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3 years ago

This is an example of an arithmetic series: 6 + 8 + 10 + 12 + . . . + (4 + 2n) + . . .

Mathematics

1 answer:

nasty-shy [4]3 years ago

5 0

True. A series is arithmetic if its terms come from an arithmetic sequence.

And a sequence is said to be arithmetic any of its two consecutive terms differ by a fixed difference, common to any consecutive pair.

As you can see, in this case, all terms differ by 2, so the sequence

$6,\ 8,\ 10,\ 12,\ \ldots,\ 4+2n$

is arithmetic, and thus the series

$6 + 8 + 10 + 12 + \ldots + (4+2n)$

is arithmetic as well.

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"In one statistics course, students reported studying an average of 9.92 hours a week, with a standard deviation of 4.54. Treati

Rudik [331]

Answer:

66.28% of students study more than 8 hours

Step-by-step explanation:

The percent of students study more than 8 hour can be calculated as

P(X>8)=?

P(X>8)=P((X-mean)/sd>(8-9.92)/4.54)

The calculated z-score is -0.42.

P(X>8)=P(Z>-0.42)

P(X>8)=P(0<Z<-0.42)+P(0<Z<∞)

P(X>8)=0.1628+0.5=0.6628.

Thus, 66.28% of students study more than 8 hours.

3 0

3 years ago

Which of the following statements are true?

lara31 [8.8K]

I believe it is C, as the graphs do look the same.

7 0

4 years ago

Suppose a jar contains 5 red marbles and 25 blue marbles. If you reach in the jar and pull out one marble at random, do not repl

dsp73

Answer:

Probability that event will have both red marbles will be 2.3% or 0.023.

Step-by-step explanation:

Given:

Total red marbles=5

Total blue marbles=25

Total number of marbles =30

To Find:

The probability that both are red without replacement of marbles.

Solution:

Now

Total sample space is 30 and total red marbles are 5

For a event that getting red marble probability is ,

=Total red marbles /total marbles.

=5/30

=1/6

So probability if getting red marble is 1/6

<em>Now for second chance there will be 4 red marbles remaining and 29 total marbles so,</em>

In second chance probability if getting red marble will be

=total red marbles present/total marbles remaining

=4/29

Now ,

The required probability will be getting both at a time

i.e probability getting red AND red marble so here AND operator which means multiple both the probability.

Probability both will have red =1/6*4/29

=4/(29*6)=2/(29*3)

=0.022988

=0.023

=2.3 %

8 0

3 years ago

1.) Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth .x squared minus 21 x equals n

Andrew [12]

Part 1
We are given $x^2-21x=-4x$ . This can be rewritten as $x^2-18x=0$ .
Therefore, a=1, b=-18, c=0.
Using the quadratic formula
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-\left(-18\right)\pm \sqrt{\left(-18\right)^2-4\left(1\right)\left(0\right)}}{2\left(1\right)}$
$x=\frac{18\pm 18}{2}$

The values of x are
$x_1=\frac{18-18}{2}=0$
$x_2=\frac{18+18}{2}=18$

Part 2
Since the values of y change drastically for every equal interval of x, the function cannot be linear. Therefore, the kind of function that best suits the given pairs is a quadratic function.

Part 3.
The first equation is $y=x^2+2$ .
The second equation is $y=3x+20$ .

We have
$x^2+2=3x+20$
$x^2-3x-18=0$
Factoring, we have
$\left(x-6\right)\left(x+3\right)=0$
Equating both factors to zero.
$x_1-6=0\rightarrow x_1=6$
$x_2+3=0\rightarrow x_2=-3$

When the value of x is 6, the value of y is
$y=3\left(6\right)+20=38$

When the value of x is -3, the value of y is
$y=3\left(-3\right)+20=11$

Therefore, the solutions are (6,38) or (-3,11)

7 0

3 years ago

In triangle ABC above, AD is perpendicular to CB. If the lengths of AD and CB were both increased by 50%, how would the area of

astra-53 [7]

Answer:

The answer is below

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. There are different types of triangles such as scalene triangle, equilateral triangle, isosceles triangle.

The area of a triangle is given as:

A = (1/2) * b * h

where b = base of triangle, h = height of triangle , A = area

Let BC = base = x, and AD = height = y, hence:

A = (1/2) * x * y = 0.5xy

If the lengths of AD and CB were both increased by 50%, hence:

new AD = y + 0.5y = 1.5y, new CB = x + 0.5x = 1.5x

The new area= (1/2) * 1.5y * 1.5x = 1.125xy

Increased area / area = 1.125xy / 0.5xy = 2.25

If the lengths are increased by 50%, the area would also increase and the new area would be 2.25 times

3 0

3 years ago