After simplifying i^61 we get the answer is i
Define Complex number
Every complex number may be represented in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element labelled i sometimes known as the imaginary unit, and satisfying the equation i² = 1.
We have the given expression : i ^ 61
Rewrite it,
i ^ 61 as (i^4)^15 * i
we know, i² = -1
so, i ^ 4 = i² * i² = -1 * -1 = 1
so, put i ^ 4 value,
⇒1^15 * i
power 1 to the 15 is 1,
⇒1 * i
⇒ i
Hence, the answer is ' i '
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can someone help me understand the working of how to get the answer??
A) The ingredient she needed = Fruit juice = 21 litres
Lemonade = 14 litres
B) The extra punch she can make = 20litres
C) The ratio of fruit juice and lemonade for second batch = 7:6
What is Ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.
A)
Let 3x be fruit juice and 2x be the lemonade
3x + 2x = 35litres
5x = 35
x = 35/5
x = 7
Then, required ingredient she needed
Fruit juice = 3x7 = 21 litres
Lemonade = 2x7 = 14 litres
B)
According to question
The amount of fruit juice she had = 12litre
Let x be 12litre
as we know that the ratio of fruit juice to the lemonade is 3 : 2
Thus,
Fruit juice = 3(x) = 12 litres
x = 12/3
x = 4
Fruit juice = 3 x 4 = 12litres
putting the value in lemonade
Lemonade = 2(4) = 8 litres
So, The extra punch she can make :
12 + 8 = 20litres
C)
The ratio for new second batch she added 4litres in lemonade
Then it become :
Fruit juice = 21 litres
Lemonade = 14 litres + 4litres = 18
The ratio will be
21:18
7:6
Thus, the ratio of fruit juice to lemonade in second batch will be 7:6
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x-intercepts of -14 and -2; passes through (-16, -8)
The equation of the parabola in intercept form exists
y = -2/7(x + 14)(x + 2).
What is meant by the equation of the parabola in intercept form?The intercept form exists y = a(x - r)(x - s), where r and s exists the x-intercepts on the graph. The intercept form will tell us if there exists two x-intercepts, one x-intercept, or no x-intercepts.
Let x-intercepts of -14 and -2; passes through (-16, -8)
The equation of the parabola in intercept form y = a(x - r)(x - s)
substitute the values in the above equation, and we get
-8 = a(-16 + 14)(-16 + 2)
simplifying the above equation, we get
-8 = a(-2)(-14)
-8 = 28a
a = -2/7
y =-2/7(x + 14)(x + 2)
Therefore, the equation of the parabola in intercept form exists
y = -2/7(x + 14)(x + 2).
The complete question is:
Write an equation of the parabola in intercept form X-intercepts of -14 and -2; passes through (-16, -8)
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what is the arithmetic mean of all of the positive two-digit integers with the property that the integer is equal to the sum of its first digit plus its second digit plus the product of its two digits?
The arithmetic mean is 59.
What is arithmetic mean?
It is the sum of collection of numbers divided by the count of the numbers.
Conider AB is the nuber satisfying the condition. Hence,
[tex]10A+B=A+B+A\times B\\9A=A\times B\\[/tex]
Since AB is a two digit number hence, [tex]A\neq 0\\[/tex]. Hence, divide both sides by [tex]A[/tex].
[tex]9=B[/tex]
Hence, B is 9 and A can take any value from 1 to 9.
Hence, numbers are 19, 29, 39, 49, 59, 69, 79, 89,99.
Now, calculate arithmetic mean as follows:
[tex]AM=\frac{Sum \ of \ numbes}{Count \ of \ numbers}\\=\frac{19+29+39+49+59+69+79+89+99}{9}\\=59[/tex]
Hence, arithmetic mean of numbers is 59.
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multistage cluster sampling with stratification, systematic sampling, simple random sampling and disproportionate stratified sampling are examples of:
Multistage cluster sampling with stratification, systematic sampling, simple random sampling and disproportionate stratified sampling are examples of probability sampling.Probability sampling is the process of selecting a sample from a population when the selection is based on the randomization principle, often known as chance or random selection.
What does stratified multistage cluster sampling mean?Multistage sampling, also known as multistage cluster sampling, involves taking a sample from a population in successively smaller groupings. In national surveys, for instance, this technique is frequently employed to collect data from a sizable, geographically dispersed population.For instance, a researcher might be interested in the various eating customs throughout western Europe. It is essentially impossible to gather information from every home. The researcher will first pick the target nations. He or she selects the states or regions to survey from among these nations.
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9y = -2x is this true or false
486,162,54 the next 3 terms of geometric sequence
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by
1
3
gives the next term. In other words,
a
n
=
a
1
r
n
−
1
.
Geometric Sequence:
r
=
1
3
This is the form of a geometric sequence.
a
n
=
a
1
r
n
−
1
Substitute in the values of
a
1
=
486
and
r
=
1
3
.
a
n
=
486
(
1
3
)
n
−
1
Apply the product rule to
1
3
.
a
n
=
486
1
n
−
1
3
n
−
1
One to any power is one.
a
n
=
486
1
3
n
−
1
Combine
486
and
1
3
n
−
1
.
a
n
=
486
3
n
−
1
Substitute in the value of
n
to find the
n
th term.
a
5
=
486
3
(
5
)
−
1
Simplify the denominator.
Tap for more steps...
a
5
=
486
81
Divide
486
by
81
.
a
5
=
6
8
(b) Then determine whether the above relation is a function.
A) Function
B Not a function
The above relation is not a function
What is a function?
A function from either a set X to just a set Y allocates precisely one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. The Persian mathematicians Al-Biruni and Sharaf al-Din al-Tusi are credited with the first known attempt to the concept of function. Originally, functions were the idealization of how a variable quantity depended on another quantity. A planet's location, for example, is a function of time. Historically, the notion was developed with the infinitesimal calculus at the end of the 17th century, and the functions investigated were differentiable until the 19th century.
The above relation is not a function
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Given :R is the midpoint of QSQR = 6x - 9 RS = 2x - 1 We need to find QS
Given :
R is the midpoint of QS
QR = 6x - 9
RS = 2x - 1
We need to find QS
So, as R is the midpoint
[tex]\begin{gathered} QR=RS \\ 6x-9=2x-1 \end{gathered}[/tex]Solve the equation to find x :
[tex]\begin{gathered} 6x-9=2x-1 \\ 6x-2x=-1+9 \\ 4x=8 \\ \\ x=\frac{8}{4}=2 \end{gathered}[/tex]Substitute with x to find QR and QS
[tex]\begin{gathered} QR=6\cdot2-9=12-9=3 \\ RS=2\cdot2-1=4-1=3 \\ \\ QS=QR+RS=3+3=6 \end{gathered}[/tex]Solve −5d +2≥7 or 2d −2>8
Answer:
for the first one: d ≥ 1
for the second one: d > 5
there are grass in a farm and the same amount of grass is grown each day. it takes 10 days for 17 cows to eat all grass in the farm. it takes 12 days for 15 cows to eat all grass in the farm. how many days does it take for 7 cows to eat all grass in the farm?
7 cows will eat all the grass on the farm in 28 days
17 cows eat all the grass on the farm in 10 days
15 cows eat all the grass in the farm in 12 days
We can see a relationship between the number of cows and the number of days. A reduction of 2 cows leads to an increase in 2 days for the cows to eat the grass.
As a result, when we reduce the cows by 4 the increase in the number of days will be 8.
Hence, to reduce the cows from 15 to 7 we will reduce the number of cows by 8 resulting in an increase in 16 days for the grass on the farm to be eaten up
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Which of the following options results in a graph that shows exponential decay?
