The number of minor damaged books in 73500 book collection is 8,673 books.
Given that, 661 books had no damage, 78 books had minor damage, and 26 books had major damage.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the minor damaged books be x.
Now, 78 : 661 :: x : 73,500
⇒ 661x = 73500 × 78
⇒ 661x = 57,33,000
⇒ x = 57,33,000 ÷ 661
⇒ x = 8,673.22
≈ 8,673
Therefore, the number of minor damaged books in 73500 book collection is 8,673 books.
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An investor puts $800 in an account that pays 2% interest compounded annually. Find the account balance after 5 years.
The account balance is $883.264 after 5 years.
The Principal amount is $800, the time given is 5 years and the rate of interest is 2%.
We have to find the account balance after 5 years.
Formula to find the amount
Amount = Principal × [tex](1 +\frac{rate}{100}) ^{time}[/tex]
Now putting the value we get,
Amount = 800 × [tex](1 + \frac{2}{100} )^{5}[/tex]
= 800 × [tex]\frac{102}{100 } ^{5}[/tex]
= 800 ×[tex]1.02^{5}[/tex]
= 800× 1.104
= 883.264
Therefore the amount is $883.264 that is the account balance after 5 years.
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is 5,521 a reasonable answer for 218x12
Answer:
No
Step-by-step explanation:
Without even answering 218*12 it is obvious this is the wrong answer
the last digit of each number determines the last digit in the answer
218 has 8 as the last number and 12 has 2
multiply them together
2*8 is 16
the last digit is 6 and not 1
Answer:
No- 218 * 12 = 2616.
Multiply with an algorithm and add the partial products up to check. You don't get 5,521 when you multiply 218 * 12.
5(22 − 9 · 2) − 2( 3 · 2 + 4) + 7?
Answer:
Here is your answer So I did the Step for you and By the way I'm from South Africa
Answer: 7
Step-by-step explanation:
5*⁵(22-²9*¹2)-⁷2*⁶(3*³2+⁴4)+⁸7=7
1)9*2=18
2)22-18=4
3)3*2=6
4)6+4=10
5)5*4=20
6)2*10=20
7)20-20=0
8)0+7=7
its takes 8 lemons and 18 cups of water to make lemonade. You have one lemon. How many water do you need to make lemonade?
How many cups of water do you need to make lemonade? 9/4 cups
How is the number of cups calculated?
Given:
8 lemons need =18 cups of water
1 lemon needs= x cups of water
By cross- multiplication method,
[tex]\frac{8}{1} =\frac{18}{x}[/tex]
8x = 18
x = 18/8
= 9/4 cups of water is needed to make lemonade
What is the cross- multiplication method?
In the cross multiplication method, we multiply the numerator of one fraction by its denominator and the first term's denominator by its numerator. We employ the cross multiplication approach to locate the answers to two linear equations.Cross-multiplication can be used to compare unlike fractions.To learn more about cross- multiplication method, refer:
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is it right? but there isn't a square root for 3. And also I need an answer for the other one.. I need a great explanation quickly help!
Answer:
[tex]x=0, \quad x=3[/tex]
Step-by-step explanation:
Given equation:
[tex]9x^2-27x=0[/tex]
Factor out the common term 9x:
[tex]\implies 9x(x-3)=0[/tex]
Zero Product Property: If a⋅b = 0 then either a = 0 or b = 0 (or both).
Using the Zero Product Property, set each factor equal to zero and solve for x:
[tex]\begin{aligned}\underline{\sf Case\; 1} & & \underline{\sf Case \;2}\\9x&=0 & x-3&=0\\\dfrac{9x}{9} & =\dfrac{0}{9} & \quad \quad x-3+3 & =0+3\\x&=0 & x&=3\end{aligned}[/tex]
Therefore, the solutions to the given equation are:
[tex]x=0, \quad x=3[/tex]
Match the ratio of side lengths to its corresponding anglemeasure.
