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3 years ago

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A psychology test has personality questions numbered 1,2,3, intelligence questions numbered 1,2,3,4, and attitude questions numb

ered 1,2. If a single question is picked at random, what is the probability that the question is an intelligence question OR has an odd number?

1 answer:

In-s [12.5K]3 years ago

6 0

Answer:

7/9.

Step-by-step explanation:

There are a total of 9 questions,

The odd numbers are 1,1,1,3,3 = a total of 5 .

Probability (it is an odd number) = 5/9.

Probability (It is an intelligence question of even number) = 2/9.

Required probability = 5/9 + 2/9

= 7/9.

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Susan invests $Z at the end of each year for seven years at an annual effective interest rate of 5%. The interest credited at th

aleksley [76]

Answer:

2.02955

Step-by-step explanation:

Given that:

Susan invests $Z as each year ends for seven years.

So we assume that Z = 1

Susan's accrued value comprises $7 invested each year at a 6 percent annual effective rate.

The cashflow interest:

The cashflow of Susan interest payments are:

Payments Time

0 1

0.05 2

2(0.05) 3

3(0.05) 4

4(0.05) 5

5(0.05) 6

6(0.05) 7

The accumulated value of this cash flow is:

$(0.05)I_{6\%} = (0.05) \dfrac{((1+0.06)_{6\%} - 6)}{0.06} \\ \\ \implies 1.1653$

So Susan accumulated values is:

X = 7 + 1.1653

X = 8.1653

Lori's accumulated value is $14, which she has set aside to plan her cash flow for interest.

The cashflow of Lori interest payments are;

Payments 0 0.025 2(0.025) 3(0.025) ......... 13(0.025)

Time 1 2 3 4 .......... 14

The accumulated value of cash flow is:

$(0.025 )(I)_{3\%} =(0.025) \dfrac{(1+0.03)_{3\%}-13}{0.03}\\ \\= 2.5719$

Now, Lori's accumulated value is:

Y = 14 + 2.5719

Y = 16.5719

Since; Susan value X = 8.1653

Lori's value Y = 16.5719

∴

$\dfrac{Y}{X}= \dfrac{16.5719}{8.1653}$

= 2.02955

7 0

3 years ago

15 players for a softball team show up for a game: (a) How many ways are there to choose 10 players to take the field? 3003 (b)

prohojiy [21]

Answer:

(a) 3003 ways

(b) 10897286400 ways

(c) 3002 ways

Step-by-step explanation:

Given

$n = 15$ --- 15 players

Solving (a) Ways of selecting 10 players.

This implies combination.

So, we have:

$r=10$

Using:

$^nC_r = \frac{n!}{(n-r)!r!}$

We have:

$^{15}C_{10} = \frac{15!}{(15-10)!10!}$

$^{15}C_{10} = \frac{15!}{5!10!}$

Simplify

$^{15}C_{10} = \frac{15*14*13*12*11*10!}{5!10!}$

$^{15}C_{10} = \frac{15*14*13*12*11}{5!}$

$^{15}C_{10} = \frac{15*14*13*12*11}{5*4*3*2*1}$

$^{15}C_{10} = \frac{360360}{120}$

$^{15}C_{10} = 3003$

Solving (b) Ways of assigning positions to 10 players.

This implies permutation.

So, we have:

$r=10$

Using:

$^nP_r = \frac{n!}{(n-r)!}$

We have:

$^{15}P_{10} = \frac{15!}{(15-10)!}$

$^{15}P_{10} = \frac{15!}{5!}$

Solve each factorial

$^{15}P_{10} = \frac{1307674368000}{120}$

$^{15}P_{10} = 10897286400$

Solving (c) Ways of choosing at least 1 woman

We have:

$Men = 10$

$Women = 5$

Ways of selecting 10 players is: (a) 3003 ways

Since the number of men are 10, there is 1 way of selecting 10 men (i.e. selection without women)

Using complement rule:

At least 1 woman = Total - No woman

$At\ least\ 1\ woman = 3003 - 1$

$At\ least\ 1\ woman = 3002$

5 0

3 years ago

It is known that the point P(-9,18) belongs to the graph of the function y=k/x. Find k.

riadik2000 [5.3K]

Answer:

$k = (-162)$ .

Step-by-step explanation:

A point of the form $(x_{0},\, y_{0})$ belongs to the graph of this function, $y = k / x$ , if and only if the equation of this function holds after substituting in $x = x_{0}$ and $y = y_{0}$ .

The question states that the point $(-9,\, 18)$ belongs to the graph of this function. Thus, the equation of this function, $y = k / x$ , should hold after substituting in $x = (-9)$ and $y = 18$ :

$y = k / x$ .

$18 = k / (-9)$ .

Solve this equation for the constant $k$ :

$\begin{aligned}k &= 18 \times (-9) \\ &= (-162)\end{aligned}$ .

Thus, $k = (-162)$ .

6 0

2 years ago

Which equation represents the graphed function?

yKpoI14uk [10]

Y= -2x + 3 is correct

5 0

3 years ago

Read 2 more answers

How would you graph, y=-x-2

Natali5045456 [20]

Well you would start at Y= 0(-x) -2. So (0, -2) then you would move to the left by 1 and move down by 1.

6 0

4 years ago