All categories

3 years ago

If n is an even integer between 1 and 1989, what is the probability that n^2 is divisible by 8

Mathematics

1 answer:

pantera1 [17]3 years ago

5 0

Answer:

0.249874

Step-by-step explanation:

After every 4 digits, n squared is divisible by 8 so we have 1989/4= 497 numbers divisible by 4 after squaring

probability n=497/1989= 0.249874

Probability n=0.249874

You might be interested in

Katerina is a botanist studying the production of pears by two types of pear trees. she noticed that Type A trees produced 20 pe

Ronch [10]

Answer:

120 pears

Step-by-step explanation:

Let the number of pears produced by Type B be x

Number of pears produced by type A=144

According to question

Type A produce 20% more pears than B

x+ x ×20%= 144

x+x× $\frac{20}{100}$ = 144

$\frac{100x+20x}{100}$ = 144

$\frac{120x}{100}$ =144

x= 144× $\frac{100}{120}$

x=120 pears

Hence, Number of pears produced by B= 120 pears

Hence, the correct answer is 120 pears

5 0

3 years ago

−6x+14<−28 OR 9x+15≤−12

Serhud [2]

Answer:x>7 or x ≤ -3

Solving the 1st inequality

-6x +14 < -28 --------------- (Collect like terms)

-6x < -28 - 14

-6x < - 42 -------------------- (Divide both sides by -6)

Note: If you decide an inequality expression by a negative value, the inequality sign changes)

-6x/-6 > -42/-6

x > 7

Solving the 2nd inequality

9x + 15 ≤ −12 ----------- (Collect like terms)

9x ≤ −12 - 15

9x ≤ −27 ------------------(Divide both sides by 9)

9x/9 ≤ −27/9

x ≤ -3

Bring both results together, we get

x>7 or x ≤ -3

The final result is complex (i.e. can't be combined together).

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Suppose approximately 75% of all marketing personnel are extroverts, whereas about 70% of all computer programmers are introvert

Setler [38]

Answer:

$P(x \ge 5) = 1.000$ ---- At least 5 from marketing departments are extroverts

$P(x=15) = 0.013$ ---- All from marketing departments are extroverts

$P(x = 0) = 0.002$ ---------- None from computer programmers are introverts

Step-by-step explanation:

See comment for complete question

The question is an illustration of binomial probability where

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$(a):\ P(x \ge 5)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

Using the complement rule, we have:

$P(x \ge 5) = 1 - P(x < 5)$

So, we have:

$P(x < 5) =P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)$

$P(x = 0) = ^{15}C_{0} * (75\%)^0 * (1 - 75\%)^{15 - 0} = 1 * 1 * (0.25)^{15} = 9.31 * 10^{-10}$

$P(x = 1) = ^{15}C_{1} * (75\%)^1 * (1 - 75\%)^{15 - 1} = 15* (0.75)^1 * (0.25)^{14} = 4.19 * 10^{-8}$

$P(x = 2) = ^{15}C_{2} * (75\%)^2 * (1 - 75\%)^{15 - 2} = 105* (0.75)^2 * (0.25)^{13} = 8.80 * 10^{-7}$

$P(x = 3) = ^{15}C_{3} * (75\%)^3 * (1 - 75\%)^{15 - 3} = 455* (0.75)^2 * (0.25)^{12} = 0.0000153$

$P(x = 4) = ^{15}C_{4} * (75\%)^4 * (1 - 75\%)^{15 - 4} = 1365 * (0.75)^4 * (0.25)^{11} = 0.000103$

So, we have:

$P(x < 5) = (9.31 * 10^{-10}) + (4.19 * 10^{-8}) + (8.80 * 10^{-7}) + 0.0000153 + 0.000103$

$P(x < 5) = 0.00011922283$

Recall that:

$P(x \ge 5) = 1 - P(x < 5)$

$P(x \ge 5) = 1 - 0.00011922283$

$P(x \ge 5) = 0.9998$

$P(x \ge 5) = 1.000$ --- approximated

$(b)\ P(x = 15)$

$n = 15$ --- marketing personnel

$p = 75\%$ --- proportion that are extroverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x=15) = ^{15}C_{15} * 0.75^{15} * (1 - 0.75)^{15-15}$

$P(x=15) = 1 * 0.75^{15} * (0.25)^{0$

$P(x=15) = 0.013$

$(c)\ P(x = 0)$

$n=5$ ---------- computer programmers

$p = 70\%$ --- proportion that are introverts

So, we have:

$P(x) = ^nC_x * p^x * (1 - p)^{n-x}$

$P(x = 0) = ^{5}C_0 * (70\%)^0 * (1 - 70\%)^{5-0}$

$P(x = 0) = 1 * 1 * (0.30)^5$

$P(x = 0) = 0.002$

3 0

3 years ago

Given a dilation with the origin O (0, 0), by observation determine the scale factor "K."

BaLLatris [955]

When the dilation is about the origin, the scale factor multiplies every coordinate. That is (considering the x-coordinate) ...
6·k = 3
k = 3/6 = 1/2

The appropriate choice is
1. 1/2

4 0

4 years ago

Read 2 more answers

To determine the inverse of a point, you?

oksano4ka [1.4K]

So if you're asked to graph a function and its inverse, all you have to do is graph the function and then switch all x and y values in each point to graph the inverse. Just look at all those values switching places from the f(x) function to its inverse g(x) (and back again), reflected over the line y = x.

8 0

4 years ago