The simplified form in base 3 for ln(3) + ln(9) is 3ln(3)
What is logarithm?logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if b^x = n, in which case one writes x = logb n.
In(9) can be written as ln3^2
which according law of logarithm is 2ln(3)
Expression becomes
ln(3) + 2ln(3) which is 3ln(3)
In conclusion, the simplified form of the expression in base 3 is 3ln(3)
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100 POINTS + BRAINLIEST
6. a) In 10 squares there are 22 dots
6. b) There are 102 squares are in the diagram which has 104 dots.
6. c) t(n) = a + (n - 1) d
7. a) mean = 6; median = 5
7. b) new card number = 14
This can be solved using geometic series concept.
What is geometric series?A geometric series is one where each pair of consecutive terms' ratios is a fixed function of the summation index. The ratio is a rational function of the summation index in a more comprehensive sense. creates what is known as a hyper geometric sequence. It is arithmetic if there is a common difference between the sequences. You can bet that anything is geometric if it has a common ratio. Similar to how the word arithmetic series denotes that each phrase is the arithmetic mean of its two neighbors, the name geometric series denotes that each term is the geometric mean of its two neighbors.
6. In the given figure we see that the dots are present here form a series.
In 1 square there are 4 dots.
In 2 squares there are 6 dots.
In 3 squares there are 8 dots.
So, they form a series.
a)
In 10 squares there are 22 dots
b)
There are 102 squares are in the diagram which has 104 dots.
c)
The formula of the series is:
t(n) = a + (n - 1) d
here a = 4 and d = 2
7.
a)
Jemina has 3 cards with the number of 5,2 and 11
Thus, mean = 5+2+11 /3 = 6
median = 5
b)
Next Jemina takes another card and the mean goes up by 2.
So, the number of new card:
2+5+x+11/4 = 8
or, 18 + x = 32
or, x = 14
So, new card number = 14
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Answer:
Step-by-step explanation:
6. a) In 10 squares there are 22 dots
6. b) There are 102 squares are in the diagram which has 104 dots.
6. c) t(n) = a + (n - 1) d
7. a) mean = 6; median = 5
7. b) new card number = 14
I need help
You buy two subs from Danny's for $5.97 each and you pay the cashier
$15. How much change will you get back?*
Answer:
3.06
Step-by-step explanation:
Answer:
You will get $3.06 back
Step-by-step explanation:
Add 5.97 + 5.97 = 11.94
then if you give the cashier $15 subtract what you owe, so 15 - 11.94 = 3.06
Match each expression to the scenario it represents.
Expressions
Scenario
the price of a game that’s been discounted
18% off its list price (x)
arrowRight
the price of a toy that sells for 18% more
than the amount (x) needed to build the toy
arrowRight
the volume of water remaining in a tank after
of its original volume (x) is drained out
arrowRight
the total amount of flour in a bakery after receiving new stock equal to of its current stock (x)
arrowRight
The expression matched with each scenario is;
Scenario 1: 0.82x
Scenario 2: 1.18x
Scenario 3: 7/10x
Scenario 4: 13/10x
AlgebraThe price of a game that’s been discounted
18% off its list price (x)
Total price = x
Discount = 18%x = 0.18x
New price = x - 0.18x
= 0.82x
The price of a toy that sells for 18% more
than the amount (x) needed to build the toy
Original price = x
Percentage increase = 18%x = 0.18x
New price = x + 0.18x
= 1.18x
The volume of water remaining in a tank after 3/10 of its original volume (x) is drained out
Original volume = x
Volume drained = 3/10x
New volume = x - 3/10x
= 7/10x
The total amount of flour in a bakery after receiving new stock equal to 3/10 of its current stock (x)
Original stock = x
New stock = 3/10x
Total stock = x + 3/10x
= 13/10x
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Tell which statement is the best estimate for the division problem 650 ÷ 8.
a.
650 ÷ 10 = 65
b.
700 ÷ 5 = 140
c.
640 ÷ 8 = 80
d.
600 ÷ 10 = 60
I put A before and my post was deleted.....
Conver 0.5 and 3/4 to a percent
Answer:
0.5 = 50%, 3/4 = 75%
Step-by-step explanation:
-3 2/7 + -6 1/6
Help with this please I dont know
Answer:
-9.45238095238
Step-by-step explanation:
Just use the fraction to add to the whole number
Answer:
=−14.73809524
Step-by-step explanation:
Please help! I dont get how to get the answer
The value of angle x in the triangle is 15°
How to find the value of x in the triangle?Given: the triangle ABC with equal sides of 9 units.
Since the triangle has equal sides, it will also have equal angles (i.e. it is an equilateral triangle).
Thus, <A = <B = < C = 4x°
Since the sum of angles in a triangle is 180°. We have:
<A + <B + < C = 180°
4x + 4x + 4x = 180°
12x = 180
x = 180/12
x = 15°
Therefore, the value of x is 15°
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HELP PLEASE giving out brainilest
9514 1404 393
Answer:
160 cm³
Step-by-step explanation:
The ratio of the linear dimensions is the square root of the ratio of areas:
scale factor B/A= √(64/144) = 8/12 = 2/3
The ratio of volumes is the cube of the scale factor:
(volume B)/(volume A) = (2/3)³ = 8/27
Then the volume of pyramid B is ...
volume B = (volume A) × (volume B)/(volume A)
= (540 cm³) × (8/27) = 160 cm³ . . . . volume of pyramid B
_____
Equivalently, the ratio of volumes is the 3/2 power of the ratio of areas.
Vb = Va(64/144)^(3/2) = (540 cm³)(4/9)^(3/2) = (540)(8/27) cm³ = 160 cm³
if a(x) = 3x+1 and b(x) = \(square root of x-4\), what is the domain of (boa)(x)
The domain of (boa)(x) is [1, ∞].
What is a domain?In Mathematics and Geometry, a domain is the set of all real numbers (x-values) for which a particular equation or function is defined.
Based on the information provided above, we have the following functions:
a(x) = 3x+1
\(b(x) = \sqrt{x-4}\)
Therefore, the composite function (boa)(x) is given by;
\(b(x) = \sqrt{3x+1 -4}\\\\b(x) = \sqrt{3x-3}\)
By critically observing the graph shown in the image attached below, we can logically deduce the following domain:
Domain = [1, ∞] or {x|x ≥ 1}.
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Help!!
[25+{14-(3x2)-2}]
the answer is on the page it is a screenshot explaining how to do it
x = 13, ¿cuál ecuación es verdadera?
3(18 - x) = 67
4(9x) = 23
2(x-3)=7
5(x-9) = 20
When x = 13, the equation that is true is option D) 5(x - 9) = 20.
To determine which equation is true when x = 13, we can substitute the value of x into each equation and see which equation holds true. Let's go through each option:
A) 3(18 - x) = 67
Substituting x = 13:
3(18 - 13) = 67
3(5) = 67
15 = 67
The equation is not true when x = 13. Therefore, option A is false.
B) 4(9x) = 23
Substituting x = 13:
4(9*13) = 23
4(117) = 23
468 = 23
Again, the equation is not true when x = 13. Therefore, option B is also false.
C) 2(x - 3) = 7
Substituting x = 13:
2(13 - 3) = 7
2(10) = 7
20 = 7
Once again, the equation is not true when x = 13. Therefore, option C is false as well.
D) 5(x - 9) = 20
Substituting x = 13:
5(13 - 9) = 20
5(4) = 20
20 = 20
Finally, the equation is true when x = 13. Therefore, option D is true.
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Note: the translated questions is
X = 13, which equation is true?
Find the slope of the line that passes through (10, 2) and (1, 6).
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Twenty members of an athletic club are studying the relationship between the time it takes an individual athlete to reach a given level of fatigue during exercise (time to fatigue, measured in minutes) and athletic performance. For each member, time to fatigue and a performance score were recorded. The computer output of the regression analysis is shown in the table.
TermCoefSE CoefTConstant39.884.249.41Time to fatigue3.920.715.52
Which of the following is a 90 percent confidence interval for the slope of the regression line relating performance score and time to fatigue? Assume that the conditions for inference are met.