Group of answer choices
f(x) = 0.6(2)x
f(x) = 3(0.7)x
f(x) = 0.4(1.6)x
f(x) = 20(3)x
The equation of a function that results in a graph that shows exponential decay is f(x) = 3(0.7)ˣ
How to determine the function that represents an exponential decay?An exponential function is represented as
f(x) = abˣ
Where
Variable a represents the initial valueVariable b represents the rateA function that represents an exponential decay would have a rate less than 1
This is represented as b <1
From the list of options, we have
f(x) = 3(0.7)ˣ
By comparing f(x) = 3(0.7)ˣ and f(x) = abˣ, we have
b = 0.7
0.7 is less than 1
Hence, the exponential decay function is f(x) = 3(0.7)ˣ
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A balcony at an apartment can hold up to 1,816 kilograms. How many 160-pound people can the balcony hold?
The balcony can hold 25 people of 160-pound weight.
According to the question,
We have the following information:
The maximum weight balcony can hold = 1816 kg
Weight of 1 person = 160 pound
Now, we will convert this weight into kilogram so that both the measurements have same units.
1 pound = 0.454 kg
160 pound = 160*0.454 kg
160 pound = 72.64 kg
Now, let's take the number of people balcony can hold to be x.
So, we have:
72.64x = 1816
x = 1816/72.64
x = 25
Hence, the number of people the given balcony can hold is 25.
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find the 2 points if the (x,-1) which are 4 units from the pooint (3,2)
The possible coordinates of the other points are (3 + √7, -1) and (3 - √7, -1)
How to calculate the coordinates of the two points?From the question, we have
Points = (3, 2) and (x, -1)Distance = 4 unitsWhere (x, -1) represents the other points
The distance between the points is the number of units between them
It is calculated using the following distance formula
d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
Where x and y represent the coordinates of the given points
Substitute the known values in d = √[(x₁ - x₂)²+ (y₁ - y₂)²]
So, we have
d = √[(3 - x)²+ (2 + 1)²]
Evaluate the expression
d = √[(3 - x)²+ 9]
Recall that d = 4
So, we have
√[(3 - x)²+ 9] = 4
Square both sides
(3 - x)²+ 9 = 16
This gives
(3 - x)² = 7
So, we have
3 - x = ±√7
Solve for x
x = 3 ± √7
Hence, the coordinates are (3 + √7, -1) and (3 - √7, -1)
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A triangle with sides 10, 24, and 25 is a right triangle True/ False
Answer:
False
Step-by-step explanation:
Check using Pythagorean theorem (proof for right triangles)
[tex]10^2+24^2=25^2[/tex]
[tex]100+576=625[/tex]
[tex]676\neq 625[/tex]
False
raul and a friend bought two tickets to see a soccer game each ticket cost $6.75 the friends pain a total of $23.50 which included a fee parking near the stadium how much did each friend pay for the parking fee what is the parking fee as a percent increase in the cost of a ticket
Answer:
Each friend paid $5 for parking.
Step-by-step explanation:
[tex]23.5[/tex] - [tex](6.75[/tex][tex](2)[/tex][tex])[/tex] = [tex]10[/tex]
[tex]10[/tex] ÷ [tex]2 = 5[/tex]
I'm not sure about the rest of the question.
This is an online ACT prep guide problem that I’m having trouble on.Below, is the answer options to this problem.A. -4B. 1C. 6D. The limit does not exist.
Step 1
Given; A graph
Required; To find f(-4)
Step 2
The graph at x=-4 has a removable discontinuity. Therefore we can then conclude that f(-4) is undefined.
Hence, f(-4) is undefined
A removable discontinuity is a point on the graph that is undefined or does not fit into the rest of the graph.
(Pythagorean Theorem MC)
Determine which set of side measurements could be used to form a right triangle.
O 9, 11, 13
O 6, 12, 17
O√8, 5, √17
O√√2. √7.9
Question 3(Multiple Choice Worth 2 points)
Previous Question
Question 1 (Answered)
>
pls helpppp
Using Pythagoras's theorem, the set of measurement that can be used to form a right triangle is √2, √7 and 9.
How to find the sides of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sides of a right angle triangle can be found using Pythagoras's theorem.
Therefore, Pythagoras's theorem is described as follows;
c² = a² + b²
where
a and b are the legs of the right trianglec is the hypotenuse of the right triangle.Therefore, the sides of the triangle that can be used to form a right triangle will have to obey the Pythagoras's theorem,
(√2)² + (√7)² = 9
2 + 7 = 9
Therefore, the last option can form a right triangle.
