Use either Gaussian elimination or Gauss-Jordan elimination to solve the given system or show that no solution exists. (If there is no solution, enter NO SOLUTION. If the system has an infinite number of solutions, use t for the parameter.) x1 + x2 + x3 = 0 x1 + x2 + 9x3 = 0
Answer:
x1 = t, x2 = -t and x3 = 0
Step-by-step explanation:
Given the system of equation
x1 + x2 + x3 = 0 .... 1
x1 + x2 + 9x3 = 0 .... 2
Subtract both equation
x3 - 9x3 = 0
-8x3 = 0
x3 = 0
Substitute x3 = 0 into equation 1
x1 + x2 + 0 = 0
x1+x2 = 0
x1 = -x2
Let t = x1
t = -x2
x2 = -t
Hence x1 = t, x2 = -t and x3 = 0
Determine the relationship between the two triangles and whether or not they can be proven to be congruent
Answer:
The two triangles are related by AAS, so the triangles are congruent.
Step-by-step explanation:
Two angles and a non-included side of one triangle are congruent to corresponding two angles and an included side in the other triangle. Therefore, we can conclude that the two triangles are related by the AAS Congruence Criterion. Hence, both triangles congruent to each other.
Installation of a certain hardware takes a random amount of time with a standard deviation of 5 minutes. A computer technician installs this hardware on 64 different computers, with the average installation time of 42 minutes. Compute a 95% confidence interval for the mean installation time. Explain your interval in context.
Answer:
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.025 = 0.975[/tex], so [tex]z = 1.96[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.96*\frac{5}{\sqrt{64}} = 1.225[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.225 = 40.775 minutes
The upper end of the interval is the sample mean added to M. So it is 42 + 1.225 = 43.225 minutes
The 95% confidence interval for the mean installation time is between 40.775 minutes and 43.225 minutes. This means that for all instalations, in different computers, we are 95% sure that the mean time for installation will be in this interval.
The 95% confidence interval for the mean installation time is (40.775, 43.225) and this can be determined by using the formula of margin of error.
Given :
Standard deviation is 5 minutes. Sample size is 64.Mean is 42 minutes.95% confidence interval.The following steps can be used in order to determine the 95% confidence interval for the mean installation time:
Step 1 - The formula of margin of error can be used in order to determine the 95% confidence interval.
[tex]M = z \times \dfrac{\sigma}{\sqrt{n} }[/tex]
where z is the z-score, [tex]\sigma[/tex] is the standard deviation, and the sample size is n.
Step 2 - Now, substitute the values of z, [tex]\sigma[/tex], and n in the above formula.
[tex]M = 1.96 \times \dfrac{5}{\sqrt{64} }[/tex]
[tex]M = 1.225[/tex]
Step 3 - So, the 95% confidence interval is given by (M - [tex]\mu[/tex], M + [tex]\mu[/tex]) that is (40.775, 43.225).
The 95% confidence interval for the mean installation time is (40.775, 43.225).
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4(y - 3) =
Use distributive property to complete the equivalent expression
Answer:
Step-by-step explanation:
4(y-3) = 4y - 4·3 = 4y - 12
The equivalent value of the expression is A = 4y - 12
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 4 ( y - 3)
On simplifying the equation , we get
A = 4 ( y - 3 )
So , the left hand side of the equation is equated to the right hand side by the value of A = 4 ( y - 3 )
Opening the parenthesis on both sides , we get
A = 4 ( y - 3 )
Using the distributive property , we get
A = 4 ( y ) - 4 ( 3 )
On further simplification , we get
A = 4y - 12
Taking the common factor as 4 , we get
A = 4 ( y - 3 ) = 4y - 12
Therefore , the value of A = 4y - 12
Hence , the expression is A = 4y - 12
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Solve the system of equations
2. The route used by a certain motorist in commuting to work contains two intersections with traffic signals. The probability that he must stop at the first signal is 0.36, the analogous probability for the second signal is 0.54, and the probability that he must stop at at least one of the two signals is 0.65. What is the probability that he must stop at exactly one signal?
Answer:
0.30
Step-by-step explanation:
Probability of stopping at first signal = 0.36 ;
P(stop 1) = P(x) = 0.36
Probability of stopping at second signal = 0.54;
P(stop 2) = P(y) = 0.54
Probability of stopping at atleast one of the two signals:
P(x U y) = 0.6
Stopping at both signals :
P(xny) = p(x) + p(y) - p(xUy)
P(xny) = 0.36 + 0.54 - 0.6
P(xny) = 0.3
Stopping at x but not y
P(x n y') = P(x) - P(xny) = 0.36 - 0.3 = 0.06
Stopping at y but not x
P(y n x') = P(y) - P(xny) = 0.54 - 0.3 = 0.24
Probability of stopping at exactly 1 signal :
P(x n y') or P(y n x') = 0.06 + 0.24 = 0.30
Jessica cuts a ribbon with a length of 12 inches into three pieces such that the length of
one piece is 3 1/2 inches and the lengths of the other two are the same. What is the length of each of the other two pieces?
A. 2 1/2 inches
B. 4 1/4 inches
C. 7 3/4 inches
D. 8 1/2 inches
Answer:
B 4 1/4
Step-by-step explanation:
Answer:
Its B. 4 1/4
Step-by-step explanation:
How it helps!
A mathematical phrase represented by numbers, variables, and operations is a(n)
pls help:)
Answer:
Expression
Step-by-step explanation:
Answer: Expression
Got this right!!!
Hope this helps!!!
I need help... plssss :))
Answer:
(1, -1), (1, -2), (2, -3), (2, -4)
NO
Step-by-step explanation:
✔️Each ordered pair is written as (input, output).
Thus, we would have the following:
(1, -1), (1, -2), (2, -3), (2, -4)
✔️This cannot be a function because every input value do not have exactly one output value related to it. A function should not have an input value related to more than one output value.
So, the answer is NO. It is not a function.
Peyton and her children went into a restaurant and where they sell drinks for $3 each
and tacos for $4 each. Peyton has $40 to spend and must buy at least 10 drinks and
tacos altogether. If Peyton decided to buy 4 drinks, determine all possible values for
the number of tacos that she could buy. Your answer should be a comma separated
list of values. If there are no possible solutions, submit an empty answer.
Answer:
7,6
Step-by-step explanation:
So in total Peyton must buy 10 items. Since she's already buying 4 drinks. We need to find the amount of tacos the max amount of tacos she can buy are 7 tacos and the minimum is 6 because if we bought less than 6 it wouldn't have met the criteria for 10 items minimum. And if we passed 7 tacos it would go past the limit of how much money Peyton has. I hope this helped:)
Find the circumference. Round to the nearest hundredth. Diameter= 16 feet
Step-by-step explanation:
[tex] = 2\pi \times r = 2\pi \times \frac{16}{2} = 2\pi \times 8 = 50.265 = 50.27[/tex]
Can someone plz do
A
C
D
Answer:
a) I think its 2n+1
c) I think its 6n+3
d) I think its 7n-4
To thank her five volunteers mai gave each of them the same number of stickers then she gave them each two more stickers altogether she gave them a total of 30 stickers
Answer: 4
Step-by-step explanation:
I got it right when i did my math
The equation which represents the given situation is 5(y + 2) = 30 and the value of y = 4.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given that,
Total number of volunteers = 5
Mai gave each of them the same number of stickers.
Let y be the number of stickers she gave to each of them.
Then she gave 2 more stickers to each of them.
Then number of stickers each has = y + 2
Total number of stickers = 30
5(y + 2) = 30
5y + 10 = 30
5y = 20
y = 4
Hence the number of stickers each one has is 4.
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A frog can hop a maximum speed of about 60 feet every 4 seconds. How far can he hop in 30 seconds
Answer:
its 180
Step-by-step explanation:
Answer:
450
Step-by-step explanation:
15x30=450
help me i need help help me help me
HELP HELP PLEASE IM BEGGING YOU HELP!
Answer:
22 * n + 4
Step-by-step explanation:
calculate the unit rate of change for each linear function using the formula. (4,9) (8,12) (16,18) (32,30)
Answer:
The unit rate of change is of [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
We are given a set of points (x,y).
To find the unit rate of change, we take two points, and divide the change in y by the change in x.
Points (4,9) and (8,12)
Change in y: 12 - 9 = 3
Change in x: 8 - 4 = 4
Unit rate of change: [tex]\frac{3}{4}[/tex]
A game decreased in price by 1/6
After the reduction it was priced at £75.
What was the original price of the game?
A rectangular room measures 21 feet by 28 feet with a 10-foot-high ceiling. The flooring is being replaced with carpeting that sells for $10.45 per square foot and entails a $149 installation fee. What is the total pricing for the carpeting with an 8.0% sales tax
9514 1404 393
Answer:
$6,797.09
Step-by-step explanation:
The area of the floor is ...
(21 ft)(28 ft) = 588 ft²
Then the cost of the carpet material is ...
(588 ft²)($10.45/ft²) = $6,144.60
The subtotal with installation fee is ...
$6,144.60 +149.00 = $6,293.60
Adding the sales tax multiplies this amount by 1 +8% = 1.08, so the final price is ...
1.08 × $6,293.60 = $6,797.09 . . . total price
Is either x = 6 or x = 8 a solution to 12 + x = 20? O A. Neither is.a solution. B. X = 6 is a solution, but x = 8 is not. C. X= 8 is a solution, but x = 6 is not D. They are both solutions. SUBMIT
Answer:
C. x = 8 is a solution, but x = 6 is not
Step-by-step explanation:
12 + 6 = 18
12 + 8 = 20
20 - 12 = 8
"Out of" is used when you want too divide . True or false ?
Answer:
I think it's true
Step-by-step explanation:
Answer: this is true
Step-by-step explanation:
The term out of is express as a fraction
Example:
1/2
This is 1 out of 2
Hope this helps ;)
What is the distance between point (8,4) and point (3,2) rounded to the nearest tenth?
Step-by-step explanation:
the answer of this question is 5.39
I have to find out what m
The cost of tuition at a 2 year school is $14,000 per academic year. Todd is eligible for $6,500 in financial aid to cover tuition each year. He will save money for one year to cover the remaining cost of tuition for his two years of school.
What is the minimum amount of money he needs to save each month?
$540
$625
$675
$1,250
Answer:
$625
Step-by-step explanation:
If Todd has to pay $14,000 in tuition for his school each year and uses $6,500 in financial aid each year all for 2 years, the money he needs to save can be modeled by:
2(-$14000 + $6500) + 2(12x) = 0.
x is the minimum amount of money he needs to save in order to cover this expense without debt.
Thus 2(-$14000 + $6500) + 2(12x) = 0 →
2(-$7500) + 24x = 0 → -$15000 + 24x = 0 →
24x = $15000 → x = $625
Answer:
$625
Step-by-step explanation:
If Todd has to pay $14,000 in tuition for his school each year and uses $6,500 in financial aid each year all for 2 years, the money he needs to save can be modeled by:
2(-$14000 + $6500) + 2(12x) = 0.
x is the minimum amount of money he needs to save in order to cover this expense without debt.
Thus 2(-$14000 + $6500) + 2(12x) = 0 →
2(-$7500) + 24x = 0 → -$15000 + 24x = 0 →
24x = $15000 → x = $625
the sum of 36 and 3c
Answer:
Step-by-step explanation:
just add 36 and 3
what minus 11 an that equalls 28
Answer:39
Step-by-step explanation:
If you add 28+11 you get 39 making 39-11=28
Need help ASAP
Will mark you brainlist
Answer:
Step-by-step explanation:
Brayden's car travels 37.1 miles per gallon.
Dylan's car travels 48.4 miles/(2 gallons) = 24.2 miles per gallon.
37.1 - 24.2 = 12.9
Dylan's car gets 12.9 miles per gallon less than Brayden's car.
The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 70 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what percentage of these commuting times are between 30 and 110 minutes
Answer:
At least 75% of these commuting times are between 30 and 110 minutes
Step-by-step explanation:
Chebyshev Theorem
The Chebyshev Theorem can also be applied to non-normal distribution. It states that:
At least 75% of the measures are within 2 standard deviations of the mean.
At least 89% of the measures are within 3 standard deviations of the mean.
An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].
In this question:
Mean of 70 minutes, standard deviation of 20 minutes.
Since nothing is known about the distribution, we use Chebyshev's Theorem.
What percentage of these commuting times are between 30 and 110 minutes
30 = 70 - 2*20
110 = 70 + 2*20
THis means that 30 and 110 minutes is within 2 standard deviations of the mean, which means that at least 75% of these commuting times are between 30 and 110 minutes
A cable TV company has a $35 installation fee and a $15 monthly rate. Write an equation in slope-intercept form to describe the cost of cable TV for any number of months. Use x for the number of months and y for the total cost.
Answer:
y=15x+35
Step-by-step explanation:
15 every month and 35 for instant charge
A cell phone company offers two plans to its subscribers. At the time new subscribers sign up, they are asked to provide some demographic information. The mean yearly income for a sample of 39 subscribers to Plan A is $55,575 with a standard deviation of $8,970. For a sample of 29 subscribers to Plan B, the mean income is $59,475 with a standard deviation of $6,942.
At the .025 significance level, is it reasonable to conclude the mean income of those selecting Plan B is larger? Hint: For the calculations, assume the Plan A as the first sample.
The test statistic is ______. (Negative amount should be indicated by a minus sign. Round your answer to 2 decimal places.)
The decision is _______
the null hypothesis that the mean of Plan B is larger.
The p-value is ______
(Round your answer to 2 decimal places.)
Answer:HI
Step-by-step explanation:HI
