There are 100 books in the library. There are non-fiction and fiction books. Write the fraction of the books that are fiction.
Answers
Let
x--------------------- > non-fiction books.------------------ > x=60
y--------------------- > fiction books.
we know that
x+y=100
y=100-x=100-60=40
the fiction books. are y=40
if 100%----------------------- > 100 books
X---------------------------- > 40
X=40*100/100=40%
40%-------------- > 40/100=20/50=2/5
the answer is
the fraction of the books that are fiction is (2/5)
Related Questions
(Will give Brainliest/5 Stars if correct answer)
Find the angle between the given vectors to the nearest tenth of a degree.
u = <8, 4>, v = <9, -9>
A) 81.6°
B) 25.8°
C) 35.8°
D) 71.6°
Answers
The angle between the two vectors is approximately 71.6 degrees
----------------------------------------------
----------------------------------------------
Work Shown:
Each time I write the word "dot" I mean "dot product".
|u| = length of vector u
|u| = sqrt(u dot u)
|u| = sqrt(<8,4> dot <8,4>)
|u| = sqrt(8*8 + 4*4)
|u| = sqrt(64 + 16)
|u| = sqrt(80)
|u| = sqrt(16*5)
|u| = sqrt(16)*sqrt(5)
|u| = 4*sqrt(5)
-----------------------
|v| = length of vector v
|v| = sqrt(v dot v)
|v| = sqrt(<9,-9> dot <9,-9>)
|v| = sqrt(9*9 + (-9)*(-9))
|v| = sqrt(81+81)
|v| = sqrt(2*81)
|v| = sqrt(2)*sqrt(81)
|v| = sqrt(2)*9
|v| = 9*sqrt(2)
-----------------------
u dot v = <8,4> dot <9,-9>
u dot v = 8*9 + 4*(-9)
u dot v = 72-36
u dot v = 36
-----------------------
cos(theta) = (u dot v)/(|u|*|v|)
cos(theta) = (36)/(4*sqrt(5)*9*sqrt(2))
cos(theta) = (36)/(36*sqrt(10))
cos(theta) = 1/(sqrt(10))
cos(theta) = sqrt(10)/10
theta = arccos(sqrt(10)/10)
theta = 71.56505
which rounds to 71.6 when rounding to one decimal place (nearest tenth)
That's why the approximate answer is roughly 71.6 degrees
Answer:
71.6°
Step-by-step explanation:
arctan(4/8) - arctan(-9/9) = 26.57° - (-45°) ≈ 71.6°
it is given that ln(y+1) - ln(y) = 1+3ln(x) . express y in terms of x in a form not involving logarithms
Answers
[tex] ln( \frac{y + 1}{y} ) = ln( {x}^{3} e) \\ \frac{y + 1}{y} = {x}^{3} e[/tex]
We transformed the logarithmic equation ln(y+1) - ln(y) = 1 + 3ln(x) into an algebraic expression, resulting in y = 1 / (e × [tex]x^3[/tex] - 1).
To express y in terms of x from the given equation ln(y+1) - ln(y) = 1 + 3ln(x), we can follow these steps:
Apply the logarithm property ln(a) - ln(b) = ln(a/b): ln((y+1)/y) = 1 + 3ln(x).Rewrite the right-hand side using exponentiation: ln((y+1)/y) = ln(e) + 3ln(x) = ln(e × [tex]x^3[/tex]).Since the natural logarithms are equal, set their arguments equal to get the equation without logarithms: (y+1)/y = e × [tex]x^3[/tex].Isolate y by solving the above equation: y + 1 = y × e × [tex]x^3[/tex], hence y = 1 / (e × [tex]x^3[/tex] - 1).This gives us the final expression of y in terms of x without involving logarithms.
A company invests a total of $40 comma 00040,000 of surplus funds at two annual rates of interest: 55% and 66one half 1 2%. It wishes an annual yield of no less than 6one fourth 1 4%. What is the least amount of money that the company must invest at the 66one half 1 2% rate? The company should invest at least how much money
at 66one half 1 2%.
Answers
x(0.065) + (40,000 - x)(0.05) = (40,000)(0.0625)
2,000 + 0.015x = 2500
0.015x = 500
x = 33,333
Therefore, the company must invest at least $33,333 at 6.5% to get an annual yield of at least 6.25%.
Annie's cafe borrows $6100 at 6% for 290 days. Find the total amount that must be repaid after 290 days. (Use a 365 day year.)
Answers
amount borrowed $6,100
interest rate 6% - assuming annual interest rate
term - 290 days of a 365 day year.
This is a simple interest computation.
Interest = Principal * interest rate * term
Interest = 6,100 * 6% * 290/365
Interest = 290.79
Total payment at the end of the 290 term would be $6,390.79.
Principal + interest → 6,100 + 290.79 = 6,390.79
The total amount that must be repaid after 290 days is $6330.67.
Explanation:To find the total amount that must be repaid after 290 days, we can use the formula:
Amount = Principal + Interest
Principal is the amount borrowed, which is $6100. Interest is calculated using the formula:
Interest = Principal * Rate * Time
Since the loan is for 290 days, we need to convert it to years by dividing by 365:
Time = 290/365 = 0.7945 years
Plugging in the values, the interest is:
Interest = 6100 * 0.06 * 0.7945 = $230.67
Adding the principal and interest together, the total amount to be repaid is:
Total Amount = Principal + Interest = $6100 + $230.67 = $6330.67
q
Find the expected number of pairs of different people, a and b, such that a picks b's name and b picks a's name. g
Answers
Evaluate the expression.
r = <9, -7, -1>, v = <2, 2, -2>, w = <-5, -2, 6>
v ⋅ w
A) <-18, 14, -2>
B) -26
C) 1
D) <-10, -4, -12>
Answers
u = <a,b,c>
v = <d,e,f>
then
u dot v = a*d + b*e + c*f = dot product of the two vectors
In words: multiply the x coordinates together, then the y together and then z together. Finally add up those three products
So,
v dot w = <2,2,-2> dot <-5,-2,6>
v dot w = 2*(-5) + 2*(-2) + (-2)*6
v dot w = -10 - 4 - 12
v dot w = -26
Answer: B) -26
the above person lied and used bots for 5 star ratings the real answer is 6.
Evaluate the expression.
r = <9, -7, -1>, v = <2, 2, -2>, w = <-5, -2, 6>
v ⋅ r (3 points)
<18, -14, 2>
You Answered -26
1
Correct Answer 6
I have no idea how to do this equation, please help
Answers
.. 10Ta +25Tb = 220
.. Ta +Tb = 10
It is convenient to solve this by substitution. Use the second equation to write an expression for Tb.
.. Tb = 10 -Ta
Now use this in the first equation.
.. 10Ta +25(10 -Ta) = 220
.. -15Ta +250 = 220 . . . . . . . collect terms
.. -15Ta = -30 . . . . . . . . . . . . . subtract 250
.. Ta = 2 . . . . . . . . . . . . . . . . . divide by the coefficient of Ta
.. Tb = 10 -2 = 8
Selection C is appropriate.
When 18 boys joined a group of why students, the ratio of boys to girls in the group became 4 : 5. Write an algebraic expression for the number of girls in terms of Y.
Answers
be careful the number of boys is in a ratio of the number of boys to the total.
Just to make sure I'm right, I solve it.
18 * 9 = 4*(y + 18)
162 = 4y + 72 Subtract 72 from both sides.
90 = 4y Divide by 4
22.5 = y Never mind the 0.5. Does it work
18/22.5 = 0.8
0.8 is the same thing as 4/5
The problem makes no sense in the real world, but it does work out mathematically.
Which is not a characteristic of an exponential parent function?
A. The range is positive real numbers (y > 0).
B. The domain is all real numbers.
C. It goes through the origin.
D. It passes through (0, 1).
Answers
Answer:C. It goes through the origin
Step-by-step explanation:
Answer:
Option C) It goes through the origin.
This is the wrong statement about the parent exponential function.
Step-by-step explanation:
We are given the following:
The characteristic of exponential parent function:
[tex]f(x) = y = b^x\\\text{where b is the base}[/tex]
A) True
The range is all positive number that is y > 0
Range can never be negative.
B) True
The domain is all real number.
C) False
It does not pass through origin.
[tex]y = f(0) = b^0 = 1[/tex]
D) True
It always passes through (0,1) as shown above.
Miguel ordered a rectangular print for his bedroom. The print is 78 feet wide and 135 feet long.
What is the area of the print?
Answers
Edit: To find the area of print you must multiply [tex] \frac{7}{8} [/tex] by [tex]1 \frac{3}{5} [/tex]. So your answer is [tex]1 \frac{2}{5} [/tex].
what is the best definition for marginal cost?
Answers
Marginal cost is the additional cost incurred when producing one extra unit of a good or service.
Marginal Cost: Marginal cost is the change in total cost that occurs when the quantity produced is increased by one unit. It represents the cost of producing one more unit of a good, encompassing all additional costs required for that extra unit.
Example: If producing one more car necessitates building an additional factory, the marginal cost includes all costs associated with setting up the new factory.
Marginal cost is the additional cost of producing one more unit of a good or service.
To calculate marginal cost, you divide the change in total cost by the change in the quantity produced. Mathematically, it can be expressed as:
Marginal Cost = (Change in Total Cost) / (Change in Quantity)
This concept is crucial in economics and business for decision-making purposes. It helps firms determine the cost-effectiveness of increasing or decreasing production levels.
For instance, if a company is considering expanding its production, understanding the marginal cost allows it to assess whether the additional revenue from selling more units will outweigh the additional costs incurred.
It is also used to make pricing decisions and optimize resource allocation. In summary, marginal cost provides insight into how production decisions impact overall costs and profitability.
There are 96 raisins and 24 cashews in each package of granola. What is the unit rate in raisins per cashew?
4
12
20
96
Answers
You are a builder and need to submit an estimate to a customer for remodeling a bathroom. Your project costs are $451.75 for labor, $332.52 for materials and $289.12 for subcontracting for plumbing. Round these amounts to whole numbers to estimate the cost of the total project.
Answers
What is 8587 divided by 12
Answers
How much interest is earned on $269 at 10% for five years?
Answers
The simple interest can be calculated using the formula:
[tex] I = \frac{PRT}{100} [/tex]
We are given :
Principal = $269
Rate of interest = 10%
Time = 5 years
Plugging the values in the formula:
[tex] I = \frac{269*10*5}{100} [/tex]
Interest = $134.5
The interest on the principal amount in 5 years at the rate of 5% will be equal to $134.5.
What is Simple interest?A quick and simple way to figure out interest on that money is to use the simple interest approach, which adds interest at the same rate for each daily cycle, and it is to the initial principal amount.
A way to figure out how much interest will be charged on an amount of money at a specific rate and for a specific duration of time is by using simple interest.
As per the question, the given data is,
Principle, P = $269
Rate, T = 10%
Time, T = 5 years
[tex]SI =(P*R*T)/100[/tex]
SI = (269 ×10 × 5)/100
SI = $134.5
Therefore, the interest earned in 5 years is $134.5.
To know more about Simple interest:
https://brainly.com/question/25845758
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Here is a list of ingredients for making cherry scones: Makes 8 cherry scones 200 grams flour 60 grams margarine 40 grams sugar 60 grams cherries 160 ml milk Sophie has 80 grams of sugar and 300 grams of flour. She has plenty of the other ingredients. What is the greatest number of cherry scones she can make?
Answers
This is a question from my homework "Rosina finds a pair of shorts on the sale rack for $12.50. This price reflects a discount of 60%. What is the original price of the shorts? What is the amount of the discount?"
Answers
12.50 ----> 40%
x ----------> 100%
Clearing x we have:
x = (100/40) * (12.50)
x = $ 31.25 (original price, without the discount)
Therefore, the discounted amount is:
(0.60) * (31.25) = 18.75 $
Answer:
The original price of the shorts is:
$ 31.25
the amount of the discount:
$ 18.75
what is 7 × (12 + 8) - 6=
Answers
Groupings
Exponents
Multiplication
Division
Addition
Subtraction
First, we simplify the terms inside the parentheses [tex](12+8)=20[/tex]. Next, following the order of operations, we multiply this by 7, to get 140. Finally, we subtract 6 to get 134.
The shorter leg of a 30°-60°-90° triangle measures 3 inches. What is the length of the hypotenuse?
A. 6 inches
B. 3sqrt3 inches
C. 9 inches
D. 6sqrt3 inches
Answers
.. 1 : √3 : 2
The hypotenuse is 2 times the length of the shorter leg, so is 6 inches, selection A.
A. 6 inches
Hope I help
the set of points (-3,4), (-1,1), (-3.-2), and (-5,1) identifies the vertices of a quadrilateral. which is the most specific describtion to tell which figure the points form?
Answers
Method 1: (simplest, can be done with pencil and paper)
Graph the points, and do a visual inspection.
