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maria [59]
3 years ago
13

For his birthday, Mr. Robin and four of his friends went to a Math museum to learn about new intergalactic math. They each got a

ticket for $12.00 and each bought the same calculator at the gift shop. If Mr. Robin spent $110 for the group's tickets and calculator, how much did each calculator cost? Write and solve an equation to describe this situation.
Mathematics
1 answer:
Helen [10]3 years ago
4 0

Answer: $10

Step-by-step explanation:

Given

Robin and his four friends bought tickets for \$12 each

If each one of them bought a calculator then the total spendings are \$110

Suppose the cost of each calculator is \$\ x

Cost per person is given by  x+\$12

For the group, it is 5(x+12)

Equate this to total spendings

\Rightarrow 5(x+12)=110\\\Rightarrow x+12=22\\\Rightarrow x=\$\ 10

thus, the cost of each calculator is \$ 10

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A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side. Show and e
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Answer:

The third side must be smaller than 20 inches and greater than 4 inches

4

Step-by-step explanation:

Let a, b and c be the lengths of triangle's sides. Then

a+b>c\\ \\a+c>b\\ \\b+c>a

Use this rule in your case. So, if a=12 and b=8, then

12+8>c\\ \\12+c>8\\ \\8+c>12

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From these inequalities, you can state that

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So, c must be smaller than 20 inches and greater than 4 inches.

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3 years ago
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14 minutes below or 6 minutes above

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3 years ago
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Mai poured `2.6` liters of water into a partially-filled pitcher. The pitcher now contains `10.4` liters. Mai wants to know how
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2 years ago
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Suppose that X has an exponential distribution with mean equal to 10. Determine the following: a. P(X > 10) b. P(X > 20) c
GrogVix [38]

Answer:

(a) The value of P (X > 10) is 0.3679.

(b) The value of P (X > 20) is 0.1353.

(c) The value of P (X < 30) is 0.9502.

(d) The value of x is 30.

Step-by-step explanation:

The probability density function of an exponential distribution is:

f(x)=\lambda e^{-\lambda x};\ x>0, \lambda>0

The value of E (X) is 10.

The parameter λ is:

\lambda=\frac{1}{E(X)}=\frac{1}{10}=0.10

(a)

Compute the value of P (X > 10) as follows:

P(X>10)=\int\limits^{\infty}_{10} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{10} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{10}\\=|e^{-0.10 x} |^{\infty}_{10}\\=e^{-0.10\times10}\\=0.3679

Thus, the value of P (X > 10) is 0.3679.

(b)

Compute the value of P (X > 20) as follows:

P(X>20)=\int\limits^{\infty}_{20} {0.10 e^{-0.10 x}} \, dx \\=0.10\int\limits^{\infty}_{20} { e^{-0.10 x}} \, dx\\=0.10|\frac{e^{-0.10 x}}{-0.10} |^{\infty}_{20}\\=|e^{-0.10 x} |^{\infty}_{20}\\=e^{-0.10\times20}\\=0.1353

Thus, the value of P (X > 20) is 0.1353.

(c)

Compute the value of P (X < 30) as follows:

P(X

Thus, the value of P (X < 30) is 0.9502.

(d)

It is given that, P (X < x) = 0.95.

Compute the value of <em>x</em> as follows:

P(X

Take natural log on both sides.

ln(e^{-0.10x})=ln(0.05)\\-0.10x=-2.996\\x=\frac{2.996}{0.10}\\ =29.96\\\approx30

Thus, the value of x is 30.

7 0
3 years ago
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