The expression that is equivalent to the given statement was reduced.
The given expression is:
[tex]\frac{(3m^{-2}n)^{-3} }{6mn^{-2} }[/tex]
What are some important power rules?Some important power rules are:
[tex](ab)^n=a^nb^n[/tex]
[tex](a^{m} )^n=a^{mn}[/tex]
[tex]a^m.a^n=a^{m+n}[/tex]
[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]a^{-m} =\frac{1}{a^m}[/tex]
So, the given expression can be written as:
[tex]\frac{3^{-3} m^{6} n^{-3} }{6mn^{-2} }[/tex]
=[tex](\frac{3^{-3} }{6} )*(\frac{m^{6} }{m} )*(\frac{n^{-3} }{n^{-2} } )[/tex]
=[tex](\frac{1}{3^{3} *6} )*m^{5} *(\frac{1}{n^{3} *n^{-2} } )[/tex]
=[tex]\frac{m^5}{162n}[/tex]
Hence, the expression that is equivalent to the given statement was reduced.
To get more about power rules visit:
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i need help its 7th grade area surface
Answer:
729 square inches
Step-by-step explanation:
9^3 or 9×9×9
(im not sure but i think thats it)
Solve the following....
[tex]2(x-3)=2x+4[/tex]
Answer:
No answer. The question is not correct. 2x-6 cannot be equal to 2x+4
Step-by-step explanation:
2(x-3) = 2x+4
2x-6 = 2x+4
This can't be true. 2x-6 cannot be equal to 2x+4:
Subtract 2x from both sides and we are left with -6 = 4: FALSE
Answer:
no solutionStep-by-step explanation:
Taking the LHS and distributing
2(x - 3)2(x) - 2(3)2x - 6Equating to the RHS
2x - 6 = 2x + 4On inputting any value for x, this equation will not be correct.
Hence, it has no solution.
The area of the rectangle below is greater than or equal to 18.13 square units. The inequality 3.7w ≥ 18.13 represents this
situation?
Answer:
so the answer is tyrany because i love to talk aboutheaarts so this is waht happened
Step-by-step explanation:
Please Help With This!!!
Will try to give out brainliest!!!
Answer: [tex]2^4,4^2,16^1[/tex]
Step-by-step explanation:
Let's evaluate each expression
Remember the little number that is the exponent means to multiply that number by itself that amount of times
[tex]8^2=[/tex]8×8=64 this is not 16
[tex]2^4=[/tex]2×2×2×2=4×4=16
[tex]2^8[/tex] we already know [tex]2^4[/tex] was enough so this must be over 16 and incorrect
[tex]4^2=[/tex]4×4=16
[tex]16^1[/tex]=16
A 2-column table with 6 rows. the first column is labeled week with entries 1, 2, 4, 6, 8, 10. the second column is labeled miles run with entries 5, 8, 13, 15, 19, 20. rita is starting a running program. the table shows the total number of miles she runs in different weeks. what is the equation of the line of best fit for the data? state each number to the thousandths place. y ≈ x
The line of best fit for the data of week and the corresponding miles run is evaluated to be: y = 4.699 + 1.671x
How does linear regression works?Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least squares method.
