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3 years ago

A safe has a 4-digit lock code that does not include zero as a digit and no digit is repeated. What is the probability

Mathematics

2 answers:

sergeinik [125]3 years ago

8 0

Answer:To find the total number of outcomes for this event, find the permutation of

⇒ 9 things taken 4 at a time.

The total number of outcomes is

⇒ 3,024.

The total number of favorable outcomes is a permutation of

⇒ 4 things taken 4 at a time.

The probability that the lock code consists of all even digits is

⇒ 24 out of 3,024.

Flura [38]3 years ago

7 0

Answer: 9, 3024, 4, 24

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Svetach [21]

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2 years ago

A rancher wants to fence in an area of 1500000 square feet in a rectangular field and then divide it in half with a fence down t

VLD [36.1K]

Answer:

6000 ft

Step-by-step explanation:

Let length of rectangular field=x

Breadth of rectangular field=y

Area of rectangular field= $1500000$ square ft

Area of rectangular field= $l\times b$

Area of rectangular field= $x\time y$

$1500000=xy$

$y=\frac{1500000}{x}$

Fencing used ,P(x)= $x+x+y+y+y=2x+3y$

Substitute the value of y

P(x)= $2x+3(\frac{1500000}{x})$

$P(x)=2x+\frac{4500000}{x}$

Differentiate w.r.t x

$P'(x)=2-\frac{4500000}{x^2}$

Using formula: $\frac{dx^n}{dx}=nx^{n-1}$

$P'(x)=0$

$2-\frac{4500000}{x^2}=0$

$\frac{4500000}{x^2}=2$

$x^2=\frac{4500000}{2}=2250000$

$x=\sqrt{2250000}=1500$

It is always positive because length is always positive.

Again differentiate w.r.t x

$P''(x)=\frac{9000000}{x^3}$

Substitute x=1500

$P''(1500)=\frac{9000000}{(1500)^3}>0$

Hence, fencing is minimum at x=1 500

Substitute x=1 500

$y=\frac{1500000}{1500}=1000$

Length of rectangular field=1500 ft

Breadth of rectangular field=1000 ft

Substitute the values

Shortest length of fence used= $2(1500)+3(1000)=6000 ft$

Hence, the shortest length of fence that the rancher can used=6000 ft

3 0

3 years ago

Estimate 25.65 + 13.23 + 6.35 by rounding each number to the nearest tenth.

sergij07 [2.7K]

Answer:

b. 25.7 + 13.2 + 6.4 = 45.3

Step-by-step explanation:

25.65 ≈ 25.7, 13.23 ≈ 13.2, 6.35 ≈ 6.4

25.65 + 13.23 + 6.35 =
25.7 + 13.2 + 6.4 =
45.3

Correct choice is b.

5 0

3 years ago