1. simplify the expression below. (x^{4}cdot x^{4}cdot x^{4})
a (3x^{4})
b (x^{12})
c (3x^{12})
d (x^{64})
2. the library is located 1.8 miles west of callies house. the grocery store is located 2.4 miles south of the library. what is the length of a straight - line between callies house and the grocery store?
3. two cylinders are shown below. find the volume of each cylinder. use 3.14 for (pi). round to the nearest hundredth.
4. which of the following functions are linear?
function a
|x|3|6|9|12|
|y|9|36|81|144|
function b
|x|5|10|15|20|
|y|8|16|24|32|
a function a
b function b
c function a and function b
d none of the above
5. the results of a movie survey are represented in the two - way frequency table below. complete the two - way frequency table.
|way to watch movies|people surveyed|male|female|total|
|stream|17|||
|theater||21||
|total|50|||

Question

Accepted Answer

### 1. Simplify the expression $x^{4}\cdot x^{4}\cdot x^{4}$
# Explanation:
## Step1: Use exponent - product rule
When multiplying powers with the same base $a^m\cdot a^n=a^{m + n}$. Here $a = x$, $m = 4$, $n = 4$ for the first two terms. $x^{4}\cdot x^{4}=x^{4 + 4}=x^{8}$.
## Step2: Multiply the result by the third term
$x^{8}\cdot x^{4}=x^{8+4}=x^{12}$
# Answer:
B. $x^{12}$

### 2. Find the length of a straight - line between Callie's house and the grocery store
# Explanation:
## Step1: Identify the problem as a right - triangle problem
The movement from Callie's house to the library (west) and then from the library to the grocery store (south) forms a right - triangle. The two legs of the right - triangle have lengths $a = 1.8$ miles and $b = 2.4$ miles.
## Step2: Apply the Pythagorean theorem
The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$, where $c$ is the hypotenuse of the right - triangle. Substitute $a = 1.8$ and $b = 2.4$ into the formula: $a^{2}=(1.8)^{2}=3.24$, $b^{2}=(2.4)^{2}=5.76$. Then $a^{2}+b^{2}=3.24 + 5.76=9$. So $c=\sqrt{9}=3$ miles.
# Answer:
3 miles

### 3. Find the volume of each cylinder
## Cylinder P
# Explanation:
## Step1: Recall the volume formula for a cylinder
The volume formula for a cylinder is $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height. For cylinder P, $r = 4.25$ in and $h = 14$ in.
## Step2: Calculate the volume
Substitute the values into the formula: $V_P=3.14\times(4.25)^{2}\times14$. First, $(4.25)^{2}=4.25\times4.25 = 18.0625$. Then $V_P=3.14\times18.0625\times14=3.14\times252.875 = 793.0225\approx793.02$ in³.
## Cylinder Q
# Explanation:
## Step1: Recall the volume formula for a cylinder
The volume formula for a cylinder is $V=\pi r^{2}h$. For cylinder Q, $r = 7$ in and $h = 8.5$ in.
## Step2: Calculate the volume
Substitute the values into the formula: $V_Q=3.14\times7^{2}\times8.5$. First, $7^{2}=49$. Then $V_Q=3.14\times49\times8.5=3.14\times416.5 = 1307.71\approx1307.71$ in³
# Answer:
Volume of cylinder P: approximately $793.02$ in³; Volume of cylinder Q: approximately $1307.71$ in³

### 4. Determine which functions are linear
# Explanation:
## Step1: Recall the form of a linear function
A linear function has a constant rate of change, and its equation is of the form $y = mx + b$, or the rate of change $\frac{\Delta y}{\Delta x}$ is constant.
For Function A: $\frac{\Delta y}{\Delta x}$ between $(3,9)$ and $(6,36)$ is $\frac{36 - 9}{6 - 3}=\frac{27}{3}=9$, between $(6,36)$ and $(9,81)$ is $\frac{81 - 36}{9 - 6}=\frac{45}{3}=15$. The rate of change is not constant.
For Function B: $\frac{\Delta y}{\Delta x}$ between $(5,8)$ and $(10,16)$ is $\frac{16 - 8}{10 - 5}=\frac{8}{5}=1.6$, between $(10,16)$ and $(15,24)$ is $\frac{24 - 16}{15 - 10}=\frac{8}{5}=1.6$, between $(15,24)$ and $(20,32)$ is $\frac{32 - 24}{20 - 15}=\frac{8}{5}=1.6$. The rate of change is constant.
# Answer:
B. Function B

### 5. Complete the two - way frequency table
# Explanation:
## Step1: Find the number of females who stream movies
The total number of people surveyed who stream movies is the sum of males and females who stream movies. The total number of people surveyed who stream movies is $50-21 = 29$. Since the number of males who stream movies is 17, the number of females who stream movies is $29 - 17=12$.
## Step2: Find the number of males who go to the theater
The total number of males surveyed is 50. The number of males who stream movies is 17, so the number of males who go to the theater is $50 - 17=33$.
## Step3: Find the number of females who go to the theater
The number of people who go to the theater is 21. The number of males who go to the theater is 33, so the number of females who go to the theater is $21-33=- 12$ (There is a mistake in the problem - setup. Assuming the total number of people who go to the theater is 21 and the total number of males surveyed is 50, if we assume the table is set up correctly in terms of row - totals, the number of females who go to the theater is $21-(50 - 17)= - 12$. Let's assume the total number of people surveyed is 50 for the whole table, and the number of people who stream movies is $x$ and who go to the theater is $y$ such that $x + y=50$. If $x = 29$ (from step 1) and $y = 21$. The number of females who go to the theater is $21-(50 - 17)= - 12$ is wrong. Let's assume the total number of people who go to the theater is 21 and the number of males who stream movies is 17. The number of males who go to the theater is $50 - 17=33$ is wrong. Let's assume the correct total number of males is $m$ and females is $f$ such that $m + f=50$. If 17 males stream and the total number of streamers is $s$ and theater - goers is $t$ with $s + t=50$. Let's assume the correct way: The number of females who go to the theater is $21-(50 - 17)= - 12$ is wrong. Let's assume the total number of people surveyed is 50. The number of males who go to the theater is $50 - 17-12=21$. The number of females who go to the theater is $21 - 21 = 0$)
The completed table:
| Way to Watch Movies | People Surveyed - Male | People Surveyed - Female | Total |
|---|---|---|---|
| Stream | 17 | 12 | 29 |
| Theater | 21 | 0 | 21 |
| Total | 50 |  | 50 |
# Answer:
| Way to Watch Movies | People Surveyed - Male | People Surveyed - Female | Total |
|---|---|---|---|
| Stream | 17 | 12 | 29 |
| Theater | 21 | 0 | 21 |
| Total | 50 |  | 50 |

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

1. Simplify the expression \(x^{4}\cdot x^{4}\cdot x^{4}\)

Step1: Use exponent - product rule

Step2: Multiply the result by the third term

Step1: Identify the problem as a right - triangle problem

Step2: Apply the Pythagorean theorem

Step1: Recall the volume formula for a cylinder

Step2: Calculate the volume

Cylinder Q

Answer:

2. Find the length of a straight - line between Callie's house and the grocery store

way to watch movies	people surveyed	male	female	total
stream	17
theater		21
total	50

x	3	6	9	12
y	9	36	81	144