The estimated population of a certain city over time is given in the table below.
Answer the questions below to determine what kind of function would best fit the
data, linear or exponential.
Number of
Years Since
Last Census,
X
Estimated
Population.
f(x)
1
48,391
2
values change
function is approximately
57,332
3
66,237
75,232
function would best fit the data because as x increases, the y
The
of this

The graph of the given line with y-intercept -4 and slope 6 is given below.

What is slope intercept form?

One of the most popular ways to represent the equation of a line is in the slope intercept form of a straight line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line ( the y-coordinate of the point where the line intersects the y-axis).

For a straight line with slope "m" and y-intercept "b," the slope-intercept form equation is:

y = mx + b.

Given, y-intercept (b) = -4

slope (m) = 6

Then, the equation of the graph will be

y = 6x - 4

The graph of the equation with points is given below:

Hence, this is the required graph of the slope-intercept form line.

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well, the total amount is really "x", which oddly enough is the 100%, but we also know that 32% of that is 8, hmmmm

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 8& 32 \end{array} \implies \cfrac{x}{8}~~=~~\cfrac{100}{32} \\\\\\ \cfrac{ x }{ 8 } ~~=~~ \cfrac{ 25 }{ 8 }\implies 8x=200\implies x=\cfrac{200}{8}\implies x=25[/tex]

True, the given function f has an inverse.

A function that can reverse into another function is known as an inverse function or anti-function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y.  Inverse functions f and g result in f(x) = y if and only if g(y) = x.

Under the given condition, we can define the function g on the set of the images  {b | b = f(a), a belongs to A}  in a way

   g(b) = a,   if f(a) = b.

This function is defined correctly on this set and is the inverse function to f.

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The inverse sine trig function would be used to solve for angle Z .

In the right angle triangle the ratio of the opposite to the hypotenuse of any acute <A is called the sine of < A

The inverse of the sine function, also known as the arcsine function, returns the angle's value when the sine function's opposite side and hypotenuse ratio are equal. It produces the angle's value.

The opposite of the sine function is the inverse sine function, also known as arcsine. Due to the fact that the sine of an angle (or sine function) is equal to the ratio of the opposite side to the hypotenuse, the sine inverse of this ratio will provide the angle's measurement.

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The cost of driving Jenna's car is $0.341/mile

From the question, we are to determine the cost of driving Jenna's car in $/mile

From the given information

The formula used to find Jenna's cost to drive her own car for work is

J = g/22 + 0.146

We are to find the cost of driving when the price of gas, g, is $4.29/gallon

Substitute g = 4.29 in the formula

J = 4.29/22 + 0.146

J = 0.195 + 0.146

J = 0.341

Hence, the cost is $0.341

Here is the complete question:

Recall the formula used to find Jenna's cost to drive her own car for work:

J = g/22 + 0.146

In this formula, J = Cost of driving Jenna's car in $/mile, and g = Cost of gas in $/gallon.

Find the cost of driving Jenna’s car (J) in $/mile when the price of gas is $4.29/gallon

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Answer:

m=30

Step-by-step explanation:

The amount of interest he will pay on this loan$12,400.

What is  interest?

The fee you pay to borrow money or the fee you charge to lend money is called interest. The most common way to represent interest is as an annual percentage of the loan amount. The interest rate on the loan is known as this percentage.

Principal = $10,000

Rate = 8%

Time = 36 months, 1 year - 12 months

36 months - 36/12= 3 years

S.I. = PRT/100

10,000*8*3/100

240,000/100 = $2,400

A = P+I = 10,000+2,400= $12,400

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Using Triangle inequality theorem Angle C of triangle CBT will be the biggest angle.

Triangle inequality. A theorem in Euclidean geometry that states that the sum of any two sides of a triangle is greater than or equal to the third side. In symbol a + b ≥ c. Basically, the theorem states that the shortest distance between two points is a straight line.

In mathematics, the triangle inequality states that for any triangle, the sum of the lengths of any two sides of it must be greater than or equal to the length of the remaining sides.

In the given triangle CBT , CB = 24 cm BT = 35 cm CT = 30 cm

We know angle opposite to larger side will be greatest therefore, angle C of triangle CBT will be the biggest angle

.

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The equation of the quadratic function is (c) f(x) = a(x + 3)² - 2

From the question, we have the table of values that can be used in our computation:

A quadratic equation is represented as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

From the graph, we have the vertex to be

(h, k) = (-3, -2)

Substitute (h, k) = (-3, -2) in f(x) = a(x - h)² + k

So, we have

f(x) = a(x + 3)² - 2

Also, from the graph, we have the point (0, 7)

This means that

a(0 + 3)² - 2 = 7

So, we have

9a = 9

Divide both sides by 9

a = 1

Substitute a = 1 in f(x) = a(x + 3)² - 2

f(x) = a(x + 3)² - 2

Hence, the equation is f(x) = a(x + 3)² - 2

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Answer:

hey um im back....

Step-by-step explanation: i was in the ER from being abused and you did not lose me don't worry i love you i was moving place to place so i did not have my phone i wish i could undo this all but im ok now love

michelle

Hello,

I hope you and your family are doing well!

To find when the populations of the two cities are equal, we can set P1(t) = P2(t) and solve for t:

120 e 0.011 t = 125 e 0.007 t

Dividing both sides by e 0.007 t:

120 = 125 * (e 0.011 t / e 0.007 t)

Using the property that e^(a+b) = e^a * e^b, we have:

120 = 125 * e^(0.011 t - 0.007 t)

120 = 125 * e^(0.004 t)

Dividing both sides by 125:

1.2 = e^(0.004 t)

Taking the natural logarithm of both sides:

ln 1.2 = ln e^(0.004 t)

ln 1.2 = 0.004 t

t = ln 1.2 / 0.004

t = approximately 8.44 years

Therefore, the populations of the two cities were equal approximately 8.44 years after 2004, or in the year 2012. To find the population of the two cities at this point in time, we can substitute t = 8.44 into either of the exponential functions:

P1(8.44) = 120 e 0.011 * 8.44 = approximately 123.88 thousand

P2(8.44) = 125 e 0.007 * 8.44 = approximately 123.88 thousand

Therefore, the populations of the two cities were equal to approximately 123.88 thousand when they were equal.

Please consider giving this answer 5 stars and brainliest if you find it helpful.

Happy Holidays!

The surface area of a snowball can be represented by the formula:

A = 4πr^2

where A is the surface area, r is the radius of the snowball, and π is a constant approximately equal to 3.14.

If the surface area of the snowball decreases at a rate of 4 cm²/min, we can represent this as a derivative:

dA/dt = -4

where dA/dt is the rate of change of the surface area with respect to time, and t is the time in minutes.

The radius of the snowball is equal to half the diameter, so we can represent the radius as:

r = d/2

where d is the diameter of the snowball.

Substituting this expression for r into the formula for the surface area and differentiating with respect to time, we get:

dA/dt = 8π(d/2)dr/dt

Setting this expression equal to -4 and solving for dr/dt, we get:

dr/dt = -4 / (8π)

= -0.5 / π

When the diameter of the snowball is 39 cm, the rate at which the diameter decreases is:

dr/dt = -0.5 / π

= -0.15915494309189533576888376337251

Therefore, the rate at which the diameter of the snowball decreases when the diameter is 39 cm is approximately -0.159 cm/min.

I hope this helps

Answer:

7,293 if I am correct.

Hope this helps!

Step-by-step explanation:

12.93 is the answer of this question.

The probability that the total time taken by a random sample of 52 customers is less than 180 minutes is 0.02%.

μ=Population mean=4

σ=Population standard deviation=2

n=Sample size=50

The sampling distribution of the sum S is roughly normal if the sample size is big (30 or more), according to the central limit theorem.

The central limit theorem tells us that the sampling distribution of the sum S is about normal because the sample size of 50 is at least 30.

The sum S's sample distribution has a mean and standard deviation of n and n, respectively.

The z-score is the value decreased by the mean, divided by the standard deviation

z = ( x -μS ) / √σS

= 150 - 50(4) / √ 50(2)

= 3.54

Using the appendix's normal probability table, get the relevant probability,

P(S < 150 ) = P(Z< -3.54)

= 0.0002

=0.02%

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

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​

Answer:

I think 50

Step-by-step explanation:

By knowing that the cost equation must be a proportional relation, we will find that the equation is:

y = $0.64*x

The cost equation is proportional, if we define y as the cost and x as the number of pounds, the equation is something like:

y = k*x

We know that for (5 + 1/2) pounds the cost is $3.52, then we can replace these values in the equation above to get.

$3.52 = k*(5 + 1/2)

$3.52/(5 + 1/2) = k = $0.64

Then the cost equation for x pounds of potatoes is:

y = $0.64*x

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The intersection of the curve with the x-axis will be at (−1, 0) and (4, 0) for each factor.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The function written in factored form is given below.

f(x) = (−x + 4) (2x + 2)

For the factor (−x + 4), we have

−x + 4 = 0

x = 4

For the factor (2x + 2), we have

2x + 2 = 0

2x = −2

x = −1

The intersection of the curve with the x-axis will be at (−1, 0) and (4, 0) for each factor.

The graph is given below.

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The equation which model the relationship between the weeks and the viewers is;

f(x) = 2160(1.5)ˣ

The distance between each number in a geometric series is known as the common ratio. The ratio between two consecutive numbers, or a number divided by the number before it in the sequence, is known as the common ratio since it is the same for all numbers or common.

Given that the expression f(x) = abˣ

Here, b is the common ratio.

Now to find the common ratio b;

To check for first and second term, 3240 / 2160 = 1.5

To check for second term and third term, 4860 / 3240 = 1.5

To check for third term and forth term, 7290 / 4860 = 1.5

To check for forth and fifth term, 10935 / 7290 = 1.5

Therefore the common ratio b is 1.5.

now to find a,

let x =0 and f(x) = 2160

Then, 2160 = a (1.5)°

a = 2160

Therefore, the equation which model the relationship between the weeks and the viewers is;

f(x) = 2160(1.5)ˣ

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The coordinates of y so that JY = (2/3)JK is Y = 2/3k

Coordinates are a pair of numbers (Cartesian coordinates), or sporadically a letter and a number, that identify a certain place on a grid, also referred to as a coordinate plane.

The x axis (horizontal) and y axis are the two axes that make up a coordinate plane (vertical)

Examining the expression given JY = (2/3)JK, it can be seen that

at the left part of the equation Y is present while at the second part of the equation Y is no replaced by 2/3k

Hence the 2/3k is equal to Y, and this represents the points that defines Y

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The value of x is [tex]x=\frac{268}{3}[/tex] = 89.33 degree.

How do you find value of x?

The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values. The letter "x" is frequently used in mathematics to denote an unknowable amount or variable. Similar to how X-rays confounded their discoverer and Malcolm X adopted the sign to stand for the lost name of his African ancestry, x also denotes the unknown in English.

x+44+x+3+x+45=360

Group like terms

x+x+x+44+3+45=360

Add similar elements: x+x+x=3 x

3 x+44+3+45=360

Add the numbers: 44+3+45=92

3 x+92=360

Move 92 to the right side

3 x=268

Divide both sides by 3

[tex]\frac{3 x}{3}=\frac{268}{3}[/tex]

Simplify

[tex]x=\frac{268}{3}[/tex]

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Answer:

3/10

Step-by-step explanation:

please mark me brainliest if this is right

The square root of 40 is approximately 6.324555320336759. This is the width of the rectangle.

What is a rectangle?

It is defined as the two-dimensional geometry in which the angle between the adjacent sides are 90 degree. It is a type of quadrilateral. It occupies area in two-dimensional planner geometry.

The area of a rectangle is given by the formula A = lw,

where A is the area, l is the length, and w is the width.

We are told that the length of the rectangle is twice the width, so we can write the formula as follows:

A = 2w * w

We are also told that the area of the rectangle is 80 square inches, so we can substitute this value into the formula:

80 = 2w * w

We can rearrange this equation to solve for w:

80 = 2w²

w² = 40

The square root of 40 is an irrational number, so the width of the rectangle is an irrational number.

Hence,  To express this number in decimal form, the square root of 40 is approximately 6.324555320336759. This is the width of the rectangle.

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Area or a circles given by the formula = radius , r

What is area?

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape.

For the circle or area given by the formula is radius ,r.

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The expression that represents the amount of money Angel would have savings in w weeks is 30+8w

The total amount of money saved after 5 weeks is $70

Which algebraic expression is required for Angel's total savings?

Total savings=30+8w

Now by substituting 5 , the number of weeks for w, we can determine total savings after 5 weeks

total savings=30+(8*5)

total savings=30+40

Total savings=$70

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The following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.

Given :

the values f ( x ) of a function f can be made arbitrarily large by taking x sufficiently close to 1 but not equal to 1.

Function :

In simple words, a function is a relationship between inputs where each input is related to exactly one output.

Every function has a domain and a co - domain.

x sufficiently close to 1 means x → 1

but x ≠ 1.

so function = [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞

Therefore the following statements which must be true is [tex]\lim_{x \to \1} _1[/tex] f ( x ) = ∞.

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By using the differentials to approximate the possible propagated error in computing the area of the end of the log is ±2π

The measurement of the radius of the end of a log = 8 inches

The possible error of radius = 1/8 inches

The area of cross section of the end of the log = πr^2

A =  πr^2

dA / dr = 2πr

dA = 2πr(dr)

Here the possible error of radius = 1/8 inches

dr = 1/8 inches

Substitute the values in the equation

dA = 2π × 8 × (± 1/8)

= ±2π

Therefore, the possible propagated error in computing the area is ±2π

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Answer:

first do criss cross the it will be like this : 2(a-3)=4*5 . Now do like as given in the picture.

The side lengths of each triangle are given as follows:

D. [tex]DE = \sqrt{13}, PQ = \sqrt{13}, EF = 2\sqrt{5}, QR = \sqrt{26}, DF = \sqrt{29}, PR = \sqrt{13}[/tex]

The side lengths of each triangle are given by the distances between the vertices.

These vertices are in the coordinate plane, hence the distance between them is found using the equation for the distance between two points.

Suppose two points in the coordinate plane with notation given as follows:

[tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Then the distance between them is given by the equation presented as follows:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Thus the side lengths are given as follows:

Meaning that option D is correct.

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Answer: If 30% of the fruits in the box are apples, then 100% - 30% = 70% of the fruits in the box are not apples. Of these non-apple fruits, 25% are pears, so the remaining fruits, 100% - 25% = 75% are oranges. Since 75% of the fruits in the box are oranges, and the total number of fruits in the box is 160, then the number of oranges in the box is 75/100 * 160 = <<75/100*160=120>>120. Answer: \boxed{120}.