Justin says that if the diameter of any circle is 15 feet then its radius must 10

A research team conducted a study showing that approximately 15% of all businessmen who wear ties wear them so tightly that they

Helen [10]

Answer:

a) 0.913

b) 0.397

c) 0.087

Step-by-step explanation:

We are given the following information:

We treat wearing tie too tight as a success.

P(Tight tie) = 15% = 0.15

Then the number of businessmen follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 15

We have to evaluate:

a) at least one tie is too tight

$P(x \geq 1) = P(x = 1) +....+ P(x = 15)\\=1 - P(x = 0)\\= 1 - \binom{15}{0}(0.15)^0(1-0.15)^{15}\\=1 - 0.087\\= 0.913$

b) more than two ties are too tight

$P(x > 2) = P(x = 3) +....+ P(x = 15)\\=1 - P(x = 0) - P(x=1) - P(x=2)\\= 1 - \binom{15}{0}(0.15)^0(1-0.15)^{15}-\binom{15}{1}(0.15)^1(1-0.15)^{14}-\binom{15}{0}(0.15)^2(1-0.15)^{13}\\=1 - 0.087 - 0.231 - 0.285\\= 0.397$

c) no tie is too tight

$P(x = 0)\\=\binom{15}{0}(0.15)^0(1-0.15)^{15}\\=0.087$

d) at least 18 ties are not too tight

This probability cannot be evaluated as the number of success or the failures exceeds the number of trials given which is 15.

The probability is asked for 18 failures which cannot be evaluated.

8 0

3 years ago

William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles t

meriva

Answer:

Each boy will get <u>25</u> marbles.

Step-by-step explanation:

Given:

William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles the last jar holds 17 marbles.

Now, to write an expression using parentheses to find number of marbles each boy get.

Let the number of marbles each boy get be $x.$

Total number of boys = 2.

Number of marbles first jar holds = 12.

Second jar holds = 21.

And third jar holds = 17.

As given, William shares marbles equally with his brother.

Now, we write the expression to find the number of marbles each boy get:

$x=\frac{(12+21+17)}{2}$

$x=\frac{12}{2} +\frac{21}{2} +\frac{17}{2}$

$x=6+10.5+8.5$

$x=25.$

Therefore, each boy will get 25 marbles.

4 0

3 years ago

-0.25 + 3 1/6 + 2 1/12<br> plz help me with this.

hjlf

Answer:

5

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Simplify.<br> (f3 – 5f + 25) – (4f2 – 12f + 9)

Neko [114]

Answer:

2f + 16

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Whats the distance between (-8,-7) (8,-4)

balandron [24]

To find the distance between points, use the distance formula.

Distance formula: $\sqrt{ (x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }$

Plug in your values for $x_{2}, x_{1}, y_{2}, y_{1}$ using (-8, -7) and (8, -4) and solve.

$\sqrt{(8 - (-8))^{2}+(-4 - (-7))^{2}}$
$\sqrt{(8+8)^{2}+(-4+7)^{2}}$
$\sqrt{(16)^{2}+(3)^{2}}$
$\sqrt{256+9}$
$\sqrt{265}$ ≈ $16.28$

Answer:
Approximately 16.28 units.

8 0

3 years ago