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2 years ago

The area of a blackboard is

Mathematics

2 answers:

noname [10]2 years ago

8 0

Answer:

3/2

Step-by-step explanation:

unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity so:

1.1/3= 3.1+1÷3=4/3

8/9÷4/3=3/2

Sonja [21]2 years ago

7 0

Answer:

<h2>There are 6 square yards of blackboard per 2 square yards per poster.</h2>

Step-by-step explanation:

The unit rate refers to how many area units of the poster are in the blackboard.

To find this rate, we just have to divide the area of the blackboard by the area of the poster.

$B=1\frac{1}{3}=\frac{4}{3}$

Where $B$ represents the area of the blackboard in square yards.

$P=\frac{8}{9}$

Where $P$ represents the area of the poster.

Now, the ratio is

$r= \frac{B}{P}=\frac{4}{3} \div \frac{8}{9}=\frac{4}{3} \times \frac{9}{8}=\frac{36}{24}\\r=\frac{6}{4}=\frac{3}{2}=1.5$

This mean that the unit rate is 1.5, that is, there are 6 square yards of blackboard per 2 square yards per poster.

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2 years ago

A certain three-cylinder combination lock has 60 numbers on it. To open it, you turn to a number on the first cylinder, then

statuscvo [17]

Answer:

(a) The number of different lock combinations is 216,000.

(b) The probability of getting the correct combination in the first try is $\frac{1}{216000}$ .

Step-by-step explanation:

The lock has three-cylinder combinations with 60 numbers on each cylinder.

The procedure of the opening lock is to turn to a number on the first cylinder, then to a second number on the second cylinder, and then to a third number on the third cylinder.

The numbers can be repeated.

(a)

There are three cylinder combinations on the lock, each with 60 numbers.

It is provided that repetitions are allowed.

Then each cylinder can take any of the 60 numbers.

So there are 60 options for the first cylinder.

There are 60 options for the second cylinder.

And there are 60 options for the third cylinder.

So the total number of possible combinations is:

Total number of combinations = 60 × 60 × 60 = 216000.

Thus, the number of different lock combinations is 216,000.

(b)

The events of getting a correct combinations of the three-cylinder combination lock implies that all the three cylinder are set at the correct numbers.

Each cylinder has 60 numbers.

This implies that there are 60 possible ways to get a correct number for the first cylinder.

The probability of getting the correct number for the first cylinder is:

P (Number on 1st cylinder is correct) = $\frac{1}{60}$ .

Similarly for the second cylinder the probability of getting the correct number is:

P (Number on 2nd cylinder is correct) = $\frac{1}{60}$ .

And similarly for the third cylinder the probability of getting the correct number is:

P (Number on 3rd cylinder is correct) = $\frac{1}{60}$ .

So the probability of getting the correct combination in the first try is:

P (Correct combination in the 1st try) = $\frac{1}{60}\times \frac{1}{60}\times \frac{1}{60}=\frac{1}{216000}$ .

Thus, the probability of getting the correct combination in the first try is $\frac{1}{216000}$ .

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2 years ago

For which of the following integrands will the table method for parts produce an antiderivative?

Sonja [21]

Answer:

x³ sin(x)

Step-by-step explanation:

Tabular method is a special form of integration by parts. It works by taking derivatives of u and integrals of dv. You multiply diagonally, then sum the results, alternating the signs.

The important thing to note is that this will produce an antiderivative only if the derivatives of u eventually become 0. So the correct choice is x³ sin(x), because the derivatives of x³ eventually becomes 0:

d/dx (x³) = 3x²

d/dx (3x²) = 6x

d/dx (6x) = 6

d/dx (6) = 0