Answer:
.321,.33,.4
Step-by-step explanation:
the point is like negative it decreases with
the big number is consider the smallest with the point while without the point the big number remains
Find the inequality represented by the graph.
Answer:
[tex]x \geqslant \frac{y + 4}{3} [/tex]Explanation;
Associated line with this equation is:
y=mx+c
when,
X=0
y=-4
so, c=-4
X=1
y=-1
[tex] - 1 = m- 4 \\ - m = - 4 + 1 \\ - m = - 3 \\ m =3 \\ [/tex]
[tex]y = 3x - 4 \\ or \: y + 4 = 3x \\ or \: \frac{y + 4}{3} = x[/tex]
Inequality representated by graph:
[tex]x \geqslant \frac{y + 4}{3} [/tex]
Hope this helps...
Good luck on your assignment...
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms. A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms. How much does each type of box weigh?
Answer:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
Step-by-step explanation:
Given:
There are two types of boxes i.e. Large and Small
Let the weight of Large boxes = L kg
Let the weight of Small boxes = S kg
As per given statement:
A delivery of eight large boxes and four small boxes has a total weight of two hundred and one kilograms.Writing equation for above:
[tex]8L + 4S = 201[/tex] ....... (1)
A delivery of three large boxes and two small boxes has a total weight of eighty two kilograms.Writing equation for above:
[tex]3L + 2S = 82 ....... (2)[/tex]
Now, by solving the equations (1) and (2), we can get the values of L and S.
Multiplying equation (2) with 2 and subtracting from equation (1):
[tex]8L + 4S = 201[/tex]
-
[tex]2 \times (3L + 2S) = 82 \times 2[/tex]
[tex]8L + 4S = 201[/tex]
-
[tex]6L + 4S = 164[/tex]
--------------------
[tex]2L = 37[/tex]
L = 18.5 Kg
Putting value of L in equation (1):
[tex]8 \times 18.5 + 4S = 201\\\Rightarrow 148 + 4S = 201\\\Rightarrow 4S = 201 - 148\\\Rightarrow 4S = 53\\\Rightarrow S = 13.25\ kg[/tex]
So, the answer is:
Weight of Large Box = 18.5 kg
Weight of Large Box = 13.25 kg
Please answer this correctly
Answer:
75%
Step-by-step explanation:
The numbers that are not 5 are 6, 7, and 8.
3 numbers are not 5 out of 4 total numbers on the spinner.
3/4 = 0.75
= 75%
Answer:
75%
Step-by-step explanation:
Total no.s = 4
Divided in parts = 25%
P(not 5) = 75%
Find σ. (Enter an exact number as an integer, fraction, or decimal.)
X ~ N(5, 3)
Answer:
[tex]X \sim N(\mu, \sigma)[/tex]
And from this case we can see that the deviation is given by:
[tex]\sigma = 3[/tex]
Step-by-step explanation:
For this case we have the following notation given:
[tex] X \sim N (5,3)[/tex]
And from this we know that the distribution for the random variable is normal and we know that in general the normal distribution is given by:
[tex]X \sim N(\mu, \sigma)[/tex]
And from this case we can see that the deviation is given by:
[tex]\sigma = 3[/tex]
a)3x-1/5=2x+3/7
b)4x/5-3x/10=2
is this what u need.....
According to the New York Stock Exchange, the mean portfolio value for U.S. senior citizens who are shareholders is $183,000. Assume portfolio values are normally distributed. Suppose a simple random sample of 51 senior citizen shareholders in a certain region of the United States is found to have a mean portfolio value of $198,000, with a standard deviation of $65,000.
a. From these sample results, and using the 0.05 level of significance comment on whether the mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation, by using the critical value method. Establish the null and alternative hypotheses.
b. What is your conclusion about the null hypothesis?
Answer:
The test statistic value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
Step-by-step explanation:
Step(i):-
Given mean of the population (μ) = $183,000
Given mean of the sample (x⁻) = $198,000
Given standard deviation of the sample (S) = $65,000.
