For every penny Sam puts into his bank, Tara puts 4 pennies into her bank. If Sam puts 10 pennies into his bank, how many pennies does Tara put into her bank? Answer options with 4 options

Answer:

 x = - 50

Step-by-step explanation:

-2/5 x - 2 = 18

-2x - 10 = 90

-2x = 100

 x = - 50

Answer:

A) -50

Step-by-step explanation:

The given equation -2/5 x - 2 = 18

Here we have to find the value of x.

Step 1: Isolate the constant.

Add 2 on both sides, we get

-2/5x - 2 + 2 = 18 +2

-2/5x = 20

Step 2: Multiply both sides by the reciprocal of -2/5

The reciprocal of -2/5 is -5/2

x = 20 * -5/2

x = -100/2

x = -50

Answer: x = -50

Answers: 1h, 2e, 3d, 4a, 5f, 6b, 7c, 8g

 Statement                                             Reason

1. JKLM is a rectangle                         1. Given

2. ∠K and ∠L are right angles            2. Definition of rectangle

3. ΔJKM and ΔMLJ are right angles   3. Definition of right triangles

4. [tex]\overline{JM}[/tex] ≅ [tex]\overline{JM}[/tex]                                         4. Reflexive Property

5. [tex]\overline{JK}[/tex]  ≅ [tex]\overline{LM}[/tex]                                        5. Definition of rectangle

6. ΔJKM ≅ Δ MLJ                                 6. HL congruency theorem

Answer:

y < -3

Step-by-step explanation:

Isolate the variable, y. Treat the > sign like an equal sign, what you do to one side, you do to the other.

8 - 5y > 23

Do the opposite of PEMDAS (Parenthesis, Exponent (& roots), Multiplication, Division, Addition, Subtraction).

First, subtract 8 from both sides

8 (-8) - 5y > 23 (-8)

-5y > 23 - 8

-5y > 15

Isolate the variable. Divide -5 from both sides. Note that when dividing a negative number from both sides, you must flip the sign.

(-5y)/-5 > (15)/-5

y < 15/-5

y < -3

y < -3 is your answer

~

Answer:

D

Step-by-step explanation:

Because it's saying what is the shape of the "Square" inside of the cylinder.

Answer:

C) rectangle, would be the best answer beacuse the shape of the dotted line clously resembles a rectangle

Step-by-step explanation:

Answer: Choice D) Opposite sides of a parallelogram are congruent

Likely a typo has been made because A, B, C, and D aren't shown. I think your teacher meant to say PQ = RS and QR = PS

A parallelogram has properties that the opposite sides are parallel, and it can be proven that the opposite sides are congruent as well.

Answer:

D is the right answer hope this helps!!!!!!!!

[tex]a,b-the\ numbers\\\\a-b=34\to a=34+b\\\\a^2+b^2\to minimum\\\\\text{substitute:}\\\\(34+b)^2+b^2\to minimum\\\\f(b)=(34+b)^2+b^2\qquad\text{use}\ (x+y)^2=x^2+2xy+y^2\\\\f(b)=34^2+(2)(34)(b)+b^2+b^2\\\\f(b)=1156+68b+2b^2\to f(b)=2b^2+68b+1156\\\\y=ax^2+bx+c\\\\if\ a>0\ then\ a\ parabola\ op en\ up\\if\ a<0\ then\ a\ parabola\ op en\ down\\\\if\ a>0\ then\ a\ parabola\ has\ a\ minimum\ at\ a\ vertex\\if\ a<0\ then\ a\ parabola\ has\ a\ maximum\ at\ a\ vertex[/tex]

[tex]\text{We have}\ a=2>0.\ \text{Therefore the parabola has the minimum at the vertex.}\\\\(h,\ k)-vertex\\\\h=\dfrac{-b}{2a};\ k=f(h)\\\\\text{We have}\ a=2\ \text{and}\ b=68.\ \text{Substitute:}\\\\h=\dfrac{-68}{2(2)}=\dfrac{-68}{4}=-17\\\\k=f(-17)=2(-17)^2+68(-17)+1156=2(289)-1156+1156=578[/tex]

[tex]\text{Therefore}\ b=-17\ \text{and}\ a=34+b\to a=34+(-17)=17.\\\\Answer:\ a^2+b^2=17^2+(-17)^2=289+289=578[/tex]

The minimum sum of their squares is [tex]\(578\)[/tex].The sum of their squares is a minimum when each number is half the difference between them.The sum of their squares is[tex]\(2 \times \left(\frac{34}{2}\right)^2\)[/tex].

Let the two numbers be [tex]\(x\)[/tex] and [tex]\(y\)[/tex], where [tex]\(x > y\)[/tex]. Given that the difference between the numbers is 34, we can express [tex]\(y\)[/tex] in terms of [tex]\(x\) as \(y = x - 34\)[/tex].

We want to find the minimum value of the sum of their squares, which is [tex]\(x^2 + y^2\)[/tex]. Substituting [tex]\(y\)[/tex] with [tex]\(x - 34\)[/tex], we get:

[tex]\[S = x^2 + (x - 34)^2\] \[S = x^2 + x^2 - 68x + 1156\] \[S = 2x^2 - 68x + 1156\][/tex]

To find the minimum value of [tex]\(S\)[/tex], we take the derivative of [tex]\(S\)[/tex] with respect to [tex]\(x\)[/tex] and set it equal to zero:

[tex]\[\frac{dS}{dx} = 4x - 68\][/tex]

Setting the derivative equal to zero gives us:

[tex]\[4x - 68 = 0\] \[x = \frac{68}{4}\] \[x = 17\][/tex]

Since [tex]\(y = x - 34\)[/tex], we substitute [tex]\(x = 17\)[/tex] to find [tex]\(y\)[/tex]:

[tex]\[y = 17 - 34\] \[y = -17\][/tex]

So the two numbers are 17 and -17. The sum of their squares is:

[tex]\[17^2 + (-17)^2 = 289 + 289\] \[= 578\][/tex]

However, since we are looking for the minimum sum of squares, we can also use the property that the sum of squares is minimum when the numbers are equidistant from their mean. The mean of the two numbers is [tex]\(\frac{34}{2}\)[/tex], so the numbers would be [tex]\(\frac{34}{2}\)[/tex] and [tex]\(-\frac{34}{2}\)[/tex]. The sum of their squares is:

[tex]\[2 \times \left(\frac{34}{2}\right)^2 = 2 \times 289\] \[= 578\][/tex]

Answer:

Similar rectangles states that the corresponding sides are in proportion.

As per the statement:

Rectangle ABCD is similar to rectangle WXYZ.

WX = 8 feet, AD = 12 feet and WZ = 16 feet.

Since. Rectangle ABCD and rectangle WXYZ are similar

then;

their corresponding sides are in proportion:

[tex]\frac{AB}{WX}=\frac{BC}{XY}=\frac{CD}{YZ}=\frac{AD}{WZ}[/tex]

To find the value of AB:

[tex]\frac{AB}{WX}=\frac{AD}{WZ}[/tex]

Substitute the given values we have;

[tex]\frac{AB}{8}=\frac{12}{16}[/tex]

Multiply both sides by 8 we have;

[tex]AB = \frac{12}{16} \times 8 = \frac{96}{16}=6[/tex]

Therefore, the value of AB is 6 units.

The value of AB in the similar rectangles ABCD and WXYZ, given that WX is 8 feet, AD is 12 feet and WZ is 16 feet, is calculated as 6 feet by using the property of similar rectangles that the ratios of their corresponding sides are equal.

The subject in question deals with similar rectangles. Since rectangle ABCD is similar to rectangle WXYZ, the ratio of their corresponding sides will be equal. This means that the ratio of side AB to side WX should be the same as the ratio of side AD to side WZ.

Given that WX is 8 feet, AD is 12 feet and WZ is 16 feet, we can set up the proportion as AB/WX = AD/WZ. Substituting the known values into this proportion we get AB/8 = 12/16.

To find the value of AB, we can cross multiply and solve for AB to get AB = (8 * 12) / 16 = 6 feet.

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Answer:

r ≈ 0.98

Step-by-step explanation:

The correlation coefficient is easily calculated by almost any scientific or graphing calculator, or by a spreadsheet. It is mainly a matter of data entry and invoking the appropriate function. Here, the correlation coefficient is computed as about 0.97716, or 0.98 when rounded to the nearest hundredth.

Answer:

The correlation coefficient is 0.0002273427

Step-by-step explanation:

Given the data of heart rate and we have to find the correlation coefficient which can be calculated as

[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^{2}-(\sum x)^{2} ] [n\sum y^{2}-(\sum y)^{2} ] }} }[/tex]

       = [tex]=\frac{12(7949)-68(1341)}{\sqrt{[12(430)-4624][12(152729)-1798281]} }[/tex]

       = [tex]\frac{4200}{(536)(34467)}[/tex]

       = 0.0002273427

Answer: (C) 1

Step-by-step explanation:

The question is asking which y-value are not represented in the graph.  IN other words, they are asking for which values are not included in the range.

You can do this by graphing the equations:

y = x + 2    for x ≥ 0     has a y-intercept of +2 with y-values increasing

y = x - 2     for x < 0     has a y-intercept of -2 with y-values decreasing

Therefore, there are no y-values between +2 and -2 (including -2). The only option provided between these values is 1, which is option C.

Step-by-step explanation:

The given function is an increasing piecewise function with a jump at x=0 from

f(0-) = -2 to f(0)=+2.

Hence values of f(x) in the interval (-2,+2] cannot be achieved, since

for all x<0, f(x)<-2, and

for all x>=0, f(x)>= +2.

See attached graph for visual explanation.

Answer:

--3 ±sqrt((-3)^2 -4(4)(-9))

-------------------------------

2(4)

Step-by-step explanation:

4x^2-5=3x+4

We need to get this in standard form to answer the question

Subtract 3x from each side

4x^2-3x-5=3x-3x+4

4x^2-3x-5=+4

Subtract 4 from each side

4x^2-3x-9 =0

a = 4

b = -3

c = -9

-b ±sqrt(b^2 -4ac)

---------------------------

2a

--3 ±sqrt((-3)^2 -4(4)(-9))

-------------------------------

2(4)

Answer:

--3 ±sqrt((-3)^2 -4(4)(-9))

Step-by-step explanation:

Answer:

Row 2

Step-by-step explanation:

To find the mean, we add all the numbers and divide by the number of numbers

Row 1:  

(6+5+3+0+4)/5 = 18/5 = 3.6

Row 2:  

(4+5+3+5+6)/5 = 23/5 = 4.6

Row 3:  

(7+1+4+5+3)/5 = 20/5 = 4.0

Row 4:  

(4+2+5+6+3)/5 = 20/5 = 4.0

The greatest mean , or the largest mean is 4.6  or Row 2

Answer:

The answer is B) Row 2

Step-by-step explanation:

If you need any help with this question please ask me! :)

Start with a line segment connecting two points, A and B. [tex]\dfrac{DA}{BA}=3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with [tex]\dfrac{DB}{BA}=2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, [tex]\dfrac{AB}{CB}=\dfrac12[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let [tex]d[/tex] be the length of AB. Then the length of CD in terms of [tex]d[/tex] is [tex]4d[/tex]. We have the coordinates of C and D, and the distance between them is [tex]\sqrt{(4-0)^2+(0-4)^2}=4\sqrt2[/tex]. So

[tex]4d=4\sqrt2\implies d=\sqrt2[/tex]

The slope of the line through C and D is

[tex]\dfrac{0-4}{4-0}=-1[/tex]

and so the equation of the line through these points is

[tex]y-4=-(x-0)\implies x+y=4[/tex]

So the coordinates of A are [tex](x,y)=(x,4-x)[/tex]. The distance between C and A is [tex]d=\sqrt2[/tex], so we have

[tex]\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1[/tex]

Since A falls to the right of C (in the [tex]x,y[/tex] plane, not just in the sketch), we know to take the positive value [tex]x=1[/tex]. Then the [tex]y[/tex] coordinate is [tex]y=4-1=3[/tex].

All this to say that A is the point (1, 3), so

[tex]2x+y=2+3=5[/tex]

The value 2x + y of  is 5.

Start with a line segment connecting two points, A and B. [tex]\frac{DA}{BA} =3[/tex] means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with [tex]\frac{DB}{BA} =2[/tex], or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, [tex]\frac{AB}{CB} =\frac{1}{2}[/tex], so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let  be the length of AB. Then the length of CD in terms of  is . We have the coordinates of C and D, and the distance between them is

[tex]\sqrt{(4-0)^2+ (4-0)^2} =4\sqrt{2}[/tex]

So

4d= 4√2 = d= √2

The slope of the line through C and D is

[tex]\frac{0- 4}{4-0} = -1[/tex]

and so the equation of the line through these points is

y- 4 = -(x- 0) =x + y =0

So the coordinates of A are (x, y) = (x,4 -x). The distance between C and A is d= √2, so we have

[tex]\sqrt{(x-0)^2+(4- x - 4)^2} = \sqrt{2x^3} = |x| \sqrt{2} = \sqrt{2} = |x| = 1[/tex]

Since A falls to the right of C (in the x, y plane, not just in the sketch), we know to take the positive value . Then the  coordinate is .

All this to say that A is the point (1, 3), so 2x + y= 2+3=5

for such more question on coordinates

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Question

Let us have four distinct collinear points a, b, c, and d on the cartesian plane. the point c is such that [tex]\dfrac{ab}{cb} = \dfrac{1}{2}[/tex] and the point d is such that [tex]\dfrac{da}{ba} = 3[/tex] and [tex]\dfrac{db}{ba} = 2[/tex] c = (0, 4), d = (4, 0), and a = (x, y), what is the value of 2x + y?

Answer:

(a). [tex]h=\frac{3V}{B}[/tex]

(b). 18 cm.

Step-by-step explanation:

We have been given the volume of pyramid is given by the formula [tex]V=\frac{1}{3}Bh[/tex], where B is the area of the base and h is the height.

(a). Let us solve the given formula for h as:

[tex]V=\frac{1}{3}Bh[/tex]  

Multiply both sides by [tex]3[/tex]:

[tex]3\cdotV=3\cdot\frac{1}{3}Bh[/tex]  

[tex]3V=Bh[/tex]

Divide both sides by B:

[tex]\frac{3V}{B}=\frac{Bh}{B}[/tex]

[tex]\frac{3V}{B}=h[/tex]

Switch sides:

[tex]h=\frac{3V}{B}[/tex]

(b). To find the height for the given pyramid, we will substitute the given values as:

[tex]h=\frac{3(216\text{ cm}^3)}{36\text{ cm}^2}[/tex]

[tex]h=\frac{648\text{ cm}}{36}[/tex]

[tex]h=18\text{ cm}[/tex]

Therefore, the height of the pyramid is 18 cm.

Answer:

392 ft

Step-by-step explanation:

Hello, Let me help you with this

to find the real length and width you can use a rule of three

Step 1

length=8 in

Let

if

2.5 in ⇔ 35 ft

8 in ⇔ X ft ?

the relation is

[tex]\frac{2.5\ in}{35\ feet}=\frac{8\ in }{x}\\\\solve\ for\ x\\\frac{x*2.5\ in}{35\ feet}=8\ in\\x*2.5\ in=8\ in *35\ feet\\x=\frac{8\ in *35\ feet}{2.5\ in}\\ x=112\ ft[/tex]  

Step 2

width=6 in

Let

if

2.5 in ⇔ 35 ft

6 in ⇔ X ft ?

the relation is

[tex]\frac{2.5\ in}{35\ feet}=\frac{6\ in }{x}\\\\solve\ for\ x\\\frac{x*2.5\ in}{35\ feet}=6\ in\\x*2.5\ in=6\ in *35\ feet\\x=\frac{6\ in *35\ feet}{2.5\ in}\\ x=84\ ft[/tex]  

Step 2

find the perimeter using

Perimeter = 2*length +2* width

replacing

Perimeter= 2*112 ft +2* 84 ft

Perimeter=224 ft +168 ft

Perimeter=392 ft

Have a nice day

Answer:

1 : 140

Step-by-step explanation:

Ratio is 30 : 4200

Divide both numbers by 30:-

= 1 : 140   (answer)

To calculate the ratio of time to words, divide the minutes by the number of words, resulting in a 30:4200 ratio. This ratio highlights the efficiency of typing, useful for productivity analysis.

The question involves calculating the ratio of time in minutes to the number of words typed. Elvie can type 4,200 words in 30 minutes. To find the ratio of time in minutes to the number of words, we divide the number of minutes by the number of words.

First, express both quantities in their simplest forms: 30 minutes and 4,200 words. Then, create the ratio as follows:

Time in minutes : Number of words = 30 : 4,200

For easier comparison or further calculations, the ratio can be simplified by dividing both terms by the greatest common divisor. However, in this case, presenting the ratio in its initial form already communicates the relationship clearly, showing how many words are typed in a given amount of time. The ratio can be crucial for understanding productivity and efficiency in typing or other time-bound tasks.

Final answer:

The cheerleaders can be lined up in 3,628,800 ways.

Explanation:

To solve this problem, we need to consider the arrangement of the cheerleaders in two rows of five people each. Since each cheerleader in the back row must be taller than the one immediately in front, we can start by arranging the taller cheerleaders in the back row.

There are 10 different heights, so we have 10 choices for the tallest cheerleader in the back row. After choosing the tallest cheerleader in the back row, there are 9 choices for the second tallest cheerleader, 8 choices for the third tallest cheerleader, and so on, until there are 6 choices for the shortest cheerleader in the back row.

Once we have arranged the back row, there are 5 cheerleaders left to be arranged in the front row. Since the heights of the cheerleaders in the front row are smaller than the heights of the cheerleaders in the back row, we can simply arrange them in any order. There are 5! (5 factorial) ways to arrange the cheerleaders in the front row.

Therefore, the total number of ways to line up the cheerleaders is: 10 x 9 x 8 x 7 x 6 x 5! = 10! = 3,628,800 ways.

Final answer:

Mark solved 90% of the problems correctly on his math quiz, calculated by dividing 18 (correct answers) by 20 (total questions) and then multiplying by 100%.

Explanation:

To calculate the percent of problems Mark solved correctly on his math quiz, we use the formula for percentages, which is: (Number of items of interest ÷ Total number of items) × 100%

In this case, Mark solved 18 out of 20 problems correctly. So, we set up the calculation as follows:

(18 ÷ 20) × 100% = 0.9 × 100% = 90%

Therefore, Mark got 90% of the problems correct on his quiz.

The percent markup is 62.5%

The work is provided in the image attached.

Answer:

3

Step-by-step explanation:

To have full outfits he can only make three

Answer:

she can make 12: A

Step-by-step explanation

add up the numbers of pants, shoes , shirts you will get 12

Answer:

yes

Step-by-step explanation:

3x × 2x can be broken down as

3 × x × 2 × x = 3 × 2 × x × x = 6 × x² = 6x²

Answer:

Chicken=97/221=0.44

Cow=47/221=0.21

Human=77/221=0.35

Step-by-step explanation:

Answer:

4/5 pi ,  14pi/5, etc

-16pi/5, -26pi/5, etc

Step-by-step explanation:

To find coterminal angles you add or subtract 2pi from the angle

Rewrite 2pi with a common denominator of 5

2pi * 5/5 = 10pi/5

-6/5 *pi + 10pi/5  = 4/5 pi

4/5pi + 10pi/5 = 14pi/5

etc

you can keep adding 2pi

or you can subtract 2pi

-6pi/5 - 10pi/5 = -16pi/5

-16pi/5 - 10pi/5 = -26pi/5

etc

you can keep subtracting 2pi

Answer:

The rate of change is 1 mile per hour per month

Step-by-step explanation:

We are given

initial speed = 3 mph

final speed =6 mph

total number of months =3

now, we can use rate of change formula

we know that

rate of change = ( final speed - initial speed)/(total number of months)

now, we can plug values

and we get

Rate of change is

[tex]=\frac{6-3}{3}[/tex] mph per month

=1 mph per month

Jason's rate of change in biking speed is 1 mile per hour per month.

Jason is training for a marathon bike ride. His average speed increases from 3 miles per hour to 6 miles per hour in 3 months. To find the rate of change in the miles per hour that Jason bikes, we use the formula:

Rate of Change = (Final Speed - Initial Speed) / Time Period

The final speed is 6 miles per hour, the initial speed is 3 miles per hour, and the time period is 3 months. Therefore:

Rate of Change = (6 - 3) mph / 3 months

Rate of Change = 3 mph / 3 months

Rate of Change = 1 mph per month

Therefore, Jason's rate of change in biking speed is 1 mile per hour per month.

Answer:

62 kg: A

Step-by-step explanation:

The black line is called line of best fit. This line shows the points plotted and how they compare to the predicted amounts. The reason why A is the correct answer is because all of the other blue points line up with the line of best fit. Since the point 62kg is NOT on the line of best fit, that is the point where experimental error may have occurred.

Answer:

The correct answer option is 42.6.

Step-by-step explanation:

We know that in a arithmetic sequence, [tex]a_{13}=1.9[/tex] and the common difference is [tex](d)=3.7[/tex].

The standard form of an arithmetic sequence is given by:

[tex]a_n=a_1+(n-1)d[/tex]

So we will substitute the given values in this formula to find the value of [tex]a_1[/tex].

[tex]a_{13}=a_1+(13-1)3.7[/tex]

[tex]1.9=a_1+(12)3.7[/tex]

[tex]1.9=a_1+44.4[/tex]

[tex]a_1=-42.5[/tex]

Now finding the 24th term"

[tex]S_{24}=a_1+(n-1)d\\\\S_{24}=-42.5+(24-1)3.7\\\\\\S_{24}=42.6[/tex].

Therefore, the 24th term of the given arithmetic sequence is 42.6.

Answer:

Just took this test the correct answer is 1.2

Answer:

a. 0.2981

Step-by-step explanation:

We are told that the lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

Let us find z-score for 260 days.

[tex]z=\frac{x-\mu}{\sigma}[/tex], where,

[tex]x[/tex] = Sample score,

[tex]\mu[/tex] = Mean  

[tex]\sigma[/tex] = Standard deviation.

Upon substituting our given values in z-score formula we will get,

[tex]z=\frac{260-268}{15}[/tex]    

[tex]z=\frac{-8}{15}[/tex]  

[tex]z=-0.53[/tex]  

Now we will use normal distribution table to find the area that corresponds to z-score of -0.53.  

From normal distribution table we get 0.29806 as our answer. Upon rounding our answer to four decimal places we will get 0.2981 as our answer.

Therefore, probability of selecting the woman whose length of pregnancy is less than 260 days will be 0.2981 and option a is the correct choice.

Answer:

About 4

Step-by-step explanation:

Answer: B: 3 Days

Step-by-step explanation:

Let x be the number of days when Jack and Emily have the same amount of money.

Then, the total amount saved by Jack =4x+55

The total amount saved by Emily  = 13x+28

According to the question,

13x + 28 = 4x + 55

13x - 4x = 55 - 28

9x = 27

x = 3

Brainiest PLZ

Answer: 7 years

Step-by-step explanation:

To find the inverse of the function f(x) = 2x - 5/3x + 4, swap x and y and solve for y. The inverse function is f-1(x) = (x - 4) / (2 - 5/3).

To find the inverse of a function, we need to swap the variables x and y and solve for y. Let's start:

f(x) = 2x - 5/3x + 4

Replace f(x) with y:

y = 2x - 5/3x + 4

To find the inverse, solve for x:

x = (y - 4) / (2 - 5/3)

Now, swap x and y to find the inverse function:

y = (x - 4) / (2 - 5/3)

Therefore, the inverse of f(x) = 2x - 5/3x + 4 is f-1(x) = (x - 4) / (2 - 5/3).

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f(t) = 2283·(30069/2283)^(t/40) . . . . . t = years after 1960

In simplest terms, the exponential function can be written from the initial value, the ratio of given values, and the time period over which that ratio was effective. The form is ...

... f(t) = (initial value) · (ratio of values)^(t/(time period))

This works for both increasing and decreasing exponentials.

_____

Using e as a base

It can be converted to an exponential with "e" as the base by taking logarithms.

ln(f(t)) = ln(2283) + (t/40)·ln(30069/2283) = ln(2283) + 0.06445011·t

Taking antilogs, this is ...

... f(t) = 2283·e^(0.06445011·t)

_____

Comment on accuracy

The final number (30,069) when including cents (30,069.00) has 7 significant digits. In order to get the function f(t) to reproduce that number to 7 significant digits, the multiplier of t in the exponential function must be accurate to 7 significant digits. (Fairly commonly, you will see it rounded to 2 or 3 significant digits. It cannot give 30069 even to 5 digits in that case.)