Toms math teacher asks 6 is 20 percent of what number tom incorrectly says 120 what’s is the correct number

G identify the solution of the recurrence relation an = 6an − 1 – 8an − 2 for n ≥ 2 together with the initial conditions a0 = 4,

maksim [4K]

Via the generating function method, let

$G(x)=\displaystyle\sum_{n\ge0}a_nx^n$

Then take the recurrence,

$a_n=6a_{n-1}-8a_{n-2}$

multiply everything by $x^n$ and sum over all $n\ge2$ :

$\displaystyle\sum_{n\ge2}a_nx^n=6\sum_{n\ge2}a_{n-1}x^n-8\sum_{n\ge2}a_{n-2}x^n$

Re-index the sums or add/remove terms as needed in order to be able to express them in terms of $G(x)$ :

$\displaystyle\sum_{n\ge2}a_nx^n=\sum_{n\ge0}a_nx^n-(a_0-a_1x)=G(x)-4-10x$

$\displaystyle\sum_{n\ge2}a_{n-1}x^n=\sum_{n\ge1}a_nx^{n+1}=x\sum_{n\ge1}a_nx^n=x\left(G(x)-a_0\right)=x(G(x)-4)$

$\displaystyle\sum_{n\ge2}a_{n-2}x^n=\sum_{n\ge0}a_nx^{n+2}=x^2\sum_{n\ge0}a_nx^n=x^2G(x)$

So the recurrence relation is transformed to

$G(x)-4-10x=6x(G(x)-4)-8x^2G(x)$
$(1-6x+8x^2)G(x)=4-14x$
$G(x)=\dfrac{4-14x}{1-6x+8x^2}=\dfrac{4-14x}{(1-4x)(1-2x)}=\dfrac1{1-4x}+\dfrac3{1-2x}$

For appropriate values of $x$ , we can express the RHS in terms of geometric power series:

$G(x)=\displaystyle\sum_{n\ge0}(4x)^n+3\sum_{n\ge0}(2x)^n=\sum_{n\ge0}\bigg(4^n+3\cdot2^n\bigg)x^n$

which tells us that

$a_n=4^n+3\cdot2^n$

3 0

2 years ago

Eliza’s parents are installing an above ground swimming pool in their backyard. The pool is a right circular cylinder with a dia

steposvetlana [31]

Answer:

H = 1781

Step-by-step explanation:

First, find the radius which is 9; 18/2. Then use cyclinder formula pi*r^2*h. Substitute values, but replace height with 6 because you are finding volume of water. Equation: pi*9^2*6

6 0

2 years ago

An oblique prism has trapezoidal bases and a vertical height of 10 units. An oblique trapezoidal prism is shown. The trapezoid h

hichkok12 [17]

Answer:

30x² cubic units

Step-by-step explanation:

The volume of an Oblique prism = Base Area × Height

This oblique prism has trapezoidal bases.

Area of a Trapezoid = 1/2 × h × ( b1+b2)

where h = height

b1 and b2 = bases of the Trapezoid.

From the question,

h = 20

b1 = x

b2 = 2x

Area of the Trapezoid =

1/2 × x ×( x + 2x)

1/2 × x × (3x)

3x²/2 square units.

Remember, the volume of an Oblique prism = Base Area × Height

Height of the prism = The distance between the 2 trapezoid bases = 20 units.

Base Area = 3x²/2 square units × 20 units

= 30x² cubic units

3 0

2 years ago

A dolphin is trying to jump through a hoop that is fixed at height of 3.5m above the surface of her pool. the dolphin leaves the

frosja888 [35]

40 degrees might be use the question box

4 0

2 years ago

A child who is trick-or-treating chooses a lollipop at random from a bowl of lollipops with mean weight 1.5 oz and standard devi

son4ous [18]

Answer:

The expected combined weight of the child's lollipop and two chocolate bars is 5.5 oz.

Step-by-step explanation:

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Addition of normal variables:

The mean is the sum of the means.

Find the expected combined weight of the child's lollipop and two chocolate bars.

Child lollipop: Mean 1.5 oz

Chocolate bars: Mean 2 oz

One lollipop and 2 bars combined

The mean will be 1.5 + 2*2 = 5.5 oz

The expected combined weight of the child's lollipop and two chocolate bars is 5.5 oz.

3 0

2 years ago