i is expression is equivalent to i233.
What is mathematical expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.Given i233
We know that i2 = -1 , if we square (i2) we get (-1)2 = 1
So, if i is multiplied to (i2), we get i3 = (-1).i = -i
Again if i is multiplied to i3 , we get i4 = (-i).i = -i2 = -(-1) = 1
Hence, all even powers of i after 2, will give answer as 1
The sequence will continue as a cycle as i, -1, -i, 1
So, i233 can be rewritten as i232 + 1= i232.i
i233 = (i2)116 .i = (-1)116 . i
Since the power 116 is even , the term becomes 1.i = i
Therefore, i233 = i
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What is the expression in rational exponent form? (^4√ 8^3)^1/3?
The simplified form of the expression ( ⁴√( 8³ ) )^1/3 in rational exponents forms is 8^1/4.
How to convert expressions to rational exponents forms?Given the expression in the question;
( ⁴√( 8³ ) )^1/3
To convert to rational exponent form, apply the exponent rule;
ⁿ√aˣ = a^x/n
Hence;
( ⁴√( 8³ ) )^1/3 = 8^3/4
So we have,
( 8^3/4 )^1/3
Now, apply the power rule to multiply the exponents.
(a^m)^n = a^mn
( 8^3/4 )^1/3
8^( 3/4 × 1/3 )
8^( 3×1/4×3 )
Multiply 3 and 1
8^( 3/4×3 )
Multiply 4 and 3
8^( 3/12 )
Cancel out the common factor of 3 and 12; 3
8^( 1/4 )
8^1/4
Therefore, the simplified of the expression is 8^1/4.
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There are 35 tickets in a bag and the ratio of winning tickets to losing tickets is 1 to 4. How many of each kind of ticket are in the
bag?
Number of winning tickets =7 and Number of losing tickets = 28. When there are 35 tickets in a bag and the ratio of winning tickets to losing tickets is 1:4
What is ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the part to the whole is 5: 10, meaning that 5 out of every 10 persons enjoy reading.Given: Total tickets = 35
The ratio of winning tickets to losing tickets = 1:4
Number of winning tickets = [tex]\frac{1}{1+4} *35[/tex]
[tex]\frac{1}{5} *35=7[/tex]
Number of losing tickets = [tex]\frac{4}{1+4} *35[/tex]
[tex]\frac{4}{5} *35[/tex]
4×7=28
Hence, Number of winning tickets =7 and Number of losing tickets = 28.
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-1 1/4 times 3 1/2 do any of y’all now this in its simplest form
Answer:
The solution is -35/8
Step-by-step explanation:
[tex] \sf - 1 \frac{1}{4} \times 3 \frac{1}{2} \\ \\ = \sf - \frac{4 \times 1 + 1}{4} \times \frac{2 \times 3 + 1}{2} \\ \\ = \sf - \frac{4 + 1}{4} \times \frac{6 + 1}{2} \\ \\ = \sf - \frac{5}{4} \times \frac{7}{2} \\ \\ = \sf - \frac{5 \times 7}{4 \times 2} \\ \\ = \sf - \frac{35}{8} \\ \\ = \sf - 4 \frac{3}{8} [/tex]
What is 2 sigma confidence interval?
Step-by-step explanation:
A two sigma confidence interval is created whenever our alternate hypothesis does not equal a value.
For example if
[tex]h_{o} = 0.36[/tex]
and
[tex]h _{a} ≠0.36[/tex]
We used a two sigma confidence interval because we are thinking a portion is either below 0.36 or above 0.36.
When solving these probability for the p value, multiply the inital result by 2 to get the p value
The 2 sigma confidence interval is a principle that states that a result will be considered significant if 95% of the population is two standards deviation from the average value.
What is the 2-sigma confidence interval?The two-sigma confidence level states that 95% of the values obtained in the results from a population should be within2 deviations from the mean. Anything below this acceptable percentage is not considered the 2-sigma confidence level.
If 68% of the score are within 1 standard deviation from the mean, then that will be considered the 1-sigma rule. If 99.7% of the score is 3 standard deviations from the mean then we can refer to that as the 3-sigma confidence interval.
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100 points! Eva is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if she spins a spinner with four equal-sized sections labeled Red, Green, Blue, Orange and rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4?
Answer:
the answer is number 4 okay
Answer:
it will roll on one of the sides after you roll it
Keddy and Miko had 1950 marbles altogether.
Keddy had 1032 fewer marbles than Miko.
How many marbles did Miko have?
