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3 years ago

gYou have a six-sided die that you roll once and ob- serve the number of dots facing upwards. What is the sample space

Mathematics

1 answer:

Aleonysh [2.5K]3 years ago

5 0

Hey!

The sample space would be sides 1, 2, 3, 4, 5, and 6, or 1-6.

A sample space is a range of possible values.

Hope this helps! :D

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One of the solutions to x2 − 2x − 15 = 0 is x = −3. What is the other solution?

Alex_Xolod [135]

If you factor the equation you can see what the solutions are. Two factor a quadratic of the form ax^2+bx+c, find two values which satisfy two conditions...

jk=ac=-15 and j+k=b=-2 so j and k must be -5 and 3 so the factors are:

(x-5)(x+3)

So the other solution is x=5

7 0

3 years ago

Read 2 more answers

What is the solution to the system?

sergey [27]

The answer is in my attachment

6 0

3 years ago

Find a power series for the function, centered at c, and determine the interval of convergence. f(x) = 9 3x + 2 , c = 6

san4es73 [151]

Answer:

$\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........$

The interval of convergence is: $(-\frac{2}{3},\frac{16}{3})$

Step-by-step explanation:

Given

$f(x)= \frac{9}{3x+ 2}$

$c = 6$

The geometric series centered at c is of the form:

$\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.$

Where:

$a \to$ first term

$r - c \to$ common ratio

We have to write

$f(x)= \frac{9}{3x+ 2}$

In the following form:

$\frac{a}{1 - r}$

So, we have:

$f(x)= \frac{9}{3x+ 2}$

Rewrite as:

$f(x) = \frac{9}{3x - 18 + 18 +2}$

$f(x) = \frac{9}{3x - 18 + 20}$

Factorize

$f(x) = \frac{1}{\frac{1}{9}(3x + 2)}$

Open bracket

$f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}$

Rewrite as:

$f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}$

Collect like terms

$f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}$

Take LCM

$f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}$

$f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}$

So, we have:

$f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}$

By comparison with: $\frac{a}{1 - r}$

$a = 1$

$r = -\frac{1}{3}x + \frac{7}{9}$

$r = -\frac{1}{3}(x - \frac{7}{3})$

At c = 6, we have:

$r = -\frac{1}{3}(x - \frac{7}{3}+6-6)$

Take LCM

$r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)$

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)

So, the power series becomes:

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}ar^n$

Substitute 1 for a

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}1*r^n$

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}r^n$

Substitute the expression for r

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n$

Expand

$\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n]$

Further expand:

$\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................$

The power series converges when:

$\frac{1}{3}|x - \frac{7}{3}| < 1$

Multiply both sides by 3

$|x - \frac{7}{3}|$

Expand the absolute inequality

$-3 < x - \frac{7}{3}$

Solve for x

$\frac{7}{3} -3 < x$

Take LCM

$\frac{7-9}{3} < x$

$-\frac{2}{3} < x$

The interval of convergence is: $(-\frac{2}{3},\frac{16}{3})$

6 0

2 years ago

Help me pleaseeeessss

wlad13 [49]

Answer:

28/53

Step-by-step explanation:

Hey There!

So they want us to find the sine of angle S

well remember is sohcahtoa

S - sine

O - opposite

H - hypotenuse

meaning that

$Sin=\frac{opposite}{hypotenuse}$

The opposite side of angle S is 28 and the hypotenuse is 53

so $sinS=\frac{28}{53}$

5 0

3 years ago

A jar contains 5 purple, 6 yellow, 8 green, and 5 orange jellybeans. What is the probability of selecting a yellow jellybean fol

Oksana_A [137]

Answer:

$\frac{5}{96}$

Step-by-step explanation:

At the beginning, the jar contains the following beans:

5 purple

6 yellow

8 green

5 orange

Therefore, the total number of jellybeans in the jar tha beginning is:

$n=5+6+8+5=24$

The number of yellow beans at the beginning is

$y=6$

Therefore, the of selecting a yellow jellybean at the beginning is

$p(y)=\frac{y}{n}=\frac{6}{24}=\frac{1}{4}$

After selecting this yellow bean, the yellow bean it is replaced in the jar, so the number of total beans is still n = 24.

And the number of purple beans inside is

$p=5$

So, the probability of selecting a purple bean at the 2nd attempt is

$p(p)=\frac{5}{24}$

Therefore, the combined probability of selecting a yellow jellybean followed by a purple one is

$p(yp)=p(y)\cdot p(p)=\frac{1}{4}\cdot \frac{5}{24}=\frac{5}{96}$

3 0

3 years ago