When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 35°31'.
If Joey is known to be standing 33 feet from the base of the tree, how tall is the tree (to the nearest foot)?
To find the height of the tree, we can use the tangent function.
Let's denote the height of the tree as h.
The tangent of the angle of depression is equal to the opposite side (height of the tree, h) divided by the adjacent side (distance between Joey and the base of the tree, 33 feet).
So, tan(35°31') = h/33.
Using a scientific calculator, we find that tan(35°31') ≈ 0.6929.
Now, we can find the height of the tree, h:
0.6929 = h/33.
Multiplying both sides of the equation by 33:
0.6929 * 33 = h.
Simplifying:
h ≈ 22.8827.
Rounding to the nearest foot, the height of the tree is approximately 23 feet.
Answers:
A)
26 ft
B)
24 ft
C)
30 ft
D)
28 ft
Based on the calculations, the height of the tree is approximately 23 feet.
None of the provided answer options (A, B, C, D) match this result.
Find the exact values of the indicated trigonometric functions.
Write fractions in lowest terms.
15 9 12
Find sin A and cos A.
To find the trigonometric functions sin A and cos A, we need additional information or a diagram that shows the relationship between the values 15, 9, and 12.
Without more information, we can't determine the exact values of sin A and cos A.
Find the median for the given frequency distribution.
two way table ( (Value Frequency)( 0 8)( 1 12)( 2 15)( 3 20)( 4 20)( 5 14) )
To find the median for the given frequency distribution, we need to first determine the cumulative frequency.
Using the given frequency distribution, we can calculate the cumulative frequency by adding up the frequencies as we go down the table:
(Value Frequency Cumulative Frequency)
0 8 8
1 12 8 + 12 = 20
2 15 20 + 15 = 35
3 20 35 + 20 = 55
4 20 55 + 20 = 75
5 14 75 + 14 = 89
The median is the middle value of the data set. Since we have a total of 89 values, the median will be the value in the 44th position (middle position if the total number of values is odd).
To determine the median, we find the value that corresponds to a cumulative frequency of 44, which is in the third class (2).
Therefore, the median for the given frequency distribution is 2.
Solve the problem.
What is the angle of elevation of the sun when a 70-ft flag pole casts a 24-ft shadow?
Round to the nearest tenth of a degree.
To find the angle of elevation of the sun, we can use the trigonometric function tangent. The tangent of an angle of elevation is given by the opposite side (height of the flagpole) divided by the adjacent side (length of the shadow).
Let h be the height of the flagpole.
Let s be the length of the shadow.
We are given that h = 70 ft and s = 24 ft.
Using the tangent function, we can write:
tan(angle of elevation) = h / s
Let's substitute the given values:
tan(angle of elevation) = 70 / 24
Using a scientific calculator, we find that tan(angle of elevation) ≈ 2.9167.
To find the angle of elevation, we take the inverse tangent (arctan) of both sides:
angle of elevation = arctan(2.9167)
Using a scientific calculator, we find that angle of elevation ≈ 70.04 degrees.
Rounding to the nearest tenth of a degree, the angle of elevation of the sun when the flagpole casts a 24-ft shadow is approximately 70.0 degrees.
Answers:
Question 12 options:
A)
69.9°
B)
71.1°
C)
18.9°
D)
20.1°
Based on the calculations, the angle of elevation of the sun when the 70-ft flagpole casts a 24-ft shadow is approximately 70.0 degrees.
None of the provided answer options (A, B, C, D) match this result.
Solve and check the equation.
Begin your work by rewriting the equation without fractions.
(5y/12) - 8 = (y/2) - 9
A)
{14}
B)
{13}
C)
{12}
D)
{10}
To solve the equation, we will begin by rewriting the equation without fractions:
(5y/12) - 8 = (y/2) - 9
First, let's eliminate the fractions by multiplying every term by the LCD, which is 12:
12 * [(5y/12) - 8] = 12 * [(y/2) - 9]
This simplifies to:
5y - 96 = 6y - 108
Next, let's get all the terms with the variable, y, on one side of the equation:
5y - 6y = -108 + 96
This simplifies to:
-y = -12
Now, let's isolate y by multiplying every term by -1:
(-1)(-y) = (-1)(-12)
This simplifies to:
y = 12
So, the solution to the equation is y = 12.
Checking the solution:
Let's substitute y = 12 back into the original equation:
(5(12)/12) - 8 = (12/2) - 9
This simplifies to:
5 - 8 = 6 - 9
-3 = -3
Both sides of the equation are equal, which means that the solution y = 12 is correct.