Answer:
1491
Step-by-step explanation:
Based on the given conditions, formulate
Rearrange unknown terms to the left side of the equation
Calculate the sum or difference
Divide both sides of the equation by the coefficient of variable
Cross out the common factor:get the result
please help, ill mark brainlyest
Answer:
x=14
Step-by-step explanation:
Lines RP and MQ intersect, creating 2 pairs of vertical angles. Vertical angles are congruent.
<RSQ and <PSM are vertical angles and therefore congruent
163=3x+9x-5
x=14
You deposit $2000 each year into an account earning 5% interest compounded annually. How much will you have in the account in 30 years?
There will be amount of $8,880.43 in the account in 30 years.
What is compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
Let A be the final amount.
Principal = $2000
r = rate = 5%
n = number of compounding in a year = 4
t = number of years the principal will be compounded = 30
The formula for compound interest:
[tex]A=P(1 +\frac{r}{n})^{nt}[/tex]
[tex]A=2000(1 +\frac{0.05}{4})^{4 \times 30}[/tex]
A = $8,880.43
I will have $8,880.43 in the account in 30 years.
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Name the property
if m = -2 then 8m = -16
Substitution property
Multiplication property
Transitive property
Division property
Answer:
Multiplication property
Step-by-step explanation:
Multiply each side by 8:
m=-2
m*8=8m
-2*8=-16
8m=-16
Enter the unknown value that makes this statement true. 20% of blank is 48
Answer:
240
Step-by-step explanation:
20%×5=100
48×5=240
Answer:
20% of 240 is 48.
Step-by-step explanation:
Forming the equation,
→ (x/100) × 20 = 48
Now the value of x will be,
→ (x/100) × 20 = 48
→ (20x/100) = 48
→ x/5 = 48
→ x = 48 × 5
→ [ x = 240 ]
Hence, the answer is 240.
6. Rodrigo is attending a 4-year college. As a freshman, he was approved for a 10-year, federal
unsubsidized student loan in the amount of $5,300 at 4.29%. He knows he has the option of
beginning repayment of the loan in 4.5 years. He also knows that during this non-payment
period, interest will accrue at 4.29%. (Round all monthly payment calculations to 2 decimal
places.)
a. How much interest will Rodrigo accrue during the 4.5-year non-payment period?
b. If Rodrigo decides to make no payments during the 4.5 years, the interest will be
capitalized at the end of that period. What will the new principal be when he begins
making loan payments?
How much interest will he pay over the life of the loan?
c. Suppose Rodrigo only paid the interest during his 4 years in school and the 6-month
grace period. What will he now pay in interest over the term of his loan?
Rodrigo will accrue 1023.17 interest during the 4.5-year non-payment period.
Define interest.The simplest way to compute interest is as a percentage of the principal. For instance, if you agreed to borrow $100 from a buddy with 5% interest, the interest you would pay would only be 5% of $100: $100(0.05) = $5. Simple Interest (S.I.) is a way for figuring out how much interest will accrue on a specific principal sum of money at a certain rate of interest. For instance, if someone borrows Rs. 5000 at a rate of 10 p.a. for two years, they will pay S.I. on the borrowed money for those two years.
Given,
For calculating interest:
Interest = Principal ×rate × time
Principal = 5300
Rate = 0.0429
Time = 4.5
Interest = 5300 × 0.0429 × 4.5
Interest = 1023.17
Rodrigo will accrue 1023.17 interest during the 4.5-year non-payment period.
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What is the value of x in the image below.
Answer:
16xthe equal parts squares
Step-by-step explanation:
if that is correct let me know of the ewuation
PLEASE HELP NEEDED URGENTLY!
. A birdbath and stand are made from
3 cylinders. The top and bottom cylinders
have radius 22 cm and height 13 cm.
The middle cylinder has radius 15 cm and
height 40 cm. The “bath” has radius 15 cm
and depth 2 cm. The birdbath and stand are
to be tiled. Calculate the area to be tiled.
Answer:
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>>Mayank made a bird - bath for his garden
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Mayank made a bird-bath for his garden in the shape of cylinder with a hemispherical depression at one end as shown in figure. The height of the hollow cylinder is 1.45 m and its radius is 30 cm. Find the total surface area of the bird-bath. (Take π=22/7)
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Updated on : 2022-09-05
Solution
verified
Verified by Toppr
Let r be the common radius of the cylinder and hemisphere and h be the height of the hollow cylinder.
Then r=30cm;h=1.45m=145cm
Total surface are of the bird-bath = curved surface area of the cylinder + curved surface area of the hemisphere
=2πrh+2πr
2
=2π(h+r)
=2×
7
22
×30(145+30)cm
2
=3.3m
2
A candy bar has 250 calories and a small
carrot has 15 calories. Write an algebraic
expression to find how many calories are in b
candy bars and c small carrots.
