What is √6 divided by √5 in simplest radical form?

A lumber yard has a scrap sheet of plywood that is 23 3/4 inches by 41 1/5 inches long what is the area of the plywood?

Sholpan [36]

Answer:

$978\frac{1}{2}\text{ inches}^2$ .

Step-by-step explanation:

We have been given that a lumber yard has a scrap sheet of plywood that is 23 3/4 inches by 41 1/5 inches long.

Since plywood is in shape of rectangle, so to find the area of plywood we will multiply the length of plywood by its width.

$\text{Area of rectangle}=\text{Length*Width}$

$\text{Area of plywood}=23\frac{3}{4}\text{ inches}\times 41\frac{1}{5}\text{ inches}$

Let us convert our mixed fractions into improper fractions.

$\text{Area of plywood}=\frac{95}{4}\text{ inches}\times \frac{206}{5}\text{ inches}$

$\text{Area of plywood}=\frac{95}{4}\times \frac{206}{5}\text{ inches}\times \text{inches}$

Upon cancelling out greatest common factors we will get,

$\text{Area of plywood}=\frac{19}{2}\times 103\text{ inches}^2$

$\text{Area of plywood}=\frac{1957}{2}\text{ inches}^2$

Now let us convert our answer into mixed fraction.

$\text{Area of plywood}=978\frac{1}{2}\text{ inches}^2$

Therefore, the area of plywood is $978\frac{1}{2}\text{ inches}^2$ .

8 0

2 years ago

1.17 A study of the effects of smoking on sleep patterns is conducted. The measure observed is the time, in minutes, that it tak

bearhunter [10]

Answer:

a.

$\bar X_F=43.7$

$\bar X_{NF}=30.32$

b.

$S_F=16.9278$

$S_{NF}=7.12783$

c.

Attached file

d.

Apparently the practice of smoking reduces the ability to fall asleep, demanding much more time in individuals who smoke, than in those who do not smoke.

Step-by-step explanation:

a, b) For the group of smoking individuals, the average time it takes to fall asleep and the standard deviation of those times is:

$\bar X_F={\frac{1}{n} \sum_{i=1}^n x_i = 43.7$

$S_F=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2}=16.9278$

a, b) For the group of non-smoking individuals, the average time it takes to fall asleep and the standard deviation of those times is:

$\bar X_{NF}={\frac{1}{n} \sum_{i=1}^n x_i = 30.32$

$S_{NF}=\sqrt{\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2}=7.12783$

c. In the attached file you can see the diagram of points for the times, in the smoking and non-smoking groups.

d. Apparently the practice of smoking reduces the ability to fall asleep, demanding much more time in individuals who smoke, than in those who do not smoke.

Download pdf

6 0

2 years ago

A motorboat takes 3 hours to travel 144 km going upstream. The trip takes 2 hours going downstream. What is the rate of the boat

allsm [11]

Let x be rate of boat in still water
let y be rate of current

we use this equation to relate quantities:
distance = speed · time

we have two unknowns so we might need to create a system of equationss

upstream:

speed (in km/h) = x - y
(we get speed of boat then subtract the current's speed from it since current is going against boat direction)

time = 3 hours

distance = 144 km

downstream:

speed (in hm/h) = x + y
(we get speed of boat then add the current's spd from it since current is going against boat direction)

time = 2 hours

distance = 144 km (same distance upstream and downstream)

using distance = speed times time

for upstream
144 = 3(x-y)
144 = 3x - 3y

for downstream
144 = 2(x+y)
72 = x + y

system of eqns:
144 = 3x - 3y
72 = x + y

solve by substitution: move 72 = x + y into x = 72 - y and subst into other equation for x

144 = 3(72 - y) - 3y
144 = 216 - 3y - 3y
144 = 216 - 6y
144 - 216 = -6y
-72 = -6y
y = 12 km/h

Use x = 72 - y to find x with y = 12: x = 72 - 12 = 60 km/h

rate of boat in still water is 60 km/h
rate of the current is 12 km/h

6 0

2 years ago

Finally, you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V s

marin [14]

Answer:

w and y are knights

Step-by-step explanation:

6 0

2 years ago

Evaluate 17.3 % of 45.94 km Give your answer rounded to 2 DP.

Katyanochek1 [597]

Answer: 17.3% of 45.94 km is 7.95 km

4 0

2 years ago