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3 years ago

1/9 (2m - 16) = 1/3 (2m + 4)

Mathematics

1 answer:

Ainat [17]3 years ago

4 0

Answer:

$m=7\frac{5}{16}$

Step-by-step explanation:

$\frac{1}{9}(2m - 16)=\frac{1}{3}(2m + 4)$

$\frac{2}{9}m - 1\frac{7}{9} =\frac{2}{3}m+ 1\frac{1}{3}$

$\frac{2}{9}m - 1\frac{7}{9} -1\frac{1}{3} =\frac{2}{3}m+ 1\frac{1}{3}-1\frac{1}{3}$

$\frac{2}{9}m - 3\frac{1}{9} =\frac{2}{3}m$

$\frac{2}{3}m-\frac{2}{9}m= \frac{2}{9}m -\frac{2}{9}m - 3\frac{1}{9}$

$\frac{4}{9}m= - 3\frac{1}{9}$

$\frac{4}{9}m/\frac{4}{9} = - 3\frac{1}{9}/\frac{4}{9}$

$m=7\frac{5}{16}$

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Find the measure of each angle.

Galina-37 [17]

<u>Given</u>:

Given that the isosceles trapezoid JKLM.

The measure of ∠K is 118°

We need to determine the measure of each angle.

<u>Measure of ∠L:</u>

By the property of isosceles trapezoid, we have;

$\angle K+\angle L=180^{\circ}$

$118^{\circ}+\angle L=180^{\circ}$

$\angle L=62^{\circ}$

Thus, the measure of ∠L is 62°

<u>Measure of ∠M:</u>

By the property of isosceles trapezoid, we have;

$\angle L \cong \angle M$

Substituting the value, we get;

$62^{\circ}=\angle M$

Thus, the measure of ∠M is 62°

<u>Measure of ∠J:</u>

By the property of isosceles trapezoid, we have;

$\angle J \cong \angle K$

Substituting the value, we get;

$\angle J =118^{\circ}$

Thus, the measure of ∠J is 118°

Hence, the measures of each angles of the isosceles trapezoid are ∠K = 118°, ∠L = 62°, ∠M = 62° and ∠J = 118°

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2 years ago

Suppose a three-seat city council election. For each seat, one progressive and one conservative is running, and voters must choo

Kitty [74]

Answer:

The probability that conservative party wins all 3 seats is 0.216

The probability that conservative party wins exactly two seats is 0.432

Step-by-step explanation:

Consider the provided information.

The probability of a conservative candidate winning is p=0.6.

The probability of one progressive candidate will win is: 1-0.6=0.4

Part (a) What is the probability that the conservative party wins all three seats?

According to binomial distribution: $b(x; n, p) =^nC_xp^x(1- p)^{n-x}$

$P(x=3) =^3C_3(0.6)^3 (0.4)^{3-3}$

$P(x=3) =(0.6)^3$

$P(x=3)=0.216$

P(conservative party wins all 3 seats) = 0.216

Hence, the probability that conservative party wins all 3 seats is 0.216

Part (a) What is the probability that the conservative party wins exactly two seats?

$P(x=2) =^3C_2(0.6)^2 (0.4)^{3-2}$

$P(x=2) =3(0.36)(0.4)$

$P(x=2) =0.432$

Hence, the probability that conservative party wins exactly two seats is 0.432

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3 years ago

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