The following data for the Week and miles run variables are provided to construct linear regression model:
Week miles run
1 5
2 8
4 13
6 15
8 19
10 20
The independent variable is Week(represented by x), and the dependent variable is miles run(represented by y). In order to compute the regression coefficients, the following table needs to be used:
Let week = x, and miles run = y, then we get this table:
x y xy [tex]x^2[/tex] [tex]y^2[/tex]
----------------------------------------------------
1 5 5 1 25
2 8 16 4 64
4 13 52 16 169
6 15 90 36 225
8 19 152 64 361
10 20 200 100 400
-----------------------------------------------------
Sum = 31 80 515 221 1244
Based on the above table, the following is calculated:
[tex]\bar X = \frac{1}{n} \sum_{i=1}^{n} X_i = \frac{ 31}{ 6} \approx 5.167[/tex]
[tex]\bar Y = \frac{1}{n} \sum_{i=1}^{n} Y_i = \frac{ 80}{ 6} \approx 13.33[/tex]
[tex]\large SS_{XX} = \sum_{i=1}^{n} X_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} X_i\right)^2 = 221 - 31^2/6 \approx 60.833[/tex]
[tex]\large SS_{YY} = \sum_{i=1}^{n} Y_i^2 - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} Y_i\right)^2 = 1244 - 80^2/6 \approx 177.33[/tex]
[tex]\large SS_{XY} = \sum_{i=1}^{n} X_i Y_i - \displaystyle\frac{1}{n}\left(\sum_{i=1}^{n} X_i\right) \left(\sum_{i=1}^{n} Y_i\right) = 515 - 31 \times 80/6 \approx 101.67[/tex]
Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:
[tex]m = \frac{SS_{XY}}{SS_{XX}} \approx \frac{ 101.67}{ 60.833} \approx 1.6712[/tex]
[tex]n = \bar Y - \bar X \cdot m = 13.33- 5.167 \times 1.6712 = 4.6986[/tex]
Therefore, we find that the regression equation is:
miles run = 4.6986 + 1.6712 Week
y = 4.6986 + 1.6712x (approximately)
To the thousandths place, it becomes:
y = 4.699 + 1.671x
Therefore, based on the information provided above, the following scatter plot and regression plot are obtained as the image attached below.
Thus, the line of best fit for the data of week and the corresponding miles run is evaluated to be: y = 4.699 + 1.671x
Learn more about linear regression here:
https://brainly.com/question/18854090
Answer:
y-1.671
4.699
Step-by-step explanation:
Write a multiplication expression that can be used to solve 2/3a = 30.
a=45
Solution:We need to multiply both sides by 3 in order to get rid of the denominator, 3:2/3a•3=30•32a=90Divide both sides by 2:a=45Hope it helps.
Do comment if you have any query.
How to do the circumference of a semicircle with a radius of 7 1/2.
Answer:
38.6 units (nearest tenth)
Step-by-step explanation:
Formulae
Diameter = 2r Circumference = 2πr(where r is the radius)
Circumference of a semicircle = diameter + half the circumference
⇒ Circumference of a semicircle = 2r + πr
Given:
[tex]\sf radius\:{(r)=7\frac12=7.5[/tex][tex]\begin{aligned}\implies \textsf{Circumference of semicircle} & = 2(7.5) + \pi(7.5)\\ & = 15+7.5 \pi\\ & = 38.5619449...\\ & = 38.6\:\sf units\:(nearest\:tenth)\end{aligned}[/tex]
Circumference
πr+2rr(π+2)7.5(3.14+2)7.5(5.14)38.6units²Julia T. earns $22.22 per hour. What is her straight time pay for a 36-hour week?
Answer: her pay was $799.92
Step-by-step explanation:
multiply the number of hours she worked by her pay per hour:
22.22(36)
= 799.92
Answer:
given:
hours worked=36hours
payment per hour=$22.22
to find:
payment in a week
solution: 22.22×36
=799.92$
ans:her total pay for a 36 hour week is $799.92
If CDEF is a kite, CD =15 find CG
Answer:
Step-by-step explanation:
CD = 15, so we have the hypotenuse.
DF = 18, but we can find a leg by 18/2 which is 9
using our pyth. theorem, 15^2=9^2+CG^2
CG = 12
Hope this helped
If abcd is also a rhombus, what must be the value of x? 13 15 18 23
Answer: it’s 13
Step-by-step explanation:
I just took the Unit Test On Edge2022
A music store charges for lessons
according to the table below. If the store
charges a constant rate of dollars to time,
which of the following could fill the empty
row?
Time (min) Cost
a. 50 minutes for $40
o Yes O No
b. 60 minutes for $42
o Yes No
c. 70 minutes for $56
o Yes No
d. 90 minutes for $72
o Yes No
Rate of change:-
(30,24)(40,32)Slope:-
m=32-24/40-30m=8/10=4/5So
Next time is off course 50 .
Price should be calculated
y=50(4/5)=10(4)=40Option A✓
Check all
Option B:-
42=(4/5)(60)42=4(12)No
Option C
56=4/5(70)56=4(14)yes
Option D
72=4/5(90)72=4(18)Yes
Please help just this that's all
Answer:
7 × 10⁴ (option D.)
Step-by-step explanation:
Take the missing value as 'x'.
5 × 10³ + x = 7.5 × 10⁴
x = (7.5 × 10⁴) - (5 × 10³)
x = (7.5 × 10000) - (5 × 1000)
x = 75000 - 5000
x = 70000
x = 7 × 10⁴ (option D.)
______
Hope it helps ⚜
[tex]5 \times {10}^{3} + ....... = 7.5 \times {10}^{4} [/tex]
to find:the true equation
solution:let the unknown be y
[tex]y = (7.5 \times {10}^{4} ) - (5 \times {10}^{3} )[/tex]
[tex]y = (7.5 \times 10000) - (5 \times 1000)[/tex]
[tex]y = 75000 - 5000[/tex]
[tex]y = 70000[/tex]
[tex]y = 7 \times {10}^{4} [/tex]
therefore, the correct answer is option D
pls help!! i rlly need this quick
Answer:
See below ~
Step-by-step explanation:
Combination Rule
ⁿCₓ = n! / (n - x)! x!#1) ²²C₂₀
²²C₂₀ = 22! / 2! 20!22 x 21 x 20! / 2! x 20!22 x 21 / 211 x 21231#2) ¹²C₈
¹²C₈ = 12! / 4! 8!12 x 11 x 10 x 9 x 8! / 4! x 8!12 x 11 x 10 x 9 / 4 x 3 x 211 x 5 x 999 x 5495Answer:
[tex]\displaystyle ^{22}C_{20} =231[/tex]
[tex]\displaystyle ^{12}C_{8} =495[/tex]
Step-by-step explanation:
Binomial Coefficients
[tex]\displaystyle \binom{n}{r} \: = \:^{n}C_{r} = \frac{n!}{(n-r)! \, r!}[/tex]
[tex]\begin{aligned}\displaystyle \implies ^{22}C_{20} & = \frac{22!}{(22-20)! \, 20!}\\\\ & =\frac{22!}{2! \, 20!}\\\\ & =\frac{22 \cdot 21 \cdot 20!}{2! \, 20!}\\\\ & =\frac{22 \cdot 21}{2 \cdot 1}\\\\ & =\frac{462}{2}\\\\ & =231\end{ailgned}[/tex]
[tex]\displaystyle \begin{aligned} \implies ^{12}C_{8} & = \frac{12!}{(12-8)! \, 8!}\\\\ & =\frac{12!}{4! \, 8!}\\\\ & =\frac{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8!}{4! \, 8!}\\\\ & =\frac{12 \cdot 11 \cdot 10 \cdot 9}{4 \cdot 3 \cdot 2 \cdot 1}\\\\ & =\frac{11880}{24}\\\\ & =495\end{aligned}[/tex]
what value makes the following equation true? x + 10 = 18
x=8
Solution:In order to determine the value of x that makes the equation true, we need to subtract 10 from both sides:x+10=18x=18-10x=8Therefore, when x=8, the equation x+10=18 is true.Hope it helps.
Do comment if you have any query.
Answer:
8 + 10 = 18
Step-by-step explanation:
no need for explanation simple addition
in which age bracket does the most number of parcitipants fall?
The most number of participants fall on the age bracket of 37-39.
hope this helps
Find the circumference and area of a circle with diameter 4 cm.
HELP ASAP PLS
Step-by-step explanation:
the formulas can be easily found on the internet.
remember, the diameter of a circle is 2 times the radius.
so, the radius of our circle here is 4/2 = 2 cm.
circumference :
2×pi×r = 2×3.14×2 = 12.56 cm
area :
pi×r² = 3.14×2² = 3.14×4 = 12.56 cm²
hey, your teacher gave you the circle, where the circumference and the area have the same quantity ! funny !
so, make double sure you use the correct unit dimensions (remember, a distance has only one dimension, an area has 2 dimensions, and a volume has 3 dimensions).
5 5/8 as an improper fraction
The improper fraction is 45/8.
Answer:
45/8
Step-by-step explanation:
to get an improper fraction, you multiply the denominator by the whole number and add the numerator to the total. So for this problem 5(8)=40+5= 45/8
Can someone help me with these 3 questions? I need them asap (Test) Screenshots are below! I will give 15 pts!
Answer:
Pythagorean Theorom: [tex]a^2+b^2=c^2[/tex]
Triangle #1
[tex]21^2+x^2=29^2[/tex]
[tex]x^2=29^2-21^2[/tex]
[tex]x=\sqrt{841-441} =\sqrt{400}=20[/tex]
Triangle #2
[tex]1.6^2+3.0^2=x^2[/tex]
[tex]x=\sqrt{1.6^2+3.0^2}=\sqrt{11.56} =3.4[/tex]
Triangle #3
[tex]x^2+40^2=41^2[/tex]
[tex]x=\sqrt{41^2-40^2}=\sqrt{81} =9[/tex]
I hope this helps!
A survey of customers at a restaurant revealed that 7 out of 10 customers preferred the restaurants new spaghetti sauce. Which graph shows a relationship between y, the number of customers who preferred the new spaghetti sauce, and x, the total of customers?
The graph that shows the proportional relationship y = 0.7x is Graph A.
What is a proportional relationship?A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:
y = kx
In which k is the constant of proportionality.
In this problem, 7 out of 10 customers preferred the restaurants new spaghetti sauce, hence the constant is given by:
k = 7/10 = 0.7.
And the equation is:
y = 0.7x.
When x = 0, y = 0, which already eliminates graphs C and D. When x = 10, y = 7, which means that Graph A is the answer to this question.
More can be learned about proportional relationships at https://brainly.com/question/10424180
if p=1(l+b), express b in terms of p and l:b=
Step-by-step explanation:
=> p=1(l+b)
=> P = 1l + 1b
=> 1l - P = 1b
=> b = 1l - P/1
~Done~
Or
p=1(l+b)
Step 1: Flip the equation.
b+l=p
Step 2: Add -l to both sides.
b+l+−l=p+−l
b=−l+p
Answer:
b=−l+p
A solid shape is made by joining two cones.
Each cone has the same radius.
One cone has
slant height = 2 × radius
The other cone has slant height = 3 × radius
The total surface area of the shape is 135. 21 cm²
Curved surface area of a cone = tırl where r is the radius and / is the slant height
Work out the radius.
The surface area of the solid shape is the amount of space on it
The radius of the two cones is 2.93 cm
How to determine the radius?The given parameters are:
Cone 1: slant height, l = 2rCone 2: slant height, L = 3rSurface area = 135. 21 cm²The surface area of the shape is calculated using:
T = πr(L + l)
So, we have:
135.21 = πr(2r + 3r)
Evaluate
135.21 = 5πr²
Divide both sides by 5π
r² = 135.21/5π
Evaluate the quotient
r² = 8.61
Take the square root of both sides
r = 2.93
Hence, the radius of the cones is 2.93 cm
Read more about surface area at:
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Which description compares the vertical asymptote(s) of Function A and Function B correctly?
Function A: f(x) = 1/x-1
Function B: (see photo)
A. Function A has a vertical asymptote at x = 1.
Function B has a vertical asymptote at x = 0.
B. Function A has a vertical asymptote at x = 1.
Function B has a vertical asymptote at x=−3.
C. Function A has a vertical asymptote at x=−1.
Function B has a vertical asymptote at x=−3.
D. Both functions have the same vertical asymptote.
Answer:
B. Function A has a vertical asymptote at x = 1.
Function B has a vertical asymptote at x=−3.
Step-by-step explanation:
You can see from the diagram that the asymptope is x = -3, but to find the asymtope for the function make denominator equal to 0 and solve because the denominator can never equal 0, (you divide a number by 0, which is mathematically impossible) therefore the function will never reach that line.
How much water does a cube-shaped tank with equal dimensions of 3.3 feet hold?
We need the volume
Side=a=3.3ftVolume:-
a³3.3³35.94ft³To find how much water the cube can hold
⇒ must find volume
⇒ which is the amount of space that a shape occupies, or
that is enclosed within the shape
The volume of a cube-shaped tank:
⇒ is the length, width, and height multiplied together
⇒ since this is a cube, all the side lengths are equal
⇒ Volume = (side-length)^3
Based on the information given
⇒ side-length is 3.3 feet
Therefore:
Volume = [tex]3.3^3 = 35.937ft^3[/tex]
Thus the cube-shaped tank can hold 35.937 cubic feet of water
Answer: 35.937 cubic feet of water
Hope that helps!
can someone please help with This !
Answer:
A. E
B. D
C. A
Trust me on this one! I used a calculator.
PLEASE HELP just need a quick answer!!! will give brainly!!!
A moving-van rental company uses the polynomial 130 + 0. 75(m – 200) to calculate the rental charges if a customer drives a van more than 200 miles in one day. In the polynomial, m is the total number of miles that the customer drove the van during the day. Use the Distributive Property to write an equivalent expression for the total cost of renting the van and driving it more than 200 miles in one day
Answer:
im not sure but i think this is the answer
Step-by-step explanation:
I think it would be 130 + 0.75m
Which simplified could be 130.75m Hope it helps! :)
0.75m - 20
[tex]130+0.75\left(m-200\right)\ =\ 0.75m-20[/tex]
Step-by-step explanation:[tex]0.75(m-200) + 130[/tex]
The slope is 0.75
Substitute m for 0 ( [tex]0.75(-200) + 130[/tex])
Evaluate the equation ( [tex]0.75(-200) + 130[/tex]) = -20, this is the y-intercept
now the equation is [tex]slope + intercept[/tex] = [tex]0.75 -20[/tex]
The mayor wants to know how the people of the city feel about a bottle tax. she sends her staff to a randomly selected block in each of the city's election districts. the staff members interview all the residents on the block that are home that day. what is the population? all the people in the city all the people who live on the block all the people who live on the block and are home that day
The population is all the people in the city, and sample is all the people who live on the block and are home that day.
What are population and sample?It is defined as the group of data having the same entity which is related to some problems. The sample is a subset of the population, it is a part of the population.
The mayor wants to know how the people of the city feel about a bottle tax. She sends her staff to a randomly selected block in each of the city's election districts.
According to the definition of the population, we can say that the population is all the people in the city because they are the same entity which have to be tested to know how the people of the city feel about a bottle tax.
If we identify the sample, so the sample is all the people who live on the block and are home when the staff members interview all the resident on the block that are home that day.
Thus, the population is all the people in the city and sample is all the people who live on the block and are home that day.
Learn more about the population and sample here:
brainly.com/question/9295991
Answer:
The mayor wants to know how the people of the city feel about a bottle tax. She sends her staff to a randomly selected block in each of the city's election districts. The staff members interview all the residents on the block that are home that day.
(A) or All the people in the city
the second part (C) or all the people who live on the block and are home that day
Step-by-step explanation:
got it right on edg
A. 5
B. 7
C. 2.6
D. 5.5
Answer:
A 5 is the distance between
Step-by-step explanation:
(-2 -2)^2 + ( 0-3)^2 = d^2
d = 5
20 points given and brainiest for correct answer
Answer:
B is correct
I = (5200)(0.06)(2.5)
Step-by-step explanation:
Brainliest would be very much appreciated
If there are two angles that are supplementary, and the first angle has a measure of 137°, what is the measure of the second angle? A. 43 degrees B. 90 degrees C. 72 degrees
Answer:
Step-by-step explana what grade math is this?
A rectangle measures 9 4/5 meters 5 3/4 meters. What is its area?
Answer:
56.35 meters squared
Step-by-step explanation:
lmk if its inches