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3 years ago

What is the value of n

Mathematics

1 answer:

Nookie1986 [14]3 years ago

7 0

Answer:

Step-by-step explanation:

The angle 160° and the interior angle of the triangle form a straight angle

interior angle = 180° - 160° = 20°

Similarly with angle 131° and the interior angle at the top of the triangle

interior angle = 180° - 131° = 49°

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

n is an exterior angle, hence

n = 20° + 49° = 69° → C

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The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest

Ksenya-84 [330]

Answer:

a) 0.7287

b) 0.9663

c) 0.237

d) 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.5 million tons of cargo per week

Standard Deviation, σ = 0 .82 million tons

We are given that the distribution of number of tons of cargo handled per week is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P( port handles less than 5 million tons of cargo per week)

P(x < 5)

$P( x < 5) = P( z < \displaystyle\frac{5 - 4.5}{0.82}) = P(z < 0.609)$

Calculation the value from standard normal z table, we have,

$P(x < 5) =0.7287= 72.87\%$

b) P( port handles 3 or more million tons of cargo per week)

$P(x \geq 3) = P(z \geq \displaystyle\frac{3-4.5}{0.82}) = P(z \geq −1.82926)\\\\P( z \geq −1.82926) = 1 - P(z < -1.829)$

Calculating the value from the standard normal table we have,

$1 - 0.0337 = 0.9663 = 96.63\%\\P( x \geq 3) = 96.63\%$

c)P( port handles between 3 million and 4 million tons of cargo per week)

$P(3 \leq x \leq 4) = P(\displaystyle\frac{3 - 4.5}{0.82} \leq z \leq \displaystyle\frac{4-4.5}{0.82}) = P(-1.829 \leq z \leq -0.609)\\\\= P(z \leq -0.609) - P(z < -1.829)\\= 0.271-0.034 = 0.237= 23.7\%$

$P(3 \leq x \leq 4) = 23.7\%$

d) P(X=x) = 0.85

We have to find the value of x such that the probability is 0.85.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 4.5}{0.82})=0.85$

$= 1 -P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.85$

$=P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.15$

Calculation the value from standard normal z table, we have,

$P( z \leq -1.036) = 0.15$

$\displaystyle\frac{x - 4.5}{0.82} = -1.036\\x = 3.65$

Thus, 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

8 0

3 years ago

In circle P with mNRQ = 60°, find the angle measure of minor arc NQ

Galina-37 [17]

Given:

m∠NRQ = 60°

To find:

The angle measure of minor arc NQ

Solution:

The inscribed angle is half of the intercepted arc.

$$\Rightarrow m\angle NRQ =\frac{1}{2} m(ar NQ)$

Multiply by 2 on both sides.

$$\Rightarrow 2 \times m\angle NRQ =2 \times \frac{1}{2} m(ar NQ)$

$$\Rightarrow 2 \ m\angle NRQ =m(ar NQ)$

Substitute m∠NRQ = 60°.

$$\Rightarrow 2\times 60^\circ=m(ar NQ)$

$$\Rightarrow 120^\circ=m(ar NQ)$

The measure of minor arc NQ is 120°.

8 0

4 years ago

Solve -4x^2 + 6x - 10 = 0 using the quadratic formula. Show each step.

Musya8 [376]

-12x-10=0 since the X can't combine with non X numbers

5 0

4 years ago

Heheh be svdbtjdjsbddb

Dennis_Churaev [7]

Did u type that by mistake

6 0

2 years ago

Read 2 more answers

If my saving x$ grows 10% every year how much will I have in:<br> 1 year<br> 2 year<br> 5 year

mote1985 [20]

Answer:

$1.1x, 1.21x, 1.61051x$

Step-by-step explanation:

If you saving grows $10 \%$ every year, then your saving is $1.1\\$ times your saving from last year. Therefore, after one year, you will have $1.1x\\$ , then after $2$ years, you will have $(1.1)^2 \cdot x=1.21x$ , then after $5$ years, you will have $(1.1)^5 \cdot x = 1.61051x$ .

5 0

3 years ago

Read 2 more answers