All categories

2 years ago

You are given a set of 5 discs, numbered 2, 3, 5, 6, and 9.

Mathematics

1 answer:

dusya [7]2 years ago

4 0

Answer:

3/5

Step-by-step explanation:

Number of numbers divisible by 3 = 3

Total numbers = 5

P (divisible by 3) = 3/5

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1 (15 Points]. Prove the following statement: is divisible by 3 if only if it is a sum of three consecutive integers. be ddvisbk

Alinara [238K]

Answer:

First. Let us prove that the sum of three consecutive integers is divisible by 3.

Three consecutive integers can be written as k, k+1, k+2. Then, if we denote their sum as n:

n = k+(k+1)+(k+2) = 3k+3 = 3(k+1).

So, n can be written as 3 times another integer, thus n is divisible by 3.

Second. Let us prove that any number divisible by 3 can be written as the sum of three consecutive integers.

Assume that n is divisible by 3. The above proof suggest that we write it as

n=3(k+1)=3k+3=k + k + k +1+2 = k + (k+1) + (k+2).

As k, k+1, k+2 are three consecutive integers, we have completed our goal.

Step-by-step explanation:

4 0

2 years ago

Styline menswear ordered short-sleeve shirts for $23 each and long-sleeve shirts for $28.50 each from Tommy Hilfiger. If the tot

Mice21 [21]

Styline menswear ordered short-sleeve shirts for $23 each and long-sleeve shirts for $28.50

short-sleeve shirts for $23

long-sleeve shirts for $28.50

Total cost = $9,862.50

Let x be the number of short - sleeve

and y be the number of long - sleeve

Total shirts = 375

x + y = 375

23x + 28.50y = 9862.50

Now we solve for x

x + y = 375 ( subtract x on both sides)

So y = 375 - x

Now plug in 375 -x for y in second equation

23x + 28.50y = 9862.50

23x + 28.50(375 - x ) = 9862.50

23x + 10687.5 - 28.50x = 9862.50

subtract 10687.5 from both sides

23x - 28.50x = -825

-5.5x = -825 (divide -5.5 on both sides)

x = 150

So number of short-sleeve = 150

7 0

3 years ago

When the product of 5 and a number is increased by5, the result is 17.Find the number

Andreas93 [3]

5n+ 5= 17

5n= 17-5

5n= 12

N= 12/5

N= 2.4

The answer is 2.4.

Hope this helps!

5 0

3 years ago

The graph of the function P(x) = −0.34x2 + 12x + 62 is shown. The function models the profits, P, in thousands of dollars for a

STatiana [176]

Answer:

0 ≤ x < 1.12 and 34.18 < x ≤ 39.87

Step-by-step explanation:

The options of the question are

−4.57 ≤ x ≤ 39.87

1.12 ≤ x ≤ 34.18

−4.57 ≤ x ≤ 1.12 and 34.18 ≤ x ≤ 39.87

0 ≤ x < 1.12 and 34.18 < x ≤ 39.87

Let

x ----> is the number of tires produced, in thousands

C(x) ---> the production cost, in thousands of dollars

we have

$C(x)=-0.34x^{2} +12x+62$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

The graph in the attached figure

we know that

Looking at the graph

For the interval [0,1.12) -----> $0\leq x$

The value of C(x) ----> $C(x) < 75$

That means ----> The production cost is under $75,000

For the interval (34.18,39.87] -----> $34.18 < x\leq 39.87$

The value of C(x) ----> $C(x) < 75$

That means ----> The production cost is under $75,000

Remember that the variable x (number of tires) cannot be a negative number

therefore

If the company wants to keep its production costs under $75,000 a reasonable domain for the constraint x is

0 ≤ x < 1.12 and 34.18 < x ≤ 39.87

3 0

3 years ago

Read 2 more answers

How to prove system of nonlinear equations has finite solutions?

nalin [4]

This is what you could do

4 0

3 years ago