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Given that 104 = 10,000, write this in logarithm form.

Answers

Answer 1

Answer:

[tex]log_{10}[/tex] 10000 = 4

Step-by-step explanation:

Using the rule of logarithms

[tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]

Here b = 10, n = 4 and x = 10000, thus

[tex]log_{10}[/tex] 10000 = 4 ← in logarithmic form

that is [tex]10^{4}[/tex] = 10000 ← in exponential form


Related Questions

Sketch a graph to envision the following scenario. Place time on the x-axis. A rock climber is 25 feet above sea level. After 8 seconds he is at sea level. (He did not fall). What is the slope of the line depicted (no units)

Answers

Answer:

Please refer to the attached graph.

Slope = -3.125

Step-by-step explanation:

Given

Time is placed on x axis.

Initially, height of rock climber is 25 feet above sea level.

[tex]t_1 =0\ sec[/tex]

[tex]h_1[/tex] = 25 feet

After 8 seconds, he is at sea level.

[tex]t_2 =8\ sec[/tex]

[tex]h_2[/tex] = 0 feet

To find:

Graph of the given points and Slope of the line depicted.

Solution:

Kindly refer to the attached graph.

Here, we have been given two points to be plotted on the xy coordinate plane.

1st point is (0, 25): Time is 0 and height above sea level is 25 ft

2nd point is (8, 0): Time is 8 seconds and height above sea level is 0 ft (i.e. he comes to sea level)

First of all, mark these points and join them with a straight line.

Please refer to attached graph.

Slope of a line is given as:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Here,

[tex]y_2 = 0\\y_1 = 25\\x_2 = 8\\x_1 = 0[/tex]

Using the formula:

[tex]m=\dfrac{0-25}{8-0}\\\Rightarrow m=-\dfrac{25}{8} = \bold{-3.125}[/tex]

Draw the image of ABC under dilation whose center is P and scale factor is 4.

Answers

Answer:

Step-by-step explanation:

Let the point P is origin (0, 0), segment AB lies on the x-axis and segment PC on the y-axis,

Coordinates of A, B and C will be (1, 0), (2, 0) and (0, 2).

When triangle ABC is dilated by a scale factor 4 about the origin,

Rule for dilation;

(x, y) → (4x, 4y)

New coordinates of the points A, B and C will be,

A(1, 0) → A'(4, 0)

B(-2, 0) → B'(-8, 0)

C(0, 2) → C'(0, 8)

By plotting points A', B' and C' we can get the dilated image A'B'C'.

Dilation involves changing the size of a shape.

Assume point P is the center of origin, then we have the following coordinates of ABC

[tex]A = (1,0)[/tex]

[tex]B = (-2,0)[/tex]

[tex]C = (0,2)[/tex]

The scale factor (k) is given as:

[tex]k= 4[/tex]

So, the dilation rule is represented as:

[tex](x,y) \to (4 \times (x,y)[/tex]

Using the above dilation rule, the following coordinates represent the image of triangle ABC

[tex]A' = (4,0)[/tex]

[tex]B' = (-8,0)[/tex]

[tex]C = (0,8)[/tex]

See attachment for the image of the dilation.

Read more about dilation at:

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In a random sample of 64 people, 48 are classified as 'successful.' Determine the sample proportion of 'successful' people.

Answers

Answer:

The sample proportion of 'successful' people is [tex]\frac{3}{4}[/tex].

Step-by-step explanation:

The sample consist of 64 people and 48 of them are 'successful'. Hence, the proportion of 'successful' people is:

[tex]p = \frac{n}{N}[/tex]

Where:

[tex]N[/tex] - People that forms the sample, dimensionless.

[tex]n[/tex] - People classified as 'successful', dimensionless.

Given that [tex]n = 48[/tex] and [tex]N = 64[/tex], the sample proportion of 'successful' people is:

[tex]p = \frac{48}{64}[/tex]

[tex]p = \frac{3}{4}[/tex]

The sample proportion of 'successful' people is [tex]\frac{3}{4}[/tex].

Solve the polynomial x² - 7x + 12 = 0 Show each step used to find the solutions.

Answers

Answer:

x=4 and x=3

Step-by-step explanation:

The first step to find all factors of 12

1,2,3,4,6,12

and their negative form

-1,-2,-3,-4,-6,-12

we must add two of these numbers to get -7

and the two numbers that add up to -7 are -3 and -4

we can simply plot them into the polynomial (x-3)(x-4)

since x-3=0

we add three to both sides to get x=3

and since x-4=0

add four to both sides

we get x=4

and now check out work which

we can use First out in last (foil) method

(x-3)(x-4)

first

x^2

out

-4x

in

-3x

last

12

now we simplify to get x^2-7x+12

so it x=4 x=3 works

Answer:

x² - 7x + 12 = 0

doing middle term factorization

x²-4x-3x+12=0

taking common from each two term

x(x-4)-3(x-4)=0

taking common

(x-4)(x-3)=0

either

x-4=0

:. x=4

or

x-3=0

x=3

:.x=4,3

Find an equation for the line tangent to the curve at the point defined by the given value of d²y/dx².​

At this point. x = 2 cos t, y = 2 sin t, t=π/4

Answers

Answer:

Step-by-step explanation:

Given:

x = 2cost,

t = (1/2)arccosx

y = 2sint

dy/dx = dy/dt . dt/dx

dy/dt = 2cost

dt/dx = -1/√(1 - x²)

dy/dx = -2cost/√(1 - x²)

Differentiate again to obtain d²y/dx²

d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)

At t = π/4, we have

(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)

A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the probability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.

Answers

Answer:

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

[tex]Sections = 10[/tex]

[tex]n(Gray) = 5[/tex]

[tex]n(Blue) = 5[/tex]

Required

Determine P(Gray and Blue)

Using probability formula;

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

Calculating P(Gray)

[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]

[tex]P(Gray) = \frac{5}{10}[/tex]

[tex]P(Gray) = \frac{1}{2}[/tex]

Calculating P(Gray)

[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]

[tex]P(Blue) = \frac{5}{10}[/tex]

[tex]P(Blue) = \frac{1}{2}[/tex]

Substitute these values on the given formula

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

In how many ways can a subcommittee of 6 students be chosen from a committee which consists of 10 senior members and 12 junior members if the team must consist of 4 senior members and 2 junior members?

Answers

Answer:

The number of ways is 13860 ways

Step-by-step explanation:

Given

Senior Members = 10

Junior Members = 12

Required

Number of ways of selecting 6 students students

The question lay emphasis on the keyword selection; this implies combination

From the question, we understand that

4 students are to be selected from senior members while 2 from junior members;

The number of ways is calculated as thus;

Ways = Ways of Selecting Senior Members * Ways of Selecting Junior Members

[tex]Ways = ^{10}C_4 * ^{12}C2[/tex]

[tex]Ways = \frac{10!}{(10-4)!4!)} * \frac{12!}{(12-2)!2!)}[/tex]

[tex]Ways = \frac{10!}{(6)!4!)} * \frac{12!}{(10)!2!)}[/tex]

[tex]Ways = \frac{10 * 9 * 8 * 7 *6!}{(6! * 4*3*2*1)} * \frac{12*11*10!}{(10!*2*1)}[/tex]

[tex]Ways = \frac{10 * 9 * 8 * 7}{4*3*2*1} * \frac{12*11}{2*1}[/tex]

[tex]Ways = \frac{5040}{24} * \frac{132}{2}[/tex]

[tex]Ways = 210 * 66[/tex]

[tex]Ways = 13860[/tex]

Hence, the number of ways is 13860 ways

What is the area of the house (including the drawing room, TV room, balcony, hallway, kitchen, and bedroom)?

Answers

Answer:

A

Step-by-step explanation:

20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are

Answers

Answer:

38,760 different ways.

Step-by-step explanation:

The question is incomplete. Here is the complete question.

20 applicants are interviewed for a job. The interviewer creates an ordered list (first to last) of the best 6 applicants. How many ways are there for the interviewer to create the list?

Since the question deals with selection, we will apply the combination rule. Generally, if r objects are to be selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

According to the question, if the the interviewer is to select 6 applicants from a pool of 20 applicants that are interviewed for a job, this can be done in 20C6 number of ways.

20C6 = 20!/(20-6)!6!

20C6 = 20!/14!6!

20C6 = 20*19*18*17*16*15*14!/14!*6*5*4*3*2

20C6 =  20*19*18*1716*15/6*5*4*3*2

20C6 = 27,907,200/720

20C6 = 38,760 different ways.

Hence, the interviewer can create the list in 38,760 different ways.

The table shows the height, in meters, of an object that is dropped as time passes until the object hits the ground. A 2-row table with 10 columns. The first row is labeled time (seconds), x with entries 0, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.6. The second row is labeled height (meters), h with entries 100, 98.8, 95.1, 89.0, 80.4, 69.4, 55.9, 40.0, 21.6, 0. A line of best fit for the data is represented by h = –21.962x + 114.655. Which statement compares the line of best fit with the actual data given by the table? According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground. According to the line of best fit, the object was dropped from a lower height. The line of best fit correctly predicts that the object reaches a height of 40 meters after 3.5 seconds. The line of best fit predicts a height of 4 meters greater than the actual height for any time given in the table.

Answers

Answer: A. According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground.

The statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

What is the line of best fit?

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

We have a line of best fit:

h = –21.962x + 114.655

As per the data given and line of best fit, we can say the object would have impacted the ground 0.6 seconds later than it did according to the line of best fit.

Thus, the statement first "According to the line of best fit, the object would have hit the ground 0.6 seconds later than the actual time the object hit the ground" is correct.

Learn more about the line of best fit here:

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The probability of the stock market going up in a single day is 51%. What is the probability that the market will go up 4 consecutive days?

Answers

Answer:

[tex]Probability = 0.068[/tex]

Step-by-step explanation:

Let P(S) represent the probability that stock market will go up in a day

Given

[tex]P(S) = 51\%[/tex]

Required

Determine the probability that stock will go up 4 consecutive days

Start by converting P(S) from percentage to decimal

[tex]P(S) = 51\%[/tex]

[tex]P(S) = \frac{51}{100}[/tex]

[tex]P(S) = 0.51[/tex]

The above expression represents the probability in a day;

For 4 days; we have:

[tex]Probability = P(S) * P(S) * P(S) * P(S)[/tex]

[tex]Probability = (P(S))^4[/tex]

Substitute 0.51 for P(S)

[tex]Probability = (0.51)^4[/tex]

[tex]Probability = 0.06765201[/tex]

[tex]Probability = 0.068[/tex] -- Approximated

Hence, the probability that stock will rise for 4 consecutive days is 0.068

Which of the following is equivalent to –2i(6 – 7i)?

Answers

Answer:

[tex]\boxed{\sf \bf \ \ -2i(6-7i)=-14-12i \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

[tex]-2i(6-7i)=-12i+14i^2=-14-12i[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

A

Step-by-step explanation:

Answer = A

What is the solution to this equation? 2x + 4 = 16

Answers

Answer:

x=6

Step-by-step explanation:

2x+4=16

2x+4-4=16-6

2x=12

x=6

Proof:

2x+4=16

2(6)+4=16

12+4=16

16=16

Hope this helps ;) ❤❤❤

Answer:

find out what x is and it is 6 it is 6 because 2 times 6 is 12 and 12 plus 4 is 16

Step-by-step explanation:

suppose a chemical engineer randomly selects 3 catalysts for testing from a group of 10 catalysts, 6 of which have low acidity & 4 have high acidity. What is the probability that exactly2 lower acidic catalysts are selected?

Answers

Step-by-step explanation:

Total catalysts = 10

Probability of 2 lower acidic catalysts = 2/10 = 1/5

What number must be added to the expression below to complete the square? x2-5x

Answers

Answer:

6.25

Step-by-step explanation:

(x-a)^2=x^2-2ax+a^2

2a=5

a=2.5

2.5 ^ 2 = 6.25

Suppose you finance a home in the amount of $425,000 at 4.3% compounded monthly for 30 years. Calculate your payment.

Answers

Answer: $1,540,194.30 .

Step-by-step explanation:

The formula to calculate the accumulated amount earned on principal (P) at rate of interest (r)[ in decimal] compounded monthly after t years :

[tex]A=P(1+\dfrac{r}{12})^{12t}[/tex]

Given:  P= $425,000

r= 4.3% = 0.043

t= 30 years

[tex]A=425000(1+\dfrac{0.043}{12})^{12(30)}\\\\=425000(1.003583)^{360}\\\\=425000\times3.62398657958\approx1540194.30[/tex]

Hence, the payment would be $1,540,194.30 .

2000 people attended a baseball game. 1300 of the people attending supported the home team, while 700 supported the visiting team. What percentage of people attending supported the home team?

Answers

Answer:

Percentage of home team supporters =65%

Percentage of visiting team supporters =35%

Step-by-step explanation:

Total attendees=2,000 people

Home team supporters=1,300

Visiting team supporters=700

What percentage of people attending supported the home team?

Percentage of people attending who supported the home team = home team supporters / total attendees × 100

=1,300/2,000 × 100

=0.65 × 100

=65%

Visiting team supporters = visiting team supporters / total attendees

× 100

=700/2000 × 100

=0.35 × 100

=35%

Alternatively,

Visiting team supporters = percentage of total attendees - percentage of home team supporters

=100% - 65%

=35%

Salema's score on a test was 80%. If the test was worth a total of 60 points, how many points did Salema earn?

Answers

Answer:

48

Step-by-step explanation:

Do 60*.80

60 represent the total points the test was worth

.80 represents the % number

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Required percentage value = a

total value = b

Percentage = a/b x 100

100% = 60

80% = 48

The points Salema earned are 48 points.

What is a percentage?

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

Salema's score = 80%

Total score in the test = 60 points

Salema's score.

= 80% of 60 points

= 80/100 x 60

= 48

Thus,

The points Salema earned are 48 points.

Learn more about percentages here:

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Your investment club has only two stocks in its portfolio. $25,000 is invested in a stock with a beta of 0.8, and $40,000 is invested in a stock with a beta of 1.7. What is the portfolio's beta? Do not round intermediate calculations. Round your answer to two decimal places.

Answers

Answer:

The portfolio beta is  [tex]\alpha = 1.354[/tex]

Step-by-step explanation:

From the question we are told that

      The  first investment is [tex]i_1 = \$ 25,000[/tex]

       The  first  beta is  [tex]k = 0.8[/tex]

      The second investment is  [tex]i_2 = \$ 40,000[/tex]

       The  second  beta is  [tex]w = 1.7[/tex]

Generally the portfolio beta is mathematically represented as

           [tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]

substituting values

          [tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]

          [tex]\alpha = 1.354[/tex]

someone please help it's Multiple Coordinate Transformations

Answers

Answer:

Step-by-step explanation:

Coordinates of the vertices of the given rectangle are,

A(-4, 5), B(-2, 5), C(-2,1) and D(-4, 1).

If the given rectangle ABCD is translated by 1 unit right and 4 units down,

Rule for the translation will be,

(x, y) → [(x + 1), (y - 4)]

Therefore, coordinates of A, B, C and D after translation will be,

A(-4, 5) → A'(-3, 1)

B(-2, 5) → B'(-1, 1)

C(-2, 1) → C'(-1, -3)

D(-4, 1) → D'(-3, -3)

Then A', B', C' and D' are reflected about the y-axis.

Rule for the reflection about y-axis will be,

(x, y) → (-x, y)

New coordinates after the reflection will be,

A'(-3, 1) → A"(3, 1)

B'(-1, 1) → B"(1, 1)

C'(-1, -3) → C"(1, -3)

D'(-3, -3) → D''(3, -3)

Finally these points are rotated 270° clockwise about the origin,

Rule to be followed,

(x, y) → (-y, x)

Therefore, new coordinates will be,

A"(3, 1) → A"'(-1, 3)

B"(1, 1) → B'"(-1, 1)

C"(1, -3) → C"'(3, 1)

D"(3, -3) → D"'(3, 3)

Sharon tried to solve an equation step by step.

9
9
15
5


=−3(e−2)
=−3e+6
=3e
=e


Step 1
Step 2
Step 3


Find Sharon's mistake.
Choose 1 answer:
Choose 1 answer:

Answers

Answer:

step 2

Step-by-step explanation:

9 = -3(e - 2)

9 = -3e + 6

9-6 = -3e

3 = -3e

divide both sides by -3

-1 = e

In how many years will
The Compounds interest
onRs. 14,000 be Rs. 4, 634 at 10%
p.a?

Answers

Answer:

3 years

Step-by-step explanation:

A = P(1 + r)^t

A = I + P

A = 14,000 + 4,634 = 18,634

18,634 = 14,000(1 + 0.1)^t

18,634/14,000 = 1.1^t

log (18,634/14,000) = log 1.1^t

log (18,634/14,000) = t * log 1.1

t = [log (18,634/14000)]/(log 1.1)

t = 3

Q-The general solution of inequality cos 2 x≤- sin x is

Answers

Answer:

x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I

Step-by-step explanation:

1−2sin2  x≤−sin x    ⇒    (2sin x+1)(sin x−1)≥0

sin x≤−1/2    or    sin x≥1

−5π/6+2nπ≤x≤−π/6+2nπ    or    , n ϵ I x=(4n+1)π/2, n ϵ I⇒    -5π6+2nπ≤x≤-π6+2nπ    or    , n ϵ I x=4n+1π2, n ϵ I     (as sin x = 1 is valid only)

In general⇒    In general    x∈[2nπ−5π/6, 2nπ−π/6]∪{(4n+1)π/2}, n ϵ I

if 2x-7 is 5 more than x+4, what is the value of 3x+5

Answers

Answer:

  53

Step-by-step explanation:

Let's start with the given relation:

  2x -7 = (x+4) +5

  x = 16 . . . . . . . . . add 7-x

  3x +5 = 3(16) +5 = 53 . . . . . multiply by 3 and add 5

The value of 3x+5 is 53.

The average person lives for about 78 years. Does the average person live for at least 1,000,000 days? (Hint: There are 367 days in each year.)
what i

Answers

Answer:

[tex]\large \boxed{\sf No}[/tex]

Step-by-step explanation:

There are 365 days in 1 year.

The average person lives for about 78 years.

Multiply 78 by 365 to find the value in days.

[tex]78 \times 365= 28470[/tex]

The average person lives for about 28470 days.

Answer: No

Explanation:

78 x 367 = 28,626 days

And 28,626 days < 1,000,000 days

So an average person cannot live 1,000,000 days

Hope this helps!

The histogram shows that nine students had grades of 80 or higher.
The histogram shows there were 22 students in the class.
The histogram shows there were 25 students in the class.
The histogram is symmetrical.
The histogram has a peak.
The histogram shows the data is evenly distributed.
The histogram shows a gap in the data

Answers

Answer:

bde

Step-by-step explanation:

Answer:

B: The histogram shows there were 22 students in the class.

D: The histogram is symmetrical.

E:The histogram has a peak.

F: The histogram shows the data is evenly distributed.

Step-by-step explanation:

edg 2020

Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line with a slope of -0.12. See the figure below. There is $28.96 in credit remaining on the card after minutes of calls. How much credit was there after 21 minutes of calls?

Answers

Answer:

Credit remaining after 21 minutes = $30.4

Step-by-step explanation:

Credit remaining on a phone card is a linear function of the total calling time.

When graphed, let the linear function representing the line is,

y = mx + b

Where 'm' = slope of the line

b = y-intercept

From the graph,

Slope of the line = -0.12

y = -0.12x + b

If this line passes through a point (33, 28.96),

28.96 = -0.12(33) + b

b = 28.96 + 3.96

b = 32.92

Therefore, the linear function is,

f(x) = -0.12x + 32.92

where x = calling time

Credit left in the card after 21 minutes,

f(21) = -0.12(21) + 32.92

      = -2.52 + 32.92

      = $30.4

In designing an experiment involving a treatment applied to 4 test​ subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 available subjects.​ (Recall that with a simple random​ sample, all samples of the same size have the same chance of being​ selected.) Answer the question below.
What is the probability of each simple random sample in this​case?

Answers

Answer:

The probability is  [tex]p(n ) = 3.18*10^{-5}[/tex]

Step-by-step explanation:

From the question we are told that

     The population size is  N =  31

      The sample size  n =  4  

 

Generally the number of way by which the n  can be selected from N is mathematically represented as

          [tex]\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}[/tex]

=>       [tex]\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}[/tex]

=>       [tex]\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }[/tex]

=>        [tex]\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}[/tex]

=>        [tex]\left 31} \atop {}} \right. C_4 = 31465[/tex]

The number of ways of selecting a particular sample size is  is   [tex]k = 1[/tex]

Therefore the probability of each simple random sample in this​ case is mathematically evaluated as  

           [tex]p(n ) = \frac{1}{31465}[/tex]  

           [tex]p(n ) = 3.18*10^{-5}[/tex]

If f is a function that f(f(x)) = 2x² + 1, which is the value of f(f(f(f(3)))? Please help!

Answers

[tex]f(f(3))=2\cdot3^2+1=19\\f(f(f(f(3))))=2\cdot19^2+1=723[/tex]

Graph the following set of parametric equations on your calculator and select the matching graph.

Answers

Answer:

Graph 2

Step-by-step explanation:

The equation x = t² - 3 is represented by exponential growth, ( t² ) so it's graph will be similar to the first graph, graph 1, in our options. Then again we have to consider the equation y = √t - 2, which will be similar to graph 4, but with a greater slope. This leaves us with a solution of graph b.

Other Questions
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