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Explanation:
Rule: If a set has n elements in it, then it will have 2^n subsets.
For example, there are n = 3 elements in the set {a,b,c}. This means there are 2^n = 2^3 = 8 subsets. The eight subsets are listed below.
{a,b,c} .... any set is a subset of itself{a,b}{a,c}{b,c}{a}{b}{c}{ } ..... the empty setSubsets 2 through 4 are subsets with exactly 2 elements. Subsets 5 through 7 are singletons (aka sets with 1 element). The last subset is the empty set which is a subset of any set. You could use the special symbol [tex]\varnothing[/tex] to indicate the empty set.
For more information, check out concepts relating to the power set.
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The problem is asking what value of n will make 2^n = 64 true.
You could guess-and-check your way to see that 2^n = 64 has the solution n = 6.
Another approach is to follow these steps.
[tex]2^n = 64\\\\2^n = 2^6\\\\n = 6[/tex]
Which is fairly trivial.
Or you can use logarithms to solve for the exponent.
[tex]2^n = 64\\\\\text{Log}\left(2^n\right)=\text{Log}\left(64\right)\\\\n*\text{Log}\left(2\right)=\text{Log}\left(64\right)\\\\n=\frac{\text{Log}\left(64\right)}{\text{Log}\left(2\right)}\\\\n\approx\frac{1.80617997398389} {0.30102999566399} \ \text{ ... using base 10 logs}\\\\n\approx5.99999999999983\\\\[/tex]
Due to rounding error, we don't land exactly on 6 even though we should.
Lesson Check (5.NF.A.1)
1. What is a rule for the sequence?
5/6, 1 1/2, 2 1/6, 2 5/6
it hard like all the from your guys web page so yeah
Answer:
Hi
Step-by-step explanation:
I'm sorry I don't understand do you need help with anything?
Brainliest if correct
Answer:
-16
-10
-4
2
Step-by-step explanation:
y = 3x - 4
x = -4, y = 3(-4) - 4 = -16
x = -2, y = 3(-2) - 4 = -10
x = 0, y = 0 - 4 = -4
x = 2, y = 3(2) - 4 = 2
[tex]5 \div 2 \sqrt{2} [/tex]
no decimals allowed
Answer:
[tex] \frac{5}{2 \sqrt{2} } \\ = \frac{5}{ 2 \sqrt{2} } \times \frac{2 \sqrt{2} }{2 \sqrt{2} } \\ = \frac{5(2 \sqrt{2}) }{(2 \sqrt{2} )(2 \sqrt{2}) } \\ = \frac{10 \sqrt{2} }{(2 \sqrt{2} {)}^{2} } \\ = \frac{10 \sqrt{2} }{4 \sqrt{( {2)}^{2} } } \\ = \frac{10 \sqrt{2} }{4 \sqrt{2 \times 2} } \\ = \frac{10 \sqrt{2} }{4(2)} \\ = \frac{ \cancel{10} \sqrt{2} }{ \cancel8} \\ = \frac{5 \sqrt{2} }{4} answer.[/tex]
When we rationalise the expression 5 / 2√2, the result obtained is 5√2 / 4
Surd operationa / √b = (a / √b) × (√b / √b)
How to rationalise the expression 5 / 2√2Expression = 5 / 2√2Rationalisation =?5 / 2√2 = (5 / 2√2) × (√2 / √2)
Clear bracket
5 / 2√2 = 5√2 / (2×2)
Simplify
5 / 2√2 = 5√2 / 4
Thus, we can conclude that the value of 5 / 2√2 is equivalent to 5√2 / 4
Learn more about surd:
https://brainly.com/question/24700530
Find the height of a triangle with base 3 m and area 9 m².
a
m
Answer:
h=6
Step-by-step explanation:
a=b x h x 0.5
9=3 x h x 0.5
9/3=3/.5=6
h=6
Answer:
The Height = 6
Step-by-step explanation:
Triangle formula bxh/2
3x6/2=9
Make b the subject of the formula, a=the square root of b-a
Step-by-step explanation:
[tex]a = \sqrt{b - a} [/tex]
firstly square
[tex] \sqrt{b- a} [/tex]
to get a-b on it's own
it's now
[tex]a = b - a[/tex]
now plus the a to cancel out the minus a to get
[tex]a {}^{2} = b[/tex]
which can also be written as
[tex]b = a {}^{2} [/tex]
dont know if that makes sense as I'm not the best at trying to explain
PLEASE ANSWER THIS QUESTIO NOW!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
2.65 pounds/week
Step-by-step explanation:
(13 1/4) / 5
13.25 / 5
= 2.65 pounds/week
Answer:
2.65 lbs per week
Step-by-step explanation:
13.25 is how many pounds
5 weeks is the length of time
pounds/length of time
13.25/5 = 2.65
2.65 lbs per week
Gabrielle is 12 years younger than Mikhail. The sum of their ages is 64. What is Mikhail's age?
years old
Answer:
Mikhail is 38
Gabrielle is 26
Step-by-step explanation:
Answer:
Let age of gab is x and then mik will be x+9
Now both of them have total sum 87
Step-by-step explanation:
Just add x+x+9 =87 2x=78, x=78÷2
X=39
The world population is projected to be 8.2 billion in 2045. At that time, there are expected to be approximately 3 billion more people in Asia than in Africa. The population for the rest of the world will be approximately 0.2 billion more than half the population of Asia. Find the projected populations of Asia, Africa, and the rest of the world in 2045.
The projected population of Asia will be approximately billion
Answer:
Since the total population will be 9.4B people
W + A+ A =9.4B
W = 0.6B + A/4
A+ 2.9B = As
A - 2.9B + As + 0.6 + A/4 = 9.4B
(9/4)*A= 11.7B
A = (4/9)*11.7B=5.2B
W = 0.6B + (5.2B/4) = 1.9B
A = 5.2B - 2.9B = 2.3B
AB and BC form a right angle at point B. If A= (-3, -1) and B= (4, 4), what is the equation of BC
A. x + 3y = 16
B. 2x + y = 12
C. -7x - 5y = -48
D. 7x - 5y = 48
Answer:
(C) -7x - 5y = -48
Step by step explanation:
We look for the equation of the line AB
We have then:
y-yo = m (x-x0)
m = (y2-y1) / (x2-x1)
m = (4 - (- 1)) / (4 - (- 3))
m = 5/7
We choose an ordered pair:
(xo, yo) = (4, 4)
Substituting:
y-4 = (5/7) (x-4)
y = (5/7) x-20/7 + 4
7y = 5x - 20 + 28
7y = 5x + 8
y = (5/7) x + 8/7
The equation of the perpendicular line is:
-7x - 5y = -48
Two different companies sell canned peaches at the following rates:
Company a: 8onces for $2.50
Company b: 6 ounces for $2.10
Which company offer the lower cost per once?
help me .
please.
have a great day
Answer: C
Step-by-step explanation:
The image represents a rectangular patio that has a length equal to 4 feet more than the width. What is the perimeter of the patio?
Answer:
4w+8 feet
Step-by-step explanation:
The perimeter of a rectangle is the sum of the lengths of its sides. Since opposite sides are identical in length, it can be computed as double the sum of adjacent side lengths. Here, the lengths are in feet.
P = 2(L+W)
P = 2((w+4) +w)
P = 4w +8
The perimeter of the patio is 4w+8 feet.
The subject has more freedom to respond to a/an ________.
A.questionnaire
B.survey
C.interview
D.experiment
Answer:
a
Step-by-step explanation:
bc it is the right answer i got it right
Rational numbers
3x - 30 using 3 as one factor
Answer:
3x - 30
3 (x-10)
Wish you a great day :)
Please answer soon!!!
Answer:
sorry but the standard is higher in than of that of my standard
apologize for the mistake
Evelyn has a summer babysitting job that pays $12 per hour. She wants to know how many hours she has to babysit to afford a new bike. The bike she wants costs $120.
Answer:
10
Step-by-step explanation:
You just gotta do 120/12 which is 10
Convert 34.0 inches into centimeters. Express your answer as decimal rounded to two places
Answer:
86.36 centimeters
Step-by-step explanation:
34 x 2.54 = 86.36
Can a parallelogram have more than 3 lines of symmetry?
Answer:
no
Step-by-step explanation:
Parallelograms have zero lines of symmetry because it is impossible to draw a line through the center of any parallelogram that divides the figure into two equal halves that are mirror images of each other.
Answer:
Technical answer no
BUT
if you are in a college/postgraduate level group theory class yes
Step-by-step explanation:
Imagine a square, and imagine 4 lines across the top, the side, and the two diagonal ones. Because the two diagonal lines of symmetry are technically the same, there are only three possible lines.
if you are in the group theory class, comment and ill give a lengthy answer on that.
Express your answer in scientific notation.
1.8x 10^-2 – 3.9 x 10^-3 =
Answer:
1.41 x 10^-2
Step-by-step explanation:
1.8 x 10^-2 - 3.9 x 10^-33 = 18 x 10^-3 - 3.9 x 10^-3
= (18-3.9) x 10^-3
= 14.1 x 10^-3
= 1.41 x 10^-2
Comment below if you have any questions! If you could mark this answer as the brainliest I would appreciate it!
Christine is making chocolate chip cookies for a bake sale. She needs ¾ cup brown sugar for each batch of cookies she makes. She wants to make 3 batches of cookies. She has 3 cups of brown sugar. Does Christine have enough brown sugar to make 3 batches of cookies? Without actually solving the problem, explain why or why not.
Given the two functions, which statement is true?
f(x) = log15 x, g(x) = ½ log15 (x + 4)
Question 14 options:
g(x) is shrunk vertically by a factor of ½ and shifted to the right 4 units compared to f(x).
g(x) is stretched vertically by a factor of 2 and shifted to the right 4 units compared to f(x).
g(x) is shrunk vertically by a factor of ½ and shifted to the left 4 units compared to f(x).
g(x) is stretched vertically by a factor of 2 and shifted to the left 4 units compared to f(x).
Answer:
g(x) is shrunk vertically by a factor of ½ and shifted to the left 4 units compared to f(x).
Step-by-step explanation:
Find f(h(-1)).
-9
2
11
-11
Answer:
f(h(-1)) = - 11 or D
Step-by-step explanation:
h(-1) = -2(-1)^2 - 3(-1) + 1
h(-1) = -2(1) + 3 + 1
h(-1) = 2
f(2) = (2t + 7)/(t - 3)
f(2) = (2*2 + 7) / (2 - 3)
f(2) = 11/-1
f(2) = - 11
Be very careful how you handle this. The way I have done it will work, but it does not work all the time.
The sure way to handle this is to put(h(n)) every place you can on the right side of f(t)
f(h(n)) = (2(h(n) + 7)) / (h(n) - 3)
A side of the triangle below has been extended to form an exterior angle of 135°. Find the value of x.
Answer:
x = 45°
Step-by-step explanation:
A straight line is 180° which we can use to solve this problem.
180° - 135° = x
x = 45°
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly.
- Heather
a. Find the slope of the line that passes through the points (2,-5) and (-2,3).
b. What are the slope and y-intercept of the equation 2x - 5y = -10?
c. Find the x value so that the line through the points (x,-9) and (0,1) has a slope of -4.
d. Write the equation of a line that passes through the point (-1,5) and has a slope of -7. Your answer should be given in the form y = mx + b.
Answer:
a) Slope: -2
b) y=2/5x+2
C) x=2.5
D) y=-7x-2
Step-by-step explanation:
I don't want to type all my work but that's what i got
Jayden's monthly bank statement showed the following deposits and withdrawals:
-−$73.59, -−$7.81, $86.90, $6.74, -−$115.75
If Jayden's balance in the account was $85.62 at the beginning of the month, what was the account balance at the end of the month?
Answer:
-17.89
Step-by-step explanation:
I think this is the answer
Start with the beginning balance then add or subtract the given amounts:
85.62 -73.59 = 12.03
12.03-7.81 = 4.22
4.22 + 86.90 = 91.12
91.12+ 6.74 = 97.86
97.86-115.75 = -17.89
Answer: -$17.89
simplify ( 3/4)2
A. 3/4
B. 6/8
C. 9/16
D. 2 1/4
Answer:
answer is C
Step-by-step explanation:
(3/4)(3/4)= 9/16
What is the area of this trapezoid?
O 18 in2
O 30 in
O 12 in?
O 22 in?
Help, PLease!! Fractions: Mixed Numbers.
Thank you!
Answer:
1 and 7/8 is the change.
Step-by-step explanation:
First, make the bottom to fractions have the same denominator so we can figure out the length of the other route. 2 and 3/8 will become 2 and 9/24.
Then 3 and 5/6 will become 3 and 20/24. Add them both to get 6 and 5/24. since we cant simplify it stays the same. so now we convert the other number for the new road so it can match the old route. 4 and 1/3 become 4 and 8/24. Now we finish off by subtracting our two numbers to get 1 and 21/24. Since we can simplify the number now becomes 1 and 7/8.
Hope this helped.
There are about 61,000 people at a soccer game. How can 61,000 be written using a power of 10?
One of the closest answers would be 3.010[tex]^{10}[/tex]
