Step-by-step explanation:
x²+12x=40
(x+6)²-6²-40=0
(x+6)²-76 = 0
.4.1 Here are the data from Exercise 2.3.10 on the num-ber of virus-resistant bacteria in each of 10 aliquots: 14 14 15 26 13 16 21 20 15 13 (a) Determine the median and the quartiles. (b) Determine the interquartile range. (c) How large would an observati
Answer:
(a)
[tex]Q_1 = 14[/tex]
[tex]Median = 15[/tex]
[tex]Q_3 = 20[/tex]
(b) [tex]IQR = 6[/tex]
Step-by-step explanation:
Given
[tex]14\ 14\ 15\ 26\ 13\ 16\ 21\ 20\ 15\ 13[/tex]
[tex]n = 10[/tex]
Solving (a): Median and the quartiles
Start by sorting the data
[tex]Sorted: 13\ 13\ 14\ 14\ 15\ 15\ 16\ 20\ 21\ 26[/tex]
The median position is:
[tex]Median = \frac{n + 1}{2}[/tex]
[tex]Median = \frac{10 + 1}{2} = \frac{11}{2} = 5.5th[/tex]
This implies that the median is the average of the 5th and the 6th data;
So;
[tex]Median = \frac{15+15}{2} = \frac{30}{2} = 15[/tex]
Split the dataset into two halves to get the quartiles
[tex]Lower: 13\ 13\ 14\ 14\ 15\[/tex]
[tex]Upper: 15\ 16\ 20\ 21\ 26[/tex]
The quartiles are the middle items of each half.
So:
[tex]Lower: 13\ 13\ 14\ 14\ 15\[/tex]
[tex]Q_1 = 14[/tex] ---- 14 is the middle item
[tex]Upper: 15\ 16\ 20\ 21\ 26[/tex]
[tex]Q_3 = 20[/tex] ---- 20 is the middle item
Solving (b): The interquartile range (IQR)
This is calculated as:
[tex]IQR = Q_3 - Q_1[/tex]
[tex]IQR = 20 - 14[/tex]
[tex]IQR = 6[/tex]
Solving (c): Incomplete details
Please help:
Given: ∠4 is congruent to ∠2
Prove: ∠3 and ∠1 are supplementary
Statements and Reasons
Answer:
See Below.
Step-by-step explanation:
We can write a two-column proof.
Statements: Reasons:
[tex]\displaystyle 1)\, \angle 4\cong \angle 2[/tex] Given
[tex]\displaystyle 2)\, \angle 3 \cong \angle 4[/tex] Vertical Angles are Congruent
[tex]\displaystyle 3) \, \angle 1 + \angle 2 = 180[/tex] Linear Pair
[tex]\displaystyle 4)\, \angle 1 + \angle 4 = 180[/tex] Substitution
[tex]\displaystyle 5) \, \angle 1 + \angle 3 = 180[/tex] Substitution
[tex]\displaystyle 6) \, \text{$\angle 3$ and $\angle 1$ are supplementary}[/tex] Definition of Supplementary Angles
g A. (Points: 7) Compute (without using a calculator) 241^257 mod 12 B. (Points: 3) Compute Z*20 C. (Points: 6) Find the multiplicative inverse of 7 in Z19
Answer:
[tex]241^{257}\ mod\ 12 =1[/tex]
[tex]7 * 20 = 140[/tex]
[tex]\frac{1}{700}[/tex]
Step-by-step explanation:
Solving (a): 241^257 mod 12
To do this, we simply calculate [tex]241\ mod\ 12[/tex]
Because [tex]a\ mod\ b = a^n\ mod\ b[/tex]
The highest number less than or equal to 241 that is divisible by 12 is 240; So:
[tex]241\ mod\ 12 = 241- 240[/tex]
[tex]241\ mod\ 12 =1[/tex]
Hence:
[tex]241^{257}\ mod\ 12 =1[/tex]
Solving (b): 7 * 20
[tex]7 * 20 = 140[/tex]
Solving (c): Multiplicative inverse of 7 in 719
The position of 7 in 719 is 700
So, the required inverse is 1/700 ---- i.e. we simply divide 1 by the number
For what value of the variable : is the value of 9-y twice as much as the value of y?
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]y = 3[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{"The value of 9-y twice as much as the value of y" can be written as:}}\\\\9-y = 2y[/tex]
⸻⸻⸻⸻
[tex]\boxed{\text{Solving for 'y'...}}\\\\9-y=2y\\------------\\\rightarrow 9 -y + y = 2y + y\\\\\rightarrow 9 = 3y\\\\\rightarrow \frac{9=3y}{3}\\\\\rightarrow 3 = y\\\\\rightarrow \boxed{y = 3}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Which functions have a range of {y e R | -
Answer:
The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values.
