Consider this example: say we want to convert x = 11 0101 1001₂ to base 3.
The binary expansion of x is
x = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰
which in base 10 reduces to
x = 512 + 256 + 64 + 16 + 8 + 1 = 857
Recall the first several powers of 3:
3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729
Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.
• How many times does the 729 go into 857? 1 time, and it leaves a remainder of 128, or
857 = 1×729 + 128 = 1×3⁶ + 128
• How many times does 81 go into 128? Also 1 time, so
128 = 1×81 + 47 = 1×3⁴ + 47
• How many times does 27 go into 47? Also 1 time,
47 = 1×27 + 20 = 1×3³ + 20
• How many times does 9 go into 20? 2 times,
20 = 18 + 2 = 2×9 + 2 = 2×3² + 2
• How many times does 1 go into 2? Also 2 times,
2 = 2 + 1 = 2×1 + 0 = 2×3⁰
So we found
857 = 1×3⁶ + 1×3⁴ + 1×3³ + 2×3² + 2×3⁰
which is the ternary expansion of x,
x = 1 011 202₃
In triangle ABC, AC=13, BC=84, and AB=85. Find the measure of angle C
Answer:
90°
Step-by-step explanation:
Angle C = arccos((84²+13²-85²)/(2×84×13))
= arccos(0/2184)
= arccos(0)
= 90°
Answered by GAUTHMATH
Between which two intergers does -3 7/8 lie?
Answer:
Step-by-step explanation:
-4 and -3
Answer:
-4 and 3 because I tookt the test and the other guy was right too
Could someone answer this for me pleasee
Answer:
4 and 6.2
Step-by-step explanation:
ABC=sqrt(2.4^2+3.2^2)=4
ABD=sqrt(2.4^2+3.2^2+4.8^2)=6.2
PLS HELP MY PARENTS R GOING TO HIT ME
Answer:
There are 104 nickels and 33 quarters
Step-by-step explanation:
Start of with the equation N = 3Q + 5. q is the amt of quarters n is the nickels. Then substitute Q with 33 since that is the amount of quarters and solve the equation for the amount of nickels that there are.
a. $30
b. $60
c. $40
d. $50
Answer:
it should be $30 so letter a
f(x)=−4x
2
+5x
\text{Find }f(6)
Find f(6)
Answer:
-114
Step-by-step explanation:
f(x) = -4x^2 +5x
Let x = 6
f(6) = -4(6)^2 +5(6)
= -4(36) +30
- 144+30
= -114
Suppose that 65% of the people who inquire about investments at a certain brokerage firm end up investing in stocks, 38% end up investing in bonds, and 36% end up investing in both stocks and bonds. What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?
Answer:
0.67 = 67% probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both).
Step-by-step explanation:
This question is solved treating these probabilities as Venn events.
I am going to say that:
Event A: Person invests in stocks.
Event B: Person invests in bonds.
65% of the people who inquire about investments at a certain brokerage firm end up investing in stocks
This means that [tex]P(A) = 0.65[/tex]
38% end up investing in bonds
This means that [tex]P(B) = 0.38[/tex]
36% end up investing in both stocks and bonds.
This means that [tex]P(A \cap B) = 0.36[/tex]
What is the probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both)?
This is [tex]P(A \cup B)[/tex], given by the following equation:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
Considering the values we have for this problem:
[tex]P(A \cup B) = 0.65 + 0.38 - 0.36 = 0.67[/tex]
0.67 = 67% probability that a person who inquires about investments at this firm will invest in stocks or bonds (or both).
I need help with this question. Pls give me an answer /steps and explanations.
[tex]\bold{30s^{5}t^{9}u^{10}v^{8}}[/tex]
Answer:
Express your answer using positive exponent.
[tex]\bold{(5st³u^{9}v^{7})(6s⁴t^{6}uv)}[/tex]
adding power of common term and multiply constant term:
[tex]\bold{5*6*s^{1+4}*t^{3+6}*u^{9+1}*v^{7+1}}[/tex]
[tex]\bold{30s^{5}*t^{9}*u^{10}*v^{8}}[/tex]
[tex]\bold{30s^{5}t^{9}u^{10}v^{8}}[/tex]
Answer:
[tex]30s^5t^9u^{10}v^8[/tex]
Step-by-step explanation:
We'll be using the following exponent property to solve this problem:
[tex]a^b\cdot a^c=(a)^{b+ c}[/tex]
This will allow us to combine terms with the same variable.
