Adding and subtracting matrices

100 members of a Gym are surveyed. The results are shown below. Given the gym member chosen at random is a female, what is the p

Lina20 [59]

Answer:

$\frac{17}{28}$

Step-by-step explanation:

There are 56 females

There is 56 females

34 are 20+

34/56 simplfies to 17/28

8 0

3 years ago

I run a book club with n people, not including myself. Every day, for 365 days, I invite three members in the club to review a b

Bezzdna [24]

<h3>Answer: 15</h3>

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Explanation:

The order doesn't matter. A group like {A,B,C} is the same as {B,A,C}.

All that matters is the overall group rather than the positioning of the members.

We'll use the nCr combination formula since order doesn't matter.

The value of n is unknown, but we know that r = 3 members are to be selected.

Let's pick a value for n at random. Let's say n = 10.

Plug n = 10 and r = 3 into the nCr formula below.

$n C r = \frac{n!}{r!(n-r)!}\\\\10 C 3 = \frac{10!}{3!*(10-3)!}\\\\10 C 3 = \frac{10!}{3!*7!}\\\\10 C 3 = \frac{10*9*8*7!}{3!*7!}\\\\ 10 C 3 = \frac{10*9*8}{3!}\\\\ 10 C 3 = \frac{10*9*8}{3*2*1}\\\\ 10 C 3 = \frac{720}{6}\\\\ 10 C 3 = 120\\\\$

Unfortunately we don't reach 365 or larger.

Let's try n = 11

$n C r = \frac{n!}{r!(n-r)!}\\\\11 C 3 = \frac{11!}{3!*(11-3)!}\\\\11 C 3 = \frac{11!}{3!*8!}\\\\11 C 3 = \frac{11*10*9*8!}{3!*8!}\\\\ 11 C 3 = \frac{11*10*9}{3!}\\\\ 11 C 3 = \frac{11*10*9}{3*2*1}\\\\ 11 C 3 = \frac{990}{6}\\\\ 11 C 3 = 165\\\\$

We're still under our target. The good news is that the nCr value is increasing.

So the idea is to do trial and error with various values of n. Keep incrementing n until nCr = nC3 is equal to 365 or larger.

Here's a table of values where r = 3 the entire time

$\begin{array}{|c|c|} \cline{1-2}\text{n} & \text{nCr}\\\cline{1-2}10 & 120\\\cline{1-2}11 & 165\\\cline{1-2}12 & 220\\\cline{1-2}13 & 286\\\cline{1-2}14 & 364\\\cline{1-2}15 & 455\\\cline{1-2}\end{array}$

The nCr values are also found in Pascal's Triangle. Each of those values are the fourth entry of each row.

When n = 14, we have nCr = 364 which is very close. We're one short unfortunately.

So we have to go for <u>n = 15</u> instead. This makes the nCr value well over 365 of course, but it guarantees that you'll have plenty of trios to choose from such that no group of three is repeated. Unfortunately some trios will be left out.

7 0

2 years ago

You have decided to invest $1000 in a savings bond that pays 4% interest, compounded semi-annually. What will the bond be worth

Evgen [1.6K]

Answer:

$2191.12

Step-by-step explanation:

We are asked to find the value of a bond after 10 years, if you invest $1000 in a savings bond that pays 4% interest, compounded semi-annually.

$FV=C_0\times (1+r)^n$ , where,

$C_0=\text{Initial amount}$ ,

r = Rate of return in decimal form.

n = Number of periods.

Since interest is compounded semi-annually, so 'n' will be 2 times 10 that is 20.

$4\%=\frac{4}{100}=0.04$

$FV=\$1,000\times (1+0.04)^{20}$

$FV=\$1,000\times (1.04)^{20}$

$FV=\$1,000\times 2.1911231430334194$

$FV=\$2191.1231430334194$

$FV\approx \$2191.12$

Therefore, the bond would be $2191.12 worth in 10 years.

3 0

3 years ago

Can sum one help me

sleet_krkn [62]

Answer:

help with what exactly

8 0

3 years ago

Graph the line with slope 1/2<br> that passes through the point (-1,2).

enyata [817]

9514 1404 393

Answer:

see the attachment for a graph

Step-by-step explanation:

With the given point and slope, the equation of the line can be written in point-slope form:

y -k = m(x -h) . . . . . line with slope m through point (h, k)

y -2 = 1/2(x +1) . . . . line with slope 1/2 through point (-1, 2)

__

Slope is the ratio of rise to run, so a slope of 1/2 means the line will rise 1 unit for each 2 units of run (to the right). If you're plotting this by hand, you can identify a second point that is 2 right and 1 up from the given point:

(-1 +2, 2 +1) = (1, 3).

You can draw your line through those two points.

8 0

3 years ago

Adding and subtracting matrices ​

Adding and subtracting matrices