All categories

3 years ago

(NO FILES OR LINKS OR RANDOM WORDS)

Mathematics

1 answer:

ehidna [41]3 years ago

3 0

Answer:

Randomly selecting a six of diamonds - 1 / 52

Randomly selecting a 7, 8, 9 or 10 - 4 / 13

Step-by-step explanation:

There is only 1 six of diamonds in a standard deck of cards. There are 52 cards in a deck, thus the probability of pulling a six of diamonds is 1 in 52.

There are 4 of each card in a deck. so they are 4 7's, 4 8's. 4 9's and 4 10's. And there are a total of 52 cards in a deck. So the probability of pulling a 7,8,9 or 10 are 4 + 4 + 4 + 4 in 52

4 + 4 + 4 + 4 = 16

16 / 52 simplified is 4 / 13 Therefore the is a 4 in 13 chance of pulling a 7 8 9 or 10

The other ones are correct

You might be interested in

Evaluate h-²g for h = 4 and g = 32. 2 1/2 8

Hunter-Best [27]

Step-by-step explanation:

h2 - g

Putting values

(4)2 - 32

8 - 32

= - 24

3 0

3 years ago

Maria has recently retired and requested an extra $444.00 per year in income. She has $ 5400 to invest in an A-rated bond that

Dimas [21]

Answer:

$2400 in A rated bond and $3000 in B rated bond.

Step-by-step explanation:

We have been given that Maria has recently retired and requested an extra $444.00 per year in income.

We can represent this information in an equation as:

$A+B=5400...(1)$

She has $5400 to invest in an A-rated bond that pays 10% per annum or a B-rated bond paying 6% per annum.

$0.10A+0.06B=444...(2)$

From equation (1), we will get:

$A=5400-B$

Substitute this value in equation (2):

$0.10(5400-B)+0.06B=444$

$540-0.10B+0.06B=444$

$540-0.04B=444$

$540-540-0.04B=444-540$

$-0.04B=-96$

$\frac{-0.04B}{-0.04}=\frac{-96}{-0.04}$

$A=2400$

Therefore, Maria should invest $2400 in A-rated bond.

Substitute $A=2400$ in equation (1):

$2400+B=5400$

$2400-2400+B=5400-2400$

$B=3,000$

Therefore, Maria should invest $3000 in B-rated bond.

6 0

3 years ago

HELP ME PLS & FAST!!

lukranit [14]

There are 6 outcomes for the cube and 4 for the spinner. So you can multiply 6 and 4. That gives you 24. The answer is C. 24. Hope this helps!

8 0

3 years ago

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that

FromTheMoon [43]

Answer:

The Taylor series is $\ln(x) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{(x-3)^n}{3^n n}$ .

The radius of convergence is $R=3$ .

Step-by-step explanation:

The Taylor expansion.

Recall that as we want the Taylor series centered at $a=3$ its expression is given in powers of $(x-3)$ . With this in mind we need to do some transformations with the goal to obtain the asked Taylor series from the Taylor expansion of $\ln(1+x)$ .

Then,

$\ln(x) = \ln(x-3+3) = \ln(3(\frac{x-3}{3} + 1 )) = \ln 3 + \ln(1 + \frac{x-3}{3}).$

Now, in order to make a more compact notation write $\frac{x-3}{3}=y$ . Thus, the above expression becomes

$\ln(x) = \ln 3 + \ln(1+y).$

Notice that, if x is very close from 3, then y is very close from 0. Then, we can use the Taylor expansion of the logarithm. Hence,

$\ln(x) = \ln 3 + \ln(1+y) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{y^n}{n}.$

Now, substitute $\frac{x-3}{3}=y$ in the previous equality. Thus,

$\ln(x) = \ln 3 + \sum_{n=1}^{\infty} (-1)^{n+1} \frac{(x-3)^n}{3^n n}.$

Radius of convergence.

We find the radius of convergence with the Cauchy-Hadamard formula:

$R^{-1} = \lim_{n\rightarrow\infty} \sqrt[n]{|a_n|},$

Where $a_n$ stands for the coefficients of the Taylor series and $R$ for the radius of convergence.

In this case the coefficients of the Taylor series are

$a_n = \frac{(-1)^{n+1}}{ n3^n}$

and in consequence $|a_n| = \frac{1}{3^nn}$ . Then,

$\sqrt[n]{|a_n|} = \sqrt[n]{\frac{1}{3^nn}}$

Applying the properties of roots

$\sqrt[n]{|a_n|} = \frac{1}{3\sqrt[n]{n}}.$

Hence,

$R^{-1} = \lim_{n\rightarrow\infty} \frac{1}{3\sqrt[n]{n}} =\frac{1}{3}$

Recall that

$\lim_{n\rightarrow\infty} \sqrt[n]{n}=1.$

So, as $R^{-1}=\frac{1}{3}$ we get that $R=3$ .

8 0

4 years ago

Can you solve this by explaining.

In-s [12.5K]

Answer:

The answer is 1

Step-by-step explanation:

Start by solving the division part of the equation. In order to do that, you have to flip the fraction (reciprocal) and switch from division to multiplication, thus getting 3 x 3 = 9. Now you have 9 – 9 + 1, and from there you can simply work from left to right and get your final answer: 1.

8 0

3 years ago

Read 2 more answers