you score 24 points in a basketball game. you make 9 shots how many three point shots and two point shots do you make

Answers

Answer 1

Answer:

6 threes where made and 3 twos where made

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Solve this differential Equation by using power series
y''-x^2y=o

Answers

We're looking for a solution

$y=\displaystyle\sum_(n=0)^\infty a_nx^n$

which has second derivative

$y''=\displaystyle\sum_(n=2)^\infty n(n-1)a_nx^(n-2)=\sum_(n=0)^\infty(n+2)(n+1)a_(n+2)x^n$

Substituting these into the ODE gives

$\displaystyle\sum_(n=0)^\infty(n+2)(n+1)a_(n+2)x^n-\sum_(n=0)^\infty a_nx^(n+2)=0$

$\displaystyle\sum_(n=0)^\infty(n+2)(n+1)a_(n+2)x^n-\sum_(n=2)^\infty a_(n-2)x^n=0$

$\displaystyle2a_2+6a_3x+\sum_(n=2)^\infty(n+2)(n+1)a_(n+2)x^n-\sum_(n=2)^\infty a_(n-2)x^n=0$

$\displaystyle2a_2+6a_3x+\sum_(n=2)^\infty\bigg((n+2)(n+1)a_(n+2)-a_(n-2)\bigg)x^n=0$

Right away we see $a_2=a_3=0$ , and the coefficients are given according to the recurrence

$\begin{cases}a_0=y(0)\na_1=y'(0)\na_2=0\na_3=0\nn(n-1)a_n=a_(n-4)&\text{for }n\ge4\end{cases}$

There's a dependency between terms in the sequence that are 4 indices apart, so we consider 4 different cases.

If $n=4k$ , where $k\ge0$ is an integer, then

$k=0\implies n=0\implies a_0=a_0$

$k=1\implies n=4\implies a_4=(a_0)/(4\cdot3)=\frac2{4!}a_0$

$k=2\implies n=8\implies a_8=(a_4)/(8\cdot7)=(6\cdot5\cdot2)/(8!)a_0$

$k=3\implies n=12\implies a_(12)=(a_8)/(12\cdot11)=(10\cdot9\cdot6\cdot5\cdot2)/(12!)a_0$

and so on, with the general pattern

$a_(4k)=(a_0)/((4k)!)\displaystyle\prod_(i=1)^k(4i-2)(4i-3)$

If $n=4k+1$ , then

$k=0\implies n=1\implies a_1=a_1$

$k=1\implies n=5\implies a_5=(a_1)/(5\cdot4)=(3\cdot2)/(5!)a_1$

$k=2\implies n=9\implies a_9=(a_5)/(9\cdot8)=(7\cdot6\cdot3\cdot2)/(9!)a_1$

$k=3\implies n=13\implies a_(13)=(a_9)/(13\cdot12)=(11\cdot10\cdot7\cdot6\cdot3\cdot2)/(13!)a_1$

and so on, with

$a_(4k+1)=(a_1)/((4k+1)!)\displaystyle\prod_(i=1)^k(4i-1)(4i-2)$

If $n=4k+2$ or $n=4k+3$ , then

$a_2=0\implies a_6=a_(10)=\cdots=a_(4k+2)=0$

$a_3=0\implies a_7=a_(11)=\cdots=a_(4k+3)=0$

Then the solution to this ODE is

$\boxed{y(x)=\displaystyle\sum_(k=0)^\infty a_(4k)x^(4k)+\sum_(k=0)^\infty a_(4k+1)x^(4k+1)}$

On his last 5 math tests, Gilbert earned: 94, 72, 83, 94, 90. What was his average score? ( Report your answer to the tenths place).

Answers

Answer:

Average of Gilbert in last 5 test = 86.6

Step-by-step explanation:

Given:

Score earned by Gilbert in last 5 test = 94, 72, 83, 94, 90

Find:

Average of Gilbert in last 5 test

Computation:

Average value = Sum of all events / Total number of events

Average of Gilbert in last 5 test = Sum of all last results / Number of results

Average of Gilbert in last 5 test = [94 + 72 + 83 + 94 + 90] / 5

Average of Gilbert in last 5 test = [433] / 5

Average of Gilbert in last 5 test = 86.6

HE is 1/3 the length of HG , HE=x-3 and HG=4x-15 find HE

Answers

Answer:

HE=3

Step-by-step explanation:

Equations

With the data provided, we can set up an equation. Then we need to solve the equation. Finally, we use the just-found value of x to calculate HE.

Data:

HE=1/3 HG

HE=x-3

HG=4x-15

Replacing the last two equations in the first:

x-3=1/3(4x-15)

Multiply both sides by 3:

3(x-3)=4x-15

Operate:

3x-9=4x-15

Moving x's to the left and numbers to the right:

3x-4x=-15+9

Joining like terms:

-x=-6

Multiply by -1:

x=6

Since HE= x-3:

HE=6-3

HE=3

Answer:

x=24

Step-by-step explanation:

HE= 1/3(HG)

x-3=1/3(4x-15)

3x-9=4x-15

-x=-24

x=24

Sky needs $6700 for school and has two options. Option A: 5 years at 5% interest with monthly payments of $126.44 Option B: 6 years at 3.5% interest with monthly payments of $103.30 Calculate the total payback on each loan and calculate how much Sky will save by choosing option B.

Answers

Answer:

148.80

Step-by-step explanation:

Take 126.44 multiply by 60 months equals 7586.40

Take 103.30 multiply by 72 months equals 7437.60

Subtract 7437.60 from 7586.40

Final answer:

The total payback for Option A would be $7,586.4 and for Option B it would be $7,437.60. The difference of $148.8 indicates the savings Sky would have by choosing Option B over Option A.

Explanation:

Firstly, to calculate the total payback for each loan, you multiply the number of payments by the monthly payment amount. For Option A, that's 5 years times 12 payments per year, times a monthly payment of $126.44. Which gives us a total payback of 5 * 12 * 126.44 = $7,586.4. Next, calculate the payback for Option B in the same way: 6 years times 12 payments per year, times a monthly payment of $103.30. Which gives us 6 * 12 * 103.30 = $7,437.60.

Then, we subtract the total payback of Option B from that of Option A to find the savings: $7,586.4 - $7,437.60 = $148.8. So, by choosing option B, Sky would save $148.8.

Learn more about Loan Comparison here:

brainly.com/question/32541612

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Marco paid $42.40 for 6.4 Gallons of gas. What is the price of 1 gallon of gas? Group of answer choices

Answers

Answer:

6.63

Step-by-step explanation:

What is the probability that a point chosen at random is in the blue region?

Answers

Answer:

Well It would about 1/10000000 if your talking about all colors, but its not specified how many blue regions other colored regions there are so I cant tell you without knowing.

Step-by-step explanation:

Just Take the amount of regions then put it under the amount of Blue regions there are then look up on a browser, Ex: What is 2/3 into a percent: 66.6 percent, And you have your answer :)

Answer:

15/17

Step-by-step explanation:

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