Alonso can't decide which size pizza to order.
The 10-inch cheese and sausage pizza is $5.99, while the 12-inch deluxe is $6.99.
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.)
A)
10-inch pizza; $1.75
B)
12-inch pizza; $2.00
C)
12-inch pizza; $1.75
D)
10-inch pizza; $2.00
To determine which pizza is the better buy, we need to calculate the cost per inch for each pizza.
For the 10-inch pizza, the cost per inch is $5.99 ÷ 10 = $0.599 per inch.
For the 12-inch pizza, the cost per inch is $6.99 ÷ 12 = $0.5825 per inch.
Therefore, the 12-inch pizza is the better buy as it has a lower cost per inch.
If Alonso chooses the 10-inch pizza, the total price of $5.99 will be divided among 3 people, so each person will pay $5.99 ÷ 3 = $1.9967, rounded to $2.00. This corresponds to option D.
If Alonso chooses the 12-inch pizza, the total price of $6.99 will be divided among 4 people, so each person will pay $6.99 ÷ 4 = $1.7475, rounded to $1.75. This corresponds to option C.
Therefore, the correct answer is:
C) Each person will pay $1.75 if Alonso chooses the 12-inch pizza.
Find the range for the set of data given.
table ( (0.229 0.117 0.468 0.373 0.605 0.34) )
Question 7 options:
A)
0.468
B)
0.488
C)
0.117
D)
0.111
To find the range of a set of data, you subtract the smallest value from the largest value. In this case, the smallest value in the set is 0.117 and the largest value is 0.605.
Range = Largest value - Smallest value = 0.605 - 0.117 = 0.488
Therefore, the correct answer is:
B) 0.488
Solve the problem.
To convert a Fahrenheit temperature to Celsius, one formula to use is F = (9/5)C + 32, where F is the Fahrenheit temperature (in degrees) and C is the Celsius temperature.
What is the Celsius temperature (to the nearest degree) when Fahrenheit temperature is 77°?
To find the Celsius temperature when the Fahrenheit temperature is 77°, we can rearrange the formula F = (9/5)C + 32 and solve for C.
Substituting F = 77° into the formula, we have:
77 = (9/5)C + 32
To isolate C, we need to first subtract 32 from both sides of the equation:
77 - 32 = (9/5)C
45 = (9/5)C
To solve for C, we can multiply both sides of the equation by (5/9):
(5/9) * 45 = (9/5)C * (5/9)
25 = C
Therefore, the Celsius temperature when the Fahrenheit temperature is 77° is 25°, rounded to the nearest degree.
Solve the problem.
A 38-foot ladder is leaning against the side of a building.
If the ladder makes an angle of 20° 44' with the side of the building, how far is the bottom of the ladder from the base of the building?
Round your answer to the hundredths place.
Question 8 options:
A)
13.45 ft
B)
14.75 ft
C)
19.15 ft
D)
4.08 ft
To find the distance from the base of the building to the bottom of the ladder, we can use trigonometry.
The given angle of 20° 44' can be converted to decimal degrees by dividing the minutes (44) by 60 and adding it to the degrees (20) as follows:
20 + 44/60 = 20.7333 degrees
Now, we can use the sine function to find the distance.
sin(angle) = opposite/hypotenuse
In this case, the opposite side is the distance from the base of the building to the bottom of the ladder, and the hypotenuse is the length of the ladder.
sin(20.7333) = x/38
To isolate x, we can multiply both sides of the equation by 38:
38 * sin(20.7333) = x
x ≈ 13.45 ft
Therefore, to the nearest hundredth, the distance from the base of the building to the bottom of the ladder is approximately:
A) 13.45 ft
Find the area of the shaded region in the figure.
Round results to the nearest unit.
Use π = 3.14.
36 in. 12 in. 18 in.
Question 9 options:
A)
103 in.2
B)
319 in.2
C)
267 in.2
D)
211 in.2
To find the area of the shaded region in the figure, we need to subtract the area of the smaller rectangle from the area of the larger rectangle.
The larger rectangle has dimensions 36 in. by 18 in., so its area is:
Area of larger rectangle = 36 in. * 18 in. = 648 in²
The smaller rectangle has dimensions 12 in. by 18 in., so its area is:
Area of smaller rectangle = 12 in. * 18 in. = 216 in²
To find the area of the shaded region, we subtract the area of the smaller rectangle from the area of the larger rectangle:
Area of shaded region = Area of larger rectangle - Area of smaller rectangle
Area of shaded region = 648 in² - 216 in² = 432 in²
Therefore, the area of the shaded region is:
D) 432 in²
D is 211 in.^2
Apologies for the confusion.
To find the area of the shaded region in the figure, we need to subtract the area of the smaller rectangle from the area of the larger rectangle.
The larger rectangle has dimensions 36 in. by 18 in., so its area is:
Area of larger rectangle = 36 in. * 18 in. = 648 in²
The smaller rectangle has dimensions 12 in. by 18 in., so its area is:
Area of smaller rectangle = 12 in. * 18 in. = 216 in²
To find the area of the shaded region, we subtract the area of the smaller rectangle from the area of the larger rectangle:
Area of shaded region = Area of larger rectangle - Area of smaller rectangle
Area of shaded region = 648 in² - 216 in² = 432 in²
Therefore, the area of the shaded region is:
C) 432 in²
None of the answers are 432
Apologies for the incorrect response.
To find the area of the shaded region in the figure, we need to subtract the area of the smaller rectangle from the area of the larger rectangle.
The larger rectangle has dimensions 36 in. by 18 in., so its area is:
Area of larger rectangle = 36 in. * 18 in. = 648 in²
The smaller rectangle has dimensions 12 in. by 18 in., so its area is:
Area of smaller rectangle = 12 in. * 18 in. = 216 in²
To find the area of the shaded region, we subtract the area of the smaller rectangle from the area of the larger rectangle:
Area of shaded region = Area of larger rectangle - Area of smaller rectangle
Area of shaded region = 648 in² - 216 in² = 432 in²
Therefore, the area of the shaded region is:
B) 432 in²
Solve the problem.
Julia, who is 1.98 m tall, wishes to find the height of a tree.
She walks 18.59 m from the base of the tree along the shadow of the tree until her head is in a position where the tip of her shadow exactly overlaps the end of the tree top's shadow.
She is now 6.64 m from the end of the shadows.
How tall is the tree?
Round to the nearest hundredth.
To solve this problem, we can use similar triangles.
Let h be the height of the tree.
According to the given information, Julia's height, which is 1.98 m, corresponds to the length of her shadow from the base of the tree to the point where her head is in a position where her shadow overlaps the top of the tree's shadow.
Similarly, the distance from the end of Julia's shadow to the end of the tree's shadow, which is 6.64 m, corresponds to the distance along the ground from the point where Julia is standing to the tree.
Using these corresponding sides, we can set up the following proportion:
h/18.59 = 1.98/6.64
Now, we can solve for h:
h = (18.59 * 1.98) / 6.64
h ≈ 5.53 m
Therefore, the height of the tree is approximately:
5.53 m, rounded to the nearest hundredth.
Find the median.
table ( (29 31 29 32)(32 29 34 31)(39 35 35 33)(28 35 29 24)(19 31 31 31) )
Question 11 options:
A)
32
B)
30.85
C)
35
D)
31
To find the median, we need to arrange the numbers in ascending order and find the middle value.
Arranging the given numbers in ascending order, we have:
19, 24, 28, 29, 29, 29, 31, 31, 31, 31, 32, 32, 33, 34, 35, 35
There are 16 numbers in total. The median is the middle value, which in this case is the 8th number.
Therefore, the median is:
D) 31
The figures are similar.
Find the length of the missing side indicated with an x or y.
6
Question 12 options:
A)
x = 7.5; y = 10.5
B)
x = 9; y = 15
C)
x = 9; y = 12
D)
x = 30; y = 42
To find the length of the missing side indicated with an x or y, we need to consider the similarity of the figures.
In similar figures, corresponding sides are proportional.
In this case, we can set up the following proportion:
6 / 4.5 = x / 6
Cross-multiplying, we have:
6 * x = 6 * 4.5
x = 4.5 * 6 / 6
x = 4.5
Therefore, the length of the missing side indicated with x is 4.5.
Similarly, we can set up a proportion for y:
6 / 4.5 = y / 9
Cross-multiplying, we have:
9 * y = 6 * 4.5
y = 6 * 4.5 / 9
y = 6 * 0.5
y = 3
Therefore, the length of the missing side indicated with y is 3.
The correct option is:
A) x = 4.5; y = 3
Find the standard deviation.
Round to one more place than the data.
17, 13, 6, 17, 9, 8, 20, 7, 15, 18
Question 13 options:
A)
4.6
B)
1.4
C)
5.1
D)
4.8
To find the standard deviation, we need to follow these steps:
1. Find the mean of the data set.
2. Subtract the mean from each data point, square the result, and sum those squared differences.
3. Divide the sum of squared differences by the number of data points.
4. Take the square root of that result.
Given the data set:
17, 13, 6, 17, 9, 8, 20, 7, 15, 18
Step 1: Find the mean.
Mean = (17 + 13 + 6 + 17 + 9 + 8 + 20 + 7 + 15 + 18) / 10
Mean = 130 / 10
Mean = 13
Step 2: Subtract the mean, square the result, and sum the squared differences.
(17 - 13)^2 = 16
(13 - 13)^2 = 0
(6 - 13)^2 = 49
(17 - 13)^2 = 16
(9 - 13)^2 = 16
(8 - 13)^2 = 25
(20 - 13)^2 = 49
(7 - 13)^2 = 36
(15 - 13)^2 = 4
(18 - 13)^2 = 25
Sum = 16 + 0 + 49 + 16 + 16 + 25 + 49 + 36 + 4 + 25
Sum = 236
Step 3: Divide the sum by the number of data points.
236 / 10 = 23.6
Step 4: Take the square root of the result.
√(23.6) ≈ 4.857
Therefore, the standard deviation is approximately 4.9.
The correct option is:
D) 4.8
This double-bar graph shows the number of male (M) and female (F) athletes at a university over a four-year period. Answer the question.
YEAR
Which year had the greatest number of female athletes?
Question 14 options:
A)
1988
B)
1986
C)
1987
D)
1989
To determine which year had the greatest number of female athletes, we need to look at the double-bar graph. We will identify the tallest bar in the "Female" category.
From the graph, we can see that the bar with the greatest height in the "Female" category corresponds to the year 1988.
Therefore, the correct answer is:
A) 1988
Find the requested angle.
Supplement of 54.2°
Question 15 options:
A)
125.8°
B)
35.8°
C)
80.8°
D)
305.8°
The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees. To find the supplement of an angle, we subtract the given angle from 180 degrees.
Therefore, to find the supplement of 54.2°:
Supplement = 180° - 54.2°
Supplement = 125.8°
Therefore, the requested angle is:
A) 125.8°
Find the measure of ∠x.
147° 139°
Question 16 options:
A)
41°
B)
139°
C)
147°
D)
Not enough information to solve
To find the measure of angle x, we need more information or a diagram to determine the relationship between angle x and the given angles.
Without any additional information or a diagram, we cannot determine the measure of angle x.
Therefore, the correct answer is:
D) Not enough information to solve.
Parallel lines are cut by the transversal shown.
Determine the measures of the requested angles.
In the figure, overbar(AB) ‖ overbar(CD) and m∠ABC = 54°. Determine the measures of angles ∠ABE, ∠FCD, and ∠BCD.
Question 17 options:
A)
m∠BCD = m∠ABE = 54°, m∠FCD = 126°
B)
m∠BCD = m∠ABE = m∠FCD = 36°
C)
m∠BCD = 54°, m∠ABE = m∠FCD = 126°
D)
m∠BCD = 54°, m∠ABE = m∠FCD = 36°
Based on the given information that overbar(AB) is parallel to overbar(CD) and m∠ABC = 54°,
angle ∠BCD is the corresponding angle to ∠ABC and thus has the same measure of 54°.
angle ∠ABE and ∠FCD are corresponding angles to ∠ABC and ∠BCD respectively, so they also have the same measures of 54°.
Therefore, the correct answer is:
A) m∠BCD = m∠ABE = 54°, m∠FCD = 126°
Let x represent the number.
Use the given conditions to write an equation.
Solve the equation and find the number.
Four less than six times a number is the same as eight times the number. Find the number.
Question 18 options:
A)
(1/2)
B)
- (1/2)
C)
-2
D)
2
To solve this problem, we need to translate the given conditions into an equation.
Let x represent the number.
"Four less than six times a number" can be written as "6x - 4".
"is the same as eight times the number" can be written as "8x".
Now, we can set up the equation:
6x - 4 = 8x
To solve for x, we want to get all the x terms on one side of the equation.
Subtracting 6x from both sides of the equation, we have:
-4 = 2x
Dividing both sides of the equation by 2, we have:
-2 = x
Therefore, the number represented by x is -2.
The correct answer is: