Auggie's vineyard consists of 240 acres upon which he wishes to plant Merlot grapes and Cabernet grapes. Profit per acre of Merlot is $400, and profit per acre of Cabernet is $300. The number of hours of labor available is 3200. Each acre of Merlot requires 20 hr of labor, and each acre of Cabernet requires 10 hr of labor. Determine how the land should be divided between Merlot and Cabernet in order to maximize profit.

Answer:

U GO TO DHS

Step-by-step explanation:

Answer:

(-3*6.3x)+(-3*1.5y)

(-18.9x)+(-4.5y)

Answer:

y=x-2

Hope this helps.

Answer:

this doesnt make sense is there any type of picture or more explanation on the question? i'll still help :)

Step-by-step explanation:

Answer: I think it is (D)

Step-by-step explanation: Its hard to explain but I hope this helps anyways!

Answer:

I think its D to so I would go with that

Answer:

721

Step-by-step explanation:

dog you in elementary school

Answer:

2.755778

Step-by-step explanation:

Just search how much pounds is 1.25 kg?

Answer:

Step-by-step explanation:

Answer:

8/15= 0.533

Step-by-step explanation:

8 divided by 15 isn't possible so according to the rules of division we introduce a (0.) then we add a (0) to the back of (8) to make it (80) which is bigger than (15) so we now have (80/15) which is (5) remaining (5) then we add the back of the (0.) it then becomes (0.5) we then step down the remaining (5) and also add a (0) at the back to make it (50) which is also bigger than (15) (50/15) which gives us (3) and a remaining (5) add (3) to the back of (0.5) to become (0.53) also still step down the remaining (5) add a zero to it to become (50) still divide by (15) gives (3) and remains (5) and it gives the same answer so it is a reoccurring decimal.

Thank you hope I was of help!!

Answer:

3

Step-by-step explanation:

Step-by-step explanation:

formula to fine slope

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

Answer:

a. Angel has a greater flat fee

b. Difference = $130

Step-by-step explanation:

Given

Rose:

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

Angel

Guests --- Charges

10 -------- $180

15 -------- $255

25 -------- $405

30 -------- $480

Solving (a): Who charges the greater flat fee?

We have that the flat fee of Rose is:

[tex]Flat\ Fee = \$50[/tex]

For Angel, we need to determine the equation of the given table

Start by calculating the slope (m) of the table

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where x and y represent any two corresponding values of the guests and the charges.

[tex](x_1,y_1) = (10, 180)[/tex]

[tex](x_2,y_2) = (30, 480)[/tex]

So: [tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes

[tex]m = \frac{480 - 180}{30 - 10}[/tex]

[tex]m = \frac{300}{20}[/tex]

[tex]m = 15[/tex]

Next, we calculate the equation using:

[tex]y - y_1 = m(x - x_1)[/tex]

Where

[tex]m = 15[/tex]

[tex](x_1,y_1) = (10, 180)[/tex]

[tex]y - 180 = 15(x - 10)[/tex]

[tex]y - 180 = 15x - 150[/tex]

Add 180 to both sides

[tex]y - 180 + 180 = 15x - 150 + 180[/tex]

[tex]y= 15x + 30[/tex]

From the equation above:

The slope = 15 --- This represents the hourly rate

and

y intercept = 30 --- This represents the flat fee

This is better represented as:

Angel

[tex]Flat\ Fee = \$30[/tex]

[tex]Rate = \$15[/tex]

and

Rose:

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

By comparison, Angel has a greater flat fee

Solving (b): Difference between total charges of 50 guests for both caterers.

For angel, the equation is:

[tex]y= 15x + 30[/tex]

and x = 50.

So:

[tex]y = 15 * 50 + 30[/tex]

[tex]y = 750 + 30[/tex]

[tex]y = 780[/tex]

For Rose,

First, we need to determine the equation.

[tex]Flat\ Fee = \$50[/tex]

[tex]Rate = \$12[/tex]

The equation is:

[tex]y = Flat\ Fee + Rate * x[/tex]

[tex]y = 50 + 12 * x[/tex]

So, the total charges for 50 guests is:

[tex]y = 50 + 12 * 50[/tex]

[tex]y = 50 + 600[/tex]

[tex]y = 650[/tex]

The difference is then calculates as:

[tex]Difference = 780 - 650[/tex]

[tex]Difference = \$130[/tex]

Step-by-step explanation:

Since x² + kx + (k + 3) is tangent to the x-axis, the quadratic function has a repeated root.

The discriminant is zero, so b² - 4ac = 0.

=> k² - 4(1)(k + 3) = 0

=> k² - 4k - 12 = 0

=> (k - 6)(k + 2) = 0

Hence k = 6 or k = -2.

The value of k is -2 and 6.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x² + kx + (k + 3) is tangent to the x-axis.

This means,

The equation has roots.

Now,

The determinant of the equation is equal to zero.

D = b² - 4ac

x² + kx + (k + 3) is in the form of ax² + bx + c.

a = 1

b = k

c = k + 3

Now,

D = 0

k² - 4(k + 3) = 0

k² - 4k - 12 = 0

k² - (6 - 2)k - 12 = 0

k² - 6k + 2k - 12 = 0

k(k - 6) + 2(k - 6) = 0

(k + 2) (k - 6) = 0

k + 2 = 0

k = -2

k - 6 = 0

k = 6

Thus,

k = -2 and 6.

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Answer:

200

Step-by-step explanation:

==================================================

Explanation:

We basically mix red and blue to get purple. The ratio needed is 2 parts red, and 3 parts blue. We can shorten this by writing 2:3

Note how we can double both parts of the ratio to get 4:6, showing that 4 drops of red correspond to 6 drops of blue, which is the answer we want.

------------------

Another approach:

x = some positive real number

(2 parts red)/(3 parts blue) = (4 parts red)/(x parts blue)

2/3 = 4/x

2x = 3*4 .... cross multiply

2x = 12

x = 12/2 .... divide both sides by 2

x = 6

So 6 drops of blue go with 4 drops of red.

Answer:

25

Step-by-step explanation:

a2+b2=c2

3^2+4^2=c^2

9+16=25

25^2=625

Sqrt of 625 = 25

Answer:

x = 5

Step-by-step explanation:

Using Pythagoras' identity in the right triangle.

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

x² = 4² + 3² = 16 + 9 = 25 ( take the square root of both sides )

x = [tex]\sqrt{25}[/tex] = 5

Answer:

The value is [tex]UCL = 10.8[/tex]  

Step-by-step explanation:

From the question we are told that

    The sample mean is  [tex]\= x = 9 \ ounce[/tex]

    The sample size is  n =  25

    The standard deviation is  [tex]\sigma = 3 \ ounce[/tex]

Given that the sample size is not large enough i.e  n<  30  we will make use of the student t distribution table  

From the question we are told the confidence level is  99.7% , hence the level of significance is    

      [tex]\alpha = (100 -99.7 ) \%[/tex]

=>   [tex]\alpha = 0.003[/tex]

Generally the degree of freedom is  [tex]df = n- 1[/tex]

=>  [tex]df = 25 - 1[/tex]

=>  [tex]df = 24[/tex]  

Generally from the student t distribution table the critical value  of  [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 24[/tex]   is  

   [tex]t_{\frac{\alpha }{2} , 24 } = 3.0 [/tex]

Generally the margin of error is mathematically represented as  

      [tex]E = t_{\frac{\alpha }{2} , 24} *  \frac{\sigma }{\sqrt{n} }[/tex]

=>     [tex]E = 3.0 *  \frac{3 }{\sqrt{25} }[/tex]

=>     [tex]E =1.8 [/tex]

Gnerally the  upper control chart limit  for 99.7% confidence is mathematically represented as

         [tex]UCL = \= x + E[/tex]

=>      [tex]UCL = 9 + 1.8[/tex]  

=>      [tex]UCL = 10.8[/tex]  

Answer:

See below for Part A.

Part B)

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

Step-by-step explanation:

Part A)

The parabola given by the equation:

[tex]y^2=4ax[/tex]

From 0 to h is revolved about the x-axis.

We can take the principal square root of both sides to acquire our function:

[tex]y=f(x)=\sqrt{4ax}[/tex]

Please refer to the attachment below for the sketch.

