First we'll consider the floor size.
In a 10 by 12 room the longest pipe that will fit lying on the floor equals the hypotenuse of a 10 by 12 triangle:
hypotenuse² = 10² + 12²
hypotenuse² = 100 + 144
hypotenuse² = 244
hypotenuse =
<span>
<span>
<span>
15.62 feet
Now we have to consider the third dimension (height = 8 feet).
The two sides would be 15.62 and 8
</span></span></span>hypotenuse² =
15.62² + 8²
hypotenuse² =
244 + 64 = 308
hypotenuse = 17.55
So, the longest pipe that would fit in that room would be 17.55 feet long.
Answer:
The ratio of the amount of flour to the amount of buttermilk=99:1
Step-by-step explanation:
Step 1: Determine quantity for each recipe
Quantity of flour=66 cups
Quantity of buttermilk=2/3 cups
Step 2: Calculate the total quantity of recipe
The expression for the total quantity is;
T=f+b
where;
T=total quantity of recipe
f=quantity of flour
b=quantity of buttermilk
In our case;
T=unknown
f=66 cups
b=2/3 cups
replacing;
T=(66)+(2/3)=66 2/3 cups
Step 3: Determine fraction of each
fraction of buttermilk=(2/3)/(66 2/3)=1/100
fraction of flour=66/(66 2/3)=99/100
Step 4: Determine ratio of flour to buttermilk
Amount of flour:amount of buttermilk
(99/100):(1/100)
The ratio of the amount of flour to the amount of buttermilk=99:1
34% of the scores lie between 433 and 523.
Solution:
Given data:
Mean (μ) = 433
Standard deviation (σ) = 90
<u>Empirical rule to determine the percent:</u>
(1) About 68% of all the values lie within 1 standard deviation of the mean.
(2) About 95% of all the values lie within 2 standard deviations of the mean.
(3) About 99.7% of all the values lie within 3 standard deviations of the mean.
Z lies between o and 1.
P(433 < x < 523) = P(0 < Z < 1)
μ = 433 and μ + σ = 433 + 90 = 523
Using empirical rule, about 68% of all the values lie within 1 standard deviation of the mean.
i. e. 
Here μ to μ + σ = 
Hence 34% of the scores lie between 433 and 523.
<span>Cost of maple syrup = $6.00 a Gallon
Cost of corn syrup = 0.80 cents a Gallon
Cost of the syrup mixture = $2.36 a Gallon
There is mixture of 50 Gallons
Lets maple syrup be x gallons, so corn syrup be 50-x gallons
Hence,
6*x + 0.80(50-x) = 2.36*50
6x + 40 - 0.8x = 118
5.2x = 78
=> x = 78/5.2 => x = 15
So Maple will be syrup be 15 gallons.
Corn syrup will be 35 gallons.</span>
