Operations that can be applied to a matrix in the process of Gauss-Jordan elimination are options 1,2 and 4.
What is gauss Jordan's elimination?Gauss-Jordan Elimination is a matrix-based technique for solving linear equations or determining a matrix's inverse.
When using Gauss Jordan elimination, the following operations may be carried out on a matrix:
1. Replacing a row with twice that row
2. Replacing a row with the sum of that row and another row
3. Swapping row
The optional row(or column) procedures that can be employed are:
1. Alternate any two rows (or columns)
2. Scalar multiples of one row (column) are added or subtracted from another row (column) occurs when a row is substituted with the sum of another row and that row.
3. Multiply any row (or column) fully by a nonzero scalar, as seen below by substituting a row with two rows.
Hence, Gauss-Jordan elimination includes options 1,2, and 4.
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Select the expression that’s is equivalent to (x-1)^2
Answer:
(x-1)^2
=x^2 - 2x + 1
Step-by-step explanation:
hope this helps
Ms. Rudolph randomly selects one student from a group of students. 14 students are wearing a black shirt, 6 students are wearing a red shirt, and 9 students are wearing a blue shirt.
Show your work to determine the PROBABILITY that the selected student is wearing a BLACK shirt?
You may write your answer as a FRACTION or DECIMAL.
Answer:
14
29 as a fraction
Step-by-step explanation:
Based on the given conditions, formulate:
14=19+14+6）
2 Calculate
14
9+14+6
Calculate
14
23+6
Calculate the sum or difference
14
29
X
Calculate the sum or difference
14
29
Alternative forms
~ 0.482759, ~ 48.275862%,
4.827586 × 10
Hope it help :)
Answer this for 28 points
Answer: I think B
Step-by-step explanation:
Write down the first three and last two terms of the binomial expansion of:
a) (3x+(2/x))^15
b) (2x-(3/x))^20
Answer:
a) [tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
b) [tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
Step-by-step explanation:
The binomial expansion formula is:
[tex](a + b)^n = a^n + \binom{n}{1}a^{n-1} b + \binom{n}{2}a^{n-2}b^2 + ... + \binom{n}{r}a^{n-r}b^{r} + ... + b^n[/tex]
The (n r) in front of each term is the binomial coefficient. This can be calculated on a calculator using the nCr button (in this case, you'd put 15C1 for (n 1), 15C2 for (n 2), etc). This can be calculated without a calculator using this formula:
[tex]\binom{n}{r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}[/tex]
In a), a = 3x, b = 2/x and n = 15.
You can plug these into the formula above to get:
[tex](3x)^{15} + 15(3x)^{14}(\frac{2}{x}) + 105(3x)^{13}(\frac{2}{x})^2 + ... + 15(3x)(\frac{2}{x})^{14} + (\frac{2}{x})^{15}[/tex]
Here's how to do this without the formula:
Start with the a^nIn the second term, you subtract 1 from a's power (in this case, 15 to 14) and add 1 to b's power (0 to 1). Then you multiply it by nCr.This keeps going until you get to b^n. To check you've done it correctly, the powers of a and b in each term should add up to n. For example, in term 3 above, a's power is 13 and b's power is 2. These add to make 15.Remember, a's power goes down by 1 each time, and b's power goes up by 1 each time. There is no b in the first term because b^0 = 1.You could 'simplify' this by expanding the brackets, but this gives you massive numbers so it's probably best to leave it like this.
Applying this to b):
a = 2x, b = -3/x, n = 20
[tex](2x)^{20} + 20(2x)^{19}(-\frac{3}{x}) + 190(2x)^{18}(-\frac{3}{x})^2 + ... + 20(2x)(-\frac{3}{x})^{19} + (-\frac{3}{x})^{20}[/tex]
If f(x)=2 sin 3x+C, then the maximum value of f(x) is:
1)C
2) C+2
3) C+3
4) C+6
Reason:
The largest sin(x) can get is 1, and the same goes for sin(3x).
Consequently, the largest 2sin(3x) can get is 2.
You can visually verify these claims by graphing each function with a tool like Desmos. Take note of the y coordinate of the highest points. See below.
Therefore, the largest f(x) = 2sin(3x)+C can get is 2+C or C+2
Which of the following is most likely the next step in the series?
Answer:
C
Step-by-step explanation:
Option C is correct, the polygon in c option is the next step in the series
What is Polygon?A polygon is a plane figure made up of line segments connected to form a closed polygonal chain.
In the first step we can see a triangle
The triangle has three sides
In the second step there is a rectangle which has four sides
The third step has pentagon which has five sides
So in next step the polygon should have six sides
Hexagon is the next step in the series
Hence, option C is correct, the polygon in c option is the next step in the series
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please helppppp i really need this.
Geometry, Angles questions
Answer:
X= 82⁰
z= 82⁰
Step-by-step explanation:
for X:
we can use co-interior angles sum up to make 180 so,
x+ 98= 180
x= 180-90= 82⁰
for z, we can use either angles on a straight line or corresponding angles
using angles on a straight line,98 + z= 180
z= 180-98= 82⁰
using corresponding anglescorresponding angles are always equal and can be found in the F shape diagram when lines are parallel
therefore X and z are corresponding angles and since we found x= 82⁰ then z= 82⁰
the diagram is not drawn to scale!!
pls
Answer:
135°
Step-by-step explanation:
That triangle in the corner is an right angle isosceles triangle as that line the midpoint of both sides :
the base angle of this triangle (x) will be :
180 = 90 + 2x
90 = 2x
x= 45
Angles on a straight line add up to 180. So to work out a :
180 = 45 + a
135 = a
Hope this helped and brainliest please
Please help me with this question
What is the value of x?
Enter your answer in the box.
Answer:
25
Step-by-step explanation:
c^2=a^2+b^2
where c = hypotenuse
so, x^2 = 24^2+7^2
x^2 = 576 + 49
x^2 = 625
x = square root of 625
x = 25
In a mathematic test 30 students obtained the following scores
3,4,7,2,9,5,2,1,8,2,3,6,9,3,4,3,4,1,5,3,3,1,7,7,7,5,6,4,6,5
a) Prepare a frequency table for the data
b) Draw a pictogram
c) Construct a barchart
Answer:
a) Prepare a frequency table for the data
Step-by-step explanation:
Guys help me with a) and b) tasks
ANSWER:
a) 40
b) 25
Thanks<3
Step-by-step explanation:
there are 2 similar triangles : ABE and DCE
that means they have the same angles, and the scaling factor from one triangle to the other is the same for every side.
and that means that
DE/AE = EC/BE (= DC/AB)
we know that
AE = AD + DE
BE = BC + EC
a.
so, we have actually
DE/(AD+DE) = EC/(BC+EC)
DE/(10+DE) = 8/(2+8) = 8/10 = 4/5
DE = 4(10+DE)/5
5DE = 4(10+DE) = 40 + 4DE
DE = 40 cm
b.
AD/DE = 3/5
BC/EC must be 3/5 too.
15/EC = 3/5
15 = 3EC/5
75 = 3EC
EC = 25 cm
the ratio of new airplanes to old air planes in a fleet of 720 planes of which 240 are old airplanes
Answer:2
Step-by-step explanation:(720-240)/(240)
Using the information in the diagram, what is the height of the tree to the nearest foot?
45 ft
54 ft
60 ft
135 ft
Answer:
60 ft
Step-by-step explanation:
a = 90
b = 108ft
the base angle can be found by using sin(x) = 120/108x2
=> x = 33.7 degrees
To find height, use tan(33.7) = Opp/ Adjacent = x / 90
=> x = 60.02 or 60 ft
The mean percent of childhood asthma prevalence in 43 cities is 2.25%. A random sample of 31 of these cities is selected. What is the probability that the mean childhood asthma prevalence for the sample is greater than 2.7%? Interpret this probability. Assume that σ= 1.27%.
The probability is
(Round to four decimal place)
The Probability that the mean childhood asthma prevalence for the sample is greater than 2.7% is 0.0357.
What is Probability ?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
For a Normal Distribution, the z-score formula
[tex]z = \dfrac{X-\mu}{\sigma}[/tex]
Here X is the mean and sigma is the standard deviation.
Mean of 2.25% = 2.25
The standard deviation of 1.27%, sigma = 1.27
For Sample 31 the value of the standard deviation is
s = 1.27/√31
s = 0.2442
Substituting the values
Z = ( 2.25 -1.27)/0.2442
Z = 1.8
the p-value from the graph of z and p = 0.9643
To determine value of probability greater than X is 1 - 0.9643 = 0.0357
The Probability that the mean childhood asthma prevalence for the sample is greater than 2.7% is 0.0357.
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[tex]2h - (6h - 5)= -1[/tex]
Answer:
[tex]h=\frac{6}{4}[/tex]
Step-by-step explanation:
[tex]2h-(6h-5)=-1\\2h-6h+5=-1\\-4h+5=-1\\-4h=-6\\\boxed{h=\frac{6}{4}}[/tex]
distribute the negative sign to the parenthesiscombine like termssubtract [tex]5[/tex] from both sidesdivide both sides by [tex]-4[/tex]11. Find the total surface area.
4 in.
6 in.
2 in.
Answer:
Appearantly, you forgot to mention the question
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is452.16 square feet? Use 3.14 for .
We need radius
Let that be r
πr²=452.163.14r²=452.16r²=144r=√144r=12ftAnswer:
12 feet
Step-by-step explanation:
It asks how many feet away from the sprinkler can water be spread. Therefore, in this scenario, we require the radius.
Area of a circle :
Area (circle) = πr²
Solving :
⇒ 452.16 = 3.14 × r²
⇒ r² = 452.16 ÷ 3.14
⇒ r = √144
⇒ r = 12 feet
Sybil can put a total mass of 950 g in her bag. she buys a book that weighs 450 g and a notebook that weighs 210 g. write an equation to represent how much more mass, m, her bag can hold. then, solve for the answer and include an explanation of how you solved the equation
Answer:
M =290
Step-by-step explanation:
Subtraction of numbers
math hw please answer quickly i dont understand
Answer:
See explanation
Step-by-step explanation:
Since she used only 1/2 of the recipe and the full recipe uses 1 cup, divide 1 by 2. The equation is 1/2=0.5.
For the lemon juice, the equation is 1/4 divided by 2. On the number line, make a dot at 1/4, and then travel backwards halfway. 1/4 divided by 2 is 1/8, or 0.125.
Hope this helps!
This Week's High Temperatures (°F)
29, 38, 45, 31, 50, 58, 62
Last Week's High Temperatures (°F)
44, 31, 66, 32, 26, 58, 78
Which measures of center and variability for the
temperatures were lower this week than last week?
Check all that apply.
mean
median
mode
range
mean absolute deviation
Done
The measures of center and variability for the
temperatures that were lower this week than last week include mean, range, mean absolute deviation.
What is a mean?It should be noted that a mean simply means the average set if numbers given.
Also, the range is the difference between the highest number and the lowest number in the data.
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Answer:
mean,range,mean absolute deviation
Step-by-step explanation:
just took it on edge
What is the length of segment BC?
Answer:
[tex]BC=x=(13;+\infty)[/tex]
Step-by-step explanation:
Existence of Triangle
[tex]x-(2x-24) < x-2 < x+(2x-24)\\[/tex]
[tex]13 < x > 11[/tex]
[tex]x=(13;+\infty)[/tex]
(TR)546 - (TR)540
pls help!
The computation of (TR)546 - (TR)540 will give a value of 3261.
How to compute the value?
TR(546) = 546(546 + 1)/2 = 273 * 547
TR (540) = 540(540 + 1)/2 = 270 * 541
273 * 547 = (270 + 3)(541 + 6)
= 270*541 + 270*6 + 541 *3 + 18
= 270*541 + 1620 + 1623 + 18
= 270*541 + 3261
TR(546) -TR (540) = 270*541 + 3261 - 270 * 541
= 3261
TR(546) -TR (540) = 3261
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80% of the sixth-grade students and 20% of the fifth-grade
students at a school went on a field trip. If there are 20 sixth-grade
students and 80 fifth-grade students, what percent of all the fifthgrade and sixth-grade students from this school went on the field
trip? I WILL MAKE U BRAINLISET
A restaurant is analyzing its customer satisfaction level. the manager performs an observational study of customers during the lunch hour on a monday and draws the conclusion that most of the customers are satisfied with the service they receive. the conclusion drawn from the study is because the sample is . in this instance, an study was conducted.
The conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate.
How to determine the conclusion of a study?
We are told that a restaurant is analyzing its customer satisfaction level. Now, the conclusion drawn was that most of the customers are satisfied with the service they receive.
Now, we can say that the conclusion drawn is not valid. This is as a result of the fact that the sample is inappropriate as it does not deal with the actual response from the customers but only observational.
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Select the correct answer from each drop-down menu. two six-sided fair dice are rolled simultaneously. the probability that the sum of the two numbers rolled is greater than 3, given that the sum of the numbers is not greater than 5, is . the probability that one of the numbers is a 6 and the sum of the two numbers is an odd number is .
Two six-sided fair dice are rolled simultaneously.... 6 and the sum of the two numbers is an odd number is mathematically given as
x=7/10
What is the sum of the two numbers?Generally, the equation for Number is mathematically given as
[tex]x=P\frac{E > 3}{Enot > 5}\\\\Therefore\\\\x=P\frac{E > 3}{E\leq5}\\\\x=P\frac{4\leq E \leq5}{E\leq5}\\\\x=P\frac{7/36}{10/36}[/tex]
x=7/10
In conclusion, the sum of the two numbers
x=7/10
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Drag each tile to the correct box.
Match each equation with its solution.
Equation
Solution
arrowRight
arrowRight
arrowRight
arrowRight
The correct match of each tile of the equation with its solution is:
n - 13 = - 12 →→→ 1n/5 = -1/5 →→→ -1n + 15 = - 10 →→→ -25How do we match each tile to the correct box?To match each tile to the correct box, we have to solve the arithmetic operations in the box, then drag the correct tile that matches our answer into the box.
From the image attached below;
1.
n - 13 = - 12
Let us add (+13) to both sides to eliminate (-13), i.e.
n - 13 + 13 = - 12 + 13
n = 1
2.
n/5 = -1/5
multiply both side by 5
n/5 × (5) = -1/5 × (5)
n = -1
3.
n + 15 = - 10
n +15 - 15 = - 10 - 15
n = -25
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Alex got 27 questions out of 30 correct. what present of the questions did he get correct?(use fish method)
if we take 30 to be the 100%, what is 27 off of it in percentage?
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} 30 & 100\\ 27& x \end{array} \implies \cfrac{30}{27}=\cfrac{100}{x} \\\\\\ \cfrac{10}{9}=\cfrac{100}{x}\implies 10x=900\implies x=\cfrac{900}{10}\implies x=90[/tex]
List the first 4 terms of a geometric sequence with the first term of 2 and a common ratio of 5.
Answer:
2, 10, 50, 250
Step-by-step explanation:
For geometric sequences, multiply the previous term by the common ratio.
Using the formula for geometric sequences [tex]a_{n} =ar^{n-1}[/tex] , with [tex]a_{n}[/tex] being the nth term (so n=4 for the fourth term), a being the first term, and r being the common ratio.
Our starting term is 2. So that is automatically the first term of the four.
Second term:
[tex]a_{2} =2*5^{2-1}=2*5^1=2*5=10[/tex]
Third term:
[tex]a_{3} =2*5^{3-1}=2*5^2=2*25=50[/tex]
Fourth term:
[tex]a_{4} =2*5^{4-1}=2*5^3=2*5*5*5=10*25=250[/tex]