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Jet001 [13]
3 years ago
12

The sum of the first 100 positive whole numbers is 5050. What is the sum of the first 100 positive odd whole number?

Mathematics
1 answer:
Rufina [12.5K]3 years ago
4 0

The series of odd numbers is:

1, 3, 5, 7, 9, 11, 13, ....

If you observe this series, it is an Arithmetic Series with first term as 1 and common difference of 2. Common difference is defined as the difference between two consecutive terms of the series. So by using the formula of sum of an Arithmetic Series, we can find the sum of first 100 positive odd whole numbers.

The formula for the sum of an Arithmetic Series is:

S_{n}=\frac{n}{2}(2a_{1}+(n-1)*d)

Here,

n = number of terms = 100

a₁ = first term = 1

d = Common Difference = 2

Using the values, we get:

S_{100}=\frac{100}{2}(2(1)+99*2)\\   \\  S_{100}=10000

Thus, the sum of first 100 positive odd whole numbers is 10,000.

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Step-by-step explanation:

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Carol successfully increases her business to 200 customers per day. However, her total cost for doing so is 50% greater than the
kramer

Carol's Steakhouse, the total cost of serving 150 customers per day is $900. Carol is interested in increasing her business, but is concerned about the effect on marginal cost.

Carol successfully increases her business to 200 customers per day. However, her total cost for doing so is 50% greater than the expected $1,600. What percent greater is the actual marginal cost than the expected marginal cost, to the nearest full perc

Answer:

214

Step-by-step explanation:

We have been given

C1 = $900

Q1 = 259

Then c2 = $1600

Q2 = 200

M = 1600-900/50

= 14

For real,

C1 = 900

C2 = 2400

Q1 = 150

Q2 = 50

1500/50 = 30

30/14 x 100

= 214

It is greater by 214 percent

5 0
3 years ago
I need help? Can anyone help me ?
Rina8888 [55]
Given a coordinate point (x, y), the first value of the point represents the value on the x-axis while the second value represent the value on the y-axis.

1.) To express the values (-4, -1), (-1, 2), (1, -4), (2, -3), (4, 3) as a table, we have:

 x          y
-4         -1
-1          2
 1         -4
 2         -3
 4          3

The values (-4, -1), (-1, 2), (1, -4), (2, -3), (4, 3) expressed as a graph have been attached as graph_1


To express the values (-4, -1), (-1, 2), (1, -4), (2, -3), (4, 3) as a mapping, we have two circles with one labelled x and the other one labelled y.
Inside the circle labelled x are the numbers -4, -1, 1, 2, 4 written vertically and inside the circle labelled y are the numbers -4, -3, -1, 2, 3 written vertically.
There are lines joining from the circle labelled x to the circle labelled y with line joining -4 in circle x to -1 in circle y, -1 in circle x to 2 in circle y, 1 in circle x to -4 in circle y, 2 in circle x to -3 in circle y, 4 in circle x to  3 in circle y.

The domain of the relation is the set of the x-values of the relation, i.e. domain is {-4, -1, 1, 2, 4}.
The range of the relation is the set of the y-values of the relation, i.e. range is {-4, -3, -1, 2, 3}

2.) To express the values (-2, 1), (-1, 0), (1, 2), (2, -4), (4, 3) as a table, we have:

 x          y
-2         1
-1         0
 1          2
 2         -4
 4          3

The values (-2, 1), (-1, 0), (1, 2), (2, -4), (4, 3) expressed as a graph have been attached as graph_2


To express the values (-2, 1), (-1, 0), (1, 2), (2, -4), (4, 3) as a mapping, we have two circles with one labelled x and the other one labelled y.
Inside the circle labelled x are the numbers -2, -1, 1, 2, 4 written vertically and inside the circle labelled y are the numbers -4, 0, 1, 2, 3 written vertically.
There are lines joining from the circle labelled x to the circle labelled y with a line joining -2 in circle x to 1 in circle y, -1 in circle x to 0 in circle y, 1 in circle x to 2 in circle y, 2 in circle x to -4 in circle y, 4 in circle x to  3 in circle y.

The domain of the relation is the set of the x-values of the relation, i.e. domain is {-2, -1, 1, 2, 4}.
The range of the relation is the set of the y-values of the relation, i.e. range is {-4, 0, 1, 2, 3}
7 0
3 years ago
Geometry
satela [25.4K]

Answer:

Option (C)

Step-by-step explanation:

From the picture attached,

Two lines 'h' and 'k' are the parallel lines and a transversal 'n' is intersecting these parallel lines at two distinct points.

By the theorem of alternate interior angles, angle 8 and angle 11 will be equal in measure.

∠8 ≅ ∠11 [Alternate interior angles]

m(∠8) = m(∠11) = 118°

Therefore, Option (C) will be the answer.

7 0
3 years ago
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