with a linear, exponential, or quadratic function.
You have to decide which of two prizes you will accept!
Prize A: $5,000 for the first month with a $100 increase every month thereafter.
Prize B: $2,000 for the first month with a 10% increase every month thereafter.
9. Create an equation for each situation (Prize A and Prize B).

Answer:

speed equals distance over time.

To and fro, distance=speed×time(ts)

distance=900×18=16,200km.

therefore, ts=16,200

since, speed = distance/time

therefore, time taken is inversely proportional to speed making D the best option.

the volume of the hexagonal prism is 184. 75 cm^3

It is important to note that the volume of a hexagonal prism is given as;

V = (2/√3) × ap2 × h

Where

From the information given, we have the values of the following parameters;

height = 10cm

apothem = 4cm

base edge = 6cm

Now, let's  substitute the value of the parameters

Volume = (2/√3) × ap^2 × h

Volume = 2/√3 × 4^2 × 10

Multiply through

Volume = 1. 1547 × 16 × 10

Volume = 184. 75 cm^3

Thus, the volume of the hexagonal prism is 184. 75 cm^3

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58 min/day  rate did she practice in minutes per day.

What is  time?

1 day = 2030 min ÷ (5 weeks × 7 days)

1 day = 2030 ÷ 35

1 day = 58 minutes

rate = 58 min/day

Therefore, 58 min/day  rate did she practice in minutes per day.

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Answer:

heat map is the answer

Answer:

Step-by-step explanation:

Congruent parts of congruent triangles are congruent, so we can easily demonstrate BD ≅ DF ≅ BF.

AB ≅ BC ≅ CD≅ DE≅ EF ≅ FA . . . . definition of regular hexagon

∠A ≅ ∠C ≅ ∠E . . . . definition of regular hexagon

ΔFAB ≅ ΔBCD ≅ ΔDEF . . . . SAS congruence

FB ≅ BD ≅ DF . . . . CPCTC

ΔBDF is equilateral . . . . definition of equilateral triangle

Answer:

Area of park = 2976 ft²

Length of park = 62 ft

Width of park = ?

Area of park = length ×width

2976 = 62 × width

width = 2976/62

=48 ft

Answer: 420 minutes in 7 hours. 2 minutes in 120 seconds.

Step-by-step explanation: Multiply 7x60, as there are 60 minutes per hour. Divide 120/60 to find how many minutes are within those many seconds.

Answer:

X = 2

Y = 1

Step-by-step explanation:

Solve by substitution

[tex]y = x - 4 \\ 2x + y = 5 \\ \\ y = x - 4 \\ 2x - 5 = - y \\ \\ y = x - 4 \\ - y = 2x - 5 \\ \\ add \: the \: two \: equations \\ \\ 0 = 3x - 9 \\ 9 = 3x \\ \frac{9}{3} = \frac{3x}{x} \\ x =3 \\ \\ substitute \: 3 \: for \: x \: in \: one \: of \: the \: equations \: to \: find \: y \\ \\ y = x - 4 \\ y = 3 - 4 \\ y = - 1 \\ \\ solution \: (3. - 1)[/tex]

Answer:

Step-by-step explanation:

here is an solution :

Answer:

Its (-3,-5)

Step-by-step explanation:

Hope This Helps:))

Answer:

Step-by-step explanation:

Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4

minus four x greater than 120

-4x > 120

x < 120/-4

There is a change in the inequality sign from greater than to less than because the inequality is been divided by -4

x < -30

Check:

-4x > 120

-4(-30) > 120

120 > 120

Therefore, Eduro's mistake of solving the inequality -4x > 120 is adding 4 to both sides instead of dividing both sides by -4

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The area is 97.211 sq units.

This part of the plane is a triangle. We can Call it δ. We can find the intercepts by setting two variables to 0 simultaneously; we'd find, for instance, that y=z=0 means 3x=15 i.e., x=3 , so that (3, 0, 0) is one vertex of the triangle. Similarly, we'd find that (0, 5, 0) and (0, 0, 15) are the other two vertices.

Next, we can parameterize the surface by

s(u,v)=[tex]\int\limits^a_b {3(1-u)(1-v),5u(1-v),15v} \, dx[/tex]

so surface element is

dS= IIsu*svII =15[tex]\sqrt{42}[/tex](1-v)dudv

Then the area of  is given by the surface integral

[tex]\int\limits^a_b {} \, \int\limits^a_b {dS} \, dx = 15\sqrt[n]{42} \int\limits^a_b {x} \, dx \int\limits^a_b {1-v} \, dudv[/tex]=97.211

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Answer: Third Graph

Step-by-step explanation:

Given inequality

|x| + 1 > 2

Subtract 1 on both sides

|x| + 1 - 1 > 2 - 1

|x| > 1

Simplify the absolute value sign

x > 1 or x < -1

Apply the inequality to the graph

Since it is less than or greater than, the circle should be hollow

Since it is less than -1 or greater than 1, one line should point to the left and another should point to the right

Therefore, it should be the Third Graph

Answer:

No real solutions.

Step-by-step explanation:

To solve this, we need to use Quadratic Formula.

Quadratic Formula:

[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ [/tex]

in the form of:

[tex]a {x}^{2} + bx + c[/tex]

Given information from the question, we can deduce:

a = -1

b = -2

c = 5

Let's substitute these values into the formula.

[tex]x = \frac{ - ( - 2) + - \sqrt{ {( - 2)}^{2} - 4( - 1)( -5)} }{2( - 1)} \\ = no \: real \: solutions[/tex]

if you punch these into the calculator.

The distributions of data can be characterized along three aspects or dimensions, namely location, spread, and shape. The spread (variance, range, interquartile range) aspects represent variation of the data or the spread of the data distributions.

About the Distribution of Data:

The idea of a distribution is fundamental to illustrating any output from a production process. Any manufacturing process output will not always produce the same value when it is measured, leading to distributions.

The measured values will naturally disperse around a central tendency value. A distribution is the name given to this dispersion around a core value. It is characterized by 3 aspects - location, spread, and shape.

Mean or median represent the location of the distribution numerically. Most common numerical measures that represent the spread are variance, range, and interquartile range. Skewness or kurtosis tell about the shape of the distribution.

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Answer:

B) 57 is the answer

Step-by-step explanation:

Let's try to make the given figure a parallelogram by extending DE and BA to F.

So now we have a complete parallelogram.

<AEF = 180 - 112 Since they are linear pairs

so, <AEF = 68

Now,

<EAF = 180 - 125 = 55

So, <AFE = 180-68-55 (interior angles of triangle sum up to 180)

<AFE = 57

Opposite angles of parallelogram are equal so,

<AFE = <BCD = 57°

Answer:

C. 4≤x≤6

Step-by-step explanation:

First things first, let’s learn the difference between domain and range. Domain is the spread of the x values and range is the spread of the y values. This means that in this question, you can rule out options A and B because those could potentially show range. Now we are left with options C and D. When we look at the first x coordinate, we see that it’s a 4. The last x coordinate is a 6. This means that the domain is greater than or equal to 4, but less than or equal to 6. You can also represent it as 4≤x≤6.

Hope that helps! Have a fantastic day!

Answer: 40 inches

Step-by-step explanation: If the 20 points on the line were spaced 1 inch apart, the result would be 20 inches. Each point you're going to is 1 inch in spacing and there is only going to be 20 inches of spacing (1 inch per point.)

For 2 inches spaced apart, the result would be simply 40 inches. You just need to add the distance of 20 more to the already distance of 20 points, since if 2 were to be divided, it would be 1, which is 20 inches in distance as stated. Another 20 points would be another inch in distance, and adding them gives you 2 inches in distance or 40 inches all together.

I apologize if I wasn't clear enough, I couldn't find a way to explain it as good as I thought it was in my mind.

Hope it helped though!

The y-intercept of the line is (0,7).

Given the pairs of a line in the coordinate plane are (x, y) (-72,25), (-54,13) and (-36,11).

First we will find the slope of the linear equation

The formula for calculating the slope between two points is equal to

m = (y₂-y₁) / (x₂-x₁)

take points (-54,13) and (-36.,11)

by substituting the values ​​in the above formula, we get

m = (11-13) / (- 36 - (- 54))

m = -2 / 18

m = -1 / 9

Now, we will find the equation for the line in point-slope form

y-y₁ = m (x-x₁)

we have m = -1 / 9 and (x₁, y₁) = (- 36.11)

Further, substitute the values ​​in the above equation, we get

y-11 = (- 1/9) (x + 36) ..... (1)

Convert the equation to the form of a slope intercept

y = mx + b

isolate the variable y in equation (1), we get

y-11 = (- x / 9) -4

y = (- x / 9) - 4 + 11

y = (- x / 9) +7

Here, b=7

Hence, the y-intercept of the line for the pairs of lines in the coordinate plane(x,y) is (-72,25), (-54,13) and (-36,11) is the point (0,7).

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Answer:

x = 2.4; y = 3.2

Step-by-step explanation:

y = 3x - 4

2x + y = 8

2x + 3x - 4 = 8

5x - 4 = 8

5x = 12

x = 12 / 5

x = 2.4

y = 3(2.4) - 4

y = 7.2 - 4

y = 3.2

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

Area models are shapes used to model or illustrate products, multiplications, divisions and quotients

The equation is given as:

4x^2+12x+9 = (2x+3)^2

Express (2x+3)^2 as the product of (2x+3) and (2x+3)

4x^2+12x+9 = (2x+3) * (2x+3)

The above means that the area model is a square.

So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

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Answer:

give it a try

Step-by-step explanation:

Okay. I'm gonna flip five coins, but I'm told the first coin is Tell there's no choice there at all. It is certain the first coin shows a tail and then I want to have four heads in a row. Okay, so one for tell which means certain getting ahead is a half chance. Again a half chance again a half and again a half So that you work out and it's 1/16. That's the answer. There's no choice about the foreheads. It just has to be head every time I said.

Based on the calculations, the sum of this geometric series is equal to 9,990.

Mathematically, the standard form of a geometric series can be represented by the following expression:

[tex]\sum^{n-1}_{k=0}a_1(r)^k[/tex]

Where:

Also, the sum of a geometric series is given by this mathematical expression:

[tex]S=\frac{a_1(1-r^n)}{1-r}[/tex]

Given the following data:

Substituting the given parameters into the formula, we have;

[tex]S=\frac{9000(1-0.1^3)}{1-0.1}\\\\S=\frac{9000(1-0.001)}{1-0.1}[/tex]

S = 9000(0.999)/0.9

S = 8,991/0.9

S = 9,990.

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Answer:

  2.57

Step-by-step explanation:

The mean absolute deviation is the mean of the absolute values of the differences from the mean.

The mean of the dataset is the sum of values, divided by their number:

  mean = (20 +16 +21 +16 +22 +16 +15)/7 = 126/7 = 18

The absolute values of the differences from 18 will have an average of ...

  mean(|differences|) = (2 +2 +3 +2 +4 +2 +3)/7 = 18/7

  mad(data) ≈ 2.57

__

Additional comment

Some calculators have the mad( ) function built-in. See the second attachment, for example.

The true statements about the functions are:

The function is given as:

f(x) = 25000 * 0.96^x

Set x = 0 to determine the initial value of the function

f(0) = 25000 * 0.96^0

Evaluate

f(0) = 25000

This means that the population of the city in 2010 is 25000 i.e. option (B) is correct

Also, we have:

f(x) = 25000 * 0.96^x

The rate at which the population decreases every year is calculated as:

r = 1 - 0.96

Evaluate the difference

r = 0.04

Express as percentage

r = 4%

This means that the rate at which the population decreases every year is 4% i.e. option (C) is correct

The population after 5 and 10 years are:

f(5) = 25000 * 0.96^5

f(5) = 20384

f(10) = 25000 * 0.96^10

f(10) = 16621

Divide these populations by the initial population in 2010

20384/25000 = 82%

16621/25000 = 66%

This means that the population decreased by 82% and 66% in 5 years and 10 years since 2010, respectively.

So, options (d) and (e) are false

Lastly, because the population function is an exponential decay function;

The function value would approach 0 as it decreases

This means that option (f) is correct

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Expert-verified answer

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Given : Chords A C and B D intersect at point E.  Length of Different segments is given in terms of x

To find :  Length of chord BD

Solution:

Chords A C and B D intersect at point E.

=> AE * CE   = BE * DE

AE = x

CE = x + 12

BE = x + 2

D = x + 5

=> x(x + 12) = (x + 2)(x + 5)

=> x² + 12x  = x²  + 7x + 10

=> 5x = 10

=> x = 2

BD = BE + DE

= x + 2 + x + 5

= 2x + 7

putting x = 2

=> BD = 2 (2) + 7

Applying the intersecting chord theorem, the length of segment CE in is: 2.5 units.

In geometry, the intersecting chords theorem is the theorem that defines the relation of the four line segments formed when two chords of a circle intersect each other at a point in the circle.

According to the intersecting chords theorem, the products of the lengths of the line segments that are formed on each chord are congruent or equal to each other.

In the diagram given, we have chords AC and BD intersecting at point E to form the following line segments:

BE = BD - DE = 7 - 2 = 5 units

DE = 2 units

AE = 4 units

CE = ?

Based on the intersecting chord theorem, we have:

(BE)(DE) = (AE)(CE)

Plug in the values

(5)(2) = (4)(CE)

10 = 4(CE)

Divide both sides by 4

10/4 = 4(CE)/4

2.5 = CE

CE = 2.5 units

Thus, applying the intersecting chord theorem, the length of segment CE in the circle given is: 2.5 units.

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The amount made per minute is $1.28 * 10^7

Fractions are written as a ratio of two numbers. For instance a/b is a fraction.

According to the question, a certain animated movie earned $1.1 * 10^9 every 9.1 * 10^1 minutes.

$1.1 * 10^9 = 9.1 * 10^1

In order to determine the amount earned per minute;

x = 1minute

Divide both expressions

1.1 * 10^9/x = 9.1 * 10^1

x = 1.1 * 10^9 /9.1 * 10^1

Divide the result

x = 1.1 * 10^9 /9.1 * 10^1

x = 0.12 *10^8
x = $1.28 * 10^7

Hence the amount made per minute is $1.28 * 10^7

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Considering the relationship between velocity, distance and time, it is found that the total distance traveled was of 380 miles.

Velocity is distance divided by time, that is:

v = d/t.

For the first day, we have that:

v = 40, t = t + 2, d = d + 20, hence:

40 = (d + 20)/(t + 2)

For the second day, we have that:

v = 60

60 = d/t

d = 60t

Then, replacing in the first equation:

40 = (60t + 20)(t + 2)

60t + 20 = 40t + 80

20t = 60

t = 3.

Then the distances are given by:

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