The cost, c(x), for a taxi ride is given by c(x) = 2x + 2.00, where x is the number of minutes.

Use the method of Gauss to find the sum.1+2+3+.....+400

nikklg [1K]

Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:

1+2+3+4+5+6+7+8+9+10

We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.

Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.

(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.

Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).

So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.

Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved

Hope this helps.

6 0

3 years ago

2 + 2 x 0<br><br> Anyone wanna join my pad✨let ?

erik [133]

Answer:

2

Step-by-step explanation:

6 0

2 years ago

A hotel wants to know if there's a relationship between gender and the way customers make room reservations. A manager takes a r

padilas [110]

Answer:

Step-by-step explanation:

Here,

H_o: The way of reservation is independent of gender.

H_a: The way of reservation is not independent of gender.

We use a chi square test because we can calculate the expected frequencies for this chart.

Doing an Expected Value Chart,

33.7625 9.7125 30.525

39.2375 11.2875 35.475

Using chi^2 = Sum[(O - E)^2/E],

chi^2 = 4.482385929

With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,

a = 3

b = 2

df = 2

Thus, the critical value is

significance level = 0.05

chi^2(critical) = 5.991464547

Also, the p value is

P = 0.106331579

Thus, comparing chi^2 and chi^2(critical) [or, p and significance level], we FAIL TO REJECT THE NULL HYPOTHESIS.

Thus, there is no significant evidence that the way of reservation is dependent of gender. [CONCLUSION]

6 0

3 years ago

What are the zeros of this function?

tatyana61 [14]

Answer:

Step-by-step explanation:

the zeroes of a function basically mean when y = 0, so basically the x-intercept(s)

in this case, the zeroes are 3 and 6

3 0

2 years ago

Read 2 more answers

onyango wishes to fence a rectangular research plot using 100 m of wire .one end of the plot has a wall already erected .calcula

earnstyle [38]

Answer:

1250 m²

Step-by-step explanation:

Let x and y denote the sides of the rectangular research plot.

Thus, area is;

A = xy

Now, we are told that end of the plot already has an erected wall. This means we are left with 3 sides to work with.

Thus, if y is the erected wall, and we are using 100m wire for the remaining sides, it means;

2x + y = 100

Thus, y = 100 - 2x

Since A = xy

We have; A = x(100 - 2x)

A = 100x - 2x²

At maximum area, dA/dx = 0.thus;

dA/dx = 100 - 4x

-4x + 100 = 0

4x = 100

x = 100/4

x = 25

Let's confirm if it is maximum from d²A/dx²

d²A/dx² = -4. This is less than 0 and thus it's maximum.

Let's plug in 25 for x in the area equation;

A_max = 25(100 - 2(25))

A_max = 1250 m²

5 0

3 years ago