==================================================
Explanation:
mu = 65 = population meansigma = 4 = population standard deviationLet's convert x = 53 to its corresponding z score
z = (x-mu)/sigma
z = (53-65)/4
z = -12/4
z = -3
This indicates we're 3 standard deviations below the mean.
Recall that the Empirical Rule states that roughly 99.7% of the data items in a normal distribution are within 3 standard deviations of the mean. That leaves 100% - 99.7% = 0.3% outside this range. This small percentage is the combined percentage in both tails. Take half of this to find the amount in the left tail only.
(0.3%)/2 = 0.15%
This then converts to 0.0015 when we move the decimal point 2 spots to the left.
If a cot α = 1 and b cos α = 1, find a2 – b 2
The equivalent expression of the different of two square is -1
Given the following expressions
a cot α = 1
a = 1/cot α = sinα/cosα
b = 1/cos α
We are to find the expression a² - b²
According to difference of two squares;
a² - b² = (a + b) (a - b)
Substitute the given expressions into the formula as shown:
[tex]a^2 - b^2 = (\frac{sin \alpha}{cos \alpha} )^2 - (\frac{1}{cos \alpha} )^2\\a^2 - b^2=\frac{sin^2 \alpha}{cos^2 \alpha} -\frac{1}{cos ^2 \alpha}\\a^2 - b^2=\frac{sin^2 \alpha-1}{cos^2\alpha}\\a^2 - b^2=\frac{-(1-sin^2\alpha)}{cos^2\alpha} \\a^2 - b^2=\frac{-os^2 \alpha}{cos^2 \alpha}\\a^2 - b^2 = -1[/tex]
This shows that the equivalent expression of the difference of two squares is -1
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pls help..........!!!!!!
Answer:
1) 1085 ÷ 7
7 )1085(155
- 7
38
- 35
× 35
- 35
0
1085 ÷ 7 = 155
2) 7104 ÷ 32
32 )7104(222
- 64
× 70
- 64
×64
- 64
××
7104 ÷ 32 = 222
3) 2244 ÷ 51
51)2244(44
- 204
×244
- 244
×××
2244 ÷ 51 = 33
4) 1584 ÷ 12
12)1584(132
- 12
×38
- 36
×24
- 24
××
1584 ÷ 12 = 132
5) 1467 ÷ 9
9)1467(163
- 9
56
- 54
27
- 27
××
1467 ÷ 9 = 163
6) 2830 ÷ 28
28)2830(101
- 28
××3
- 0
30
- 28
×2
2830 ÷ 28 = 101 with the remainder 2
7) 9090 ÷ 45
45)9090(202
- 90
××9
- 0
90
- 90
××
9090 ÷ 45 = 202
8) 7000 ÷ 62
62)7000(112
- 62
×80
- 62
180
- 125
×55
7000 ÷ 62 = 112 with the remainder 55
9) 1150 ÷ 15
15)1150(76
- 105
×100
- 90
10
1150 ÷ 15 = 76 with the remainder 10
Hope that my answer is right and helpful to you
Gabriella answered 72 questions correctly on her multiple choice history final and earned a grade of 36%. How many total questions were on the final exam?
Answer:
There were 200 Questions on the Final.
Step-by-step explanation:
Which statements about the area of the faces of the rectangular prism are true? Select all that apply.
Two of the faces have an area of 30 ft2.
There is only one face with an area of 48 ft2.
Two of the faces have an area of 40 ft2.
The front face has an area of 30 ft2.
The top face has an area of 40 ft2.
Answer: The front face has an area of 30 ft2. , The top face has an area of 40 ft2. ,
Step-by-step explanation: SOrry if im wrong
Answer: A, C, D
Step-by-step explanation:
You buy a new notebook for school the notebook cost to buy or one dollar Martha comes to $3.46And the taxIs 6%How much of the percentWhat is the markupAnd whatIs your finalPrice for The notebook with tax
Answer:
AHHHH I LOVE YOUR PROFILE PICTURE GOKU IS THE BEST <3 :D
Edgar uses his cell phone all the time, even though it's more expensive between
8 a.m. and 6 p.m. The daytime rate costs 10¢ per minute between 8 a.m. and 6
p.m., while it is 3¢ per minute all other times. If Edgar spent 60 minutes on the
phone at night and 60 minutes during the day, how much would he owe?
Answer:21600
Step-by-step explanation:
Multiply 60 by 2, then by 3. Add 120 and 180 to get 21600.
Quis
bentuk akar dari
[tex] \sqrt{18} + \sqrt{32} - 3 \sqrt{8} = [/tex]
Answer:
[tex]\sqrt{18} + \sqrt{32} - 3 \sqrt{8} = \\ = \sqrt{9 \times 2} + \sqrt{16 \times 2} - 3 \sqrt{4 \times 2} \\ =3 \sqrt{2} + 4 \sqrt{2} - 3 \times 2 \sqrt{2} \\ = 3 + 4 - 6 \sqrt{2} \\ = 7 - 6 \sqrt{2} \\ = 1 \sqrt{2} [/tex]
Semoga membantu
Answer:
[tex]\sqrt{18} + \sqrt{32} - 3 \sqrt{8} = 1 \sqrt{2} [/tex]
Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each. Find the total amount bought. If she paid ₱500 bill, find her change.
Step-by-step explanation:
Total amount is:
3*17.80 + 5*38.85 + 3*60.50 + 2*78.85 = 586.85If the numbers are correct ₱500 won't be enough as the total amount exceeds it.
Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each. Find the total amount bought. If she paid ₱500 bill, find her change.
Statement:Mother bought 3 cans of sardines at ₱17.80 each, 5 cans of milk at ₱38.85 each, 3kg sugar at ₱60.50 each, and 2 cans of corn beef at ₱78.85 each.
Solution:The total amount for which she had brought the items
= ₱ (3×17.80 + 5×38.85 + 3×60.50 + 2×78.85)
= ₱ (53.40 + 194.25 + 181.50 + 157.70)
= ₱ 586.85
Answer:The total amount for which she had brought the items is ₱ 586.85.
I cannot solve the second part of the sum because the amount exceeds ₱ 500.
Hope it helps
Please help! It’s for geometry and I don’t understand
The answer is 54.
Angle 6 is equal to angle 7 so we can substitute angle 7 in for any equations that require angle six what we would want to do is (13x + 9)°+(5x + 9)°= 180°, then you would combine like terms which would then give you 18x+18=180 after this you want to isolate your variable by subtracting 18 from both sides which would give you 18x=162 then you would divide 162 by 18 to give you x=9 next to find angle 6 you would substitute x in the equation so it would be (5(9)+9) 5 multiplied by 9 then add 9 which would give you 45 + 9 which equals out to 54.
who ever helps me gets brainiest
Question 8 measurements. Angle H (acute) Angle M (obtuse) Angle K (acute)
Question 9 measurements. Angle P (right) Angle Q (obtuse) Angle R (acute) Angle S (obtuse) Angle T (right)
Any angle that is visibly smaller than 90° in shape is an acute angle.
Any angle that has a square denoted inside the angle means that it is a 90° angle, therefore implying that it is a right angle.
Any angle that is visibly bigger than 90° in shape is an obtuse angle.
Note that in the Q.8, the total summation of the interior angles for a triangle is 180°. In this case, ∠H & ∠K can be safely assumed to be smaller than right angles, which means that ∠M would be either a right angle or obtuse. However, it is not given that ∠M is a right angle, and so the answer is obtuse.
a. Angle H: acute angle
b. Angle M: obtuse angle
c. Angle K: acute angle
It is given that angles P & T are right angles (as denoted by the squares). Therefore, angle Q & S are obtuse, and angle R is acute, based on visible differences:
a. angle P: Right angle.
b. angle Q: Obtuse angle.
c. angle R: Acute angle.
d. angle S: Obtuse angle.
e. angle T: Right angle.
Usually you will not be using visibility to solve the angle measurements, but in this case, it is not stated that shapes are not drawn to scale. Therefore, you can safely assume based on what the angles look like to answer.
what angles of rotational symmetry are there for a regular pentagon
Answer:
a regular pentagon has 72 degrees
Step-by-step explanation:
On Saturday morning, Ahmed decided to take a bike ride from one end of the 15-mile bike trail to the other end of the bike trail and back. His average speed the first half of the ride was 2 mph faster than his speed on the second half. Find an expression for Ahmed's total travel time. If his average speed for the first half of the ride was 12 mph, how long was Ahmed's bike ride?
The expression which relates the total time taken and the time taken for the trip is [15s + 15(s+2)] / s² + 2s and 2.32 hours respectively.
Travel time = distance ÷ speed
Second half of the trip :
Speed = s mph Distance covered = 15 milesTime taken for second half of trip :
Time taken = 15 / s
First half of the trip :
Speed = s + 2 mphTime taken for first half of trip :
Time taken = 15 / (s+2)
Total time taken :
First half + second half
15/(s+2) + 15/s = [15s + 15(s+2)] / s² + 2s
B)
If s = 12
Substitute s = 12 into the expression :
[15(12) + 15(12+2)] / 12² + 2(12)
[180 + 210] / 144 + 24
390 / 168
= 2.32 hours
Therefore, the total time taken is 2.32 hours.
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Clarissa climbs into the back of the truck to tie the lawn mower in place. If she does 528 joules of working raising herself to the truck bed, how much force did she apply?
how do I solve 8 - 4x + 5y when x = -2 and y = 6
Here is a linear equation in two variables: 2x+4y−31=123
Answer:
y=−11x+77/2
Step-by-step explanation:
The procedure for solving simultaneous linear equations now called Gaussian elimination appears in the ancient Chinese mathematical text Chapter Eight: Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations.[4]
Systems of linear equations arose in Europe with the introduction in 1637 by René Descartes of coordinates in geometry. In fact, in this new geometry, now called Cartesian geometry, lines and planes are represented by linear equations, and computing their intersections amounts to solving systems of linear equations.
The first systematic methods for solving linear systems used determinants, first considered by Leibniz in 1693. In 1750, Gabriel Cramer used them for giving explicit solutions of linear systems, now called Cramer's rule. Later, Gauss further described the method of elimination, which was initially listed as an advancement in geodesy.[5]
In 1844 Hermann Grassmann published his "Theory of Extension" which included foundational new topics of what is today called linear algebra. In 1848, James Joseph Sylvester introduced the term matrix, which is Latin for womb.
Linear algebra grew with ideas noted in the complex plane. For instance, two numbers w and z in {\displaystyle \mathbb {C} }\mathbb {C} have a difference w – z, and the line segments {\displaystyle {\overline {wz}}}{\displaystyle {\overline {wz}}} and {\displaystyle {\overline {0(w-z)}}}{\displaystyle {\overline {0(w-z)}}} are of the same length and direction. The segments are equipollent. The four-dimensional system {\displaystyle \mathbb {H} }\mathbb {H} of quaternions was started in 1843. The term vector was introduced as v = x i + y j + z k representing a point in space. The quaternion difference p – q also produces a segment equipollent to {\displaystyle {\overline {pq}}.}{\displaystyle {\overline {pq}}.} Other hypercomplex number systems also used the idea of a linear space with a basis.
Arthur Cayley introduced matrix multiplication and the inverse matrix in 1856, making possible the general linear group. The mechanism of group representation became available for describing complex and hypercomplex numbers. Crucially, Cayley used a single letter to denote a matrix, thus treating a matrix as an aggregate object. He also realized the connection between matrices and determinants, and wrote "There would be many things to say about this theory of matrices which should, it seems to me, precede the theory of determinants".[5]
Benjamin Peirce published his Linear Associative Algebra (1872), and his son Charles Sanders Peirce extended the work later.[6]
The telegraph required an explanatory system, and the 1873 publication of A Treatise on Electricity and Magnetism instituted a field theory of forces and required differential geometry for expression. Linear algebra is flat differential geometry and serves in tangent spaces to manifolds. Electromagnetic symmetries of spacetime are expressed by the Lorentz transformations, and much of the history of linear algebra is the history of Lorentz transformations.
The first modern and more precise definition of a vector space was introduced by Peano in 1888;[5] by 1900, a theory of linear transformations of finite-dimensional vector spaces had emerged. Linear algebra took its modern form in the first half of the twentieth century, when many ideas and methods of previous centuries were generalized as abstract algebra. The development of computers led to increased research in efficient algorithms for Gaussian elimination and matrix decompositions, and linear algebra became an essential tool for modelling and simulations.[5]
Vector spaces
Main article: Vector space
Until the 19th century, linear algebra was introduced through systems of linear equations and matrices. In modern mathematics, the presentation through vector spaces is generally preferred, since it is more synthetic, more general (not limited to the finite-dimensional case), and conceptually simpler, although more abstract.
A vector space over a field F (often the field of the real numbers) is a set V equipped with two binary operations satisfying the following axioms. Elements of V are called vectors, and elements of F are called scalars. The first operation, vector addition, takes any two vectors v and w and outputs a third vector v + w. The second operation, scalar multiplication, takes any scalar a and any vector v and outputs a new vector av. The axioms that addition and scalar multiplication must satisfy are the following. (In the list below, u, v and w are arbitrary elements of V, and a and b are arbitrary scalars in the field F.)[7]
The number of pages that Ana, Hillary, Roger, and Juan can read in a day is shown below:
Ana read 15% of her 46-page book.
Hillary read 11% of her 72-page book.
Roger read 12% of his 68-page book.
Juan read 14% of his 69-page book.
Who can read the greatest number of pages in a day?
Please help me!!!!!!!!!!!! Thanks!
so i am struggling e
Answer:
17
Step-by-step explanation:
[tex]perimeter = 2(length + breadth) \\ breadth = (perimeter \div 2) - length[/tex]
[tex]72 \div 2 = 36 \\ 36 - 19 = 17[/tex]
Answer:
y is 17 mm
Step-by-step explanation:
perimeter formula is p= 2l +2w
19 is width
19+19 = 38
72-38=34
34/2= 17
17 is length
I hope it is right:)
Hello Brainly members !!!
Give me solution of above question
Question refer to Attachment
(Spam answers will be reported .)
Please find attached photograph for your answer.
Hope it helps
ray4918 here to help.
i hope its help you✌✌✌✌✌
If women always married men who were 2 years older
than themselves, what would the correlation between the ages
of husband and wife be?
(a) 2
(b) 1
(c) 0.5
(d) 0
(e) Can't tell without seeing the data
Answer:
If you were to create a scatterplot using sample ages such as : (30,32),(33,35),(47,49), etc. You will begin to see a perfect linear relationship, which would mean the correct correlation is 1.
(hope it helps! <3)
plzzzzzzzzz help and the answer choice i have on there is not the answer just where i accidently hit lol
Answer:
B is the answer
Step-by-step explanation:
Given ∆TOM with vertices T(-1, 8), O(-3, 3), and M(-6, 7). (a) Graph ∆TOM on the axes provided below. (Draw it in your notes) (b) On the same set of axes, graph ∆T'O'M', the image of ∆TOM reflected over the line y = -x. (c) On the same set of axes, graph ∆T"O"M", the image of ∆T'O'M' reflected over the x-axis.
Answer:
i dont know if i did this right buut
Step-by-step explanation:
i need help on this
please give me solving steps
trying to solve for X
Answer:
10
Step-by-step explanation:
Given is an isosceles triangle and so:
3x + 20 = 5x export like terms to the same side of the equation
20 = 5x - 3x
20 = 2x divide both sides by 2
10 = x
If you pay $43 for a set of Pokémon cards online that were listed for $40 what is the tax percent you were charged
Amount of tax paid = 43-40 = 3
Tax rate = 3/40 = 0.75
0.75 x 100 = 7.5%
Tax rate = 7.5%
An item on sale costs 65% of the original price. The original price was $25.
Answer:
$16.25
65% = 0.65
0.65 x $25 = $16.25
Hope this helps! (And I think thats what the question was)
pLS help me with thisss:((((((
Answer:
C and B
Step-by-step explanation:
(6)
[tex]\frac{3x-7y}{8}[/tex] × [tex]\frac{6}{3x-7y}[/tex] ← cancel 3x - 7y on numerator and denominator
= [tex]\frac{1}{8}[/tex] × [tex]\frac{6}{1}[/tex] = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex] → C
(7)
[tex]\frac{6x}{x^2-9}[/tex] ÷ [tex]\frac{8}{4x-12}[/tex]
Factorise the denominators of both fractions
x² - 9 = x² - 3² = (x - 3)(x + 3) ← difference of squares
4x - 12 ← factor out 4 from each term
= 4(x - 3)
Then rewrite as
[tex]\frac{6x}{(x-3)(x+3)}[/tex] ÷ [tex]\frac{8}{4(x-3)}[/tex] ← cancel 8 and 4 by 4
= [tex]\frac{6x}{(x-3)(x+3)}[/tex] ÷ [tex]\frac{2}{x-3}[/tex]
• leave first fraction, change ÷ to × , turn second fraction ' upside down'
= [tex]\frac{6x}{(x-3)(x+3)}[/tex] × [tex]\frac{x-3}{2}[/tex] ← cancel x - 3 on numerator and denominator
= [tex]\frac{6x}{x+3}[/tex] × [tex]\frac{1}{2}[/tex] ← cancel 2 and 6 on numerator and denominator
= [tex]\frac{3x}{x+3}[/tex] → B
If covariance between two variables is near 0, it implies that:
Answer:
If the two random variables are independent, the covariance will be zero. It means they don't have any linear relationship.
Step-by-step explanation:
F(x)= x^3+4x^2-5x-20;x+4
A football field is 360 feet long 160 feet wide. What is the area of the football field?
Answer:The area of the field is 57600 square feet.
Step-by-step explanation:
Answer:
57600 square feet.
Step-by-step explanation:
360 x 160 = 57600.
Youth Group Trip
The youth group is going on a trip to an amusement park in another part of the state. The trip costs each
group member $150, which includes $85 for the hotel and
two one-day combination entrance and meal plan
passes. How much is the park per person?
a Write an equation representing the cost of the trip. Let P be the cost of the park pass. What’s the answer?!?!
Answer:
$32.50 = p
Step-by-step explanation:
$150 = 85 = 85 +85 + 2p
65/2 = 2p/2
need help with this question
Answer:
...
Step-by-step explanation:
Answer:
Step-by-step explanation:
A) ∠1 = ∠2 {Alternate angles are equal}
6x + y - 4 = x - 9y + 1
6x + y = x - 9y + 1 + 4
6x + y = x - 9y + 5
6x - x + y + 9y = 5
5x + 10y = 5
Divide the entire equation by 5
x + 2y = 1 -------------(I)
∠2 + ∠3 = 180 {Linear pair}
x - 9y + 1 + 11x + 2 = 180
x + 11x - 9y = 180 - 2 - 1
12x - 9y = 177
Divide the whole equation by 3
4x - 3y = 59 -------------(II)
B) Multiply equation (I) by 3 and multiply equation (II) by 2. Thus y will be eliminated and we can find the value of x.
(I)* 3 3x + 6y = 3
(II)*2 8x - 6y = 118 {Now add}
11x = 121
x = 121/11
x = 11
Plugin x = 11 in equation (I)
11 + 2y = 1
2y = 1 -11
2y = -10
y = -10/2
y = -5
C) ∠1 = 6x + y - 4
= 6*11 - 5 - 4
= 66 - 5 - 4
= 57
∠2 = x - 9y + 1
= 11 -9*(-5) + 1
= 11 + 45 + 1
= 57
∠3 = 11x + 2
= 11*11 + 2
= 121 + 2
= 123