Answer:
9.72°
Step-by-step explanation:
Step one
Given data
let the hypotenuse be the distance the cyclist traveled = 6.5km
and let the opposite be the height of the mountain = 1.1 km
Step two:
<u>Applying SOH CAH TOA</u>
sin ∅= opp/hyp
∅= sin-1 opp/hyp
∅= sin-1 1.1/6.5
∅= sin-1 0.169
∅= sin-1 0.169
∅=9.72°
Answer:
Explained below.
Step-by-step explanation:
The regression equation to predict amount of precipitation (in inches) in July from the average high temperatures (in degrees Fahrenheit) in July is as follows:
PRECIP = 2.0481 + 0.0067 HIGH
(1)
The value of the slope of the regression line is, 0.0067.
(2)
The predictor variable in this context is the average high temperatures (in degrees Fahrenheit) in July.
(3)
The response variable in this context is the amount of precipitation (in inches) in July.
(4)
The slope of a regression line is average rate of change in the dependent variable with one unit change in the independent variable.
The slope here is 0.0067.
This value implies that the average rate of change in the amount of precipitation (in inches) in July increases by 0.0067 inches with every 1°F increase in the average high temperatures.
(5)
Compute the mount of precipitation for a city that has an average high temperature in July of 87.31°F as follows:
PRECIP = 2.0481 + 0.0067 HIGH
= 2.0481 + 0.0067 × 87.31°F
= 2.633077
≈ 2.63 inches.
Answer:
Step-by-step explanation:
The answer is 3 /8/33.
step by step explanation
First, we can write:
x
=
3
.
¯¯¯¯
24
Next, we can multiply each side by
100
giving:
100
x
=
324
.
¯¯¯¯
24
Then we can subtract each side of the first equation from each side of the second equation giving:
100
x
−
x
=
324
.
¯¯¯¯
24
−
3
.
¯¯¯¯
24
We can now solve for
x
as follows:
100
x
−
1
x
=
(
324
+
0
.
¯¯¯¯
24
)
−
(
3
+
0
.
¯¯¯¯
24
)
(
100
−
1
)
x
=
324
+
0
.
¯¯¯¯
24
−
3
−
0
.
¯¯¯¯
24
99
x
=
(
324
−
3
)
+
(
0
.
¯¯¯¯
24
−
0
.
¯¯¯¯
24
)
99
x
=
321
+
0
99
x
=
321
99
x
99
=
321
99
99
x
99
=
3
×
107
3
×
33
x
=
3
×
107
3
×
33
x
=
107
33
Now, we can convert this improper fraction to a mixed number:
x
=
107
33
=
99
+
8
33
=
99
33
+
8
33
=
3
+
8
33
=
3
8
33
3
.
¯¯¯¯
24
=
3
8
33
We let k be the proportionality constant for the relationship between number of hours, h and speed of the walker, s.
h = k/s
Substituting the known values,
12 = k/5
k = 60
For the second scenario,
h = k/s
Substituting the calculated value for k and the given value for speed,
h = (60)(3 miles/hour)
h = 20 hours
h = 20 hours
Therefore, it will take 20 hours to walk with a speed of 3 miles per hour.
Ok, so if the angle is 120 degrees, its one third of the full cake (which is 360 degrees). So the area of the whole circle (worked out with area = pi * r^2 where r is 30) gives 900*pi, and so one third of that (because her slice is one third) is 300pi.