Mean of the sample size 'n' = 51
level of significance α = 0.05
Step(ii):-
Null hypothesis : H₀ : There is no significance difference between the means
Alternative Hypothesis :H₁: There is significance difference between the means
Test statistic
[tex]t = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]t = \frac{198,000- 183,000 }{\frac{ 65,000}{\sqrt{51} } }[/tex]
t = 1.64
Step(iii)
Degrees of freedom ν = n-1 = 51-1 =50
t₀.₀₅ = 2.0086
The calculated value t = 1.64 < 2.0086 at 0.05 level of significance
Null hypothesis is accepted
Final answer:-
There is no significance difference between the means
The mean portfolio value for all senior citizen shareholders in this region might not be the same as the mean value reported for their counterparts across the nation
In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
Answer:
Stratified sampling
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
Population divided into groups. Some members of each group are surveyed. This is stratified sampling
Let mZA = 40°. If zB is a complement of ZA, and ZC is a supplement of ZB, find these measures.
mZB =
mZC =
Angle b= 50
Angle c= 130
Complementary angles are two angles that add to equal 90
Supplementary angles are two angles that add to equal 180
To find the measurement of angle b, subtract 40 from 90 (50)
To find the measurement of angle c, subtract 50 from 180 (130)
The measures of complementary and supplementary angles are given by m∠B = 50° and m∠C = 130°
What are Supplementary and Complementary Angles?Supplementary angles are two angles that add up to 180 degrees. In other words, if angle A and angle B are supplementary, then:
A + B = 180°
Complementary angles are two angles that add up to 90 degrees. In other words, if angle A and angle B are complementary, then:
A + B = 90°
Given data ,
If m∠A = 40°, then its complement ∠B = 90° - m∠A = 90° - 40° = 50°.
Since ∠C is a supplement of ∠B, we know that m∠C + m∠B = 180°.
Therefore, we can solve for m∠C by rearranging this equation to get:
m∠C = 180° - m∠B
Substituting the value we found for m∠B, we get:
m∠C = 180° - 50° = 130°
Hence , the angles are mZB = 50° and mZC = 130°.
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- (3/4) times (- 3/8) times ___= -3/4
Answer:
x = -8/3
Step-by-step explanation:
Step 1: Write equation
-3/4(-3/8)(x) = -3/4
Step 2: Multiply
9/32(x) = -3/4
Step 3: Divide
x = -3/4/(9/32)
x = -3/4(32/9)
x = -8/3
Answer:
-8/3
Step-by-step explanation:
-(3/4) x (-3/8)= 9/32
9/32 times (-8/3) = -3/4
Answer: -8/3
There are two boxes containing only black and orange pens.
Box A has 4 black pens and 16 orange pens.
Box B has 2 black pens and 3 orange pens.
A pen is randomly chosen from each box. List these events from least likely to most likely.
Event 1: choosing a black pen from Box A.
Event 2: choosing a black or orange pen from Box A.
Event 3: choosing a white pen from Box B.
Event 4: choosing a black pen from Box B.
Answer:
Event 3 -> Event 1 -> Event 4 -> Event 2
Step-by-step explanation:
The probability of choosing a certain pen is the number of that pen in the box over the total number of pens in the box.
So we have that:
Event 1: We have 4 black pen and 20 total pens, so P = 4 / 20 = 1 / 5
Event 2: All pens are black or orange so the probability is 1.
Event 3: We don't have white pens, so the probability is 0.
Event 4: We have 2 black pen and 5 total pens, so P = 2 / 5
Listing from least likely to most likely, we have:
Event 3 -> Event 1 -> Event 4 -> Event 2
Decide whether the Experiment is a Binomial Experiment. If it is not, explain why:
You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.
You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.
Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.
Answer:
Experiment 1 and 3 are clear binomial experiments.
Experiment 2 needs tweaking to be a binomial experiment.
Check Explanation.
Step-by-step explanation:
A binomial experiment is one in which
1) The probability of success doesn't change with every run or number of trials.
2) It usually consists of a fixed number of runs/trials with only two possible outcomes, a success or a failure.
3) The outcome of each trial/run of a binomial experiment is independent of one another.
Checking each of the experiments one at a time
- You observe the gender of the next 850 babies born at a local hospital. The random variable represents the number of boys.
For this experiment,
1) The probability of success doesn't change with every run or number of trials as it is a 50% chance that each child examined is a boy.
2) It consists of a fixed number of runs (850) with only two possible outcomes, success (if it's a boy) and failure (if it's a girl).
3) The probability of each trial being a boy is independent from all the other trials.
Hence, this experiment is a binomial experiment.
- You draw a marble 350 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.
For this experiment,
1) If the marbles aren't being replaced after each draw, the probability of success, that is, picking a particular marble colour changes from trial to trial.
2) Although, it consist of a fixed number of runs/trials, there are more than two possible outcomes with 3 types of colours. Unless the experiment focuses on one colour and treats the other two colours as 'others', this condition too isn't satisfied.
3) Without replacement, the probability of success (picking a particular marble colour) in one trial isn't independent of the other trials.
This is not a binomial experiment as it doesn't satisfy all the required conditions to be one.
- Testing a cough suppressant using 820 people to determine if it is effective. The random variable represents the number of people who find the cough suppressant to be effective.
1) The probability of success doesn't change with every run or number of trials as it is the same chance that each person finds the cough suppressant to be effective.
2) It consists of a fixed number of runs (820) with only two possible outcomes, success (cough suppressant is effective) and failure (cough suppressant isn't effective).
3) The probability of each trial being a person that finds the cough suppressant to be effective, is independent from all the other trials.
Hence, this experiment is a binomial experiment.
Hope this Helps!!!
What is 75miles/hr in feet/second?(1mile = 5280feet)
Answer:
110 feet/sec
Step-by-step explanation:
75 miles x 5280 feet
= 396000
396000/60 min
=6600
6600/60 secs
=110 feet/second
Suppose that you spin the double wheel pictured to the right. Assuming that the wheels are independent and each outcome is equally likely, determine the probability that you get red on both wheels.
A spinner consists of two concentric unequal circular wheels with the smaller one placed on the larger. The smaller wheel is divided into 8 equal sectors. The number of sectors for each color is as follows, where the label is listed first and the number of sectors is listed second: red, 3; blue, 2; yellow, 1; grey, 2. The larger wheel is divided into 12 equal sectors. The number of sectors for each color is as follows, where the label is listed first and the number of sectors is listed second: red, 4; blue, 2; yellow, 2; grey, 2; green, 2.
B=blue
G=green
Y=yellow
R=red
g=grey
The probability is:_________
Answer:
0.125
Step-by-step explanation:
Smaller Wheel
Total Number of Equal Sectors = 8
The number of Red sectors =3
The probability of obtaining red on the smaller wheel [tex]=\dfrac38[/tex]
Larger Wheel
Total Number of Equal Sectors = 12
The number of Red sectors =4
The probability of obtaining red on the larger wheel [tex]=\dfrac{4}{12}[/tex]
Assuming that the wheels are independent and each outcome is equally likely, the probability that we get red on both wheels
[tex]=\dfrac38 \times \dfrac{4}{12}\\\\=\dfrac18\\\\=0.125[/tex]
The probability is: 0.125
You are reading the draft of a scientific paper that your co-worker has written. In the paper, he draws a sample from a population and computes the following two confidence intervals for : A 95% confidence interval of (90.21,100.37) A 99% confidence interval of (93.61.98.53) How do you know your co-worker made a mistake? He computed more than one confidence interval using the same sample data. Your co-worker did not round to 3 decimal places in his confidence interval upper and lower bounds The 99% confidence interval should be wider than the 95% confidence interval He is not a statistic, so it doesn't make any sense to compute confidence intervals for it. There is nothing wrong with his statements.
Answer:
The correct option is (C).
Step-by-step explanation:
The general form of a confidence interval is:
[tex]CI=SS\pm CV\cdot SE[/tex]
Here,
SS = Sample statistic
CV = critical value
SE = standard error
The width of the confidence interval is:
[tex]\text{Width}=2\cdot CV\cdot SE[/tex]
The width of the confidence interval is dependent upon the critical value and hence dependent upon the confidence level.
As the confidence level increases the critical value increases hence in turn increasing the width of the interval.
And as the confidence level decreases the critical value decreases hence in turn decreasing the width of the interval.
In this case the 95% confidence interval is, (90.21,100.37).
And the 99% confidence interval is, (93.61.98.53).
It is clear by looking at the two intervals that the 95% confidence interval is wider than the 99%. Thus, this clearly indicates that the co-worker made a mistake.
The correct option is (C).
Researchers fed mice a specific amount of Dieldrin, a poisonous pesticide, and studied their nervous systems to find out why Dieldrin causes seizures. The absolute refractory period, time required for nerves to recover after a stimulus, was measured and varies Normally. The measurements, in milliseconds, for six mice were 2.2, 2.4, 2.5, 2.5, 2.6, and 2.7. (10 points) Part A: Find the mean refractory period and the standard error of the mean. (2 points) Part B: Calculate a 98% confidence interval for the mean absolute refractory period for all mice when subjected to the same treatment. (4 points) Part C: Suppose the mean absolute refractory period for unpoisoned mice is known to be 2.3 milliseconds. Dieldrin poisoning should slow nerve recovery and therefore increase this period. Do the data give good evidence to support this theory? What can you conclude from a hypothesis test? Justify your response with statistical reasoning. (4 points)
Answer:
Step-by-step explanation:
Part A
Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48
Standard deviation = √(summation(x - mean)²/n
n = 6
Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484
Standard deviation = √(0.1484/6
s = 0.16
Standard error = s/√n = 0.16/√6 = 0.065
Part B
Confidence interval is written as sample mean ± margin of error
Margin of error = z × s/√n
Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5
Therefore, z = 3.365
Margin of error = 3.365 × 0.16/√6 = 0.22
Confidence interval is 2.48 ± 0.22
Part C
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 2.3
For the alternative hypothesis,
H1: µ > 2.3
This is a right tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 6
Degrees of freedom, df = n - 1 = 6 - 1 = 5
t = (x - µ)/(s/√n)
Where
x = sample mean = 2.48
µ = population mean = 2.3
s = samples standard deviation = 0.16
t = (2.48 - 2.3)/(0.16/√6) = 2.76
We would determine the p value using the t test calculator. It becomes
p = 0.02
Assuming significance level, alpha = 0.05.
Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.
Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $43,000 and $61,600. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired.
Required:
a. What is the planning value for the population standard deviation (to the nearest whole number)?
b. How large a sample should be taken if the desired margin of error is as shown below (to the nearest whole number)?
1. $500?
2. $200?
3. $100?
Answer:
a. 4650
b.
1. 332
2. 2076
3. 8306
Step-by-step explanation:
a. The planning value for population standard deviation is,
s = (maximum - minimum) / 4
s = (61600 - 43000) / 4
s = 4650
that is, it would be 4650, the planning value for population standard deviation
b. we have to:
n = (z * s / E) ^ 2
z for confidence level 95% is 1.96, E = 500; 200; 100
replacing:
1.
n = (1.96 * 4650/500) ^ 2
n = 332.2 = 332
2.
n = (1.96 * 4650/200) ^ 2
n = 2076.6 = 2076
3.
n = (1.96 * 4650/100) ^ 2
n = 8306.4 = 8306
piece-wise functions
Answer:
see the attachment for a graphdomain: all real numbersrange: -6 and y>-5Step-by-step explanation:
The graph below was created by a graphing utility.
It shows no horizontal gaps: f(x) is defined for all values of x, so the domain is all real numbers.
It shows a vertical gap between y=-6 and y>-5. So, the range is in two parts:
{-6} ∪ {y > -5}
Please answer this correctly
Answer:
3/4
Step-by-step explanation:
There are 3 numbers greater than 1. 2, 3, and 4. Since there are 4 numbers total, we get a 3/4 chance.
Answer:
3/4
Step-by-step explanation:
There are four options and 3 of them =3 or greater than 1
P(3 or greater than 1) = 3/4
Given that triangle DAE ~ triangle BAC, what is the length of side AE?
Answer:
12
Step-by-step explanation:
For polygons that are similar to each other, the ratio of their corresponding sides are usually equal to each other, as they are proportional.
Therefore, given that ∆DAE is similar to ∆BAC, AD = 6, AB = 6+4 = 10, AE = x, AC = x + 8, therefore:
AD/AB = AE/AC
6/10 = x/(x+8)
Cross multiply
6*(x+8) = x*10
6x + 48 = 10x
Subtract 6x from both sides
48 = 10x - 6x
48 = 4x
Divide both sides by 4
48/4 = x
x = 12
Length of side AE = 12
Please answer this correctly
Answer:
80%
Step-by-step explanation:
The probability of getting a four is 1/5
The probability of getting a odd is3/5
So u add them and it gives u 4/5 which in decimal is .8 which in percent is 80%
Hope this helps
what expression is equivalent to 6+(-x)+2x(-7)+2x
Answer:
I hope this will help you :)
Step-by-step explanation:
6+(-x)+2x(-7)+2x
6-x+2x✖️(-7)+2x
6-x-14+2x
6-14-x+2x
-8+x
A supermarket charges 3.24 for a carton of milk. They mark up the milk by 35% in order to make a profit. What is the original cost of the milk
Answer:
$ 2,4
Step-by-step explanation:
135% .............$ 3,24
100% .............$ x
x = 3,24×100/135
= 324/135
= $ 2,4
Please only answer if you are 100% sure about the answer.
Answer:
Choice C.
Step-by-step explanation:
Your choice is correct
2 stands for a starting point which is 2 feet from the home
As the ant moves, over time, the distance increases according to the function
y
X
Find the slope of the line that passes through the points
(2, -5) and (7, 1).
y
-5
6
2
7
1
Step 1: Choose (X1,Y1).
4
2.
-4
-2
2
4
6
8
Answer:
slope = [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 5) and (x₂, y₂ ) = (7, 1)
m = [tex]\frac{1+5}{7-2}[/tex] = [tex]\frac{6}{5}[/tex]
The required slope of the line passes through the points (2, -5) and (7, 1) is m = 6/5
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Let's apply this formula to the given points:
m = (1 - (-5)) / (7 - 2)
m = 6 / 5
Thus, the required slope of the line passes through the points (2, -5) and (7, 1).
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Use the place value chart to write 9.807.
Answer:
9 ones, 8 tenths, 0 hundredths, 7 thousandths
Step-by-step explanation:
Answer:
9 thousands
8 hundreds
0 tens
7 ones
Step-by-step explanation:
Hope it helped!
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. If he can ride 10 mph faster than he can walk, how much time (in hr) should he allow to walk a 25-mile trail? (Hint: How fast can he walk?) ________ hr. (enter a fraction)
Answer:
The answer is [tex]\frac{25}{4}[/tex]
Step-by-step explanation:
Velocity formula:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
A tourist can bicycle 28 miles in the same time as he can walk 8 miles. He can ride 10 mph faster than he can walk:
This means that:
[tex]v = \frac{8}{t}[/tex]
And
[tex]v + 10 = \frac{28}{t}[/tex]
[tex](v + 10)t = 28[/tex]
From the first equation:
[tex]vt = 8[/tex]
So
[tex]vt + 10 = 28[/tex]
[tex]8 + 10t = 28[/tex]
[tex]10t = 20[/tex]
[tex]t = \frac{20}{10}[/tex]
[tex]t = 2[/tex]
He walks 8 miles in two hours, so:
[tex]v = \frac{8}{2} = 4[/tex]
4 miles per hour.
How much time (in hr) should he allow to walk a 25-mile trail?
This is t when [tex]d = 25[/tex]. So
[tex]v = \frac{d}{t}[/tex]
[tex]4 = \frac{25}{t}[/tex]
[tex]4t = 25[/tex]
[tex]t = \frac{25}{4}[/tex]
The answer is [tex]\frac{25}{4}[/tex]
Identify whether each phrase is an expression, equation, or inequality.
Answer:
Step-by-step explanation:
a+b-c+d is expression
1/3<r/9 is inequality
and the last one is an equation
an inequality contains one of the 4 symbols
in an expression there is no equal sign
Determine whether the pair of equations represent parallel lines, perpendicular lines, or neither.
12x + 4y = 16
24x + 8y = 36
Answer:
Parallel
Step-by-step explanation:
Parallel lines have the same slope but different y-intercepts. If you multiply the top equation by 2, you get:
2(12x + 4y = 16)
24x + 8y = 32
This shows that both lines have the same slope, but then you find the y-intercepts, they are different:
1st equation y-int = 4
2nd equation y-int = 9/2 or 4.5
A group of up to 40 people are going to a trip to Washington DC. Some will travel in a van that holds 12 people, and the rest will buy train tickets. Write an inequality that can be used to find the number of train tickets that the group will need.
You are told up to 40 people are going and that the van holds 12.
40-12 = 28
So up to 28 people will need to buy train tickets.
Let n be the number of people buying train tickets and x is the total number of people going
N <= (x-12)
Find two positive numbers whose product is 16 and whose sum is a minimum. (If both values are the same number, enter it into both blanks.) (smaller number) (larger number)
Answer:
4 and 4
Step-by-step explanation:
We have 2 numbers that will be X and Y
X * Y = 16 => Y = 16 / X
We must minimize the sum, therefore:
S = X + Y
S = X + 16 / X
we derive and equal 0 and we are left with:
dS / dA = 1 - 16 / (X ^ 2) = 0
1 = 16 / X ^ 2
X ^ 2 = 16
X = 4
in the case of Y:
Y = 16/4 = 4
Therefore the numbers are 4 and 4.
The two positive numbers are 4 and 4
Let the two numbers be x and y
If the product of both numbers is 16, hence;
xy = 16 ........................... 1
If the sum will be at the minimum, hence x + y = minimum
From equation1, x = 16/ y
Substitute into the second equation to have;
16/y + y = A(y)
A(y) = 16/y + y
For the expression to be at a minimum, hence dA/dy = 0
dA/dy = -16/y² + 1
0 = -16/y² + 1
0 - 1 = -16/y²
-y² = -16
y = √16
y = 4
Recall that xy = 16
4x= 16
x = 4
Hence the two positive numbers are 4 and 4
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