The vector y is orthogonal to the vector u v.
Is it true that the vector y is orthogonal to the vector u v?Since y is orthogonal to both u and v, it implies that the dot product of y with each of u and v is zero. Let's denote the dot product as y · u and y · v, respectively.
Now, we need to determine if y is orthogonal to the vector u v, which is the sum of u and v. To prove this, we need to show that the dot product of y with u v is also zero, that is, y · (u v) = 0.
To verify this, we can expand the dot product y · (u v) using the distributive property: y · (u v) = y · u + y · v.
Since y is orthogonal to both u and v, we know that y · u = 0 and y · v = 0. Therefore, y · (u v) = 0 + 0 = 0.
The result y · (u v) = 0 confirms that the vector y is orthogonal to the vector u v, which is the sum of u and v.
Therefore, the statement holds true, and the vector y is indeed orthogonal to the vector u v.
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(4x⁴-4x²-x-3) ÷ (2x²-3)
so far i have 2x²+1+?/2x²-3
what is the question mark?
Answer:
[tex]2x^2+1-\dfrac{x}{2x^2-3}[/tex]
Step-by-step explanation:
Use the long division method to divide polynomials:
[tex]\large \begin{array}{r}2x^2\phantom{)))))}+1\phantom{)}\\2x^2-3{\overline{\smash{\big)}\,4x^4-4x^2-x-3\phantom{)}}}\\\underline{-~\phantom{(}(4x^4-6x^2)\phantom{-b))))))}}\\0+2x^2-x-3\phantom{)}\\\underline{-~\phantom{()}(2x^2\phantom{))))}-3)}\\-x\phantom{))))))}\end{array}[/tex]
Therefore:
[tex]\dfrac{4x^4-4x^2-x-3}{2x^2-3}=2x^2+1-\dfrac{x}{2x^2-3}[/tex]
Find the difference. express the answer in scientific notation. (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline)
The difference between (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline) is 1. 43 × 10^11
How to determine the notation
Given the expression
(5. 29 × 10^11) - (3. 86 × 10 ^11)
First, find the common factor
10^11 ( 5. 29 - 3. 86)
Then substract the values within the bracket
10^11 (1. 43)
Multiply with the factor, we have
⇒1. 43 × 10^11
Thus, the difference between (5.29 times 10 superscript 11 baseline) minus (3.86 times 10 superscript 11 baseline) is 1. 43 × 10^11
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Answer:
A
Step-by-step explanation:
Find the difference. Express the answer in scientific notation.
(5.29 times 10 Superscript 11 Baseline) minus (3.86 times 10 Superscript 11 Baseline)
1.43 times 10 Superscript 11
9.15 times 10 Superscript 11
1.43 times 10 Superscript 22
9.15 times 10 Superscript 22
In a survey of 300 college graduates, 46% reported that they entered a profession closely related to their college major. If 9 of those survey subjects are randomly selected without replacement for a follow-up survey, what is the probability that 3 of them entered a profession closely related to their college major
Probability is 17.5% that 3 of them entered a profession closely related to their college
According to the statement
we have given that survey of 300 college graduates, 46% reported that they entered a profession closely and
We know that For each college graduate, there are only two possible outcomes. Either they have entered a profession closely related to their college major, or they have not. The probability of a college graduate having entered a profession closely related to their college major is independent of other college graduates, so we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
This is P(X = 3) when n = 8. and the value of p is 0.46 put the value in the binomial formula then the outcome of answer will 17.5%
So, Probability is 17.5% that 3 of them entered a profession closely related to their college
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Please help with this
Answer:
the answer is 8
Step-by-step explanation:
thats what i got
determine the fall (drop) on 20' of drainage piping with a 1/4" per ft. grade
The Fall (drop) of drainage piping is: A. 5".
Fall (drop) of drainage pipingIn order to determine the fall (drop) of drainage piping we would need to multiply the drainage piping by the inch per feet.
Hence:
Using this formula
Fall (drop) of drainage piping = Drainage piping× inch per feet
Where:
Drainage piping=20
Inch per feet=1/4"
Let plug in the formula
Fall (drop) of drainage piping =20×1/4"
Fall (drop) of drainage piping =5"
Therefore the correct option is A. 5".
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find the exact value of sin (x-y) if sinx=4/9 and siny=1/4
Answer:
sin(x - y) = 0.21
Step-by-step explanation:
we have the sin values which we need to get cos values
sin (A-B) = sin A cos B - sin B cos A
sin² A + cos² A = 1
sin x = 4/9
cos² x = 1 - sin² x = 1 - 16/81 = 65/81
cos² x = 65/81
cos x = √65/9
sin y = 1/4
cos² y = 1 - sin² y = 1 - 1/16 = 15/16
cos² y = 15/16
cos y = √15/4
sin(x − y) = sin x cos y - sin y cos x
sin(x - y) = 4/9 √15/4 - 1/4 √65/9
sin(x - y) = (4√15-√65)/36
sin(x - y) = 0.21
socratic Narad T
Answer: C
Step-by-step explanation:
on edg
Someone help me please
Answer:
2√10
Step-by-step explanation:
We can use the Pythagorean theorem to solve this because it is a right triangle. a^2+b^2 = c^2
7^2-3^2 = x^2
49-9 = x^2
40 = x^2
√4*√10 = 2√10
Calculate the first difference between 7, and where 7,-688. 2
The difference between the numbers given is 6.882.
How to illustrate the information?Based on the information given, it should be noted that difference means subtraction.
The difference between the numbers given will be:
= 7 - (7 - 6.882)
= 7 - 0.118
= 6.882
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Find the area of the region defined by the region defined by the inequality 2|x| + 3|y-1| ≤ 6
If [tex]x[/tex] and [tex]y-1[/tex] have the same sign, then either
[tex]x>0,y>1 \implies 2|x| + 3|y-1| = 2x + 3(y-1)=6 \implies 2x + 3y = 9[/tex]
or
[tex]x<0,y<1 \implies 2|x| + 3|y-1| = -2x - 3(y-1) = 6 \implies 2x + 3y = -3[/tex]
If [tex]x[/tex] and [tex]y-1[/tex] have opposite sign, then
[tex]x>0,y<1 \implies 2|x| + 3|y-1| = 2x - 3(y-1) = 6 \implies 2x -3y = 3[/tex]
or
[tex]x<0,y>1 \implies 2|x| + 3|y-1| = -2x + 3(y-1) = 6 \implies 2x-3y = -9[/tex]
This is to say that the region has boundaries given by these two sets of parallel lines, so we can equivalently describe the region with the set
[tex]R = \left\{(x,y) \mid -3\le2x+3y\le9 \text{ and } -9\le2x-3y\le3\right\}[/tex]
The area of [tex]R[/tex] is given by the double integral
[tex]\displaystyle \iint_R dx\,dy[/tex]
To compute the area, change the variables to
[tex]\begin{cases}u = 2x + 3y \\ v = 2x - 3y\end{cases} \implies \begin{cases}x = \frac14(u+v) \\ y = \frac16(u-v)\end{cases}[/tex]
The Jacobian for this transformation is
[tex]J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix}1/4 & 1/4 \\ 1/6 & -1/6\end{bmatrix}[/tex]
with determinant [tex]\det(J) = -\frac1{12}[/tex]. Then the integral transforms to
[tex]\displaystyle \iint_R dx\,dy = \iint_R |J| \, du \, dv = \frac1{12} \int_{-3}^9 \int_{-9}^3 dv\, du[/tex]
which is 1/12 the area of a square with side length 12. Hence the integral evaluates to
[tex]\displaystyle \iint_R dx\,dy = \frac1{12}\times12^2 = \boxed{12}[/tex].
The ratio of two numbers is 2/3, and their sum is 535. One of the numbers is:
(Select one)
A. 242
B. 321
C. 667
D. 408
One of the numbers would be 321. Hence option B is true.
Used the concept of the Number system that states,
A writing system used to express numbers is known as a number system. It is the mathematical notation used to consistently express the numbers in a particular set using digits or other symbols.
Given that,
The ratio of the two numbers is 2/3, and their sum is 535.
Let us assume that,
The two numbers are x and y.
Hence we have;
[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex] .. (i)
And, [tex]x + y = 535[/tex] .. (ii)
From equation (i);
[tex]\dfrac{x}{y} = \dfrac{2}{3}[/tex]
[tex]x = \dfrac{2y}{3}[/tex]
Substitute the above value of x in (ii);
[tex]x + y = 535[/tex]
[tex]\dfrac{2y}{3} + y = 535[/tex]
[tex]2y + 3y = 535 \times 3[/tex]
[tex]5y = 1605[/tex]
[tex]y = 321[/tex]
From equation (i);
[tex]x = \dfrac{2y}{3}[/tex]
[tex]x = \dfrac{2\times 321}{3}[/tex]
[tex]x = 214[/tex]
Therefore, the number is 321. So option B is true.
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An account pays 8% per year simple interest. in year 1, the amount in the account is $850. how much is in the account in year 6?
Answer:
Step-by-step explanation:
$1,248.92
the graph of the derivative of a function f crosses the x-axis 3 times. what does this tell you about the graph of f
Answer:
the graph of f has 3 turning points
Step-by-step explanation:
The graph of a function has a turning point (local extreme) where the derivative is zero and changes sign.
DerivativeThe derivative of a function tells you the slope of that function's graph. When the derivative is positive, the function is increasing. When the derivative is negative, the function is decreasing.
Turning PointWhere the derivative changes sign from positive to negative, the graph of the function changes direction from increasing to decreasing. At the point where the derivative is zero (between positive and negative), the graph is neither increasing nor decreasing. A tangent to the function at that point is a horizontal line, and the function itself is at a local maximum, a turning point.
The reverse is also true. When the derivative changes sign from negative to positive, the function changes from decreasing to increasing. The turning point where that occurs is a local minimum.
3 CrossingsIf the derivative crosses the x-axis (changes sign) 3 times, then there are three local extremes in the graph of f. The graph of f has 3 turning points.
__
Additional comment
In the attached graph, we have constructed a derivative function (red) that crosses the x-axis 3 times. It is the derivative of f(x), which is shown in blue. The purpose is to show the local extremes of f(x) match the zero crossings of the derivative.
ا سکول کے پرنسپل کے نام سکول میں ہم نصابی سرگرمیوں کا اہتمام کرنے کی درخواست ھیے ۔
Answer:
Step-by-step explanation:
F(x)= x(x+3)(x+1)(x-4) has zeros at x=-3
Answer: C) Sometimes positive; sometimes negative
============================================================
Explanation:
Pick a value between x = -1 and x = 0. Let's say we go for x = -0.5
Plug this into f(x)
f(x) = x(x+3)(x+1)(x-4)
f(-0.5) = -0.5(-0.5+3)(-0.5+1)(-0.5-4)
f(-0.5) = -0.5(2.5)(0.5)(-4.5)
f(-0.5) = 2.8125
We get a positive value.
This shows that f(x) is positive on the region of -1 < x < 0
----------------
Now pick a value between x = 0 and x = 4. I'll use x = 1
f(x) = x(x+3)(x+1)(x-4)
f(1) = 1(1+3)(1+1)(1-4)
f(1) = 1(4)(2)(-3)
f(1) = -24
Therefore, f(x) is negative on the interval 0 < x < 4
----------------
In short, f(x) is both positive and negative on the interval -1 < x < 4
It's positive when -1 < x < 0
And it's negative when 0 < x < 4
Answer:
sometimes positive sometimes negative
Step-by-step explanation:
I did it on Khan Academy
Instructions: Find the missing segment in the image below.
Answer: 7
Step-by-step explanation:
By the triangle proportionality theorem,
[tex]\frac{?}{21}=\frac{3}{9}\\\\?=7[/tex]
an equation for loudness, in decibles, is L=10log10 R where R is the relative intensity of the sound. Sounds that reach levels of 120 decibles or more are painful to humans what is the relative intensity of 120 decibles
Considering the logarithmic loudness equation, the relative intensity of 120 decibels is of [tex]R = 10^{12}[/tex].
What is the logarithmic loudness equation?The equation is:
[tex]L = 10\log{R}[/tex]
In which:
L is the loudness, in decibels.R is the relative intensity.For this problem, we have that L = 120, hence the relative intensity is found as follows:
[tex]120 = 10\log{R}[/tex]
[tex]\log{R} = 12[/tex]
[tex]R = 10^{12}[/tex]
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Speedy Swift is a package delivery service that serves the greater Atlanta, Georgia, metropolitan area. To maintain customer loyalty, one of Speedy Swift's performance objectives is on-time delivery. To monitor its performance, each delivery is measured on the following scale: early (package delivered before the promised time), on-time (package delivered within 15 minutes of the promised time), late (package delivered more than 15 minutes past the promised time), or lost (package never delivered). Speedy Swift's objective is to deliver 99% of all packages either early or on-time.
Speedy collected the following data for last month's performance:
On-time On-time Early Late On-time On-time On-time On-time Late On-time
Early On-time On-time Early On-time On-time On-time On-time On-time On-time
Early On-time Early On-time On-time On-time Early On-time On-time On-time
Early On-time On-time Early Early Early On-time Loss On-time Early
Late Late Late On-time On-time On-time On-time On-time On-time On-time
On-time Late Early On-time Early On-time Lost On-time On-time On-time
Early Early On-time On-time Late Early Early On-time On-time On-time
On-time On-time Early On-time Early On-time Early On-time Late On-time
On-time Early On-time On-time On-time Late On-time Lost On-time On-time
On-time On-time On-time On-time On-time Early Early On-time On-time On-time
(a) What scale is used to measure delivery performance? What kind of variable is delivery performance?
(b) Construct a frequency table for delivery performance for last month.
(c) Construct a relative frequency table for delivery performance last month.
(a) The scale used in the analysis is qualitative as the data is not assigned any numeric value.
The daily performance is an ordinal variable, as the values assigned are ranked according to an order of the delivery time.
(b) The frequency table of the given data is:
Variable Frequency
Early 23
On-time 65
Late 9
Lost 3
Total 100.
(c) The relative frequency table for the given data is:
Variable Frequency Relative frequency
Early 23 23/100 = 0.23 = 23%
On-time 65 65/100 = 0.65 = 65%
Late 9 9/100 = 0.09 = 9%
Lost 3 3/100 = 0.03 = 3%
(a) The scale used in the analysis is qualitative as the data is not assigned any numeric value.
The daily performance is an ordinal variable, as the values assigned are ranked according to an order of the delivery time.
(b) The frequency table is a table showing frequency of each variable for the number of times they appear in the data.
The frequency table of the given data is:
Variable Frequency
Early 23
On-time 65
Late 9
Lost 3
Total 100.
(c) The relative frequency for a variable is the ratio of its frequency to the total frequency.
The relative frequency table for the given data is:
Variable Frequency Relative frequency
Early 23 23/100 = 0.23 = 23%
On-time 65 65/100 = 0.65 = 65%
Late 9 9/100 = 0.09 = 9%
Lost 3 3/100 = 0.03 = 3%
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Answer:
C.
Step-by-step explanation:
how do you graph y=12/x
Answer: [tex]\frac{12}{x}[/tex] is an asymptote
Step-by-step explanation:
Apply a table, and plug in values of x into the equation. For example f(2)=[tex]\frac{12}{2} =6[/tex]. That's one of the points on the graph that we just found (2,6)
What three-dimensional object would be generated by the rotation of the semi circle about the x axis ?
If a semicircle is rotated about the x axis of the graph then the resulting three dimensional shape will be a sphere.
Given a semicircle on a graph.
A semicircle is a half circle .A sphere is a geometrical object that is a three dimensional shape , It is the set of points that are all at the same distance r from given point in three dimensional shape.
Rotation is basically an action of rotating around an object or an axis.
If a semicircle is rotated about x axis then the resulting figure will be a sphere. This is because of the fact that when the semi circle is rotated about the x axis then all the points will be at equal distance in all directions from the center.
Hence if a semicircle is rotated about x axis then the resulting figure will be a sphere.
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a pot contains 5 black beads and 7 white beads.another pot contain 6 white beads. if one beads is drawn from each pot without looking, what will be the probability of getting atleast one white beads?
Step-by-step explanation:
is there something missing in the question ?
or is this meant to be a trick question ?
let me repeat :
pot1 contains 5 black and 7 white beads
pot2 contains 6 white beads (and nothing else, right ?)
then one bead is drawn from each pot.
so, 1 bead from pot1, and 1 bead from pot2.
the bead from pot1 is either white or black.
the bead from pot2 is white for sure.
so, the probability to get at least 1 white bead is 100% or 1, as there will be always the white bead taken from pot2.
Solve the system of equations.
2x+y = 7
x - 2y = 6
Put your answer as a coordinate point, or use "no solution" or "infinitely many solutions"(aka "the set of all real numbers").
Answer:
Ans: (4,-1)
Step-by-step explanation:
Lets keep:
2x+y=7 --- equation 1
x - 2y=6 ----- equation 2
equation 2 x 2: 2x - 4y=12 -------equation 3
now subtract equation 1 from equation 3
2x - 4y = 12
(-) 2x + y = 7
----> -5y = 5 [ Divide both sides by -5 ]
------> y= -1
Substitute y= -1 into eqaution 1
----> 2x + -1 = 7 [ add 1 to both side]
----> 2x = 8 [Divide by 2 on both sids]
----> x=4
Ans: (4,-1)
the number 40 cannot be decomposed into prime factors
True
either
False
[tex]\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\large{\textsf{\textbf{\underline{\underline{Answer : \:}}}}}}[/tex]
False, because the number 40 is a composite number, those that cannot be broken down are called Prime Numbers.
Prime numbers are numbers that are used to decompose any number, but prime numbers cannot be decomposed, since they only have two Divisors, which are 1 and itself.
[tex]~\sf{Atte: Murdock:)}[/tex]
Answer: False
Step-by-step explanation:
All whole numbers can be decomposed into prime factors. For the number 40, the prime factorization would be [tex]2 * 2 * 2*5[/tex]. Since all 4 of those numbers are prime numbers, the answer is false.
CAN SOMEONE SHOW ME HOW TO DO THIS PLEASE!
3.5 ft If the ADA guidelines state that a wheelchair ramps angle of elevation must equal 4.8°, would a ramp with the following dimensions be up to code? Show your work and explain. (Picture is
not drawn to scale.)
40 ft
Ꮎ°
Answer:
∠α = 5.001°
a easy calculator for this is:
https://www.calculator.net/right-triangle-calculator.html?av=3.5&alphav=&alphaunit=d&bv=40&betav=&betaunit=d&cv=&hv=&areav=&perimeterv=&x=57&y=16
Quadrilateral A'B'C'D' is the result of rotating quadrilateral ABCD by 60 about
the origin
y
0
Select all of the correct statements about the unchanged properties of quadrilateral
ABCD and quadrilateral A'B'C'D.
Choose all answers that apply.
O
B
3 4/5 6
BC and BC are both parallel to the y-axis
2B and B' have the same measures.
D and D' have the same coordinates.
None of the above
Activate
Answer: B
Step-by-step explanation:
A) False. Rotations do not preserve parallelism.
B) True. Rotations are rigid motions and thus preserve angle measure.
C) False. A rotation that changes the location of every point except for the center of rotation.
In a math class of $30$ students, $12$ out of $15$ girls are freshmen and $11$ out of $15$ boys are freshmen. What is the probability that in a randomly selected group of five students from the class, there will be two freshmen girls and three freshmen boys
The probability of selecting five students from the class, where there will be two freshmen girls and three freshmen boys is 0.23 approximately.
What is Probability ?Probability is the game of chance. Probability of an event is the ratio of the required outcome to the total possible outcome.
Given that In a math class of 30 students, 12 out of 15 girls are freshmen and 11 out of 15 boys are freshmen. In Probability, the word "and" means multiplication
The probability that in a randomly selected group of five students from the class, there will be two freshmen girls and three freshmen boys can be expressed as follow
12/15 x 11/14 x 11/15 x 10/14 x 9/13
132/210 x 990/2730
130680/573300
0.2279
Therefore, the probability that in a randomly selected group of five students from the class, there will be two freshmen girls and three freshmen boys is 0.23 approximately.
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The number 321.8 is 34% of x. What is the value of x rounded to the nearest whole number?
Answer:
946
Step-by-step explanation:
Let's make an equation :
34% of x = 321.8
Covert 34% into decimal by dividing by 100 :
34 ÷ 100 = 0.34
Rewrite equation with decimal form :
0.34x = 321.8
Divide both sides by x to make x the subject :
x = 321.8 ÷0.34
x = 946.470588235
To the nearest whole number will be 946 as 4 rounds it down
So our final answer will be 946
Hope this helped and have a good day
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
[tex]\qquad \sf \dashrightarrow \: \dfrac{34}{100} \sdot x = 321.8[/tex]
[tex]\qquad \sf \dashrightarrow \: x = \cfrac{(321.8) \sdot(100)}{34} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 946.47[/tex]
Round off to nearest whole number :
[tex]\qquad \sf \dashrightarrow \: x = 946[/tex]
there are three red marbles 5 green marbles 2 blue marbles in a bag which of the follwing are true
Answer:
4 and 1
Step-by-step explanation:
The area of a sector of a circle of radius 8cm is 45cm². Find the size of the angle subtended at the centre of the circle, correct to one decimal place. (Take π = 22/7)
The size of the angle subtended at the center of the circle is θ = 80.5397°
What is the Area of the Sector?In circles, a sector is said to be a part of a circle made of the arc of the circle together with its two radii. This means that it is a portion of the circle formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc.
The formula for Area of a sector is given as;
A = θ/360 x πr²
where;
θ is the central angle of the sector
r is radius
Given data ,
The area of a sector of a circle of radius 8cm is 45cm²
On simplifying , we get
A = θ/360 x πr²
45 = θ/360 ( 22/7 ) ( 8 )²
45 = ( θ/360 ) ( 201.1428 )
Divide by 201.1428 on both sides , we get
( θ/360 ) = 0.22372159
Multiply by 360 on both sides , we get
θ = 80.5397
Hence , the angle is θ = 80.5397°
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2. Rotate the following points 180°.
a.) B(-2,-5) →B'( )
b.) B(-4,1) B'( )
c.) In the graphs above connect the pre-image point B to the origin. Then connect
the origin to the image point B. What angle has been formed?
Answer:
hi helo bol ke gatu jama gol ke
(14x2 + 13x + 12) + (7x2 + 20x + 4)
Answer:
21x^2 + 33x + 16
Step-by-step explanation:
(14x^2 + 13x + 12) + (7x^2 + 20x + 4)
Combine like terms:
14x^2 + 7x^2 = 21x^2
13x + 20x = 33x
12 + 4 = 16
Thus:
21x^2 + 33x + 16
Answer:
21x^2 + 33x + 16.
Step-by-step explanation:
(14x2 + 13x + 12) + (7x2 + 20x + 4) Remove the parentheses:
= 14x2 + 13x + 12 + 7x2 + 20x + 4 Bring like terms togethher:
= 14x^2 + 7x^2 + 13x + 20x + 12 + 4
= 21x^2 + 33x + 16.