Consider the formulae from Inverse Trigonometry,
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{\text{ Opposite Leg}}{\text{ Hypotenuse}}) \\ \theta=\tan ^{-1}(\frac{\text{ Opposite Leg}}{\text{ Adjacent Leg}}) \\ \theta=\cos ^{-1}(\frac{\text{ Adjacent Leg}}{\text{ Hypotenuse}}) \end{gathered}[/tex]Solve for the first angle as,
[tex]\begin{gathered} \theta=\cos ^{-1}(0.139) \\ \theta\approx82^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 82 degrees approximately.
Solve for the second angle as,
[tex]\begin{gathered} \theta=\tan ^{-1}(0.249) \\ \theta\approx14^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 14 degrees approximately.
Solve for the third angle as,
[tex]\begin{gathered} \theta=\sin ^{-1}(0.469) \\ \theta\approx28^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 28degrees approximately.
Solve for the fourth angle as,
[tex]\begin{gathered} \theta=\cos ^{-1}(0.682) \\ \theta\approx47^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 47 degrees approximately.
Solve for the fifth angle as,
[tex]\begin{gathered} \theta=\sin ^{-1}(0.848) \\ \theta\approx58^{\circ} \end{gathered}[/tex]Thus, the required angle measure is 58 degrees approximately.
please help
with answer
Answer:
-12 is the answer
Step-by-step explanation:
Substitute 1/4 for a and 6 for b in the equation
-8ab
-8(1/4)(6) Multiply
-8(1.5) Multiply
-12
what is 12 times 12 i just need to know
Answer:
144
Step-by-step explanation:
12 * 12 = 144
Answer:
It's 144.
..............
If f(x) = kx^3+ x^2 − kx + 2, find a number k such that the graph of f contains the point (k, -10)
If we write [tex]k[/tex] where we see [tex]x[/tex] in the equation and set the result equal to [tex]-10[/tex], we get the result.
[tex]f(k)=k(k)^3+k^2-k(k)+2[/tex][tex]=k^4+k^2-k^2+2[/tex][tex]=k^4+2=-10[/tex][tex]k^4=-12[/tex][tex]k_{1}=\sqrt[4]{3}(-1-i)[/tex][tex]k_{2}=\sqrt[4]{3}(-1+i)[/tex][tex]k_{3}=\sqrt[4]{3}(1-i)[/tex][tex]k_{4}=\sqrt[4]{3}(1+i)[/tex]In the diagram below of triangle DEF, G is a midpoint of D E and H is a midpointof EF. If MZGHE = x + 52, and mZDFH = 96 – 102, what is the measureof ZDFH?
According to the given figure, angles GHE and DFH are corresponding angles, which are equal because GH and DF are parallels. So, we can express the following
[tex]m\angle GHE=m\angle DFH[/tex]Replacing the given expressions, we have
[tex]x+52=96-10x[/tex]Let's solve for x
[tex]\begin{gathered} x+10x=96-52 \\ 11x=44 \\ x=\frac{44}{11} \\ x=4 \end{gathered}[/tex]Then, we find the measure of the angle DFH
[tex]\begin{gathered} m\angle DFH=96-10x=96-10\cdot4=96-40 \\ m\angle DFH=56 \end{gathered}[/tex]Hence, the angle DFH measures 56°.51 points composite functions need help soon
Answer:
(f∘g)(12) = 24
Step-by-step explanation:
Pre-SolvingWe are given the functions f(x)=4x+8 and [tex]g(x)=\sqrt{x+4}[/tex]. We want to find (f∘g)(12).
(f∘g)(12) means that we first find the value of g(12), and then plug that value into f(x).
SolvingFirst, we find g(12). To do this, substitute x as 12.
[tex]g(12) = \sqrt{12 + 4}[/tex]
Add 12 and 4 together under the radical.
[tex]g(12) = \sqrt{16}[/tex]
Take the square root of 16.
g(12) = 4
Now, substitute 4 as x in f(x) = 4x + 8.
f(4) = 4(4) + 8
Multiply.
f(4) = 16 + 8
Add 16 and 8 together.
f(4) = 24
f(4) has the same value as (f∘g)(12), since 4 is the value of (g)(12), and then the value of g(12) was plugged in as x in f(x).
Therefore, (f∘g)(12) is 24.
The highest temperature recorded in the town of Westgate this summer was 95°F. Last winter, the lowest temperature recorded was −5°F. Find the difference between these extremes.
the diagram shows triangle ABC. D is on the point AB such that CD is perpendicular to AB. AC=9.4cm, AD=5.2cm and BD=7.8cm. Work out the size of angle ABC.
Answer:
45°
Step-by-step explanation:
Triangles ADC and BDC are right triangles, since CD⊥AB.
Use Pythagorean to find the length of CD:
CD² + AD² = AC²CD² + 5.2² = 9.4²CD² = 9.4² - 5.2²CD² = 61.32CD = √61.32CD = 7.83Use trigonometry to find the angle ABC:
tan (∠ABC) = CD/BDtan (∠ABC) = 7.83/7.8tan (∠ABC) = 1.0 (rounded)m∠ABC = arctan 1m∠ABC = 45°2w - 15w - 18 = -83 solve for w simplify as much as possible
Answer:
w = 5
Step-by-step explanation:
2w - 15w - 18 = -83
combine w on left side:
-13w - 18 = -83
add 18 to both sides:
-13w - 18 + 18 = -83 + 18
-13w = -65
divide both sides by -13:
-13w/-13 = -65/-13
w = 5
Reasonableness
Lexi subtracts 9,405 from 11,138.
Should her answer be greater than or less than 2,000?
Explain.
(Help meeee)
Answer:
I believe that it should be less than 2,000.
Step-by-step explanation:
11038 < 11405 = 9405 + 2000
11038 - 9405 < 2000
Donnie writes an absolute value equation to determine the values that are 0.8 units from 3.5.
What equation does Donnie write and what values does he find?
Enter your answer in decimal form by filling in the boxes.
Absolute value equation |x- ___ | = ___
The values that are 0.8 units from 3.5 are ___ and ___
The absolute value equation which correctly represents the situation as described is; | x- 3.5 | = 0.8.
The values which are 0.8 units from 3.5 as given are therefore; 4.3 and 2.7.
What values are 0.8 units from 3.5 as described in the task content?It follows from the task content that the numbers which are 0.8 units away from 3.5 on the number line be determined.
On this note, the correct representation of the situation above involves an absolute value equation such that;
| x- 3.5 | = 0.8
Hence, to solve the equation; (x- 3.5) = 0.8 OR (x- 3.5) = -0.8.
x = 0.8 + 3.5. OR. x = -0.8 + 3.5
x = 4.3 OR x = 2.7.
Ultimately, the required values are; 4.3 and 2.7.
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prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called
Prediction of the mean value of the dependent variable y for values of the independent variables x 1, x 2, . . . , x q that are outside the experimental range is called extrapolation of data.
What is extrapolation of data?In statistics and mathematics, especially in the branch of data-science it is quite common to use a range of values from a parameter to predict the values of the dependent variable.
One of the most common applications of this is regression equations, when pairs of one of the independent variables with the dependent variable are used to predict the dependent variable.
In the case of this problem, we want to predict the dependent variable, but with values that are outside the experimental range, hence we extrapolate the data inside the experimental range for values that are outside the experimental range.
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simplyfy 5x-2x
How?!
Answer: 3x
Step-by-step explanation:
5x-2x=
5*x-2*x=
x(5-2)=
x*3=3x
Answer:3x
Step-by-step explanation:
combine like terms
5x-2x
2x is a negative
so 5-2=3
so in conclusion 3x
Tia rounds a number, x, to 3 sf.
The result is 7.68.
Write the error interval for x in the form a ≤
x < b.
If Tia rounds a number, x, to 3 sf and the result is 7.68. the error interval for x in the form a ≤ x < b is 7.685 ≤ x ≤ 7.684
What is error interval?The accuracy thresholds that apply when a number has been rounded or truncated are known as error intervals. In other words, they represent the range of values that a number might have taken had it not been rounded off or truncated.
To do this, we consider the smallest and largest numbers that could be rounded or truncated to a value while maintaining a certain level of accuracy.
We know that if this digit is smaller than 5, then we round down.
Then the largest number that can be rounded down to 7.68 is:
7.684
Now we want to find the smallest number that can be rounded up to 7.68
We know that if the next digit is 5 or bigger, then we round up.
Then the number 7.685 is rounded up to 7.68
Then the error interval is:
7.685 ≤ x ≤ 7.684
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urgent pls help!!!!
The number that makes the mixed fraction equation true is -1.
What number makes the equation true?The number that makes the equation true is calculated by applying the following formula as follows;
The given equation;
-7 ¹/₂ + ? = - 8 ¹/₂
The solution of the equation is calculated as follows;
Convert each mixed fraction into improper fraction;
-7 ¹/₂ = -15/2
-8 ¹/₂ = -17/2
-15/2 + ? = -17/2
Collect the similar terms together as follows;
? = -17/2 + 15/2
? = (-17 + 15) / 2
? = -2/2
? = - 1
Thus, the number that makes the equation true is -1.
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A bag contains ten tlles labeled B, C, D, E, F, G, H, I, J, and K. One tile will be randomly picked.What is the probability of picking a letter that is not a vowel?Write your answer as a fraction in simplest form.
The number of vowels is:
[tex]2[/tex]The total number of tiles is:
[tex]10[/tex]Therefore, the total number of letters not vowels is given by:
[tex]10-2=8[/tex]Hence, the probability of picking a letter that is not a vowel:
[tex]\frac{8}{10}=\frac{4}{5}[/tex]Therefore the required probability is 4/5
what two numbers make a product of 50 and a sum of -15?
Find the percent change. State whether it is an increase or decrease. Round to the nearest tenth of a percent.
From 68 to 63
The percentage increase is 7.9 %.
The given numbers are 68 and 63.
What is the percent change?Percentage change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage.
Here, old value = 63 and new value = 68
Difference = 68-63 =5
Percentage increase = Difference of old value and new value ÷ old value
= 5/63 × 100
= 0.0793 × 100
= 7.93 %
≈ 7.9 %
Therefore, the percentage increase is 7.9 %.
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NEED HELP ASAP - 100 POINTS (Algebra 2)
When solving quadratic equations, there are benefits to utilizing one method over the other. In your own words, explain what the advantages may be of using the method of completing the square to solve quadratic equations.
Answer:
Step-by-step explanation:
Comment
That's an awful lot of points to give away. Ten or 15 should be enough.
Completing the square.
1. First of all you can find the minimum or maximum immediately.
2. Second it cuts out the need to use the givens (a, b, c) in the quadratic formula which can at times be very cumbersome.
3. It gives you the opportunity to estimate the x and y roots without calculating them. Estimating on a test is a very valuable asset.
How to solve? 14x(4x + y)
Answer:
| 56x² + 14xy
Step-by-step explanation:
14x(4x + y)
Apply the Distributive Property
14x x 4x + 14xy
Multiply the monomials
56x² + 14xy
Apply the distributive property on 4x + y, distributing 14x.
14x(4x + y)
(14x x 4x) + (14x x y)
56x + 14xy
victor had a goal of making a 90 on each of his math tests. at the end of the year, he was within 5 points of his goal for each test. what are the maximum and minimum scores that he could have received?
Answer: he could have gotten 100 or 0
Step-by-step explanation: he could have had alot of tests and gotten 100 on all of them to even out the one zero.
Using the SSS congruence criterion, what additional information is needed to show that ARST AUTS?
WILL GIVE BRAINLIEST
Write an equation of the parabola that passes through the points (1, – 9), (0, – 8), and (2, -8).
Answer: y = x^2 - 2x - 8
Step-by-step explanation:
Evaluate. Write your answer as a whole number or as a simplified fraction.
36.
When you divide powers with the same base (in this case, 6), you subtract the exponents.
See details:
[tex]\frac{6^{8} }{6^{6} } \\8-6=2\\6^{2}=36[/tex]
Marsha used a graphing calculator to graph an expense and a revenue function for her family’s printing business. The graph looked like the one below.
Answer:
a
Step-by-step explanation: