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Serga [27]
3 years ago
6

Division in colone 42735 divided by 5 42735:5

Mathematics
1 answer:
8090 [49]3 years ago
3 0
8547 itu jawabannya dek
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Two intersecting lines have of point(s) in common.
Dmitry [639]

Answer:A line segment

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
A toy manufacturer makes lightweight balls for indoor play. The large basketball uses 4 ounces of foam and 20 minutes of labor a
trapecia [35]

Answer:

(24, 224 ) i.e. 24 basketball and 224 footballs

Step-by-step explanation:

<em>Basketball :</em>

uses 4 ounces of foam

20 minutes of labor

profit = $2.50

<em>Football :</em>

uses 3 ounces of foam

30 minutes of labor

profit = $2

Manufacturer has :

768 ounces of foam , 120 labor hours per week,

<u>using the simplex method to determine the optimal production schedule so as to maximize profits </u>

lets assume

x = number of basketball

y = number of footballs

maximize = 2.5 x + 2y  from a linear programming problem

attached below is the detailed solution

6 0
3 years ago
George is considering two different investment options. The first option offers 7.4% per year simple interest on the
jok3333 [9.3K]

Answer:

Part A: The value of the simple interest investment at the end of three years is $12,220

Part B: The value of the compounded quarterly interest investment at the end of three years is $12,134.08

Part C: The simple interest investment is better over the first three years

Part D: I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

Step-by-step explanation:

Part A:

A = P + P r t, where

  • A represents the value of the investment
  • P represents the original amount
  • r represents the  rate in decimal
  • t represents the time in years

∵ George deposits $10,000

∴ P = 10,000

∵ First option offers 7.4% per year simple interest

∴ r = 7.4% = 7.4 ÷ 100 = 0.074

∵ He may not withdraw any of  the money for three years after

   the initial deposit

∴ t = 3

- Substitute all of these values in the formula above

∴ A = 10,000 + 10,000(0.074)(3)

∴ A = 10,000 + 2,220

∴ A = 12,220

The value of the simple interest investment at the end of three years is $12,220

Part B:

A=P(1+\frac{r}{n})^{nt}, where

  • A represents the value of the investment
  • P represents the original amount
  • r represents the  rate in decimal
  • n is a number of periods of a year
  • t represents the time in years

∵ George deposits $10,000

∴ P = 10,000

∵ The second option offers a 6.5% interest rate compounded quarterly

∴ r = 6.5% = 6.5 ÷ 100 = 0.065

∴ n = 4 ⇒ quarterly

∵ He may not withdraw any of  the money for three years after

   the initial deposit

∴ t = 3

- Substitute all of these values in the formula above

∴ A=10,000(1+\frac{0.065}{4})^{(4)(3)}

∴ A=10,000(1.01625)^{12}

∴ A = 12,134.08

The value of the compounded quarterly interest investment at the end of three years is $12,134.08

Part C:

∵ 12,220 > 12,134.08

∴ The simplest interest investment is better than the compounded

    interest investment at the end of three years

The simple interest investment is better over the first three years

Part D:

I advise George to invest his money in the compounded interest investment if he will keep the money for a long time

Look to the attached graph below

  • The red line represents the simple interest investment
  • The blue curve represents the compounded interest investment
  • (Each 1 unit in the vertical axis represents $1000)
  • After 0 years and before 4.179 years the red line is over the blue curve, that means the simple interest is better because it gives more money than the compounded interest
  • After that the blue curve is over the red line that means the compounded quarterly is better because it gives more money than the simple interest

4 0
3 years ago
Someone please help me with these 2 problems :(
k0ka [10]
If the discriminant b^2-4ac is 0, then you have TWO EQUAL, REAL ROOTS.

If you're given the x-intercepts, you can determine the factors of the polynomial as follows:   Take -3, change the sign and write (x+3).  Take 5, change the sign and write (x-5).  Then the eq'n of the parabola is

f(x) = (x+3)(x-5) = x^2 - 2x -15, in which a=1, b = -2 and c= -15.

You can find the x-coordinate of the vertex, which is also the equation of the axis of symmetry, using

x= -b / (2a).    Here, x = -(-2) / (2[1]), or  x = 1

Find the y-coordinate by subbing 1 for x in the equation above:

y = (1)^2 - 2(1) - 15  =  1 - 2 - 15  =  -16

The vertex is at (1, -16) and the equation of the axis of symm. is x = 1.
7 0
3 years ago
Find the equation for the plane that contains the line x=−1+3t , y=1+2t, z=2+4t and is perpendicular to the plane containing the
Ivan

Let L be the line given by the vector equation

(-1,1,2) + \lambda(3,2,4) \ , \lambda \in \mathbb{R}.

First, we use the director vectors of the lines L1 and L2 to get the

vector equation of the plane containing them, which we denote by \Pi_1. This is,

\\\\\Pi_1  : (1,-1,5) + \alpha (2,-1,6) + \beta (1,1,-3) \ , \alpha, \beta \in \mathbb{R}\\\\\\

We observe that \vec{N} = (2,-1,6)\times(1,1,-3) = (-3,12,3) \ne (0,0,0). Therefore, the vector equation of \Pi_1 defines a plane and \vec{N} is a normal vector to \Pi_1.

 

Finally, the vector equation for the wanted plane, which we denote by \Pi, is

\Pi : (-1,1,2) + r(3,2,4) + s(-3,12,3), r,s \in \mathbb{R} \ .

Thus, if s = 0, then L \subset \Pi and since \vec{N} is parallel to \Pi, then it is perpendicular to \Pi_1.

8 0
3 years ago
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