Step-by-step explanation:
idontknow
According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0746 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 318 independent returns from this year, what is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Answer:
0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Step-by-step explanation:
We use the normal approximation to the binomial to solve this question.
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
Approximately 0.0746 of the tax returns filed are fraudulent or will contain errors.
This means that [tex]p = 0.0746[/tex]
Random sample of 318 independent returns
This means that [tex]n = 318[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 318*0.0746 = 23.7228[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{318*0.0746*0.9254} = 4.6854[/tex]
What is the probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS?
Using continuity correction, this is [tex]P(X \geq 23 - 0.5) = P(X \geq 22.5)[/tex], which is 1 subtracted by the p-value of Z when X = 22.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22.5 - 23.7228}{4.6854}[/tex]
[tex]Z = -0.26[/tex]
[tex]Z = -0.26[/tex] has a p-value of 0.3974.
1 - 0.3974 = 0.6026
0.6026 = 60.26% probability that at least 23 will be fraudulent or will contain errors that are purposely made to cheat the IRS
Which graph shows the solution to this system of linear inequalities?
y<-1/3x+2
y<_2x-3
Answer:
C
Step-by-step explanation:
Since all the graphs have the same line, you’re just looking for the correct shaded region. Since for both equations you want the shaded region to be less than the line, answer c solves the inequality.
Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.
Week Sales (1,000s of gallons)
1 17
2 22
3 20
4 24
5 18
6 17
7 21
8 19
9 23
10 21
11 16
12 23
(a) Using a weight of
1
2
for the most recent observation,
1
3
for the second most recent observation, and
1
6
for third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.)
Compute four-week and five-week moving averages for the time series.
Week Time Series Moving
Value Average Forecast
1 17
2 22
3 20
4 24
5 18
6 17
7 21
8 19
9 23
10 21
11 16
12 23
(b) Compute the MSE for the four-week moving average forecasts. (Round your answer to two decimal places.)
Compute the MSE for the five-week moving average forecasts. (Round your answer to two decimal places.)
(c) What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? MSE for the three-week moving average is 11.12.
Answer:
Use suitable identity to find the product (3-2x)(3+2x).Find the remainder when x³+ 3x²+3x+1 is divided by x+1.On a plane surface we can find straight lines.8√15 + 2√3The decimal form of 36 100(a-b)³ = a ³- ........ 3 + 3ab²-b³In the Cartesian plane the horizontal line is called .........The coefficient of x² in 2-x²+ x³ is -1.√225 is an irrational number.The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).
Pls someone help these answers are on chegg so if u have a subscription pls answer these ill make u brainliest ! Below is a table representing data, measuring the percentage of various
groups owning a home
Percentage owning a
home
1st Generation
Hispanic Americans
N=899
43
50
2nd Generation
Hispanic Americans
N=351
1st Generation Asian
Americans N=2,684
2nd Generation Asian
Americans N=566
58
51
Test whether there is a significant difference in the proportion of
homeowners between 1st and 2nd generation Hispanic Americans. Set alpha at .05
The obtained Z test is ?
The probability of obtaining
this Z-test statistic is ?
This is _? Than our alpha level. Therefore we ___? The null hypothesis and conclude that there ____? A significant difference in the proportion of homeowners between 1 st generation and 2nd generation hispanic americans.
The table is not clear, so i have attached it.
Answer:
z statistic is -2.26
This is less than our alpha level,therefore we reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners between first generation and second generation Hispanic Americans
Step-by-step explanation:
From the attached table, we can see that;
first-generation hispanic americans; (N = 899 and percentage = 43%
second-generation hispanic americans; N = 351 and percentage = 50%
first-generation asian americans; (N = 2,684 and percentage = 58%
second-generation asian americans; N = 566 and percentage = 51%
Z-score formula in this case is;
z = (p1^ - p2^)/(√(p^(1 - p^)((1/n1) + (1/n2))
Where;
p^ = (p1 + p2)/(n1 + n2)
For, hispanic americans we have;
p1^ = 0.43 × 899 = 386.57
p2^ = 0.5 × 351 = 175.5
p^ = (386.57 + 175.5)/(899 + 351)
p^ = 0.45
Thus;
z = (0.43 - 0.5)/(√(0.45(1 - 0.45)((1/899) + (1/351))
z = -2.26
From z-distribution table, we have;
P-value = 0.01191
Since we have 2 samples, then probability = 2 × 0.01191 = 0.02382
This is less than our alpha level of 0.05,therefore we reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners between first generation and second generation Hispanic Americans.
Suppose 58% of the population has a retirement account. If a random sample of size 570 is selected, what is the probability that the proportion of persons with a retirement account will be less than 57%
Answer:
The probability that the proportion of persons with a retirement account will be less than 57%=31.561%
Step-by-step explanation:
We are given that
n=570
p=58%=0.58
We have to find the probability that the proportion of persons with a retirement account will be less than 57%.
q=1-p=1-0.58=0.42
By takin normal approximation to binomial then sampling distribution of sample proportion follow normal distribution.
Therefore,[tex]\hat{p}\sim N(\mu,\sigma^2)[/tex]
[tex]\mu_{\hat{p}}=p=0.58[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\frac{p(1-p)}{n}}[/tex]
[tex]\sigma_{\hat{p}}=\sqrt{\frac{0.58\times 0.42}{570}}[/tex]
[tex]\sigma_{\hat{p}}=0.02067[/tex]
Now,
[tex]P(\hat{p}<0.57)=P(\frac{\hat{p}-\mu_{\hat{p}}}{\sigma_{\hat{p}}}<\frac{0.57-0.58}{0.02067})[/tex]
[tex]P(\hat{p}<0.57)=P(Z<-0.483)[/tex]
[tex]P(\hat{p}<0.57)=0.31561\times 100[/tex]
[tex]P(\hat{p}<0.57)[/tex]=31.561%
Hence, the probability that the proportion of persons with a retirement account will be less than 57%=31.561%
True or False: The points T, Z, W and U coplanar in the following image
Answer:
False
Step-by-step explanation:
Points T & W are coplanar. Point Z is on both planes, so it depends on how you see it. HOWEVER, Point U is on another plane (plane Q to be exact), so points T, Z, W, and U are NOT coplanar.
Hope it helps (●'◡'●)
Tracy leaves the beach at 3:00 p.m. and drives along the highway at 55 mph. One hour later, Quinn leaves the same beach and drives along the same highway in the same direction at 65 mph. How many hours will it take Quinn to catch up to Tracy?
10 hours
6.5 hours
8.5 hours
15 hours
Answer:
8.5 hours
Step-by-step explanation:
55 x 9.5 (add extra hour) = 552.5 miles
65 x 8.5 (actual time spent) = 552.5 miles
The time taken for Quinn to catch up to Tracy during the journey is 8.5 hours.
Time of motion of Tracy and QuinnThe time of motion of tracy and quinn is determined by using the following equation as shown below;
For tracy, d = 55(t + 1)
For Quinn, d = 65t
where;
55(t + 1) = 65t
55t + 55 = 65t
55 = 10t
t = 55/10
t = 5.5 hours
3 hour from noon + 5.5 hours = 8.5 hours
Learn more about time of motion here: https://brainly.com/question/2364404
#SPJ2
A traveling salesman figures it costs 19 cents for every mile he drives his car. How much does it cost him (in dollars) a week to drive his car if he travels 340 miles a week?
Answer:
$64.60
Step-by-step explanation:
$0.19 x 340 = $64.6, which simplifies to $64.60.
Answer:
$64.60
Step-by-step explanation:
Just multiply 340 by 19, then convert into American Currency.
Find the length of an arc of a circle with a 8-cm radius associated with a central angle of 240 degrees. Give your answer in exact and approximate form to the nearest hundredth.
Answer:
l = 1920 cm
Step-by-step explanation:
Given that,
The radius of circle, r = 8 cm
The central angle is 240 degrees
We need to find the length of the arc. We know that,
[tex]l=r\theta[/tex]
Where
l is the length of the arc
So,
[tex]l=8\times 240[/tex]
[tex]\implies l=1920\ cm[/tex]
so, the length of the arc is equal to 1920 cm.
Find the equation and check answer of (−8x=−2x−8)
Answer:
x = 4/3
Step-by-step explanation:
you need to move -8x to the right side.0=6x-8then, you need to move -8 to the left side.8=6xyou can get answer!x = 4/3
A large on-demand, video streaming company is designing a large-scale survey to determine the mean amount of time corporate executives watch on-demand television. A small pilot survey of 10 executives indicated that the mean time per week is 12 hours, with a standard deviation of 3 hours. The estimate of the mean viewing time should be within 0.25 hour. The 95% level of confidence is to be used. How many executives should be surveyed? (Use z Distribution Table.)
How many executives should be surveyed? (Round the final answer to the next whole number.)
Answer:
554 executives should be surveyed.
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 Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
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.
Standard deviation of 3 hours.
This means that [tex]\sigma = 3[/tex]
The 95% level of confidence is to be used. How many executives should be surveyed?
n executives should be surveyed, and n is found with [tex]M = 0.25[/tex]. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.25 = 1.96\frac{3}{\sqrt{n}}[/tex]
[tex]0.25\sqrt{n} = 1.96*3[/tex]
[tex]\sqrt{n} = \frac{1.96*3}{0.25}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*3}{0.25})^2[/tex]
[tex]n = 553.2[/tex]
Rounding up:
554 executives should be surveyed.
Explain how to divide a decimal by a decimal
Answer:
To divide a decimal by another decimal:
Move the decimal point in the divisor to the right until it is a whole number.
Move the decimal point in the dividend to the right by the same number of places as the decimal point was moved to make the divisor a whole number.
Then divide the new dividend by the new divisor
Step-by-step explanation:
see in the example
Exponential and Alogarithmic Functions - Alegebra question
Answer:
Step-by-step explanation:
f(x)=3x-7 and g(x)=(1/3)x+7 are inverses of each other.
.True
.False
Answer:
False
Step-by-step explanation:
Sorry for the lat reply hopefully you still have that question ready. But basically in order for these equations to be considered inverses of one another it has to map its domain value and switch it to the range value and in this case it does not match the inverse when graphed.
Solve this
4 X (10 - 3+2)
Answer:
36
Step-by-step explanation:
10-3=7+2=9
4×9=36
36 is the answer
1. Using the factorisation method, simplify the following √32
Answer:
[tex]4 \sqrt{2} [/tex]
[tex] \sqrt{32} = \sqrt{16 \times 2} = 4 \sqrt{2} [/tex]
A rectangular field 50 meters in width and 120 meters in length is divided into two fields by a diagonal line. What is the length of fence (in meters) required to enclosed one of these fields?
A-130
B-170
C-180
D-200
E-300
Answer:
E. 300
Step-by-step explanation:
A rectangle split in half diagonally yields 2 right triangles.
((For this problem, you are probably supposed to use the pythagorean theorem to find the diagonal length, and then calculate perimeter (length of fence around triangular field). In other words:
(sqrt( (50m)^2 + (120m)^2 )) + 50m + 120m)
))
By definition, the hypotenuse (diagonal) is the longest side.
This means that it must be longer than 120m.
If you add the 2 sides (50m + 120m), you get 170m.
Since the third side has to be longer than 120m, the answer _must_ be over 290m (170m + 120m).
300m is the only answer that fits.
Thane Company is interested in establishing the relationship between electricity costs and machine hours. Data have been collected and a regression analysis prepared using Excel. The monthly data and the regression output follow:
Month Machine Hours Electricity Costs
January 2,300 $ 19,100
February 2,700 $ 22,400
March 1,700 $ 14,200
April 2,900 $ 24,400
May 3,600 $ 28,950
June 3,100 $ 23,400
July 3,900 $ 25,450
August 3,300 $ 23,450
September 1,800 $ 16,900
October 3,500 $ 27,400
November 4,500 $ 32,400
December 4,000 $ 28,450
Summary Output
Regression Statistics
Multiple R 0.957
R Square 0.917
Adjusted R2 0.908
Standard Error 1,586.26
Observations 12.00
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 5,970.52 1,766.77 3.38 0.01 2,033.90 9,907.13
Machine Hours 5.76 0.55 10.49 0.00 4.54 6.98
The percent of the total variance that can be explained by the regression is:
Answer:
0.924
Step-by-step explanation:
R² = 0.854
R = √0.854
R = 0.924
Hence, the correlation Coefficient of electricity tarrif is 0.924 ; this correlation Coefficient value, depicts a strong positive correlation between machine hours and cost of electricity. And can he interpreted to mean that ; Electricity tarrif increases as machine hours increases and also decreases as machine hours decreases.
Please I need help!!!!!!!!
Answer:
10 is the correct answer
Answer:
Go with the third option 10!
i hope this helped!
simple equation:
6m=12
Step-by-step explanation:
Divide both sides of the equation by the same term6m/6 =12/6
Cancel terms that are in both the numerator and denominatorDivide the numbersm=2
Answer:
m=2
Step-by-step explanation:
Divide 6 on both sides
6m / 6 = 12/6
m= 12/6 = 2
So, m=2
Verification:
LHS = 6m m=2
6 * 2 = 12
RHS = 12
Both the LHS and RHS are same, so our answer is correct
Verify that the equation is an identity.
Step-by-step explanation:
We need to prove that ,
cot x / csc x - csc x / cot x = - tan x sec x .
LHS :-
> cot x / csc x - csc x / cot x
> cos x / sin x ÷ csc x - sin x × csc x / cos x
> cosx - 1/ cos x
> cos² x - 1 / cos x
> - sin²x / cosx
> -sin x / cos x × sin x
> -tan x sin x
= RHS
Hence Proved !
95, 86, 78, 71, 65, 60 _____
Answer:
hello there here is your answer
51 is your next term.
Step-by-step explanation:
you are subtracting 9 from each number
95-9= 86
86-9=78
78-9=65
65-9=60
60-9=51
so on and so on
Hope this help
have a good day
bye
Step-by-step explanation:
[tex]here \: is \: your \: solution: - \\ \\ given \: number \: = 95.86.78.71.65.60 \\ \\ = > 95 - 9 = 86 \\ \\ = > 86 - 8 = 78 \\ \\ = > 78 - 7 = 71 \\ \\ = > 71 - 6 = 65 \\ \\ = > 65 - 5 = 60 \\ \\ \: now \: follow \: the \: sequence \: \\ \\ subtract \: 4 \: from \: 60 \\ \\ = > 60 - 4 = 56 \\ \\ = > \: \: 56 \: \:( ANSWER✓✓✓)[/tex]
Q.No.4. Ali is hiking on the hill, whose height is given by f(u,v)=n^2 e^((u+n)/(v+n)). Currently, he is positioned at point (3,5). Find the direction at which he moves down the hills quickly. (5 points) Where n is the product of first and second digit of your arid number e.g. 19-arid-435 take n=4x3=12
Answer:
///////
Step-by-step explanation:
Solve the system of equations below.
x + y = 7
2x + 3y = 16
A. (5, 2)
B. (2, 5)
C. (3, 4)
D. (4, 3)
Answer:
A. (5, 2)
Step-by-step explanation:
Given
[tex]\begin{cases}x+y=7,\\2x+3y=16\end{cases}[/tex],
Multiply the first equation by 2, then subtract both equations to get rid of any terms with [tex]x[/tex]:
[tex]\begin{cases}2(x+y)=2(7),\\2x+3y=16\end{cases}\\\implies 2x+2y=14,\\2x+3y=16,\\2x-2x+2y-3y=14-16,\\-y=-2,\\y=\boxed{2}[/tex]
Substitute [tex]y=2[/tex] into any equation to solve for [tex]x[/tex]:
[tex]x+y=7,\\x+2=7,\\x=7-2=\boxed{5}[/tex]
Since coordinates are written as (x, y), the solution to this system of equations is (5, 2).
Answer:
A. ( 5 , 2 )
Step-by-step explanation:
solve by elimination methodIn order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.
x + y = 7, 2x + 3y = 16To make x and 2x equal, multiply all terms on each side of the first equation by 2 and all terms on each side of the second by 1.
2x + 2y = 2 × 7, 2x + 3y = 16Simplify.
2x + 2y = 14, 2x+3y=16Subtract 2x+3y=16 from 2x+2y=14 by subtracting like terms on each side of the equal sign.
2x - 2x + 2y - 3y = 14 - 16Add 2x to -2x. Terms 2x and -2x cancel out, leaving an equation with only one variable that can be solved.
2y - 3y = 14 - 16Add 2y to -3y.
-y = 14 - 16Add 14 to -16.
-y = -2Divide both sides by -1.
y = 2Substitute 2 for y in 2x+3y=16. Because the resulting equation contains only one variable, you can solve for x directly.
2x + 3 × 2 = 16Multiply 3 and 2
2x + 6 = 16Subtract 6 from both sides of the equation.
2x = 10Divide both sides by 2.
x = 10The system is now solved.
x = 5 and y = 2
The durations (minutes) of 26 electric power outages in Shah Alam over the past five years are shown below. 32 44 25 66 27 12 62 9 51 4 17 50 35 99 30 21 12 53 25 2 18 24 84 30 17 17 (a) Find the mean, median and mode.
Answer:
Mean = 33.31
Median = 26
Mode = 17
Step-by-step explanation:
Given the data:
32 44 25 66 27 12 62 9 51 4 17 50 35 99 30 21 12 53 25 2 18 24 84 30 17 17
Reordered data : 2, 4, 9, 12, 12, 17, 17, 17, 18, 21, 24, 25, 25, 27, 30, 30, 32, 35, 44, 50, 51, 53, 62, 66, 84, 99
The mean, xbar = Σx / n = 866 /26 = 33.31
The median = 1/2(n+1)th term
Median = 1/2(27)th term = 13.5th term
Median = (13 + 14)th / 2
Median = (25 + 27) / 2 = 26
The mode = 17 (highest frequency)