In [tex](5st^3u^9v^7)(6s^4t^6uv)[/tex], we have four variables, [tex]s[/tex], [tex]t[/tex], [tex]u[/tex], and [tex]v[/tex].
Let's start with the [tex]s[/tex] terms, [tex]5s[/tex] and [tex]6s^4[/tex]. The number in front of each term is called the coefficients, and can be multiplied directly. Remember that if there is no exponent written, it's the same thing as if there was an exponent of 1.
Therefore, combine using the exponent property I mentioned above:
[tex]5\cdot 6\cdot s^1\cdot s^4=30\cdot s^{1+4}=30s^5[/tex]
Next, we'll move on to the [tex]t[/tex] terms, [tex]t^3[/tex] and [tex]t^2[/tex].
Combine using the exponent property:
[tex]t^3\cdot t^6=t^{3+6}=t^9[/tex]
Repeat for the [tex]u[/tex] and [tex]v[/tex] terms:
[tex]u^9\cdot u=u^{9+1}=u^{10}[/tex]
[tex]v^7\cdot v=v^{7+1}=v^8[/tex]
Finally, combine all the terms together:
[tex]\implies \boxed{30s^5t^9u^{10}v^8}[/tex]
Solve the system of equations:
y = 2x - 4
y = x2 - 4
Answer:
y=2x-4
Step-by-step explanation:
y=x2-4
ygjn bcgh ccfjm kbhh
Use similar triangles to determine the equation of the line with a slope of 1/2 that passes through the point (0,2)
Answer:
The answer is (A)
Step-by-step explanation:
What type of angle is angle R?
A. obtuse
B. right
C. straight
D. acute
Answer:
A. Obtuse
Step-by-step explanation:
Angle R is greater than 90°.
Answer:
Obtuse
Step-by-step explanation:
We know this because the angle is larger than 90 degrees which is also known as an obtuse :)
What is the product of 2x and 4x2−3xy+y2?
A.6x3−x2y+xy2
B.8x3−6x2y+2xy2
C.2x3−x2y−xy2
D.6x3−5x2y+2xy2
E.−8x3+6x2y−2xy2
Please help
[tex]\bf \large \rightarrow \: \:2x \: \: ( \: 4 {x}^{2} \: - \: 3xy \: + \: {y}^{2} \: )[/tex]
[tex]\bf \large \rightarrow \: \: 8 {x}^{3} \: - \: 6 {x}^{2}y \: + \: 2x {y}^{2} [/tex]
Option ( B) is the correct answer
find the value or x.
-
a. 5
b. 11
c. 25
d. 31
write the equation of the line that passes through the point (-2,4) and (5,8). Put your answer in fully reduced point slope form, unless it is a vertical or horizontal line.
Answer:
y-4=4(x+2)/7
Step-by-step explanation:
slope(m) = (8-4)/(5-(-2)) =4/7
b = 4-(4/7)×(-2) = 36/7
y = mx+b
y = 4x/7+36/7
in point-slope form,
y-4=4(x+2)/7
A bag contains eight tiles labeled A, B, C, D, E, F, G, and H. One tile will be randomly picked.
What is the probability of picking a vowel?
Write your answer as a fraction.
Answer:
1/4
Step-by-step explanation:
Count all of the vowels (this will be your numerator):
A and E
2
Count all of the letters (this will be your denominator):
A, B, C, D, E, F, G, and H
8
Write this as a fraction:
2/8
Simplify:
2/8 = 1/4
HEEEEEEEEEEEEEEEEEEEELP
Answer:
5:30 PM
Step-by-step explanation:
35 mp ½ hour = 70 mph
245 miles ÷ 70 mph = 3½ hours
2PM + 3½ hours = 5:30 PM
Since opening night, attendance at Play A has increased steadily, while attendance at Play B first rose and then fell. Equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. On what day(s) was the attendance the same at both plays? What was the attendance?
Play A: y=25x+136
Play B: y=-x^2+44x+76
Answer: Day 4 and 15
Step-by-step explanation:
Set up system of equations:
[tex]25x+136=-x^2+44x+76[/tex]
Simplify:
[tex]x^2-19x+60=0[/tex]
Factor: Both factors must be positive as the days can only be natural numbers.
[tex](x-15)(x-4)=0[/tex]
x=4,15
Step by step solution please
Answer: A, C, D
Step-by-step explanation:
To find which logarith simplifies to 2, we first need to know how they work.
We now know that [tex]log_a(a^x)=x[/tex].
This tells us that only A, C, D would work.
[tex]8^2=64\\ \\6^2=36\\\\10^2=100[/tex]
Note: whenever you have a log that doesn;t specify the base, it is always 10, as shown in D.
HELP QUICK ILL GIVE BRAINLIEST
Answer:
here's the answer to your question
Answer: √18
√(4-1)^2 + (5-2)^2
√9 + 9
√18
Answered by Gauthmath must click thanks and mark brainliest
the Marked price of a book is rupees 160 if it is sold at 15% discount find the discount amount and selling price
answer is 15%
Step-by-step explanation:
cost prices of book =160
selling prices of book =136
now,rate of discount =loss% (as discount only leads to some kind of loss)
so CP>SP
so loss=CP-SP =160-136=24
loss%= (loss/CP)÷100
=(24/160)÷100
=15%
so rate of discount =15%
Janice's age was two-third of her elder sister's age now. If Janice's elder sister was x years old three years ago, determine Janice's age three years later in terms of x.
Answer: Her sister's age 3 years ago = x
so, her age now = x+3
so Janice's present age = 2/3 of (x+3) {as Janice's present age is two-third of her sister's age now}
Therefore, Janice's age determining the value of x is 2/3 of (x+3).
NEEDED ASAP will MARK THE CORRECT ONE
Answer:
→ m∠ABE + m∠EBC =180°
→ m∠ABF + m∠FED + ∠DBC =180°
→ ∠ABF ≅ ∠EBC
→ ∠ABE ≅ FBC
~OAmalOHopeO
Write an inequality that represents the set of all numbers shown on the number line
-8 and -1
Answer:
-8 is less than -1
Step-by-step explanation:
If you look at a number line
-8 -7 -6 -5 -4 -3 -2 -1 0
Which one is closest to 0. -1, therefore it is greater
The set of all numbers shown on the number line 8 < -1.
What is a number line?A number line is a horizontal line that has numbers in equal intervals. The numbers included on the line can be negative or positive taking zero as a reference point at the center called the origin.
The horizontal straight lines in which the integers are placed in equal intervals increase as we go right. The horizontal straight lines in which the integers are placed in equal intervals decreases as we go left.
A number line can be described as an instant line with numbers positioned at identical intervals or segments alongside its period. a variety of lines may be extended infinitely in any route and is commonly represented horizontally.
Learn more about the number line here:-https://brainly.com/question/24644930
#SPJ2
I NEEDDD HELPPPP ASAPPPP ITS URGENTTT!!!!
Answer:
(x-6)^2+(y-14)^2=4
Step-by-step explanation:
Cos (x-[tex]\frac{5}{6}[/tex])=[tex]\frac{\sqrt{2} }{2}[/tex]
Answer:
Solution given;
Cos (x-[tex]\frac{5}{6}[/tex])=[tex]\frac{\sqrt{2} }{2}[/tex]
Cos (x-[tex]\frac{5}{6}[/tex])=Cos45°
equating corresponding value
(x-[tex]\frac{5}{6}[/tex])=45°
x=45°+5/6
x=45.83°
HELP ASAP!!
Image point N'(12, -6) was dilated from the pre-image point N(4, -2). What was the scale factor used?
A. 1/3
B. 3
c. 1/4
D. 4
Answer:
Step-by-step explanation:
I'm pretty sure its b
Help please !!!!!!!!!!
Answer:
D
Step-by-step explanation:
A function means that each input value (in this case, x) has only one output value (y). The vertical line test states that if a vertical line intersects with the relation more than once, it is not a function. Therefore, as a vertical line at x=0 intersects with the graph twice, the graph fails the vertical line test
Explain the relationship between an inda vidual and a society
Answer:
The relation between individual and society is very close. Essentially, “society” is the regularities, customs and ground rules of antihuman behavior. ... Man is biologically and psychologically equipped to live in groups, in society. Society has become an essential condition for human life to arise and to continue.
NEED ASAP PLZZZ HELP
Answer:
the 1 one will be the answer
The perimeter of a rectangle is 34 units. Its width is 6.5 units.
LAT. write an equation to determine the length
Answer:
please mark me brainlist
Step-by-step explanation:
