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2 years ago

At a military function, three cannons are fired at intervals of 12

Mathematics

1 answer:

Morgarella [4.7K]2 years ago

3 0

Answer:

144 seconds

Step-by-step explanation:

To do solve this question, we must find the LCM (least common multiple) of 12, 16, and 18.

Let's start by prime factorizing (finding the prime factors) all the numbers.

$12\rightarrow3*4\rightarrow2*2*3$

$16\rightarrow4*4\rightarrow2*2*2*2$

$18\rightarrow2*9\rightarrow2*3*3$

Now, we must find the greatest quantity of each [prime] number and multiply them together to obtain the least common multiple.

Upon further evaluation of the [prime] factors, we can see that we need four 2s and two 3s. Therefore...

$2*2*2*2*3*3=2^4*3^2=16*9=144$

They will be fired together again after 144 seconds.

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A student has four sticks of wood that measures 3 inches, 4 inches, 5 inches, and 6 inches.Can the student use any three of thes

saw5 [17]

Answer:

Yes, the student can use three of these sticks to make a right triangle.

Step-by-step explanation:

The measure of four sticks = 3 inches, 4 inches, 5 inches and 6 inches.

Now, in a right angled triangle, by PYTHAGORAS THEOREM the three sides of the triangle base, perpendicular and hypotenuse are in the given following relation :

$(Base)^{2} + (Perpendicular)^{2} = (Hypotenuse)^{2}$

Now, here among all four sticks

$(3)^{2} +(4)^{2} = 9 + 16 = 25$

and $25 = (5)^{2}$

So, there exists three sticks of length 3 in, 4 in and 5 inches which satisft Pythagoras Theorem , such that:

$(3)^{2} + (4)^{2} = (5)^{2}$

So, the required length sticks are 3 inches, 4 inches and 5 inches.

Hence, the student use three of these sticks to make a right triangle.

5 0

3 years ago

3. A clothing manufacturing company makes two types of jogging pants, design A and design B. the design A jogging pants sells to

andriy [413]

Answer:

z(max) = 256000 Php

x₁ = 10

x₂ = 110

Step-by-step explanation:

Jogging pants design Selling Price Cost

weekly production

Design A x₁ 2500 1750

Design B x₂ 2100 1200

1. z ( function is : )

z = 2500*x₁ + 2100*x₂ to maximize

First constraint weekly production

x₁ + x₂ ≤ 120

Second constraint Budget

1750*x₁ + 1200*x₂ ≤ 150000

Then the model is

z = 2500*x₁ + 2100*x₂ to maximize

Subject to

x₁ + x₂ ≤ 120

1750*x₁ + 1200*x₂ ≤ 150000

General constraints x₁ ≥ 0 x₂ ≥ 0 both integers

First table

z x₁ x₂ s₁ s₂ cte

1 -2500 -2100 0 0 0

0 1 1 1 0 = 120

0 1750 1200 0 1 = 150000

Using AtoZmath online solver and after 6 iterations the solution is:

z(max) = 256000 Php

x₁ = 10

x₂ = 110

3 0

3 years ago

Consider the triangle below.

Pepsi [2]

The measure of angle P is 29 degrees

The sum of an interior angle of a triangle is 180 degrees. Given the following parameters:

m<M = 15x + 5

m<N = 3x + 2

m<P = 5x - 11

Taking the sum and equating to 180 degrees:

m<M + m<N + m<P = 180 degrees

15x + 5 + 3x + 2 + 5x - 11 = 180

23x - 4 = 180

23x = 184

x = 184/23

x = 8

Get the measure of m<P

m<P = 5x - 11

m<P = 5(8) - 11

m<P = 40 - 11

m<P = 29 degrees

Hence the measure of angle P is 29 degrees

Learn more on angles here: brainly.com/question/25770607

7 0

2 years ago

If your bill at a restaurant is $44.33, tax is 6.5% and you want to leave a 15% tip how much $ is your total bill? Round your an

alexandr402 [8]

Answer:

53.83

Step-by-step explanation:

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2 years ago

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Which of the following are solutions to the graph?

Maru [420]

Answer:

im too late

Step-by-step explanation:

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2 years ago