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Prachi conducted an experiment to determine the relationship between the number of hours,
t, spent studying the night before the test and the number of questions,
q, answered correctly on the test. She used the given equation to model her results.

q=-3(t-2)^(2)+45
What is the best interpretation of the number 2 in Prachi's model?
Choose 1 answer:
(A) In this experiment, a student who did not study would answer 2 questions correctly.
(B) In this experiment, a student answered 2 more questions correctly for every hour of study.
(C) In this experiment, a student who studied for 2 hours would answer the most questions correctly.
(D) In this experiment, the first 2 hours of studying did not influence the number of questions the student answered correctly.

Prachi conducted an experiment to determine the relationship between the number of hours, $t$ , spent studying the night before the test and the number of questions, $q$ , answered correctly on the test. She used the given equation to model her results. $\newline$ $q=-3(t-2)^{2}+45$ $\newline$ What is the best interpretation of the number $2$ in Prachi's model? $\newline$ Choose $1$ answer: $\newline$ (A) In this experiment, a student who did not study would answer $2$ questions correctly. $\newline$ (B) In this experiment, a student answered $2$ more questions correctly for every hour of study. $\newline$ (C) In this experiment, a student who studied for $2$ hours would answer the most questions correctly. $\newline$ (D) In this experiment, the first $2$ hours of studying did not influence the number of questions the student answered correctly.

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Find a value using two-variable equations: word problems

Full solution

Q. Prachi conducted an experiment to determine the relationship between the number of hours,

t

, spent studying the night before the test and the number of questions,

q

, answered correctly on the test. She used the given equation to model her results.

\newline

q=-3(t-2)^{2}+45

\newline

What is the best interpretation of the number

2

in Prachi's model?

\newline

Choose

1

answer:

\newline

(A) In this experiment, a student who did not study would answer

2

questions correctly.

\newline

(B) In this experiment, a student answered

2

more questions correctly for every hour of study.

\newline

(C) In this experiment, a student who studied for

2

hours would answer the most questions correctly.

\newline

(D) In this experiment, the first

2

hours of studying did not influence the number of questions the student answered correctly.

Identify Role of $2$ : The equation given is $q = -3(t - 2)^2 + 45$ . Identify the role of the number $2$ within the equation.
Recognize Vertex Form: Recognize that the number $2$ is inside the parentheses, which means it's part of the vertex form of a quadratic equation. The vertex form is $q = a(t - h)^2 + k$ , where $(h, k)$ is the vertex of the parabola.
Understand Vertex Context: Understand that in the context of this problem, the vertex $(2, k)$ indicates the point where the number of questions answered correctly, $q$ , is at its maximum. This is because the coefficient of the squared term, $-3$ , is negative, indicating a downward opening parabola.
Conclude Maximum Hours: Conclude that the number $2$ represents the number of hours studied that results in the maximum number of questions answered correctly. This corresponds to option $(C)$ .

More problems from Find a value using two-variable equations: word problems

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b(t)

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\newline

\int_{0}^{6} b^{\prime}(t) d t=93

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1

\newline

t=6

minutes, the temperature of the brownies is

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degrees Celsius.

\newline

t=6

minutes, the brownies have an instantaneous rate of temperature change of

93

degrees Celsius per minute.

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(C) During the first six minutes, the temperature of the brownies increases an average of

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(D) The temperature of the brownies increased by

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The number of subscribers to a magazine is changing at a rate of

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\newline

\int_{8}^{10} r^{\prime}(t) d t=7

\newline

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\newline

(A) As of month

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(B) The average rate of change in subscribers between month

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10

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(C) The number of subscribers increased by

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(D) The rate of change of number of subscribers increased by

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Question

A grocery store receives a shipment of bananas. The percent of the shipment that is still suitable for sale is decreasing at a rate of

r(t)

percent of the original shipment per day (where

t

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t=2

, the grocery store found

85 \%

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\newline

0.85+\int_{2}^{4} r(t) d t=0.6 \text { mean? }

\newline

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(A) As of the fourth day,

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(C) Between the second and fourth day, another

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Question

The number of people exposed to a certain illness is increasing at a rate of

r(t)

people per day (where

t

is the time in days). At

t=12

115

people exposed to the illness.

\newline

115+\int_{12}^{20} r(t) d t

\newline

1

\newline

(A) The change in the number of people exposed to the illness between days

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20

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(B) The change in the rate at which people are exposed to the illness between days

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(C) The time it takes for

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Question

The population of a town grows at a rate of

r(t)

people per year (where

t

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t=3

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1000

\newline

1000+\int_{3}^{8} r(t) d t=1500

\newline

1

\newline

(A) The town's population grew by

1500

t=3

t=8

\newline

(B) The town's population grew at a rate of

1500

people per year at

t=8

\newline

(C) The average rate at which the population grew between

t=3

t=8

1500

people per year.

\newline

t=8

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Question

The value of a computer is decreasing at a rate that is proportional at any time to the value of the computer at that time.

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How much will the computer be worth after

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\$ 0

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\$ 66

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Question

11(1.022)^{t}

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\newline

1

022

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\newline

1

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(A) The per capita GDP in the US was

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(B) The maximum per capita GDP occurred

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\newline

(C) The per capita GDP in the US is multiplied by approximately

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Question

Carbon dating involves the measurement of the amount of carbon

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t

\newline

R(t)=2^{-0.00175 t}

\newline

If one sample was

3

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\newline

1

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(A) The ratio of the older sample would be

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(B) The ratio of the newer sample would be

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(D) The ratio of the newer sample would be the cube of the ratio of the older sample.

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Question

D=1,874-0.55 t

\newline

D

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t

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1

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\newline

1

\newline

(A) The glacier moves

0.55

meters per day closer to the shore.

\newline

(B) The glacier moves

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meters per day closer to the shore.

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(C) The glacier moves

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meters per day further from the shore.

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(D) The glacier moves

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meters per day further from the shore.

Posted 8 months ago

Question

Derin's boyfriend in Japan is

\$0.19

per minute. The rate to call her family in Turkey is

\$0.12

per minute. Derin wants to spend at least

30

minutes calling her family in Turkey. Which of the following systems of inequalities best represents the relationship between

J

, the number of minutes Derin calls Japan, and

T

, the number of minutes Derin calls Turkey?

\newline

1

\newline

0.19J+0.12T \leq 25

\newline

T \leq 30

\newline

0.19J+0.12T \geq 25

\newline

T \leq 30

\newline

0.19J+0.12T \leq 25

\newline

T \geq 30

\newline

0.19J+0.12T \geq 25

\newline

T \geq 30

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