exponential regression equation that models these data rounding all values to the nearest
thousandth.
Use this equation to algebraically determine the altitude, to the nearest hundredth of a kilometer,
when the air pressure is 29 kPa.
Compute the center of mass x ¯ on a rod of density ρ ( x ) = 5 x 3 + x e - x with x ∈ ( 0 , 5 ) .
Answer: My answer is long so I cannot write my answer here so i have attached my answer to your question (Notepad)
Step-by-step explanation:
Answer:
Step-by-step explanation:
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Factorise 2 + x^3 - 3x^6
answer is (2 + 3x^3)(1 - x)(1 + x + x^2)
need working out
Let w = x^3
Square both sides to find that w^2 = (x^3)^2 = x^(3*2) = x^6
In short: w^2 = x^6
The given expression 2+x^3-3x^6 turns into 2+w-3w^2 and rearranges into -3w^2+w+2
Set this equal to zero and use the quadratic formula. We'll plug in
a = -3b = 1c = 2So,
[tex]w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-1\pm\sqrt{(1)^2-4(-3)(2)}}{2(-3)}\\\\w = \frac{-1\pm\sqrt{25}}{-6}\\\\w = \frac{-1\pm5}{-6}\\\\w = \frac{-1+5}{-6} \ \text{ or } \ w = \frac{-1-5}{-6}\\\\w = \frac{4}{-6} \ \text{ or } \ w = \frac{-6}{-6}\\\\w = -\frac{2}{3} \ \text{ or } \ w = 1\\\\[/tex]
If w = -2/3, then that rearranges to the following
w = -2/3
3w = -2
3w+2 = 0
This makes (3w+2) a factor of -3w^2+w+2
If w = 1, then it rearranges to w-1 = 0.
This makes (w-1) a factor of -3w^2+w+2
--------------------
To summarize the previous section, we found the factors of -3w^2+w+2 were:
(3w+2)(w-1)It leads to (3w+2)(w-1)
We must stick a negative out front because the leading coefficient is negative.
Therefore, -3w^2+w+2 = -(3w+2)(w-1)
You can use the FOIL rule to confirm.
--------------------
Recall we made w = x^3
Let's replace each w with x^3
-(3w+2)(w-1)
-(3x^3+2)(x^3-1)
This tells us that 2+x^3-3x^6 factors to -(3x^3+2)(x^3-1)
The next task is to factor x^3-1 using the difference of cubes factoring rule.
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
x^3 - 1^3 = (x-1)(x^2 + x*1 + 1^2)
x^3 - 1 = (x-1)(x^2 + x + 1)
--------------------
So,
2+x^3-3x^6
-3x^6 + x^3 + 2
-(3x^3+2)(x^3-1)
-(3x^3+2)(x-1)(x^2 + x + 1)
-(2 + 3x^3)(-(1-x))(1 + x + x^2)
(2 + 3x^3)(1 - x)(1 + x + x^2)
Take careful notice that x-1 turned into -(1-x) in the 3rd step. The negative out front for -(1-x) cancels out with the original negative out front.
A fair coin is trowsed twice what probability of optioning
1. Excalty one head
2. No tail
3. A least two tails
4. A head and two tails
The probability of obtaining a specific outcome on a coin toss is 1/2. Using this information, we can calculate the probabilities for the following outcomes:
1. Excalty one head = 1/2
2. No tail = 1/4
3. A least two tails = 1/2
4. A head and two tails = 3/8
Probability can be defined as the ratio of favorable outcomes to the total number of events.
To obtain exactly one head, we can either get a head on the first toss and tails on the second, or tails on the first toss and heads on the second. The probability of each of these outcomes is (1/2) × (1/2) = 1/4. Therefore, the probability of obtaining exactly one head is the sum of these two probabilities, which is 1/4 + 1/4 = 1/2.
To obtain no tails, we must get heads on both tosses. The probability of this is (1/2) × (1/2) = 1/4.
To obtain at least two tails, we must get tails on both tosses or tails on the first toss and heads on the second. The probability of getting tails on both tosses is (1/2) × (1/2) = 1/4, and the probability of getting tails on the first toss and heads on the second is also 1/4. Therefore, the probability of obtaining at least two tails is the sum of these two probabilities, which is 1/4 + 1/4 = 1/2.
To obtain one head and two tails, we must get heads on one of the tosses and tails on the other two tosses. There are three ways to do this: heads on the first toss and tails on the second and third, heads on the second toss and tails on the first and third, or heads on the third toss and tails on the first and second.
The probability of each of these outcomes is (1/2) × (1/2) × (1/2) = 1/8.
Therefore, the probability of obtaining one head and two tails is the sum of these three probabilities, which is 1/8 + 1/8 + 1/8 = 3/8.
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