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Help on this question
Answer: Yes
Step-by-step explanation: 250-250
An outlier is when some of the data is spread farther away from the rest of the data. It is far off from other data
suppose that the antenna lengths of woodlice are approximately normally distributed with a mean of inches and a standard deviation of inches. what proportion of woodlice have antenna lengths that are more than inches? round your answer to at least four decimal places.
Proportion = 0.2119
P (X is less than or equal to 0.18) = P [(X-μ)/ sigma is less than or equal to (0.18-0.22)/ 0.05] = P(Z is less than or equal to -0.80). Using z-table proportion = 0.2119
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What is the area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)
6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)
What is triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
The given three vertices are D(1, 1), E(3, −1), and F(4, 4)
we need to find the area of triangle
Area of triangle=1/2|x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂)|
x₁=1, x₂=3, x₃=4, y₁=1, y₂=-1, y₃=4
put in the formula
Area of triangle=1/2|1(-1-4)+3(4-1)+4(1-(-1))|
=1/2|-5+9+8)|
=1/2 |12|
=6 square units.
Hence 6 square units is area of a triangle whose vertices are D(1, 1), E(3, −1), and F(4, 4)
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-1 (4/5) in the simplest form
Find the distance between the two points rounding to the nearest tenth (if necessary).
(6,7) and (4,−1)
Answer:
8.2 units (nearest tenth)
Step-by-step explanation:
Distance between two points
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where (x₁, y₁) and (x₂, y₂) are the two points.
Given points:
(x₁, y₁) = (6, 7)(x₂, y₂) = (4, -1)Substitute the given points into the distance formula and solve for d:
[tex]\implies d=\sqrt{(4-6)^2+(-1-7)^2}[/tex]
[tex]\implies d=\sqrt{(-2)^2+(-8)^2}[/tex]
[tex]\implies d=\sqrt{4+64}[/tex]
[tex]\implies d=\sqrt{68}[/tex]
[tex]\implies d=8.2 \; \sf (nearest\;tenth)[/tex]
Therefore, the distance between the two given points is 8.2 units to the nearest tenth.
what are the coordinates of a’?
Answer:
(1,3)
Step-by-step explanation:
You are at (-3,5). Ordered pairs are written (x,y) The x tells you how far right or left you are from the origin (0,0) and the y tells you how high above or below You are from the origin (0,0).
(-3+ 4,5 -2) We are 3 unit to the right of (0,0) to begin with and the directions tell us to go 4 more units right. We will now be 1 units to the right of zero. We started at 5 units above zero, the directions tells us to move two units down. That would be at 3.
So, our new order pair will be (1.3)
Question number three in the photo provided.
Using the Central Limit Theorem, the formulas are given as follows:
Standard deviation: [tex]\sigma_{\overline{p}} = \sqrt{\frac{p(1 - p)}{n}}[/tex].Mean: [tex]\overline{p} = p[/tex].What does the Central Limit Theorem state?The Central Limit Theorem states that a random variable X with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] can have the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
A distribution of proportions, with a proportion p in a sample of size n, also respects the Central Limit Theorem, as the the sampling distribution of the sample proportion will be approximately normal with mean and standard deviation given as follows:
Mean: [tex]\overline{p} = p[/tex].Standard deviation: [tex]\sigma_{\overline{p}} = \sqrt{\frac{p(1 - p)}{n}}[/tex].More can be learned about the Central Limit Theorem at https://brainly.com/question/25800303
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Find the requested angle supplement of 123^%A/246B/33C/57D/237
Given: The angle
[tex]123^0[/tex]To Determine: The supplement of the given angle
Solution
Please note that two angle are supplement if they are add up to 180⁰
So if the supplement is x. Therefore
[tex]\begin{gathered} x+123^0=180^0 \\ x=180^0-123^0 \\ x=57^0 \end{gathered}[/tex]Hence, the supplement of 123⁰ is 57⁰, OPTION C
Help me pleaze its hard !!
