The two numbers whose sum is 100 and whose product is a minimum are: x= 50 and y= 50.
To find two numbers whose sum is 100 and whose product is a minimum, we can use the Second Derivative Test. Let's start by defining the two numbers as x and y. We know that:
x + y = 100
We want to find the minimum value of xy. So, let's define a function f(x) = xy. We can rewrite this function in terms of one variable:
f(x) = x(100 - x) = 100x - x^2
Now, let's find the critical point of this function by taking the derivative:
f'(x) = 100 - 2x
Setting f'(x) = 0 to find the critical point:
100 - 2x = 0
x = 50
So, the critical point is x = 50. To determine whether this is a minimum or maximum, we need to find the second derivative:
f''(x) = -2
Since f''(50) < 0, we know that the critical point x = 50 is a maximum. Therefore, to find the minimum value of f(x), we need to evaluate f at the endpoints of the interval [0, 100]:
f(0) = 0
f(100) = 0
Since f(x) is decreasing from x = 0 to x = 50, and increasing from x = 50 to x = 100, the minimum value of f(x) occurs at x = 50. Therefore, the two numbers whose sum is 100 and whose product is a minimum are:
x = 50
y = 100 - x = 50
So, the two numbers are 50 and 50.
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In the study of pesticide use and breast cancer, researchers evaluated pesticide use during the entire life of the respondents. How would you expect the results to have been affected if the researchers collected exposure history spanning the previous 20 years only?
Answer:
Kindly check explanation
Step-by-step explanation:
A common problem with most research designs is bias, which could be introduced win several ways one if which is the favored selection of certain variables rather than being randomized. In the scenario above, the sampling time frame introduces a bias into the design as the tune span of pesticide use does not allay with that of the exposure history of the respondent. Therefore an entire lifetime evaluation of one variable and just 20 years evaluation of the other introduces a sampling bias into the research design. Similarly, evaluation the type of pesticide usage over certain time period may need to be considered as the effect of very old pesticides may differ from those used very recently.
Mrs. Gafni feeds her dog, Rusty, 3/4 cup of dog food each day. How much does she feed Rusty each week? Write the answer as a mixed number.
Answer: 5¹/₄ cups of dog food
Step-by-step explanation:
There are seven days in a week.
If she feeds the dog 3/4 every day, the amount she feeds Rusty every week is:
= 3/4 * 7
= 21/4
= 5¹/₄ cups of dog food
sasasaasasasasassasasasasasasasasasasasasasasa
Answer:
tatatatatatatatatatatatatata
Step-by-step explanation:
the duck is so cute
Answer:
DUCKYYY :DDD
Step-by-step explanation:
HELP!!!!!!!!!!!!!!!!!!!!!!! :)
Hey there!
The answers are as follows:
7.)
m∠1 = 85
m∠2 = 95
m∠3 = 85
m∠4 = 85
8.)
m∠1 = 60
m∠2 = 120
m∠3 = 60
m∠4 = 120
9.)
they all equal 90
10.) No. Parallel lines do not cross each other, but these, if extended, would cross. You could use a protractor by measuring corresponding angles, and if they aren't equal, they aren't parallel.
Have a terrifcly amazing day!
Zenaida shares 1/5 bag of cookies equally among herself and 2 her friends. What fraction of the cookie bag will each girl receive?
Answer:
1/15
Step-by-step explanation:
1/5 divided by 3
=1/5 times 1/3
= 1 × 1
-------
5 × 3
= 1/15
Answer:
The answer is 1/10
Step-by-step explanation:
1/5 divided by 2
1/5 times 1/2
1 x 1 = 1
5 x 2 = 10
1/10
n times 8.
The algebraic expression is _____.
Please help my assignment is due today
Answer:
Hope this helps, thank you !!
The cash register subtracts $4.00 from a $20 Coffee Cafe gift card for every medium coffee the customer buys. Use the graph to write an equation in slope-intercept form to represent this situation
Ć
9
e. m5 =
j. mZ11 =
P
12. If a || D, mZ2 = 63°, and m29 = 105°, find the measure of each missing angle.
a. mZ1 =
e. m26 =
a
i. mZ11 =
6
4
b. m.Z3 =
f. m27 =
j. mZ12 =
7
8
11
12
b
c. m 24 =
g. mZ8 =
10/9
1413
k. mZ13 =
d. m.25 =
d
h. mZ10 =
I. m Z14 =
For questions 13-15, find the values of x and y if I || m.
13.
(10x
17)
I am so confused RN what are u asking
Which of these statements is correct? Select all that apply.
A. A solution to the equation x
2 = 7 is x = √49
B. A solution to the equation x
2 = 15 is x = √15
C. A solution to the equation x
2 = 38 is x = ³√38
D. A solution to the equation x
3 = 3 is x = ³√27
Answer:
A and B lowkey don't feel like doing the rest cause I'm slow
Step-by-step explanation:
part of me wants to say that the answer is A , but the other part of me is saying the answer is D, which one is it?
Answer:
Pretty sure it's A
What is the value of: (3.3) + (-1) - (-1.7)
Answer:
4
Step-by-step explanation:
3.3 + -1 is 2.3
2.3 - -1.7 is 4
a x + b y is equal to 12
Answer:
y= -a*x + 12
b b
Step-by-step explanation:
ax+by=12 (subtract "ax" from both sides so that the one on the left will become zero and we will have "by" )
by= -ax+12(divide both side by "by" so that we will have the equation as "y=mx+b")
finally the result will be:
y= -a*x + 12
b b
help pls it has to be in an equation and ill mark brainliest.
