Determine whether the ordered pair is a solution of the equation. Show your work to receive credit.

The access code for a garage door consists of three digits. Each digit can be any number from 1 through 5, and each digit can b

Papessa [141]

Answer:

(a) 125

$(b) \dfrac{1}{125}$

$(c) \dfrac{124}{125}$

Step-by-step explanation:

We are given that access code consists of 3 digits.

Each digit can be any digit through 1 to 5 and can be repeated.

Now, this problem is equivalent to the problem that we have to find:

The number of 3 digit numbers that can be formed using the digits 1 to 5 with repetition allowed.

(a) We have 3 places here, unit's, ten's and hundred's places respectively and each of the 3 places have 5 possibilities (any digit allowed with repetition).

So, total number of access codes possible:

$5\times 5 \times 5 = 125$

(b) Suppose, an access code is randomly selected, what is the probability that it will be correct.

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Here, only 1 code is correct, so

Number of favorable cases = 1

Total number of cases = 125

So, required probability:

$P(E) = \dfrac{1}{125}$

(c) Probability of not selecting the correct access code on first time:

$P(\overline E) = 1-P(E)\\\Rightarrow P(\overline E) = 1-\dfrac{1}{125}\\\Rightarrow P(\overline E) = \dfrac{125-1}{125}\\\Rightarrow P(\overline E) = \dfrac{124}{125}$

So, the answers are:

(a) 125

$(b) \dfrac{1}{125}$

$(c) \dfrac{124}{125}$

7 0

3 years ago

Kevin was multiplying 1.5 by 0.1. Which statement is true about the product? A. It will be greater than 1.5. B. It will be less

Anastaziya [24]

The answer should be B because it turns to .15

5 0

3 years ago

How much

morpeh [17]

Answer:

She would need at least 11 buses leaving 17 spare seats.

Step-by-step explanation:

171+22+13= 206

206/20= 10.3

10.3 = 11

3 0

2 years ago

Which table represents a linear function that has a slope of 5 and a y-intercept of 20?

erastovalidia [21]

Answer:

The first image.

x | y

-4 | 0

0 | 20 <--- When x = 0, the y value is the y-intercept.

4 | 40

8 | 60

Step-by-step explanation:

To check the slope, we can use the equation (y₂ - y₁) ÷ (x₂ - x₁) using any two pairs given. For this example, I'll use (-4, 0) and (4, 40).

x₂ y₂ x₁ y₁

(0 - 40) ÷ (-4 - 4)

(-40) ÷ (-8)

<u>Slope = 5</u>

<u></u>

~Hope this helps!~

8 0

3 years ago

Read 2 more answers

2+x-(3-z); use x=6, and z=1

Nataly_w [17]

Answer:

Step-by-step explanation:

$2+x-(3-z)\\ x=6\\ z=1\\= 2+6-(3-1)\\\\\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}\\\\\mathrm{Calculate\:within\:parentheses}\:\left(3-1\right)\::\quad 2\\=2+6-2\\\\\mathrm{Add\:and\:subtract\:\left(left\:to\:right\right)}\:2+6-2\:\\:\quad 6$

4 0

3 years ago

Read 2 more answers