Andre received $60 for his birthday and put it in his piggy bank. Each week, he puts 3 more dollars in his bank. The amount of money in dollars D in his bank is given by D = 3w + 60 where w is the number of weeks he has saved 3 dollars. His sister Lana helped him find how much money he will have after 4, 15, 20, and 36 weeks. This table shows her results. What is the rate of change using Lana’s values for D and w? Is this a linear model or non-linear model?
W 4 weeks 15 weeks 20 weeks 36 weeks
D D= 3w =60 D = 3w + 60 D = 3w + 60 D = 3w + 60
= 3*4 +60 = 3 * 15 = 3 * 20 + 60 = 3 * 36 + 60
= 12 + 60 = 45 + 60 = 60 + 60 = 108 + 60
= 72 = 105 = 120 = 168
A.
The rate of change varies. It is a linear model.
B.
The rate of change varies. It is a non-linear model.
C.
The rate of change is . It is a linear model.
D.
The rate of change is 3. It is a linear model.
Answers
The original equation D = 3w + 60 is in the form y = mx + b, in which m is always the rate of change. In this case, m = 3, so the rate of change is 3.
Also, when the rate of change is constant, the equation is always linear. If the equation was plotted on a coordinate plane, it would create a straight line.
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b. how long does it take you to jog around the park? it takes you minutes to jog around the park.
Answers
Answer:
Part a) The system of equations is
Part b) The number of minutes it takes you to jog around the park is
Step-by-step explanation:
Part a) Write a system of linear equations
Let
x-----> the number of minutes it takes you to jog around your block
y---> the number of minutes it takes you to jog around the park
we know that
----> equation A
----> equation B
Part b) How long does it take you to jog around the park?
Multiply equation A by -1 both sides
------>
----> equation C
Adds equation B and equation C
Find the value of x
Final answer:
Write the information as a system of linear equations: 2x + y = 10 and 2x + 3y = 22. Solving these equations, we find that it takes 6 minutes to jog around the park.
Explanation:
Given the information provided in the question, we first need to represent the given information through a system of linear equations. Following the instructions in the question, let x represent the time in minutes to jog around the block, and y represent the time in minutes to jog around the park.
From the given problem, we know:
- 2x + y = 10
- 2x + 3y = 22
To find how long it takes you to jog around the park (the value of y), we can use the method of substitution or elimination. In this case, let's use the method of substitution: we can start by solving the first equation for 2x, giving us 2x = 10 - y.
Substituting that into the second equation gives us 10 - y + 3y = 22, simplifying which leads to 2y = 12, and further simplification yields y = 6. Therefore, it takes you 6 minutes to jog around the park.
Learn more about system of linear equations here:
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Answers
Answer:
The cost of the 1 muffin is $1.5 and 1 quart of milk cost is $3 .
Step-by-step explanation:
Let us assume that the cost of one muffins be x.
Let us assume that the cost of one 1 quarts of milk be y.
As given
The cost of 8 muffins and 2 quarts of mil is $18.
Than the equation becomes
8x + 2y = 18
As given
The cost of 3 muffins and 1 quart of milk is $7.50.
Than the equation becomes
3x + 1y = 7.50
Two equations are
8x + 2y = 18 and 3x + 1y = 7.50
Multiply 3x + 1y = 7.50 by 2 and subtracted from 8x + 2y = 18 .
Thus
8x - 6x + 2y - 2y = 18 - 15
2x = 3
x = 1.5
Put x = 1.5 in 3x + 1y = 7.50
3 × 1.5 + y = 7.50
y = 7.50 - 4.5
y = 3
Therefore the cost of the 1 muffin is $1.5 and 1 quart of milk cost is $3 .
b) (7/2, 15)
c) (7, 15)
d) (6, 5)
Answers
= (7/2, 15/2)
a. (7/2, 15/2)
B. Events A and B are dependent because P(A|B) = P(A)
C. Events A and B are independent because P(A|B) = P(B)
D. Events A and B are dependent because P(A|B) P(A)
Answers
The statement that is true is Option (A) Events A and B are independent because P(A|B) = P(A).
What is conditional probability ?
In probability theory, conditional probability is a measure of the probability of an event occurring, given that another event has already occurred. In conditional probability, we always deal with two or more mutually exclusive events.
How to identify the correct statement ?
Given that the probability that Edward purchases a video game from a store is 0.67 (event A), and the probability that Greg purchases a video game from the store is 0.74 (event B). The probability that Edward purchases a video game (given that Greg has purchased a video game) is 0.67.
Thus we can see that both the events A and B are mutually exclusive events . Also A and B are both independent events means they do not have any relation of simultaneously occurring.
P(A/B) means that the probability that A will occur given that B has already occurred.
As both the events are independent, therefore when A will occur, it will have no relationship with event B.
∴ P(A/B) = P(A) .
Thus the statement that is true is Option (A) Events A and B are independent because P(A|B) = P(A).
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Events A and B are independent because P(A|B) = P(A).
Given two events A and B, the conditional probability P(A|B) is the probability that A happends, knowing that B has happened. If the two events are dependent, knowing that B has already happened will change the probability of A. If, instead, knowing that B has happened doesn't change the probability of A, it means that A doesn't depend on B, and thus the events are independent.
Answers
a){-5,13}
b){-7,11}
c){1,7}
d){-1,5}
Answers
x² ⇒ x * x
-5 ⇒ -5 * 1
-4 ⇒ -5 + 1
(x + 1)(x - 5) = x(x-5) + 1(x-5)
x² - 5x + 1x - 5 = x² - 4x - 5
x + 1 = 0
x = -1
x - 5 = 0
x = 5
y = x² - 4x - 5
y = -1² - 4(-1) - 5
y = 1 + 4 - 5
y = 5 - 5
y = 0
y = x² - 4x - 5
y = 5² - 4(5) - 5
y = 25 - 20 - 5
y = 0