7. use patterns and structure what is the pattern for the following sequence of numbers? use the rule to find the next 3 numbers in the sequence. 2,5,8,11,... 8. check for reasonableness is 90 a reasonable estimate for the sum of 48.11 + 25.68 + 14.95? explain. 9. carlos is building a birdhouse. the piece shown will be used for the roof. what is the perimeter of the piece? 4.5 in. 4.5 in. 6.36 in. 10. jaya takes $10 to the basketball game. at the concession stand, pizza costs $4.85, peanuts cost $3.40, and a bottle of water costs $2.50. estimate to determine whether jaya has enough money to purchase all three items. explain. 11. higher order thinking monthly rainfall totals for a florida city are shown in the table. during this 3 - month period, did the city have more than 20 inches of rain? explain why an estimate is sufficient in answering the question. rainfall month amount (inches) april 7.49 may 8.2 june 5.12 12. naomi buys a shirt for $23.95, a pair of gym shoes for $84.99, and a pair of jeans for $57.75. how much does naomi spend in all? 13. find the perimeter of a rectangle that is 26.349 cm long and 15.037 cm wide.

Question

Accepted Answer

### 7.
# Explanation:
## Step1: Identify the pattern
The common - difference between consecutive terms is $5 - 2=3$, $8 - 5 = 3$, $11 - 8=3$. The pattern is an arithmetic sequence with a common difference $d = 3$.
## Step2: Find the next 3 numbers
The next number after $11$ is $11+3 = 14$.
The number after $14$ is $14 + 3=17$.
The number after $17$ is $17+3 = 20$.
# Answer:
The pattern is an arithmetic sequence with a common difference of 3. The next 3 numbers are 14, 17, 20.

### 8.
# Explanation:
## Step1: Round the numbers
Round $48.11$ to $48$, $25.68$ to $26$, and $14.95$ to $15$.
## Step2: Calculate the sum of the rounded numbers
$48+26 + 15=89$.
Since $89$ is close to $90$, $90$ is a reasonable estimate.
# Answer:
Yes, 90 is a reasonable estimate because when we round $48.11$ to $48$, $25.68$ to $26$, and $14.95$ to $15$, the sum $48 + 26+15 = 89$ which is close to 90.

### 9.
# Explanation:
## Step1: Recall the perimeter formula for a triangle
The perimeter $P$ of a triangle is $P=a + b + c$, where $a$, $b$, and $c$ are the side - lengths of the triangle.
## Step2: Substitute the values
Here, $a = 4.5$ in, $b = 4.5$ in, and $c = 6.36$ in. So $P=4.5+4.5 + 6.36=15.36$ in.
# Answer:
The perimeter of the triangular piece is $15.36$ inches.

### 10.
# Explanation:
## Step1: Round the costs
Round $4.85$ to $5$, $3.40$ to $3$, and $2.50$ to $3$.
## Step2: Calculate the sum of the rounded costs
$5+3 + 3=11$.
Since $11>10$, Jaya does not have enough money.
# Answer:
No, Jaya does not have enough money. When we round the costs of pizza ($4.85$ to $5$), peanuts ($3.40$ to $3$), and water ($2.50$ to $3$), the sum is $5 + 3+3=11$ which is more than the $10$ dollars she has.

### 11.
# Explanation:
## Step1: Round the rainfall amounts
Round $7.49$ to $7.5$, $8.2$ to $8$, and $5.12$ to $5$.
## Step2: Calculate the sum of the rounded amounts
$7.5+8 + 5=20.5$.
Since $20.5>20$, an estimate is sufficient because we are just trying to determine if the sum is greater than 20. Rounding gives us a quick way to make this determination.
# Answer:
Yes, the city had more than 20 inches of rain. An estimate is sufficient because by rounding the rainfall amounts ($7.49$ to $7.5$, $8.2$ to $8$, $5.12$ to $5$) and adding them ($7.5+8 + 5 = 20.5>20$), we can quickly determine if the total is greater than 20.

### 12.
# Explanation:
## Step1: Add the costs
$23.95+84.9+57.75=(23.95 + 57.75)+84.9=81.7+84.9 = 166.6$.
# Answer:
C. $\$166.69$ (There may be a small rounding - off difference in the multiple - choice options, but the closest value to $166.6$ is $166.69$).

### 13.
# Explanation:
## Step1: Recall the perimeter formula for a rectangle
The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.
## Step2: Substitute the values
$l = 26.349$ cm and $w = 15.037$ cm. So $P=2(26.349+15.037)=2\times41.386 = 82.772$ cm.
# Answer:
The perimeter of the rectangle is $82.772$ cm.

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

7.

Step1: Identify the pattern

Step2: Find the next 3 numbers

Step1: Round the numbers

Step2: Calculate the sum of the rounded numbers

Step1: Recall the perimeter formula for a triangle

Step2: Substitute the values

Answer:

8.