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3 years ago

The perimeter of an equilateral triangle is 63 inches. If the length of each side is (4x-3), find the value of x.

Mathematics

1 answer:

sashaice [31]3 years ago

6 0

Answer:

The value of x is 6

Step-by-step explanation:

The perimeter of an equilateral triangle is P = 3 × S, where S is the length of each side

∵ The perimeter of an equilateral triangle is 63 inches

∴ P = 63 inches

→ By using the rule of the perimeter above

∵ P = 3 × S

→ Equate the right sides of P

∴ 3 × S = 63

→ Divide both sides by 3

∴ S = 21 inches

∴ The length of each side is 21 inches

∵ The length of each side is (4x - 3)

→ Equate (4x - 3) by the length of each side

∴ 4x - 3 = 21

→ Add 3 to both sides

∵ 4x - 3 + 3 = 21 + 3

∴ 4x = 24

→ Divide both sides by 4 to find x

∴ x = 6

∴ The value of x is 6

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3 years ago

At a Noodles & Company restaurant, the probability that a customer will order a nonalcoholic beverage is .51.

satela [25.4K]

Answer:

$P(x\geq 7)=0.1886$

Step-by-step explanation:

The variable x, that said the number of customer that will order a nonalcoholic beverage in a sample of n customers follows a binomial distribution. Because we have n identical and independent events with a probability p of success and (1-p) of fail.

So, the probability that x customers will order a nonalcoholic beverage is:

$P(x)=\frac{n!}{x!(n-x)!}*p^{x}*(1-p)^{n-x}$

Where n is the size of the sample and p is the probability that a customer order a nonalcoholic beverage, so replacing the values, we get:

$P(x)=\frac{10!}{x!(10-x)!}*0.51^{x}*(1-0.51)^{10-x}$

Now, the probability that at least 7 will order a nonalcoholic beverage is equal to:

$P(x\geq 7)=P(7)+P(8)+P(9)+P(10)$

Where:

$P(7)=\frac{10!}{7!(10-7)!}*0.51^{7}*(1-0.51)^{10-7}=0.1267\\P(8)=\frac{10!}{8!(10-8)!}*0.51^{8}*(1-0.51)^{10-8}=0.0494\\P(9)=\frac{10!}{9!(10-9)!}*0.51^{9}*(1-0.51)^{10-9}=0.0114\\P(10)=\frac{10!}{10!(10-10)!}*0.51^{10}*(1-0.51)^{10-10}=0.0011$