Answer:
I would rather use:
(b) 10,000 batches of 10 observations each.
Step-by-step explanation:
It is easier to have 10,000 batches of 10 observations each than to have 50 batches of 2,000 observations. Human errors are reduced with fewer observations. For example, Hadoop, a framework used for storing and processing big data, relies on batch processing. Using batch processing that divides the 100,000 stationary waiting times into 10 observations with 10,000 batches each is more efficient than having 2,000 observations with 50 batches each.
the image is located below
Answer:
288 ft³
Step-by-step explanation:
Volume of the pyramid,
base area × height × (1/3)
= (9×8)×12/3
= 72×4
= 288 ft³
Evaluate cosA/2 given cosA=-1/3 and tanA >0
Answer:
[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]
Step-by-step explanation:
Given that:
[tex]cosA=-\dfrac{1}3[/tex]
and
[tex]tanA > 0[/tex]
To find:
[tex]cos\dfrac{A}{2} = ?[/tex]
Solution:
First of all,we have cos value as negative and tan value as positive.
It is possible in the 3rd quadrant only.
[tex]\dfrac{A}{2}[/tex] will lie in the 2nd quadrant so [tex]cos\dfrac{A}{2}[/tex] will be negative again.
Because Cosine is positive in 1st and 4th quadrant.
Formula:
[tex]cos2\theta =2cos^2(\theta) - 1[/tex]
Here [tex]\theta = \frac{A}{2}[/tex]
[tex]cosA =2cos^2(\dfrac{A}{2}) - 1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =cosA+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =-\dfrac{1}3+1\\\Rightarrow 2cos^2(\dfrac{A}{2}) =\dfrac{2}3\\\Rightarrow cos(\dfrac{A}{2}) = \pm \dfrac{1}{\sqrt3}[/tex]
But as we have discussed, [tex]cos\dfrac{A}{2}[/tex] will be negative.
So, answer is:
[tex]\bold{cos\dfrac{A}{2} = -\dfrac{1}{\sqrt3}}[/tex]
Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank.
About_____% of the area is between z = 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
About_____% of the area is between z = 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
Complete Question
Find the indicated area under the curve of the standard normal distribution, then convert it to a percentage and fill in the blank.
About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
About_____% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
Answer:
About 97.219% of the area is between z = - 2.2 and z = 2.2 (or within 2.2 standard deviations of the mean).
Step-by-step explanation:
From the question given we can see that they both are the same so 1 will just solve one
Now the area under this given range can be represented mathematically as
[tex]P ( -2.2 < z < 2.2) = P(z < 2.2 ) - P(z < -2.2 )[/tex]
Now from the z-table
[tex]p(z < 2.2 ) = 0.9861[/tex]
and
[tex]p(z < - 2.2 ) = 0.013903[/tex]
So
[tex]P ( -2.2 < z < 2.2) = 0.9861 - 0.013903[/tex]
[tex]P ( -2.2 < z < 2.2) = 0.97219[/tex]
So converting to percentage
[tex]P ( -2.2 < z < 2.2) = 0.97219 * 100[/tex]
[tex]P ( -2.2 < z < 2.2) = 97.219 \%[/tex]
13
R
S
12
What's the length of QR?
A) 1
B) 17.7
C) 6.7
OD) 5
Answer:
5
Step-by-step explanation:
This is a right triangle, so we can use the Pythagorean theorem
a^2+b^2 = c^2
where a and b are the legs and c is the hypotenuse
QR^2 + 12^2 = 13^2
QR^2 +144 =169
QR^2 = 169-144
QR^2 =25
Take the square root of each side
QR = sqrt(25)
QR =5
A system of equations consists of the two equations shown.
{4x+5y=18
6x−5y=20
Which procedure will produce a single equation in one variable? Select all the procedures that apply.
A. Subtract the first equation from the second equation.
B. Subtract the second equation from the first equation.
C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.
D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.
E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.
F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order.
Answer:
C, D, E and F
Step-by-step explanation:
Given
4x+5y=18
6x−5y=20
Required
Determine which procedure will result in a single equation in one variable
To do this; we'll test each of the options
A. Subtract the first equation from the second equation.
[tex](6x - 5y=20) - (4x+5y=18)[/tex]
[tex]6x - 4x - 5y - 5y = 20 - 18[/tex]
[tex]2x - 10y = 2[/tex] --- This didn't produce the desired result
B. Subtract the second equation from the first equation.
[tex](4x+5y=18) - (6x - 5y=20)[/tex]
[tex]4x - 6x + 5y + 5y =18 - 20[/tex]
[tex]-2x + 10y = -2[/tex] --- This didn't produce the desired result
C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.
First Equation
[tex]18 * (4x+5y=18)[/tex]
[tex]72x + 90y = 324[/tex]
Second Equation
[tex]18 * (6x - 5y=20)[/tex]
[tex]108x - 90y = 360[/tex]
Add Resulting Equations
[tex](72x + 90y = 324) + (108x - 90y = 360)[/tex]
[tex]72x + 108x + 90y - 90y = 324 + 360[/tex]
[tex]72x + 108x = 324 + 360[/tex]
[tex]180x = 684[/tex] --- This procedure is valid
D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.
First Equation
[tex]-6 * (4x+5y=18)[/tex]
[tex]-24x - 30y = -108[/tex]
Second Equation
[tex]4 * (6x - 5y=20)[/tex]
[tex]24x - 20y = 80[/tex]
Add Resulting Equations
[tex](-24x - 30y = -108) + (24x - 20y = 80)[/tex]
[tex]-24x + 24x - 30y -20y = -108+ 80[/tex]
[tex]-50y = -28[/tex]
[tex]50y = 28[/tex] --- This procedure is valid
E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.
First Equation
[tex]3 * (4x+5y=18)[/tex]
[tex]12x + 15y = 54[/tex]
Second Equation
[tex]-2 * (6x - 5y=20)[/tex]
[tex]-12x + 10y = -40[/tex]
Add Resulting Equations
[tex](12x + 15y = 54) + (-12x + 10y = -40)[/tex]
[tex]12x - 12x + 15y - 10y =54 - 40[/tex]
[tex]5y = 14[/tex] --- This procedure is valid
F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order
First Equation
[tex]3 * (4x+5y=18)[/tex]
[tex]12x + 15y = 54[/tex]
Second Equation
[tex]2 * (6x - 5y=20)[/tex]
[tex]12x - 10y = 40[/tex]
Subtract equation 1 from 2 or 2 from 1 will eliminate x;
Hence, the procedure is also valid;
Let f(x)=x^3-6x+3 i. find the domain of the function and f’(x) in the domain.
Domain of a any cubic function [tex]f(x)=ax^3+bx^2+cx+d[/tex] is defined to be always [tex]\mathbb{R}[/tex].
The derivative with respect to x of your cubic function is,
[tex]\dfrac{d}{dx}f(x)=f'(x)[/tex]
to find the derivative of a polynomial function, simply take a derivative of each factor and sum them up,
[tex]\dfrac{d}{dx}x^3=3x^2[/tex] by the rule [tex]\dfrac{d}{dx}x^m=mx^{m-1}[/tex] where [tex]m\in\mathbb{R}[/tex]
[tex]\dfrac{d}{dx}-6x=-6[/tex]
[tex]\dfrac{d}{dx}3=0[/tex]
So the derivative is,
[tex]f'(x)=3x^2-6[/tex]
both derivative and the original function have equal domain.
Hope this helps :)
Step-by-step explanation:
[tex]thank \: you[/tex]
A sports stadium has a capacity of 42,000. On a
particular night, 35,000 spectators attend an event. At
the end of the event, spectators leave the stadium at a rate
of 320 spectators every minute. If m represents the
number of minutes after spectators begin to leave the
stadium, which of the following inequalities describes
the times when there are still spectators in the stadium?
A) 42,000 - 35,000m < 320
B) 35,000 - 320m > 0
C) 35,000 + 320m < 42,000
D) 320m < 87,000
Answer:
B
Step-by-step explanation:
The inequality will be 35000-320m>0
X-3y=-3; ( ,4), (12, ) complete each ordered pair
Answer:
(9,4) and (12,5)
Step-by-step explanation:
x-3y=-3
y=4, x-3*4=-3, x=9. (9,4)x=12, 12-3y=-3, y=5. (12,5)The sum of the product of a number x and 14, and 13
Answer:
ax+182
Step-by-step explanation:
a*x+14*13
ax+182
Estimate the mean exam score for the 50 students in Prof. Burke's class.
Score
f
40 but less than 50
21
50 but less than 60
39
60 but less than 70
40
70 but less than 80
34
80 but less than 90
28
Total
162
Group of answer choices
65.56
63.78
64.89
62.34
The mean of the exam score is 65.56
The given exam data is as follows;
Possible Score range ----------- frequency (f) -------- score (x) -----------(fx)
40 - 50 ------------------------- 21 ------------------- -----45 -------------- 945
50 - 60 --------------------------- 39------------------------55 ---------------2145
60 - 70 ----------------------------- 40---------------------- 65 ---------------- 2600
70 - 80 ------------------------------ 34 --------------------- 75 ----------------- 2550
80 - 90 ------------------------------ 28 --------------------- 85 ---------------- 2380
Note:[tex]score (x) = \frac{sum \ of \ the \ range }{2} , \ example \ \frac{40+49.99}{2} \approx 45[/tex]
The sum of the frequency (f) = 162
The sum of fx, ∑fx = 10620
The mean of the exam score:
[tex]\bar x = \frac{\Sigma fx }{\Sigma f} = \frac{10620}{162} = 65.56[/tex]
Therefore, the mean of the exam score is 65.56
To learn more about grouped mean calculation please visit: https://brainly.in/question/20735794
What value does the 2 in the number 0.826?
Answer:
.02
Step-by-step explanation:
2 is in "Hundredths' place in .826
So, the number is multiplied with 1/100 or .01
=> 2 x 1/100
=> 2/100
=> .02
=> 2 x .01
=> .02
The value of 2 in .826 is .02
The given line segment has a midpoint at (−1, −2). On a coordinate plane, a line goes through (negative 5, negative 3), (negative 1, negative 2), and (3, negative 1). What is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment? y = −4x − 4 y = −4x − 6 y = One-fourthx – 4 y = One-fourthx – 6
Answer:
y = -4x - 6.
Step-by-step explanation:
We are given (-5, -3), (-1, -2), and (3, -1) for points of a line. First, we need to find the slope.
(-2 - -3) / (-1 - -5) = (-2 + 3) / (-1 + 5) = 1 / 4.
A perpendicular bisector would have a slope of -4, which is the negative reciprocal of 1/4.
Now that we have the slope, we can say that the equation is y = -4x + b. To find what is b, we can say that y = -2 and x = -1.
-2 = -4(-1) + b
-2 = 4 + b
b + 4 = -2
b = -6
So, the equation of the perpendicular bisector is y = -4x - 6.
Hope this helps!
Answer:
y = -4x - 6.
Step-by-step explanation:
Just took the test and got it right
hi plz help ASAP tyyy ^^
Answer:
26.75 units²
Step-by-step explanation:
This shape can be split into 3 triangles and a square. Find the area of each shape then add them all up.
[tex]A(Square)=2(2)=4\\\\A(Triangle)=\frac{1}{2}(2)(2)=2\\\\A(Triangle)=\frac{1}{2}(5)(2)=5\\\\A(Triangle)=\frac{1}{2}(9)(3.5)=15.75\\\\A(Shape)=4+2+5+15.75=26.75[/tex]
Therefore, the area of the shape is 26.75 units².
solve for x: 5x+3+8x-4=90
Answer:
[tex]x = 7[/tex]
Step-by-step explanation:
We can solve the equation [tex]5x+3+8x-4=90[/tex] by isolating the variable x on one side. To do this, we must simplify the equation.
[tex]5x+3+8x-4=90[/tex]
Combine like terms:
[tex]13x - 1 = 90[/tex]
Add 1 to both sides:
[tex]13x = 91[/tex]
Divide both sides by 13:
[tex]x = 7[/tex]
Hope this helped!
Answer:
x = 7
Step-by-step exxplanation:
5x + 3 + 8x - 4 = 90
5x + 8x = 90 - 3 + 4
13x = 91
x = 91/13
x = 7
probe:
5*7 + 3 + 8*7 - 4 = 90
35 + 3 + 56 - 4 = 90
(07.03. 07.04 MC)
Part A: The area of a square is (4x2 + 20x + 25) square units. Determine the length of each side of the square by factoring the area expression completely. Show
your work (5 points)
Part B: The area of a rectangle is (4x2 - 9y2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work
(5 points)
Answer:
A) 4x^2+20x+25=(2x)^2+2*(2x)*5+5^2=(2x+5)^2
Area=(side)^2, side=sqrt(area)=sqrt((2x+5)^2)=2x+5
B) 4x^2-9y^2=(2x-3y)(2x+3y), these are the dimensions of the rectangle
A) The length of each side of the square is (2x + 5).
B) The dimensions of the rectangle are (2x - 3y) and (2x + 3y).
Used the concept of a quadratic equation that states,
An algebraic equation with the second degree of the variable is called a Quadratic equation.
Given that,
Part A: The area of a square is [tex](4x^2 + 20x + 25)[/tex] square units.
Part B: The area of a rectangle is [tex](4x^2 - 9y^2)[/tex] square units.
A) Now the length of each side of the square is calculated by factoring the area expression completely,
[tex](4x^2 + 20x + 25)[/tex]
[tex]4x^2 + (10 + 10)x + 25[/tex]
[tex]4x^2 + 10x + 10x + 25[/tex]
[tex]2x (x + 5) + 5(2x + 5)[/tex]
[tex](2x + 5) (2x+5)[/tex]
Hence the length of each side of the square is (2x + 5).
B) the dimensions of the rectangle are calculated by factoring the area expression completely,
[tex](4x^2 - 9y^2)[/tex]
[tex](2x)^2 - (3y)^2[/tex]
[tex](2x - 3y) (2x + 3y)[/tex]
Therefore, the dimensions of the rectangle are (2x - 3y) and (2x + 3y).
To learn more about the rectangle visit:
https://brainly.com/question/2607596
#SPJ4
An integer is eight less than three times another if the product of two integers is 35 then find the integers
You are going to decorate one wall of your bedroom by putting a border along the top. The wall is a square wall with an area of 256 square feet what is the length of the border that you will need for your wall?
Answer:
16 ft
Step-by-step explanation:
Each edge of wall = √256 ft = 16 ft
Start with the number 2380.
Divide by 10,
The 8 will end up in the _____ place.
The 8 will end up in the "ones place".
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to find the 8 will end up in which place
A negative divided by a negative is positive, then;
2380/ 10 = 238
Therefore, The 8 will end up in the _ ones_ place.
Learn more about division here:
brainly.com/question/26411682
#SPJ2
1/3 is part of which set of numbers?
Answer:
[tex] \frac{1}{3} [/tex]Rational number as denominator is not equal to zero and numerator is a integer.
Rational numbers. denoted by [tex] \mathbb Q[/tex]
1/3 is clearly not a natural number or integer.
it is a fraction, =0.333 , it fits the definition of rational number ([tex] \frac pq [/tex]).
If the weight (in grams) of cereal in a box of Lucky Charms is N(470,5), what is the probability that the box will contain less than the advertised weight of 453 g?
Answer:
The probability that the box will contain less than the advertised weight of 453 g is 0.00034.
Step-by-step explanation:
Let X represent the weight (in grams) of cereal in a box of Lucky Charms.
It is provided that X follows a Normal distribution with parameters, μ = 470 and σ = 5.
Compute the probability that the box will contain less than the advertised weight of 453 g as follows:
[tex]P(X<453)=P(\frac{X-\mu}{\sigma}<\frac{453-470}{5})[/tex]
[tex]=P(Z<-3.4)\\=0.00034[/tex]
*Use the z-table.
Thus, the probability that the box will contain less than the advertised weight of 453 g is 0.00034.
If Discriminant > 0 :
What is "m" in ( 2x^2 + 4x + 1 - 3m=0) ?
The given equation is in the form ax^2+bx+c = 0 with
a = 2b = 4c = 1-3mD = discriminant
D = b^2 - 4ac
D = 4^2 - 4(2)(1-3m)
D = 16 - 8(1-3m)
D = 16 - 8 + 24m
D = 24m + 8
D > 0
24m + 8 > 0
24m > -8
m > -8/24
m > -1/3
As long as m is larger than -1/3, then the discriminant is positive. There are infinitely many solutions to pick from.
What is 2/6 times 1/6
Answer:
1/9
Step-by-step explanation:
2/6*1/6=2*1/6*6 or 1/9.
Answer:
1/18
Step-by-step explanation:
1. multiply across
2*1 and 6*6
2/36
2. divide by 2 to simplify
2/2 and 36/2
1/18
pls answer and you will be blessed :)
Answer:
2
Step-by-step explanation:
It is the only one that makes sense
Solve the right triangle.
a = 3.3 cm, b = 1.7 cm, C = 90°
Round values to one decimal place.
Answer:
A = 62.7°B = 27.3°c = 3.7Step-by-step explanation:
tan(A) = a/b = 3.3/1.7
A = arctan(33/17) ≈ 62.7°
B = 90° -A = 27.3°
c = √(a²+b²) = √(3.3² +1.7²) = √13.78
c ≈ 3.7
At the end of March, Jerry bought a plant that was $16.2 inches tall. During April, the plant grew 2] inches,
and during May, the plant grew another 2 inches. How tall was the plant at the beginning of June?
O 18.2 inches
O 19 inches
0 21 inches
21 inches
Answer:
20.2 inches
Step-by-step explanation:
The plant starts at 16.2 inches
The first month it grows 2 inches
16.2+2 =18.2 inches
Then the next month it grows 2 inches
18.2+2 = 20.2 inches
find the circle through (-4,sqrt(5) with center (0,0)
Answer:
Circle Equation : x² + y² = 21
Step-by-step explanation:
So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.
The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,
( √5 )² + ( 4 )² = r²,
5 + 16 = r²,
r = √21
In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -
( x - 0 )² + ( y - 0 )² = (√21 )²
Circle Equation : x² + y² = 21
Help me please ?! ❤️❤️
Answer:
Hey there!
Point K has coordinates of (-2, -5)
Hope this helps :)
Answer:
Point K
Step-by-step explanation:
Since they're asking us to find (-2,-5) first we need to move 2 points to the left and then 5 points down.
When all possible differences between pairs of population means are evaluated not with an F test, but with a series of regular t tests, the probability of at least one:
Answer:
When all possible differences between pairs of population means are evaluated not with an F test, but with a series of regular t tests, the probability of at least one:
A. type I error is larger than the specified level of significance.
B. type II error is larger than the specified level of significance.
C. type I error is smaller than the specified level of significance.
D. type II error is smaller than the specified level of significance.
Answer : Type I error is larger than the specified level of significance.( A )
Step-by-step explanation:
An F test is a test that is used to test whether the variances between pairs of populations are equal while a T test is a test used to check if a pair of population are equal not considering the fact that the variances of the population are different .
When a T test is used to evaluate all possible differences between pairs of population instead of F test there is a probability of atleast one type 1 error larger than the specified level of significance.
Can somebody explain how these would be done? The selected answer is incorrect, and I was told "Nice try...express the product by first multiplying the coefficients...then adding your "like term" angles...for instance, cos (2pi/5) + cos (-pi/2) = cos (2pi/5 + -pi/2)...then use the calculator in RADIAN mode to evaluate." Doing those steps, I got the correct constant but a coefficient that was completely off. For the second one, I was told "Good effort...express the quotient by first dividing the coefficients...then subtract your "like term" angles...for instance, cos (2pi/5) - cos (-pi/2) = cos (pi/6 - pi/3)...Finally, use the calculator (in radian MODE) to evaluate."
Answer:
Solution ( Second Attachment ) : - 2.017 + 0.656i
Solution ( First Attachment ) : 16.140 - 5.244i
Step-by-step explanation:
Second Attachment : The quotient of the two expressions would be the following,
[tex]6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,
( 1 ) cos(x) = sin(π / 2 - x)
( 2 ) sin(x) = cos(π / 2 - x)
If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,
( 1 ) [tex]\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}[/tex]
( 2 ) [tex]\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}[/tex]
These two identities makes sin(π / 10) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and cos(π / 10) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex].
Therefore cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], and sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex]. Substitute,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right][/tex]
Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex]
And now simplify this expression to receive our answer,
[tex]6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right][/tex] ÷ [tex]2\sqrt{2}\left[0-i\right][/tex] = [tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i[/tex],
[tex]-\frac{3\sqrt{5+\sqrt{5}}}{4}[/tex] = [tex]-2.01749\dots[/tex] and [tex]\:\frac{3\sqrt{3-\sqrt{5}}}{4}[/tex] = [tex]0.65552\dots[/tex]
= [tex]-2.01749+0.65552i[/tex]
As you can see our solution is option c. - 2.01749 was rounded to - 2.017, and 0.65552 was rounded to 0.656.
________________________________________
First Attachment : We know from the previous problem that cos(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}[/tex], sin(2π / 5) = [tex]\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}[/tex], cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting we receive a simplified expression,
[tex]6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}[/tex]
We know that [tex]6\sqrt{5+\sqrt{5}} = 16.13996\dots[/tex] and [tex]-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots[/tex] . Therefore,
Solution : [tex]16.13996 - 5.24419i[/tex]
Which rounds to about option b.
PLEASE HELP ASAP, I WILL GIVE BRAINLIEST!
9. What is another name for BD?
10. What is another name for AC?
11. What is another name for ray AÉ?
12. Name all rays with endpoint E.
13. Name two pairs of opposite rays.
14. Name one pair of rays that are not opposite rays.
Answer:
#9. Segment DB
#10 Segment CA
#11. Ray EA
#12. Ray EB, Ray EC, Ray ED, Ray EA
#13 Ray EA & Ray EC
#14. Ray EB and Ray EC
Step-by-step explanation:
For future reference, if you are asked to give another name for a segment, just flip the letters around (same for rays.).
Opposite Rays are rays that share 1 common endpoint, but extend in opposite directions ( together they make a 180 degree angle). Ray EB & EC share an endpoint, but they do not extend in opposite directions.
Hope this helps!