Question
The function defined by f(t)=12(1+0.03)t can be used to determine the population, in thousands, of a town t years since 1955. According to the function, what was the population of the town in 1955 and what was the percent increase in population from year to year?

Enter a number in each box to correctly complete the sentence.

Answer:

Improper fraction

Step-by-step explanation:

2×3/5

=6/5 i.e Improper fraction

A circle can be characterized by its center's location and its radius' length. The correct option is A.

A circle can be characterized by its center's location and its radius' length. Let the center of the considered circle be at (h,k) coordinate and the radius of the circle be 'r' units. Then, the equation of that circle would be:

(x-h)² + (y-k)² = r²

The given graph is the graph of a circle that has its origin at (0,0) and has a radius of 4 units, therefore, the equation will be,

(x-0)² + (y-0)² = 4²

x² + y² = 16

Multiply both the sides of the equation by 2,

2x² + 2y² = 32

Hence, the correct option is A.

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The type of data that would be best displayed in a dot plot is the correspondent to the third option.

A dot plot is a plot where in the horizontal axis different numbers or properties (discrete set, usually we want smaller ranges, just so the graph are easier to read.) are marked, and above these, we mark dots, that represents how many times these are repeated on the data set.

We don't want large ranges (like in the first option 725 to 2450) because it means that we need to mark 725 points, or we need to find a common factor so each point represents more than one unit.

So, we need to have discrete data and with ranges not to large. The only option that meets both conditions is the third one, where on the horizontal axis we would have each of the 15 school dental clinics, and the dots would represent the number of dentist volunteering on each of them.

Then the correct option is the third one.

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Answer:

3rd option

Step-by-step explanation:

Answer:

25

Step-by-step explanation:

c^2=a^2+b^2

where c = hypotenuse

so, x^2 = 24^2+7^2

x^2 = 576 + 49

x^2 = 625

x = square root of 625

x = 25

The inverse of a quadratic parent function with a limited domain is given by the square root function, hence option C is correct.

Supposing we have a function y = f(x), to find the inverse, we exchange x and y, and isolate y.

The quadratic function is:

[tex]y = x²[/tex]

Exchanging and isolating y:

[tex]x = y^2[/tex]

[tex]y^2 = x[/tex]

[tex]y = \sqrt{x}[/tex]

[tex]f^{-1}(x) = \sqrt{x}[/tex]

Hence option C is correct.

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The expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.

It is defined as the combination of constants and variables with mathematical operators.

We have an expression:

g  = 2hm

To make m as the subject and solve it:

Divide the above expression by 2h on both sides:

g/2h = m  or

m = g/2h

Thus, the expression g = 2hm can be written as in terms of g and h when m is the subject is m = g/2h.

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For both problems, we can use the section formula.

1) [tex]P=\left(\frac{(1)(1)+(5)(-9)}{6}, \frac{(1)(8)+(5)(3)}{6} \right)=\boxed{\left(-\frac{22}{3}, \frac{23}{6} \right)}[/tex]

2) [tex]Z=\left(\frac{(2)(7)+(1)(1)}{3}, \frac{((2)(5)+(1)(2)}{3} \right)=\boxed{(5, 4)}[/tex]

Answer:

The answer with 4 cubes 2x2

Step-by-step explanation:

D it has 5 cubs in all,if you see A,B,C,they do not have cuds

Answer:

A ≈ 9.6 units²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = product of 2 sides × sin (angle between them ) , that is

A = 3 × 5 × sin40° = 15 × sin40° ≈ 9.6 units² ( to the nearest tenth )

The approximate equation is n = (ln 6)/10 and approximate value is n = 0.179.

In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

Here, given equation; (we are using n in place of t)

          -5.e¹⁰ⁿ = -30

      On dividing -5 both sides, we get

           -5.e¹⁰ⁿ/-5 = -30/-5

                e¹⁰ⁿ  = 6

 Taking 'ln' on both side, we get

             10n = ln 6

              n = (ln 6)/10

              n = 1.791759/10

              n = 0.179

Thus, the approximate equation is n = (ln 6)/10 and approximate value is n = 0.179.

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Answer:

46 degrees

Step-by-step explanation:

Answer:

It's the third one hun :>

Answer:

yup third one

Step-by-step explanation:

parabolas are ALWAYS a U shape ;-)

The values of x and y from the figure are 22.5 and 10 respectively

The angles that meet at a point X are equal and vertically opposite

From the diagram shown

6x - 5 = 8x - 50

6x - 8x = -50 +  5

-2x = -45

x = 22.5

Similarly

2y + 30 = 3y + 20

2y - 3y = 20 - 30

-y = -10

y = 10

Hence the values of x and y from the figure are 22.5 and 10 respectively

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[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Since the two lines intersects each other we can conclude that :

and

[ That's because they form vertical opposite angle pair ]

So, let's solve for x and y ~

[tex]\qquad \sf  \dashrightarrow \:6x - 5 = 8x - 50[/tex]

[tex]\qquad \sf  \dashrightarrow \:8x - 6x = - 5 + 50[/tex]

[tex]\qquad \sf  \dashrightarrow \:2x = 45[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{45}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 22.5[/tex]

And

[tex]\qquad \sf  \dashrightarrow \:2y + 30 = 3y + 20[/tex]

[tex]\qquad \sf  \dashrightarrow \:3y - 2y = 30 - 20[/tex]

[tex]\qquad \sf  \dashrightarrow \:y = 10[/tex]

I hope the steps are clear ~ let me know if you have doubts ~

Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, translation, rotation and dilation.

Triangle RST is reflected across the x-axis and translated 5 units to the left to form triangle R"S"T"

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The quotient when 48a³bc²is divided by 3abc will be 16a²c.

The information given is that we should find the quotient of 48a³bc² ÷ 3abc.

This can be expressed as:

48a³bc² ÷ 3abc = (3 × 16 × a³ × b × c²) / (3 × a × b × c)

= 16a²c

In this case, the quotient when 48a³bc²is divided by 3abc will be 16a²c.

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5 blue, 4 red = 9 total

Probability (Blue, Blue)  = 5/9 x 5/9 = 25/81 = 0.30864

Probability (Red, Red) = 4/9 x 4/9 = 16/81 = 0.19753

Probability (Blue,Blue) or (Red,Red) = 25/81 + 16/81 = 41/81 = 0.506173

Fraction answer = 41/81

Decimal answer = 0.506173 (round off as needed)

Answer:

8/27

Step-by-step explanation:

So an exponent is basiclly when you multiply the number as many times as the exponent says. In this case it saying 3 so you would do 2/3*2/3*2/3 and then you would get 8/27. I hope this helps.

Answer:

16

Step-by-step explanation:

The range is the distance between the largest number and the smallest number. To find the range, you take the smallest number and subtract it from the largest number. In this case, the smallest number is -9 and the largest number is 7. 7 minus -9 is a double negative, so you can also do 7+9=16. 16 is the range.

34.............................. ........

Answer:

(X+3)(x-10)

(X+3)(X+2)

Answer:

(x+8)(4x-9)

Step-by-step explanation:

Rewrite expression 4x^2 + 32x - 9x - 72

Factor out 4x  4x(x+8) - 9x - 72

Factor out x+8  4x(x+8) - 9(x+8)

Simplify (x+8)(4x-9)

Answer:

b = 1/3

Step-by-step explanation:

The general structure of equations in slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept.

The given equation is already in slope-intercept form. In other words, you have already been given "m" and "b". Therefore, the value which corresponds with the y-intercept is (1/3).

f(x) = mx + b

f(x) = -(2/9)x + 1/3

Answer:

almost 567 students

Step-by-step explanation:

all fruits = 23+18+34+27+18 = 120

possibility of selecting an orange as favourite fruits by one student = 34/120 = 17/60

possibility of selecting an orange as favourite fruits by 2000 students = 17/60×2000 =1700/3 = 566.6666...=567 students

Answer:

1593 pandas 13 years ago.

Difference? ≈271 pandas

Keyword:

"Increase"

Step-by-step explanation:

Use the equation:

x + (x × P%) = y

x(1 + P%) = y

x = 1864/(1 + 17%)

x = 1864/(1 + 0.17(17%))

x = 1864/1.17

x = 1593.1624 ≈ 1593

The number of doctors that would be needed for the 35-bed wing is 38.

The first step is to determine the number of doctors needed for one bed : 463 / 423

The second step is to multiply the ratio gotten in the first step by the number of beds in the new wing: (463 / 423) x 35 = 38.21 = 38

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Answer:12-16=-4

Step-by-step explanation:the answer is the same way it’s just flipped