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3 years ago

Quadrilateral WXYZ is a Parallelogram. Find the value of each variable.

Mathematics

1 answer:

Arisa [49]3 years ago

3 0

Answer: a=3, b=1

A parallelogram have its opposite sides equal and parallel.

Step-by-step explanation:

SO, the quadrilateral WXYZ have its opposite sides equal as its a parallelogram.

From the given figure the side XY= WZ and XW= YZ, which gives two equations i.e

Equation 1 is 3a-4=a+2 and Equation 2 is b+1=2b

Solving Equation 1 Solving equation 2

3a-a = 2+4 2b-b = 1

2a = 6 b=1

a = 3

So, by solving the two equations a=3 and b=1.

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Suppose you toss a fair coin 10 times, let X denote the number of heads. (a) What is the probability that X=5? (b) What is the p

zubka84 [21]

Answer: The required answers are

(a) 0.25, (b) 0.62, (c) 6.

Step-by-step explanation: Given that we toss a fair coin 10 times and X denote the number of heads.

We are to find

(a) the probability that X=5

(b) the probability that X greater or equal than 5

(c) the minimum value of a such that P(X ≤ a) > 0.8.

We know that the probability of getting r heads out of n tosses in a toss of coin is given by the formula of binomial distribution as follows :

$P(X=r)=^nC_r\left(\dfrac{1}{2}\right)^r\left(\dfrac{1}{2}\right)^{n-r}.$

(a) The probability of getting 5 heads is given by

$P(X=5)\\\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}\\\\\\=\dfrac{10!}{5!(10-5)!}\dfrac{1}{2^{10}}\\\\\\=0.24609\\\\\sim0.25.$

(b) The probability of getting 5 or more than 5 heads is

$P(X\geq 5)\\\\=P(X=5)+P(X=6)+P(X=7)+P(X=8)+P(X=9)+P(X=10)\\\\=^{10}C_5\left(\dfrac{1}{2}\right)^5\left(\dfrac{1}{2}\right)^{10-5}+^{10}C_6\left(\dfrac{1}{2}\right)^6\left(\dfrac{1}{2}\right)^{10-6}+^{10}C_7\left(\dfrac{1}{2}\right)^7\left(\dfrac{1}{2}\right)^{10-7}+^{10}C_8\left(\dfrac{1}{2}\right)^8\left(\dfrac{1}{2}\right)^{10-8}+^{10}C_9\left(\dfrac{1}{2}\right)^9\left(\dfrac{1}{2}\right)^{10-9}+^{10}C_{10}\left(\dfrac{1}{2}\right)^{10}\left(\dfrac{1}{2}\right)^{10-10}\\\\\\=0.24609+0.20507+0.11718+0.04394+0.0097+0.00097\\\\=0.62295\\\\\sim 0.62.$

(c) Proceeding as in parts (a) and (b), we see that

if a = 10, then

$P(X\leq 0)=0.00097,\\\\P(X\leq 1)=0.01067,\\\\P(X\leq 2)=0.05461,\\\\P(X\leq 3)=0.17179,\\\\P(X\leq 4)=0.37686,\\\\P(X\leq 5)=0.62295,\\\\P(X\leq 6)=0.82802.$

Therefore, the minimum value of a is 6.

Hence, all the questions are answered.

3 0

4 years ago

Need help with this find the value of x

dolphi86 [110]

Answer: x = √58
Decimal: 7.6157710 (Not Rounded)

Explanation: Using pythagorean theorem because it’s used for right triangle when mostly trying to find the hypotenuse.

3^2 + 7^ = c^2

6 0

2 years ago

Please help me with this question!

Alina [70]

Answer:

see explanation

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°, thus

∠1 = 180° - (72 + 57)° = 180° - 129° = 51°

The right angle at the left vertex is composed of 72° and ∠2, thus

∠2 = 90° - 72° = 18°

57° and ∠3 form a straight angle and are supplementary, thus

∠3 = 180° - 57° = 123°

∠4 = 180° - (∠2 + ∠3 ) ← sum of angles in a triangle

∠4 = 180° - (18 + 123)° = 180° - 141° = 39°

4 0

3 years ago

Do you use the greatest common factor or the least common multiple to add two fractions? In this example what is it? 4/5+5/6 lea

Alenkinab [10]

Answer:

30 is the least common factor or lcm

Step-by-step explanation:

when adding fractions you always have to find the lcm

8 0

3 years ago

A sequence is represented by the formula an=-5+a(n-1). If a4 = 20, what is the 6th term in the sequence?

Citrus2011 [14]

Answer:

Step-by-step explanation:

Formula :

aₙ = -5 + aₙ₋₁

Finding a₅ :

a₅ = -5 + a₄
a₅ = -5 + 20
a₅ = 15

Finding a₆ :

a₆ = -5 + a₅
a₆ = -5 + 15
a₆ = <u>10</u>

4 0

2 years ago