The population of a city is modeled by the equation P(t)=232012e0.23t where t is measure in years. If the city continues to grow at this rate, approximately how many years will it take for the population to reach one million? Round your answer to two decimal places

Answer:

shown in explanation

Step-by-step explanation:

a) ∆EPB similar to ∆ERG

b) angle BEP = angle GER (common angle shared)

angle EPB = angle ERG (corresponding angles, PB//RG, parallelogram)

therefore through Angle-Angle similarity test, ∆EPB is similar to ∆ERG

or explanation can also be shortened to

∆EPB is similar to ∆ERG (AA, similarity)

c) since proven they are similar ∆, then we can proceed to use property of ratio of corresponding sides being equal

[tex] \frac{pb}{rg} = \frac{ep}{er} [/tex]

RG = 200+300=500m

[tex] \frac{200}{500} = \frac{ep}{ep + 350} [/tex]

cross multiply (from what I've learnt)

2ep+700=5ep

ep= 700/3 = 233 ⅓m (answer for length EP)

Do the same for length BE(using ratio of corresponding sides)

[tex] \frac{be}{ge} = \frac{pb}{rg} [/tex]

[tex] \frac{be}{be + 400} = \frac{200}{500} [/tex]

cross multiply again to get:

5BE = 2BE + 800

BE = 800/3 = 266 ⅔ m (answer for length BE)

Answer: 1/3

Step-by-step explanation:

-1/9 / -1/3 = ?

Keep: -1/9

Change: *

Flip: -3/1

Solve: -1/9 * -3/1 = 3/9

Simplify: 1/3

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Equation:}[/tex]

[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]

[tex]\huge\textbf{Simplify it:}[/tex]

[tex]\mathsf{-\dfrac{1}{9}\div - \dfrac{1}{3}}[/tex]

[tex]\huge\textsf{Convert:}[/tex]

[tex]\mathsf{= -\dfrac{1}{9} \times -\dfrac{3}{1}}[/tex]

[tex]\huge\textsf{Multiply:}[/tex]

[tex]\mathsf{= \dfrac{-1\times3}{9\times -1}}[/tex]

[tex]\mathsf{= \dfrac{-3}{-9}}[/tex]

[tex]\mathsf{= \dfrac{-3 \div -3}{-9\div-3}}[/tex]

[tex]\mathsf{= \dfrac{1}{3}}[/tex]

[tex]\huge\textbf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\dfrac{1}{3}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

18

Step-by-step explanation:

When dilating a segment by a scale factor, we multiply the original length by the scale factor to find the length.

2*9 = 18

The value of x such that the vertices 3x + 10 and x + 60 are equal is 25

Vertices are the endpoints or corners of a shape (such as triangle, square, rectangle and related shapes)

The two vertices are given as:

3x + 10 and x + 60

The condition on the two vertices are not given.

So, we assume that the vertices are equal (as in the base angles of an isosceles triangle)

So, we have the following equation

3x + 10 = x + 60

Subtract x from both sides of the equation

2x + 10 = 60

Subtract 10 from both sides of the equation

2x = 50

Divide both sides of the equation by 2

x = 50/2

Evaluate the quotient

x = 25

Hence, the value of x such that the vertices 3x + 10 and x + 60 are equal is 25

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Answer: draw the line using a ruler on which you have identified points 2 7/16 inches apart.  

Step-by-step explanation:    On your ruler graduated in inches with marks at 1/16-inch intervals, locate the 0 mark and the mark 1/16 inch before the half-inch mark between 2 and 3 inches.Draw your line along the edge of the ruler between the two marks you have identified: 0 and 2 7/16. The line will be 2 7/16 inches long.

If the parent function is transformed by:

The graph of the parent function is a parabolic curve which opens in the y-axis direction and with its vertex at the origin on a cartesian coordinate.  

By critically observing the graph of this parent function [f(x) = x²], we can infer and logically deduce that the transformed curve is a downward opening parabola which has a vertex at (-5, -2).

Thus, if the parent function is transformed by:

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The test statistic based on the probability illustrated is -2.57.

The basic training is given as 103 hours. The variance is also given as 9.

The test statistic will be:

= (102 - 104/3/✓60)

= -1/(3/7.7)

= -2.57.

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Answer:

1. 60%

2. He paid Rs. 1285.71

Step-by-step explanation:

1.

He buys an item for x.

He sells the item with a 25% of the marked price, and he still makes a 20% profit over his cost x.

He must sell for x + 20% of x which is the same as 1.2x.

Let the markup be y%.

Since he gives a 25% discount over the marked price, he sells for 75% of the marked price.

0.75(x + y% of x) = 1.2x

0.75(x + xy/100) = 1.2x

x + xy/100 = 1.6x

Divide both sides by x.

1 + y/100 = 1.6

Multiply both sides by 100.

100 + y = 160

y = 60

Remember that y is in percent, so the markup must be 60%.

Check:

He buys an item for $10.

He applies a markup of 60%. 1.6 × $10 = $16.

He has a price of $16 for this item.

Now he gives a 25% discount. That means the discounted price is 75% of the marked price.

75% of $16 = $12

He sells at a 25% discount for $12.

Compare the actual selling price after the 25% discount with this cost.

$12 compared to $10.

$12/$10 = 1.2 = 120%

Since he sells for 120% of the original price, the markup is 20% which is what he wanted.

2.

The cost to the seller is x.

If he sells it at a 20% profit, then he sells it for 1.2x

Now he gives a discount of 5%, so the final selling price after discount is

0.95(1.2x)

The profit is the difference between what he sold it for, 0.95(1.2x), and what he bought is for, x, and it is Rs. 180.

0.95(1.2x) - x = 180

1.14x - x = 180

0.14x = 180

x = 1285.71

Answer: He paid Rs. 1285.71

Answer:

8

Step-by-step explanation:

The cos of 30 is [tex]\sqrt{x}[/tex] / 2.  Since the adjacent angle is 4 times that.  We would multiply 2 x 4 and get 8

Answer:

Graphs A and B

Step-by-step explanation:

Graphs A & B are using x-values 1-6 and stop there, which is what the domain is trying to find. Though, for the other graphs, these graphs are rather starting at 1 via the domain, while not going up to 6 on the domain.

The probability that a three shows on at least one of the dice is 11/36.

It should be noted that of probability means the likelihood of the occurence of an event.

The probability that a three shows on at least one of the dice will be:

= 11/36

This can be seen from the table that is attached.

The probability that the total is less than 8 will be:

= 21/36

= 7/12

Here, there are 21 places where the total is less than 8.

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The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.

Generally, the equation for the probability is mathematically given as

[tex]P( X < x) = p( Z < x - \mu / \sigma)[/tex]

Therefore

[tex]P( X > x) = 0.021[/tex]

[tex]P( X < x ) = 1 - 0.021\\\\\p( X < x) = 0.979[/tex]

[tex]P( Z < x - \mu / \sigma) = 0.979[/tex]

The z score for the probability of 0.979 is 2.034, according to the table of z values.

[tex]x - \mu / \sigma \\\\x= 2.034[/tex]

In the given equation, replace the values of mu and sigma with their respective values, and then solve for x.

[tex]x - 35.5 / 2.5 \\x= 2.034[/tex]

In conclusion, The average annual rainfall will be more than 40.6 inches in about 2.1 percent of the years.

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Answer:

x = 12

Step-by-step explanation:

6x - 4 and 112 are same- side interior angles and sum to 180° , that is

6x - 4 + 112 = 180

6x + 108 = 180 ( subtract 108 from both sides )

6x = 72 ( divide both sides by 6 )

x = 12

Answer:

x = 12

Step-by-step explanation:

Consecutive Interior Angles Theorem

When a straight line intersects two parallel straight lines, the consecutive interior angles formed are are supplementary (sum to 180°).

Therefore:

⇒ 6x - 4 + 112 = 180

⇒ 6x + 108 = 180

⇒ 6x + 108 - 108 = 180 - 108

⇒ 6x = 72

⇒ 6x ÷ 6 = 72 ÷ 6

⇒ x = 12

volume = (1/3) * π * r² * h

= 1/3* 22/7 * (3.5*3.5) * 5 ( 22/7 is the value of π)

=64.1

Answer:

If you need a pi in your answer: 20.417 [tex]\pi[/tex] (rounded to the nearest thousanth)

If you don't: 64.141 (rounded to the nearest thousanth)

Step-by-step explanation:

The formula of the volume of a cone: [tex]V = \pi r^2\frac{h}{3}[/tex]

--> V = Volume, r = Radius, h = Height

In other words, the volume of the cone is the area of the circle x height x 1/3 x pi.

Since the radius of the cone is 3.5, you square that number.

--> (3.5)^2 = 12.25

The height is 5, so h/3 will be 5/3.

The volume = [tex]\pi[/tex] x 12.25 x 5/3

--> 20.416666... [tex]\pi[/tex]

--> 64.14085....

Step-by-step explanation:

(f+g)(x)=4x-1+2x²+3===> 2x²+4x+2

Using it's concept, the probability that the teenager picked at random is male and their favorite hobby is playing video games is:

[tex]\frac{1}{16}[/tex].

A probability is given by the number of desired outcomes divided by the number of total outcomes.

Researching this problem on the internet, it is found that out of 32 teenagers, 2 are males who prefer playing videogames, hence the probability is:

[tex]p = \frac{2}{32} = \frac{1}{16}[/tex]

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The support pole must be approximately 7.8 meters long.

Based on all the information given in the statement, we prepare a geometric diagram that describes the system formed by the high-security fence and the support pole. The representation is attached below. Lastly, the length of the pole is found by using the law of sines:

l/sin 84° = 6 m /sin 50°

l = 6 m × (sin 84°/sin 50°)

l ≈ 7.790 m

The support pole must be approximately 7.8 meters long.

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the point-slope form is:

y + 5 = -(9/11)*(x - 3)

A line that passes through a point (x₁, y₁) and has a slope m, can be written in point-slope form as:

y - y₁ = m*(x - x₁)

Here we know that the line passes through (3, -5) and (-8, 4).

Then the slope is:

[tex]m = \frac{-5 - 4}{3 - (-8)} = \frac{-9}{11}[/tex]

And we can use (3, -5) as the point (x₁, y₁), then the point-slope form is:

y + 5 = -(9/11)*(x - 3)

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The correct order of reasons that complete the proof about the rectangle and square is that D. definition of congruence, distance formula if two consecutive sides of a rectangle are congruent, then it's a square.

It should be noted that congruence simply means an agreement or a correspondence between shapes.

In geoemtry, it should be noted that figures are said to be congruent if it is possible to superpose one of them on another.

It should be noted that the opposite sides of a rectangle are parallel while in a square, all the sides that are given are equal.

Therefore, the correct order of reasons that complete the proof about the rectangle and square is the definition of congruence, and that if two consecutive sides of a rectangle are congruent, then it's a square.

In conclusion, the correct option is D.

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We know that this ratio is directly because the two magnitudes go up.

In this case we will get the proportionality constant by dividing any term of the second magnitude by the first.

[tex]9 \: \div \: 3 \: = \: \boxed{3}[/tex]

Now that we know that k = 3, we can know how much "y" will be if x = 5.

We just multiply:

[tex]3 \: \times \: 5 \: = \: \boxed{ \bold{ 15}}[/tex]

The probability that the nest set of cars that would enter the lot is a sedan is given as 80 percent

The total number of trials can be seen to be 20 in number. The numbers that represents the sedan are 0, 1, 2

Now we would have to count the number of trials in these 20 that have 0, 1, 2

In the table we have 16 of these 0, 1 or 2 numbers

Hence we would have

16 /20

= 0.8

= 80 percent

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[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{4}{10}\times x\right)-(2 \times x)+\frac{8}{5}=\frac{4}{5} \end{gathered}$}[/tex]

Reduce the fraction 4/10, to its minimum expression, extracting and canceling 2.

Combine [tex]\bf{\frac{2}{5}x }[/tex] and -2x to get [tex]\bf{-\frac{8}{5}x}[/tex].

Subtract 8/5 from both sides.

Since 4/5 and 5/8 have the same denominator, join their numerators to subtract them.

Subtract 8 from 4 to get -4.

Multiply both sides by [tex]\bf{-\frac{5}{8}}[/tex], the reciprocal of [tex]\bf{-\frac{5}{8}}[/tex].

Multiply -4/5 by -5/8 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

Reduce the fraction 20/40 to its lowest expression by extracting and canceling 20.

The simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2

Since the carpenter built a square table with side length x.  Next, he will build a rectangular table by tripling one side and halving the other.

To find the area of the rectangular table, we know that Area, A = LW where

Now, since the length of the square is x, and the rectangular table has one side of the square tripled and halving the other side .

So,

let

So, the area of the rectangular table A = LW

= x/2 × 3x

= 3x²/2

So, the simplified expression for the area of the rectangular table is Three-halves x squared, 3x²/2

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Factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)

For us to determine if a set of inequality  function has a solution, we will equate the functions and determine the point of intersection if there are any,

Given the inequalities

y ≤ x^2 - 3

y > -x^2 + 2

Equate

x^2 - x = -x^2 + 2

Collect like terms

2x^2 - x - 2 = 0

In order to determine the value of x, we will factorize and get the value of x and then substitute into any of the equation to get the solution in coordinate form (x, y)

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You don't shade a region when graphing just a line, but you do when graphing an inequality.

It should be noted that a graph is a diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.

It should be noted that an inequality is a relation that makes a non-equal comparison between two numbers or other mathematical expressions.

This is used most often to compare the two numbers on the number line by their size.

On the other hand, the graphing inequalities shows what part of the number line contains values that will be able to satisfy the given inequality.

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Answer:

The ANSWER is 1/2 x (3/5) : (9/15) (-6/4) : (4/1) = -3/16 = -0.1875

Step-by-step explanation:

Multiple: 1/2 * 3/5 = 1 · 3/2 · 5 = 3/10

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(3, 10) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half multiplied by three fifths is three tenths.

Divide: the result of step No. 1 : 9/15 = 3/10 : 9/15 = 3/10 · 15/9 = 3 · 15/10 · 9 = 45/90 = 45 · 1/45 · 2 = 1/2

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 9/

15 is 15/9) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 45 gives 1/2.

In other words - three tenths divided by nine fifteenths is one half.

the result of step No. 2 * (-6/4) = 1/2* (-6/4) = 1 · (-6)/2 · 4 = -6/8 = -3 · 2/4 · 2= -3/4

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-6, 8) = 2. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - one half multiplied by minus six quarters is minus three quarters.

Divide: the result of step No. 3 : 4 = -3/

4 : 4 = -3/4 · 1/4 = -3 · 1/4 · 4 = -3/16

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 4/

1 is 1/4) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - minus three quarters divided by four is minus three sixteenths.

The value of the given expression is 11.57

Division are written as a ratio of two values. Given the expression below

5+6+6+2^6 ÷ 7

Simplify to have:

(11+6+64)÷ 7

Simplify the expression in parenthesis

81÷ 7

11.57

Hence the value of the given expression is 11.57

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Answer: 5020

Step-by-step explanation:

10^3= 1000

1000*5.02=5020

= 4×8 +2×3 -1+9

___________

20

= 8+6-9

_______

20

= 14 - 9

_______

20

= 5

____

20