The area of a surface of revolution is given by:

[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]

Where r(x) is the distance between f and the axis of revolution.

From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:

[tex]r(x)=y(x)=\sqrt{4ax}[/tex]

Now, we will need to find f’(x). We know that:

[tex]f(x)=\sqrt{4ax}[/tex]

Then by the chain rule, f’(x) is:

[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]

For our limits of integration, we are going from 0 to h.

Hence, our integral becomes:

[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]

Combine roots;

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]

Simplify:

[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]

Integrate. We can consider using u-substitution. We will let:

[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]

We also need to change our limits of integration. So:

[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]

Hence, our new integral is:

[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]

Simplify and integrate:

[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]

FTC:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]

Simplify each term. For the first term, we have:

[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]

We can factor out the 4a:

[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]

For the second term, we have:

[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]

Simplify:

[tex]\displaystyle =(2a)^3[/tex]

Hence:

[tex]\displaystyle =8a^3[/tex]

Thus, our equation becomes:

[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]

We can factor out an 8a^(3/2). Hence:

[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Simplify:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

Hence, we have verified the surface area generated by the function.

Part B)

We have:

[tex]y^2=36x[/tex]

We can rewrite this as:

[tex]y^2=4(9)x[/tex]

Hence, a=9.

The surface area is 1000. So, S=1000.

Therefore, with our equation:

[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]

We can write:

[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]

Solve for h. Simplify:

[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]

Divide both sides by 8π:

[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]

Isolate term:

[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]

Raise both sides to 2/3:

[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]

Hence, the value of h is:

[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]

You seem to have left out that 0 ≤ x ≤ h.

From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is

[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]

We have

y(x) = 2√(ax)   →   y'(x) = 2 • a/(2√(ax)) = √(a/x)

so the integral is

[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]

[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]

[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]

[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]

Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :

[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]

[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]

[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]

[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]

[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]

Answer:

the answer is D

Step-by-step explanation:

A. √123 = 11.09

11.09-11 = 0.09

B. √115 = 10.72

11-10.72 = 0.28

C. √118 = 10.86

11-10.86 = 0.14

D. √120 = 10.95

11-10.95 = 0.05 ( the smallest difference )

Answer:

polygon

Step-by-step explanation:

A polygon is any 2-dimensional shape formed with straight lines. Triangles, quadrilaterals, pentagons, and hexagons are all examples of polygons. A rhombus has 4 sides.

Hope this helps:) Have a great day!

Answer:

1000

Step-by-step explanation:

Answer:

(105 x 30) + (105 x 5) + m

Step-by-step explanation:

Answer:

(105 x 30) + (105 x 5) + m

Step-by-step explanation:

Hope this helped have an amazing day!

Answer:

42

Step-by-step explanation:

uih

Step-by-step explanation:

[tex]\bullet\hookrightarrow\sf 7 (x+4)=21 [/tex]

[tex]\bullet\Rrightarrow\sf 7x+28=21 [/tex]

[tex]\bullet\rightarrowtail\sf 7x=21-28 [/tex]

[tex]\bullet\twoheadrightarrow\sf 7x=-7 [/tex]

[tex]\bullet\looparrowright\sf x=\dfrac{-7}{7}[/tex]

[tex]\bullet\rightharpoonup\sf x=-1 [/tex]

Answer:

kinetic energy

Step-by-step explanation:

When a person runs, their body must convert potential energy into kinetic energy.

Answer:

Answer is 9 Broski mark as brainliest

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

9.3

Step-by-step explanation:

6.2 x 15/10= 9.3

Answer:

Scientific notation is 1.6 x 10^16 and in regular format is:

160000000000000000

Answer:

21

Step-by-step explanation:

you plug in 5 for a and 6 for b and solve.

The value of the expression 3 + (a + 4)(8 - b) when a = 5 and b = 6 is 21

3 + (a + 4)(8 - b)

when,

a = 5 and b = 6

= 3 + (5 + 4) (8 - 6)

= 3 + 9 (2)

= 3 + 18

= 21

Therefore, the value of the expression 3 + (a + 4)(8 - b) when a = 5 and b = 6 is 21

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