Answer:
Given that [tex]\int\limits^a_b {\frac{1}{2\pi } e^{-1/2} x} \, dx[/tex] is not the easiest equation to solve, and that
the values at the convenient ± 1 sigma,± 2 sigma,± 3 sigma are irrational
using the "rule-of-thumb" "empirical rule" is typically "close enough"
given that the whole probability analysis by definition has some uncertainty in it
Step-by-step explanation:
The percentages of a normal distribution data lies within three standard deviations of its mean for empirical rule while it's definite for actual percentages.
What is the empirical rule?The empirical rule is also referred to as the 68-95-99.7 rule and it can be defined as a rule in statistics which states that:
The middle 68% of a normal distribution would be within one standard deviation of its mean (µ ± σ).The middle 95% of a normal distribution would be within two standard deviations of its mean (µ ± 2σ).The middle 99.7% of a normal distribution would be within three standard deviations of its mean (µ ± 3σ).In Statistics, there is a difference between percentages calculated by using the empirical rule and the actual percentages because a normal distribution data lies within three standard deviations of its mean for the former but it is definite for the latter.
In conclusion, the empirical rule is more important to researchers and statistician because it can be used to determine outcomes and gain insight even when all the data aren't available.
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Which products result in a perfect square trinomial? Select three options.
Answer:
(- x + 9)(- x - 9)
(x y + x)(x y + x)
(2 x - 3)(- 3 + 2 x)
(16 - x squared)(x squared - 16)
(4 y squared + 25)(25 + 4 y squared)
Step-by-step explanation:
Which function is shown in the graph below?
Please help I need help
Answer:
2 1/3
Step-by-step explanation:
Worth 10 pts
Plssssssssssssssssss help
Will give brainliest
Answer: [tex]2\sqrt{2}+\sqrt{3}\\\\[/tex]
a = 2 and b = 1
=======================================================
Explanation:
Set the expression equal to the given form we want. Then square both sides so we get rid of the outer-most square root
[tex]\sqrt{11+4\sqrt{6}} = a\sqrt{2}+b\sqrt{3}\\\\\left(\sqrt{11+4\sqrt{6}}\right)^2 = \left(a\sqrt{2}+b\sqrt{3}\right)^2\\\\11+4\sqrt{6} = \left(a\sqrt{2}\right)^2+2*a\sqrt{2}*b\sqrt{3}+\left(b\sqrt{3}\right)^2\\\\11+4\sqrt{6} = 2a^2+2ab\sqrt{2*3}+3b^2\\\\11+4\sqrt{6} = 2a^2+3b^2+2ab\sqrt{6}\\\\[/tex]
In the third line, I used the rule that (x+y)^2 = x^2+2xy+y^2
-------------------
At this point, we equate the non-radical and radical terms to get this system of equations
[tex]\begin{cases}11 = 2a^2+3b^2\\ 4\sqrt{6} = 2ab\sqrt{6}\end{cases}[/tex]
The second equation turns into 4 = 2ab when we divide both sides by sqrt(6)
Then 4 = 2ab turns into ab = 2 after dividing both sides by 2.
We're told that a,b are rational numbers. Let's assume that they are integers (which is a subset of the rational numbers).
If so, then we have these four possibilities
a = 2, b = 1a = -2, b = -1a = 1, b = 2a = -1, b = -2If a,b are negative, then you'll find that [tex]a\sqrt{2}+b\sqrt{3}[/tex] overall is negative. But this contradicts that [tex]\sqrt{11+4\sqrt{6}}[/tex] is positive. So a,b must be positive.
Let's assume that a = 1 and b = 2. If so, then,
2a^2+3b^2 = 2(1)^2+3(2)^2 = 14
but we want that result to be 11 instead.
Let's try a = 2 and b = 1
2a^2+3b^2 = 2(2)^2+3(1)^2 = 11
which works out perfectly.
Therefore,
[tex]\sqrt{11+4\sqrt{6}} = 2\sqrt{2}+\sqrt{3}\\\\[/tex]
---------------------------------
Checking the answer:
Use a calculator to find that
[tex]\sqrt{11+4\sqrt{6}} \approx 4.5604779\\\\2\sqrt{2}+\sqrt{3} \approx 4.5604779\\\\[/tex]
both have the same decimal approximation, so this is a fairly informal way to confirm the answer.
Another thing you can do is to take advantage of the idea that if x = y, then x-y = 0
So if you want to see if two things are equal, you subtract them. You should get exactly 0 or something very small (pretty much equal to 0).
A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the 2nd row, 23 in the 3rd row. How many seats are there in total
Answer:
8428
Step-by-step explanation:
According to the Question,
Given, A theater has 56 rows of seats. If there are 13 seats in the first row, 18 in the 2nd row, 23 in the 3rd row.We have a number sequence 13, 18, 23, ...
We can say that this is an arithmetic sequence because of the common difference 'd', is equal to 5, and the first term 'a1' is equal to 13.The formula for the sum of an arithmetic sequence with n terms is given is [tex]S_n= \frac{n}{2} [2a_1+(n-1)d]S[/tex] .Substitute the given values into the equation to solve for the sum of the 56 rows of seats.
[tex]S_56= \frac{56}{2}[2(13)+(56-1)(5)]\\S_{56}=28\left[26+275\right]\\S_{56}=28\left[301\right]\\S_{56}=8428[/tex]
Therefore, there are 8428 seats in all.
If the circumference is 56cm find the area of the circle
Answer:
The First answer
Step-by-step explanation:
56 divided by 2 is the radius which is 28 and that squared times pi is 2464
6
2
Add
3
+
7. Simplify the answer and write as a mixed number.
.
Question Help: Video
Submit Question
Answer:
1 11/21
Step-by-step explanation:
Use common denominator of 3 * 7 = 21
2/3 * 7/7 = 14/21
6/7 * 3/3 = 18/21
-------------------------
14/21 + 18/21 = 32/21
Reduce
32/21 = 1 11/21
Answer: 1 11/21
Step-by-step explanation:
Data: 2/3+6/7=x
Step one, Find the common denominator
(2/3)x7(for each number)=14/21
(6/7)x3(for each number)=18/21
Reason: To add fractions, you always have to find the common denominator(so you can make the denominator the same for each fraction). The common denominator of 3 and 7 is 21 and since what you do to the bottom has to be done to the top, you multiply 2 by 7 and 6 by 3 to end up with 14/21 and 18/21.
Step two, add
14/21+18/21=32/21=1 11/21
Reason: Since we have our common denominators, we just have to add and, with fractions, you only add the top(numerator) and not the bottom(denominator) you end up with 32/14 but when made into a mixed fraction(by dividing the bottom into the top and leaving the remainder on the top) you get 1 11/21 which can't be simplified.
So since it can't be simplified, it's your answer
I hope this helps!
What type of solutions will a quadratic equation have when the discrimination b^2 - 4ac in the quadratic formula is negative? (plz give explanations)
a - two nonreal solutions
b - one real solution
c - two real solutions
d - no solutions
Answer:
Step-by-step explanation:
The discriminant comes from the quadratic formula. We use the discriminant to determine, before factoring, what types of solutions we can expect when we do factor. In the quadratic formula, the discriminant is under a square root sign. If the number under a square root sign is negative (meaning the discriminant is negative), we will not have real number solutions because you can't have a negative number under a square root. So a is your choice.
Answer:
a
Step-by-step explanation:
PLEASE HELP MEE 1616,
What is the value of f in the equation 7f-1=6
Answer:
f=1
Step-by-step explanation:
Answer:
Then vaule of f is 1
Step-by-step explanation:
The vaule of f is 1 because 7 x 1 = 7 - 1 =6
What is the measure of ZR?
8
8
P
R.
A. 32°
B. 40°
O
C. Cannot be determined
D. 64°
Answer:
option A
Step-by-step explanation:
since the two sides of the triangle are equal the given triangle is an isosceles triangle.
Base angles of an isosceles triangle are equal.
angle P = angle R
32 degree = angle R
The measure of <QRP = 32 degree.
What is an Isosceles Triangle?An isosceles triangle is one with two sides that are the same size and a third side that is a different size.
According to the isosceles triangle theorem, if two sides of a triangle are congruent, the angles across from those sides are likewise congruent.
We have,
A triangle whose two sides are 8 unit each and an angle 32.
As, we know a triangle whose two sides are equal is said to be isosceles triangle.
So, the given triangle is isosceles.
Now, angle opposite to equal sides are also equal.
so, <QPR = <QRP = 32 degree
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gregory wants to buy a new video game system priced at $179.00. if the sales tax is 6%, what is the total amount he will pay for the video game system
Answer:
$189.74
Step-by-step explanation:
Since the sales tax is 6%,
179x0.06=10.74
Add to the starting price, 179.00+10.74=189.74!
I hope this helped!
Find the midpoint of the line segment with these endpoints: (-4,3), (-1,5)
In which quadrant is the midpoint?
Answer:
(-5/2, 4)
Second quadrant
Step-by-step explanation:
Mathematically, we can calculate the midpoint using the formula;
(x,y) = (x1 + x2)/2, (y1 + y2/2
We have;
(x,y) = (-4-1)/2, (3+5)/2
(x,y) = (-5/2, 4)
to get the quadrant, as we can see, this is negative x and positive y and that makes it the 2nd quadrant
Mrs. Ramirez's income increased 140% last year. To model this percent, use ____________
A.grid #1 only
B.grid #2 only
C.grids #1 and #2 only
D.grids #1 and #3 only
Answer: grid #1 and grid #3
Step-by-step explanation:
grid 3 is 100% out of 100% making one whole and grid 1 has 40 out of 100 squares filled. 100 + 40 = 140/140%
A walking path across a park is represented by the equation y = -3x - 6. A
new path will be built perpendicular to this path. The paths will intersect at
the point (-3, 3). Identify the
equation that represents the new path.
Answer:
y = 1/3 x +4
Step-by-step explanation:
m = 1/3
3 = 1/3(-3) + b
3 = -1 +b
b=4
Find m>X
21.04
22.62
67.38
68.96
Answer:
67.38 degrees
Step-by-step explanation:
Here, we want to find the value of the angle at X
We are going to use the appropriate trigonometric ratio here
From the question, the vertex X faces the side 12 and that makes the side the opposite
The side 13 faces the right angle and that makes it the hypotenuse
The trigonometric ratio that connects both is the sine
so we have that;
sine X = 12/13
X = arc sin (12/13)
X = 67.38
Math help please show work I will mark Brainlist if correct
Answer:
Step-by-step explanation:
(1).
(a). 1 m ≈ 3.28 ft.
128 m ≈ 419.84 ft.
(b). 1 yd. ≈ 0.0009144 km
3910 yd. ≈ 3.58 km
(2). 1 m ≈ 0.0006214 mi.
10 000 m ≈ 6.2 mi.
Solve the system by substitution.
y = -5x
y= -7x – 14
Answer:
x = -7 y = 35
Step-by-step explanation:
-5x = -7x - 14
2x = -14
x = -7
y = -5(-7)
y = 35
Which of the following regression equations best fits the data shown below?
Answer:
the answer is A
Step-by-step explanation:
sorry if im worng
john bought a new game system for $529 how much is he in debt
Answer:
Depending on how much he had before he bought the game system.
What is the fractional equivalent of the repeating decimal 0.3
Answer: 0.3 repeating as a fraction is equal to 1/3explanation:
Determine the intercepts of the line.
y
=
11
x
+
6
Answer:
intercepts are (-6/11 , 0) and ( 6,0 )
Someone help
Please with the one I have circled everyone keeps saying it’s 15 but it’s incorrect when I put it in please help
Answer:
w
Step-by-step explanation:
Monday = 4
Tuesday = 1/3 w (where w is the miles walked on Wednesday)
Wednesday = w
Total = 24
4 + 1/3 w + w = 24
Combine like terms
4 + 4/3 w = 24
Subtract 4 from each side
4/3 w = 20
Multiply each side by 3/4
w = 20 *3/4
w = 15
In the equation when we start, we need to put the variable, not the solution
At the end we have the solution
I need help ASAP √34x√y=34
What’s the answer !?
Answer:
y:3 4
Step-by-step explanation:
[tex]\sqrt{34} x \sqrt{y} :34\\\sqrt{34y}:34\\34y:1156\\[/tex]
[tex]y:34\\\sqrt{34} \sqrt{34}:34\\ 34:34\\y:34[/tex]
Which points are solutions to the system of inequalities shown below?
Check all that apply.
ys X+4
y>x
Xs6
D A. (7,9)
OB. (3,8)
C. (4,5)
OD. (5,9)
O E. (2,2)
F. (6,8)
Answer
It is (7,9) (5,9) and (6,8)
Step-by-step explanation:
Find the slope of the line containing the points (2,7) and (-5, -4).
Answer:
5
Step-by-step explanation:
Solve for x. x-6 8x + 24
Answer:
x = 18
Step-by-step explanation:
The 2 angles lie on a straight line and sum to 180° , then
x - 6 + 8x + 24 = 180
9x + 18 = 180 ( subtract 18 from both sides )
9x = 162 ( divide both sides by 9 )
x = 18
[tex]\sf \bf {\boxed {\mathbb {TO\:FIND :}}}[/tex]
The value of [tex]x[/tex].
[tex]\sf \bf {\boxed {\mathbb {SOLUTION:}}}[/tex]
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { x\:=\:18}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\red{:}}}}}[/tex]
We know that,
[tex]\sf\pink{Sum\:of\:angles\:on\:a\:straight\:line\:=\:180°}[/tex]
➪ [tex]x[/tex] - 6 + 8[tex]x[/tex] + 24 = 180°
➪ 9[tex]x[/tex] + 18 = 180°
➪ 9[tex]x[/tex] = 180° - 18
➪ 9[tex]x[/tex] = 162
➪ [tex]x[/tex] = [tex]\frac{162}{9}[/tex]
➪ [tex]x[/tex] = 18
Therefore, the value of [tex]x[/tex] is 18.
Now, the two angles are:-
( [tex]x[/tex] - 6 ) = ( 18 - 6 ) = 12°( 8[tex]x[/tex] + 24 ) = ( 8 x 18 + 24 ) = 144 + 24 = 168°[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
✒ 12° + 168° = 180°
✒ 180° = 180°
✒ L. H. S. = R. H. S.
[tex]\sf\blue{Hence\:verified.}[/tex]
[tex]\huge{\textbf{\textsf{{\orange{My}}{\blue{st}}{\pink{iq}}{\purple{ue}}{\red{35}}{\green{ヅ}}}}}[/tex]
PLZ HELP WILL GIVE BRAINLY IF RIGHT!!!
-2(x-4)=4x+2x+8
Answer:
x = 0
Step-by-step explanation:
-2(x-4)=4x+2x+8
Distribute
-2x +8 =4x+2x+8
Combine like terms
-2x+8 =6x+8
Add 2x to each side
-2x+2x+8 =6x+2x+8
8 = 8x+8
Subtract 8 from each side
8-8 = 8x+8-8
0 = 8x
Divide by 8
0=x
Answer:
x = 0
Step-by-step explanation:
-2(x-4) = 4x+2x+8
-2x+8 = 6x+8
8-8 = 6x+2x
0 = 8x
x = 0
Hope this will help and if so, then please mark me as brainliest.
The value of a car has decreases by 5% each year. Sophie bought a car two years ago for £10000 work out the value now .
Answer:
£9000
Step-by-step explanation:
= £10 000× 5 ×2
100
= 1000
= £10 000-1000
= £9000
Find the remaining sides and angles in the triangle. Round your answers to the nearest tenth.
mZA = 55°, mZB = 44°, and b = 68
a. m2C = 81°, a = 96.7, c =80.2
b. m2C = 81°, a = 80.2, c = 96.7
C. m2C = 81°, a = 89.2, c = 57.7
d. m2C = 81°, a = 57.7, c =89.2
Answer:
The answer is "Option b".
Step-by-step explanation:
[tex]m\angle A = 55^{\circ}\\\\m\angle B = 44^{\circ}\\\\m\angle C = 180^{\circ}-(55^{\circ}+44^{\circ})\\\\[/tex]
[tex]= 180^{\circ}-99^{\circ}\\\\=81^{\circ}\\\\[/tex]
[tex]\frac{a}{\sin 55^{\circ}}= \frac{68}{\sin 44^{\circ}}\\\\a = \frac{68 \ \sin 55^{\circ}}{\sin 44^{\circ}}\\\\a= 80.2^{\circ}\\\\\frac{c}{\sin 81^{\circ}}= \frac{68}{\sin 44^{\circ}}\\\\c = \frac{68 \ \sin 81^{\circ}}{\sin 44^{\circ}}\\\\c= 96.7^{\circ}\\\\[/tex]
which of the expressions are equivalent to the one below? check all that apply.
5 x (8+3)
A. 55
B. 5 x 24
C. 43
D. 5 x 8 + 5 x 3
Step-by-step explanation:
Hola supiste algo bro o no