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3 years ago

A rope is 14 2/5 yards long. If it is cut into 8 equal pieces, how long will each piece be?

Mathematics

2 answers:

Rudiy273 years ago

5 0

1.8 yard long i believe

lesya692 [45]3 years ago

5 0

We need to start by making it into an improper fraction

14 2/5 = 72/5 then divide it by 8

72 1 72
--- × --- = -----
5 8 40

then simplify

9/5 is your answer

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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

2 years ago

To rent a certain meeting room, a college charges a reservation fee of $49 and an additional fee of $5.40 per hour. The chemistr

elena-14-01-66 [18.8K]

Answer:

The maximum amount of money the chemistry club can spend without going over their buget is $81.4 ... With a total of 6 hours their allowed to use the room for.

Step-by-step explanation:

$49 is our constant and will not change. 5.40 however will. Let's use variable h for the amount hours they can rent the room for. Now we can make an inequality;

49+ 5.40h < 86.80

5.40h < 86.80

5.4h< 37.8

h< 7

Now that we know h will have to be less than seven for the chemistry club to spend less than their buget we can find that 6 is the maxium amount of hours they can spend in the room while staying within their budget.

(This answer does not consider decimals or half hours)

6 0

2 years ago

_30. Solve the following logarithmic equation: log8(x + 9) + 3 = 3

Bezzdna [24]

Answer:

Step-by-step explanation:

using the rule of logarithms

$log_{b}$ x = n ⇒ x = $b^{n}$

$log_{8}$ (x + 9) + 3 = 3 ( subtract 3 from both sides )

$log_{8}$ (x + 9) = 0 , then

x + 9 = $8^{0}$ = 1 ( subtract 9 from both sides )

x = - 8

7 0

2 years ago

latoya is going for a run. she runs at a speed of 6 miles per hour for 9.6 miles. for how many hours does she run?

LenKa [72]

$\begin{array}{ccc}6mi&-&1h\\9.6mi&-&xh\end{array}\ \ |cross\ multiply\\\\6x=1\cdot9.6\\\\6x=9.6\ \ \ |divide\ both\ sides\ by\ 6\\\\\boxed{x=1.6\ (h)}$

7 0

3 years ago

Which of the following are solutions to the equation below? Check all that apply. 15x2 - 44x + 32 = 0

krek1111 [17]

If you want to find the solutions for this you have to factor it. Since it's a second degree polynomial, you'll have 2 solutions. Factoring this using the quadratic formula, you'll get factors of (5x-8)(3x-4). Solving these for x you get x = 8/5 and x = 4/3.

6 0

3 years ago