True or false: f(x) is a function.
A
2
f(x)

The population of the town in 5 years is 12763

The given parameters are:

Initial value (a) = 10000

Rate (r) = 5%

A population growth model is represented as:

[tex]y = a(1 + r)^x[/tex]

So, we have:

[tex]y = 10000 * (1 + 5\%)^x[/tex]

In 5 years, we have:

[tex]x = 5[/tex]

So, we have:

[tex]y = 10000 * (1 + 5\%)^5[/tex]

Evaluate

[tex]y = 12763[/tex]

Hence, the population in 5 years is 12763

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Answer:

D

Step-by-step explanation:

6b>-18

b>-3

This is shown by the line going from -3 into infinity.

Answer:

6b > -18

Step-by-step explanation:

[tex]6b > -18 \\then \\b >\frac{-18}{6} \\then\\b > -3[/tex]

Answer:

Converge

Step-by-step explanation:

Given geometric series

[tex]1,000+200+40+8+\dfrac{8}{5}+...[/tex]

The first term of this geometric series is [tex]a_1=1,000.[/tex]

Next terms can be obtained by dividing by 5 or multiplying by [tex]\frac{1}{5}:[/tex]

[tex]a_2=1,000\cdot \dfrac{1}{5}=200\\ \\a_3=200\cdot \dfrac{1}{5}=40\\ \\a_4=40\cdot \dfrac{1}{5}=8\\ \\a_5=8\cdot \dfrac{1}{5}=\dfrac{8}{5}\\ \\...[/tex]

The sum of this infinite geometric series is

[tex]S=\dfrac{a_1}{1-q}=\dfrac{1,000}{1-\frac{1}{5}}=\dfrac{1,000}{\frac{4}{5}}=1,250[/tex]

Hence, this series is convergent

Answer:

6

Step-by-step explanation:

Using the sine ratio in the right triangle and the exact value

sin45° = [tex]\frac{1}{\sqrt{2} }[/tex], then

sin45° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3\sqrt{2} }{hyp}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )

hyp = 3[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] = 3 × 2 = 6

Answer:

The inequality that represents the graph is  y < [tex]\frac{1}{4}[/tex]x + 2

Step-by-step explanation:

i) the region below a dashed line through the points (4,3) and (0,2) is shaded.

ii) first we find the equation of the line passing through the points (4,3) and (0,2)

(y - 3) = [tex](\frac{3 - 2}{4 - 0})[/tex](x - 4)    ⇒    y - 3 =  [tex]\frac{1}{4}[/tex](x - 4)  

⇒  4y - 12 = x - 4       ⇒     4y = x + 8      ⇒     y = [tex]\frac{1}{4}[/tex]x + 2

iii) for the area shaded below the line whose equation is given in ii) above the inequality that will represent the shaded region is given by

 y < [tex]\frac{1}{4}[/tex]x + 2

The graph represents the inequality y < 1/4x + 2. The inequality was calculated based on the information given: points the line goes through, shading below the line, and the line being dashed all determine the inequality's form.

To determine the inequality graphed, we first need to find the equation of the line. The line passes through the points (4, 3) and (0, 2), so we can use these points to find the slope of the line.

The formula for the slope (m) is [tex](y2 - y1)/(x2 - x1).[/tex]. Plug in the coordinates of the two points into this formula: ([tex]3 - 2) / (4 - 0) = 1/4[/tex] So, our slope is 1/4.

Given a slope (m) of 1/4 and the y-intercept (b) of 2, we can write the equation of the line in slope-intercept form (y = mx + b) as y = 1/4x + 2.

One key part of your question is that the region below this line is shaded. In the language of inequalities, shading below the line corresponds to 'y is less than' the line's equation. Also, the line is dashed, meaning that the points on the line are not included in the solution, which we denote as 'less than' rather than 'less than or equal to'.

So, the inequality represented by this graph is y < 1/4x + 2.

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Answer:

B

Step-by-step explanation:

Linc c moving upward will intersect line b

Option (B) shows that lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that:

Lines a, b, and c are coplanar. Lines a and b intersect.

Line c intersects only with line b

As we can see in the picture, the lines are given:

As we know, the coplanar plane is the plane in which all lines or points lie (ie. in the same plane) known as coplanar.

In option (B) the lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.

Thus, option (B) shows that lines a, b, and c are coplanar. Lines a and b intersect. Line c intersects only with line b.

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There are 162 base ball cards

Solution:

Let "a" be the number of baseball training cards

Let "b" be the number of basket ball training cards

Trent has a collection of 198 baseball and basketball training cards

Therefore,

a + b = 198 -------- eqn 1

He has 4.5 times as many baseball cards as basketball cards

Number of baseball cards = 4.5(number of basketball cards)

a = 4.5b --------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

4.5b + b = 198

5.5b = 198

b = 36

Substitute b = 36 in eqn 2

a = 4.5(36)

a = 162

Thus there are 162 base ball cards

Trent have 162 baseball cards in his collection.

Trent has a collection of 198 baseball and basketball training cards, with baseball cards being 4.5 times as many as basketball cards. To find out how many baseball cards Trent has, we can set up a system of equations.

Let x be the number of basketball cards.

Since the number of baseball cards is 4.5 times the number of basketball cards, the number of baseball cards is 4.5x.

The total number of cards is 198, so x + 4.5x = 198.

Solving this equation, we find x = 36. Therefore, the number of baseball cards Trent has is 4.5*36 = 162 baseball cards.

Answer:

2

Step-by-step explanation:

There are 2 units of distance separating -5 and -3.

Answer:

w=5

Step-by-step explanation:

First you have to write out the equation. Then you distribute negative 4 to 3w then you distribute -4 to -1 you get 4. Then you need to combine like terms and you get 3W. then you need to subtract four from each side you get 15 equals 3W then divide aside by three and you get W equals five

Answer:

1a : a branch of mathematics that deals usually with the nonnegative real numbers including sometimes the transfinite cardinals and with the application of the operations of addition, subtraction, multiplication, and division to them. b : a treatise on arithmetic. 2 : computation, calculation.

Step-by-step explanation:

Final answer:

Arithmetic is a branch of mathematics dealing with numbers, including operations like addition, subtraction, multiplication, and division; it is recognized for its universality and foundational importance in various fields of study.

Explanation:

Arithmetic is a fundamental branch of mathematics that involves the study and manipulation of numbers. It includes the basic operations of addition, subtraction, multiplication, and division. These operations are essential for understanding and working with numbers in both simple and complex mathematical contexts, such as the calculation of quantities, relationships, and patterns. Arithmetic is universally acknowledged for its constant and indubitable truths, such as two plus three always equalling five. This branch of mathematics is not only vital in academic settings but is also crucial in everyday decisions and processes regardless of the period or location. Arithmetic serves as the basis for more advanced mathematical studies and is woven intricately into various fields such as physics, astronomy, and engineering, highlighting its foundational importance in the sciences and beyond.

The point (1, 9) with a slope of 4 on a graph corresponds to the answer of 13.

The answer is 13.

To calculate this, we use the formula for the equation of a straight line: y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = 4x + 9. Substituting x = 1 into the equation gives y = 4(1) + 9 = 13.

Therefore, the point (1, 9) has a slope of 4 on the graph.

Answer:

1 1/6

Step-by-step explanation:

because it takes more to get to 12 than 6

11/6 is bigger because if you convert both into decimal form

11/6=1.83

14/12=1.16

Answer:

see attached picture please

Answer:

10 is the greatest common factor

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF).

10

Answer:

Step-by-step explanation:

You need to find out how many cabinets it is

Final answer:

To determine how many knobs Mr. Edwards needs to buy for his kitchen cabinets, we need to know the total number of cabinets since he needs 2 knobs for each cabinet.

Explanation:

Mr. Edwards wants to buy new knobs for his kitchen cabinets. To determine how many knobs he needs to buy, we would need to know the exact number of kitchen cabinets he has. However, the information about Chelsea and her trip to Europe, her being a shop-a-holic and physics lover, and the estimation of the number of pairs of shoes that can fit in her closet seem to be unrelated to Mr. Edwards's question. Therefore, to answer Mr. Edwards's query, we need the number of cabinets to calculate the total number of knobs. If there are X cabinets, Mr. Edwards would need to purchase 2X knobs.

Answer:

0.00019120128

Step-by-step explanation:

1.6x1.6x1.6 x .00004668

Answer:

If each grid square represents one block, then the number of box he walked will be 30 blocks.

Step-by-step explanation:

Tommy walks from his home to the mall and then walks to a movie theater.

His home is at (0,0), the mall is at (0,8) and the movie theater is at (7,8).

Now, distance from (0,0) to (0,8) is 8 units and the distance from (0,8) to (7,8) is 7 units.

So, total distance covered is (8 + 7) = 15 units.

After leaving the theater Tommy walks to the store before returning home.

The store is at (7,0).

Now, the distance from (7,8) to (7,0) is 8 units and the distance from (7,0) to (0,0) is 7 units.

So, total distance covered is (8 + 7) = 15 units.

If each grid square represents one block, then the number of the box he walked will be (15 + 15) = 30 blocks. (Answer)

Answer:

The dimensions of the rectangle are;

Width = 3 inches

Length = 9 inches

Step-by-step explanation:

Given;

We want to determine the dimensions of the rectangle;

Forming an equation, we get;

2 ( x + x + 6) = 24

4x + 12 = 24

With the equation we can solve for x

4x = 24 - 12

4x = 12

  x = 3

and (x + 6) = 9

Therefore;

Width = 3 inches

Length = 9 inches

The width of the rectangle is 3 inches and the length is 9 inches.

Let's assume that the width of the Rectangle dimensions is represented by 'w' inches.

Since the length is 6 inches more than the width, we can represent it as 'w + 6' inches.

The perimeter of a rectangle is the sum of all its sides.

In this case, the formula for the perimeter is 2(w + l), where w represents the width and l represents the length.

So, for this problem, we have the equation 2(w + w + 6) = 24.

Simplifying this equation, we get 4w + 12 = 24.

Solving for 'w', we find that the width is 3 inches.

Plugging this value back into the equation for the length, we find that the length is 9 inches.

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Answer: 32

Step-by-step explanation:

4 cubed 2 divided by 4

Simply is

4 to the power 3 multiplied by 2 divided by 4

4*4*4*2/4

128/4= 32

Answer

-8/3 (fraction)

or in decimal form it would be -2.6 (the six would be repeating)

Step-by-step explanation:

Answer : 8

7 + 9 + 6 + 10 + 8 = 40

40/5 (5 is the number of sales calls) = 8

Answer:

Step-by-step explanation:it is the second option. :)

Answer:

Top right = second choose

Step-by-step explanation:

Answer:16x-15

Step-by-step explanation:

3x-9+13x-6

Collect like terms

3x+13x-9-6

16x-15

Answer:

[tex]\displaystyle \frac{d}{dx}[\tan x] = \sec^2 x[/tex]

General Formulas and Concepts:

Pre-Calculus

Calculus

Differentiation

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Step-by-step explanation:

*Note:

This is a known trigonometric derivative.

Step 1: Define

Identify

[tex]\displaystyle y = \tan x[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

The derivative of tanx in calculus is sec^2x, which represents the slope of the curve at any point x for the function tanx.

The derivative of a function measures how the function changes as its input changes. In calculus, the derivative is a concept that describes the rate at which a quantity changes.

In the context of your question, the derivative of tanx or tangent x is sec^2x or secant squared x. This is a standard result that is usually memorized in calculus courses and can be derived using the limit definition of the derivative and trigonometric identities.

To put it in simpler terms, if tanx were the equation of a curve, the derivative (sec^2x) would represent the slope of that curve at any point x. This is key to understanding how the function behaves at different points and predicting its future behavior.

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Answer:

The special quadrilateral formed by connecting the midpoints of the sides of the original quadrilateral is :  a rhombus

Step-by-step explanation:

Look at the photo below for the figure

:)

Answer:

The correct option is third one m∠2 =106° , m∠3 =37°.

Therefore,

[tex]m\angle 2 = 106\°\\m\angle 3 = 37\°[/tex]

Step-by-step explanation:

Given:

Consider ABCD as a Rhombus such that,

∠A = ∠1 = 106°

∠C = ∠2

∠BDC = ∠3

AB=BC=CD=DA

To Find:

∠2 = ?

∠3 = ?

Solution:

ABCD is a Rhombus

∠A ≅ ∠C  ............opposite angles of Rhombus are equal. ( property )

Substituting the values we get

∠1 = ∠2

But ∠1 = 106°

∴ ∠2 = 106°    ....... Transitive property,

As BC = CD   ...Given

ΔBCD is an Isosceles triangle

∴ ∠CBD ≅ ∠BDC = ∠3  ........base angle of Isosceles triangle are congruent.

we know that in a triangle,

Sum of measures of all angles is 180°

in Triangle BCD

[tex]\angle 3 +\angle 2 +\angle 3 =180[/tex]

Substituting the values we get

[tex]2m\angle 3 =180-106=74\\\\\angle 3=\dfrac{74}{2}=37\\\\m\angle 3 = 37\°[/tex]

Therefore,

[tex]m\angle 2 = 106\°\\m\angle 3 = 37\°[/tex]

Answer:

The actual weight is 1.1% less (100 - 98.9) than the labeled weight.

Step-by-step explanation:

1. Let's review the information given to us to answer the question properly:

Labeled weight of the bag of chocolates = 0.384 pounds

Actual weight of the bag of chocolates = 0.3798 pounds

2.  How much have you or lighter are the chocolates and the stated on the label. Show your reasoning.

Let's find how much we have comparing the labeled weight and the actual weight, using a Direct Rule of Three, this way:

Weight               Percentage

0.384                    100 %

0.3798                      x %

0.384x = 0.3798 * 100

0.384x = 37.98

x = 37.98/0.384

x = 98.9 (Rounding to one decimal place)

The actual weight is 1.1% less (100 - 98.9) than the labeled weight.

The chocolates are 0.0042 pounds lighter than what is stated on the label.

The difference in weight between the labeled weight and the actual weight of the chocolates is 0.0042 pounds. This means that the chocolates are 0.0042 pounds lighter than the label indicates.

To calculate this, subtract the actual weight from the labeled weight: 0.384 - 0.3798 = 0.0042 pounds.

So, the chocolates are 0.0042 pounds lighter than what is stated on the label.

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Answer:

The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.

Step-by-step explanation:

Let's find out the pattern Zack is using to water his garden, this way:

First week =  1 3/8  gallons of water

Second week = 1 3/4 gallons of water = 1 3/8 + 3/8 = 1 6/8 = 1 3/4

Third week = 2 1/8 gallons of water = 1 3/4 + 3/8 = 1 6/8 + 3/8 = 2 1/8

The constant of adding every week is 3/8 gallons, therefore,

Fourth week = 2 1/8 + 3/8 = 2 4/8 = 2 1/2 gallons of water

Fifth week = 2 1/2 + 3/8 = 2 4/8 + 3/8 = 2 7/8 gallons of water

The correct answer is that Zack used 2 7/8 gallons to water his garden on the fifth week.

Following the pattern of increasing water usage by 3/8 gallons each week, Zack will use 2 7/8 gallons of water in the fifth week.

Zack watered his garden with increasing amounts of water over the first three weeks. Since there is a pattern, we can deduce the amount of water he will use in the fifth week by identifying the pattern and then continuing it.

Observing the pattern, we see that Zack is increasing the amount of water by 3/8 gallons each week. The progression in gallons is:

Continuing this pattern:

Therefore, Zack will use 2 7/8 gallons of water on the fifth week.

The graph which shows the pre-image of quadrilateral ABCD and the image A’ B’ C’ D’ after the rotation is graph number 1.

Rotation of a figure is the transformation of it about a point in either clockwise or anticlockwise direction.By rotating, a figure changes the point of the figure.

The quadrilateral ABCD and point E in the graphed in the figure below. This quadrilteral is rotated r(135°, E) in order to construct quadrilteral A’ B’ C’ D’ .

The rotation of the figure is 135 degrees. This angle can be break as,

[tex]\theta=135\\\theta=90+45[/tex]

The angle is rotated 90 and 45 degrees. To rotate 90 degree, the angle must be flliped 90 degree clockwise from point E keeping the point c at center.

After this the 45 degree more the figure is rotated. This is shown accurately in the figure A.

Thus, the graph which shows the pre-image of quadrilateral ABCD and the image A’ B’ C’ D’ after the rotation is graph number 1.

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Yolanda's was 25 years old when they were married.

Step-by-step explanation:

Let,

Age of Xavier = x

Age of Yolanda = x + 4

Combined age = 126

According to given statement;

Xavier's age + Yolanda's age = 126

[tex]x+(x+4)=126\\x+x+4=126\\2x=126-4\\2x=122\\[/tex]

Dividing both sides by 2

[tex]\frac{2x}{2}=\frac{122}{2}\\x=61[/tex]

Yolanda's age = x+4 = 61+4 = 65

Age when married = 65 - 40 = 25

Yolanda's was 25 years old when they were married.

Keywords: word problems, addition

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