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A group of friends ran in a $200$ -meter race. The graph in the $t$ - $d$ plane shows Ryan's distance, $R$ , Beatriz's distance, $B$ , and Grace's distance, $G$ , all in meters, $t$ seconds since the start of the race. Who stopped running temporarily before the race was over?

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Math Problems

Grade 7

Evaluate two-variable equations: word problems

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More problems from Evaluate two-variable equations: word problems

Question

The function

b(t)

gives the temperature (in degrees Celsius) of a pan of brownies by time

t

(in minutes).

\newline

What does

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

mean?

\newline

Choose

1

answer:

\newline

(A) At

t=6

minutes, the temperature of the brownies is

93

degrees Celsius.

\newline

B) At

t=6

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

93

degrees Celsius per minute.

\newline

93

degrees Celsius per minute.

\newline

(D) The temperature of the brownies increased by

93

degrees Celsius in the first six minutes.

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Posted 9 months ago

Question

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

r(t)

subscribers per month (where

t

is time in months).

\newline

What does

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

mean?

\newline

Choose

1

answer:

\newline

(A) As of month

10

, the magazine had

7

subscribers.

\newline

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

8

and month

10

was

7

subscribers per month.

\newline

7

between

t=8

and

t=10

months.

\newline

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

7

subscribers per month between

t=8

and

t=10

months.

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Posted 9 months ago

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

is the time in days). At

t=2

, the grocery store found

85 \%

of the shipment to be suitable for sale.

\newline

What does

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

\newline

Choose

1

answer:

\newline

(A) As of the fourth day,

60 \%

of the bananas suitable on the second day are still suitable.

\newline

(B) Between the second and fourth days,

60 \%

of the remaining bananas became unsuitable for sale per day.

\newline

60 \%

of the bananas became unsuitable for sale.

\newline

(D) As of the fourth day,

60 \%

of the shipment was still suitable for sale.

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Posted 9 months ago

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

, there were

115

people exposed to the illness.

\newline

What does

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

represent?

\newline

Choose

1

answer:

\newline

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

12

and

20

\newline

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

12

and

20

\newline

20

more people to be exposed to the illness

\newline

(D) The number of people exposed to the illness at

t=20

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Posted 9 months ago

Question

The population of a town grows at a rate of

r(t)

people per year (where

t

is time in years). At

t=3

, the town's population was

1000

people.

\newline

What does

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

mean?

\newline

Choose

1

answer:

\newline

(A) The town's population grew by

1500

people between

t=3

and

t=8

\newline

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

1500

people per year at

t=8

\newline

t=3

and

t=8

1500

people per year.

\newline

(D) At

t=8

, the town's population was

1500

people.

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Posted 9 months ago

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.

\newline

The computer is worth

\$ 850

initially, and it is worth

\$ 306

after

2

years.

\newline

How much will the computer be worth after

5

years?

\newline

Choose

1

answer:

\newline

(A)

\$ 0

\newline

(B)

\$ 66

\newline

(C)

\$ 79

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Posted 9 months ago

Question

The expression

11(1.022)^{t}

models the per capita gross domestic product (GDP) of the US, in thousands of dollars, as a function of the number of years since

1950

\newline

What does

1

022

represent in this expression?

\newline

Choose

1

answer:

\newline

(A) The per capita GDP in the US was

\$ 1022

1950

\newline

(B) The maximum per capita GDP occurred

1

022

years after

1950

\newline

1

022

each year.

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Posted 9 months ago

Question

Carbon dating involves the measurement of the amount of carbon

-14

in a sample. Archaeologists sometimes use carbon dating to estimate the number of years since an organism died. The function shows the ratio,

R(t)

, of carbon

-14

remaining in a sample to the original amount of carbon

-14

after

t

years.

\newline

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

\newline

If one sample was

3

times as old as another sample of the same material, how would the carbon

-14

ratios of the samples relate?

\newline

Choose

1

answer:

\newline

(A) The ratio of the older sample would be

3

times the ratio of the newer sample.

\newline

(B) The ratio of the newer sample would be

3

times the ratio of the older sample.

\newline

\newline

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

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Posted 9 months ago

Question

D=1,874-0.55 t

\newline

The distance,

D

, in meters, between an antarctic glacier and the coast

t

days after January

1

2010

is approximated by the equation. How does the distance between the glacier and the coast change over time?

\newline

Choose

1

answer:

\newline

(A) The glacier moves

0.55

meters per day closer to the shore.

\newline

(B) The glacier moves

1,874

meters per day closer to the shore.

\newline

0.55

meters per day further from the shore.

\newline

(D) The glacier moves

1,874

meters per day further from the shore.

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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

Choose

1

answer:

\newline

(A)

0.19J+0.12T \leq 25

\newline

T \leq 30

\newline

(B)

0.19J+0.12T \geq 25

\newline

T \leq 30

\newline

(C)

0.19J+0.12T \leq 25

\newline

T \geq 30

\newline

(D)

0.19J+0.12T \geq 25

\newline

T \geq 30

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Posted 8 months ago

View all (54)

A group of friends ran in a 200200200-meter race. The graph in the ttt-ddd plane shows Ryan's distance, RRR, Beatriz's distance, BBB, and Grace's distance, GGG, all in meters, ttt seconds since the start of the race. Who stopped running temporarily before the race was over?

A group of friends ran in a $200$ -meter race. The graph in the $t$ - $d$ plane shows Ryan's distance, $R$ , Beatriz's distance, $B$ , and Grace's distance, $G$ , all in meters, $t$ seconds since the start of the race. Who stopped running temporarily before the race was over?