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4 years ago

Find the length of LM. Show your work.

Mathematics

1 answer:

Fantom [35]4 years ago

7 0

Answer:

LM = 20

Step-by-step explanation:

Use the Sine rule to calculate the length of LM

We require to find ∠N using sum of angles in a triangle.

∠N = 180° - (53 + 44)° = 180° - 97° = 83°, then

$\frac{LN}{sin44}$ = $\frac{LM}{sin83}$ ( cross- m ultiply )

LM × sin44° = LN × sin83°, that is

LM × sin44° = 14 × sin83° ( divide both sides by sin44° )

LM = $\frac{14sin83}{sin44}$ = 20

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sdas [7]

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3 years ago

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lukranit [14]

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3 years ago

Suppose the contact rate for a phone survey is 78% and that 22% of people will participate in that survey. Assume that agreeing

Gnoma [55]

Remember that, for independent events, the probability that both occurr is the product of the individual probabilities.

a) Probability of being contacted: 78% = 0.78

Probaility of refusing: 1 - 22% = 1 -0.22 = 0.78

Combined probability: 0.78*0.78 = 0.6084

b) The probability of failing to contact or making contact and not geeting them to agree 1 - the probability of contacting and getting them to agree.

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4 years ago

A restaurant sells about 330 sandwiches each day at a price of $6 each $.25 decrease in price. 15 more sandwiches are sold per d

zmey [24]

Answer:

restaurant should charge $(6-0.25) = $5.75per sandwich to maximize daily revenue.

the revenue is $1983.75

Step-by-step explanation:

to calculate current revenue= $6 x 330 = $1980

suppose x as the number of times the price to be dropped by $0.25

then find new price.. i.e

new price= $(6-0.25x)

and, new sell=330 +15x sandwiches

therefore, the new revenue would be= (6-0.25x)(330 +15x)

in order to maximize the current revenue, simplify the above equation and make it complete square using x

(6-0.25x)(330 +15x)

=1980-82.5x +90x -3.75 $x^{2}$

=1980 + 7.5x -3.75 $x^{2}$

=1980-3.75 (-2x+ $x^{2}$ ) ----> taking out common

now, to make a complete square lets add and subtract 1 inside the parentheses

=1980-3.75(-1+1-2x+ $x^{2}$ )

=1980 +3.75 -3.75( $x^{2}$ -2x +1)

=1983.75 -3.75 $(x-1)^{2}$ ---->(1)

as $(x-1)^{2}$ is positive always, minimize the other term in order to maximize the total revenue.

so the minimum possible value of $(x-1)^{2}$ = 0

therefore, x=1

putting x in eq(1) the revenure becomes,

$(1983.75-0)=> $1983.75

therefore, restaurant should charge $(6-0.25) = $5.75per sandwich to maximize daily revenue.

the revenue is $1983.75

3 0

3 years ago