3.92±1.734(0.71)
The confidence interval for the slope of the regression line relating performance score is 0.71
sample size (n) = 20
slope (b1) = 3.92 and SE of slope = 0.71
Degrees of freedom = 20 - 2 = 18
Using t-table we get, t-critical value at significance level of 0.10 with 18 degrees of freedom is,
tα/2=1.734
The 90% confidence interval for the slope of the regression line relating performance score and time to fatigue is,
B1±Tα/2*SE
3.92±1.734(0.71) (c)
Regression analysis is a statistical measure that is used in many different fields, including investing, finance, sales, marketing, science, mathematics, and others. It tries to figure out how closely one dependent variable is related to a set of other changing variables. They are commonly referred to as independent variables.
For example, how commodity prices relate to the shares of companies that trade in those commodities.
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To order a class ring, students must decide on a gold, sliver, or white gold band and one of 15 stones. They must also choose from one of 30 activity symbols to put in the side. How many different ring selection are there?
The total number of rings available for selection is 1350.
The combination is a process of knowing the number of ways of selecting a smaller set of articles from a larger set of articles where the order of selection is invariant.
If we select r items from n items in no particular order, the number of ways of doing so is calculated using combinations by the formula:
nCr = n!/{ r! (n - r)! }.
In the question, we are given that to order a class ring, students must decide on gold, silver, or white gold band and one of 15 stones. They must also choose from one of 30 activity symbols to put on the side.
We are asked the number of different ring selections there.
For the band:
Options available, n = 3.
Options to select, r = 1.
Thus, using combinations, the number of ways of selecting 1 band from 3 bands = 3C1 = 3!/{1! (3 - 1)! } = 3!/1!2! = 3.
For the stone:
Options available, n = 15.
Options to select, r = 1.
Thus, using combinations, the number of ways of selecting 1 stone from 15 stones = 15C1 = 15!/{1! (15 - 1)! } = 15!/1!14! = 15.
For the symbol:
Options available, n = 30.
Options to select, r = 1.
Thus, using combinations, the number of ways of selecting 1 symbol from 30 symbols = 30C1 = 30!/{1! (30 - 1)! } = 30!/1!29! = 30.
The total number of rings available is the product of the three.
Thus, the total number of rings available for selection = 3*15*30 = 1350.
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you are helping your sister plan her sweet 16. the venue you want to host it at charges $75 for every 3 guest as well as a rental deposit of $200 write an equation to determine the total party cost
Answer:
y = 25x + 200
Step-by-step explanation:
y = the total cost of the party
x = the number of guests
75/3 = 25
25 is the cost per guest.
Helping in the name of Jesus.
1. What is the measure
of ZABC?
A
98⁰
B
tc
2.
Answer:
∠ ABC = 49°
Step-by-step explanation:
the chord- tangent angle ABC is half the measure of the intercepted arc AB
∠ ABC = \(\frac{1}{2}\) AB = \(\frac{1}{2}\) × 98° = 49°
Can someone help me
The scale factor that was used to convert triangle ABC into the image in A ' B ' C ' is 1 / 2.
How to find the scale factor ?To find the scale factor, you need to find the length of a side of triangle ABC and then the length of the corresponding side in A ' B ' C '.
The side length we will pick is AB which is:
= 6 - 2
= 4 units
The side length of the other triangle is A' B' :
= 3 - 1
= 2 units
The scale factor is:
= 2 / 4
= 1 / 2
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This table gives a few (x,y) pairs of a line in the coordinate plane. What is the y intercept of the line?
Answer:
0,34
Step-by-step explanation: when you do x2-x1/y2-y1 with the coordinates you get slope plug that in the the y= mx+b equation with any one of the coordinates and you get the y intercept.
If someone have all the proofs of this I’ve been trying since yesterday PLEASE
Answer:
Please see steps below
Step-by-step explanation:
Notice the following:
(a) Angles 5 and 1 are alternate angles between parallel lines, and then they must be congruent (equal in measure) \(\angle 1 \,=\,\angle 5\)
(b) Angles 6 and 3 are also alternate angles between parallel lines, so they must be congruent (equal measure) \(\angle 3 \,=\,\angle 6\)
Therefore, instead of expressing the addition:
\(\angle 5\,\,+\,\,\angle 2\,\,+\,\,\angle 6\)
we can write:
\(\angle 1\,\,+\,\,\angle 2\,\,+\,\,\angle 3\)
which in fact clearly add to \(180^o\)
Are these right? Geometry by the way
Answer:
ABM is 60; DBC is 60; CBM is 120; HGF is 120; EFM is 120
Step-by-step explanation:
asap
Five students, Jeremiah, Claire, Alyssa, Brody, and Hudson, line up one behind the
other. How many different ways can they stand in line?
Answer:
25 dfferent ways
Step-by-step explanation:
The answer is 25 different ways because since there are students and thy line up behind each other you would do 5 times 5 which equals to 25.
contracts for two construction jobs are randomly assigned to one or more of three firms, a, b, and c. the joint distribution of y1, the number of contracts awarded to firm a, and y2, the number of contracts awarded to firm b, is given by the entries in the following table. y1 y2 0 1 2 0 1 9 2 9 1 9 1 2 9 2 9 0 2 1 9 0 0 find cov(y1, y2). (round your answer to three decimal places.) cov(y1, y2)
The value of covariance cov(y1, y2) is -0.222
y1
y2 0 1 2 Total
0 1/9 2/9 1/9 4/9
1 2/9 2/9 0 4/9
2 1/9 0 0 1/9
Total 4/9 4/9 1/9 1
marginal distribution of y2:
y2 P(y2) y2P(y2) y2^2P(y2)
0 4/9 0.0000 0.0000
1 4/9 0.4444 0.4444
2 1/9 0.2222 0.4444
total 1 0.66667 0.88889
E(y2) = 0.6667
E(y2^2) = 0.8889
Var(y2) = E(y2^2)-(E(y2))^2=0.4444
marginal distribution of y1
y1 P(y1) y1P(y1) y1^2P(y1)
0 4/9 0.0000 0.0000
1 4/9 0.4444 0.4444
2 1/9 0.2222 0.4444
total 1.00 0.6667 0.8889
E(y1) = 0.6667
E(y1^2) = 0.8889
Var(y1)= σy = E(y1^2)-(E(y1))^2 = 0.4444
E(XY) =∑xyP(x,y)=0.2222
Cov(y1,y2) = -0.222
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Without looking, Russell took 97 coins out of a jar of equal-valued coins. Is this a random sample of the coins in the jar? yes or no
Answer:
Step-by-step explanation:
No, this is not a random sample of the coins in the jar. A random sample is one where each coin in the jar has an equal chance of being selected. If Russell took 97 coins out of a jar without a specific method of selection, it is not considered a random sample.
If f(2) = 13 and f '(x) ≥ 2 for 2 ≤ x ≤ 7, how small can f(7) possibly be?
Answer:
23
Step-by-step explanation:
We are given that
f(2)=13
\(f'(x)\geq 2\)
\(2\leq x\leq 7\)
We have to find the possible small value of f(7).
We know that
\(f'(x)=\frac{f(b)-f(a)}{b-a}\)
Using the formula
\(f'(x)=\frac{f(7)-f(2)}{7-2}\)
\(f'(x)=\frac{f(7)-13}{5}\)
We have
\(f'(x)\geq 2\)
\(\frac{f(7)-13}{5}\geq 2\)
\(f(7)-13\geq 2\times 5\)
\(f(7)-13\geq 10\)
\(f(7)\geq 10+13\)
\(f(7)\geq 23\)
The small value of f(7) can be 23.
#7 find the answer with the offering 20% discount
Given a discount of 20% and a manufacturer's coupon of $200, the price after the discount and coupon, (C ∘ D)(x), is 0.8x - 200.
What is a discount?A discount is an amount that reduces the price of a retail item.
Discounts are offered as rates and the discounted price is computed by multiplying the discount factor and the price.
Discount rate on offer = 20%
Discounting factor = 80% or 0.8 (100 - 20%)
Manufacturer's coupon off the price = $200
Let the price of the bureau = x
The price after the discount (discounted price) is given by D(x)
D(x) = 0.8x
The price after the coupon = C(x) = x - 200
The price after applying the discount and the coupon, (C ∘ D)(x) = 0.8x - 200
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Complete Question:Wilson's Warehouse sells a certain brand's bureau. They are offering a 20% discount in addition to accepting a manufacturer's coupon for $200 off. Let the price of the bureau be x. If the price after the discount is given by D(x) and the price after the coupon is C(x), find (C ∘ D)(x).
Computer systems analysts
Database administrators
Computer software engineers,
systems software
Gaming and sports book writers
and runners
Environmental science and
protection technicians, including
health
Manicurists and pedicurists
Physical therapists
Physician assistants
504
650
119 154
350 449
18 24
36
78
47
100
220
29.0
28.6
28.2
28.0
28.0
27,6
27.1
146
34
99
5
10
22
47
18
Bachelor's degree
Bachelor's degree
Bachelor's degree
Short-term on-thi
Associate degree
Postsecondary vocational award
Master's degree
Master's degree
173
66
83
27.0
Based on the above table, what is the fastest growing listed occupation for those without a college degree?
a. Gaming and sports book writers and runners
b. Dental assistants
c. Marriage and family therapists
d. Manicurists and pedicurists
Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners.
Therefore option A is correct.
What is a college degree?The college degree is described as a qualification awarded to students after completing the requirements for a specific course of study of which the two most common types of degrees are the Bachelor of Arts and Bachelor of Science.
With reference to the table, the occupations that do not require a college degree are:
Gaming and sports book writers and runnersEnvironmental science and protection technicians, including healthManicurists and pedicuristsWe were able to conclude that Based on the above table , the fastest growing listed occupation for those without a college degree is Gaming and sports book writers and runners with a rate of 24.6%.
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5
Up to now in her Algebra course, Lucy has earned 154 out of a total of 180
points. If there will be 1000 total points in the class, what percentage of the
remaining points must she earn in order to have an overall average of 90% in the
class?
Answer:
846 because 1000-154 is 846 .
A student flips four different coins at the same time. Which choice shows all of the possibilities for the results of the coin toss? (H = heads, T = tails)
A HH, TT, HT, TH
B HHHT, HTTT, HHTT
C HHH, TTT, HTH, HTT
D HHHH, HTHH, HTTH, HTTT, TTTT
Answer:
D
Step-by-step explanation:
Please mark brainliest
Answer:
This is the event X1=H. There are 8 outcomes in this event. Let C be the event that the first flip and the third flip are both heads. So A and B would not be the answer so I am guessing it is D and if I am right pls mark me brainless
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options.
The radius of the circle is 3 units.
The center of the circle lies on the x-axis.
The center of the circle lies on the y-axis.
The standard form of the equation is (x – 1)² + y² = 3.
The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
The x-axis is where the circle centre is located. Three units make up the circle's radius. This circle's radius coincides with the radius of the circle whose equation is x² + y² = 9.
What is the circle's equation when its centre is on the x-axis?The y coordinate of a circle's centre will be 0 if the circle's centre is on the x-axis. The circle's equation will therefore have the generic form x2 + y2 + 2gx + c = 0, where g and c are constants.
Circle's standard equation is written as:
x²+y²+2gx+2fy+C=0
Centre is (-g, -f)
radius = √g²+f²-C
Given a circle whose equation is : x²+y²-2x-8=0
Get the centre of the circle
2gx = -2x
2g = -2
g = -1
Similarly, 2fy = 0
f = 0
Centre = (-(-1), 0) = (1, 0)
This demonstrates circle's centre is on the x-axis.
r = radius = √g²+f²-C
radius = √1²+0²-(-8)
radius =√9 = 3 units
The circle has a radius of three units.
For the circle x²+y²=9, radius is expressed as:
r² = 9
r = 3 units
As a result, this circle's radius matches that of the circle whose equation is x² + y² = 9.
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What’s the 6th term of 23,92,368
Answer:
23552
Step-by-step explanation:
23, 92, 368... is a geometric sequence.
first term = a = 23
common ratio = r = 2 term ÷ first term = 92 ÷ 23 = 4
nth term = \(ar^n^-^1\)
6th term = \(23*(4)^6^-^1\)
\(=23*4^5\)
\(=23*1024\)
\(=23552\)
Hope this helps :)
Pls brainliest...