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nexus9112 [7]
3 years ago
8

Brigette has guitar lessons every fifth day and singing lessons every third day. If she had a guitar lesson and a singing lesson

on May 5, when will be the next date on which she has both guitar and singing lessons?
Mathematics
1 answer:
musickatia [10]3 years ago
7 0

Brigette has guitar lessons every fifth day and singing lessons every third day. If she had a guitar lesson and a singing lesson on May 5, when will be the next date on which she has both guitar and singing lessons?

Answer: May 20

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Show that n(n+1)(n+2) is divisible by 6<br>Solution<br>(​
vladimir2022 [97]

Proof by induction

Base case:

n=1: 1*2*3=6 is obviously divisible by six.

Assumption: For every n>1 n(n+1)(n+2) is divisible by 6.

For n+1:

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

(n(n+1)(n+2)+3(n+1)(n+2))

We have assumed that n(n+1)(n+2) is divisble by 6.

We now only need to prove that 3(n+1)(n+2) is divisible by 6.

If 3(n+1)(n+2) is divisible by 6, then (n+1)(n+2) must be divisible by 2.

The "cool" part about this proof.

Since n is a natural number greater than 1 we can say the following:

If n is an odd number, then n+1 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

If n is an even number" then n+2 is even, then n+1 is divisible by 2 thus (n+1)(n+2) is divisible by 2,so we have proved what we wanted.

Therefore by using the method of mathematical induction we proved that for every natural number n, n(n+1)(n+2) is divisible by 6. QED.

6 0
3 years ago
There are 400 students at a sports camp. Two hundred students play soccer, 100 students play baseball, and 100 students play bas
kaheart [24]
That woul be pie chart graph, as it is suited to describe thevdifferent parts of something. In this context, it refers to the total studentsvatva sport camp, whereas they are taking part in activities.
6 0
3 years ago
Read 2 more answers
The correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.
fgiga [73]

Answer: 59.91%.

Step-by-step explanation:

  • We know that the fraction of the variability in data values accounted by a model is given by r^2 , where r is the coefficient of correlation.

We are given , that the correlation between a car’s engine size and its fuel economy (in mpg) is r = - 0.774.

Then, the fraction of the variability in fuel economy is accounted for by the engine size would be r^2=( - 0.774)^2=0.599076\approx59.91\%

[Multiply 100 to convert a decimal into percent]

Hence, the fraction of the variability in fuel economy is accounted for by the engine size is 59.91%.

None of the options are correct.

5 0
4 years ago
Safety regulations require that the time between airplane takeoffs (on the same runway) will be at least 2 minutes. When taking
Xelga [282]

Answer:

1 plane

Step-by-step explanation:

Let's suppose the number of planes waiting or on the runway " P "

the number of planes taking off per hour ' P_{takeoff}'

the time for waiting and the runway T_{wr} so:

P = P_{takeoff}   x T_{wr}

P_{takeoff} = 18 airplanes per hour

we know that 1 min = 60s

36s = 36/60 = 0.6 min

Also, 3 min and 30 s = 3 + 30/60 = 3.5 min

Next to find the time for waiting and the runway

∴T_{wr}= 0.6 + 3.5  = 4.1 min/60 (converting into hour)

T_{wr}= 0.068 hour

P = 18x0.068 = 1.23

therefore, there is 1 plane either on the runway or waiting to take off

So, there is 1 plane either on the runway or waiting to take off

Read more on Brainly.com - brainly.com/question/13622877#readmore

5 0
3 years ago
BIG POINTS!
nlexa [21]
The volume V of a cone with radius r is one-third the area of the base B times the height h.
so,
 
The answer is 57.3248408
8 0
3 years ago
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