A farmer uses two types of fertilizers. A 50lb bag of fertilizer A contains 6 lb of nitrogen and 3lb of phosphorus. A 50 lb bag of fertilizer B contains 4 lb each of nitrogen and phosphorus. The minimum requirements for a field are 480 lb of nitrogen and 240 lb of phosphorus. If a 50lb bag of fertilizer A costs $35 and a 50 lb bag of fertilizer B costs $25 find the amount of each type of fertilizer the farmer should use to minimize his cost while still meeting the minimum requirements. mathematically formulate and state the problem.

Use the Chain Rule:

[tex]\frac{d}{dx} [f(g(x))] = f'(g(x)) * g'(x)[/tex]

Given Information:

[tex]f(x) = x^5\\ g(x) = \frac{cos(x)}{1} +sin(x)\\ f(g(x)) = ( \frac{cos(x)}{1} +sin(x))^5\\ \\ f'(x)=5x^4\\ g'(x)=\frac{-sin(x)}{1} + cos(x)\\f'(g(x))*g'(x)=5(\frac{cosx)}{1} + sin(x))^4*(\frac{-sin(x)}{1} + cos(x))[/tex]

The answer is:

[tex]5(\frac{cosx)}{1} + sin(x))^4*(\frac{-sin(x)}{1} + cos(x))[/tex]

Answer:

Answer: 5/9 as a decimal is 0.556.

5/9 ≈ 0.56 rounded to the nearest hundredth, good luck

Answer:

Hello!

After reviewing the problem you have provided I have come up with the correct solution:

x= 9

Step-by-step explanation:

To come up with this solution you have to first realize that the smaller triangle is a proportionally scaled down version of the entire larger triangle! (I will show what I mean in a linked picture)

So after we have realized that the smaller triangle is a scaled down version of the larger one, we can then create a formula or ratio to calculate the value of the missing side of the larger triangle (being x+6=??).

To create the formula/ratio I divided 10inches by 4inches. Thus the larger triangle is 2.5 times larger than the smaller one.

I then use this ratio to figure out the missing length of the larger triangle by doing:

6inches x 2.5 = 15inches.

I then inputed the 15inches into the formula of the missing side:

x+6=15

Subtracted 6 from both sides to simplify, and came up with the solution!

x=9

Let me know if this helps!

Answer:

The rule for a profit-maximizing perfectly competitive firm is to produce the level of output where Price= MR = MC, so the raspberry farmer will produce a quantity of 90, which is labeled as e in Figure 4 (a). Remember that the area of a rectangle is equal to its base multiplied by its height.

Is the wrong answer, the correct answer is 1,436.4

Answer:

D. Multiply both sides by -7

Step-by-step explanation:

So solving would look like this

m/-7 < 14

m > -2

Remember when multiplying by a negative the sign flips, hope that helps :)

[tex] \large╚»★«╝ { \mathcal{Answer }}╚»★«╝[/tex]

The Correct option among them is B

_____________________________________

The other options have one variable each, but according to the given question there should be two variables in the inequality.

The only choice satisfying the conditions is Option B

having two variables in it ( that is "m" and "n" )

[tex] ꧁ \: \large \frak{Eternal \: Being } \: ꧂[/tex]

Answer:

8 plus five is 13..

Step-by-step explanation:

Answer:

the ancwer is 1536

Step-by-step explanation:

i used a coculater

[tex]f(x) = -4x-1\\\\g(x) = x^2 -5 \\\\g(-2) = (-2)^2 -5 = 4 -5 =-1\\\\(f \circ g)(-2)\\\\=f(g(-2))\\\\=f(-1)\\\\=-4(-1) -1 = 4-1=3[/tex]

[tex]\frac{x}{5} +3=2\\\frac{x}{5} =-1\\x=-5[/tex]

Let me know if you need any clarification, I just don't have much to say on a simple question like this

Step-by-step explanation:

6³×(½)³

=> 216÷8 = 27.

hope this helps you.

Step-by-step explanation:

if I understand this correctly as logarithm of 64 to the base of 64, then the answer is clearly 1

64¹ = 64.

Answer:

yellow: x=6

red: y=4

blue: y=-2

Step-by-step explanation:

Step-by-step explanation:

Sum of 7 + (-3) = 7 +.- 3 = 7 - 3 = 4

( As + × - = -)

Sum of -3+7 = 4

We observe that both are same .

Answer:

they both give the same answer

Step-by-step explanation:

7+(_3)=+4

_3+7=+4

Answer:

Step-by-step explanation:  If you roll the die twice, the probability of getting a even number both times is (1/2)(1/2) ... A probability experiment consists of rolling a 6 sided die

Answer:

150 cm square

Hope this helps!

For a square:

A = s2, where s = side (the length and the width are the same)

625 = s2

±25 = s

length of rectangle = 1.4 · length of square

length of rectangle = 1.4(25)

length of rectangle = 35

Answer:

[tex]-\frac{5}{8}\\-9.2%\\\\-0.001[/tex]

-3/4, -5/8, -9.2%, -0.001, 4.6%, 5%, 33%

Step-by-step explanation:

[tex]-\frac{3}{4}=-75[/tex]%                                     4.6%

Let's do the process of elimination to find our answers

[tex]-\frac{5}{8}=-62.5[/tex]% this would be in between because - 62.5% would be after -75%

[tex]\frac{5}{100}=5[/tex]% this fraction equals to a positive percentage which would be after 4 so not this one

[tex]-0.001 = -0.1[/tex]% this number would come after -75%, -62.5%, -9.2%and before 4.6% so this would be one

[tex]-0.75= -75[/tex]% we already have the percentage so not this one

33% this number would come after 4.6% so not this one

-9.2% this would be between them because its -9 and it will be after -75% and -62.5%

Answer:

2.92 rounded

Step-by-step explanation:

:))

Answer:

1875

Step-by-step explanation:

Answer:

5.Math is a very different one that

Ok

Answer:

b is ur answer

Step-by-step explanation

hope this helps :)

Answer:

The length of the other leg is [tex]4\sqrt{3}[/tex]

Step-by-step explanation:

There are 2 ways to solve this.

1) Pythagorean theorem (the harder way)

A 30-60-90 triangle is a right triangle, and therefore you can use the pythagorean theorem to calculate the measure of 1 side given the 2 others.

[tex]a^2+b^2=c^2\\a^2+4^2=8^2\\a^2+16=64\\a^2=48\\a=\sqrt{48}\\a=6.9282...[/tex]

That's one solution, but its not a very nice number or the exact answer you probably want. Instead, you can simplify the root.

First, you need to factor 48:

[tex]2*24=48\\2*12=24\\2*6=12\\2*3=6[/tex]

The prime factors of 48 are:

[tex]2*2*2*2*3=48[/tex]

Then, you need to find perfect squares:

[tex](2*2)*(2*2)*3=48\\2^2*2^2*3=48[/tex]

And finally, you can remove those like this:

[tex]\sqrt{48} =\sqrt{2^2*2^2*3} \\\sqrt{48} =2\sqrt{2^2*3} \\\sqrt{48} =2*2\sqrt{3} \\\sqrt{48} =4\sqrt{3}[/tex]

The length of the other leg is [tex]4\sqrt{3}[/tex]

2) 30-60-90 triangle relationships (the easier way)

There are 4 simple rules here:

They're actually pretty easy to remember. You can multiply the short leg by 2 or √3, and 2 is greater than √3 (check a calculator). The hypotenuse of course is also longer than the long leg, so you have to multiply by 2 to get it. Then for the long leg, the only option is to multiply by √3. The same works in reverse for both of those.

Here, we have the short leg. You can check that with the pythagorean theorem again to be sure:

[tex]a^2+4^2=8^2\\a^2+16=64[/tex]

Because 16 is less than half of 64, a has to be the longer leg. Using the rules above, multiply the short leg by √3 to get the answer:

[tex]4 * \sqrt{3} \\4\sqrt{3}[/tex]

Same answer as the previous method.

Answer: He sold 1,800 merchandise

Step-by-step explanation: 426 - 300 = 126 ÷0.07 = 1,800

I dont know if im right though

Answer:

9×y

Step-by-step explanation:

the

answer

of

the

given

is 9y

Answer:

David= 30

Maria= 15

Trey= 20

Step-by-step explanation:

If David sent 30 messages, then half as as many as that would be 15, the amount that Maria sent. 5 more than what Maria would be what Trey sent, 20.

Answer:

[tex]\large\sf{average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}[/tex]

Step-by-step explanation:

Given the American customer satisfaction index scores that increased from 61 in 2002, to 71 in 2014:

In order to solve for the average rate of change, we could simply use the average rate of change formula:

Average rate of change = Change in output/Change in input

[tex]\huge\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}}[/tex]

Let (x₁, y₁) = (61, 2002)

    (x₂, y₂) = (71, 2014)

Substitute these values into the average rate of change formula:

[tex]\BIGG\sf{Average\:rate\:of\:change\:=\:\frac{\triangle{y}}{\triangle{x}}\:=\:\frac{(y_2\: -\: y_1) }{(x_2\: -\: x_1)}\:=\frac{2014\:-\:2002}{71\:-\:61}\:=\:\frac{12}{10}\:=\:\frac{6}{5}}[/tex]

[tex]\large\bf\sf{Therefore,\:the\:average\:rate\:of\:change= \frac{6}{5}\:=\:1.2}[/tex].

Answer: -30

Step-by-step explanation: