Ask question

Ask question

All categories

4 years ago

9

A profile of the investments owned by an agent’s clients follows: 228 own annuities. 220 own mutual funds. 98 own life insurance

and mutual funds. 93 own annuities and mutual funds. 16 own annuities, mutual funds, and life insurance. 45 more clients own only life insurance than own only annuities. 290 own only one type of investment (i.e., annuity, mutual fund, or life insurance). Calculate the agent’s total number of clients.

1 answer:

Naddik [55]4 years ago

6 0

Answer:

Total number of clients =500

Step-by-step explanation:

<em>Refer to the Venn diagram for the pictorial representation.</em>

Let x represent the number of clients for annuities only,

Then number of clients for life insurance only = x+45

Number of clients for annuities and mutual funds only = 93-16 = 77

Number of clients for life assurance and mutual funds only = 98-16 =82

Number of clients for mutual funds only = 220 -(77+16+82) =45

from the question 290 own only one type of investment.

x+x+45+45 =290

2x+90=290

2x=290-90

2x=200

$x=\frac{200}{2}$

x=100.

clients for annuities only = 100

clients for Life insurance only =x+45= 100+45=145

228 clients own annuities,

number of clients that own annuities and life assurance only = 228-(100+77+16)

=228-193

=35

Total number of clients = sum of all the spaces in the Venn diagram.

= 100+77+16+35+45+82+145

=500 clients

You might be interested in

What term is 1/1024 in the geometric sequence,-1,1/4,-1/6..?

Trava [24]

Answer:

$\large\boxed{\text{sixth term is equal to}\ \dfrac{1}{1024}}$

Step-by-step explanation:

The explicit formula for a geometric sequence:

$a_n=a_1r^{n-1}$

$a_n$ - n-th term

$a_1$ - first term

$r$ - common ratio

$r=\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=...=\dfrac{a_n}{a_{n-1}}$

We have

$a_1=-1,\ a_2=\dfrac{1}{4},\ a_3=-\dfrac{1}{6},\ ...$

The common ratio:

$r=\dfrac{\frac{1}{4}}{-1}=-\dfrac{1}{4}\\\\r=\dfrac{-\frac{1}{6}}{\frac{1}{4}}=-\dfrac{1}{6}\cdot\dfrac{4}{1}=-\dfrac{2}{3}\neq-\dfrac{1}{4}$

<h2>It's not a geometric sequence.</h2>

If $a_3=-\dfrac{1}{16}$ then the common ratio is $r=\dfrac{-\frac{1}{16}}{\frac{1}{4}}=-\dfrac{1}{16}\cdot\dfrac{4}{1}=-\dfrac{1}{4}$

Put to the explicit formula:

$a_n=-1\left(-\dfrac{1}{4}\right)^{n-1}$

Put $a_n=\dfrac{1}{1024}$ and solve for <em>n </em>:

$-1\left(-\dfrac{1}{4}\right)^{n-1}=\dfrac{1}{1024}\qquad\text{use}\ a^n:a^m=a^{n-m}\\\\-\left(-\dfrac{1}{4}\right)^n:\left(-\dfrac{1}{4}\right)^1=\dfrac{1}{1024}\\\\-\left(-\dfrac{1}{4}\right)^n\cdot(-4)=\dfrac{1}{1024}\\\\(4)\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{1024}\qquad\text{divide both sides by 4}\ \text{/multiply both sides by}\ \dfrac{1}{4}/\\\\\left(-\dfrac{1}{4}\right)^n=\dfrac{1}{4096}\\\\\dfrac{(-1)^n}{4^n}=\dfrac{1}{4^6}\qquad n\ \text{must be even number. Therefore}\ (-1)^n=1$

$\dfrac{1}{4^n}=\dfrac{1}{4^6}\iff n=6$

5 0

3 years ago

Which is true regarding chords and diameters of circles?

Gelneren [198K]

Answer:

Both chords and diameters have two endpoints on a circle. Diameters must intersect the center of a circle.

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A bank employee notices an abandon checking account with a balance of $360 the bank charges an $5 monthly fee for the account. E

raketka [301]

The function will be
$y=360-5x$
where y is the balance, and x is the number of month.
The raph will be a line on the xy-plain which starts at the point (0, 360), and end in the point (72, 0).
Hope it helps.

4 0

3 years ago

Milton purchases of 5 gallon aquarium for his bedroom to fill the ground with water uses the container with the capacity of 1 qu

fgiga [73]

We know that

the capacity of container is 1 quart--------> 0.25 gallon------> 1/4 gallon
so
1/4 gallon-----------------> 1 time
5 gallons----------------> X times?
X=5/(1/4)--------> X=20 times

the answer is
20 times

8 0

3 years ago

How can you tell when a pattern shows counting on by tens

FromTheMoon [43]

All the number end in a zero 10 20 30 40 50 60 70 80 90

4 0

4 years ago