Rick used 4 2/3 yards of fabric to sew 3 1/2 shirts. what is the unit rate of cloth he used in terms of yards per shirt

Micah rows his boat on a river 4.48 miles downstream, with the current , 0.32 hours. He rows back upstream the same distance, ag

AnnZ [12381]

Short Answer: Current speed = 3 miles per hour. Given details for downstream distance of 4.48 miles at time 0.32 hours and upstream distance of the same 4.48 miles taking 0.56 hours. Using the equation d = r*t, we equate distances for both directions leading to a function in terms of the current speed. With each correction to solve ultimately yields the current speed as 3 mph.

5 0

2 months ago

Add 0.0025 kg, 1750 mg, 2.25 g, and 825,000 μg, and express the answer in grams.

lawyer [12517]

Answer:

6.75g

Step-by-step explanation:

The initial step is to convert all values to grams using rules of three, followed by summation.

In a rule of three calculation, the first step is identifying the measures and how they interrelate; whether their connection is direct or inverse.

In direct relationships, as one measure increases, so does the other.

In inverse relationships, as one measure increases, the other decreases.

Problems involving unit conversion, like this, illustrate a direct relationship between measures.

First step: convert 0.0025kg to grams

One kilogram equals 1000 grams, so:

1kg - 1000g

0.0025kg - xg

x = 1000*0.0025 = 2.5g

Thus, 0.0025kg is equal to 2.5g

Second step: handle 1750 mg

One gram consists of 1000mg, so:

1g - 1000mg

xg - 1750mg

1000x = 1750

$x = \frac{1750}{1000}$

x = 1.75g

Therefore, 1750 mg converts to 1.75g

2.25g is fine

Third step: convert 825,000 μg to grams

One gram consists of 1,000,000 micrograms, so:

1g - 1,000,000 μg

xg - 825,000 μg

1,000,000x = 825,000

$x = \frac{825,000}{1,000,000}$

x = 0.25g

So, 825,000 μg equals 0.25g

Final step: sum all values

0.25g + 2.25g + 1.75g + 2.50g = 6.75g

8 0

3 months ago

The computers of six faculty members in a certain department are to be replaced. Two of the faculty members have selected laptop

lawyer [12517]

Answer:

a. $\frac{1}{15}$

b. $\frac{2}{5}$

c. $\frac{14}{15}$

d. $\frac{8}{15}$

Step-by-step explanation:

There are four desktop computers and two laptops.

On a specific day, we will set up 2 of these computers.

To find:

a. What is the probability that both selected computers are laptops?

b. What is the probability that both computers are desktops?

c. What is the probability that at least one computer is a desktop?

d. What is the probability that at least one of each type of computer is included?

Solution:

Using the probability formula for event E:

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

a. The number of successful outcomes for both computers being laptops = $_2C_2$ = 1

Total possible outcomes = 15

The needed probability is $\frac{1}{15}$ .

b. The successful outcomes for both being desktop computers = $_4C_2=6$

Total possible outcomes = 15

The required probability is $\frac{6}{15} = \frac{2}{5}$ .

c. For at least one desktop:

Two scenarios exist:

1. 1 desktop and 1 laptop:

Successful outcomes = $_2C_1\times _4C_1 = 8$

2. Both are desktops:

Successful outcomes = $_4C_2=6$

Total successful outcomes = 8 + 6 = 14

The needed probability is $\frac{14}{15}$ .

d. 1 desktop and 1 laptop:

Successful outcomes = $_2C_1\times _4C_1 = 8$

Total outcomes = 15

The required probability is $\frac{8}{15}$ .

8 0

2 months ago