Therefore, the correct answer is C) {12}.
Johnny can't decide which size pizza to order.
The 10-inch cheese and sausage pizza is $4.99, while the 12-inch deluxe is $5.99.
If he gets the 10-inch pizza, the total price will be divided among 3 people.
If he chooses the 12-inch pizza, then the total price will be divided among 4 people.
Which is the better buy?
How much will each person pay? (Use 3.14 for π.)
Question 14 options:
A)
10-inch pizza; $1.66
B)
12-inch pizza; $1.50
C)
10-inch pizza; $1.50
D)
12-inch pizza; $1.66
To determine which pizza is the better buy, we need to compare the price each person will pay for each option.
For the 10-inch pizza:
The price is $4.99, and it will be divided among 3 people.
Price per person = $4.99 / 3
Price per person ≈ $1.6633
For the 12-inch pizza:
The price is $5.99, and it will be divided among 4 people.
Price per person = $5.99 / 4
Price per person ≈ $1.4975
Comparing the price per person for each option:
For the 10-inch pizza, each person will pay approximately $1.6633.
For the 12-inch pizza, each person will pay approximately $1.4975.
Based on these calculations, the better buy is the 12-inch pizza, where each person will pay approximately $1.50.
Therefore, the correct choice is B) 12-inch pizza; $1.50.
Provide an appropriate response.
For the stem-and-leaf plot below, what are the maximum and minimum entries?
1 | 0 8
1 | 6 6 6 7 8 9
2 | 0 1 1 2 3 4 4 5 6 6
2 | 7 7 7 8 8 9 9 9
3 | 0 1 1 2 3 4 4 5 5
3 | 6 6 6 7 8 8 9 9
4 | 1 7
Question 16 options:
A)
max: 41; min: 10
B)
max: 47; min: 18
C)
max: 38; min: 7
D)
max: 47; min: 10
To determine the maximum and minimum entries from the given stem-and-leaf plot, we look at the largest and smallest values in the dataset.
Looking at the plot:
1 | 0 8
1 | 6 6 6 7 8 9
2 | 0 1 1 2 3 4 4 5 6 6
2 | 7 7 7 8 8 9 9 9
3 | 0 1 1 2 3 4 4 5 5
3 | 6 6 6 7 8 8 9 9
4 | 1 7
The maximum entry is 47, as seen in the largest value in the plot.
The minimum entry is 10, as seen in the smallest value in the plot.
Therefore, the correct answer is D) max: 47; min: 10.
Convert the following.
0.090 m^2 to square centimeters
Question 17 options:
A)
90 cm^2
B)
9000 cm^2
C)
9 cm^2
D)
900 cm^2
To convert square meters to square centimeters, we need to multiply the measurement by a conversion factor.
1 square meter = 10,000 square centimeters
Given the area of 0.090 square meters, we can convert it to square centimeters as follows:
0.090 square meters * 10,000 square centimeters/square meter = 900 square centimeters
Therefore, the correct answer is B) 900 cm^2.
B is 9000
D is 900
Apologies for the mistake.
To convert 0.090 square meters to square centimeters:
1 square meter = 10,000 square centimeters
0.090 square meters * 10,000 square centimeters/square meter = 900 square centimeters
Therefore, the correct answer is C) 900 cm^2.
Find the range for the set of data given.
table ( (0.172 0.114 0.518 0.369 0.619 0.29) )
Question 18 options:
A)
0.114
B)
0.518
C)
0.118
D)
0.505
To find the range for a set of data, we need to calculate the difference between the largest and the smallest values in the set.
Given the data set: {0.172, 0.114, 0.518, 0.369, 0.619, 0.29}
The largest value is 0.619, and the smallest value is 0.114.
Range = Largest value - Smallest value
Range = 0.619 - 0.114
Range = 0.505
Therefore, the correct answer is D) 0.505.
Cindy wants to secure sequins on a piece of felt shaped like a trapezoid with a height of 9 cm and bases of 20 cm and 14 cm.
What is the cost of all the sequins if sequins cost $0.60 per cm2 of coverage?
Question 20 options:
A)
$25.80
B)
$121.80
C)
$91.80
D)
$31.20
To find the cost of the sequins, we first need to calculate the total area of the trapezoid.
The formula for the area of a trapezoid is given by:
Area = (1/2) * (base1 + base2) * height
Given that base1 = 20 cm, base2 = 14 cm, and height = 9 cm, we can substitute these values into the formula:
Area = (1/2) * (20 + 14) * 9
Area = (1/2) * 34 * 9
Area = 17 * 9
Area = 153 cm^2
Now that we have the total area of the trapezoid (153 cm^2), we can calculate the cost of the sequins.
Sequins cost $0.60 per cm^2 of coverage.
Cost of sequins = Total area * cost per cm^2
Cost of sequins = 153 cm^2 * $0.60/cm^2
Cost of sequins = $91.80
Therefore, the cost of all the sequins is $91.80.
The correct answer is C) $91.80.
Let x represent the number.
Use the given conditions to write an equation.
Solve the equation and find the number.
Six less than ten times a number is the same as twelve times the number. Find the number.
The given conditions can be written as an equation:
10x - 6 = 12x
To solve this equation, we can start by simplifying it:
10x - 12x = 6
Combining like terms:
-2x = 6
To isolate x, we divide both sides of the equation by -2:
-2x / -2 = 6 / -2
This simplifies to:
x = -3
The number that satisfies the given conditions is x = -3.
Find the standard deviation.
Round to one more place than the data.
18, 10, 10, 13, 6, 11, 6, 18, 17, 24
Question 30 options:
A)
5.3
B)
1.5
C)
5.4
D)
5.8
To find the standard deviation, we can follow these steps:
1. Find the mean of the data set.
2. Subtract the mean from each data point.
3. Square each difference.
4. Find the mean of the squared differences.
5. Take the square root of the mean of squared differences.
First, let's find the mean of the data set:
mean = (18 + 10 + 10 + 13 + 6 + 11 + 6 + 18 + 17 + 24) / 10
mean = 133 / 10
mean = 13.3
Now, subtract the mean from each data point and square each difference:
(18 - 13.3)^2 = 22.09
(10 - 13.3)^2 = 11.56
(10 - 13.3)^2 = 11.56
(13 - 13.3)^2 = 0.09
(6 - 13.3)^2 = 53.29
(11 - 13.3)^2 = 5.29
(6 - 13.3)^2 = 53.29
(18 - 13.3)^2 = 22.09
(17 - 13.3)^2 = 13.69
(24 - 13.3)^2 = 113.61
Next, find the mean of the squared differences:
mean of squared differences = (22.09 + 11.56 + 11.56 + 0.09 + 53.29 + 5.29 + 53.29 + 22.09 + 13.69 + 113.61) / 10
mean of squared differences = 305.98 / 10
mean of squared differences = 30.598
Finally, take the square root of the mean of squared differences:
standard deviation = √30.598
standard deviation ≈ 5.52
Therefore, the standard deviation rounded to one more place than the data is approximately 5.5.
Among the answer options, the closest value is D) 5.8. Note that 5.8 is not the exact standard deviation, but it is the closest value among the options provided.
Find the mean of the set of data.
table ( (3.5 1.6 2.4 3.7 4.1)(3.9 1.0 3.6 4.2 3.4)(3.7 2.2 1.5 4.2 3.4)(2.7 0.4 3.7 2.0 3.6) )
Round your answer to two decimal places.
Question 36 options:
A)
3.27
B)
2.80
C)
2.94
D)
3.09
To find the mean (average) of the set of data, we need to sum up all the numbers and divide by the total count.
Given the data set:
3.5, 1.6, 2.4, 3.7, 4.1
3.9, 1.0, 3.6, 4.2, 3.4
3.7, 2.2, 1.5, 4.2, 3.4
2.7, 0.4, 3.7, 2.0, 3.6
First, add up all the numbers:
3.5 + 1.6 + 2.4 + 3.7 + 4.1 + 3.9 + 1.0 + 3.6 + 4.2 + 3.4 + 3.7 + 2.2 + 1.5 + 4.2 + 3.4 + 2.7 + 0.4 + 3.7 + 2.0 + 3.6 = 62.5
Next, count the total number of values in the data set, which is 20.
Finally, divide the sum by the total
So what is the answer?
Which of these is the correct choice?
Question 36 options:
A)
3.27
B)
2.80
C)
2.94
D)
3.09
Find the mode or modes.
The weights (in ounces) of 14 different apples are shown below.
table ( (5.0 5.5 4.6 6.9 4.1 5.0 5.5)(5.7 6.0 6.9 5.0 4.8 6.9 4.4) )
Question 40 options:
A)
5.5, 6.9
B)
5.0, 6.9
C)
5.0
D)
None