Answer:
c. 3.6 and 10.4 hrs
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviations of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean 7, standard deviation 1.7.
For about 95% of students, nightly amount of sleep is between
7 - 2*1.7 = 7 - 3.4 = 3.6 hours
7 + 2*1.7 = 7 + 3.4 = 10.4 hours
So the correct answer is:
c. 3.6 and 10.4 hrs
You can use the identity
cos(x)² +sin(x)² = 1
to find sin(x) from cos(x) or vice versa.
(1/4)² +sin(x)² = 1
sin(x)² = 1 - 1/16
sin(x) = ±(√15)/4
Then the tangent can be computed as the ratio of sine to cosine.
tan(x) = sin(x)/cos(x) = (±(√15)/4)/(1/4)
tan(x) = ±√15
There are two possible answers.
In the first quadrant:
sin(x) = (√15)/4
tan(x) = √15
In the fourth quadrant:
sin(x) = -(√15)/4
tan(x) = -√15
Your answer is 31.2 hope that helps
Let X = the number of pennies.
The number of nickels would be 2X
A penny is 0.01 and a nickel is 0.05
Now you have:
0.01x + 2(0.05x) = 8.80
Simplify:
0.01x + 0.10x = 8.80
Combine like terms:
0.11x = 8.80
Divide both sides by 0.11:
x = 8.80 / 0.11
x = 80
Pennies = X = 80 total pennies.
Nickels = 2x = 2 *80 = 160 nickels.
Answer:
-45
Step-by-step explanation:
v=179-224
v=-45
v=-45
