The **volume** of the** solid **is 207.23 cm³.

**Volume of the Solid:**

**Volume** is the area occupied by an **object/matter** (solid, liquid, gas) within a 3D **object.** Alternatively, the** volume of a three-dimensional **object is generally defined as the** capacity** of the **object** that matter can hold.

For example, the volume of a **cubic box** indicates how much water or other substance it can contain. For ice cream cups, the **amount **of **ice cream** that can fit in the cup without gaps corresponds to the **volume **of the ice cream cup.

Now, based on the question:

**Volume of Solid = Volume of Cylinder + Volume of Cone**

Volume of Cylinder = πr²h

v= 3.14 * (3)² * 6

v = 169.56

**Volume Of Cone:**

**Cone volume** defines the **space** or **volume of the cone**. A cone is a **three-dimensional geometric shape **with a **circular base **that tapers from a **flat base** to a point called an apex or vertex. A cone is formed by a series of **line segments**, half-lines, or lines connecting vertices that are common to all points on the** base** in a plane that does not contain **vertices**. A cone can be thought of as a series of **noncongruent disks** that overlap each other such that the ratios of the radii of **adjacent disks** are kept constant.

We know that :

**Volume of Cone** = πr² h/3

v = 3.14 * (3)² * 4/3

v = 37.7

Now,

Volume of Solid = 169.56 + 37.7

= 207.26 cm³

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Evaluate each expression if a=2.5 and b=-8

-|b=2a|

3|b+6|-|a|

**Answer: First=Undefined (if you had a typo, please respond and I will edit)**

**Second=3.5**

**Step-by-step explanation:**

-|b=2a|

-|-8=2(2.5)|

-8=5

Undefined

3|b+6|-|a|

3|-8+6|-|2.5|

3|-2|-2.5

3*2-2.5

6-2.5

3.5

Please Help!

Reduce The following -

4:8

3:9

10:2

3:18

**Answer:**

4:8=1:2

3:9=1:3

10:2=5

3:18 is the same thing as 3:18

A(-2, 5), and B(2, 3), find the coordinate so that p is 4/5 of the way from A to B

The **coordinates **of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in **simplest form** is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].

When the numerator and denominator have no common factors other than one, the **fraction **is in its **simplest form**. Use division to find the **simplest form **of a **fraction**.

Given set of points

A(-2, 5)

B(2, 3)

ratio 3:5 or r = 3/5

We will use the following formula to find the **coordinate **

[tex]$x=\frac{x_1+r x _2}{1+r}[/tex]

[tex]$y=\frac{y _1+r y _2}{1+r}$[/tex]

Substitute the values in the formula

[tex]$ x=\frac{-2+(3 / 5) 2}{1+3 / 5}[/tex] [tex]$y=\frac{5+(3 / 5) 3}{1+(3 / 5)}[/tex]

[tex]$x=\frac{-2+6 / 5}{5+3 / 5}[/tex] [tex]$ y=\frac{59 / 5}{5+8 / 5}$[/tex]

[tex]$x=\frac{-10+6 / 5}{8 / 5}[/tex] [tex]$ y=\frac{25+9 / 5}{8 / 5}$[/tex]

[tex]$x=\frac{-4}{8}[/tex] [tex]$y=\frac{17}{4}$[/tex]

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

Thus, the **coordinates **of the point P on directed line segment AB that partitions AB in the ratio of 3:5 in **simplest form** is x = -1/2 and y = 3[tex]\frac{1}{4}[/tex].

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Full question:

Given the points A(-2, 5) and B(2, 3), find the coordinates of the point P on directed line segment AB that partitions AB in the ratio of 3: 5. Write the answer in lowest simplified fraction if necessary.

Use transformations to solve the inequality. Write down all the steps

**Answer:**

u ≤ 15

**Step-by-step explanation:**

=> u/3 ≤ 5

Multiplying both sides by 3

=> 3×u/3 ≤ 5 ×3

=> u ≤ 15

Find the value of x.

**Answer:**

x=15

**Step-by-step explanation:**

[tex]\angle A+\angle B+\angle C=180^\circ\\(5x-27)^\circ+(7x-26)^\circ+[180^\circ-(10x-23)^\circ]=180^\circ\\12x-53+180-10x+23=180\\2x-30+180=180\\2x-30=0\\2x=30\\x=15[/tex]

**Answer:**

**x = 15.**

**Step-by-step explanation:**

By the External angle of a triangle theorem:-

The external angle = the sum of the 2 opposite internal angles.

So:

10x - 23 = 7x - 26 + 5x - 27

10x - 7x - 5x = -27 - 26 + 23

-2x = -30

**x = 15.**

Linear equation with colors lines black orange green and blue

The **graph **of Linear equation with **colors **lines black, orange, green and blue is shown in figure.

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Given that;

Linear equation with colors lines black orange green and blue.

Now, We know that;

The **graph **of linear equation is always a straight line.

Hence, The graph of** Linear equation** with colors lines black orange green and blue is shown in figure with straight line.

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i need help with this please hurry!!!

So on solving the provided question, we can say that **fraction **we have are [tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex] = 14/6

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many **units **of a certain size there are. 8, 3/4. A whole includes fractions. The **ratio **of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

here the fraction we have are

[tex]4\frac{2a}{3} + \frac{1a}{4} - \frac{1a}{a} (b - 7)[/tex]

12/3 + 12/4 + 15/2

14/6

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Aiden run at a contant peed of 3. 5 meter per econd for 1/2 hour. Then, he walk at a rate of 1. 6 meter per econd for 1/2 hour. How far did Aiden run and walk in 60 minute?

Aiden run and walk in 60 minute, then the **distance** = 9180 meters

Given that,

Aiden run at a **constant peed **of 3. 5 meter per second for 1/2 hour.

Then, he walk at a rate of 1. 6 meter per second for 1/2 hour.

(1) 3. 5 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

[tex]\frac{1}{2}[/tex] hour = 1800 seconds

Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.

So,

We can write,

Distance = **speed** * time

3.5 * 1800 = 6300 meters (Equation-1)

(2) 1. 6 meter per second for 1/2 hour.

We can,

1 hour = 3600 seconds

Then,

[tex]\frac{1}{2}[/tex] hour = 1800 seconds

So,

We can write,

**Distance** = speed * time

1.6 * 1800 = 2880 meters (Equation-2)

Then,

We can add the equation - 1 and 2,

= 6300 meters + 2880 meters

= 9180 meters

Therefore,

Aiden run and walk in 60 minute, then the **distance** = 9180 meters

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What is the slope when y 10?

After solving, the **slope **when y = -10 is 0.

In the given question, we have to find the **slope** when y = -10.

The** formula** known as the slope relates to the method for calculating a line's steepness and inclination. The **x and y coordinates** of the locations along the line can be used to determine the slope of the lines. It is the ratio of the change in the y-axis to the change in the x-axis, to put it another way.

By utilizing the **line equation**, the slope of any line may be expressed as

y = mx + b, where m = slope.

When we compare the given equation y = -10 by the standard equation, we get m = 0.

So the slope when y = -10 is 0.

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A lot measures 63.41 feet. What is the measurement in feet’s inches and fractions of an inch? Answe to the nearest 1/16

The measurement 63.42 feet after **conversion **is 760.92 inches.

**What is conversion of measurement?**

By multiplying or dividing a number, a **conversion factor **can be used to change one set of units to another. If a **conversion **is required, the right **conversion factor **to an equivalent value must be applied. The correct **conversion factor**, for instance, is 12 inches to 1 foot when converting between inches and feet.

Here the given measurement is ,

=> 63.41 feet

To convert feet into inches we need to multiply by 12. Then

=> 63.41 × 12 = 760.92 inches.

Hence the given measurement into inches 760.92 inches.

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A triangle has angles that measure 30o, 60o, and 90o. The hypotenuse of the triangle measures 10 inches.

The best **estimate** for the perimeter of the triangle will be** 23.7 inches**.

In Δ ABC ∠B =90° , ∠C = 30° , ∠A = 60° and** hypotenuse** AC = 10 inches

It has been described in the attachment.

Now, we shall calculate side AB and BC by using **Trigonometric Ratios**.

Sin 30° = AB / AC

or, AB = 10 × Sin 30° = 10 × 0.5 = 5 inches

And, ** Cos 30°** = CB / AC

or,CB = 10 × Cos 30° = 10 × 0.866 = 8.66 inches

Now, we **calculate** the perimeter of the given** triangle**

The **perimeter** of the triangle is = AB + BC + CA

= (5.0 + 8.66 + 10.0 ) inches

= 23.66 inches ≈ 23.7 inches

Hence, the best **estimate **for the perimeter of the triangle will be **23.7 inches**.

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**The co**mplete question is:

A triangle has angles that measure 30°, 60°, and 90°. The hypotenuse of the triangle measures 10 inches. Which is the best estimate for the perimeter of the triangle? Round to the nearest tenth.

In DABC AB=17cm, AD=15cm, BC=13cm and BD is perpendicular to AC. Calculate the length of BD

The **length **of **BD **is approximately **22.67cm**.

**What is the Pythagorean theorem?**

The **Pythagorean theorem **is a fundamental result in mathematics that states that in a right-angled triangle, the square of the length of the **hypotenuse **(the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (the legs). It is named after the ancient Greek mathematician **Pythagoras**, who by tradition is credited with its discovery and proof, although it is often argued that it is knowledge that was already known to the ancient **Babylonians **and **Indians**.

The theorem can be written mathematically as:

c^2 = a^2 + b^2

This is a classic problem in **trigonometry **known as the **Pythagorean theorem **in a right triangle. Since BD is perpendicular to AC, we can use the **Pythagorean theorem **to find the length of BD, which states that in a right triangle, the square of the length of the hypotenuse (BD in this case) is equal to the sum of the squares of the other two sides (AB and AD).

So, BD^2 = AB^2 + AD^2

We are given that AB = 17cm and AD = 15cm, so we can substitute those values into the equation and solve for BD:

BD^2 = (17cm)^2 + (15cm)^2 = 289 + 225 = 514

To find the length of BD, we take the square root of both sides:

BD = √514cm

BD ≈ 22.67cm

Hence, the **length **of **BD **is approximately **22.67cm**.

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If a triangle ha a 22° angle and a 46° angle, what can be etablihed about the third angle meaure and the type of triangle?

The third **angle** measure is 112°, and the triangle is an **obtuse triangle.**

A triangle has 3 **angles**, and the sum of all angles inside a triangle is 180°.

So, 22 + 46 + x = 180

x = 112°

Since the triangle contains an angle measure greater than 90° (the 46° angle), it is an obtuse triangle.

An obtuse triangle is a triangle with one angle measure **greater than 90°**. In this triangle, the angle measure of 46° is the obtuse angle, and the other two (22° and 112°) are acute angles. Obtuse triangles are often used in construction and engineering applications because of their **stability**. The third angle measure is 112°, and the triangle is an **obtuse triangle.**

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7. Find FH

F

37-

H 13

G

FH = _

Therefore , the solution of the given problem of** triangle** comes out to be is 22 miles away.

Given its three sides and three vertices, a triangles is a polygon. A fundamental **geometric** shape, it. Triangle ABC refers to a triangle that has the points A, B, and C as its corners. When four parts are not collinear, a solitary plane and triangle are discovered in geometric **shapes**. Triangles are known as polygons because of their upper right and three corners. A triangle's three points of intersection are referred to as its corners. By multiplying triple triangle angles, 180 degrees can be obtained.

Here,

The given number indicates that FG is 8 & GH is 14.

FG + GH = FH thanks to the segment addition postulate.

In the equation FG Plus GH = FH, 8 should be used in place of FG and 14 should be used in place of GH.

This results in FH = 8 + 14 => FH = 22.

Therefore, is 22 miles away.

Therefore , the solution of the given problem of triangle comes out to be is 22 miles away.

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The complete question is " Find FH in the given triangle FGH where FG=8,GH=14 and the FH is the equal to sum of FG and GH"

d) Consider your answer in part (e). What is the probability that P-P is greater

than the value found in part (a)? Show your work.

The **probability **that [tex]\hat{p}_D-\hat{p}_E[/tex] is **greater than **0.1917 is 0.4681.

Simply put, **probability **measures how likely something is to occur. We can discuss the probabilities of various **outcomes**, or how likely they are, whenever we are unsure of how an event will turn out. **Statistics **is mainly the study of events subject to **probability**.

In Population D:

Population **Proportion **:Turtles have shell length greater than 2 feet = 0.3

Random Sample = 40

Turtles have shell length greater than 2 feet in random sample = 15

In Population E:

Population **Proportion **:Turtles have shell length greater than 2 feet = 0.2

Random Sample = 60

Turtles have shell length greater than 2 feet in random sample = 11

Let [tex]\hat{p}_D[/tex] represents sample proportion for D

Let [tex]\hat{p}_E[/tex] represents sample proportion for E

[tex]$ \text{SampleProportion} =\frac{\text { Count of Success }}{\text { Size of the population }}$[/tex]

[tex]$$\begin{aligned}\hat{p}_D & =\frac{\text { Turtles have a shell length greater than } 2 \text { feet in random sample }}{\text { Random Sample }} \\& =\frac{15}{40} \\& =0.375\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\hat{p}_E & =\frac{\text { Turtles have a shell length greater than 2 feet in random sample }}{\text { Random Sample }} \\& =\frac{11}{60} \\& =0.183\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\text { Difference in sample proportion } & =\hat{p}_D-\hat{p}_E \\& =0.375-0.183 \\& =0.1917\end{aligned}$$[/tex]

[tex]$$\begin{aligned}\hat{\boldsymbol{p}} & =\frac{X_1+X_2}{N_1+N_2} \\& =\frac{15+11}{40+60} \\& =0.26\end{aligned}$$[/tex]

[tex]$$\begin{aligned}Z & =\frac{\left(\hat{p}_D-\hat{p}_E\right)-\left(p_D-p_E\right)}{\sqrt{\hat{p}(1-\hat{p}) \times\left(\frac{1}{n_1}+\frac{1}{n_2}\right)}} \\& =\frac{(0.375-0.183)-(0.3-0.2)}{\sqrt{0.26 \times 0.74 \times\left(\frac{1}{40}+\frac{1}{40}\right)}} \\& =\frac{0.0917}{\sqrt{0.1924 \times 0.04166}} \\& =0.0087\end{aligned}$$$$[/tex]

[tex]\begin{aligned}P\left(\hat{p}_D-\hat{p}_E\right. & > 0.1917) \\& =P(Z > 0.0087) \\& =1-P(Z \leq 0.0087) \\& =0.4681\end{aligned}$$[/tex]

Therefore, The **probability **that [tex]\hat{p}_D-\hat{p}_E[/tex] is **greater than **0.1917 is 0.4681.

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Adam earn 13.72 each hour that he works.He works 9 hours each week.How much does Adam earn each week.

**Answer:**

**He makes $123.48 a week**

Which of the ratios below is equivalent to 1:3? Select all that apply.

A) 4:12

B) 6:18

C) 6:2

D) 8:24

E) 5:8

**Answer:**

A, B,D

**Step-by-step explanation:**

I need help, answer quick and pls explain

The** LCM **of the numbers 1 - x² and (x - 1)³** **is (1 - x²)(x - 1)

An equation is a** expression **that shows the **relationship** between numbers and variables.

The least common multiple (LCM) of a set of numbers is the sm**allest number **that can be **divisible** by the set of numbers

Given the numbers:

1 - x² and (x - 1)³

(1 - x²) = (1 - x)(1 + x) = -1(x - 1)(x + 1)

(x - 1)³ = (x - 1)(x - 1)(x - 1)

The LCM = -1(x + 1)(x - 1)(x - 1) = -1(x² - 1)(x - 1) = (1 - x²)(x - 1)

The** LCM **is (1 - x²)(x - 1)

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A system of equations is given.

Equation 1: 4x − 6y = 10

Equation 2: 9x + 2y = 7

Explain how to eliminate x in the system of equations.

**Step-by-step explanation:**

multiply both equations with factors so that the terms of the targeted variable (in our case x) have the same constant factor. and then we can subtract one equation from the other, abd the variable is eliminated in the result.

in our case the least common multiple of 4 and 9 is 36.

so, we multiply equation 1 by 9, and equation 2 by 4, abd then we subtract

36x - 54y = 90

- 36x + 8y = 28

-------------------------

0 -62y = 62

so, x is "eliminated", and we can solve for y : y = -1.

and then we can use one of the original equations to solve for x.

e.g.

9x + 2×-1 = 7

9x - 2 = 7

9x = 9

x = 1

**Answer:**

First, we'll need to find the LCM (least common multiple) which, in this case, is 36. Now that we know this, we can get 4x and 9x to be 36x and -36x so that they can cancel out. To do this, **we have to multiply Equation 1 by 9 and Equation 2 by -4**.

9(4x - 6y = 10) is equivilant to 36x - 54y = 90

-4(9x + 2y = 7) is equivilant to -36x - 8y = -28

Now that we have our new system of equations, we can proceed with the process of elimination! The first step is to add the two equations together. This will result in:

-62y = 62 we have successfully eliminated x!

The last step will be to divide both sides by -62

-62y/-62 = 62/-62

y = -1

PLSSS HELP IF YOU TURLY KNOW THISS

**Answer:**

The answer is 0

**Step-by-step explanation:**

**The rules of signs:**

**+ * - = -**

**- * - = +**

**- * + = -**

**+ * + = +**

**So, using the rules of signs, your question is basically asking, what is 5-5, for which the answer is 0.**

The graph shows a linear function. Which equation is best represented by this graph?

**Answer:**

C

**Step-by-step explanation:**

The graph passes through [tex](-2,-5)[/tex] but not [tex](2,5)[/tex].

Eliminate B and D.The line is steep, and has a slope of more than 1.

Eliminate A.(4x - 8) - (3x + 10)

[tex](4x - 8) - (3x + 10)[/tex]

Distribute negative sign:

[tex]4x-8+-1(3x)+(-1)(10)[/tex]

[tex]4x-8-3x-10[/tex]

Combine Like Terms:

[tex](4x-3x)+(-8-10)[/tex]

[tex]=\fbox{x - 18}[/tex]

**Answer:**

[tex]x - 18[/tex]

**[tex]4x - 8 - 3x - 10 \\ 4x - 3x - 8 \times 10 \\ x - 18[/tex]**

In two or more complete sentences, compare the number of -intercepts in the graph of f(x) =x^2 to the number of x-

intercepts in the graph of g(x) = x^2 +2. Be sure to include the transformations that occurred between the parent function

f(x) and its image g(x).

The number of **y-intercepts** for g(x) is larger than that for f. (x). The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).

When it comes to geometry, a coordinate system is a technique that uses one or more integers or coordinates to specify the exact location of points or other geometrical objects on a manifold, such as Euclidean space. Locating a point or item on a **two-dimensional plane** requires the usage of pairs of integer coordinates. Two numbers known as the x and y coordinates serve as a description of a point's location on a 2D plane. a collection of figures that signify exact locations. Most often, the figure contains two numerals. The first number denotes the distance from front to rear, and the second number denotes the **distance** from top to bottom. In (12.5), for example, there are 12 units below and 5 above.

given

The graph of f(x) is moved two units to the right and three units downward to get the graph of g. (x).

The standard form allows us to state that f(x) has vertex (0,0) and g(x) has vertex (2,-3).

Given that a>0, f(x) and g(x) are ascending parabola.

Since the origin is f(x vertex, )'s f(x) has just one y-intercept, or (0,0).

Given that g(x) is an upward parabola with a vertex at (2,-3), g(x) has two y-intercepts.

Because of this, the number of y-intercepts for g(x) is larger than that for f. (x).

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the time required to complete a job varies inversely as the number o people working. it took 4 hours for 7 electricians to wire a building. how long would it have taken 3 electricians to have done the job

The **time** taken by 3 electricians to complete the work is 9 1/3 hours.

When one quantity's value rises relative to another's **decrease** or vice versa, it is said that the two are **inversely proportionate**.

It implies that the two quantities exhibit opposing behaviors in nature. For instance, the relationship between **time** and **speed** is inverse.

If x and y are **inversely proportionate** to each other

=> x ∝ 1/y

=> xy = k [ where 'k' is proportionality constant ]

Here we have

The** time** required to complete a job **varies inversely **to the number of people working. It took 4 hours for 7 electricians to wire a building.

Let x be the **time** and y be the number of **people **

Given that the time required to complete a job varies **inversely** to the number of people working.

=> xy = k ---- (1) [ Since they are inversely proportional to each other ]

Given that it took 4 hours for 7 electricians to wire a building.

=> 4(7) = k

=> k = 28

Substitute k = 28 given number of electricians y = 3 in equation (1)

=> x (3) = 28

=> x = 28/3 = 9 1/3hrs

Therefore,

The **time** taken by 3 electricians to complete the work is 9 1/3 hours.

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PLS HELP i rlly need to get this done

**Answer:**

1. yes

2. no

3. no

4. yes

**Step-by-step explanation:**

What is a pixel Mcq?

The fundamental color-programming unit on a computer screen or in a digital image is the pixel, a word that was created from the phrase "picture element." Consider it more as a conceptual than a physical unit. In a digital display, **pixels** are the smallest unit.

The smallest component of a **visual display** or digital image is a pixel, also known as a picture element. A grid of pixels is used to create computer screens. Red, blue, and green illumination components make up each pixel, which may produce millions of distinct colors by combining them in various ways and at various intensities.

For instance, a computer with a display resolution of 1280 x 768 will create up to 98,3040 pixels on a display screen. The number of pixels per inch of the monitor screen affects **image quality**; more pixels per inch produce better images.

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Please explain how to work out angle BAC

The angle **measure **BAC is the sum of angles BAD and CAD.

Angles are the figure formed by the **intersection **of two lines or rays by sharing a common point. This point is called the **vertex **of the angle.

Given a **triangle **ABC.

A line is drawn inside the triangle from vertex A to the **opposite **side BC.

Given that AD = BD = CD.

That is the line AD **bisects **the line BC.

So here we have two smaller triangles ABD and ACD.

Two corresponding sides of both the triangles are **equal**.

Then the third side is also equal.

AB = AC

And we get angle A is bisected.

By the angle bisector **theorem**,

Measure of angle BAC = Measure of angle BAD + Measure of angle CAD

Hence, Measure of angle BAC = Measure of angle BAD + Measure of angle CAD

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What is the length of ? Two perpendicular lines R S and P Q within a circle intersect at the point P. The lengths of the line segments are labeled as follows. R T equals x, T S equals x, P T equals 4, and T Q equals 16. Figure not drawn to scale A. 8 B. 10 C. 16 D. 20

**Answer:**

16

**Step-by-step explanation:**

option c 16 is the answer

The table gives the annual global plastic production over time, in years, since 1960.

Fit an exponential model to this data.

The exponential model indicates that plastic production has (1) _____ per year. The model predicts that plastic production 15 years after 1960 was closest to (2) _____ million metric tons. Because the correlation coefficient indicates (3) _____

correlation between the model and the data, this prediction (4) _____.

Answer options:

1-

increased by 4.9 metric tons

decreased by 4.9 metric tons

increased by 4.9%

decreased by 4.9%

2-

40

60

70

3-

moderate

strong

weak

4-

is unreliable

can be accepted with confidence

The **exponential **model indicates that plastic production has increased by 4.9% per year.

**Fit an exponential model to this data**

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Pls help me with this

The **percent **of the bug eaten each day is 67% and the percent of the bug remaining each day is 33%.

A function is a relation from a set A to a set B where the **elements **in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

f(x) = 500 (0.67)ˣ

Part A :

x = 0 ⇒ f(x) = 500 (0.67)⁰ = 500

x = 1 ⇒ f(x) = 500 (0.67)¹ = 335

x = 2 ⇒ f(x) = 500 (0.67)² = 224.45

x = 3 ⇒ f(x) = 500 (0.67)³ = 150.3815

Part B :

Here 0.67 is the **decay **rate.

That is the **rate **of decay of the bug is 0.67.

67% of the bugs are decaying with each day.

Part C :

Percent of bugs remaining each day = 100% - 67% = 33%

Part D:

f(x) < 40

500 (0.67)ˣ < 40

(0.67)ˣ < 40 / 500

(0.67)ˣ < 0.08

Taking **logarithms **on both sides,

㏒ (0.67)ˣ < ㏒ 0.08

x ㏒ (0.67) < ㏒ 0.08

x (-0.1739) < (-1.0969)

Dividing doth sides by (-0.1739), the sign of **inequality **changes because of dividing by a **negative **number.

x > 6.3

Hence the **percentage **of the bugs eaten and remained are calculated.

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