Answer:
30 degrees
Step-by-step explanation:
Keep this in mind, ALL triangles must equal 180 degrees.
This is an acute triangle, hence one of the angles is 90 degrees. To find the other two angles, we must solve for x. Since we know the sum of all angles in this triangle must equal 180 degrees, we know for setting up our equation, all the angles should equal 180.
Now solve for x by isolating x
Our x is -7, now that we know that the numerical value of x is -7, replace x with -7 for angle A.
-7 + 37 = 30
<A is 30 degrees.
<u>Check your work</u>
Plug in -7 where you see x.
Turns out this was a 30-60-90 triangle. ✅
Answer:
Step-by-step explanation:
Given
Required
The volume of the sphere
This is calculated as:
So, we have:
This gives:
Answer:
Y-3
Step-by-step explanation:
Answer:
6 miles north and 3 miles west
Step-by-step explanation:
If you picture these miles on a graph, you start at (0,0). Then you go 8 miles south (0, -8). Then 3 miles east (3, -8). Finally, 2 miles north (3, -6). You are 3 miles east and 6 miles south, so you go the opposite directions.
Answer:
a) 229 and 305 days
b) 229 days or less
c) 305 days or more
Step-by-step explanation:
The Empirical Rule(68-95-99.7 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 deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 267
Standard deviation = 19
(a) Between what values do the lengths of the middle 95% of all pregnancies fall?_____________and___________days
By the Empirical rule, 95% of all pregnancies fall within 2 standard deviations of the mean.
So
267 - 2*19 = 229 days
to
267 + 2*19 = 305 days
(b) How short are the shortest 2.5% of all pregnancies?______days or less
95% of all pregnancies fall within 2 standard deviations of the mean. The other 5% are more than 2 standard deviations from the mean. Since the distribution is symmetric, 2.5% is more than 2 standard deviations below the mean(shortest 2.5%) and 2.5% is more than 2 standard deviations above the mean(longest 2.5%). So
267 - 2*19 = 229 days
c) How long do the longest 2.5% of pregnancies last?________days or more
Explanation in b)
267 + 2*19 = 305 days
