g Find two positive numbers whose sum is 380 and whose product is a maximum. You MUST use optimization methods to solve this.

Answers

Answer 1

Answer:

The first number is 190 and the second number is also 190

Step-by-step explanation:

let the first number = x

let the second number = y

The sum of the numbers is given by;

x + y = 380

y = 380 - x

The objective function is given by;

F = xy

F = x(380 -x)

F = 380x - x²

Take the derivative of the function;

F' = 380 - 2x

Find the critical points;

380 - 2x = 0

2x = 380

x = 380 / 2

x = 190

Determine the second number, y;

y = 380 - x

y = 380 - 190

y = 190


Related Questions

what is 1 3/8 divided by 1/2?​

Answers

Answer:

2.75 or 2 3/4

Step-by-step explanation:

Answer:

11/4

Step-by-step explanation:

First start by writing the equation using only fractions:

11/8 / 1/2 =

Next, change the sign to multiplication by taking the reciprocal of the second number:

11/8 * 2 =

Then multiply the two numbers together:

22/8 =

And finally, simply the fraction:

11/4

Jorge wants to buy a shirt for $35. How much will Jorge’s shirt cost in Fresno? Here is the percent in the picture

Answers

the answer would be 37.87875 cause you just add 35 + 8.225%

Plzzz help this is a quick question

Answers

Answer:

Option 2

Step-by-step explanation:

Option 1 is wrong because:

-√16  = -4, therefore we can conclude -20.5 isn't greater than -√16

Option 3 is wrong because:

Using common knowledge, we know that π (pi) = 3.14159265...

Simplify the expression.
ky + y + y =

Answers

Answer:

ky + 2y

Step-by-step explanation:

ky + y + y

~Combine like terms

ky + 2y

Best of Luck!

Answer:

ky + 2y

Step-by-step explanation:

ky = ky (it stays the same)y + y = 2yPut them together: ky + 2y

I hope this helps!

!!20 points!!Choose the answer that best represents the situation described below.
John takes a job after school to earn money to buy a surfboard. He knows
that the more hours he works, the more money he will make.
A. The amount of money John makes is a function of the number of
hours he works.
B. The number of hours John works is a function of the amount of
money he makes
C. John's job is a function of his interest in surfing.

Answers

Answer:

B

Step-by-step explanation:

Answer:

A. The amount of money he makes is a function

Brain weights are normally distibuted with mean 1400.48 grams and standard deviation 106.33 grams. Find the 80th percentile of this distribution.

Answers

Answer:

The 80th percentile of the distribution is 1,490.01 grams

Step-by-step explanation:

Here, we want to find the 80% of the distribution

80% means 80/100 = 0.8

We need to get the z-score equivalent to 80th percentile;

This is equal to 0.842

Mathematically;

z-score = (x - mean)/SD

we want to calculate x here;

0.842 = (x - 1400.48)/(106.33)

106.33(0.842) + 1400.48 = x

x = 1,490.00986 which is 1,490.01 grams to 2 decimal places

If (Triangle)ABC is similar to (Triangle)EDC, what is the value of x?

Answers

Answer:

37.5 (G)

Step-by-step explanation:

Set up a proportion:

[tex] \frac{40}{100} = \frac{15}{x} [/tex]

Next cross multiply

[tex](15)(100) = (40)(x)[/tex]

[tex]1500 = 40x[/tex]

Lastly solve for x by dividing both sides by 40

[tex]\frac{1500}{40} = \frac{40x}{40} [/tex]

[tex]x = 37.5[/tex]

A recipe calls for 5 cups of sugar for 30 servings . How many cups of sugar are needed to make 8 servings?

Answers

1 1/4 cup
30/5=6
1 cup= 6 servings

another word for the perimeter of a circle is the
a- center
b- circumference
c- radius
d- diameter ​

Answers

Answer:

B

Step-by-step explanation:

Answer:

Another word for perimeter is the circumference. Please mark as helpful if it is helpful!

ES
To rent a certain meeting room, a college charges a reservation fee of $39 and an additional fee of $5.70 per hour. The film club
wants to spend less than $67.50 on renting the meeting room.
What are the possible amounts of time for which they could rent the meeting room?
Use t for the number of hours the meeting room is rented, and solve your inequality for t.

Answers

t<5

39 + 5.7t < 67.5

-39

5.7t < 28.5

divide by 5.7

t < 5

When writing
the equation of a line in slope-intercept
form, how can you determine the value of
m in y = mx + b if you know the coordinates
of two points on the line?

Answers

Slope is rise over run meaning the difference in y coordinates over the difference in x coordinates. If you have two points you have:

(x1,y1) and (x2,y2) this makes

m = (y2 - y1)/(x2 - x1)

What is 17/40 as a decimal

Answers

Answer: 0.425

Step-by-step explanation:

what is the value of x? exactly

Answers

Answer:

wouldn't it be 90 degrees?

Step-by-step explanation:

if anyone would help I would give you brainliest

Answers

Answer:

[tex]x = 14.[/tex]

Step-by-step explanation:

[tex]using \: the \: sum \: of \: angles : \\ (7x - 11) + (2x - 3 ) + (5x - 2) = 180 \\ 14x - 16 = 180 \\ 14x = 196 \\ x = 14[/tex]

A medical school claims that more than 28% of its students plan to go into general practice. To test this claim, a random sample of 130 of the school's students is selected. Of these, 32% of them plan to go into general practice. Find the P-value for this test of the school's claim.

Answers

Answer:

The p-value of the test is 0.1314.

Step-by-step explanation:

In this case we need to test the claim made by a medical school that more than 28% of its students plan to go into general practice.

The hypothesis can be defined as follows:  

H₀: The proportion of students planning to go to general practice is 28%, i.e. p = 0.28.  

Hₐ: The proportion of students planning to go to general practice is more than 28%, i.e. p > 0.28.

The information provided is:  

 n = 130

[tex]\hat p=0.32[/tex]

Compute the test statistic value as follows:  

 [tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

    [tex]=\frac{0.32-0.28}{\sqrt{\frac{0.28(1-0.28)}{130}}}\\\\=1.12[/tex]

The test statistic value is 1.12.  

Compute the p-value as follows:  

 [tex]p-value=P(Z>1.12)\\[/tex]

                 [tex]=1-P(Z<1.12)\\\\=1-0.86864\\\\=0.13136\\\\\approx 0.1314[/tex]

The p-value of the test is 0.1314.

*Use the z-table.

Pls Help - *Brainliest*​

Answers

Answer:

A, B, E

Step-by-step explanation:

I hope this helps!!!

Your friend has a mold that holds 3/4 of a cup of root beer if she has six cups of root beer how many popsicles can she make

Answers

Answer:

8

Step-by-step explanation:

If you turn 8 into a fraction you'll get 24 / 4

then you divide 24/4 by 3/4 you'll get 8

Answer:

Your friend can make 8 popsicles

Explanation:

Convert any mixed numbers to fractions.  Then your initial equation becomes:

6/1 ÷ 3/4 = ?

Applying the fractions formula for division (flip the second fraction and multiply):

6/1 x 4/3 = 24/3

Simplify 24/3, the answer is:

8 popsicles

Hopefully this helps! Sorry if wrong. You are loved and you are beautiful/handsome!

-Bee

15% of students in class are left handed. If there are 6 students who are left handed how many students are in the class

Answers

The answer is there are 40 students in that class

Which number is rational?
v2
pi
v10
v16

Answers

Answer:The square root of 16 is rational.

Step-by-step explanation:

Help with this math please

Answers

Answer:

The answer is -20 .

Step-by-step explanation:

You have to substitute x = -4 into the function :

[tex]f(x) = 3x - 8[/tex]

[tex]f( - 4) = 3( - 4) - 8[/tex]

[tex]f( - 4) = - 20[/tex]

Answer:

Step-by-step explanation:

f(x) = 3x - 8

f(-4) = 3*(-4) - 8

f(-4)  = -12 - 8

f(-4) = - 20

-20 is what goes in the box.

Find a radical expressions for the perimeter of the shaded triangle Simplify the expression.​

Answers

Answer:20+4√17

Step-by-step explanation:

2 of 3 sides are 16 and 4 units . The angle between them is 90 degrees.

So we can find the length of the third side using Pitagor theorem.

c= SQRT( 16²+4²)= sqrt (256+16)= sqrt (272)

So the perimeter of the shaded triangle is equal to

P= 4+16+sqrt(272)=20+4√17

The radical expressions for the perimeter of the shaded triangle is  20 + 4√17

What is the triangle?

In terms of geometry, the triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

We have a rectangle shown in the picture with dimensions.

Using Pythagoras theorem;

The inclined length = √(4²+16²) = √272 = 4√17

The perimeter of the shaded region = 16 + 4 + 4√17

Perimeter = 20 + 4√17

Thus, the radical expressions for the perimeter of the shaded triangle is  20 + 4√17

Learn more about the triangle here:

brainly.com/question/25813512

#SPJ2

Tom works for a constant hourly wage of w dollars. Which answer shows the correct relationship between e Tom total earnings in a week and h the number of hours he worked during the week

Answers

Answer:

e = wh

Step-by-step explanation:

I WILL MAKE U BRAINLIEST PLZ HELP (Simplify. Enter the answer in the box.
[tex] \sqrt[3]{512} [/tex]

Answers

Answer:

It is 8

Step-by-step explanation:

my recipe for apple cider punch calls for 2 quarts of apple cider, three teaspoons of cinnamon, and one pint of lemon-lime soda. This will make enough for 8 people. in my neighborhood, there are 40 people. how much do I need of each ingredient for my neighborhood to share

Answers

Answer:✨

10 quarts of apple cider, 15 teaspoons of cinnamon, 5 pints of lemon lime soda.

✨Step-by-step explanation:✨

40 people in your neighborhood ÷ 8 people (how much 1 recipe can feed) = 5 punches so you can feed 40 people

2 quarts of apple cider x 5 = 10 quarts of apple cider

3 teaspoons of cinnamon x 5 = 15 teaspoons of cinnamon

1 pint of lemon-lime soda x 5 = 5 pints of lemon-lime soda

-10x + 35-37 OR 3x – 10 <-25

Answers

Answer:

3x – 10 < -25   →    x < -5

-10x + 35-37     →   -10x - 2

Plz mark brainliest:)

Can someone please help asap

Answers

Answer:

h= 5hx4     c= 6cx4

Step-by-step explanation:

i have been stuck on this problem please someone answer this its getting annoying

Answers

Answer:

circumference = 150.72cm

area = 1808.64cm²

Step-by-step explanation:

the formula for circumference = 2πr

the formula for area = πr²

24cm is the radius (r)

so therefore

circumference = 2(3.14)(24)

= 150.72cm

area = (3.14)(24)²

= 1808.64cm

im not too great at math- but I think this is correct ^^

The circumference of the circle is
150.79645 cm
And the area is
1809.55737 cm^2

Hope this helps !

What’s the total amount Janet has to repay after three years?

Answers

Answer:

What are the number to find the amount I thin you're missing information

Step-by-step explanation:

Answer:

2,315.25

Step-by-step explanation:

the equation Y=1 1/2X represents the number of cups of dried fruit, Y. needed to make X pounds of granola. Determine whether each point would be on the graph of this proportional relationship
(1 1/2,1) (4,6) (18,12) (0,0) (2 1/2. 3 3/4 )

Answers

Answer:

[tex]2.\ \ (4,6)[/tex]

[tex]4.\ \ (0,0)[/tex]

[tex]5.\ \ (2\frac{1}{2},3\frac{3}{4})[/tex]

Step-by-step explanation:

Given

[tex]y = 1\frac{1}{2}x[/tex]

Required

Determine if the given points is on the graph

First,, we rewrite [tex]y = 1\frac{1}{2}x[/tex] as

[tex]y = \frac{3}{2}x[/tex]

[tex]1.\ \ (1\frac{1}{2},1)[/tex]

This can be interpreted as:

[tex]x = 1\frac{1}{2}[/tex]

[tex]y = 1[/tex]

Substitute [tex]x = 1\frac{1}{2}[/tex]

[tex]y = \frac{3}{2} * 1\frac{1}{2}[/tex]

[tex]y = \frac{3}{2} * \frac{3}{2}[/tex]

[tex]y = \frac{9}{4}[/tex]

This isn't equal to the given value of y.

Hence: [tex](1\frac{1}{2},1)[/tex] is not a point on the graph

[tex]2.\ \ (4,6)[/tex]

Here,

[tex]x = 4[/tex]

[tex]y = 6[/tex]

Substitute [tex]x = 4[/tex]

[tex]y = \frac{3}{2} * 4[/tex]

[tex]y = \frac{3 * 4}{2}[/tex]

[tex]y = \frac{12}{2}[/tex]

[tex]y = 6[/tex]

This point is on the graph

[tex]3.\ \ (18,12)[/tex]

Here,

[tex]x = 18[/tex]

[tex]y = 12[/tex]

Substitute [tex]x = 18[/tex]

[tex]y = \frac{3}{2} * 18[/tex]

[tex]y = \frac{3 * 18}{2}[/tex]

[tex]y = \frac{54}{2}[/tex]

[tex]y = 27[/tex]

This isn't equal to the given value of y.

Hence: [tex](18,12)[/tex] is not a point on the graph

[tex]4.\ \ (0,0)[/tex]

Here, we have

[tex]x = 0[/tex]

[tex]y = 0[/tex]

Substitute [tex]x = 0[/tex]

[tex]y = \frac{3}{2} * 0[/tex]

[tex]y = 0[/tex]

Hence:

This point is on the graph

[tex]5.\ \ (2\frac{1}{2},3\frac{3}{4})[/tex]

Here

[tex]x =2\frac{1}{2}[/tex]

[tex]y = 3\frac{3}{4}[/tex]

Substitute [tex]x =2\frac{1}{2}[/tex]

[tex]y = \frac{3}{2} * 2\frac{1}{2}[/tex]

[tex]y = \frac{3}{2} * \frac{5}{2}[/tex]

[tex]y = \frac{15}{4}[/tex]

[tex]y = 3\frac{3}{4}[/tex]

Hence:

This point is on the graph

The period of is....


If you are right I will mark you brainliest.

Answers

Answer:

π/4

Step-by-step explanation:

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