See graph attached.
Method 2: by observations, without need to take square-roots (for distances)
We note that:
1. the x-coordinates of the first and third points are the same (-3), meaning that they lie on the same vertical line.
2. the y-coordinates of the second and fourth points are the same (1), that means that they lie on the same horizontal line. So the diagonals are at right angles to each other, intersecting at P(-3,1).
These two observations tell us that the figure is either a square, rhombus, or a kite, or an arbitrary quadrilateral that has orthogonal diagonals.
3. AC=4-(-2)=6, BD=-1-(-5)=4, diagonals are not equal, so cannot be a square.
4. PA=(4-1)=3, PB=(-3-(-1))=2, diagonals bisect each other, so it is a rhombus (not a kite).
how to set the answer up
Answers
Let s and g represents the numbers of suits and gowns produced.
The number of zippers used is 2s+g.
The number of buttons used is 5s+8g.
In order to use all of the available zippers and buttons, we must have ...
2s + g = 1715s + 8g = 576Cramer's rule tells you the solution to the system
ax +by = cdx +ey = fIs given by
x = (bf-ey)/(bd-ea)y = (cd-fa)/(bd-ea)Using this rule on the equations for zippers and buttons, we have
... s = (1·576 -8·171)/(1·5 -8·2) = -792/-11 = 72
... g = (171·5 -2·576)/-11 = -297/-11 = 27
72 suits and 27 gowns can be made from available zippers and buttons.
David was looking at his limousine bill and saw that the total number of miles he has ridden in the car was tracked, as shown below: Month Miles 5 580 6 695 7 810 8 925 The function representing David's miles per month is f(m) = 115m + 5. What does the 115 represent?
Answers
The number of additional miles each month.
Which statement about the following argument is true?
Argument:
If it snows, the roads will get slippery.
It's snowing.
Therefore, the roads are slippery.
A:The argument is valid by the Law of Syllogism.
B: The argument is valid by the Law of Detachment.
C: The argument is invalid.
D: The argument is valid but does not follow the Law of Syllogism or the Law of Detachment.
Answers
2. Determine the contrapositive statement of the conditional, so we have...
If you live in Idaho, then you do not live in New York City.
3. If ticket prices are low and the line to purchase them is short, then I will go to the show.
4. If Satish takes the Tuesday 8:00am Chemistry class or the Tuesday 8:00am Physics class, then he will finish the program.
Prove: tan(x-y)+tan(y-z)+tan(z-x)=tan(x-y)tan(y-z)tan(z-x)
Answers
=> tan(z-x) = (tan(y-x) - tan(y-z))/(1+tan(y-x).tan(y-z))
by given formula.
Multiply both sides by (1+tan(y-x).tan(y-z)):
tan(z-x).(1+tan(y-x).tan(y-z)) = tan(y-x)-tan(y-z)
=> -tan(y-x) + tan(y-z) + tan(z-x) = -tan(y-x).tan(y-z).tan(z-x)
=> tan(x-y) + tan(y-z) + tan(z-x) = tan(x-y).tan(y-z).tan(z-x),
since tan(x-y) = -tan(y-x).
Please put me as brainlest if it is correct
The price of a bicycle was increased from $300 to $450. What percent of the original price is the increased price?
Answers
The percentage increase is 50% than the original price.
The price of a bicycle was increased from $300 to $450. What percent of the original price is the increased price?
Calculate the increase: $450 - $300 = $150.
Calculate the percentage increase: ($150 / $300) x 100% = 50%.
If a one dollar bill is 0.0001 meters thick, how many meters tall would a stack of 4 trillion one dollar bills be?
Answers
so use the decimal thing 1st.
so 1*4,000,000,000, and thats ur answer
Answer:
[tex]4*10^{8}\text{ meters}=400,000,000\text{ meters}[/tex].
Step-by-step explanation:
We have been given that a one dollar bill is 0.0001 meters thick. We are asked to find the height of a stack of 4 trillion one dollar bills.
We know that [tex]\text{1 trillion}=10^{12}[/tex]. To find the thickness of a stack of 4 trillion one dollar bills we will multiply 0.0001 by 4 trillion.
Let us convert 0.0001 into scientific notation as:
[tex]0.0001=1\times 10^{-4}[/tex]
[tex]\text{The height of 4 trillion one dollar bills}=4*10^{12}\times 1\times 10^{-4}\text{ meters}[/tex]
Using exponent property [tex]a^b\times a^c=a^{b+c}[/tex] we will get,
[tex]\text{The height of 4 trillion one dollar bills}=4*10^{12-4}\text{ meters}[/tex]
[tex]\text{The height of 4 trillion one dollar bills}=4*10^{8}\text{ meters}=400,000,000\text{ meters}[/tex]
Therefore, the stack of 4 trillion one dollar bills would be [tex]4*10^{8}\text{ meters}=400,000,000\text{ meters}[/tex].
can u show me common core way how to get the answer to this problem 4 1/5. ×4 3/8
Answers
1.) You must covert the whole numbers into fractions.
[tex]4 \frac{1}{5} \: will \: become \: \frac{21}{5} [/tex]
(multiply the denominator by the whole number, which in this case is 4, then add the answer to the numerator).
[tex]4 \frac{3}{8 \: } \: will \: become \: \frac{35}{8} [/tex]
(same steps will apply as before except in this case there is a different denominator and numerator).
There is no need to make the denominators the same number since it is multiplication and not addition or subtraction (the same can be done with division expect there is one crucial difference which I can explain if you want, in the comments).
2.) Next set up the equation to multiply:
[tex] \frac{21}{5} \times \frac{35}{8} [/tex]
5 and simplify (also note that the only way you can't simplify is across)
[tex] \frac{21}{5} \times \frac{7}{8} [/tex]
3.) Now multiply across:
NUMERATOR
21 × 7 = 147
DENOMINATOR
5 × 8 = 40
It will come together to be 147/40 or 3 27/40
Miss Cohan purchased a bottle of vitamins for $7.99 a bottle of aspirin for $6.49 and a bottle of mouthwash for $2.99 she gave the clerk two $10 bills how much change did she receive
Answers
Paul and jose are trying to measure the height of a tree. paul is standing 19m from the foot of the tree and measures the angle of elevation to the top of the tree to be 59o. jose measures it to be 43o, how far is jose from the base of the tree?
Answers
We know that Paul is 19m from the base of the tree and its elevation angle to the top of the tree is 59°. We also know that the elevation angle of Jose and the top of the tree is 43°, but we don't know the distance between Paul of Jose, so lets label that distance as [tex]x[/tex].
Now we can build a right triangle between Paul and the tree and another one between Jose and the tree as shown in the figure. Lets use cosine to find h in Paul's trianlge:
[tex]cos(59)= \frac{19}{h} [/tex]
[tex]h= \frac{19}{cos(59)} [/tex]
[tex]h=36.9[/tex]
Now we can use the law of sines to find the distance [tex]x[/tex] between Paul and Jose:
[tex] \frac{sin(43)}{36.9} = \frac{sin(16)}{x} [/tex]
[tex]x= \frac{36.9sin(16)}{sin(43)} [/tex]
[tex]x=14.9[/tex]
Now that we know the distance between Paul and Jose, the only thing left is add that distance to the distance from Paul and the base of the tree:
[tex]19m+14.9=33.9m[/tex]
We can conclude that Jose is 33.9m from the base of the tree.
According to the Rational Root Theorem, which number is a potential root of f(x) = 9x8 + 9x6 – 12x + 7?
Answers
Answer:
All the potential root of f(x) are [tex]\pm 1,\pm7, \pm \frac{1}{3},\pm \frac{7}{3}, \pm \frac{1}{9},\pm \frac{7}{9}[/tex].
Step-by-step explanation:
According to the rational root theorem, all the potential root of f(x) are defined as
[tex]x=\pm\frac{p}{q}[/tex]
Where, p is factor of constant term and q is factor of leading coefficient.
The given function is
[tex]f(x)=9x^8+9x^6-12x+7[/tex]
Here, constant term is 7 and leading coefficient is 9.
Factors of 7 are ±1, ±7 and the factors of 9 are ±1, ±3, ±9.
Using rational root theorem, all the potential root of f(x) are
[tex]x=\pm 1,\pm7, \pm \frac{1}{3},\pm \frac{7}{3}, \pm \frac{1}{9},\pm \frac{7}{9}[/tex]
Therefore all the potential root of f(x) are [tex]\pm 1,\pm7, \pm \frac{1}{3},\pm \frac{7}{3}, \pm \frac{1}{9},\pm \frac{7}{9}[/tex].