It is to be noted that the Diagonals of a parallelogram bisect each other. Here in PQSR, it does bisect PT =ST and QT = TR). Hence, PQSR is a parallelogram.
IGHJ is a paralellogram. This is because the opposite sides of a parallelogram are congruent. Here, H = I and G = J. Hence, IGHJ is a parallelogram.
CABD is a parallelogram because of the alternative interior angles ACB = CBD and ABC = BCD.
VWYX is NOT a parallelogram. The rule states that if opposites sides are congruent then the quadrilateral is a parallelogram. In this case, clearly, line VW ≠ XY and VX ≠ WY.
What is a parallelogram?A parallelogram, rhombus, rectangle, or square is a quadrilateral with opposing sides that are congruent and parallel.
There are six crucial parallelogram qualities to understand:
Contrary sides are equivalent (AB = DC).Angles opposite each other are congruent (D = B).Consecutive angles are additive (A + D = 180°).If one angle is correct, all angles are correct.A parallelogram's diagonals cross one other.A parallelogram is divided into two congruent triangles by its diagonals.Learn more about parallelograms:
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Tara's office recycled a total of 60 kilograms of paper over 3 weeks. How many weeks will it take Tara's office to recycle a total of 80 kilograms of paper? Solve using unit rates.
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HElP ME Please!!!!!!!! I need help
Answer:
b x 8 = 40 and 40 / 8 =b
Step-by-step explanation:
well, 8 charms makes one bracelet, so add up 8 until you run out of charms:
8 8 + 8 = 16 16 + 8 = 24 24 + 8 = 32 32 + 8 = 40We only have 40 charms, so we can make 5 bracelets!
Now, plug this number (5) back into the equations:
b x 8 = 40
(5) x 8 = 40
40 = 40
this checks out!
40 - 8 = b
40 - 8 = (5)
32 = 5
32 does not equal 5, so this equation doesn't work.
40 / 8 = b
40 / 8 = (5)
5 = 5
This equation works :)
b + 8 = 40
(5) + 8 = 40
13 = 40
13 does not equal 40, so this is also a bad equation..
since b x 8 = 40 and 40 / 8 = b both produced the right results, we know those two are our answers!
this is a little hard for me help me out please
The simplified form of the expression as a fraction is -43/390.
Solving expressions and simplifying fractionsFractions are expression written as a ratio of two integers. For instance, a/b are known as fractions.
Given the expression below:
[2-|-2/3-2(-1/5)|]÷(-13)
In order to solve the expression, we will use the PEMDAS rule to have:
[2-|-2/3-2(-1/5)|]÷(-13)
[2-|-2/3+1/10)|]÷(-13)
Find the LCM
[2-|-20+3/30|]÷(-13)
[2-|-17/30|]÷(-13)
[2-(17/30)]÷(-13)
[60-17/30]÷(-13)
43/30÷(-13)
Change the division sign to multiplication
43/30÷(-13)
43/30 * -1/13
-43/390
This gives the simplified form of the expression.
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Please help me with this, i really need help
Answer:
See below, where we have used the definitions of vertical angles and complementary angles, and used the substitution property of equality.
Step-by-step explanation:
You want a proof that angles complementary to congruent angles are congruent. That is, ∠1 ≅ ∠4.
Statement . . . . Reason1. ∠1 and ∠3 are complementary . . . . given
2. ∠2 and ∠4 are complementary . . . . given
3. ∠2 ≅ ∠3 . . . . vertical angles are congruent
4. ∠1 +∠3 = 90° . . . . definition of complementary
5. ∠2 +∠4 = 90° . . . . definition of complementary
6. ∠1 +∠3 = ∠2 +∠4 . . . . substitution property of equality
7. ∠1 +∠2 = ∠2 +∠4 . . . . substitution property of equality
8. ∠1 = ∠4 . . . . subtraction property of equality
9. ∠1 ≅ ∠4 . . . . definition of angle congruence
__
Additional comment
The idea of congruence applies to the shape of the geometry. The idea of equality applies to the measures of the angles. Angles are congruent when they have the same measure.