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2 years ago

Three times a number m

Mathematics

1 answer:

8090 [49]2 years ago

3 0

Answer:

Step-by-step explanation:

3 x n

simplifies to be

hope this helps

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You always need some time to get up after the alarm has rung. You get up from 10 to 20 minutes later, with any time in that inte

Mama L [17]

Answer:

a) P(x<5)=0.

b) E(X)=15.

c) P(8<x<13)=0.3.

d) P=0.216.

e) P=1.

Step-by-step explanation:

We have the function:

$f(x)=\left \{ {{\frac{1}{10},\, \, \, 10\leq x\leq 20 } \atop {0, \, \, \, \, \, \, otherwise }} \right.$

a) We calculate the probability that you need less than 5 minutes to get up:

$P(x$

Therefore, the probability is P(x<5)=0.

b) It takes us between 10 and 20 minutes to get up. The expected value is to get up in 15 minutes.

E(X)=15.

c) We calculate the probability that you will need between 8 and 13 minutes:

$P(8\leq x\leq 13)=P(10\leqx\leq 13)\\\\P(8\leq x\leq 13)=\int_{10}^{13} f(x)\, dx\\\\P(8\leq x\leq 13)=\int_{10}^{13} \frac{1}{10} \, dx\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot [x]_{10}^{13}\\\\P(8\leq x\leq 13)=\frac{1}{10} \cdot (13-10)\\\\P(8\leq x\leq 13)=\frac{3}{10}\\\\P(8\leq x\leq 13)=0.3$

Therefore, the probability is P(8<x<13)=0.3.

d) We calculate the probability that you will be late to each of the 9:30am classes next week:

$P(x>14)=\int_{14}^{20} f(x)\, dx\\\\P(x>14)=\int_{14}^{20} \frac{1}{10} \, dx\\\\P(x>14)=\frac{1}{10} [x]_{14}^{20}\\\\P(x>14)=\frac{6}{10}\\\\P(x>14)=0.6$

You have 9:30am classes three times a week. So, we get:

$P=0.6^3=0.216$

Therefore, the probability is P=0.216.

e) We calculate the probability that you are late to at least one 9am class next week:

$P(x>9.5)=\int_{10}^{20} f(x)\, dx\\\\P(x>9.5)=\int_{10}^{20} \frac{1}{10} \, dx\\\\P(x>9.5)=\frac{1}{10} [x]_{10}^{20}\\\\P(x>9.5)=1$

Therefore, the probability is P=1.

3 0

2 years ago

Two cones have the same radii but one has a height four times larger than the other. How many small cones would be needed in ord

hram777 [196]

Since the radius is the same but the height changes, the volume would change by the multiple of the height.
In this case the volume of the larger cone would be 4 times as large as the smaller cone so you would need 4 small cones

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2 years ago

PLS HELP ME I CANT DO IT AND JMBEING TIMED

tamaranim1 [39]

Answer:

For A+B

a. 0.3+0.8 = 1.1

b. 1.2+1.4 = 2.6

c. 3.4 + 4.2 = 7.6

d. 2.25 + 2.95 = 5.20

For B-A

a. 0.8-0.3 = 0.5

b. 1.4-1.2 = 0.2

c. 4.2-3.4 = 1.2

d. 2.95-2.25 = .070

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2 years ago

Factorise: x³ + 32x + 20.

LenKa [72]

Answer:

cant be factored

Step-by-step explanation:

7 0

2 years ago

The length of a rectangle is 8 feet more than its width. If the width is increased by 4 feet and the length is decreased by 5 fe

alexgriva [62]

Let the width be x.

Length is 8 feet more than width. Length = x + 8

Area = x(x + 8)

width increased by 4, that is, (x + 4)
Length decreased by 5, (x + 8 - 5) = (x + 3)

Area = (x + 4)(x +3)

Area remains the same

x(x + 8) = (x+4)(x +3)

x² + 8x = x(x +3) + 4(x +3)

x² + 8x = x² +3x + 4x +12

x² + 8x = x² +7x +12 Eliminate x² from both sides

8x = 7x + 12

8x - 7x = 12

x = 12

Dimensions of original rectangle : x, x + 8

12, 12 +8 = 12, 20

Original rectangle is 20 feet by 12 feet

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2 years ago

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