Answer:
250b calories in b, bars 15c calories in c, carrots
Step-by-step explanation:
What is the answer to this??
If you know basic geometry I think this should be simple
which of the following set of numbers could represent the three sides of a right triangle? {60,63,87} {57,76,94} {42,56,69} {36,78,85}
Answer:
{60,63,87}
Step-by-step explanation:
The increase in a person’s body temperature T(t), above 98.6ºF, can be modeled by the function T (t) = StartFraction 4 t Over t squared + 1 EndFraction, where t represents time elapsed. What is the meaning of the horizontal asymptote for this function?
The horizontal asymptote of T(t)=0 means that the temperature will not increase above 98.6F as time elapses.
Given,[tex]T(t)=\frac{4t}{t^2+1}\\[/tex]
where, t represents time elapse it means 't' reaches to infinity
In function [tex]\lim_{n \to \infty} f(n)[/tex], f(n) is called as horizontal asymptote of the function.
then the above equation can be written as
[tex]T(t)=\lim_{t \to \infty}\frac{4t}{t^2+1}\\\\=\lim_{t \to \infty}\frac{4t}{t(t+\frac{1}{t})}\\\\=\lim_{t \to \infty}\frac{4}{(t+\frac{1}{t})}\\\\=\frac{4}{\infty +0}\\\\=0[/tex]
Hence,the horizontal asymptote of T(t) is 0 it means there is no increase in the temperature above 98.6F.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!
Suppose y varies inversely with x, and y=-3 when x=13 What is an equation for the inverse variation?
Answer:
y = - 39/xStep-by-step explanation:
Inverse variation equation:
y = k/x, where k- constant of variationGiven x = 13, y = - 3Find the value of k- 3 = k/13k = - 3*13k = - 39The equation is:
y = - 39/xAnswer:
y = -39/x
Step-by-step explanation:
Formula we use,
→ y = k/x
→ k = xy
Now the value of k will be,
→ k = xy
→ k = 13 × (-3)
→ [ k = -39 ]
Then the inverse equation is,
→ y = k/x
→ -3 = -39/13
→ [ y = -39/x ]
Hence, the answer is y = -39/x.
4.2 x 10^8 is how many times the value of 2.1 x 10^2
A. 2 x 10^4
B. 2 x 10^6
C. 2.1 x 10^6
D. 2.1 x 10^4
4.2 x 10^8 is 2*10^6 times the value of 2.1 x 10^2 when division is performed.
How can the number of times can be calculated?The concept that will be used to solve the question is division operation.
We were given 4.2 x 10^8 which is greater than 2.1 x 10^2
The operation can be expressed as :
4.2 x 10^8 =( n *2.1 x 10^2)
where n = the number of times that 4.2 x 10^8 is greater than 2.1 x 10^2
Then make n the subject of the formular which is
n = 4.2 x 10^8/2.1 x 10^2
n = 2*10^6
Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.
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-7 + x/2 = -5 what does this equal to???????
Answer: This equation, when simplified would be x = 4
Step-by-step explanation:
That's what I believe it is
Can i get help on these
Please notice that #1 there is boxes on them please dont count those or just dont mind them there not related
and number 2 is not answered yet it just shows that.
The expression that is similar to [tex]\frac{2^{3} . 2^{4} }{2^{12} }[/tex] is [tex]\frac{1}{2^{5} }[/tex]
What is indices?Index (indices) in Maths is the power or exponent which is raised to a number or a variable. For example, in number [tex]2^{4}[/tex], 4 is the index of 2. The plural form of index is indices. In algebra, we come across constants and variables. The constant is a value which cannot be changed.
In the expression [tex]\frac{2^{3} . 2^{4} }{2^{12} }[/tex] all the indices have a common base 2
From numerator [tex]2^{3}[/tex] x [tex]2^{4}[/tex] = [tex]2^{3 + 4}[/tex] which [tex]2^{7}[/tex]
so since the base at the numerator is same as that at the denominator we subtract their exponents
so that we have,
[tex]2^{7 - 12}[/tex] = [tex]2^{-5}[/tex]
which can further be written as [tex]\frac{1}{2^{5} }[/tex]
In conclusion the simplified form of the expression is [tex]\frac{1}{2^{5} }[/tex]
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vn: Do What's Next ces start with the terms 2 and 8. he next two terms of the arithmetic sequence 2, 8, 2, 48. he next two terms of the geometric sequence 2, 8, o possible next terms of a sequence 2, 8, ric nor arithmetic. t
One possible pair of next terms: 0, 1
A second possible pair of next terms: 14, 32
What is arithmetic progression?
The difference between two successive words in an arithmetic progression sequence, often known as A.P., is always the same. The common difference is the term for the constant. It is a technique for calculation that has been used for centuries to get precise results for everyday calculations such as measurements, labelling, and other kinds of everyday calculations. The word "arithmos" in Greek, which simply means "numbers," is where the phrase first appeared.What is Geometric progression?
When one term is varied by another by a common ratio, the series is referred to as a geometric progression or sequence. When we multiply the previous term by a constant (which is non-zero), we get the following term in the sequence.The difference of these numbers is 6, so the next two terms of an arithmetic sequence would be 8+6 = 14, and 14+6 = 20.
The ratio of these numbers is 4, so the next two terms of a geometric sequence would be 8×4 = 32, and 32×4 = 128.
Any pair of numbers can be used that is not (14, 20) or (32, 128).
The next two terms could be 0 and 1, or they could be 14 and 32.
2, 8, 0, 1 . . . is a sequence of no particular type
2, 8, 14, 32 . . . is a sequence of no particular type
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What is the frequency of yellow
light with E= 3.4 x 10-19 J?
h=6.626 x 10-34 J. S
x 10²¹ Hz
[?] x 10⁰
Answer:
5.131 × 10¹⁴ Hz
Step-by-step explanation:
Planck relation
[tex]\large\boxed{E = hf}[/tex]
where:
E = Energy of the photon (J).h = Planck's constant (J · s).f = frequency of light produced (Hz).Given values:
E = 3.4 × 10⁻¹⁹ Jh = 6.626 × 10⁻³⁴ J · sSubstitute the given values into the formula and solve for f:
[tex]\implies 3.4 \times 10^{-19}=(6.626 \times 10^{-34})f[/tex]
[tex]\implies f=\dfrac{3.4 \times 10^{-19}}{6.626 \times 10^{-34}}[/tex]
[tex]\implies f=\dfrac{3.4}{6.626} \times \dfrac{10^{-19}}{10^{-34}}[/tex]
[tex]\implies f=0.5131\times 10^{(-19-(-34))}[/tex]
[tex]\implies f=0.5131 \times 10^{15}[/tex]
[tex]\implies f=5.131 \times 10^{14}[/tex]
Sara takes 45 minutes to make 3 bracelets. At this rate, how long will it take Sara to make 21 bracelets?
Group of answer choices
225 minutes
315 minutes
135 minutes
270 minutes
Answer:
315 minutes
It takes 15 minutes for 1 bracelet. 15 minutes multiplied by 21 bracelets is 315. Lmk if you need more help
Answer: 315 minutes.
Step-by-step explanation:
To solve this, we need to find out how long it takes to make one bracelet first.
If it takes 45 minutes to make 3 bracelets, we need to divide 45 by 3, which gives us 15.
This means it takes 15 minutes to make one bracelet.
Now, we need to multiply 15 by 21.
15 x 21 = 315.
This means it will take 315 minutes to make 21 bracelets.
There are two solutions for the quadratic equation, 9x^2 + 4 = 0. Which of the choices below describes the solutions.
A. One real and one complex solution
B. Two real solutions
C. Two complex solutions.
Answer:
C. Two complex solutions.
Step-by-step explanation:
[tex]1. \ 9x^2+4=0;\\x^2=-\frac{4}{9};\\x=_-^+ \frac{2}{3} i;[/tex]
2. two complex solutions, the correct answer is C.
Add. State answer in simplest form. 1/3x + 5/7y
Answer:
[tex] \dfrac{7x + 15y}{21} [/tex]
Step-by-step explanation:
[tex] \dfrac{1}{3}x + \dfrac{5}{7} y = [/tex]
[tex] = \dfrac{7}{21} x + \dfrac{15}{21} y [/tex]
[tex] = \dfrac{7x + 15y}{21} [/tex]
Find the value of X. The diagram is not to scale.
The value of x is given by 13.
The above angle of the triangle is vertically opposite to the angle 110.
So, the above not mentioned angle of triangle is = 110.
We know from Angle sum property of a triangle that the sum of all interior angles of a triangle is 180.
So, from the given figure we can write that,
110 + 57 + x = 180
167 + x = 180
x = 180-167
x = 13
Hence the value is, x=13.
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Peter's Party Zone sells cups in packages of 666 and plates in packages of 888.
Shaniya is hosting a birthday party for her little sister and wants to have the same number of each item.
What is the least number of packages of plates Shaniya needs to buy?
Least number of packages of plates Shaniya needs to buy=24
Based on the given problem above, it is mentioned that in one pack of cups has 6 and one pack of plates has 8. Therefore, the least number of packages of plates that Shaniya needs to buy is 3 packages and for the cups, it would be 4 packages. 4 x 6 is 24 cups, and 3 x 8 would be 24 plates.
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(11 - 2i) - (9 - 8i)
