Answers
Recall the following property of exponents:
[tex]a^b\cdot a^c=a^{b+c}[/tex]
[tex]\implies 216^{-3k}\cdot 216^{-2k}=216^{-3k-2k}=216^{-5k}[/tex]
Now, notice that 6² = 36 and 6³ = 216, which means that
[tex]216^{-5k}=36^{2k-1} \iff (6^3)^{-5k}=(6^2)^{2k-1}[/tex]
Recall another property of (real) exponents:
[tex](a^b)^c=a^{bc}[/tex]
[tex]\implies(6^3)^{-5k}=6^{3(-5k)}=6^{-15k}\text{ and }(6^2)^{2k-1}=6^{2(2k-1)}=6^{4k-2}[/tex]
So we have
[tex]216^{-5k}=36^{2k-1} \iff 6^{-15k}=6^{4k-2}[/tex]
Since both sides are equal powers of 6, that must mean that the exponents must be equal, so
[tex]-15k=4k-2[/tex]
Solve for k :
[tex]-15k-4k=(4k-4k)-2[/tex]
[tex]-19k=-2[/tex]
[tex]k=\dfrac{-2}{-19}=\boxed{\dfrac2{19}}[/tex]
Related Questions
if 300 apples cost 17600 how much does 1 apple cost
Answers
Answer:
58.67 17600/ 300 = 58.67
for a repair job an electrician charges an hourly rate of d dollars plus a flat fee of 50 the electricion charged a total if 114 for a 4-hour repair job. Part B. What is the value of D
Answers
Answer:
B. 4d + 50 = 114
Step-by-step explanation:
Given parameters:
Hourly rate = $d/hr
Flat fee = $50
Charge for the 4hrs = $114
Number of hours = 4hrs
To find d;
Total cost = $114;
$114 = Flat fee + (rate per hour x number of hours)
$114 = $50 + 4d
The value of d can be calculate using;
4d + 50 = 114
The value of d is 4d + 50 = 114
what is the rule for that
Answers
Answer:
The constant rule being followed is that the sum of x and y in every case is 5
Since the sum of x and y is 5, we can say that the value of y is 5-x
So we can define a function for this rule:
f(x) = 5 - x
Answer:
y = -x + 5Step-by-step explanation:
From the table we see that:
1. It is linear relationship as the difference in values change in linear increment2. Rate of change is - 1 as y-values drop by 1 unit3. y-intercept is 5 as per the first row (0, 5)Considering the above observations we can put equation:
y = - x + 5-4(7a + 5) = -160
What does A = to? :)
Answers
Answer:
a=5
Step-by-step explanation:
first, let's distribute on the left side.
-4(7a+5)=-160
-28a-20=-160 distribution
-28a=-140 adding 20 on both sides
a=5 dividing by -28 on both sides
there's your answer!
__,__,__,89,115,141 so
Answers
Answer:
11, 37, 63, 89, 115, 141
Step-by-step explanation:
Subtract 89 from 115 and you get 26.
Subtract 115 from 141 and you get 26.
Its a pattern, subtract 26 from 89 and you get 63, keep subtracting 26.
Answer:
11, 37, 63, 89, 115, 141
Step-by-step explanation:
Every time you proceed right you add 26 to the last number.
Every time you go left you take away 26 from the last number
Hope this helps:)
(just add until 89 is 115 and add the answer to 115 and see if the answer adds up)
QUESTION 2
84 is 30% of what number?
Answers
Answer: 280
Step-by-step explanation:
100/30=3.(3)
3.(3)*84=280
Answer:
280
Step-by-step explanation:
Maggie's brother is 4 years younger than four times her age. The sum of their ages is 31.
How old is Maggie?
Plzzzzzz hellp
Pllllzzzz
Answers
Answer:
Maggie is 7 years old
Step-by-step explanation:
Attached is an image that explains the question. Hope this helps!
The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following. x 1 2 4 8 16 p(x) 0.05 0.15 0.25 0.30 0.25 (a) Compute E(X) (in GB). (Enter your answer to two decimal places.) GB (b) Compute V(X) (in GB2) directly from the definition. (Enter your answer to four decimal places.) GB2 (c) Compute the standard deviation of X (in GB). (Round your answer to three decimal places.) GB (d) Compute V(X) (in GB2) using the shortcut formula. (Enter your answer to four decimal places.) GB2
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
x: ____ 1____ 2____ 4____ 8____ 16
p(x): _0.05_ 0.15__ 0.25__0.30__ 0.25
E(X) : Σ[(X). P(X)]
Σ(1*0.05) + (2*0.15) + (4*0.25) + (8*0.30) + (16 * 0.25)
= 7.75
B)
E(x) = u = 7.75
Var(X) = E[(x - u)²*p(x)] = (1 - 7.75)^2 * 0.05 + (2 - 7.75)^2 * 0.15 + (4 - 7.75)^2 * 0.25 + (8 - 7.75)^2 * 0.30 + (16 - 7.75)^2 * 0.25 = 27.7875
C)
Standard deviation (s)
s = √Var(x)
s= √27.7875
s = 5.271
D)
VAR(X) = E(X²) - (E(X))²
E(X²) = Σx²*p(x)
E(X²) = Σ(1^2 * 0.05 + 2^2 * 0.15 + 4^2 * 0.25 + 8^2 * 0.30 + 16^2 * 0.25) = 87.85
V(X) = E(X^2) - (E(X))^2 = 87.85 - 7.75^2 = 27.7875
Kimora drove with frankie to her mothers house which is 310 miles away. If it took them 6 hours, what was their average speed ?
Answers
Answer:
51.6 was the average speed
Step-by-step explanation:
speed= distance/time
how many centiliters are in 3 quarts?
Answers
Answer:
283-284
The real answer is like 283.906
how many inches smaller is a 13.26 inch worm than a 14.13 inch worm
Answers
How many atoms is 4.00 grams of iron
(Fe)?
Answers
Answer:
226
Step-by-step explanation:
PLS HELP ASAP
Explain how to estimate the product of 12 x 6. Use complete sentences in your answer.
WRITER
I need a written response pls not just the answer
Answers
Answer:
10×6 with 20% added = 60+12 = 72
Step-by-step explanation:
There are several ways to estimate the product of these numbers. One way is to round 12 to 10, then multiply 10×6 to get 60 as an estimate. You know this estimate is low, because you rounded down from 12 to 10. You know that a better estimate will be about 20% higher, because 12 is 20% higher than 10.
The product can be computed mentally by recognizing that 12 is 6×2, so the product will be 6²×2. Most schools have you memorize your times tables at least through 10×10, so you already know that 6² is 36. Doubling that value (to 72) gives you the value of 6×12.
Another way to estimate the product is to round 12 to 10 and 6 to 5. Again, you know each of these "stand-in" values needs to be increased by 20% to match the real values. Then the product estimate is 10×5 = 50, and you judge that to be low by 20% +20% = 40%. 40% more than 50 gives you a refined estimate of 70, but you know that, too, is low by a small amount. (Percentage changes can only be added accurately when they are very small. The true error is 44%, which is 20%+20%+(20%)(20%).)
You want to estimate the number of students in your middle school who play video
games. Which of the following would represent a random, valid sample?
O 10 students from your homeroom class
O Your 5 best friends at the lunch table
100 randomly selected people from your apartment complex
O 100 students selected randomly as their enter your middle school in the morning
Answers
Answer:
100 students selected randomly as their enter your middle school in the morning
Step-by-step explanation:
Answer:
C (100 students selected randomly from your middle school)
Step-by-step explanation:
The first one is wrong because its only 10 people from your homeroom.
The next one is also wrong sense its only 5 people who could also share the same interests as you.
The next one is wrong because its not from their middle school
That leaves us with the last one, its selected randomly with a lot of people involved from their middle school.
There are 450 cars in the car lot about 28% of them are hybrid cars. About how many cars are hybrid cars? Explain your reasoning.
Answers
Answer:
there are 126 hybrid cars.
Step-by-step explanation:
28% of 450 is 126
ta-daaa
Could anybody help with this question? My teacher didn’t give a review so I’m not sure what to do. Any help is appreciated!
Answers
Answer: 6
Step-by-step explanation: set the equations equal to each other then solve. plug that number into the equation for AB
Solve for x: x + b = C
Answers
Answer:
x=C-b
Step-by-step explanation:
Subtract b from both sides to get x alone.
You earn $9.50 per hour at your summer job. Write and solve an inequality to find the number of hours you need to work to buy a camera that costs $247. define the variable. create an inequality. Solve.
Answers
h
represent hours worked.
Now, we know the pay for one hour of work is
$
9.50
. So, the amount of pay for
h
hours worked is given by
9.50
h
.
Furthermore, since we're saving for a camera that costs
$
247
,
we want at LEAST
$
247
(but it's okay if we have more). So, we'll be using
≥
in the inequality.
So, our inequality is
9.50
h
≥
247
To solve, we simply divide both sides by
9.50
:
h
≥
247
9.50
h
≥
26
You need to work at least
26
hours to buy the digital
hi please help ): picture is included
Answers
Answer:
a
Step-by-step explanation:
the over all total equals 200 and you can not subtract the 2 variables to get the total you have to add them
Habiba wants to buy a new laptop. She purchases it for $950 and finances it for 3 years at an interest rate of 9.2%. How much interest will she pay?
Answers
Interest rate: 9.2%
Time: 3 years
Interest payment: $262.2
What is the slope of the line represented by the equation y = 4/5x - 3?
-3
-4/5
4/5
3
Answers
Answer:
4/5 is the slope of the line represented by the equation y = 4/5x - 3
A survey in 2012 indicated that college freshmen carry a mean credit card debt of $611 but the median of their credit card debt is $47. Create a data set of five freshmen students so that the data set has a mean and median that is the same as that of the surveyed college freshmen. , , , ,
Answers
Answer:
$27, $30, $47, $1093, $1851
Step-by-step explanation:
The median is the middle number and the mean is the average. When averaging all the numbers above, you get 611 and the middle number is 47.
The possible data set is $27, $30, $47, $1093, and $1851.
What is the mean?The average of a group of variables is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
To create a data set of five freshmen students with the same mean and median as the surveyed college freshmen:
Arrange the five numbers in ascending order to create the data set.
For example, one possible data set is:
$27, $30, $47, $1093, $1851
The mean of this data set is (28+ 40 + 47 + 1090 + 1850) / 5 = $611, which is the same as the mean of the surveyed college freshmen.
The median of this data set is 47, which is also the same as the median of the surveyed college freshmen.
Therefore, $27, $30, $47, $1093, and $1851 are the points of the data set.
To learn more about the mean;
brainly.com/question/13451489
#SPJ2
Write the equation of the line that passes through (-1,2) and (4,-2)
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1) Which of these situations can be represented by the opposite of 80? Select all that apply. *
a) An airplane descends 80m.
b) An elevator ascends 80m.
c) The cost of a train ticket drops $80.
d) You remove 80 songs from an iPhone.
e) Suzy's grandmother is 80 years old.
Answers
Answer:
D because if you remove the song there will be no more numberrs which is the opposite.
Situations A, C and D are the correct answers.
From the options, we need to check the situations opposite to 80.
What are integers?An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.
Now,
Situation A: An aeroplane descends 80 m, this can be represented in integer form as -80.
Situation B: An elevator ascends 80 m, this can be represented in integer form as 80.
Situation C: The cost of a train ticket drops by $80, which can be represented in integer form as -80.
Situation D: You remove 80 songs from an iPhone, which can be represented in integer form as -80.
Situation E: Suzy's grandmother is 80 years old, which can be represented in integer form as 80.
Therefore, situations A, C and D are the correct answers.
To learn more about integers visit:
https://brainly.com/question/15276410.
#SPJ2
Can someone help me please
Answers
Answer:
-729, so x9
Step-by-step explanation:
-81×9=-729 hope it helps!
Which are correct representations of the inequality -3(2x - 5) < 5(2-x)? Select two options. A)x< 5
B)-6x - 5 < 10-X
C)-6x + 15 < 10 - 5x
D)6 -3 1 2 3 5 6 7
E)-7-6 --5 4 3 2 1 1 2 3
Answers
Answer:
C and D or 3 and 4 0-0
Step-by-step explanation:
Answer:
C and D
Step-by-step explanation:
EDG 2021
Which single transformation can be applied to the graph of y = 72 StartRoot x EndRoot to produce the graph of y = 9 StartRoot x EndRoot?
- vertical translation
- vertical compression
- horizontal translation
- horizontal compression
Answers
Answer:
vertical....
Step-by-step explanation:
NawfSide 38 Baby
Answer:
B vertical compression
Step-by-step explanation:
edge :)
A line has a slope of -2/3 and passes through the point -3 and eight what is the equation of the line
Answers
Answer:
Y=-2/3x+10
Step-by-step explanation:
We have the slope -2/3, so we can find the y intercept by plugging in the given coordinate (-3,8). if y=mx+b, 8=-2/3(-3)+b. If you simplify the equation, you would get 8=-2+b, and then you would get 10=b. 10 would then be the y intercept.
Which angle is a vertical angle with Angle EFD?
Answers
Answer:
Angle AFB
Step-by-step explanation:
What is the solution to the following equation?
X-3(2x-8)= -25
A. X= 11
B. X= 14
C. X=10
D. x=5
Answers
Answer: X-3(2x-8)= -25
A. X= 11
B. X= 14
C. X=10
D. x=5
Step-by-step explanation: