Answer:
The angle 6 measures 54 degrees
Step-by-step explanation:
Angle 6 is congruent to angle 7 ("-2x+34") as it is an opposite angle in straight line intersection. But angle 6 is congruent to angle 2 (-9x-36) due to the two horizontal lines being parallel. So we can write the following equality to determine the value of x:
-2x + 34 = -9x -36
7x = -70
==> x = -10
Now we can answer the question: the angle 6 is
-2x + 34 = -2(-10)+34 = 54 degrees
Answer:
At least 37.74% of the procedures takes between 97.6 and 125.6 minutes
Step-by-step explanation:
The percentage is the area of the standard normal distribution curve between the values 97.6 and 125.6
The standard normal variate of the given data is found as
Thus for the given values Z is calculated as under
Similarly for the other value we have
Thus the area between the calculated values can be found from standard normal distribution table to be 37.74%
Answer:
V=3.098 yd³
Step-by-step explanation:
To answer this question we need to work with formula of the Volume of rectangular prism, the patio. Once it is required 1 inch deep. Some relations will be useful.
As 1 yard = 1 feet/3
1 yard = 1 inch/36
1 feet=12 inches
a) 23 feet 9 inches
23 ft 9''=23 +9/12=23.75 ft
b)10 feet 1 inch
10 feet 1" = 10ft + 1/12=10.083 ft
c)4 inches: 4/12 =0.33
V= w.l.h
V=23.75*10.083*0.33=79.025 ft³
Converting from cubic yard to cubic feet:
V≈79.025 : 27 yd³=2.926 yd³
Considering the possible spillage due to uneven base. ( adding 5%of V)
V≈ 2.92+0.05*(2.92)=3.098 yd³
Step 1:
Start by setting it up with the divisor 5 on the left side and the dividend 33 on the right side like this:
5 ⟌ 3 3
Step 2:
The divisor (5) goes into the first digit of the dividend (3), 0 time(s). Therefore, put 0 on top:
0
5 ⟌ 3 3
Step 3:
Multiply the divisor by the result in the previous step (5 x 0 = 0) and write that answer below the dividend.
0
5 ⟌ 3 3
0
Step 4:
Subtract the result in the previous step from the first digit of the dividend (3 - 0 = 3) and write the answer below.
0
5 ⟌ 3 3
- 0
3
Step 5:
Move down the 2nd digit of the dividend (3) like this:
0
5 ⟌ 3 3
- 0
3 3
Step 6:
The divisor (5) goes into the bottom number (33), 6 time(s). Therefore, put 6 on top:
0 6
5 ⟌ 3 3
- 0
3 3
Step 7:
Multiply the divisor by the result in the previous step (5 x 6 = 30) and write that answer at the bottom:
0 6
5 ⟌ 3 3
- 0
3 3
3 0
Step 8:
Subtract the result in the previous step from the number written above it. (33 - 30 = 3) and write the answer at the bottom.
0 6
5 ⟌ 3 3
- 0
3 3
- 3 0
3
Which equals 6
