By applying the Gaussian-Jordan algorithm to the given system of equations, we can find the reduced row-echelon form (rref) of the system. The resulting rref shows that the system is consistent, and the solution is x = 1, y = -28/17, and z = -28/17.
We start by writing the augmented matrix of the system:
[ -2 3 1 -2 ]
[ -3 1 3 -4 ]
[ 0 2 -1 0 ]
To obtain the rref, we perform row operations to eliminate the coefficients below and above the pivots. Our goal is to transform the matrix into the following form:
[ 1 0 0 a ]
[ 0 1 0 b ]
[ 0 0 1 c ]
First, we divide the first row by -2 to make the pivot in the first column 1:
[ 1 -3/2 -1/2 1 ]
[ -3 1 3 -4 ]
[ 0 2 -1 0 ]
Next, we perform row operations to eliminate the coefficient -3 in the second row:
[ 1 -3/2 -1/2 1 ]
[ 0 2/2 9/2 -7 ]
[ 0 2 -1 0 ]
Then, we divide the second row by 2 to make the pivot in the second column 1:
[ 1 -3/2 -1/2 1 ]
[ 0 1 9/4 -7/2 ]
[ 0 2 -1 0 ]
Now, we perform row operations to eliminate the coefficient 2 in the third row:
[ 1 -3/2 -1/2 1 ]
[ 0 1 9/4 -7/2 ]
[ 0 0 -17/4 7 ]
Finally, we divide the third row by -17/4 to make the pivot in the third column 1:
[ 1 -3/2 -1/2 1 ]
[ 0 1 9/4 -7/2 ]
[ 0 0 1 -28/17 ]
The resulting rref shows that the system is consistent, and the solution is x = 1, y = -28/17, and z = -28/17.
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Dani has only 1/2 of a cup of baking mix. She needs 3/4 of a cup for one batch of muffins. Which solution method shows how much of a batch of muffins Dani can make?
Answer:
Step-by-step explanation:
Dani has only 1/2 of a cup of baking mix. She needs 3/4 of a cup for one batch of muffins. Which solution method shows how much of a batch of muffins Dani can make?
Find the slope of the line
Answer:
2/3
Step-by-step explanation:
Answer:
Slope = -6
Step-by-step explanation:
simplify each of the following.
5.1.
[tex]2 sin(90 - x ) - cos(360 - x)[/tex]
Step-by-step explanation:
[tex]2 \sin(90 - x) - \cos(360 - x) [/tex]
[tex]2 \cos(x) - \cos(x) [/tex]
[tex] \cos(x) [/tex]
Will give crown for the RIGHT answer please do not mess around or give me weird links
Answer:
28
Step-by-step explanation:
HELP PLEASEEEE IT WOULD HELP ME OUT A LOT
Answer:
Step-by-step explanation:
Mikel is trying to save for college expenses. He has a job, but can only afford to put $20 per month aside. He has 4 years until he will need to pay for college. How much will he have saved by the end of 4 years?
Answer:
960
20 times 12 moths to get 240 then multiply that by 4 years and get 960 .
Step-by-step explanation:
sorry if wrong ]
have a good day /night
may i pleae have a branlliest .
20 x 12=240 x 4 =960
Answer:
960
Step-by-step explanation:
A bakery made 55 boxes of rolls. Each box holds 12 rolls. How many rolls were made in all?
Make an equation to represent the problem. Drag numbers and symbols to the lines.
55
12
+
X
Describe a situation that can be represented by the integer - 6
Answer:
One Chilly Night, Elijah Was Sleeping but Then Woke Up. He Realized It Was 45 Degrees According To the AC Monitor, So He Changed it To 70 Degrees But The Monitor Broke And Changed to -6 DEGREES!!
Step-by-step explanation:
A situation that can be represented by the integer - 6 was envisaged.
What are integers?An integer is a whole number (not a fractional number) that can be positive, negative, or zero.
One day maths teacher decided to take a random test
There were 16 questions each of 4 marks and 1 mark deduction for each wrong answer, with no penalties for non-attempt.
David was so good at guessing. He guessed all the 16 answers out of which 2 were correct and 14 were incorrect.
So, the total marks that David got = 4(2)-1(14) = 8-14 =-6
Thus, a situation that can be represented by the integer - 6 was envisaged.
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If 25% of a number is 65 and 60% of the same number is 156, find 35% of that number.
Answer:
35% of that number is 91.
Step-by-step explanation:
we need to first find 25% of what number equals 65.
65×100÷25 = 260
Then, if you use the same method again, 60% of 260 would be 156.
We know "that" number is 260, and all we need to do is find 35% of it.
35% of 260 = 91
Hope this helped :)
what two number have an absolute value of 12?
Answer:
The absolute value of 12, is 12...
Step-by-step explanation:
Answer:
-12
Step-by-step explanation:
The circumference of a circle is 127 cm. What is the area,
in
square centimeters?
Express your answer in terms of Pi.
Tuition for one year at Mount Tusk University is $13,400. Elijah has saved
$1,800 for this year's tuition. His parents have agreed to pay $5,000 this
year, and he earned a football scholarship for $3,500. Elijah hopes to earn
the rest of the money through his work-study job tutoring in the math
center. How much money does Elijah need to earn tutoring? (Enter the
quantity only)
Your answer
Answer:
The answer is 3,100
Step-by-step explanation:
If you subtract the 8,500 from his parents and his football scholarship you get 4,900 and then take the 1,800 from his saved money, You get what he still needs, which is 3,100.
In a survey of 3203 adults, 1447 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. Interpret the results. A 99% confidence interval for the population proportion is ??
Answer:
(0.4291, 0.4743)
Step-by-step explanation:
Using the relation :
p ± Zcritical * Sqrt[(p(1-p)) / n]
P = x / n =. 1447 / 3203 = 0.4517
1 - p = 0.5483
Zcritical at 99% = 2.575
Sqrt[(p(1-p)) / n] = sqrt(0.4517(0.5483)) / 3203) = 0.008793
p ± Zcritical * 0.008793
Lower boundary = 0.4517 - (2.575 * 0.008793) = 0.4291
Upper boundary = 0.4517 + (2.575 * 0.008793) = 0.4743
(0.4291, 0.4743)
Suppose you place a $35 bet on a horse with a 2:7 odds against winnning. Determine the winning payout for this horse.
The winning payout for the horse is $45
To determine the winning payout for the horse, you need to use the following formula:
Odds against winning: B / (A + B)
Betting amount: X Payout: X + (X * B / A)where A is the denominator of the odds and B is the numerator of the odds.
Here, the odds against winning are 2:7.
So, the denominator (A) is 7 and the numerator (B) is 2.
The betting amount is $35.
Plugging these values into the formula:
Payout = 35 + (35 * 2 / 7)
Payout = $45.
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selects a piece of candy and eats it (so it is NOT replaced!) Then selects a piece of candy and eats it. Find the probability of each event
Question:
There are 30 candies in a box, all identically shaped. 5 are filled with coconut, 10 with caramel, and 15 are solid chocolate.
You randomly select a piece of candy and eat it (so it is NOT replaced!), then select a second piece. Find the probability of each event
(a) The probability of selecting two solid chocolates in a row.
(b) The probability of selecting a caramel and then a coconut candy.
Answer:
[tex](a)[/tex] [tex]P(Chocolates) = \frac{7}{29}[/tex]
[tex](b)[/tex] [tex]P(Caramel\ and\ Coconut) = \frac{5}{87}[/tex]
Step-by-step explanation:
Given
[tex]Coconut = 5[/tex]
[tex]Caramel = 10[/tex]
[tex]Chocolate = 15[/tex]
[tex]Total = 30[/tex]
For probabilities without replacement, 1 is subtracted after the first selection.
So, we have:
Solving (a): Two solid chocolates
This is calculated as:
[tex]P(Chocolates) = P(First\ Chocolate) * P(Second\ Chocolate)[/tex]
[tex]P(Chocolates) = \frac{n(Chocolate)}{Total} * \frac{n(Chocolate) - 1}{Total - 1}[/tex]
[tex]P(Chocolates) = \frac{15}{30} * \frac{15 - 1}{30 - 1}[/tex]
[tex]P(Chocolates) = \frac{15}{30} * \frac{14}{29}[/tex]
[tex]P(Chocolates) = \frac{1}{2} * \frac{14}{29}[/tex]
[tex]P(Chocolates) = \frac{7}{29}[/tex]
Solving (a): Caramel and Coconut
This is calculated as:
[tex]P(Caramel\ and\ Coconut) = P(Caramel) * P(Coconut)[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{n(Caramel)}{Total} * \frac{n(Coconut)}{Total - 1}[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{10}{30} * \frac{5}{30- 1}[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{10}{30} * \frac{5}{29}[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{1}{3} * \frac{5}{29}[/tex]
[tex]P(Caramel\ and\ Coconut) = \frac{5}{87}[/tex]
Given: ΔWXY is isosceles with legs WX and WY; ΔWVZ is isosceles with legs WV and WZ. Prove: ΔWXY ~ ΔWVZ. Complete the steps of the proof.
a. ASA (Angle-Side-Angle)
b. SAS (Side-Angle-Side)
c. SSS (Side-Side-Side)
d. CPCTC (Corresponding Parts of Congruent Triangles are Congruent)
We have proven that ΔWXY is similar to ΔWVZ using the ASA criterion.
We have,
To prove that ΔWXY is similar to ΔWVZ, we can use the ASA (Angle-Side-Angle) criterion.
Here are the steps of the proof:
Proof:
- Given: ΔWXY is isosceles with legs WX and WY; ΔWVZ is isosceles with legs WV and WZ.
Since ΔWXY is isosceles, we have WX ≅ WY. (Given)
Since ΔWVZ is isosceles, we have WV ≅ WZ. (Given)
We also know that ΔWXY and ΔWVZ share the common side segment WZ. (Common side)
Let's consider the angles: ∠WXY and ∠WVZ. Since ΔWXY is isosceles, we have ∠WXY ≅ ∠WYX. (Isosceles triangle property)
Similarly, since ΔWVZ is isosceles, we have ∠WVZ ≅ ∠WZV. (Isosceles triangle property)
Now, we have two pairs of congruent angles: ∠WXY ≅ ∠WYX and ∠WVZ ≅ ∠WZV.
We already know that WX ≅ WY and WV ≅ WZ.
By the ASA criterion, if two pairs of corresponding angles and the included side are congruent, then the triangles are similar.
Applying the ASA criterion, we conclude that ΔWXY ~ ΔWVZ. (Angle-Side-Angle)
Therefore,
We have proven that ΔWXY is similar to ΔWVZ using the ASA criterion.
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using the equation y=x , what would be the value of y if the value of x is 2
Answer:
y = 2
Step-by-step explanation:
y = x
x = 2
Plug in the given value.
y = (2)
This is already simplified.
Therefore, when x = 2, y = 2.
Hope this helps!
Solve the system using substitution. Show all work.
( 4х + 5y = 7
у = 3х + 9
Answer:
(4x+5y=7
y=3x+9
4x+5(3x+9)=7
4x+15x+45=7
19x=7-45
19x= -38
19×/19=-38/19
x= -2
whlie y=3x+9
y=3(-2)+9
y= -6+9
y=3 end solution
x= -2,y= 3
Jasmine scored a 85 on the last math test. The class average was a 76 with a standard deviation of 4.5. So, XN(76,4,5) Jasmine's Z-score is This tells you that 85 is standard deviations to the left or right) of the mean, 14. The number of problems on all math exams are normal distributed. What is the probability a randomly selected math exam has fewer than 15 questions if the mean is 20 questions with a standard deviation of 2.5? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary. A city has around 890 thousand people. There are 123 parks in this city. What is the number of parks per capita in this city? Write your answer in scientific notation.
Jasmine's Z-score is 2. The number of parks per capita in the city is [tex]1.38 * 10^-4[/tex] in scientific notation.
To calculate Jasmine's Z-score, we can use the formula:
Z = (X - μ) / σ
where X is the individual score (85), μ is the mean (76), and σ is the standard deviation (4.5).
Z = (85 - 76) / 4.5
Z = 9 / 4.5
Z = 2
Since Jasmine's Z-score is 2, this tells us that her score of 85 is 2 standard deviations to the right of the mean.
Now let's calculate the probability of randomly selecting a math exam with fewer than 15 questions using the mean of 20 and a standard deviation of 2.5.
To apply the empirical rule, we need to determine how many standard deviations 15 is away from the mean.
Z = (X - μ) / σ
Z = (15 - 20) / 2.5
Z = -5 / 2.5
Z = -2
Since 15 is 2 standard deviations to the left of the mean, we can use the empirical rule to estimate the probability.
According to the empirical rule:
The data is within one standard deviation of the mean for about 68% of the time.
The data is within 2 standard deviations of the mean for about 95% of the time.
99.7% of the data are contained within a 3 standard deviation range around the mean.
Since 15 is beyond 2 standard deviations to the left, the probability of randomly selecting a math exam with fewer than 15 questions would be very close to 0. In this case, we can assume it's effectively 0%.
Now let's calculate the number of parks per capita in the city with 890,000 people and 123 parks.
Number of parks per capita = Number of parks / Population
Number of parks per capita = 123 / 890,000
To write the answer in scientific notation, we can express 890,000 as 8.9 x 10^5:
Number of parks per capita =[tex]123 / (8.9 * 10^5)[/tex]
Calculating the result:
Number of parks per capita =[tex]1.38 * 10^-4[/tex]
Therefore, the number of parks per capita in the city is[tex]1.38 * 10^-4[/tex] in scientific notation.
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can you guys help me please as much as you can ^^
Answer:
Step-by-step explanation:
m<1 = 50
m<2 = 22
m<3 = 108
m<4 = 50
m<5 = 65
m<6 = 50
m<7 = 43
m<8 = 65
m<9 = 75
m<10 = 18
m<11 = 25
m<12 = 40
m<13 = 115
m<14 = 65
m15 = 115
Find the value of the expression below
when x =3/4
4x² + 8x - 5
Answer:
4x² + 8x - 5
= 4(3/4)² + 8(3/4) - 5
= 4 × 9/16 + 24/4 - 5
= 36/16 + 24/4 - 5
= 9/4 + 6 - 5
= 9/4 +1
= 3.25
Step-by-step explanation:
Hope it helps!!
"6 less than the quotient of a number and 5"
Answer:
[tex]\frac{n}{5} - 6[/tex]
Step-by-step explanation:
Quotient of a number and 5 means n/5
6 less than n/5 means n/5 - 6
Answer:
the product of a triple a number and 19
Step-by-step explanation:
but i'm not 100% sure so don't quote me
Please help me, I’m struggling.
A: 116 square cm
B: 106 square cm
C: 143 square cm
Answer:
The answer is A. 116 square cm
Step-by-step explanation:
What is the value of the output when the
input is 18?
Answer:
Any number less than greater than or equal to 18
Step-by-step explanation:
the functions y=x^2+ (c/x^2) are all solutions of equation: xy′ 2y=4x^2, (x>0). find the constant c which produces a solution which also satisfies the initial condition y(6)=4. c= ______--
The constant c that produces a solution satisfying the initial condition y(6) = 4 is c = 24.
To find the constant c that satisfies the given equation and the initial condition, we need to substitute the function y = x² + (c/x²) into the differential equation and solve for c. The given equation is xy' * 2y = 4x².
First, we differentiate y with respect to x to find y',
y = x² + (c/x²)
y' = 2x - (2c/x³)
Now we substitute y and y' into the differential equation,
xy' * 2y = 4x²
x(2x - (2c/x³)) * 2(x² + (c/x²)) = 4x²
Simplifying,
2x³ - 2cx + 4c = 4x²
Rearranging,
2x³ - 4x² - 2cx + 4c = 0
Now we substitute x = 6 and y = 4 (from the initial condition y(6) = 4) into the equation,
2(6)³ - 4(6)² - 2(6)c + 4c = 0
432 - 144 - 12c + 4c = 0
288 - 8c = 0
8c = 288
c = 36
Therefore, the constant c that produces a solution satisfying the initial condition y(6) = 4 is c = 36.
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maths equation : solve (2 - x)² < 4/25
Answer:
8/5 < x < 12/5
Step-by-step explanation:
(2 - x)² < 4/25
2 - x < ±2/5
2 - x < 2/5
-x < -8/5
x > 8/5
2 - x > -2/5
-x > -12/5
x < 12/5
Therefore, your answer is 8/5 < x < 12/5
Which would be the next step? Does anyone know? Please, help.
Answer:
∠DAB = ∠DBA
Then AD=DB from above statement
This XP set is worth a maximum points 1) As of 5/12/22. 72.7% of the residents of Washington state were fully vaccinated against CV19. Also, the population of our state is about 74 million people. a) Suppose that random samples of size n 50 are selected from this state's population. Let X represent the number people in each sample that are fully vaccinated against CV19 The variable X has an approximately Binomial distribution, with n 50 and D 727 Using the special Binomial formulas, compute the mean and the sigma of Round each value to the nearest tenth b) Refer to part . Which specific values of this variable X are within 3- sigma of its mean value? (OW, what are the common numbers of fully vaccinated people you'd expect to find in samples of this size, given the 72.7% fully vaccinated percentage?) c) Refer to part a. Use your calculator / technology like the "binompat and "binomcd commands on the TI-84) to help answer the following questions Report each probability correct to four decimal places Find the probability that one of these samples has exactly 35 fully vaccinated people in ite find the value of PX - 3571 Is this an unusual event using the 5% probability criterion? 10 Find the probability that one of these samples has 25 or fewer fully vaccinated people in it be find the value of PX $25)) is this an unusual event, using the 5% probability criterion? 30 IP 3: DO %: . $ 4 % 5 . # 3 $ 4 % 5 & 7 6 > 0 00 9 E R T T Y U 0 P D F G H J I KL < < C V B N M 1
Random samples of size 50 are taken from this population, and the number of fully vaccinated individuals in each sample, represented by the variable X, follows an approximately binomial distribution with n = 50 and p = 0.727.
(a) Using the binomial formulas, the mean (μ) of X is calculated as np, which is 50 * 0.727 = 36.4, rounded to the nearest tenth. The standard deviation (σ) is given by the square root of np(1-p), which becomes √(50 * 0.727 * 0.273) ≈ 4.1.(b) To determine the values within 3 sigma of the mean, we calculate 3 times the standard deviation (3σ) and find the range around the mean: 36.4 ± 3 * 4.1, resulting in the range of approximately 24.1 to 48.7. Therefore, the common numbers of fully vaccinated people expected in samples of this size, given the 72.7% vaccination rate, would fall within this range.(c) By using appropriate commands on a calculator or technology, the following probabilities can be determined:
The probability of one sample having exactly 35 fully vaccinated people is obtained from the binomial distribution as P(X = 35), which can be calculated using the binompdf command.
The value of P(X ≤ 25) can be found using the binomcdf command, representing the probability of having 25 or fewer fully vaccinated people in a sample. The probabilities should be reported to four decimal places for accuracy.
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Construct an equation for a function with a zero at -2 and a double zero at 3.
Step-by-step explanation:
feeling the compa
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Shirley is saving money to buy a computer.
• The computer she will buy costs $1,200.00
• She has already saved $300.00
Shirley will save $60.00 per week until she has enough money to buy
the computer.
Answer:
It will take her 15 weeks to have enough money for the computer.
Step-by-step explanation:
$1200 - $300 = $900
900 divided by 60 gives you 15
Therefor, it'll take Shirley 15 weeks to save $1200.