Answers
(These values are the same as in the given matrix)
The bottom row's answer boxes are: 0, 1, -9/13=======================================================
Explanation:
Row echelon form will have us turn the "3" into a 0. To do this, we multiply everything in row 1 by the value -3
Row 1 is initially: 1, -4, 3
Multiply that row by -3 to get: -3, 12, -9
Then add these values to the values in row 2 and we get:
-3+3 = 0
12+1 = 13
-9+0 = -9
These three sums replace what you see in row 2
This is the new matrix we have now
[tex]\left[\begin{array}{ccc}1 & -4 & 3\\0 & 13 & -9\end{array}\right][/tex]
Again the first row has not changed. Only the second row has been altered.
The next and last step is to turn that 13 into a 1. Recall we want the pivot positions to be 1. Divide everything in row 2 by 13 to get this accomplished.
0---> 0/13 = 0
13 ----> 13/13 = 1
-9 ---> -9/13
we now have
[tex]\left[\begin{array}{ccc}1 & -4 & 3\\0 & 1 & \frac{-9}{13}\end{array}\right][/tex]
We stop here since we don't need to get the matrix into reduced row echelon form (RREF) and instead only need to get it into row echelon form (REF). Throughout this whole process, row 1 has not changed.
Related Questions
Which measure of center would you use to compare the populations represented by the box plots?
Which measure of variability would you use to compare the populations represented by the box plots?
Answers
Answer:
Median and Interquartile range (IQR)
Step-by-step explanation:
I did it :)
20 pts if you answer
I REPORT UNNECESSARY ANSWERS
Answers
Answer:
C) 1/12
Step-by-step explanation:
P(2) = 1/6
P(Tail) = 1/2
1/6 × 1/2
1/12
Keio and Taylor relapse after school to train for the baseball team the ratio of the number of laps Kyle ran to the number that Taylor 2 to 3 Kyle ran six slabs how many laps did Taylor
Answers
Answer: 9 miles
Step-by-step explanation: 6 divided by 2 is 3 and 3 times 3 is 9.
What is the function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units?
Answers
Given:
The parent function is [tex]f(x)=x^2[/tex]
We need to determine the function g(x) created from the function f(x) by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units.
Shift left 9 units:
The rule to shift the graph c units to the left is given by
[tex]y=f(x+c)[/tex]
where c is the positive real number.
Hence, to shift the graph 9 units to the left is given by
[tex]f(x)=(x+9)^2[/tex]
Vertical stretch by a factor of 4:
The rule to stretch the graph vertically by a factor of c is given by
[tex]y=cf(x)[/tex]
where [tex]c>1[/tex]
Hence, to stretch the graph vertically by a factor of 4, we have;
[tex]f(x)=4(x+9)^2[/tex]
Shifting 5 units up:
The rule to shift the graph c units upward is given by
[tex]y=f(x)+c[/tex]
where c is the positive real number.
Hence, to shift the graph 5 units upward is given by
[tex]f(x)=4(x+9)^2+5[/tex]
Therefore, the function [tex]g(x)=4(x+9)^2+5[/tex] is created from the graph [tex]f(x)=x^2[/tex] by moving the graph left 9 units, vertically stretching it by a factor of 4 and shifting up 5 units.
Hence, the graph g(x) is [tex]g(x)=4(x+9)^2+5[/tex]
The function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units is g(x) = 4*(x+9)^2 + 5.
Explanation:To generate the function g(x) from f(x) = x^2, you will perform several transformations on it:
A horizontal shift of 9 units to the left. To do this, you change the x inside the function to (x+9). A vertical stretch by a factor of 4. To do this, you multiply the whole function by 4.A vertical shift of 5 units up. To do this, you add 5 to the entire function.So, after performing these transformations to f(x) = x^2, you get the function g(x) = 4*(x+9)^2 + 5.
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SOLVE X/5+3=2
A)-5
B)25
C)5
D)-1/5
Answers
Answer:
b 25
Step-by-step explanation:
Answer:
A)-5 if its without parenthasis around 5+ 3
Step-by-step explanation
2 minus 3 is -1 and -1 times 5 is -5
A quarter is worth of a dollar. Haley needs to exchange dollar bills to get quarters to do her laundry in coin washers and dryers. How many quarters will she get for $13?
Answers
Answer:
52 quarters
Step-by-step explanation:
-We know that a quarter dollar is equivalent to $0.25
[tex]\$1=4 \ Quarters[/tex]
-Given that Haley has $13, we multiply this amount by 4 since $1 has 4 quarters to obtain the number of quarters:
[tex]Q=13\times 4\\\\=52[/tex]
Hence, Hayley will get 52 quarters.
Perbandingan kelereng Faiz dan Bayu 4 : 11. Jumlah kelereng mereka 60 buah. Selisih kelereng keduanya adalah
Answers
The difference in the number of their marbles is 28 Buah.
The ratio of Faiz's marbles to Bayu's marbles is given as 4:11. If the total number of marbles they have is 60, you can find the number of marbles each of them has.
Let x be the common multiplier for both parts of the ratio. Then, Faiz has 4x marbles, and Bayu has 11x marbles.
The total number of marbles is the sum of their marbles:
4x + 11x = 60
Combine like terms:
15x = 60
Divide by 15 to find x :
x = 4
Now, substitute x back into the expressions for Faiz and Bayu's marbles:
- Faiz's marbles: [tex]\( 4x = 4 \times 4 = 16 \)[/tex]
- Bayu's marbles: [tex]\( 11x = 11 \times 4 = 44 \)[/tex]
The difference in the number of their marbles is [tex]\( 44 - 16 = 28 \)[/tex].
So, the correct answer is: C. 28 Buah
Complete question:
Perbandingan kelereng Faiz dan Bayu 4:11. Their total color is 60. The best color of them is ...
16 pieces
24 pieces
28 pieces
44 pieces
You have a wire that is 74 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum
Answers
Answer:
32.55 cm
Step-by-step explanation:
Let x = the length of wire that becomes a circle.
Then 74 - x = the length of wire that becomes a square
Circumference of circle + perimeter of square = 74
1. Expression for the side of the square
P = 4s = 74 - x
s = ¼(74 - x)
2. Expression for the radius of the circle
C = 2πr = x
r = x/(2π)
3. Expression for the total area
[tex]\begin{array}{rcl}\text{Total area} & = &\text{area of circle+ area of square}\\A & = & \pi r^{2} + s^{2}\\& = &\pi \left(\dfrac{x}{2 \pi}\right)^{2} + \left (\dfrac{1}{4}(74 - x)\right)^{2}\\\\ & = & \dfrac{x^{2}}{4 \pi} + \dfrac{1}{16}(5476 - 148x + x^{2})\\\\ & = & 0.07958x^{2} + 342.25 - 9.25x + 0.0625x^{2}\\A & = & 0.1421x^{2} -9.25x + 342.25 \\ \end{array}[/tex]
This is the equation of a parabola.
In standard form,
ƒ(x) = 0.1421x² -9.25x + 342.24
a = 0.1421; b = -9.25; c = 342.24
The parabola opens upwards, because a > 0. Therefore, the vertex is a minimum.
The vertex of a parabola occurs at
x = -b/(2a) = 9.25/(2 × 0.1421) = 9.25/(0.2842) = 32.55
The circumference of the circle is 32.55 cm.
The graph below shows that the area of the circle is a minimum when x = 32.55 cm
in the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the
Answers
Answer:
71
Step-by-step explanation:
because the theorem is sum of the square
The answer is d. hypotenuse.
Here's why:
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs).
So, if you have a right triangle with legs of length a and b, and hypotenuse of length c, the equation would be: a^2 + b^2 = c^2.
Therefore, the sum of the squares of the legs (a^2 + b^2) is equal to the square of the hypotenuse (c^2).
The other options are incorrect because:
a. shorter leg: The theorem doesn't differentiate between the lengths of the legs, it simply states that the sum of their squares is equal to the square of the hypotenuse.
b. longer leg: Same as above, the theorem doesn't consider the individual lengths of the legs, just their squares.
c. sum of the angles: The Pythagorean Theorem deals with the sides of a right triangle, not its angles. The sum of the angles in any triangle is always 180 degrees.
Complete Question:
In the Pythagorean Theorem, the sum of the squares of the legs is equal to the square of the
a. shorter leg
b. longer leg
c. sum of the angles
d. hypotenuse
What is the expression of 8 more than a number x
Answers
"more" means added to, or addition. So 8 more than 'x' is:
x + 8
Advertisers often refer to CPM (Cost per thousand people reached) when quoting advertising rates. If a website
promises to reach 23,000 people for $1,540, what is the CPM? (Round to the nearest dollar.)
a) $67
b) $108
c) $150
d) $185
Answers
Answer:
$67
Step-by-step explanation:
There are 23 thousand clicks, so as it pays per thousand you need to divide $1 540 by 23, which results in 66.9.... reacurring which when rounded is (a) for $67.
A circle has a radius of 32 inches. Find the circumference of the circle to the nearest tenth. Use 3.14 for PI.
Answers
The calculation of the circumference of a circle with a radius of 32 inches, using 3.14 for PI, gives a result of 201.0 inches.
Explanation:The subject of this question involves calculating the circumference of a circle. The formula used to find the circumference of a circle is 2πr, where r is the radius of the circle. Here, π is approximated to 3.14 as given in the question, and the radius r is given as 32 inches.
Substituting the given values into the formula, we get circumference = 2 * 3.14 * 32 = 200.96 inches. Thus, the circumference of the circle to the nearest tenth is "201.0 inches."
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John goel is to have more then -7 dollors in hisaccount by the end of this mounth. the varible d is the nuber of dollor in johns bank account at the end of the mounth. Whrite an lineqwalatiy in terms of d that is true only if john meets hif monthy goal
Answers
Answer:
d > - 7
Step-by-step explanation:
John is to have more then -7 dollars in his account by the end of this month.
Now, the variable d is the number of dollars in John's bank account at the end of the month.
Therefore, the inequality in terms of d that is true only if John meets his monthly goal will be
d > - 7 (Answer)
Histidine has 3 nitrogens. arrange the indicated nitrogens in decreasing order of basicity (1 = most basic, 3 = least basic). if there are fewer than 3 nitrogens in the molecule, leave that answer space blank. if two nitrogens have the same basicity, give them the same number. histidine
Answers
Answer:
Nitrogen 7 = 1 ---- Most Basic
Nitrogen 1 = 2
Nitrogen 3 = 3 ------ Least Basic
Step-by-step explanation:
The basicity of amino acids is as a result f the unshared pair of electrons in the Nitrogen atoms.
Part of the rule of basicity of organic compounds(amino acids) posits that:
The more unstable an electron pair is, the more basic it is.
From the diagram attached below;
Nitrogen 7 posses and unstable electron due to the lone pair of electron in the NH₃⁺ which renders it most basic .
Nitrogen 1 and 3 are in ring form thereby they are less basic But nitrogen 1 is more basic compared to nitrogen 3 because lone pair on Nitrogen 1 is not involved in resonance unlike Nitrogen 3 that is resonance stabilized (i.e alternating by a resonance effect).
Another phenomenon to deduce the basicity of Histidine is the effect of hybridization.
Basicity of Organic Compounds increases with decreasing s character.
Therefore, the trend of basicity is as follows: sp³ > sp² > sp
Because in sp; the lone pairs are most stable, hence least basic
And in sp³; the lone pairs are least stable; hence most basic.
Therefore; From the diagram attached below:
Nitrogen 7 = 1 ---- Most Basic
Nitrogen 1 = 2
Nitrogen 3 = 3 ------ Least Basic
what is the limit of the infinite series?
Answers
Answer:
Zero
Step-by-step explanation:
There is no solution to this.
What is twice a number minus 4 is less than three times the number?
Answers
2x-4<3x
treat the < sign as a = sign
2x-4=3x
subtract 2x form both sides
-4=x
put the < sign back
-4-4 is less than than x or
x is greater than -4
Answer:
[tex]n > -4[/tex]
Step-by-step explanation:
Step 1: Convert into an expression
Twice a number minus 4 is less than three times the number
[tex]2n - 4 < 3n[/tex]
Step 2: Solve for the number
[tex]2n - 4 - 2n < 3n - 2n[/tex]
[tex]-4 < n[/tex]
Answer: [tex]n > -4[/tex]
Which graph represents a vertical translation by 4 units down of the function f(x)=2x?
Answers
4 units DOWN would mean that the k-value is -4, which is put at the very end of the equation. hope this helped!
The equation of function which have vertical translation by 4 unit will be
f(x)= 2x - 4
To understand more, check below explanation.
Translation of function:The equation of function is given as,
[tex]f(x)=2x[/tex]
If we have to shift graph of function a unit down. then required equation will be, [tex]f(x)=2x-a[/tex]
If we have to shift graph of function b unit up. then required equation will be, [tex]f(x)=2x+b[/tex]
We have to do vertical translation by 4 units down of the function f(x)=2x.
Hence, required equator will be [tex]f(x)=2x-4[/tex]
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Brad is putting up a 10 foot diameter circular flower garden in his yard. He will put plastic edging along the flowerbed. How many feet of edging will Brad need to enclose his flower garden?
Answers
Answer:
10π feet, or about 31.42 feet
Step-by-step explanation:
Diameter = 2 times radius, so the radius is 5 feet.
The question is asking us for the circumference - the distance around the circle. Plug our radius into the formula.
C = 2πr
C = 2π(5)
C = 10π feet = about 31.42 feet
Answer:
20 Pi feet or 62.8318530718 ft
Step-by-step explanation:
Find the circumference
Pi X diameter
radius = 1/2 diameter
radius *2 = 20
20 * Pi
Which set of three angles could represent the interior angles of a triangle? 26 degrees, 51 degrees, 103 degrees 29 degrees, 54 degrees, 107 degrees 35 degrees, 35 degrees, 20 degrees 10 degrees, 90 degrees, 90 degrees
Answers
Answer:
26 °, 51 °, 103 °
Step-by-step explanation:
-A triangle is a 3-sided regular polygon.
-The sum of it's interior angles add up to 180°.
-Only the 26 °, 51 °, 103 ° set add exactly up to 180° and therefore satisfies the triangle's interior angles condition.
Answer:
The answer A trust me
Step-by-step explanation:
If sec0= 25/24 find cot0
Answers
Answer:
cot θ = 24/7
Step-by-step explanation:
This will be difficult to explain without a diagram, but let's proceed.
Since sec θ = 25/24 (secant θ is equal to hypotenuse/adjacent) the hypotenuse of the triangle is 25 and the side adjacent to θ will be equal to 24. To find the opposite side-length you can use the Pythagorean theorem.
25^2 = 24^2 + a^2 (You can use either a or b as the variable)
625 = 576 + a^2 (Subtract 576 from each side)
a^2 = 49
a = 7 (The sqrt of 49 is 7 | This is the side-length of the opposite side relative to θ)
Since cotangent is always adjacent/opposite:
cot θ = 24/7
Which equations are equivalent to y = two-thirds x minus 4 when written in slope-intercept form? Check all that apply.
3 x minus 2 y = 4
2 x minus 3 y = 12
Negative 4 (2 x minus 3 y) = negative 4 (12)
2 (x + 6) = 3 y
2 x minus 3 y = 4
Answers
Answer:
2 x minus 3 y = 12
Negative 4 (2 x minus 3 y) = negative 4 (12)
Step-by-step explanation:
y = two-thirds x minus 4
y = (⅔)x - 4
Multiply the entire equation by 3
3y = 2x - 12
2x - 3y = 12
Multiply both sides by -4
-4(2x - 3y) = -4(12)
Answer:
b
Step-by-step explanation:
I need another help again my bros
Answers
Answer:
a = 15.59 c= 31.18
27 tan 30 = a
c cos 30 = 27
c = 27/cos30
c = 31.18
simplify: square root 108+square root 125-square root 75
Answers
Answer:
[tex]11\sqrt{3} + 5\sqrt{5}[/tex]
Step-by-step explanation:
[tex]\sqrt{108}+\sqrt{125} - \sqrt75}[/tex]
1. [tex]\sqrt{108} = 6\sqrt{3}[/tex]\
2. [tex]\sqrt{125} = 5\sqrt{5}[/tex]
3. [tex]\sqrt{75} = 5\sqrt{3}[/tex]
4. Add [tex]6\sqrt{3} + 5\sqrt{3} = 11\sqrt{3}[/tex]
your left with [tex]11\sqrt{3}+5\sqrt{5}[/tex]
Answer:
12
Step-by-step explanation:
Two lines are perpendicular if they cross a 45° angle true or false
Answers
Answer: False
Step-by-step explanation:
A growth medium is inoculated with 1,000 bacteria, witch grow at rate of 15% each day. What is the population of the culture 6 days after inoculation?
Answers
Answer: the population of the culture 6 days after inoculation is 2313.
Step-by-step explanation:
The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
y = b(1 + r)^ t
Where
y represents the population after t days.
t represents the number of days.
b represents the initial population.
r represents rate of growth.
From the information given,
b = 1000
r = 15% = 15/100 = 0.15
t = 6 days
Therefore
y = 1000(1 + 0.15)^6
y = 1000(1.15)^6
y = 2313
How many minutes is it from 4:00 to 4:30
Answers
Answer:
30 minutes
Step-by-step explanation:
Just look at the minutes only. Since you need 4 o'clock to 4:30, its only 30 minutes.
Answer:
30 minutes
Step-by-step explanation:
All you have to do is subtract 4:30 and 4:00 and get 30 minutes.
Please help me idk this
Answers
Answer:
34.54 inches.
Step-by-step explanation:
The formula for the circumference of the circle is given as [tex]C=\pi d[/tex], where [tex]\pi[/tex] is rounded to 3.14 and d is the diameter of the circle, 11 inches. Simply plug these values into the equation for the circumference to get your answer:
[tex]C=\pi d\\C=(3.14)*(11)[/tex]
C = 34.54 inches
Answer:
34.54 inches
Step-by-step explanation:
C=πd
d=11
C = 11 * 3.14
C = 34.54 inches
A box contains 400 black pens and 50 red pens. Jose said the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1, P(not black) + P(not red) = 1. Do you agree with him? Complete the explanation to answer the question.
I (disagree/agree) with Jose that the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1.
Answers
Answer:
I agree with Jose that the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1.
Step-by-step explanation:
If we sum the probability of not black and probability of not red, we will get 1.
The probability of not black means probability of red i.e 50/450
The probability of not red means probability of black i.e 400/450.
When we add the probability, we get 1.
50/450 + 400/450 = 450/450 = 1
Invariably, the statement is same as finding probability of black and probability of red; just that the value are interchanged.
6.5% of people in the U.S. Have A- blood type. You randomly select 6 Americans and ask them if their blood type is A-. a) Find the probability that all 6 are type A-. b) Find the probability that at most 4 of them are type A-. c) Find the mean and standard deviation.
Answers
Answer:
a) 7.54189*10^-8
b) 0.99999999
c) E ( X ) = 0.39 , s ( X ) = 0.604
Step-by-step explanation:
Solution:-
- We will assume the proportion of people with A- blood group is independent and remains constant for a fairly small sample of n = 6 Americans selected at random.
- We will denote a random variable X = The number of americans out of 6 that have blood group type A-.
- The random variable is assumed to follow binomial distribution.
- The probability of success is the proportion of people in U.S that have blood group type A-, p = 0.065:
X ~ Bin ( 6 , 0.065 )
Where, r represents the number of americans out of selected 6 have blood group A-. The pmf of a binomial variate is given as:
P ( X = r ) = nCr * ( p ) ^r * ( 1 - p ) ^ ( n - r )
a) Find the probability that all 6 are type A-
- We will pmf given above and set r = 6. And evaluate the resulting probability:
P ( X = 6 ) = 6C6 * ( p )^6 * ( 1 - p ) ^ ( 0 )
= p^6
= ( 0.065 )^6
= 7.54189*10^-8
b) Find the probability that at most 4 of them are type A-
- We will pmf given above and evaluate the following expression:
P ( X ≤ 4 ) = 1 - P ( X = 5 ) - P ( X = 6 )
P ( X ≤ 4 ) = 1 - 6C5 * ( p )^5 * ( 1 - p ) ^ ( 1 ) - p^6
= 1 - 6*(0.065)^5 ( 0.935 ) - 0.065^6
= 1 - 6.50923*10^-8 - 7.54189*10^-8
= 0.99999999
c) Find the mean and standard deviation.
- The mean E ( X ) of the defined random variable distributed binomially is given by:
E ( X ) = n*p = 6*0.065 = 0.39 people
- The mean s( X ) of the defined random variable distributed binomially is given by:
s ( X ) = √n*p*q = √(6*0.065*0.935) = 0.604
Which name accurately describes the figure shown below and why?.
Answers
Answer:
the third answer is right
Step-by-step explanation:
its a rhombus because the 4 sides are of equal length and the opposite sides are parallel but there are no right angles.