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3 years ago

Find the value of each variable so that PQRS is a parallelogram. Explain what allows you to do this.

Mathematics

1 answer:

Nataly [62]3 years ago

4 0

Answer:

$x = 5$

$y = 16$

Step-by-step explanation:

Given

See attachment for parallelogram

Required

Find variables x and y

Solving for x, we have:

$5x = 25$ ---- Opposite sides of a parallelogram

$\frac{5x}{5} = \frac{25}{5}$ ------ Divide both sides by 5

$x = 5$

Solving for y, we have:

$3y - 1 = 47$ ---- Opposite sides of a parallelogram

$3y = 1 + 47$ ------ Collect like terms

$3y = 48$

$\frac{3y}{3} = \frac{48}{3}$ ---- Divide both sides by 3

$y = 16$

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4 years ago

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3 years ago

at a particular high school, 42% of the students participate in sports and 25% of the students participate in drama. if 53% of t

baherus [9]

The probability that a student participates in both sports and drama is $0.14$ .

<h3>What is the formula for P(AUB), where A and B are any two events?</h3>

If $A$ and $B$ are any two events, then the probability of the joint event $(A\cup B)$ is given by the following formula: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$

Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.

Suppose $S$ denotes that "a student participates in sports" and $D$ denotes that "a student participates in drama".
So, we have $P(S)=\frac{42}{100}=0.42$ , $P(D)=\frac{25}{100}=0.25$ , $P(S\cup D)=\frac{53}{100}=0.53$ .

We want to find the probability that a student participates in both sports and drama i.e., we want to find $P(S\cap D)$ .

By the above formula, we obtain:

$P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\Longrightarrow P(S\cap D)=P(S)+P(D)-P(S\cup D)\\\Longrightarrow P(S\cap D)=0.42+0.25-0.53\\\therefore P(S\cap D)=0.14=\frac{14}{100}$

Therefore, the probability that a student participates in both sports and drama is $0.14$ .

To learn more about probability, refer: brainly.com/question/24756209

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2 years ago

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