Tcap Subpart 1-2 Part two, (I havent signed up yet, sadly).
An ice cream cone is 12 centimeters tall and has a radius of 4 centimeters.
Which measure is closest to the volume, in cubic centimeters, of the ice cream cone?
A 50.3
B 201.1
c 603.2
D 804.2
To find the volume of the ice cream cone, we can use the formula for the volume of a cone: V = (1/3)πr^2h, where r is the radius and h is the height.
Plugging in the values given:
V = (1/3)π(4^2)(12)
V = (1/3)π(16)(12)
V = (1/3)(192)π
V = 64π
To find the decimal approximation of this volume, use the value of π as approximately 3.14:
V ≈ 64(3.14)
V ≈ 200.96
The measure closest to the volume of the ice cream cone is 201.1 cubic centimeters, which corresponds to option B.
the typing rate for Marsha is shown in the graph. The typing rate for Clay is shown in the table.
Clays typing rate is Minutes:3 Words typed:54
Minutes:5 Words typed:90
Minutes: 7 words typed:126
Based on this information, which statement is true?
A
Clay types at a rate of 161616 words per minute, which is faster than Marsha.
B
Marsha types at a rate of 161616 words per minute, which is faster than Clay.
C
Clay types 222 more words per minute than Marsha.
D
Marsha types 222 more words per minute than Clay
To find the typing rate for Clay and Marsha, we need to calculate the words per minute for each based on the information given.
For Clay:
- When Clay types for 3 minutes, he types 54 words.
- So, his typing rate is 54 words / 3 minutes = 18 words per minute.
- When Clay types for 5 minutes, he types 90 words.
- So, his typing rate is 90 words / 5 minutes = 18 words per minute.
- When Clay types for 7 minutes, he types 126 words.
- So, his typing rate is 126 words / 7 minutes = 18 words per minute.
For Marsha, we are given a graph that shows her typing rate, which we do not know. Therefore, we cannot use the information provided to compare her typing rate with Clay's typing rate.
So, the correct statement is:
A) Clay types at a rate of 18 words per minute, which is faster than Marsha.
What is the volume, in cubic inches, of a sphere with an
18
18-inch diameter?
Enter your answer in the space provided.
The formula to calculate the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere.
Given that the diameter of the sphere is 18 inches, the radius is half of the diameter, which is 9 inches.
Plugging in the radius value into the formula:
V = (4/3)π(9^3)
V = (4/3)π(729)
V = 972π
To find the volume in cubic inches, we can use the approximate value of π as 3.14:
V ≈ 972(3.14)
V ≈ 3050.16 cubic inches
Therefore, the volume of a sphere with an 18-inch diameter is approximately 3050.16 cubic inches.
For 1200, a business can post an advertisement for 30 days. For 1500 the advertisement will be posted for 60 days. The relationship comparing cost to days is linear. Which function can be used to model the relationship between cost,y and the number of days, x , that an advertisement will be posted?
A: y= 300x + 1200
B: y= 1200x+ 300
C: y= 10x +900
D: y= 900x + 10
To determine the linear relationship between the cost (y) and the number of days (x) for posting an advertisement, we can use the given information points (1200, 30) and (1500, 60).
We can find the slope (m) of the line using the formula:
m = (y2 - y1) / (x2 - x1)
m = (1500 - 1200) / (60 - 30)
m = 300 / 30
m = 10
Now that we have the slope, we can input one set of data points into the equation y = mx + b to solve for the y-intercept (b).
Using the point (1200, 30):
1200 = 10(30) + b
1200 = 300 + b
b = 900
Therefore, the equation representing the relationship between cost (y) and number of days (x) for posting an advertisement is:
y = 10x + 900
So, the correct choice is:
C: y = 10x + 900
Which equation represents a linear function?
Y=x (2-3x)
y=x1/2(x-3)-2x
y=x1/2x^2+3x-1
y=x1/2x(2x-1)+3
A linear function is a straight line represented by an equation with a degree of 1.
Looking at the given equations:
1. Y = x(2-3x) - This equation contains a term that is squared, so it is not linear.
2. y = 1/2(x-3) - 2x - This equation also contains expressions that are squared and multiplied together, so it is not linear.
3. y = 1/2x^2 + 3x - 1 - This equation contains a term that is squared, so it is not linear.
4. y = 1/2x(2x-1) + 3 - This equation simplifies to y = x^2 - 1/2x + 3, which contains a term that has a degree of 2, so it is not linear.
Therefore, none of the given equations represent a linear function.