Using the square formula, the value of (1+i)^4 is -4.
The square formula is the algebraic identity which is used to find the square or difference of the sum of two terms. The square of sum of the two terms and can be calculated by multiplying the binomial by itself. The general form of square formula to find the square of the sum of two terms is given by: (a + b)^2 = a^2 + 2ab + b^2 where a and b are variables.
The given expression can be rewritten as binomial with exponent:
((1 + i)^2)^2
Using the square formula to find the square of the sum of two terms to the (1 + i)^2. Hence,
(1 + i)^2 = 1 + 2i + i^2
As 'i' iota is the square root of negative 1, i^2 = -1
1 + 2i -1 = 2i
Therefore,
(2i)^2 = 4i^2 = 4*-1 = -4
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3 letters are typed, with repetition allowed. what is the probability that all 3 will be vowels? write your answer as a percent. round to the nearest hundredth of a percent as needed.
The probability that all 3 will be vowels will be .01 to the nearest hundredth
Probability is the study of the odds of an outcome occurring, which are determined by the ratio of favorable examples to probable cases.
There are 26 English alphabets, each with five vowels and twenty-one consonants. As a result, the likelihood of selecting a consonant's alphabet is 21/26.
First of all, we need to know the number of vowels in the 26 letters.
There are 5 vowels among the 26 letters,
probability (3 vowels of 3)
= (5/26)*(5/26)(5/26) multiplication of probability of each letters
=0.1923*0.1923*0.1923
≈0.0071
≈0.71%
or .01 to the nearest hundredth
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Are the ratios 3:4 and 11:20 equivalent
Answer:
nah
Step-by-step explanation:
find the volume of the given solid. bounded by the cylinders z = 5x2, y = x2 and the planes z = 0, y = 4
1024/3 units³ is the required volume of the given solid using the triple integral theorem.
What is the triple integral formula?As the name implies, triple integrals are 3 sequential integrations, used to determine a volume or to integrate into a 4th dimension, over 3 other independent dimensions.
∭Ef(x,y,z)dV=∬D[∫u2(x,y)u1(x,y)f(x,y,z)dz]dA.
So, we must use the triple integral formula in rectangular coordinates to get the volume of the solid (v):
[tex]V=\iiint d y d x d z[/tex] ...(1)
The solid is restricted by the following intervals:
[tex]y \in\left[x^2, 16\right], x \in[-4,4], z \in[0,4][/tex]
Then, this triple integral is now characterized as:
[tex]V=\int_0^4 \int_{-4}^4 \int_{x^2}^{16} d y d x d z[/tex]
Now we continue to integrate again to get the volume:
[tex]\begin{aligned}& V=\int_0^4 \int_{-4}^4\left(16-x^2\right) d x d z \\& V=\left.\int_0^4\left(16 \cdot x-\frac{x^3}{3}\right)\right|_{-4} ^4 d z \\& V=\frac{256}{3} \int_0^4 d z=\frac{1024}{3}\end{aligned}[/tex]
Therefore, 1024/3 units³ is the required volume of the given solid using the triple integral theorem.
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Complete question:
Use a triple integral to find the volume of the given solid. The solid is bounded by the parabolic cylinder y = x2 and the planes z = 0, z = 4, y = 16.
Evaluate: tan (15pi-2t)
After evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).
What are trigonometric identities?Trigonometric identities are equality conditions in trigonometry that hold for all values of the variables that appear and are defined on both sides of the equivalence.
These are identities that, geometrically speaking, involve certain functions of one or more angles.
Pythagorean identities, reciprocal identities, sum and difference identities, and double-angle and half-angle identities are the main trigonometric identities.
We must apply the sine rule and the cosine rule to the non-right-angled triangles.
So, we have the function:
tan (15π - 2t)
Now, evaluate as follows:
(15π - 2t)
Rewrite using trigonometric identities:
- sin(2t)/cos(2t)
Rewrite using trigonometric identities:
- tan(2t)
Therefore, after evaluating the given function using trigonometric identities, we have the resultant answer that is - tan(2t).
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Write each expression as a product.
(a+b)^2-(b+c)^2
The (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² using difference of two squares.
What is the difference of two squaresConsidering two numbers a and b, the difference of their squares written as a² - b² is equal to the the product of the sum of the numbers and the difference of the numbers, that is (a + b)(a - b).
We have from the question two squares which are (a + b)² and (b + c)² and we shall express their difference as a product as follows:
(a + b)² - (b + c)² = [(a + b) + (b + c)][(a + b) - (b + c)]
open brackets and simplify;
(a + b)² - (b + c)² = (a + b + b + c)(a + b - b - c)
add and subtract like terms;
(a + b)² - (b + c)² = (a + 2b + c)(a + b - b - c)
(a + b)² - (b + c)² = (a + 2b + c)(a - c)
In conclusion, we have that (a + 2b + c)(a - c) is the product of the expression (a + b)² - (b + c)² that is a difference of two squares.
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6² subtracted 4 divided 2
Answer: For problem a is 16 and problem b is 34 i wasn't sure which problem it was so i did both
Step-by-step explanation:
problem a problem b
(6²-4)/2 or 6²-4/2
| |
[tex]6^2=36\\[/tex] [tex]6^2=36[/tex]
36-4=32 36-4/2
32/2=16 36-2=34
16 34
the function c gives the temperature, in degrees celsius, that corresponds to a temperature of x degrees fahrenheit. if a temperature increased by 19.8 degrees fahrenheit, how much did the temperature increase in degrees celsius?
When the temperature increased by 19.8 degrees fahrenheit , the temperature in degrees Celsius got increased by 11 degree
The equation C that gives the temperature in degree Celsius is
C = [tex]\frac{5}{9}(x - 32)[/tex]
Where x denotes the degree Fahrenheit
According to the question,
Temperature has increased by 19.8 degree Fahrenheit
So, let the new temperature be " x' "
x' = x + 19.8
Therefore, For calculating temperature in degree Celsius
=> C' = 5/9 (x' - 32)
Substituting the value of x'
=> C' = 5/9 (x + 19.8 - 32)
=> C' = 5/9 ( x - 32) + 5×19.8/9
=> C' = C + 99/9
=> C' = C + 11
Hence , The temperature increased by 11 degree Celsius
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suppose a new production method will be implemented if a hypothesis test supports the conclusion that it reduces the mean operating cost per hour. (a) state the appropriate null and alternative hypotheses if the mean cost for the current production method is $280 per hour.
The null and alternative hypotheses are:
H₀ : µ ≥ 280
Hₐ : µ < 280
It would be claiming µ < 280 when the new method does not lower costs. This mistake could result in implementing the method when it would not lower costs.
It would be claiming µ ≥ 260 when the method really would lower costs. This mistake could result in not implementing a method that would lower costs.
We know that the type 1 occurs when we reject the null hypothesis when it is true and the type 11 error occurs when we do not reject the null hypothesis when it is not true. For the given scenario, the type 1 error is to reject the null and conclude that new method not lower costs, when actually it lowers.
Hence we get the required answer.
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simplify.4x3−12x24x2 7x−22x2−6x5x2 11x 2
The answer for this Simplifiction 4x3−12x24x2 7x−22x2−6x5x2 11x 2 using BODMASS rule is -19316
What is BODMASS?=4*3-12*24*27*-22*2-6*5*211*2
=-19316
To simplify a phrase, use various techniques to make it shorter and simpler. The actions needed to simplify things are carried out in a predetermined sequence known as BODMASBracket = B0 = ofDivide by DM is for multiplicationA = AdditionS=SumS=SubtractMaking something simpler makes it easier to understand, grasp, or use it. It could entail simplifying complicated concepts, eliminating superfluous details, or drawing diagrams or models.an explanation that leaves out extraneous information and condenses complexity.Statement simplification is rewriting the same algebraic expression in a compact form and without any like terms. Making something less complex means simplifying it.To learn more about BODMASS refer to:
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Write all classifications that apply to the real number −2.
A. natural number, terminating decimal
B. rational, integer, whole number
C. rational, integer, whole number, natural number, terminating decimal
D. terminating decimal, integer, rational
Answer: D
Step-by-step explanation:
-2 is not a repeating decimal.
It is not a fraction
And it is a rational number
if x and y and w are independent binomial random variables with parameters (n,p), (m,p) and (k,p)respectively, with p representing the probability of success, what is the distribution of x y w?
Any value x not explicitly associated with a positive probability is taken as P(X=x) = 0. The function pX(x)= P(X=x) for any x in the range of X is given as a probability. It is often called the probability mass function of a discrete random variable X.
Binomial Distribution:
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a series of n independent experiments, each asking a yes-no question and each with its own It has a Boolean result: success (for probability p) or failure (for probability q = 1-p). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a series of results is called a Bernoulli process. For one trial, d. H. n = 1, binomial distribution is Bernoulli distribution. The binomial distribution is the basis for the common binomial test of statistical significance.
The binomial distribution is commonly used to model the number of successes in a sample of size n drawn from a population of size N with replacement. If sampling is performed without replacement, the resulting distribution is hypergeometric rather than binomial because the plots are not independent. However, for N much larger than n, the binomial distribution remains a good approximation and is widely used.
In the binomial distribution, the trials to be investigated must have the same probability of success. For example, if you toss a coin, the probability of flipping the coin is 1/2. 0.5 for each trial because there are only two possibilities.
Binomial Random Variable:
This is a special kind of discrete random variable. A binomial random variable counts the number of times a particular event occurs over a fixed number of trials or trials.
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distance formula definition
The distance formula is a mathematical equation that can be used to calculate the distance between two points in a coordinate system. It is typically expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) and (x2,y2)
The distance formula is an equation used to calculate the distance between two points in a coordinate system. To use it, you must know the x- and y-coordinates of each point. The equation is expressed as d = √(x2−x1)2+(y2−y1)2, where (x1,y1) are the x- and y-coordinates of the first point, and (x2,y2) are the x- and y-coordinates of the second point. The result, d, is the distance between the two points. To calculate the distance, you must first subtract the x-coordinate of the first point from the x-coordinate of the second point, then square the result. Next, subtract the y-coordinate of the first point from the y-coordinate of the second point and square the result. Finally, add the two squared numbers and take the square root of the sum. The result is the distance between the two points.
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Find the value of a for which v = [6 -10 4 a] is in the set H = span
The value of a for which v is a linear combination is given as follows:
a = -8.
How to obtain the value of a?v will be a linear combination of the set H if it can be obtained as the solution of a system of equations from the set H.
From the vectors, the system is defined as follows:
-x = -1.2x - y = 4.5x + 4y - 3z = -6.-x + 3y - z = a.From the first equation, the value of x is obtained as follows:
-x = -1
x = 1.
From the second equation, the value of y is obtained as follows:
2x - y = 4
2 - y = 4
y = 2 - 4
y = -2.
From the third equation, the value of z is obtained as follows:
5x + 4y - 3z = -6.
5 - 8 - 3z = -6
3z = 3
z = 1.
Then the value of a needed for the linear combination is of:
a = -x + 3y - z
a = -1 - 6 - 1
a = -8.
Missing InformationThe problem is given by the image shown at the end of the answer.
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if f(x)=x²+9 and g(x)=x-9 find g(f(-2))
The value of composite function g(f(-2) is when f(x) = x^2+9 and g(x) = x-9 is 4
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.
We are given two functions f(x) = x^2+9 and g(x) = x-9
and we are asked to find g(f(-2))
this term means we first substitute f(x) in the place of x in function g
We get
g(f(x))= f(x) - 9
Now substitute the value of f(x) in the above function
g(f(x))= x^2+9 -9
g(f(x))= x^2
g(f(-2))= (-2)^2
g(f(-2))= 4
Hence the value of the function if 4
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5 1/5 - 1 3/4 what’s the answer
Answer: 69/20
Step-by-step explanation:
5 1/5 = 26/5
1 3/4 = 7/4
26/5 - 7/4
= 104/20 - 35/20
= 69/20
The value of the test statistic for the test H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9 is
The value of the test statistic for the test is 1.52
How to determine the value of the test statistic for the test?From the question, we have the following parameters that can be used in our computation:
H0: μ = 3.8, Ha : μ > 3 with n = 52, x⎯⎯ = 4.2 and s = 1.9
The above parameters mean that
Sample mean = 3.8Number of samples = 52x = 4.2Standard deviation = 1.9The value of the test statistic for the test is calculated as
[tex]t = \frac{x - \mu_0}{s/\sqrt n}[/tex]
Substitute the known values in the above equation
[tex]t = \frac{4.2 - 3.8}{1.9/\sqrt {52}}[/tex]
Evaluate the equation
t = 1.52
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Solve pls brainliest
Answer:
A, D, E, and F are all equivalent expressions.
Step-by-step explanation:
A. 1:
1 is already a simplified fraction, so there is nothing to do.D. 4:
4 is already a simplified fraction, so there is nothing to do.E. 1.
28.:
This expression is not a fraction, but rather a mixed number. To convert it to a fraction, we first need to rewrite it as an improper fraction. To do this, we take the whole number (1) and multiply it by the denominator (28), and then add the numerator (0):1.28 = 1 * 28 + 0 = 28Then we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 4:28/4 = 7F. 1
22:
We can simplify this fraction by dividing both the numerator and denominator by their greatest common factor, which is 1:1/22 = 1/22
I hope this helps! Let me know if you have any questions.
Find the common ratio of the geometric sequence
17, -34, -68, ...
The common ratio of the geometric sequence will be negative 2.
Given that:
Geometric sequence: 17, -34, -68, .....
A series of non-zero integers where every term after the first is obtained by increasing the one before it by a constant, non-zero value known as the scale factor.
Let a₁ be the first term and r be the common ratio. Then the nth term of the geometric sequence is given as,
aₙ = a₁ · (r)ⁿ⁻¹
The common ratio of the geometric sequence is calculated as,
r = (-34) / (17)
r = - 2
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5x - 4y= 10
10x - 8y = 20
Answer:
infinite number of solutions
Step-by-step explanation:
5x - 4y = 10 → (1)
10x - 8y = 20 → (2)
multiply (1) by - 2
- 10x + 8y = - 20 → (3)
ad (2) and (3) term by term
0 + 0 = 0
0 = 0 ← true statement
this indicates the system has an infinite number of solutions
What is the sum of all interior angles of a 32-sided regular polygon?
169°
180°
5,400°
5,580°
Answer: 5,400
Step-by-step explanation:
In a triangle, the sum of angles is is 180. In a quadrilateral, the sum of angles is 360. In a pentagon, the sum of angles is 540. We can see that as the every time the number of sides increases by 1, the interior angle sum increases by 180.
Let's subtract the given amount of sides by the amount of sides in a triangle to see how many sides it has increased by.
32 - 3 = 29.
Now we multiply the increase in sides by 180 to get how much the interior angle sum has increased.
29 * 180 = 5220.
Finally add back the sum of angles in a triangle.
5220 + 180 = 5,400.
Answer:
5,400
Step-by-step explanation:
5220 + 180 = 5,400
What is 2/3 of 1 5/16
Answer:
7/8
Step-by-step explanation:
2/3 * 1 5/16 =
2/3 * (1 + 5/16)=
2/3 * (16/16 + 5/16)= -> common denominator numbers are easy to simplify
2/3 * (16+5)/16 =
2/3 * 21/16=
(2*21)/(3*16)=
42/48=
21/24=7/8
Ben reads 6 pages of a book in 8 minutes, 9 pages in 12 minutes, and 30 pages in 40 minutes.
If m represents the number of minutes and p represents the number of pages, which equation represents the number of pages Ben reads per minute?
The equation that represents the number of pages Ben can read per minute is p = (3/4)m.
What is Direct Proportion:
The two quantities are said to be in a directly proportionate relation when the connection between them is such that if we increase one, the other will also increase, and if we reduce one, the other quantity will also drop.
If x and y are in direct proportion then
=> x ∝ y
=> x = ky [ where k is constant ]
Here we have,
Ben reads 6 pages in 8 minutes
9 pages can be read in 12 minutes
30 pages can be read in 40 minutes
And the number of minutes = m
Number of pages = p
If observe the given data,
When the number of pages increases, the number of minutes are also increasing, So here we can conclude that the number of minutes is directly proportional to the number of pages
=> p ∝ m
=> p = km --- (1)
[ where k is constant ]
From the given data,
At p = 6 pages, m = 8 minutes
=> 6 = k(8)
=> k = 6/8 = 3/4
From (1)
=> p = (3/4)m
Therefore,
The equation that represents the number of pages Ben can read per minute is p = (3/4)m
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a pollster wishes to estimate the true proportion of u.s. voters who oppose capital punishment. what is the smallest number of voters that should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%? (hint: use a 'worst case scenario' of p
To be 95% confident that the true proportion is calculated to within 2%, 62 voters must be questioned.
Given,
A pollster wishes to estimate the true proportion of US. voters who oppose capital punishment.
We have to find the smallest number of voters that should be surveyed in order to be 95% confident that the true proportion is estimated to within 2%
Here,
To obtain the sample size,
n = z² pq / ME²
Where,
P is the proportion of voters
M. E is the margin of error.
q is the proportion of non-voters
z is the corresponding z score
The z score for the 95% confidence interval is 1.96.
n = 1.96² pq / 0.05²
n = 1536.64 pq
If 0.2 is the proportion of voters, then 0.2 is the fraction of non-voters.
n = 1536.64 pq = 61.42
≈ 62 voters
Therefore,
62 voters can be surveyed in order to be 95% confident that the true proportion is estimated to within 2%
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I need help ! Solve for x.
The solution for x in the pentagon is 90
How to determine the solution for x?From the question, we have the following parameters that can be used in our computation:
Shape = pentagon
This means that
n = 5
The sum of the internal angles is calculated as
Angles = 180(n - 2)
Substitute the known values in the above equation, so, we have the following representation
Angles = 180(5 - 2)
So, we have
Angles = 540
This means that
x + 90 + 90 + 135 + 135 = 540
So, we have
x + 450 = 540
Evaluate
x = 90
Hence, the value of x is 90
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the base of a triangle is seven more than twice the height. the area of the triangle is 73.5 square feet. find the measures of the base and height of the triangle.
The base and height of the triangle are 21 and 7 respectively.
What is the base and height of a triangle?Area of the triangle = [tex]\frac{1}{2} bh[/tex]
= 73.5
Where, b is the base of a triangle
h is the height of the triangle
Let the base of the triangle = b
Here, b = 2h + 7
Area of the triangle = 1/2 (2h +7)h = 73.5
[tex]= > 2h^{2} +7h = 73.5*2 \\\\= > 2h^{2} +7h = 147\\\\= > 2h^{2} +7h -147 = 0\\\\= > h = 7[/tex]
Height of the triangle = h = 7
Base of the triangle = b = 2h + 7
= 2(7) +7
b = 21
The base and height of the triangle are 21 and 7 respectively.
What is the area of a triangle?The total amount of space allotted to a triangle's three sides in a two-dimensional plane is known as the area of a triangle. Half of the product of a triangle's base and height is the basic formula for calculating its area. Whether it be a scalene triangle, isosceles triangle, or equilateral triangle, this formula works for all triangle kinds. You should keep in mind that a triangle's base and height are parallel to one another. The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another.To learn more about triangles, refer:
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PLEASE HELP EASY EASY EASY
Answer:
12
Step-by-step explanation:
2 is 40 percent of 5
12 is 40 percent of 30
Answer:
15 people would be running out of 30
Step-by-step explanation:
30/2
First to compliment my hw gets 20 points and Brainly
Answer:
bro fr has the nicest notes not just for the points but like actually
Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.
y = (smaller slope)
y = (larger slope)
Answer:
y = -x - 1 ; y = 11x - 25
Step-by-step explanation:
y = x² + x
y-(-3) = m(x-2)
y = x²+x
y + 3 = mx - 2m
y = x² + x
y = mx - 2m - 3
x² + x = mx - 2m - 3
x² + x - mx + 2m + 3 = 0
x² + (1-m)x + 2m + 3 = 0
discriminant = m² + 1 - 2m -4 (2m + 3)
m² + 1 - 2m - 8m - 12
m² - 10m - 11
the line is tangent so the discriminant must be equal to 0
m² - 10m - 11 = 0
(m-11)(m+1) = 0
m = 11
m = -1
y + 3 = -(x-2)
y+ 3 = -x + 2
y = -x + 2 - 3
y = -x - 1
y + 3 = 11(x-2)
y + 3 = 11x - 22
y = 11x -22 - 3
y = 11x - 25
The perimeter of a square is 60 cm. Find the
area of the square.
Step-by-step explanation:
SOLUTIONSince a perimeter is a total distance around the figure.
And a square is a quadrilateral(with four sides) which are equal.To find the length of each side,divide the perimeter by 4.
60 cm÷4 = 15 cmSince,Area of square = side×side = 15cm×15cm = 225cm^2hope it helps you.
Answer:
Area of square = 225 cm²
Step-by-step explanation:
Perimeter of square formula,
→ P = 4 × side
→ P = 4a
Now the side of square will be,
→ P = 4a
→ 4a = 60
→ a = 60/4
→ [ a = 15 cm ]
Then the area of square will be,
→ (a)²
→ (15)²
→ 225 cm²
Hence, area of square is 225 cm².
write 312 as a product of prime factors
Answer: 312=(2)(2)(2)(3)(13)
Step-by-step explanation:
312 | 2
156 | 2
78 | 2
39 | 3
13 | 13
Hence, 312=(2)(2)(2)(3)(13)
