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2 years ago

12

What is missing from the frequency chart below

1 answer:

saw5 [17]2 years ago

4 0

Answer:

a

Step-by-step explanation:

A. The tallies are missing

(I think this can be the answer )

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The population, in millions, of a city t years after 1990 is given by the equation P(t) = 2.9 + 0.08t. In this function, A) 0.08

dedylja [7]

The answer would be 2.9 million is the population of the city in 1990 and 0.08 million is the increase per year in the population.

Hope this helps!

4 0

3 years ago

Read 2 more answers

13.10. Suppose that a sequence (ao, a1, a2, ) of real numbers satisfies the recurrence relation an -5an-1+6an-20 for all n> 2

Gwar [14]

a. This recurrence is of order 2.

b. We're looking for a function $A(x)$ such that

$A(x)=\displaystyle\sum_{n=0}^\infty a_nx^n$

Take the recurrence,

$\begin{cases}a_0=a_0\\a_1=a_1\\a_n-5a_{n-1}+6a_{n-2}=0&\text{for }n\ge2\end{cases}$

Multiply both sides by $x^{n-2}$ and sum over all integers $n\ge2$ :

$\displaystyle\sum_{n=2}^\infty a_nx^{n-2}-5\sum_{n=2}^\infty a_{n-1}x^{n-2}+6\sum_{n=2}^\infty a_{n-2}x^{n-2}=0$

Pull out powers of $x$ so that each summand takes the form $a_kx^k$ :

$\displaystyle\frac1{x^2}\sum_{n=2}^\infty a_nx^n-\frac5x\sum_{n=2}^\infty a_{n-1}x^{n-1}+6\sum_{n=2}^\infty a_{n-2}x^{n-2}=0$

Now shift the indices and add/subtract terms as needed to get everything in terms of $A(x)$ :

$\displaystyle\frac1{x^2}\left(\sum_{n=0}^\infty a_nx^n-a_0-a_1x\right)-\frac5x\left(\sum_{n=0}^\infty a_nx^n-a_0\right)+6\sum_{n=0}^\infty a_nx^n=0$

$\displaystyle\frac{A(x)-a_0-a_1x}{x^2}-\frac{5(A(x)-a_0)}x+6A(x)=0$

Solve for $A(x)$ :

$A(x)=\dfrac{a_0+(a_1-5a_0)x}{1-5x+6x^2}\implies\boxed{A(x)=\dfrac{a_0+(a_1-5a_0)x}{(1-3x)(1-2x)}}$

c. Splitting $A(x)$ into partial fractions gives

$A(x)=\dfrac{2a_0-a_1}{1-3x}+\dfrac{3a_0-a_1}{1-2x}$

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n$

so that for $|3x|$ and $|2x|$ , or simply $|x|$ , we have

$A(x)=\displaystyle\sum_{n=0}^\infty\bigg((2a_0-a_1)3^n+(3a_0-a_1)2^n\bigg)x^n$

which means the solution to the recurrence is

$\boxed{a_n=(2a_0-a_1)3^n+(3a_0-a_1)2^n}$

d. I guess you mean $a_0=2$ and $a_1=5$ , in which case

$\boxed{\begin{cases}a_0=2\\a_1=5\\a_2=13\\a_3=35\\a_4=97\\a_5=275\end{cases}}$

e. We already know the general solution in terms of $a_0$ and $a_1$ , so just plug them in:

$\boxed{a_n=2^n+3^n}$

8 0

3 years ago

If 100% = $64, how much is 10%?

bezimeni [28]

Answer: 6.4

100 percent = 64

10 percent = 6.4

6 0

4 years ago

Read 2 more answers

Write solutions to the systems of inequalities that should lie on the double- shade region

Vadim26 [7]

Answer:

(1,1) (2,2) (1,2) (1,5) (4,4) (4,5)

there are a lot more but those are some.

Step-by-step explanation:

6 0

3 years ago

Find the missing side length.

Mandarinka [93]

Answer:

The missing side length is 5 cm

Step-by-step explanation:

We see that 4cm is on the top and 9 cm is on the bottom.

All we need to do is subtract 4 from 9

9-4=5

The missing side length is 5 cm

Hope this helps! Plz award Brainliest : )

5 0

4 years ago