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3 years ago

Find all the numbers such that the sum of twice the number and 8 is greater than or equal to tour times the number

Mathematics

1 answer:

Wittaler [7]3 years ago

5 0

Answer:

Step-by-step explanation:

Let the number = x

2x + 8 ≥ 4x Subtract 2x from both sides.

8 ≥ 4x - 2x Combine

8 ≥ 2x Divide by 2

8/2 ≥ 2x/2 Combine

4 ≥ x

What this means is that the largest value the x can have is 4. Any number greater that 4 will make the use of ≥ incorrect.

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New codes to destroy the First Order are known to exist. With probability 0.6, the codes are hidden by Leia; with probability 0.

elixir [45]

Answer: (a). 0.62 (b). 0.53

Step-by-step explanation:

Let us start by defining some events seen:

Given;

L rep the event that codes hidden Leia

BB represents the codes hidden in BB-8

H is the event that codes hidden by Hah

C-3PO rep the codes hidden in C3PO

Giving the probabilities, we have that

P(L) = probability that codes are hidden by Leia = 0.6

P(H) = probability that codes are hidden by Hah = 0.4

where P(BB/L) = 70/10 i.e 70%

P(C-3PO/L) = 1 - P(BB/L) = 1 - 7/10 = 3/10

Also, P(BB/H) = 1/2 = P(C-3PO/H)

We can say that Han Solo is likely to hide them in aceta BB-8 and C-3PO

To begin,

(a). The question tell us to find the probability that the codes are with BB-8.

First of all, we find P(BB).

P(BB) = P(L)*P(BB/L) + P(H)*P(BB/H)

solving this we get

P(BB) = 0.6*7/10 + 0.4*1/2 = 0.62

Therefore, the probability that the codes are with BB-8 = 0.62

(b). The second question says;

Given that the codes are with C-3PO, what is the probability the codes were hidden by Han Solo?

This tell us to find P(H/C-3PO)

P(H/C-3PO) = P(C-3PO/H)*P(H) / P(C-3PO/H) + P(C-3PO/L)*P(L)

inputting the values gives us;

P(H/C-3PO) = 1/2 * 0.4 / ( 1/2 *0.4 + 3/10 *0.6) = 0.53

SO we have that the probability the codes were hidden by Han Solo = 0.53

cheers I hope this was helpful!!

3 0

3 years ago

A company manufactures two different sizes of boat lifts. The smaller lift requires 1 hour in the welding department and 2 hours

qaws [65]

Answer:

The solution that optimizes the profit is producing 0 small lifts and 50 large lifts.

Below are all the steps explained in detail.

The graph is attached.

Explanation:

1. Name the variables:

x: number of smaller lifts
y: number of larger lifts

2. Build a table to determine the number of hours each lift requires from each department:

Number of hours

small lift large lift total per department

Welding department 1x 3y x + 3y

Packaging department 2x 1y 2x + y

3. Constraints

150 hours available in welding: x + 3y ≤ 150
120 hours available in packaging: 2x + y ≤ 120
The variables cannot be negative: x ≥ 0, and y ≥ 0

Then you must:

draw the lines and regions defined by each constraint
determine the region of solution that satisfies all the constraints
determine the vertices of the solution region
test the profit function for each of the vertices. The vertex that gives the greatest profit is the solution (the number of each tupe that should be produced to maximize profits)

4. Graph

See the graph attached.

Here is how you draw it.

x + 3y ≤ 150
draw the line x + 3y = 150 (a solid line because it is included in the solution set)
shade the region below and to the left of the line

2x + y ≤ 120
draw the line 2x + y ≤ 120 (a solid line because it is included in the solution set)
shade the region below and to the left of the line

x ≥ 0 and y ≥ 0: means that only the first quadrant is considered

the solution region is the intersection of the regions described above.

take the points that are vertices inside the solutoin region.

5. Test the profit function for each vertex

The profit function is P(x,y) = 25x + 90y

The vertices shown in the graph are:

(0,0)
(0,50)
(42,36)
(60,0)

The profits with the vertices are:

P(0,0) = 0
P(0,50) = 25(0) + 90(50) = 4,500
P(42,36) = 25(42) + 90(36) = 4,290
P(60,0) = 25(60) + 90(0) = 1,500

Thus, the solution that optimizes the profit is producing 0 smaller lifts and 90 larger lifts.

3 0

3 years ago

Further mathematics: Find the derivative of the function x^2 y + (xy)^3 +3x=0 at (-1 , 3)

vesna_86 [32]

Answer:

Step-by-step explanation:

Implicit differentiation:

x^2 y + (xy)^3 + 3x = 0

x^2 y + x^3y^3 + 3x = 0

Using the product rule:

2x* y + x^2*dy/dx + 3x^2 y^3 + x^3* (d(y^3)/dx) + 3 = 0

2xy + x^2 dy/dx + 3x^2 y^3 + x^3* 3y^2 dy/dx + 3 = 0

dy/dx(x^2 + 3y^2x^3) = (-2xy - 3x^2y^3 - 3)

dy/dx= (-2xy - 3x^2y^3 - 3) / (x^2 + 3y^2x^3)

At the point (-1, 3).

the derivative = (6 - 81 - 3)/(1 -27)

= -78/-26

= 3.

8 0

2 years ago

Read 2 more answers

If your car gets 34 miles per gallon of gas and you have traveled 153 miles how many gallons of gas have you used

velikii [3]

4.5 gallons? 153 divide it by 34 = 4.5 gallons ?

6 0

3 years ago

Find the smaller of 2 consecutive numbers if the sum of the smaller and twice the larger is -4

vesna_86 [32]

Answer:

Step-by-step explanation:

n = the smaller even integer

n +2 = the next even integer

The wording of the question translates into:

2n + (n+2) = -4

3n +2 = -4

3n = -6

n = -2

8 0

2 years ago

Find all the numbers such that the sum of twice the number and 8 is greater than or equal to tour times the number​

Find all the numbers such that the sum of twice the number and 8 is greater than or equal to tour times the number