The logarithmic expansion of logs(20x + 5y) by using the properties of logarithmic is log(5)+log(4x+y).
The basic logarithmic function is of the form f(x) = logₐx(r)n = logₐx, where a > 0. It is the inverse of the exponential function aⁿ = x. Log functions include natural logarithm (ln) or common logarithm (log). Logarithmic functions is very useful in various mathematical computations.
Given that, log(20x+5y) and we have to expand it by using the properties of logarithms. So, let's proceed to solve the question.
log(20x+5y)
we can write 20 in terms of powers like 20 = (2²)x5
log((2².5)x+5y)
log(5(2².5x/5+5y/5))
log(5(2²x+y))
log(5(4x+y))
∵ log(ab) = log(a)+log(b)
⇒log(5(4x+y)) = log(5)+log(4x+y)
Hence, on expanding log(20x+5y) by using the properties of logarithms we get log(5)+log(4x+y) as our required answer.
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If LM = 22 and MN = 15, find LK
Find the volume generated by rotating the given region about the specified line. I tried it 4 different times and have 1 try left! Please help only if you're sure of how to do it
Using integrals, the volume generated by rotating the given region about the specified line is of 0.8π cubic units.
How to use integrals to find the volume of a curve?Rotating a function f(x) around a function g(x), the volume is given by the following integral:
[tex]V = \pi \int_{a}^{b}[f(x) - g(x)]^2 dx[/tex]
In which a and b are the intersection points of the curve.
For this problem, from the graph, we have that:
[tex]f(x) = 2\sqrt[4]{x}[/tex].g(x) = 2x.a = 0.b = 1.Hence:
[tex]V = \pi \int_{0}^{1}[2\sqrt[4]{x} - 2x]^2 dx[/tex]
[tex]V = \pi [\int_{0}^{1} 4\sqrt{x} - 8x\sqrt{x} + 4x^2 dx][/tex]
[tex]V = \pi \left[\frac{8}{3}x^{\frac{3}{2}} - \frac{16}{5}x^{\frac{5}{2}} + \frac{4}{3}x^3}\right]_{x=0}^{x=1}[/tex]
[tex]V = \pi \left[\frac{8}{3} - \frac{16}{5} + \frac{4}{3}\right][/tex]
[tex]V = \pi \left[4 - \frac{16}{5}\right][/tex]
[tex]V = \frac{4\pi}{5}[/tex]
V = 0.8π cubic units.
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There are 15 floors of an office building each floor is 10 2/5 feet tall 24 9/10 feet of the building are completed 1 1/4 feet of the building can be finished each day how many days are needed to complete the building
The days it would take to complete the building is 104 22/25 days.
How many days would it take to complete the building?A fraction is a non-integer that has a numerator and a denominator. The numerator is the number above. While the denominator is the number below. An example of a fraction is 1/4.
A mixed number is a number that has a whole number and a proper fraction. A proper fraction is a non-integer in which the numerator is less than the denominator. An example of a mixed number is 3 1/2.
The first step is to determine the total height of the office bulding = height of each floor x total number of floors
15 x 10 2/5
15 x 52/5 = 780 /5 = 156
The next step is to determine the floors left to complete the office building :
156 - 24 9/10 = 131 1/10 feet
The last step is to divide the feet that can be built each day by the number of floors needed to complete the builfing :
1311/10 ÷ 1 1/4
1311 / 110 ÷ 5/4
1311 / 10 x 4/5 = 104 days 44/50
104 22/25 days
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One integer is selected at random from integers 8 through 38. Find the probability that the number is odd
Answer: 0.48387
Step-by-step explanation:
Solution set = {9,11,13,15,17,19,21,23,25,27,29,31,33,35,37}
Sample Set = {8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38}
out of the 31 numbers, 15 are odd
15/31 = 0.48387 probability.
0.50x +0.15(30) = 23.5
Answer: x=38
Step-by-step explanation:
SOLVE FOR X
STEPS FOR SOLVING LINEAR EQUATION
0.50x+0.15(30)=23.5
Multiply 0.15 and 30 to get 4.5.
0.5x+4.5=23.5
Subtract 4.5 from both sides.
0.5x=23.5−4.5
Subtract 4.5 from 23.5 to get 19.
0.5x=19
Divide both sides by 0.5.
[tex]x=\frac{19}{0.5}[/tex]
Expand [tex]\frac{19}{0.5}[/tex] by multiplying both numerator and the denominator by 10.
[tex]x=\frac{190}{5}[/tex]
Divide 190 by 5 to get 38.
x=38
6216÷21 please show me the work
Therefore, on dividing 6216 by 21 we get 126
Given 6216 / 21
21 ) 6216 ( 296
42
(-)................... (By subtracting these two numbers we get )
201
189
(-)..................
126
126
.(-)..........................
0
Therefore 6216 / 21 = 126
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7h
t: h²k²
-7k
k² - h²
Answer:
i'm pretty sure it's the second option
Step-by-step explanation:
Use the graph of the line to answer the questions. what is an equation of the line in slope-point form? _____
How can the point-slope form be written in function notation?
_______
The slope-point form is y + 1 = (1/4) (x +2)
The function notation for the point-slope form is f(x) = -1 + (1/4) (x +2)
From the graph, we get two points (x₁, y₁) = (-2, -1) and (x₂, y₂) = (2,0)
Slope, m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
= [tex]\frac{0 --1}{2--2}[/tex]
= 1/4
The slope-point form of a line is (y-y₁) = m(x-x₁), where (x, y) is the general point on the line, (x₁, y₁) is a given point on the line and m, the slope of the line.
So here the slope-point form of the line is,
(y- -1) = 1/4(x- -2)
⇒ y + 1 = (1/4) (x +2)
For the function notation, we put y = f(x) simply and write it as,
f(x) = -1 + (1/4) (x +2)
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the first one is c
the second is B
Step-by-step explanation:
Which of the following is an existential quantifier?
Oa) Few
Ob) None
Oc) Every
O d) All
Answer:
A
Step-by-step explanation:
It might be the best one!
ANSWER RIGHT AWAY PLEASE!
question one: simply the exponents. (show your work)
- 21^0 = ?
- (2/3)^-2 = ?
question two: Solve the problem. (leave your answer as a base number with an exponent and show your work)
- 4^6 / 4^2 = ?
question three: Convert the number into numerical form. (show your work)
- 8.723 x 10^-10 = ?
question four: Solve the problem. (leave your answer in scientific notion and show your work)
- 5.1 x 10^8 - 2.3 x 10^3 = ?
- 6 x 10^5 x 1.1 x 10^7 = ?
PLEASE ANSWER I WILL GIVE 100 POINTS TO ANYONE WHO ANSWERS AND MARK BRAINLIEST AT LEAST ANSWER THE ONES YOU KNOW
Answer:
1. 1, 9/4
2. 4^4
3. -0.0000000008723
4. -5100023*10^2, -6.6*10^(12)
Step-by-step explanation:
[tex]21^0 = 1;\ n^0\ always\ is\ 1.\\(\frac{2}{3})^{-2} = (\frac{3}{2})^2 = \frac{3^2}{2^2} = \frac{9}{4}; n^m\ is\ performed\ by\ doing\ n*n,\ m\ times.\\i.e.,\\ n^2=n*n;\\n^3=n*n*n;\\ n^4=n*n*n*n\\\\\frac{4^6}{4^2};\ original\\\\\frac{(4^2)^3}{4^2};\ (n^{mc}\ can\ be\ rewritten\ as\ (n^m)^c\\\\\frac{4^2}{4^2}*\frac{(4^2)^2}{1};\ split\ the\ fraction\ into\ two\ parts\ because\ of\ multiplication\ rules.\\\\1*4^4;\ \frac{n}{n}\ can\ be\ written\ as\ 1.\ \frac{n}{1}\ can\ be\ written\ as\ n.\\\\4^4[/tex]
Technically, [tex]4^4[/tex] is 256, but the answer is requested as a number with an exponent.
-8.723 * 10^-10 would be -0.0000000008723.
10^-10 = [tex]\frac{1}{10^{10}}[/tex], which would mean you must move your decimal left by the number of places indicated by the exponent.
[tex]-5.1*10^8-2.3*10^3 = x\\-51*10^7-23*10^2 = x\\10^7=10^{5+2}=10^5*10^2\\-5100000*10^2-23*10^2=x\\-5100023*10^2=x;\ combine\ like\ terms.\\-6*10^5 * 1.1*10^7 = x\\-6*1.1*10^5*10^7;\ rewrite\ for\ simplification.\\-6.6*10^{12}=x[/tex]
what is |x|-7=1 what is the answer
Answer:
it is x=8 or x=-8
Step-by-step explanation:
|x|-7=1
+7 +7
x=8 or x=-8
i'm doing absolute value in math rn so this should be right!! have a good day
An English instructor asserted that students' test grades are directly proportional to the amount of time spent studying.
Lisa studies 6 hr for a particular test and gets a score of 76. At this rate, how many hours would she have had to
study to get a
score of 91?
Answer:
7.18421051
Step-by-step explanation:
76 ÷ 6 = 12.6666667
91 ÷ 12.6666667 = 7.18421051
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whats 20,973 rounded to the nearest thousand
Answer:
21000
Step-by-step explanation:
21000
Answer these 3, please. ( Statistics )
1) This narrative is an example of a sample survey.
2) This narrative is an example of an experiment.
3) This narrative is an example of an observational study.
What is the type of Statistical study?
There are some common methods of data collection in statistical studies which are sample survey, observational study, experiments e.t.c
A sample survey is a survey that is done by taking a sample of people or items that represent a larger population.
An observational study is a type of study whereby a researcher utilizes observed information to gain more information about a group of individuals.
An experiment is where a researcher purposely applies different treatments to different groups and then does a comparison of the groups to determine if there is any difference in a specific variable of interest.
1) This narrative is an example of a sample survey because he studied a sample of 50 people who exercise regularly to determine if their blood pressures are low or average.
2) This narrative is an example of an experiment because we see that he studies 20 people who exercise and another 20 who don't exercise and uses the result to generate a conclusion about both groups.
3) This narrative is an example of an observational study because he is using the information he gets from the question he asks every fifth patient to learn about a group of individuals.
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There are 35 students in a class. Fifteen of them are men and 20 of them are women. The mean height of the men is 69.65 inches, and the mean height of all 35 students is 66.85 inches. What is the mean height of the women?
Answer:
64.75
Step-by-step explanation:
The total heights of men is m
so m/15 = 69.65 => m = 1044.75
The total heights of all students is s
so s/35 = 66.85 => s = 2339.75
so the total heights of women = 2339.75 - 1044.75 = 1295
The mean height of women = 1295/20 = 64.75
9. Your family is looking for a new Internet company. Comcast has a $50 installation fee
and $60 per month for Internet. Centurylink has no installation fee and $60 per month.
Your grandparents decide to register with Comcast the sametime your family registers
with Centurylink. At what month will your family pay the same as your grandparents?
Answer:
in the heaven or hell hhhvgvcgdgghh
What kind of numbers are −5 and 7?
-5 and 7 are real and rational numbers also they are integers.
What is a rational number ?Numbers which can be written in the form of p/q are rational numbers where q must not be zero.
According to the given question we have to determine what kind of numbers are -5 and 7.
In a most simple way we can say that - 5 is an negative integer and 7 is a positive integer.
But -5 can be written as -5/1 which is a rational number also and 7 can also be written as 7/1 so we can also say they are integers al well as rational numbers.Lastly they are real numbers as they don't have any imaginary part 'i' in it.
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. Compare the value of the 4's in this number
64,432
Write your statement
The 4 on the right is 10 times larger than the 4 on the left! (=^.^=)
The angles of a triangle add up to 180 degrees.
The second angle is 20 degrees larger than the smallest angle.
The third angle is 3 times as big as the smallest angle.
Find the measure of the smallest angle (in degrees).
Answer:
32 degrees
Step-by-step explanation:
You want the smallest angle of a triangle in which the other two angles are 20 degrees larger than the smallest, and 3 times the smallest.
SetupThe sum of angles is 180 degrees. The three angles are x, (x+20), and (3x). Their sum is ...
x +(x +20) +3x = 180
SolutionCollecting terms gives ...
5x +20 = 180
5x = 160 . . . . . . subtract 20
x = 32 . . . . . . divide by 5
The smallest angle is 32 degrees.
Un terreno tiene 205 metros y cada metro cuesta 315 cuánto vale el terreno
Answer:
64,765
Step-by-step explanation:
multiplicas porque dice que uno cuesta 315 entonces si hay 205 hay 64,765
1000 divided by 3 answer
Answer:333R1 or as a mixed fraction 33 1/3. I believe this is right :]
Step-by-step explanation:
Six friends each use $2-off coupons to but themselves a movie ticket. They spend a total of $42. What is the price of one movie ticket without coupon?
Modelling the situation, it is found the price of the ticket without the coupon is of $9 when all the six friends spent $ 42 to buy the tickets.
Total money spent by 6 friends on purchasing of the movie tickets = $ 42
So, the money spent for the purchase of 1 ticket will be calculated by dividing the $ 42 by 6.
So, cost of 1 ticket = 4 42 / 6 = $ 7
Coupon is of $2-off.
This means that with the coupon, $2 is subtracted from the ticket price.
So, price of ticket will be = $ 7 + $ 2 = $ 9.
Therefore, the price of the ticket without the coupons will be $ 9.
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How many even 2 digit positive integers can be written using the numbers 2,4,5,8
Answer: 12 different even 2 digit positive numbers can be witten
Step-by-step explanation:
the even numbers are 44, 24, 54, 84, 22, 42, 52, 82, 28, 48, 58, 88
A line passes through the point (-2, 6) and has a slope of -8.
Write an equation in slope-intercept form for this line.
The given equation of the straight line is y +8x+10=0
We are required to find the equation of a straight line passing through the point (-2, 6) and has a slope of -8.
An equation of a straight line can be easily found if the slope and any of the points is given
The general form of equation is given by
y-y1 = m (x-x1)
where x1,y1 is the coordinate of the known point
m is the slope of the line
It is given that the coordinate of the known point is (-2,6)
the slope is given to be -8
Thus using these values to form the equation,
y-6 = -8 (x--2)
y-6 = -8 (x+2)
y-6 = -8x-16
y+8x-6+16=0
y+8x+`10=0
Hence, The straight line equation is y +8x+10=0
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PLEASE HELP ME TY!!!!!!
Answer:
3.82×10^7
Step-by-step explanation:
3.82e+7= 3.82×10^7
Please answer the screenshot
The set of ordered pairs that represents a function is the third option.
{ (4, 1), (-6, 6), (5, -2), (-4, 1)}
Which set of ordered pairs represents a function?
For a relation that maps elements x (inputs) into elements y (outputs), we will have ordered pairs of the form (x, y) that define the relation.
Now, a relation is only a function if input are only mapped to only one output.
For example, if you look at the first set of ordered pairs, you can see that the input x = -4 appears twice with two different outputs, then this relation does not represent a function.
For the second set the same thing happens for the input x = -8, and for the last set the same happens for the input x = -8
The only set where each input appears only once is the third one:
{ (4, 1), (-6, 6), (5, -2), (-4, 1)}
This relation represents a function, so this is the correct option.
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Calculate the length of a chord of a circle of radius 26cm if the chord is 10cm from the center of the circle
Answer: see explanation
Step-by-step explanation:
The 10 cm distance is measured perpendicularly to the chord, forming a right angle and bisecting the chord. Thus half of the chord, the segment from the center of the chord, and a radius to the end of the chord form a right triangle. The hypotenuse is 26 cm and one leg is 10 cm, so the other leg is given by the Pythagorean theorem: a^2 + 10^2 = 26^2, giving a = 24 cm. Since a is half the chord, the chord is 2a = 48 cm in length.
Hence, the length of a chord of a circle is [tex]48cm[/tex].
What is the circle?
A circle is defined as a two-dimensional figure, which is round in shape where all the points on the surface of the circle are equidistant from the center point is called “[tex]P[/tex]”.
Here given that,
A circle of radius [tex]26[/tex]cm if the chord is [tex]10[/tex]cm from the center of the circle.
So,
The [tex]10[/tex]cm from the center of the circle is perpendicular of the chord and the hypotenuse is [tex]26[/tex]cm .
As we know
[tex]H^2=B^2+P^2[/tex] .......[tex](1)[/tex]
Substituting the values in the equation [tex](1)[/tex], we get
[tex](26)^2=(10)^2+B^2\\B^2=676-100\\B^2=576\\B=\sqrt{576}\\B=24cm[/tex]
Hence, the length of a chord of a circle is [tex]48cm[/tex].
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|3x|-4=2x-4 Solve for x
Answer:
Your answer is x=0
How many inches are in 75 mm
Answer: 2.95 I think
Step-by-step explanation:
Ann and Ben translate documents from German into English.
A set of documents that would take Ann 10 days would take Ben 12 days.
Ann starts to translate the documents.
After 2 days Ann and Ben both work on translating the documents.
How many more days will it take to complete the work?
You must show your working.
Using the together rate, it will take more 3.45 days to complete the work.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.
The together rate is given by the sum of each separate rate.
For this problem, the rates are given as follows,
Ann,1/10 = 0.1
Ben,1/12 = 0.0833
Together,1/x
Hence the amount completed in 2 days is:
2 x (0.1 + 0.0833) = 0.3666
The amount it would take them to complete 100% of the project working together is found by the together rate as follows,
x = 60/11
x = 5.45 days.
The time it would take to do the remaining 100 - 36.66 = 63.34% of the project is,
0.6334 x 5.45 = 3.45 days.
It will take more 3.45 days to complete the work.
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