In 2012, the population of a city was 5.57 million. The exponential growth rate was 3.69% per year.
A) find the exponential growth function.
B) Estimate the population of the city in 2018.
C) When will the population of the city be 8 million?
D) Find the doubling time.

Answer:

The solution of the equation is 15

Step-by-step explanation:

* Lets explain how to solve the problem

- The equation is 3(2x + 5) = 3x + 4x

- The solution of the equation is the value of x

Lets find the value of x

- The left hand side is 3(2x + 5) lets simplify it

- Multiply the two terms of the bracket by 3

∵ 3(2x+ 5) = 3 × 2x + 3 × 5

∴ 3(2x + 5) = 6x + 15

- The right hand side is 3x + 4x

∵ They are like terms, then we will add them

∴ 3x + 4x = 7x

- Now equate the left hand side and the right hand side

∴ 6x + 15 = 7x

- Subtract 6x from the two sides

∴ 15 = 7x - 6x

∴ x = 15

∵ x is the solution of the equation

∴ The solution of the equation is 15

ANSWER

C. $ 7.00

EXPLANATION

It was given that four students had the following amounts of money in their pockets: $3.14, $.67, $2.45, and $1.14.

To find the amount of money they have in total, we add all their monies together to get:

$3.14+$0.67+$2.45+$1.14

This will give us a total of $7.00

Answer:

7.40

Step-by-step explanation:

to get the total money for the four student you have to do addition.

3.14

2.45

1.14

+0.65 to get $7.40

Answer:

[tex]y=8\cdot \left(\dfrac{1}{2}\right)^x.[/tex]

Step-by-step explanation:

If the graph of exponential function passes through the points (0,8) and (6,0.125), then the coordinates of these points sutisfy the equation [tex]y=a\cdot b^x:\\[/tex]

[tex]8=a\cdot b^0\Rightarrow a=8,\\ \\0.125=8\cdot b^6\Rightarrow \dfrac{1}{8}=8\cdot b^6,\\ \\b^6=\dfrac{1}{64},\\ \\b^6=\dfrac{1}{2^6}\Rightarrow b=\dfrac{1}{2}.[/tex]

Thus, the equation of exponential function is

[tex]y=8\cdot \left(\dfrac{1}{2}\right)^x.[/tex]

Answer:

[tex]\large\boxed{\dfrac{10}{5!\times2!}=\dfrac{1}{24}}[/tex]

Step-by-step explanation:

[tex]n!=1\cdot2\cdot3\cdot...\cdot n\\\\5!=1\cdot2\cdot3\cdot4\cdot5=120\\2!=1\cdot2=2\\\\\dfrac{10}{5!\times2!}=\dfrac{10}{120\cdot2}=\dfrac{1}{24}[/tex]

Answer:

20 4/5

Step-by-step explanation

13/5 x 8/1 = 104/5= 20 4/5

The product of [tex]\(1 \frac{3}{5}\)[/tex] and [tex]\(8\)[/tex] is calculated by first converting the mixed number to an improper fraction and then multiplying the two fractions together.

Step 1: Convert [tex]\(1 \frac{3}{5}\)[/tex] to an improper fraction.

To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fractional part and add the numerator of the fractional part. Then, place the result over the original denominator.

For [tex]\(1 \frac{3}{5}\)[/tex] , the whole number is [tex]\(1\)[/tex], and the fractional part is [tex]\(\frac{3}{5}\)[/tex]. So, we have:

[tex]\[ 1 \times 5 + 3 = 5 + 3 = 8 \][/tex]

Thus, [tex]\(1 \frac{3}{5}\)[/tex]  as an improper fraction is [tex]\(\frac{8}{5}\)[/tex].

Step 2: Multiply the improper fraction by \(8\).

Now, we multiply [tex]\(\frac{8}{5}\)[/tex] by [tex]\(8\)[/tex] . When multiplying fractions, we multiply the numerators together and the denominators together:

[tex]\[ \frac{8}{5} \times 8 = \frac{8 \times 8}{5} \][/tex]

Step 3: Simplify the product.

[tex]\[ \frac{8 \times 8}{5} = \frac{64}{5} \][/tex]

So, the product of [tex]\(1 \frac{3}{5}\)[/tex]  and [tex]\(8\)[/tex] is [tex]\(\frac{64}{5}\)[/tex].

To express this as a mixed number, we divide [tex]\(64\)[/tex] by [tex]\(5\):[/tex]

[tex]\[ 64 \div 5 = 12 \text{ remainder } 4 \][/tex]

Thus, [tex]\(\frac{64}{5}\)[/tex]  as a mixed number is [tex]\(12 \frac{4}{5}\)[/tex].

The final answer is[tex]\(12 \frac{4}{5}\) or \(\frac{64}{5}\).[/tex]

Answer:

[tex]\large\boxed{a.\ 7200\pi\ mm^2}[/tex]

Step-by-step explanation:

The formula of a surface area of a cylinder:

[tex]S.A.=2\pi r(r+H)[/tex]

r - radius

H - height

We have r = 40mm and H = 50mm. Substitute:

[tex]S.A.=2\pi(40)(40+50)=80\pi(90)=7200\pi\ mm^2[/tex]

Answer:

[tex]S_a = (13mm)^2 \cdot 6 = 1014 mm^2[/tex]

Step-by-step explanation:

For this case we must find the value of "x" of the following equation:

[tex]x ^ 2-9 = 0[/tex]

So:

We add 9 to both sides of the equation:

[tex]x ^ 2-9 + 9 = 9\\x ^ 2 = 9[/tex]

We apply square root on both sides of the equation to eliminate the exponent on the left side:

[tex]x = \pm \sqrt {9}[/tex]

Thus, the solutions are:

[tex]x_ {1} = + 3\\x_ {2} = - 3[/tex]

ANswer:

[tex]x_ {1} = + 3\\x_ {2} = - 3[/tex]

Opcion C

Answer:

6=1/2z

6÷1/2=1/2÷1/2z

6÷1/2=z

6×2/1 = z

z=12

Answer:

[tex]2sin(x)*cos(x)*sec(x)*csc (x)=2[/tex]

Step-by-step explanation:

Remember the identities:

[tex]sec(x)=\frac{1}{cos(x)}\\\\csc(x)=\frac{1}{sin(x)}[/tex]

Ginven the expression:

[tex]2sin(x)*cos(x)*sec(x)*csc (x)[/tex]

You need to substitute [tex]sec(x)=\frac{1}{cos(x)}[/tex] and [tex]csc(x)=\frac{1}{sin(x)}[/tex] into it:

[tex]2sin(x)*cos(x)*sec(x)*csc (x)=2sin(x)*cos(x)*\frac{1}{cos(x)}*\frac{1}{sin(x)}[/tex]

Now, you need to simplify.

Remember that:

[tex]\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}[/tex]

And:

[tex]\frac{a}{a}=1[/tex]

Then, you get:

[tex]=\frac{2sin(x)*cos(x)}{cos(x)*sin(x)}}=2[/tex]

Answer:

10 feet

Step-by-step explanation:

Area of rectangle

A = L * W

W = A/L

W = 80 / 8

W = 10

Answer

10 feet

The Area of the rectangle is the product of length and width. The width of the rectangle is 10 ft.

For a rectangle with length and width L and W units, we get:

Area of the rectangle = (L × W) unit^2

Perimeter of the rectangle = 2(L + W) units

Given the area of the rectangle is 80 ft², while the length of the rectangle is 8 feet. Therefore, the width of the rectangle will be,

Area of the rectangle = Length × width

80 ft² = 8 ft × width

width = 10 ft

Hence, the width of the rectangle is 10 ft.

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Answer:

(B) 3.6

Step-by-step explanation:

Coordinate of A = (-3, 9)

Coordinate of B = (-1, 6)

[tex]\text {Distance = }\sqrt{(- 3 - (-1) )^2 + (9 - 6)^2}[/tex]

[tex]\text {Distance = }\sqrt{(- 2 )^2 + (3)^2}[/tex]

[tex]\text {Distance = }\sqrt{13}[/tex]

[tex]\text {Distance = }3.6[/tex]

Answer:

B

Step-by-step explanation:

Calculate the distance using the distance formula

d = √ (x₂ - x₁ )² + (y₂ - y₁ )²

with (x₁, y₁ ) = A(- 3,9) and (x₂, y₂ ) = B(- 1, 6)

d = [tex]\sqrt{-1+3)^2+(6-9)^2}[/tex]

  = [tex]\sqrt{2^2+(-3)^2}[/tex]

  = [tex]\sqrt{4+9}[/tex]

= [tex]\sqrt{13}[/tex] ≈ 3.6 → B

Answer:

(- 3, 6)

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y) → (- x, y), hence

(3, 6) → (- 3, 6)

The image of the point (3, 6) reflected across the y-axis is (-3, 6) since only the x-coordinate changes sign.

Reflection of a point across the y-axis in a Cartesian coordinate system involves changing the sign of the x-coordinate of the point while keeping the y-coordinate the same. For point (3, 6), when it is reflected across the y-axis, the x-coordinate becomes the opposite sign, while the y-coordinate remains unchanged. Therefore, the image of the point (3, 6) after reflection across the y-axis is at (-3, 6). This transformation elucidates the geometric effect of y-axis reflection, showcasing how points are mirrored across the axis while maintaining their vertical position, essential in geometry, graphics, and spatial reasoning for analyzing symmetrical patterns and transformations.

Answer:

y = -1-x

Step-by-step explanation:

Answer:

h=3

Step-by-step explanation:

The given function is

[tex]g(x)=x^2-6x+14[/tex]

We add and subtract the square of half the coefficient of x to obtain;

[tex]g(x)=x^2-6x+(-3)^2-(-3)^2+14[/tex]

Identify the first three terms as a perfect square trinomial;

[tex]g(x)=(x-3)^2-9+14[/tex]

Simplify;

[tex]g(x)=(x-3)^2+5[/tex]

Comparing this to

[tex]g(x)=a(x-h)^2+k[/tex]

We have h=3 and k=5

Answer: h=3

the other answer on this page is right

Step-by-step explanation:

5•(9/15)+7= 9/3 +21/3= 30/3=10

Answer:

The volume of the ornament is [tex]6\frac{2}{3}\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the ornament is equal to the sum of  the volume of the two congruent square pyramids

so

[tex]V=2[\frac{1}{3}b^{2} h][/tex]

we have

[tex]b=2\ in[/tex]

[tex]h=2.5\ in[/tex]

substitute

[tex]V=2[\frac{1}{3}(2)^{2} (2.5)][/tex]

[tex]V=\frac{20}{3}\ in^{3}[/tex]

Convert to mixed number

[tex]\frac{20}{3}=\frac{18}{3}+\frac{2}{3}=6\frac{2}{3}\ in^{3}[/tex]

Answer:

C

Step-by-step explanation:

X axis is the answer to you question because it’s going across not up nor down

The answer is A. The x-axis

Answer:

C.  2,160π

Step-by-step explanation:

took test

The linear velocity at the end of the blade is 13571.7 inches per minute by using the circumference of the circle that the blade makes to calculate the linear velocity at the end of the blade.

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Here, The total distance in 1 minute is 60 times circumference of the circle made by the end of the blade of the lawnmower.

Since, The blade is 36 inches long, it can be taken as radius of that circle.

The circumference is thus calculated as;

⇒ linear velocity = 226.19 × 60

                           = 13571.7 inches per minute

Thus, The linear velocity at the end of the blade is 13571.7 inches per minute.

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Answer:

A

Step-by-step explanation:

To convert degrees to radians

radian measure = degree measure × [tex]\frac{\pi }{180}[/tex]

Hence

radian measure = 150° × [tex]\frac{\pi }{180}[/tex]

Cancel both 150 and 180 by 30, then

radian measure = 5 × [tex]\frac{\pi }{6}[/tex] = [tex]\frac{5\pi }{6}[/tex]

Final answer:

To convert 150 degrees to radians, multiply 150 by π/180 to get 5/6 * π or approximately 2.61799 radians.

Explanation:

To convert 150 degrees to radians, we use the fact that one complete revolution is 360 degrees which is equal to 2π radians (approximately 6.28318 radians). From this, we can derive that 1 degree is equal to π/180 radians. We multiply the value in degrees by π/180 to get the equivalent in radians.

150 degrees * π/180 radians/degree = 150/180 * π radians = 5/6 * π radians.

Therefore, 150 degrees is equal to 5/6 times π or approximately 2.61799 radians.

Answer:

84ft^2

Step-by-step explanation:

Relying on formula S(area) =a(base) *h(height )

Answer:

84ft2

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The set of equations that best represent the given information is B. a + b = 12, a = b + 8. This represents both conditions: the sum of the two numbers is 12 and a is 8 more than b.

The best representation of the given information is provided by option B. a + b = 12, a = b + 8. This is because it accurately portrays both conditions mentioned in the question. The first part of the equation, a + b = 12, represents the information that the sum of the two numbers a and b is 12. The second part of the equation, a = b + 8, represents the information that the first number, a, is 8 more than the second number, b.

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Answer:

option d

13 , 173 , 29933

Step-by-step explanation:

Given in the question a function, f(x) = x² + 4

initial value x0 = -3

First iteration

f(x0) = f(-3) = (-3)² + 4 = 13

x1 = 13

Second iteration

f(x1) = f(13) = (13)² + 4 = 173

x2 = 173

Third iteration

f(x2) = f(173) = (173)² + 4 = 29933

x3 = 29933

Answer:

1. (-2,0)

2. (0,2)

I'm confirming the answer above. These are also the answers on Edge-nuity. I use Edge-nuity

Step-by-step explanation:

A local maximum occurs over the interval  (-2,0)  

A local minimum occurs over the interval  (0,2)

We may calculate the maximum of a continuous and twice differentiable function f(x) by first differentiating it with respect to x and then equating it to 0.

A local maximum occurs over the interval (-2,0)  

A local minimum occurs over the interval  (0,2)

Hence, local maximum and local minimum occurs at  (-2,0)  and (0,2).

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I believe that the answer is A 137-186,

that is the answer if you use  the Karvonen formula

Karvonen formula : target training HR = resting HR + (0.6 [maximum HR -resting HR]).

1. Resting Heart Rate (RHR) = your pulse at rest

2. Maximum Heart Rate (MHR) = 220- your age

3. Heart Rate Reserve (HRR)= Maximum Heart Rate - Resting Heart Rate  

sorry idk why my answer was deleted

Answer: That would be A mate 137-186

Step-by-step explanation:

t = p(x)

The reason I put the x in the parentheses is because I’m not sure what the variable is supposed to be. But x stands for how many kilograms she buys, so you can out in the correct variable later.

Hope this helps!

If it does I would appreciate it if you could make me brainliest.

Answer:

t = pk

Step-by-step explanation:

Let

k = kilograms

You need another variable than just t and p.

p needs to be multiplied by another variable that represents kilograms. I used

k because kilograms starts with k.

Hey, so sorry for answer so late! I wasn't on here for a while, and I didn't get your message until I logged back in.

1.) C. 8, because if you add 3 and 5, you get 8, which is your answer.

2.) D. 9, because 9/2 equals 4.5

3.) A. 0, because if you start off with zero and add 6, you will get 6.

4.) D. y = x - 5, because when you subtract 5 from 42.50, you get 37.50, which is our desired result.

Hope this helps ya, and again, sorry about the inconvenience of answering so late. Feel free to ask more questions by messaging me on this question. Have a good day :D

If the output of the function is 5, then the input is

1. 8. ( optionC)

2. 9 ( Option D)

3. 0( option A)

4. The equation for the situation is y = x -5 ( option D).

It expresses a unique output for each input, exemplified by f(x) in algebraic terms.

In the equation;

y = x -3

the output is y

therefore;

5 = x -3

x = 5+3 = 8

Therefore the input value is 8.

2. The input value will be

x = y × 2

x = 4.5 ×2 = 9

3. The input value will be

x = 6 - 6

= 0

4. let y be the cost after the coupon and x is before the coupon

y = x - 5

Answer:

The measure of  angle x is 90°

Step-by-step explanation:

Given the figure in which

∠1=88°, ∠6=89°

we have to find the value of x.

∠5=∠6=89°   (∵ Vertically opposite angles)

∠1+∠4=∠6  ( ∵ By exterior angle property)

88°+∠4=89°

∠4=89°-88°=1°

As AC=CB (both are radii of same circle)

∴ ∠4=∠3=1°

Now, by exterior angle property

x=∠5+∠3=89°+1°=90°

Hence, the measure of  angle x is 90°

Applying the angle of intersecting chords theorem, the value of x in the diagram showing the circle is: C. 90.

According to the angle of intersecting chords theorem, the measure of the angle formed at the point of intersection of two chords inside a circle equals half the sum of the intercepted arcs.

89 = 1/2(88 + x) [based on the angle of intersecting chords theorem]

2(89) = 88 + x

178 = 88 + x

178 - 88 = x

x = 90° (Option C).

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Final answer:

The initial velocity at which she threw the cap is 20 m/s.

Explanation:

Since the cap comes back to her hand at the same height, the initial vertical velocity of the cap is 0 m/s. The acceleration due to gravity is -10 m/s². Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time, we can solve for the initial velocity. In this case, v = 0 m/s, a = -10 m/s², and t = 2.0 s. Plugging in these values, we get:

0 = u + (-10)(2.0)

0 = u - 20

u = 20 m/s

So the initial velocity at which she threw the cap is 20 m/s.

Answer:

0.65454545454 or -30/46 or 65.454545454%

Hope This Helps!   Have A Nice Day!!

Answer:

-36/55

Step-by-step explanation: