Given that IJ = 2, we know that IJ is the radius of the circle.
The area of the shaded sector is given as . Since the area of a sector is given by (angle of sector/360) * pi * r^2, we can set up the equation:
(x/360) * pi * 2^2 =
Solving for x:
x = (180/pi)*
We know that the arc JLK corresponds to the angle x, thus the length of JLK is (x/360)2pi*IJ = (x/180)*IJ * T = (180/pi) * T.
Lz + A= [; ; ;] 13 _ [ ( 2 3 ] c [: ;] 5 . [ '| E [,] Which of the 25 matrix products AA, AB, AC defined? Compute those products that are defined_ ED, EE are
we can compute A=3 by 3 matrix, B= 1 by 3 matrix
C=2 by 2 matrix D= 3 by 1 matrix and E= 1 by 1 matrix ,
We can compute only AA ,AD,BA, BD,CC,DB,EE,
[tex]We\ have \ A=\left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \\\\B=[1\ 2 \ 3]\\\\C=\left[\begin{array}{ccc}1&1\\1&1&\end{array}\right] \\\\D=\left[\begin{array}{ccc}1\\1\\1\end{array}\right] \\\\E=[3][/tex]
So ,we have to produced 25 matrix -
AA,AB,AC,AD,AE
BA,BB,BC,BD,BE
CA,CB,CC,CD,CE
DA,DB,DC,DD,DE
EA,EB,EC,ED,EE
To multiply two matrix column of first matrix equal to row of second matrix.
So we can compute A=3 by 3 matrix, B= 1 by 3 matrix
C=2 by 2 matrix D= 3 by 1 matrix and E= 1 by 1 matrix ,
We can compute only AA ,AD,BA, BD,CC,DB,EE,
[tex]AA=\left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \\\\AA=\left[\begin{array}{ccc}-2&-2&-2\\4&1&-2\\10&4&-2\end{array}\right] \\\\AD=\left[\begin{array}{ccc}0\\1\\6\end{array}\right] \\\\CC=\left[\begin{array}{ccc}2&2\\2&2\\\end{array}\right] \\\\EE=[9][/tex]
So we can compute A=3 by 3 matrix, B= 1 by 3 matrix
C=2 by 2 matrix D= 3 by 1 matrix and E= 1 by 1 matrix ,
We can compute only AA ,AD,BA, BD,CC,DB,EE,
The complete question is :-
Let the matrices,
[tex]A=\left[\begin{array}{ccc}1&0&-1\\2&1&0\\3&2&1\end{array}\right] \\\\B=[1\ 2 \ 3]\\\\C=\left[\begin{array}{ccc}1&1\\1&1&\end{array}\right] \\\\D=\left[\begin{array}{ccc}1\\1\\1\end{array}\right] \\\\E=[3][/tex]
Which of the 25-matrix products AA, AB, AC ......EE are defined? Compute those products that are defined.
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Add or subtract. Write in simplest form. 6 1/3 + 1 2/3 + 5 5/9
PLEASE HELP...PLEASE
Answer:
(4,8) (0,2) (-6,-7)
Step-by-step explanation:
Perpendicular means it sort of makes a cross with 90º angle from the already existing line. Imagine it starts at (4,8) coordinate and comes falling to the left, passing through p(-4,-4) coordinate, the points it will go through will be (4,8) (0,2) and (-6,-7) respectively.
A sure way to do this is to mark every point that's on the table below and see which ones form a perpendicular line with the original.
7.) +9 – +16 = N
8.) +85 – +12 = N
9.) –6 –2 = N
10.) +13 – +12 = N Someone please need it right now
Arithmetic operations on the directed numbers gives;
7) -7
8) +73
9) - 8
10) + 1
What are directed numbers?Any given number which has either a positive or negative sign is a directed number. Thus all numbers are directed in one way or the other. Some examples are: 8, +2, - 8.35, 10, 520 etc.
Performing an arithmetic operations on the given question, we have;
7) +9 - + 16 = +9 -(+16)
applying the rule of signs
+9 - (+16) = + 9 - 16
= -7
8) +85 - + 12 = +85 - (+12)
applying the rule of signs
+85 - (+12) = +85 - 12
= +73
9) -6 - 2
applying the rule of signs
-6 -2 = -8
10) +13 - + 12 = +13 - (+12)
applying the rule of signs
+13 - (+12) = +13 - 12
= +1
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find the position vector of a point r which divides the line joining two points p and q whose position vectors are externally in the ratio 1 : 2. also, show that p is the mid point of the line segment rq
So, the position vector of a point r is (1-1/3)p + (1/3)q.
The position vector of a point can be found using the following formula:
r = (1-λ)p + λq
where λ is the scalar value that represents the ratio in which the point divides the line segment.
In this case, the ratio of the point dividing the line segment is 1:2. So, λ = 1/3.
Substituting the values of p and q, we get:
r = (1-1/3)p + (1/3)q
To show that point p is the midpoint of the line segment rq, we can use the following property of midpoints:
The position vector of the midpoint of a line segment with endpoints p and q is given by (p+q)/2.
In this case, the position vector of point p is (1-1/3)p + (1/3)q, and the position vector of point q is (2/3)p + (2-2/3)q = (2/3)p + (4/3)q
So, the midpoint of the line segment rq is given by:
((1-1/3)p + (1/3)q + (2/3)p + (4/3)q)/2 = (3/3)p + (5/3)q
which is (p+q)/2, so p is the midpoint of the line segment rq
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Help
A machine that drills holes for wells drilled to a depth of−72 feet in one day (24 hours).
At this rate, how many hours will it take until the drill reaches its final depth of −132 feet?
At the same rate, a machine take 44 hours until the drill reaches its final depth of −132 feet.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
We have to given that;
A machine that drills holes for wells drilled to a depth of−72 feet in one day (24 hours).
Now, Let a machine drill holes reaches its final depth of −132 feet in x hours.
Hence, By definition of proportion, we get;
⇒ 72 / 24 = 132 / x
⇒ x = 132 × 24 / 72
⇒ x = 3,168 / 72
⇒ x = 44 hours
Thus, It take 44 hours to reaches its final depth of −132 feet.
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find the distance from to each of the following. (a) the -plane (b) the -plane (c) the -plane (d) the -axis (e) the -axis (f) the -axis
The distance between the xy, yz, and xz planes are 5, 3, and 7.
Multivariable Calculus
This question relates to multivariable calculus.
a) Distance of point (x, y, z) from the XY-plane
The |z co-ordinate of the point| = |z|
distance of the point (3, 7, -5) from xy plane
|-5|=5
b) Distance of point (x, y, z) from yz plane
The |x coordinate of the point| = |x|
Therefore, the distance of the point (3, 7, -5) from yz plane is
|3|=3
c) Distance of point (x, y, z) from xz plane
The |y coordinate of the point| = |y|.
The distance of the point (3, 7 -5) from the xz-plane is
|7|=7
d) Distance of point (x, y, z) from the x-axis
The distance of the points from the x-axis is
[tex]x^{2} =y^{2} +z^{2} \\\\x=\sqrt{y^{2} +z^{2} } \\\\x=\sqrt{7^{2}+(-5)^{2} } \\\\x=\sqrt{74}[/tex]
e) Distance of point (x, y, z) from the y-axis
[tex]y=\sqrt{x^{2} +z^{2} } \\\\y=\sqrt{3^{2}+(-5)^{2} } \\\\y=\sqrt{34}[/tex]
f) Distance of point (x, y, z) from the z-axis
[tex]z=\sqrt{x^{2} +y^{2} } \\\\z=\sqrt{3^{2}+7^{2} } \\\\z=\sqrt{58}[/tex]
From the calculations above,
The distance of (3, 7, -5) from the xy plane = 5The distance of (3, 7, -5) from the yz-plane = 3The distance of (3, 7, -5) from the xz-plane = 7The distance of (3, 7, -5) from the x-axis = √74The distance of (3, 7, -5) from the y-axis = √34The distance of (3, 7, -5) from the z-axis = √58To know more about the distance of a point:
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Yushio is borrowing $3,525 from Houghtonville National Bank for 2 years at 12.6%
simple interest. How much will he need to repay the loan?
Answer:
3000
Step-by-step explanation:
Answer:
Answer:
$1,392
Step-by-step explanation:
1,200(0.08)(2) = 192
1,200 + 192 = $1,392
Step-by-step explanation:
in a survey of 260 college students, the following data were obtained: 64 had taken a mathematics course, 94 had taken a computer science course, 58 had taken a business course, 28 had taken both a mathematics and a business course, 26 had taken both a mathematics and a computer science course, 22 had taken both a computer science and a business course, and 14 had taken all three types of courses.
There were 64 students who had taken a mathematics course. Of those 64, 28 had also taken a business course, and 26 had also taken a computer science course. This leaves 10 students who had taken only a mathematics course.
To calculate this, we start by subtracting the number of students who had taken all three courses (14) from the total number of students who had taken a mathematics course (64).
Then we subtract the number of students who had taken both a mathematics and a business course (28) and the number of students who had taken both a mathematics and a computer science course (26) from the result. This gives us 10 students who had taken only a mathematics course.
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Draw a polygon with the given conditions in a coordinate plane 19. A rectangle with a perimeter of 18units
According to the information, to create a rectangle polygon with a perimeter of 18 units, we must put sides of 3 units and bases of 6 units.
What is a polygon?A polygon is a term that refers to a plane geometric figure composed of a finite sequence of consecutive line segments that enclose a region in a plane. These segments are called sides, and the points at which they intersect are called vertices.
A rectangle is a polygon with four sides and four vertices that is characterized by having two of its sides longer than the other two sides. Therefore, to draw a rectangle with a perimeter of 18 units we must distribute the measurements as follows:
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non-decreasing function over r is continuous at any point except on a countable set using g delta set
A discontinuity the left and right limits still need to exist but are different.
Since bounded, growing sequences of numbers have limits, a non-decreasing function can only have leap discontinuities, which means that at
Every leap indicates that one interval is missing from the function's range, and these intervals are all disconnected (since the function is non-decreasing, the skipped intervals march up the y-axis).
Since there are only a finite number of discontinuous intervals, there can only be a finite number of discontinuity sites (to see this last bit, just pick a rational number in each interval).
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Noah had 151 stamps. He had has 42 more stamps than Jonas. How many stamps did Jonas have? How many stamps must Noah give to Jonas so that they each have the same number of stamps?
=109
No. of stamps that Noah should give to Jona to get equal no. of stamps = 151 -31=130 and 109+31=130 So now they get an equal share.-12y - 16 i dont understand this please explain to me with a good explanation
Answer: -4(3y+4)
Step-by-step explanation:
First I found the Great common divisor (-4) and took that number and divided -12y and -16 with it getting 3y and 4 and then I set it up as if I was trying to get -12y and -16 so the best way to do that is to use the distributive property so I put 3y and 4 in parentheses like this (3y+4) then I added the -4 on to get the answer of -4(3y+4)
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{-12y - 16}[/tex]
[tex]\large\text{Let us look for the GCF for each of your numbers because it can}\\\large\text{make this equation somewhat easier to solve.}[/tex]
[tex]\mathsf{-12x \rightarrow -1, -2, -3, -4, -6, -12, \ \& \ -x}\\\\\mathsf{-16 \rightarrow -1, -2, -4, -8, \& -16}\\\\\large\text{Thus, your GCF for both of your numbers is: \boxed{- 4 }}\large\checkmark[/tex]
[tex]\large\text{So, let us put }\rm{-4}\large\text{ in front of your parentheses because we had to factor}\\\large\text{out the common like term they shared together.}[/tex]
[tex]\large\text{Now simplify it furthermore}[/tex]
[tex]\huge\text{This leaves your answer as:}[/tex]
[tex]\huge\boxed{\mathsf{-4(3y + 4)}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Suppose we know that set A has n subsets, S1, S2,..., Sa If set B consists of the elements of A and one more ele- ment so |B| = |A| + 1 show that B must have 2n subsets.
B must have 2n subsets since it has two corresponding subsets for each subset of A series (S1, S2,..., Sa), one of which contains the extra element and the other of which does not.
Set B's size is |B| = |A| + 1 since it includes all of the components of set A plus an additional element. There must be two equivalent subsets in set B for each subset of A (S1, S2,..., Sa), one of which must contain the extra element and the other of which must not. This extra element must be present in at least one subset. B must therefore have a total of 2n subsets. For instance, if set A has the three subsets S1, S2, and S3, then set B will have the same three subsets plus S1 plus the extra element, S2 plus the extra element, and S3 plus the extra element, for a total of six subsets.
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The figure below is a square find the length of size x in simplest radical form with a rational denominator
x² + x² = 4
2x² = 4
x² = 2
x=√2
hope it helps
Can anyone help me? It's hard for me to solve this problem
*Debt payments of $2,100 and $1,950 are due in six months and nine months, respectively. What single payment is required to settle both debts in one month? Assume a simple interest rate of 6.30% p.a. and use one month from now as the focal date.
The required single payment is required to settle both debts in one month is $4071.26.
What is Simple interest?Simple interest is the amount of interest charged on a specific pripal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
According to question:We have,
Interest of 12 month = 6.30%
For one month = 6.30/12
= 0.525% per month
Total debt = $2,100 + $1,950
Total debt = $4050
Interest of one month = 0.525% of $4050
= $21.26
Net debt = $4050 + $21.26.
Thus, required single payment is required to settle both debts in one month is $4071.26.
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How do you solve these step by step (circled problems)
To create a dot plot, we have to first choose an appropriate scale for the given number line, and then mark a dot over the given numbers.
What is a dot plot?Data points are represented as dots on a graph with an x- and y-axis in a dot plot, sometimes referred to as a strip plot or dot chart, which is a straightforward type of data visualization. These kinds of graphs are employed to visually represent particular data patterns or groups.
To create a dot plot, we have to first choose an appropriate scale for the given number line, and then mark a dot over the given numbers.
For the first question:
Scale on the number line from the first tick, 310 to 335.
For the second question:
Scale on the number line from the first tick, 18 to 31.
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this week lee got a promotion at work that came with a 5% pay increase. if now his monthly salary is 1732.5, how much was he making before the raise
Answer:
1650
Step-by-step explanation:
1732.5 / (1+5%) = 1732.5 / 1.05 = 1650
A system of linear equations with more equations than unknowns is sometimes called an overdetermined system. Can such a system be​consistent? Illustrate your answer with a specific system of three equations in two unknowns.​ chosse from the below option.
a)Yes, overdetermined systems can be consistent. For​ example, the system of equations below is consistent because it has the solution
Answer: (Type an ordered​ pair here _____)
x1=2, x2=4, x1+x2=6
(A). Yes, overdetermined systems can be consistent.
As, the system of equations below is consistent because it has a solution
x1 = 2 , x2 = 4 , x1 + x2 = 6.
We have,
'Over-determined system is a system of linear equations, in which there are more equations than unknowns'.
If we have m equations and n variables where m>n (more equations than variables), then system can be consistent if last m−n equations are linear combinations of previous ones.
For e.g. Let us consider the system,
x + y = 1
x - y = 1
3x + y = 3
solving these equations, we can see
The only intersection point is (1,0). Thus, x= 1 and y= 0 is the solution of this system.
Thus, over-determined system can be consistent.
According to the options,
Hence, option A is correct.
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40% divided by 100 x 200
Answer:
0.8
Step-by-step explanation:
.40 / 100x200
Assume that the duration of human pregnancies can be described by a Normal model with mean 265 days and standard deviation 17 days.
a) What percentage of pregnancies should last between 269 and 282 days?
b) At least how many days should the longest 10% of all pregnancies last?
c) Suppose a certain obstetrician is currently providing prenatal care to 67 pregnant patients. Let y represent the mean length of their pregnancies. According to the
Central Limit Theorem, what is the distribution of this sample mean, y? Specify the model, mean, and standard deviation.
d) What's the probability that the mean duration of these patients' pregnancies will be less than 258 days?
a) The percentage of pregnancies should last between 269 and 282 days is 18%
b) The days should the longest 10% of all pregnancies last is 291 days.
c) According to the Central Limit Theorem, the distribution of this sample mean is 265. The model is a Normal model, and standard deviation is 17/(√(67)).
d) The probability that the mean duration of these patients' pregnancies will be less than 258 days is 0.03 or 3%
How do we determine the values?a) To find the percentage of pregnancies that should last between 269 and 282 days, we need to find the proportion of the area under the normal distribution curve that falls between those two values. This can be done using a standard normal table or calculator. Using a calculator, we find that the proportion of the area under the curve between 269 and 282 days is approximately 0.18 (or 18%).
b) To find the longest 10% of all pregnancies, we need to find the duration that corresponds to the 90th percentile. We can use the standard normal table or calculator to find that the duration that corresponds to the 90th percentile is approximately 291 days.
c) According to the Central Limit Theorem, the distribution of the sample mean, y, is a normal distribution with a mean of 265 days (the population mean) and a standard deviation of 17/(√(67)) days. So the model is a Normal model with mean 265 and standard deviation 17/(√(67))
d) To find the probability that the mean duration of these patients' pregnancies will be less than 258 days, we need to find the proportion of the area under the normal distribution curve that falls to the left of 258 days. Using a calculator, we can find that the proportion of the area under the curve to the left of 258 days is approximately 0.03 (or 3%).
Therefore, the correct answers are as given above
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Lana picked the number of apples somebody illustration out of these apples 2/3 are green apples how many apples are green
Which of the following are not the lengths of the sides of a 30°-60°-90° triangle?
A. 1/2, √3/2, 1
B. 5/2, 5√3/2, 10
C. √2, √6,2√2
D. 3,3√3,6
Answer:
C
Step-by-step explanation:
C. √2, √6,2√2 are not the lengths of the sides of a 30°-60°-90° triangle.
In a 30°-60°-90° triangle the ratio of the sides are always the same, the hypotenuse is twice the length of the shorter leg, and the longer leg is √3 times the length of the shorter leg.
A. 1/2, √3/2, 1 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 1, the longer leg is 1√3=√3 and the hypotenuse is 12=2.
B. 5/2, 5√3/2, 10 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 5/2, the longer leg is (5/2)*√3=5√3/2 and the hypotenuse is (5/2)*2=5
D. 3,3√3,6 are the lengths of the sides of a 30°-60°-90° triangle. As the shorter leg is 3, the longer leg is 3√3=3√3 and the hypotenuse is 32=6
So, option C is not the lengths of a 30°-60°-90° triangle.
3 > y-2 graph the solution
Answer:
12345678901234567890
Help me pls!!!!!!!! I NEED HELPPP
It is said that one of the keys to becoming money savvy is to learn how to separate "needs" from "wants". Please explain why this is true. (EXTRA POINTS UR OWN WORDS!!!!!
Answer:
absolutely
Step-by-step explanation:
Needs are for survival in life like food, rent or mortgage, utilities, and other expenses. Transportation costs, insurance coverage, and any clothing and tools you need for work are included in this part of your budget. A want includes expenses that you can comfortably live without and is not essential for survival.
in four football games, antoine carried the ball for 98, 146, 84, and 105 yards. how many total yards did antoine have for the four games?
Answer: she had 433 yards
Step-by-step explanation:
Find all possible 2×2
matrices A that for any 2×2 matrix B, AB = BA.
Hint: AB = BA must hold for all B. Try matrices B that have lots of zero entries.
Answer:
Step-by-step explanation:
Consider the following four matrices:
(1000),(0010),(0100),(0001).
See what happens when you solve the equation AB=BA
for each of those four (let B
be each one of those four). To facilitate it, write A=(acbd)
You will get a set of equations for the entries of a
which are easily solved. This trick is quite general.
let be the circle with radius centered at the origin. let be the vector field defined by . find the flux of coming out of the circle through the curve .
The flux of the vector field F is the integral of the normal component of the vector field over the surface.
The flux of the vector field F is the integral of the normal component of the vector field over the surface. In this case, the surface is the circle with radius r centered at the origin and the normal component of the vector field is just the z-component, which is equal to 2x. The integral of the normal component of the vector field over the circle is given by
Φ = ∫C 2x ds = ∫0 2π r2 2cosθ dθ
= 4πr2
This is the flux of the vector field F coming out of the circle.
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12
Solve for x.
9
X+4
2x
will give brainliest
The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.
What is the quadratic equation?
A quadratic equation is a type of polynomial equation of degree 2, that can be written in the form of ax^2 + bx + c = 0 where x is the variable, a,b,c are constant and a is not equal to zero.
To solve for x in the equation 9/(x+4) = 2x, we can first clear the fractions by multiplying both sides of the equation by (x+4). This gives us:
9 = 2x*(x+4)
Then we can simplify the right side of the equation:
9 = 2x^2 + 8x
Next, we can move all the x terms to one side of the equation and all the constants to the other side:
2x^2 + 8x - 9 = 0
Now we can use the quadratic formula to solve for x:
x = (-b +/- sqrt(b^2 - 4ac)) / 2a
where a = 2, b = 8, and c = -9
So we have:
x = (-8 +/- sqrt(8^2 - 42-9)) / 2*2
x = (-8 +/- sqrt(64 + 72)) / 4
x = (-8 +/- sqrt(136)) / 4
x = (-8 +/- 4*sqrt(17)) / 4
x = (-2 +/- sqrt(17))
So the solutions for x are x = -2 + sqrt(17) and x = -2 - sqrt(17)
The solution for x is x = -2 + sqrt(17) and x = -2 - sqrt(17) will give the brainliest.
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