MATHEMATICS HIGH SCHOOL

find the minimum value of p=10x+26y the constraints are x+y less than or equal to 6, 5x+y greater than or equal to 10, x+5y greater than or equal to 14

Answers

Answer 1

Answer:

Answer:

Minimum value of $p=10x+26y$ is 80 at (1.5,2.5)

Step-by-step explanation:

We are given

The objective function is, Minimize $p=10x+26y$

With the constraints as,

$x+y\leq 6\n5x+y\geq 10\nx+5y\geq 14$

So, upon plotting the constraints, we see that,

The boundary points of the solution region are,

(1,5), (1.5,2.5) and (4,2).

So, the minimum values at these points are,

Points $p=10x+26y$

(1,5) $p=10x* 1+26* 5$ i.e. p = 140

(1.5,2.5) $p=10* 1.5+26* 2.5$ i.e. p= 80

(4,2) $p=10* 4+26* 2$ i.e. p = 92

Thus, the minimum value of $p=10x+26y$ is 80 at (1.5,2.5).

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Two spheres have are such that the radius of the bigger sphere is 3 times bigger than the smaller. What is the ratio of the area?

Answers

Answer:

1 : 27

Step-by-step explanation:

Radius of sphere one = r₁ = x units

Radius of sphere 2 = r₂ = 3*x = 3x units

Ratio of area of two sphere's = r₁³ : r₂³

= x³ : (3x)³

$= (x^(3))/(3^(3)*x^(3))\n\n= (1)/(3^(3))\n\n= (1)/(27)$

= 1 : 27

Which expression gives the surface area of a sphere with radius r?A. r2
B. 4r3
C. 4r2
D. 4r2

Answers

The surface area of a sphere is the area of four great circles . . . 4 π r² .

Apparently, either 'C' or 'D' was supposed to be the correct choice,
but the π got lost in the pantry on the way to the printer.

Answer:

Area of sphere is given by $4\cdot \pi\cdot r^2$

Step-by-step explanation:

The surface area of sphere is given by:

$\text{Area of sphere}=4\cdot \pi\cdot r^2$

Option C and D are correct but $\pi$ is missing in the options

Option A and B are incorrect.

$\pi=3.14$ to solve the area of sphere when radius is given a constant value.

If the volume for 3-D polyhedra A is 300 cm3 and the volume for 3-D polyhedral B is 900 cm3. How many times bigger is the volume of pyramid B than pyramid A? Select one:
a. 3%
b. 30%
c. 300%
d. 3000%

Answers

Answer:

c. 300%

Step-by-step explanation:

In order to solve this problem you just have to divide the bigger polyhedral by the smaller polyhedral:

$(900 cm^(3) )/(300cm^(3))$

As this is equal to 3, you know that the bigger polyhedral is 3 times bigger than the smaller polyhedral so now you just make a rule of three, if an object that is 100% bigger than other is 1 time bigger, what would be the percentage of an object that is 3 times bigger?

$(1)/(100)=(3)/(x)$

Once you clear the X the equation would look like this:

$x=(3*100)/(1)$

$x=300$

Hello Marie,

V(B)/V(A)=900/300=3=300/100=300%

Between 1998 and 2018, inflation for prices of goods and services has been about 51%. Suppose a salon charged $18 for a basic haircut in 1998 and has been raising prices by a steady percentage each year to keep up with inflation.What is the price of a haircut at the salon in 2008? Explain or show your reasoning.

In 2003, the salon charged $19.95 for a basic haircut. Find the cost of the basic haircut in 2013. Explain your reasoning.

Answers

9514 1404 393

Answer:

$22.12
$24.51

Step-by-step explanation:

For some growth factor f each year, the growth factor over 20 years is given as ...

f^20 = 1 +0.51 = 1.51

Then the growth factor in 10 years is ...

f^10 = (f^20)^(1/2) = √1.51 ≈ 1.22882

a) In the 10 years between 1998 and 2008, the price of a basic haircut would rise to ...

$18 × 1.22882 ≈ $22.12 . . . price in 2008

b) In the 10 years between 2003 and 2013, the price of a basic haircut would rise to ...

$19.95 × 1.22882 ≈ $24.51 . . . price in 2013

Please help 50 pts and brainliest if correct

Answers

Answer:

Step-by-step explanation:

it makes sense yah?

Answer:

C) Three fourths of the fish he caught were less than 50.5 pounds

If 3x-1=11,what is the value of x^2+x

Answers

We can set the 2nd equation to y that way we have something to solve for
$\left \{ {{3x-1=11} \atop {x^2+x=y}} \right.$
First we solve our first equation by moving the one to the other side
$3x=12$
Then we divide by 3 on each side
$x=4$
So now we can plug 4 into the x's of the 2nd equation
$4^2+4=y\n 16+4=y\n 20=y$

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