The amount a basketball coach spends at a sporting goods store depends on the number of basketballs the coach buys. The situation is represented by the function rule ab.
a.
Make a table of values and graph the function rule. Is the graph continuous or discrete? Explain.
b.
Suppose the coach spent $144 before tax. How many basketballs did she buy?
Question content area bottom
Part 1
a. Complete the following table of values.
b
0
1
2
3
4
a
enter your response here
enter your response here
enter your response here
enter your response here
enter your response here
(Simplify your answers.)
a. 0, 1, 2, 3, 4 (Number of basketballs)
b. 0, $144, $288, $432, $576 (Amount spent at the sporting goods store)
The table of values is:
Number of basketballs (x): 0, 1, 2, 3, 4
Amount spent ($): 0, 144, 288, 432, 576
b. The coach spent $144 at the sporting goods store. Looking at the second column of the table, we can see that she bought 1 basketball.
y is 5 less than the product of 6 and x.
The situation can be represented by the function rule: y = 6x - 5.
To find a table of values for this function, we can choose different values for x and then substitute them into the function rule to find the corresponding values of y.
Table of values:
x | y
-----------------
0 | - 5
1 | 1
2 | 7
3 | 13
4 | 19
To graph this function, we can plot the points from the table of values on the coordinate plane and connect them with a straight line.
The graph of the function y = 6x - 5 will be a straight line with a slope of 6 and a y-intercept of -5.
The graph is continuous, as it consists of a connected line.
Write a function rule to represent the situation.
the total cost C for g grams of ham if each gram costs $3.49
The function rule to represent the situation is: C = 3.49 * g
Write a function rule that represents the situation.
The price p of a pizza is $6.75 plus $0.85 for each of the t toppings on the pizza.
p=
(Use integers or decimals for any numbers in the expression. Do not include the $ symbol in your answer.)
The function rule to represent the situation is: p = 6.75 + 0.85t
Light travels about 186,000 mi/s. The function d(t)=186,000t gives the distance d(t), in miles, that light travels in t seconds. How far does light travel in 38 s?
d(38) =
To find how far light travels in 38 seconds, we need to substitute t = 38 into the function d(t) = 186,000t and evaluate it.
d(38) = 186,000 * 38
d(38) = 7,068,000
Therefore, light travels approximately 7,068,000 miles in 38 seconds.
Find the range of the function for the given domain.
f(x)=2x - 3; {-2,-1,0,1,2}
To find the range of the function f(x) = 2x - 3 for the given domain {-2, -1, 0, 1, 2}, we need to substitute each value of x into the function and find the corresponding y-values.
For x = -2:
f(-2) = 2(-2) - 3 = -4 - 3 = -7
For x = -1:
f(-1) = 2(-1) - 3 = -2 - 3 = -5
For x = 0:
f(0) = 2(0) - 3 = 0 - 3 = -3
For x = 1:
f(1) = 2(1) - 3 = 2 - 3 = -1
For x = 2:
f(2) = 2(2) - 3 = 4 - 3 = 1
The range of the function for the given domain {-2, -1, 0, 1, 2} is {-7, -5, -3, -1, 1}.
Find a reasonable domain and range for the function. Then graph the function.
A car can travel 33 mi for each gallon of gasoline. The function d(x)=33x represents the distance d(x), in miles, that the car can travel with x gallons of gasoline. The car's fuel tank holds 10 gal.
A reasonable domain for the function would be the number of gallons of gasoline the car can hold, which in this case is between 0 and 10 gallons.
Domain: [0, 10]
A reasonable range for the function would be the distance the car can travel given the number of gallons of gasoline filled up, which can be between 0 and the maximum distance the car can travel (33 miles per gallon multiplied by 10 gallons).
Range: [0, 330]
In other words, the car can travel between 0 and 330 miles with 0 to 10 gallons of gasoline.
To graph the function d(x) = 33x, we can plot the points (x, d(x)) where x represents the gallons of gasoline and d(x) represents the distance traveled.
The graph will be a straight line that passes through the points (0, 0) and (10, 330).
(Note: It is not drawn to scale.)
Here is a rough sketch of the graph:
```
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________________________
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The x-axis represents the gallons of gasoline and the y-axis represents the distance traveled in miles. The line starts at the origin (0, 0) and increases linearly with a slope of 33. As x increases, the distance traveled also increases proportionally.
answer
I apologize for the confusion. Here is an accurate graph of the function d(x) = 33x, representing the distance the car can travel with x gallons of gasoline:
```
^
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----------------->
0 1 2 3 4 5 6 7 8 9 10
```
The x-axis represents the gallons of gasoline (from 0 to 10) and the y-axis represents the distance traveled in miles. The graph is a straight line with a positive slope of 33, indicating that as the number of gallons increases, the distance traveled also increases in a proportional manner.
Choose the correct domain below.
A. 0 ≤ x ≤ 33
B. 0 ≤ x ≤ 10
C. 10 ≤ x ≤ 33
D. 0 ≤ x ≤ 330
The correct domain for the function is B. 0 ≤ x ≤ 10.
This is because x represents the number of gallons of gasoline in the car's fuel tank, and the car's fuel tank holds 10 gallons. Therefore, the number of gallons can range from 0 to 10.
Choose the correct range below.
A.10 ≤ d(x) ≤ 330
B.0 ≤ d(x) ≤ 10
C. 10 ≤ d(x) ≤ 33
D.0 ≤ d(x) ≤ 330
The correct range for the function is A. 10 ≤ d(x) ≤ 330.
This is because d(x) represents the distance traveled by the car, and it can range from 10 miles (if the car uses 0 gallons of gasoline) to 330 miles (if the car uses the full tank of 10 gallons). Therefore, the range of d(x) is from 10 to 330 miles.
nope
I apologize for the confusion. The correct range for the function is D. 0 ≤ d(x) ≤ 330.
Since the car can travel between 0 and 330 miles with 0 to 10 gallons of gasoline, the range of the function d(x) = 33x is from 0 to 330 miles.
7,9 ,11 ,13 ,15 , __, __, __
To find the missing terms in the sequence 7, 9, 11, 13, 15, __, __, __, we can observe that each term is obtained by adding 2 to the previous term.
Starting from 15, we can add 2 repeatedly to find the missing terms:
15 + 2 = 17
17 + 2 = 19
19 + 2 = 21
Therefore, the missing terms are 17, 19, and 21.
The complete sequence is: 7, 9, 11, 13, 15, 17, 19, 21.
Tell whether the sequence is arithmetic. If it is, identify the common difference.
-1,9 ,19 ,29 , ...
Yes, the given sequence -1, 9, 19, 29, ... is an arithmetic sequence.
To determine the common difference, we can observe that each term is obtained by adding 10 to the previous term.
9 - (-1) = 10,
19 - 9 = 10,
29 - 19 = 10.
Therefore, the common difference in this arithmetic sequence is 10.
Find the second, fourth, and eleventh terms of the sequence described by the rule.
A(n)(n1)()
Question content area bottom
Part 1
A(n) = 5 + (n - 1)(2)
A(2) =
enter your response here (Simplify your answer. Type an integer or a decimal.)
To find the second term of the sequence, we substitute n = 2 into the given rule:
A(n) = 5 + (n - 1)(2)
A(2) = 5 + (2 - 1)(2)
A(2) = 5 + (1)(2)
A(2) = 5 + 2
A(2) = 7
Therefore, the second term of the sequence is 7.
To find the fourth term of the sequence, we substitute n = 4 into the given rule:
A(n) = 5 + (n - 1)(2)
A(4) = 5 + (4 - 1)(2)
A(4) = 5 + (3)(2)
A(4) = 5 + 6
A(4) = 11
Therefore, the fourth term of the sequence is 11.
To find the eleventh term of the sequence, we substitute n = 11 into the given rule:
A(n) = 5 + (n - 1)(2)
A(11) = 5 + (11 - 1)(2)
A(11) = 5 + (10)(2)
A(11) = 5 + 20
A(11) = 25
Therefore, the eleventh term of the sequence is 25.
Find the second, fourth, and eleventh terms of the sequence described by the rule.
A(n) = 5 + (n - 1)(2)
A(2) =
enter your response here (Simplify your answer. Type an integer or a decimal.)
To find the second term of the sequence, we substitute n = 2 into the given rule:
A(n) = 5 + (n - 1)(2)
A(2) = 5 + (2 - 1)(2)
A(2) = 5 + (1)(2)
A(2) = 5 + 2
A(2) = 7
Therefore, the second term of the sequence is 7.
A(4)
To find the fourth term of the sequence, we substitute n = 4 into the given rule:
A(n) = 5 + (n - 1)(2)
A(4) = 5 + (4 - 1)(2)
A(4) = 5 + (3)(2)
A(4) = 5 + 6
A(4) = 11
Therefore, the fourth term of the sequence is 11.
A(11)
To find the eleventh term of the sequence, we substitute n = 11 into the given rule:
A(n) = 5 + (n - 1)(2)
A(11) = 5 + (11 - 1)(2)
A(11) = 5 + (10)(2)
A(11) = 5 + 20
A(11) = 25
Therefore, the eleventh term of the sequence is 25.
You borrow $350 from a friend the first week and pay the friend back $10 each week thereafter. Write the first six terms in the sequence. Explain what the sixth term means in the context of the situation.
To write the first six terms in the sequence, we start with the initial borrowing of $350 and then subtract $10 each week for repayment.
First term: $350
Second term: $350 - $10 = $340
Third term: $340 - $10 = $330
Fourth term: $330 - $10 = $320
Fifth term: $320 - $10 = $310
Sixth term: $310 - $10 = $300
The sixth term, $300, represents the remaining amount owed to the friend after six weeks of repayment. In the context of the situation, it means that after six weeks, the borrower still owes $300 of the initial $350 borrowed.
no
I apologize for the confusion. Let's start again.
The first term in the sequence represents the amount borrowed, which is $350.
The second term represents the amount borrowed minus the first payment of $10, which is $350 - $10 = $340.
The third term represents the previous amount borrowed minus the next payment of $10, which is $340 - $10 = $330.
The fourth term represents the previous amount borrowed minus the next payment of $10, which is $330 - $10 = $320.
The fifth term represents the previous amount borrowed minus the next payment of $10, which is $320 - $10 = $310.
The sixth term represents the previous amount borrowed minus the next payment of $10, which is $310 - $10 = $300.
Therefore, the first six terms in the sequence are: $350, $340, $330, $320, $310, $300.
In the context of the situation, the sixth term ($300) represents the remaining amount owed to the friend after six weeks of repayment.