Answer:
y = 1/6x+2
Step-by-step explanation:
1/6=slope 2=y int. hope this kinda helps
Please help!!!!!!!!!!!!!!!!!!!!!
On a team, 4 girls and 2 boys scored a total of 28 points. The difference between the number of points scored by the 4 girls and the number of points scored by the 2 boys is 12. Each girl scored the same number of points and each boy scored the same number of points. Find the number of points scored by each girl and each boy Each girl scored points.
Answer:
Each girl earned 2 points
Each boy earned 5 points
Step-by-step explanation:
Let x represent the number of points one girl earned
Let y represent the number of points one boy earned
4x + 2y = 28
4x - 2y = 12
8y = 40
y = 5 points
4x + (2)(5) = 28
4x + 20 = 28
4x = 8
x = 2 points
Each girl earned 2 points
Each boy earned 5 points
Please hurry!!!!!!!!!!!!!!!!!!
Answer:
38
Step-by-step explanation:
Range is the largest number minus the smallest number
55-17=38
I hope I hurried enough
Answer:
Your question is not proper.Here, you said that range of data. But where is the data? How can you expect answer without giving proper question?
Graph this function: y+6=1/2(x-1)
Answer:
Hope this helps! Have a great day!
Step-by-step explanation:
Answer:
[tex]y=\frac{1}{2}x-\frac{13}{2}[/tex]
Step-by-step explanation:
Move all terms not containing y to the right side of the equation.
[tex]y = \frac{x}{2}-\frac{13}{2}[/tex]
Rewrite
[tex]y=\frac{1}{2}x-\frac{13}{2}[/tex]
Use the slope-intercept form to find the slope and y-intercept.
Slope: [tex]\frac{1}{2}[/tex]
y-intercept: [tex](0, -\frac{13}{2})[/tex]
good luck, hope this helps :)
Which of the following number is odd? *
A. 68,458
B. 92,162
C.28,952
D. 28,923
Answer:
D. 28,923
Step-by-step explanation:
We are given four numbers and are asked to find out which number is odd.
An odd number is a number that cannot be split evenly, if it is split, it will end up in either a fraction or a decimal.
Even numbers are the opposite, so which would be the answer?
This would be D. 28,923. 28,923 divided by 2 gives you a decimal. Which is 14461.5, all the other choices give you whole numbers.
Helpppppp!!!!!!!!!!!!!!!!!!!!!!!!!
-75x + 200 represents a bank account balance after x months. What is the initial amount in the
account? What is the rate of change?
I need help please!!
Answer:
Step-by-step explanation:
i think 90
which function defines the sequence -16,-22,-28,-34 where f(10)= -70
Answer:
f(n) = -6n - 10.
Step-by-step explanation:
This is arithmetic sequence with first term a1 = -16 and common difference d = -6.
So f(n) = a1 + d(n - 1)
= -16 - 6(n - 1)
= -16 - 6n + 6
= -6n - 10.
Checking:
f(10) = -6(10) - 10 = -70.
The function that defines the sequence is f(n) = -6n - 10.
What is an Arithmetic Sequence ?A sequence of numbers which have a relation between them and the consecutive numbers increase or decrease by a fixed amount is called as an Arithmetic Sequence.
The sequence given is -16,-22,-28,-34
This is arithmetic sequence
first term a1 = -16
common difference d = -6.
The nth term of an arithmetic sequence is given by
f(n) = a1 + d(n - 1)
f(n) = -16 - 6(n - 1)
f(n)= -16 - 6n + 6
f(n)= -6n - 10.
To verify this
f(10) = -6(10) - 10 = -70.
Therefore , The nth term is given by f(n)= -6n - 10.
To know more about Arithmetic Sequence
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If A = 56, then find c
Answer:
Since A= 56 then B=56 so A+B=112
The whole tringle must be 180 degrees
So 180-112=68
SO C=68
I believe
Daily ticket sales for a music festival are as follows: 454, 635, 454, 843, 1951, 1999. What are the mean, median, and mode of the data?
Please help me...???
Answer:
Step-by-step explanation:
77
Answer:
16.5 in³
Step-by-step explanation:
Length(L) = 2.2 in
breadth (b) = 1.5 in
height (h) = 5 in
Volume of the cuboid
= L * b * h
= 2.2 * 1.5 * 5
= 16.5 in³
Plz help me step by step explanation would help for work plzzzz And Thank you PLEASE
Answer:
i hope this helps
Step-by-step explanation:
Answer:
r = -43. that's the result
ANSWER ASAP THEIRS A SCREEN SHOT TO HELP SHOW
AND TELL WHY PLEASE
write the equation of the line in fully simplified slope-intercept form.
Step-by-step explanation:
świnka pepapomoże to zmieniam o tym zakładem ubezpieczeń i bankowości elektronicznej na tablecie i
Help due tonight
Solve the following system of equations.
3x + y = -21
-3x - 3y = 15
X=
y =
Answer:
I have solved it in elimination method if you need it in another method let me know.
Step-by-step explanation:
3x+y=21
-x-y=5
2x=26
x=13
-3×13-3y=15
y= -18
5TH GRADE MATH GIVING BRAINLIESTT
Answer:
graph A
Step-by-step explanation:
When the cost is at 4 dollars, the feet is at 1. Hope this helps!
Answer:
A
Step-by-step explanation:
The only number that comes across 4x and 1y is a.