A month of the year is chosen at random. What is the probability that the month starts with the letter J or the letter M?

Find a formula for the sum of the first n even positive integers.

melisa1 [442]

So even postive integers are by defention in form 2k where k is a natural number so
let the sum of even integers to n=S
S=2(1+2+3+4+5+6+7+8+......+k-1+k
divide bith sides of equation 1 by 2
0.5S=1+2+3+4+5+...........+k-1+k
S=2(k+(k-1)+..............................+2+1)
divide both sides of equation 2 by 2
0.5S=k+k-1+..............................+2+1)
by adding both we will get
___________________________
S=(k+1)(k)
so the sum will be equal to
S=
${k}^{2} + k$
so let us test the equation
for the first 3 even number there sums will be
2+4+6=12
by our equation 3^2+3=12
gave us the same answer so our equation is correct

7 0

3 years ago

3/4x=-18 what is the answer?

Afina-wow [57]

Answer:

X= 24

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

3/4*x-(18)=0

Step by step solution :

Step 1 :

3

Simplify —

4

Equation at the end of step 1 :

3

(— • x) - 18 = 0

4

Step 2 :

Rewriting the whole as an Equivalent Fraction :

2.1 Subtracting a whole from a fraction

Rewrite the whole as a fraction using 4 as the denominator :

18 18 • 4

18 = —— = ——————

1 4

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

2.2 Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

3x - (18 • 4) 3x - 72

————————————— = ———————

4 4

Step 3 :

Pulling out like terms :

3.1 Pull out like factors :

3x - 72 = 3 • (x - 24)

Equation at the end of step 3 :

3 • (x - 24)

———————————— = 0

4

Step 4 :

When a fraction equals zero :

4.1 When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

3•(x-24)

———————— • 4 = 0 • 4

4

Now, on the left hand side, the 4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

3 • (x-24) = 0

Equations which are never true :

4.2 Solve : 3 = 0

This equation has no solution.

A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.3 Solve : x-24 = 0

Add 24 to both sides of the equation :

x = 24

One solution was found :

x = 24

6 0

3 years ago

Ryan fills a bath with

S_A_V [24]

Answer:

38.8 litres

Step-by-step explanation:

22.6 + 18.7 = 41.3

41.3 - 2.5 = 38.8

38.8 litres

4 0

2 years ago

Read 2 more answers

it costs $20 per hour to bowl and $3 for shoe rental. Write a verbal model and an algebraic expression to represent the cost for

katen-ka-za [31]

3 + 20x, where x= the number of hours bowled. A verbal diagram is where you say amount to pay per hour * number of hours + price of shoe rental = total cost.

5 0

3 years ago

46÷6=? R ? What is the remainder for 46÷6= All i'm asking for is just the remainder.

Rom4ik [11]

Answer:

7.66666666667

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers