What aspects fall under the right to freedom?
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This question is incomplete, here's the complete question.
See attached venn diagram.
How many women at the party are under 30?
How many men at the party are not under 30?
How many women are at the party? How many people are at the party?
Answer:
- 16 women under 30
- 22 men not under 30
- 44 women at the party
- 81 people at the party
Explanation:
A Venn diagram has overlapping circles, each one containing all the components of a group. Where the circles
The overlap reveals the elements that different groups have in common.
Total of people at the party:
22 men not under 30
+
15 men under 30
+
16 women under 30
+
28 not men, nor under 30
Total = 81 people at the party
If there are 22 men not under 30, and 15 men under 30, it means there´re 37 men and 44 women at the party.
Why Did the Professional Dog Walker ao Out of business, math worksheet Answers:
Q1. sin27° = x/8
Solution:
We have to solve for x, therefore, we will rearrange the given equation for x.
We get,
x = 8 × sin27°
Using the calculator,
sin27° = 0.45
Now substitute the value of sin27° into the main equation.
we get,
x = 8 × 0.45
x = 3.63 (rounded to the nearest hundredth)
Q2. tan 18° = n / 75
Solution:
We have to solve for n, therefore, we will rearrange the given equation for n.
We get,
n = 75 × tan 18°
Using the calculator,
tan 18° = 0.32
Now substitute the value of tan 18° into the main equation.
we get,
x = 75 × 0.32
x = 24.37 (rounded to the nearest hundredth)
Q3. sin40° = 4 / a
Solution: We have to solve for a, therefore, we will rearrange the given equation for a.
We get,
a = 4 ÷ sin40°
Using the calculator,
sin40° = 0.64
Now substitute the value of sin40° into the main equation.
we get,
a = 4 ÷ 0.64
a = 6.25 (rounded to the nearest hundredth)
Q4. cos5° = 92 / y
Solution: We have to solve for y, therefore, we will rearrange the given equation for y.
We get,
y = 92 ÷ cos5°
Using the calculator,
Cos5° = 0.99
Now substitute the value of cos5° into the main equation.
we get,
y = 92 ÷ 0.99
y = 92.92 (rounded to the nearest hundredth)
Q5: Given the shape attached, therefore, using the triangle given, we have:
Angle of elevation = 35°
length of Opposite side to the angle = x
Length of Hypoteneus = 12
Calculations:
Using the SOH CAH TOA rules:
SOH stands for SineФ = Opposite ÷ Hypotenuse.
length of the adjacent side to the angle = x
Length of Hypoteneus = 30
Calculations:
Using the SOH CAH TOA rules:
length of the adjacent side to the angle = 85
length of the opposite side to the angle = x
Calculations:
Using the SOH CAH TOA rules:
length of the adjacent side to the angle = 9
length of the opposite side to the angle = x
Calculations:
Using the SOH CAH TOA rules:
Hence,
length of the adjacent side to the angle = x
length of the opposite side to the angle = 100
Calculations:
Using the SOH CAH TOA rules:
Q1. sin27° = x/8
Solution:
We have to solve for x, therefore, we will rearrange the given equation for x.
We get,
x = 8 × sin27°
Using the calculator,
sin27° = 0.45
Now substitute the value of sin27° into the main equation.
we get,
x = 8 × 0.45
x = 3.63 (rounded to the nearest hundredth)
Q2. tan 18° = n / 75
Solution:
We have to solve for n, therefore, we will rearrange the given equation for n.
We get,
n = 75 × tan 18°
Using the calculator,
tan 18° = 0.32
Now substitute the value of tan 18° into the main equation.
we get,
x = 75 × 0.32
x = 24.37 (rounded to the nearest hundredth)
Q3. sin40° = 4 / a
Solution: We have to solve for a, therefore, we will rearrange the given equation for a.
We get,
a = 4 ÷ sin40°
Using the calculator,
sin40° = 0.64
Now substitute the value of sin40° into the main equation.
we get,
a = 4 ÷ 0.64
a = 6.25 (rounded to the nearest hundredth)
Q4. cos5° = 92 / y
Solution: We have to solve for y, therefore, we will rearrange the given equation for y.
We get,
y = 92 ÷ cos5°
Using the calculator,
Cos5° = 0.99
Now substitute the value of cos5° into the main equation.
we get,
y = 92 ÷ 0.99
y = 92.92 (rounded to the nearest hundredth)
Q5: Given the shape attached, therefore, using the triangle given, we have:
Angle of elevation = 35°
length of Opposite side to the angle = x
Length of Hypoteneus = 12
Calculations:
Using the SOH CAH TOA rules:
SOH stands for SineФ = Opposite ÷ Hypotenuse.
CAH stands for CosineФ = Adjacent ÷ Hypotenuse.
TOA stands for TangentФ = Opposite ÷ Adjacent.
Hence,
SineФ = Opposite ÷ Hypotenuse
Substituting the values:
Sine35° = x ÷ 12
0.5735 = x ÷ 12
x = 0.5735 × 12
x = 6.88 (rounded to the nearest hundredth)
Q6: Given the shape attached, therefore, using the triangle given, we have:
length of the adjacent side to the angle = x
Length of Hypoteneus = 30
Calculations:
Using the SOH CAH TOA rules:
Hence,
CosineФ = Adjacent ÷ Hypotenuse
Substituting the values:
Cos54° = x ÷ 30
0.5877 = x ÷ 30
x = 0.5877 × 30
x = 17.63 (rounded to the nearest hundredth)
Q7: Given the shape attached, therefore, using the triangle given, we have:
length of the adjacent side to the angle = 85
length of the opposite side to the angle = x
Calculations:
Using the SOH CAH TOA rules:
Hence,
TangentФ = Opposite ÷ Adjacent
Substituting the values:
tan22° = x ÷ 85
0.4040 = x ÷ 85
x = 0.4040 × 85
x = 34.34 (rounded to the nearest hundredth)
Q8: Given the shape attached, therefore, using the triangle given, we have:
Angle of elevation = 16°
length of the opposite side to the angle = x
Length of Hypoteneus = 14
Calculations:
Using the SOH CAH TOA rules:
Hence,
CosineФ = Adjacent ÷ Hypotenuse
Substituting the values:
Sine16° = x ÷ 14
0.2756 = x ÷ 14
x = 0.2756 × 14
x = 3.86 (rounded to the nearest hundredth)
Q9: Given the shape attached, therefore, using the triangle given, we have:
length of the adjacent side to the angle = 9
length of the opposite side to the angle = x
Calculations:
Using the SOH CAH TOA rules:
Hence,
TangentФ = Opposite ÷ Adjacent
Substituting the values:
tan65° = x ÷ 9
2.1445 = x ÷ 9
x = 2.1445 × 9
x = 19.30 (rounded to the nearest hundredth)
Q10: Given the shape attached, therefore, using the triangle given, we have:
Angle of elevation = 51°
length of the adjacent side to the angle = x
Length of Hypoteneus = 70
Calculations:
Using the SOH CAH TOA rules:
Hence,
CosineФ = Adjacent ÷ Hypotenuse
Substituting the values:
Cos51° = x ÷ 70
0.6293 = x ÷ 70
x = 0.6293 × 70
x = 44.05 (rounded to the nearest hundredth)
Q11: Given the shape attached, therefore, using the triangle given, we have:
Angle of elevation = 36°
length of the opposite side to the angle = 15
Length of Hypoteneus = x
Calculations:
Using the SOH CAH TOA rules:
Hence,
CosineФ = Adjacent ÷ Hypotenuse
Substituting the values:
Sine36° = 15 ÷ x
0.5877 = 15 ÷ x
x = 15 ÷ 0.5877
x = 25.52 (rounded to the nearest hundredth)
Q12: Given the shape attached, therefore, using the triangle given, we have:
length of the adjacent side to the angle = x
length of the opposite side to the angle = 100
Calculations:
Using the SOH CAH TOA rules:
Hence,
TangentФ = Opposite ÷ Adjacent
Substituting the values:
tan65° = 100 ÷ x
2.1445 = 100 ÷ x
x = 100 ÷ 2.1445
x = 46.63 (rounded to the nearest hundredth)
Q13: When a 25-ft ladder is leaned against a wall, it makes a 72° with the ground. How high up on wall does the ladder reach?
The angle of elevation from the ground = 72°
length of the wall opposite to the angle = X
Length of ladder (Hypoteneus) = 25 feet
Calculations:
Using the SOH CAH TOA rules:
Hence,
SineФ = Opposite ÷ Hypotenuse
Substituting the values:
Sine72° = x ÷ 25
0.9510 = x ÷ 25
x = 25 ÷ 0.9510
x = 23.77 (rounded to the nearest hundredth)
ANSWERS TO QUESTION 14 AND 15 ARE ATTACHED