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Fiesta28 [93]
3 years ago
14

Prove by mathematical induction. 2n<(n+2)!, for n ≥ 0, where n ∈ ℤ

Mathematics
1 answer:
Mekhanik [1.2K]3 years ago
6 0

The question is difficult for a beginner like me

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Suppose a scientist reported the following data regarding the presence bacteria during the first four hours of testing for a new
OlgaM077 [116]

The recursive geometric sequence that models this situation is:

f(n) = 0.9f(n-1)

f(1) = 90000

<h3>What is a geometric sequence?</h3>

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

It can be represented by a recursive sequence as follows:

f(n) = qf(n-1)

With f(1) as the first term.

In this problem, the sequence is: 90.000: 81,000; 72,900; 65,610, hence:

q = \frac{65610}{72900} = \cdots = \frac{81000}{90000} = 0.9

f(1) = 90000

Hence:

f(n) = 0.9f(n-1)

f(1) = 90000

More can be learned about geometric sequences at brainly.com/question/11847927

7 0
2 years ago
Question in the image below:
horrorfan [7]

Answer:

x = 5/33 or 0.151515151

Step-by-step explanation:

7(-6x-2) = 8(3x-4)

step 1: simplify the equation.

-42x - 14 = 24x - 4

step 2: isolate the variable (using the balance method).

-42x - 14 + 14 = 24x - 4 + 14

-42x = 24x + 10

-42x - 24x = 24x - 24x + 10

-66x = 10

step 3: solve for x.

x = 10 ÷ -66

x = 5/33

4 0
3 years ago
Carla has 1 gallon of paint. She is going to pour it into a paint tray that measures 10 inches wide, 10 inches long, and 7 cm de
STatiana [176]
To determine the correct statement in the choices presented, we first have to solve the area of the tray. We assume it to be in a rectangular form so the area is:

Area = 10 in x 10 in x 7/2.54 in = 275.59 in³ for the paint tray
1 gallon paint = 231 in³ paint

Therefore, the correct answer is the first option. <span>The paint will not fill the tray by 44.59 in</span>³<span>.</span>
7 0
3 years ago
Read 2 more answers
What is the correct graph of the function 2x - y = 2?
kolbaska11 [484]

Answer:

slope: 2 2. y-intercept: 2 2.

Step-by-step explanation:

Any line can be graphed using two points.

5 0
3 years ago
the system of equations is graphed on the coordinate plane y=-1/2x-1 and y=1/4x-4 enter the coordinates of the solution to the s
pochemuha

Answer:

The coordinates are ( 4, -3).

Step-by-step explanation:

We can find the coordinates by solving the 2 equations

y =  1/4x-4

y = -1/2x-1

As both left sides of the equation are y we can say:

-1/2x-1 = 1/4x-4

-1/2x - 1/4x = -4 + 1

-3/4 x = -3

x = -3 * -4/3

x = 4.

- and y = 1/4(4) - 4 = -3.

7 0
3 years ago
Read 2 more answers
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