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natta225 [31]
2 years ago
13

Jill flipped a coin 40 times. The coin landed as heads 28 times and tails 12 times. Based on her results, which of the following

is true?
Mathematics
2 answers:
ella [17]2 years ago
8 0
There are many conclusions we can come to for this!

70% of the flips were heads, and 30% are tails

28/40 was heads, and 12/40 were tails

There were more heads than tails

There were 14 more heads than tails

:)
zaharov [31]2 years ago
3 0
I don't see any "following", but whatever is the question both results are true
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1) Use power series to find the series solution to the differential equation y'+2y = 0 PLEASE SHOW ALL YOUR WORK, OR RISK LOSING
iogann1982 [59]

If

y=\displaystyle\sum_{n=0}^\infty a_nx^n

then

y'=\displaystyle\sum_{n=1}^\infty na_nx^{n-1}=\sum_{n=0}^\infty(n+1)a_{n+1}x^n

The ODE in terms of these series is

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

\displaystyle\sum_{n=0}^\infty\bigg(a_{n+1}+2a_n\bigg)x^n=0

\implies\begin{cases}a_0=y(0)\\(n+1)a_{n+1}=-2a_n&\text{for }n\ge0\end{cases}

We can solve the recurrence exactly by substitution:

a_{n+1}=-\dfrac2{n+1}a_n=\dfrac{2^2}{(n+1)n}a_{n-1}=-\dfrac{2^3}{(n+1)n(n-1)}a_{n-2}=\cdots=\dfrac{(-2)^{n+1}}{(n+1)!}a_0

\implies a_n=\dfrac{(-2)^n}{n!}a_0

So the ODE has solution

y(x)=\displaystyle a_0\sum_{n=0}^\infty\frac{(-2x)^n}{n!}

which you may recognize as the power series of the exponential function. Then

\boxed{y(x)=a_0e^{-2x}}

7 0
3 years ago
Which statement about this system of equations is true? A. The system has no solution. B. The system has a unique solution at (0
SCORPION-xisa [38]

Answer:

A. The system has no solutions

Step-by-step explanation:

Step 1: Check to see if the 2 lines share 1 slope

slope of blue line = \frac{y2-y1}{x2-x1} =\frac{7-6}{3-0}=\frac{1}{3}

slope of red line = \frac{y2-y1}{x2-x1} =\frac{-3-(-4)}{3-0}=\frac{1}{3}

Step 2: Realize that lines with the same slope never touch

We know lines with the same slope are parallel to each other so they won't collide

Step 3: Know what the question is asking you

When they ask for solutions to the system of equations they are asking you to find out where they intersect

Step 4: Find answer

Because we know this is a parallel line they will never intersect causing this system to never have an answer or solution

Therefore the answer is A. The system has no solutions

8 0
3 years ago
Read 2 more answers
What must m∠QPS be for PQRS to be a parallelogram?
just olya [345]

Answer:

It’s B

Step-by-step explanation:

4 0
3 years ago
Please help me! I need help on this question!
schepotkina [342]

Answer:

C and A

Step-by-step explanation:

expand the things in parentheses so for C

1/2(x + 16) = 1/2(x) + 1/2(16) = 1/2 x + 8

same process for A

5 0
3 years ago
Josh is building a sandbox for his little sister. He uses these plans, which have a scale of 2 in. : 3 ft.
skelet666 [1.2K]

Answer:

Width of 6ft and length of 9ft

Step-by-step explanation:

The sandbox has a ratio of 2:3. If you plug the numbers in with the ratio, you can find the actual dimensions.

Let x be the length

Let y be the width

(Length)

2in / 3ft = 6in / (x)ft

2in / 3ft = 6in / <u><em>9ft </em></u>

(Width)

2in / 3ft = 4in / (y)ft

2in / 3ft = 4in / <em><u>6ft</u></em>

6 0
2 years ago
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