Consider the following graph: What is the average slope/rate of change between (0, 1) and (2, 4)? 2/3 What is the average slope/rate of change between (-2, 1/4) and (-1, 1/2)? -1/4 Is the slope/rate of change constant (not changing/the same)? No Is the function linear? No

Answers

Answer 1

a) The average slope or rate of change between (0, 1) and (2, 4) is 3/2.

b) The average slope or rate of change between (-2, 1/4) and (-1, 1/2) is 1/4.

c) The slope or rate of change is not constant between these two pairs of points, since the average slopes are different.

d) The function connecting these pairs of points is not a linear function.

Define a slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The average slope or rate of change between two points (x1, y1) and (x2, y2) on a line is given by:

average slope = (y2 - y1) / (x2 - x1)

For the points (0, 1) and (2, 4), the average slope is:

average slope = (4 - 1) / (2 - 0) = 3/2

For the points (-2, 1/4) and (-1, 1/2), the average slope is:

average slope = (1/2 - 1/4) / (-1 - (-2)) = 1/4

When the average slopes of these two pairs of points differ, the slope or rate of change is not constant. As a result, the function connecting these point pairs is not linear.

Because a linear function has a constant slope, a function with a variable slope cannot be linear.

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Related Questions

Triangle AABC, right angled at C, is given. Height and the median from point C form an angle y.
The measure of larger acute angle of AABC is:
A 45°-
B
C
D
60° +
90°
24
92
2
92
4

Answers

The measure of the larger acute angle of ΔABC is: α = 45° + φ/2. Option A.

How do you solve for the larger acute angle of ΔABC ?

Let's denote the angles of triangle ΔABC as follows:

∠A = x

∠B = y

∠C = 90° (right-angled triangle)

Let D be the midpoint of AB, so CD is the median. Let E be the point on AB such that CE is the height from point C.

Since CD is the median, we know that angle ∠ECD = φ.

In right-angled triangle ΔCEB, we have:

∠CEB = 90° - y

Now, let's examine triangle ΔCED. We know that the sum of the angles in a triangle is 180°. Therefore:

∠CED + ∠CEB + ∠ECD = 180°

Substitute the known values:

∠CED + (90° - β) + φ = 180°

Since ∠CED and ∠A are supplementary angles, we can also write:

∠CED = 180° - x

Now substitute this value into the previous equation:

(180° - x) + (90° - y) + φ = 180°

Simplify the equation:

270° - x - y + φ = 180°

Subtract 90° from both sides:

180° - x - y + φ = 90°

From this equation, we get:

x + y = 90°

Substitute this value back into the equation involving φ:

180° - (90°) + φ = 90°

Simplify:

90° + φ = 90°

Therefore, the measure of the larger acute angle of ΔABC is:

x = 45° + φ/2 (option a)

the above answer is in response to the full question below;

Triangle ΔABC, right angled at C, is given. Height and the median from point C form an angle φ. The measure of larger acute angle of Δ ABC is:

a. 45⁰ + φ/2

b. 60⁰ + φ/2

c. 90⁰ - φ/2

d. 2φ

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Eight percent of all college graduates hired by companies stay with the same company for more than five years. The probability, rounded to four decimal places, that in a random sample of 14 such college graduates hired recently by companies, exactly 2 will stay with the same company for more than five years is _?_.

Answers

P(X=2) &= {14\choose 2}(0.08)^2(0.92)^{12} \

&= \frac{14!}{2!(14-2)!}(0.08)^2(0.92)^{12} \

[tex]\sf\implies\:&=\frac{14\times13}{2\times1}(0.08)^2(0.92)^{12}[/tex]

&= 91(0.08)^2(0.92)^{12} \

&\approx \boxed{0.2166

[tex]\begin{align}\huge\colorbox{black}{\textcolor{yellow}{\boxed{\sf{I\: hope\: this\: helps !}}}}\end{align}[/tex]

[tex]\begin{align}\colorbox{black}{\textcolor{white}{\underline{\underline{\sf{Please\: mark\: as\: brillinest !}}}}}\end{align}[/tex]

[tex]\textcolor{lime}{\small\textit{If you have any further questions, feel free to ask!}}[/tex]

[tex]\huge{\bigstar{\underline{\boxed{\sf{\color{red}{Sumit\:Roy}}}}}}\\[/tex]

16
Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?
О А.
m. All rights reserved.
2 Fr
Arc
Length
Q Search
I:
3=
IA
>
0

Answers

A graph that correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r is: C. graph C.

How to calculate the length of the arc?

In Mathematics and Geometry, if you want to calculate the length of an arc formed by a circle, you will divide the central angle that is subtended by the arc by 360 degrees and then multiply this fraction by the circumference of the circle.

Mathematically, the length of an arc formed by a circle can be calculated by using the following equation (formula):

Arc length = 2πr × θ/360

In this context, we can reasonably infer and logically deduce that the arc length is directly proportional to the radian measure of the central angle.

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Need help on question 20. Plsss help

Answers

The calculated distance between the tree and the zip line is 9.21 units

Evaluating the distance between the tree and the zip line

From the question, we have the following parameters that can be used in our computation:

y = -6/7x + 7

This represents the zip line

Convert the equation to standard form

This gives

7y = -6x + 49

So, we have

6x + 7y - 49 = 0

This means that

A = 6, B = 7 and C = -49

From the point (6, 14), we have

x = 6 and y = 14

The distance between the tree and the zip line is then calculated as

[tex]d = \frac{|ax + by + c|}{\sqrt{a^2 + b^2}}[/tex]

By substitution, we have

[tex]d = \frac{|6 * 6 + 7 * 14 - 49|}{\sqrt{6^2 + 7^2}}[/tex]

This gives

[tex]d = \frac{85}{9.22}[/tex]

Divide

d = 9.21

Hence, the distance between the tree and the zip line is 9.21 units

Answers

The remaining ribbon will be 14 feet.

Olga decorates blankets with ribbon she has 12 yards of ribbon

and, she uses 22 feet of the ribbon to decorates blankets

Now, we have to find the she decorates the blankets how many feet of ribbon will remain?

Firstly, Convert the yard into feet

We know that:

There are 3 feet in 1 yard

So, 36 feet in 12 yards

Now, The remaining ribbon will be the original amount less the amount used.

=> 36 - 12 = 14 feet

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Input Signals: P = 0 and Q = 1.

Answers

The output of the OR gate will be 1.

What is a NOT Gate?

An important component for electronics and computing, the NOT gate or inverter is a basic digital logic gate. It is designed with one input and output that conduct logical negation.

Essentially, this means it turns the input signal to its opposite. When given an input binary value at "1," the method generates "0" as the output and vice versa.

Two input signals, P=0 and Q=1, are subjected to the following process. The message carried by Q is inverted via a NOT gate using its negation feature, returning Q' = 0 at its output.

The resultant value of Q' (evaluated as zero), is then processed using an OR logic operation along with input P into another gate. Outputs from an OR port may only produce "1" if any of the input signal(s) carry a 1. As one of the inputs from this specific procedure provides "0", the result will inevitably be "1".

Consequently, a final analysis reveals that regardless of what the initial value for P was, the result obtained formulating the two signals through a NOT and OR devices matches an outcome of "1".

Answers

Answer:

2x³-5x² - 2x + 1

Step-by-step explanation:

We are given

f(x) = 2x³ - 5x²

g(x) = 2x - 1

and asked to find (f - g)(x)

(f - g)(x) is nothing but f(x) - g(x)

(f- g)(x) = f(x) - g(x) = 2x³-5x² - (2x - 1)

= 2x³-5x² - 2x + 1

What is the equation through the points: (6, 10), (5, -6)

ASAP please

Answers

Answer: y=16x - 86

Step-by-step explanation:

Evaluate (11/16−(3/4)2)×1

Answers

Answer:

-166/, -0.82,

Step-by-step explanation:

The above fraction, decimal are all evaluated answer for (11/16−(3/4)2)×1

If sun x= 4/5 what is the value of b? 22.5 3b

Answers

By following trigonometry identities we get b equals **7**

Define trigonometry identities?

Trigonometric identities are equations involving trigonometric functions that hold for all possible values of the variables that occur and for which both sides of the equation are specified. These identities come in use if trigonometric function-based formulas need to be made simpler 1.

There are numerous distinctive trigonometric identities that involve a triangle's side length and angle 2. Only the right-angle triangle 2 is covered by the trigonometric identities. The three main trigonometric functions are sine, cosine, and tangent, while the other three are cotangent, secant, and cosecant.

Some of the most popular trigonometric identities are listed below:

sin²(x) + cos²(x) = 1

- tan(x) = sin(x)/cos(x)

- cot(x) = cos(x)/sin(x)

- sec(x) = 1/cos(x)

- csc(x) = 1/sin(x)

- sin(2x) = 2sin(x)cos(x)

- cos(2x) = cos²(x) - sin²(x)

- tan(2x) = (2tan(x))/(1 - tan²(x))

The use of these identities

.One angle in a right triangle is x°, where sin x°=4/5 . With this knowledge, we can use the inverse sine function (arcsin) to calculate the value of x, which gives us x = arcsin(4/5) = 0.9272952180016122 radians .

In addition, we are informed that NL = 22.5 and NM = 3b. We can get the value of LM, which is equal to√(NL2 + NM2), using the Pythagorean theorem. 2. When the given values are substituted, we obtain LM = √((22.5)2 + (3b)2) = sqrt(506.25 + 9b2).

LM is equivalent to b times cos(x°) since it is the polar opposite of the right angle. Consequently, we can write:

b cos(x°) = √(506.25 + 9b²)

Substituting x = arcsin(4/5), we get:

b cos(arcsin(4/5)) = √(506.25 + 9b²)

Simplifying this equation using trigonometric identities, we get:

b * (√1 - sin²(arcsin(4/5)) = sqrt(506.25 + 9b²)

b × (√(1 - (4/5)²)) = sqrt(506.25 + 9b²)

b× (√(1 - 16/25)) = sqrt(506.25 + 9b²)

b× (√(9/25)) = sqrt(506.25 + 9b²)

3b/5 = √(506.25 + 9b²)

Squaring both sides of the equation, we get:

9b²/25 = 506.25 + 9b²

Solving for b, we get:

b = 7

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Select the statement that is true a.16.7-8=2.9×3 b. 4×3.2=17.8-5 c.10.5÷5+1=8.8÷4 d.

Answers

Answer:

4 x 3.2 = 12.8

17.8 - 5 =12.8

so,

4 x 3.2 = 17.8-5

12.8=12.8

Help asap!! Please help I don’t get this

Answers

The value of arc CD is 110⁰.

The value of arc AD is 120⁰.

What is the measure of the angle?

The value of arc CD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

angle DEC = ¹/₂ (360 - 2x100) (sum of angle at a point)

angle DEC = ¹/₂ (360 - 200)

angle DEC = 80⁰

The value of arc CD is calculated as follows;

80 = ¹/₂ (CD + 50) (intersecting chord theorem)

2 x 80 = CD + 50

160 = CD + 50

CD = 110⁰

Arc AD = 360 - (50 + 80 + 110) (sum of angles in a circle)

arc AD = 120⁰

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Liam works at a zoo. He was looking at some data showing the masses of their
5
55 African elephants. The mean mass of the elephants was
3
,
800

kg
3,800kg3, comma, 800, start text, k, g, end text, and the median mass was
3
,
600

kg
3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed
2
,
700

kg
2,700kg2, comma, 700, start text, k, g, end text.

Answers

The effect Lola's mass decreasing has on the the mean and median

: No change in Median weightMean reduced by 180 kg

How do we calculate?

Given values :

5 African elephants

The mean mass of the elephants was 3800 kg

The median mass of the elephants was 3600 kg

The smallest elephant, named Lola, weighed 2700 kg

Lola then got very sick and lost weight until her mass reached 1800 kg

2700 , A , 3600 , B , C

as Median is 3600 and lowest is 2700

now 2700 becomes 1800

1800 , A , 3600 , B , C

so Median remains the same as 3600

So we notice no change in Median

The mean mass of the elephants = 3800 kg

=> total weight = 5 x 3800 = 19000 kg

2700 kg becomes 1800 kg

total mass = 19000 - 2700 + 1800

= 181000 kg

The following can be inferred :

New Mean = 18100/5 = 3620 kg

Mean reduced by 3800 - 3620 = 180 kg

No change in Median weight

Mean reduced by 180 kg

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The dimensions of the box below are reduced by half. What is the ratio of the volume of the new box to the volume of the original box?

please help!!!!
u will get 100 points!!!!

Answers

Answer:

1:8

Step-by-step explanation:

The original volume of the box can be calculated by multiplying the length, height, and width:

V = l x h x w = 40 x 8 x 20 = 6,400 cubic inches

If each of the dimensions is reduced by half, the new dimensions become:

Length = 20 inches

Height = 4 inches

Width = 10 inches

The volume of the new box can be calculated as follows:

V_new = l x h x w = 20 x 4 x 10 = 800 cubic inches

The ratio of the volume of the new box to the volume of the original box is:

V_new / V = 800 / 6,400 = 1/8

Therefore, the ratio of the volume of the new box to the volume of the original box is 1:8.

Answer:

I think it's 1 : 8

Step-by-step explanation:

if you don't understand, you can ask me

#CMIIW

3⋅f(−4)−3⋅g(−2) = ?
Ayuda por favor

Answers

The value of the 3 × f( - 4 ) - 3 × g( - 2 ) is 40

Given the following expression 3 × f( - 4 ) - 3 × g( - 2 ), to find the required values, we can assume that;

f( - 4 ) = 15

g( - 2 ) = 5

Substitute the given parameters into the expression to have:

3 × f(- 4 ) - 3 × g(- 2) = 3 × 15 - 3 × 5

= 45 - 5

= 40

Hence the value of the 3 × f( - 4) - 3 × g( - 2) is 40

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Carmen invested $2,000 in a mutual fund that is front-loaded, with a loading rate of 4.75 %. What was the
loading charge of this fund? (3 points)

Answers

Answer:

$95

Step-by-step explanation:

Carmen invested $2,000 in a mutual fund with a loading rate of 4.75%. To calculate the loading charge, we can multiply the amount invested by the loading rate: $2,000 * 4.75% = $95. So, the loading charge for this mutual fund was $95.

This is an example of a(n)

Answers

Answer:

shape

Step-by-step explanation:

Add 2 1/3 + 4 5/8 writ your answer as a mixed number

Answers

Usually, a mixed number is the simplest way to express an improper fraction – but sometimes, the fraction ... Don't express the answer as a decimal. Instead ... So, add the whole number back in to get a final result of 6 1/2. ... Write out the factors for the numerator of your fraction, then write out the factors for the denominator.

the expression when c=56 and d=10

Answers

The numeric value of the expression 3c + 4d when c = 56 and d = 10 is given as follows:

208.

How to calculate the numeric value of a function or of an expression?

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The expression for this problem is given as follows:

3c + 4d.

Hence the numeric value of the expression is given as follows:

3 x 56 + 4 x 10 = 208.

Missing Information

The expression is:

3c + 4d.

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If f(x) is defined as follows, find (a) f(-3), (b) f(0), and (c) f(4).
x²
if x < 0
if x = 0
3x + 3 ifx>0
f(x) = 0
(a) f(-3)= (Simplify your answer.)
THE

Answers

For the given question the values,

f(-1) = 1f(0) = 0f(3) = 13

Given value of the function when the condition for x is less than '0' is =

f(x) = x² for x < 0

The value of the function when the condition x is equals to '0' is =

f(x) = 0 for x = 0

The value of the function when the condition x is greater than '0' is =

f(x) = 3x + 4 for x > 0

From the above information,

To find f(-1) we have to use the x value as x². So, f(-1) = (-1)² = 1

To find f(0) we have to use x value as 0. So, f(0) = 0

To find f(3) we have to use the x value as 3x + 4. So, f(3) = 3(3) + 4 = 13.

From the above analysis, we find the values of f(-1), f(0), and f(3).

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Question is in the image. Please help me solve these

Answers

Answer:

Step-by-step explanation:

Find the exact value of each of the remaining trigonometric functions of θ.
tan θ= -3/5, sec θ>0.

Answers

If given trigonometric functions of θ are tan θ= -3/5, sec θ>0, the exact value of sin θ is 3/√(34).

To find the value of sin θ, we can use the Pythagorean identity: sin²θ + cos²θ = 1.

First, we need to find the value of cos θ. We know that sec θ = 1/cos θ and sec θ > 0, which means that cos θ > 0. Therefore, we can use the identity: tan²θ + 1 = sec²θ to find the value of cos θ.

tan θ = -3/5

tan²θ = 9/25

sec²θ = tan²θ + 1 = 34/25

cos²θ = 1/sec²θ = 25/34

cos θ = √(25/34) = 5/√(34)

Now, we can use the Pythagorean identity to find sin θ:

sin²θ + cos²θ = 1

sin²θ = 1 - cos²θ

sin²θ = 1 - 25/34

sin²θ = 9/34

sin θ = √(9/34) = 3/√(34)

In trigonometry, the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) are used to relate the angles of a triangle to its sides. The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words, sin θ = opposite/hypotenuse.

Knowing the value of sin θ is important because it allows us to calculate the values of the other trigonometric functions. For example, cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse, so we needed to find the value of cos θ to calculate sin θ.

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Please help me!

Sloan keeps quarters and dimes in a jar, he just counted and has $23.45. If Sloane has 52 dimes in the jar, how many quarters does he have?

Answer in standard form, NEED EQUATION

x =
y =

Answers

Sloan has 73 quarters and 52 dimes kept in the jar

What is an equation?

An equation is an expression that shows how numbers and variables using mathematical operators.

Let x represent the number of quarters in the jar.

1 dime = $0.10, and 1 quarter = $0.25

Hence:

He counted $23.45, of which he had 52 dimes, hence:

0.10(52) + 0.25x = 23.45

5.2 + 0.25x = 23.45

x = 73

Sloan has 73 quarters

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Consider the five points
(0,0),(0,5),(6,0),(3,4),(−1,8)
in
R
2

and name them
(x
i

,y
i

)
for
i=1,…,5
. The objective is to find two coefficients
a,b∈R
such that the boundary of the ellipse
ax
2
+by
2
=1
is as close to the above 5 points as possible. To this end, we define the error function: \[ f(a, b)=\sum_{i=1}^{5}\left(a x_{i}^{2}+b y_{i}^{2}-1\right)^{2} \] Calculate the optimal values of
(a,b)
by finding the local minima of the error function
f(a,b)
.

Answers

The optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).

What is a function?

A function is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output.

To find the optimal values of (a,b), we need to minimize the error function f(a,b). We can do this by taking partial derivatives of f(a,b) with respect to both a and b, and then setting them equal to zero:

∂f/∂a = 2∑([tex]x_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex]+ b [tex]y_{i}^{2}[/tex] - 1) = 0

∂f/∂b = 2∑([tex]y_{i}^{2}[/tex])(a [tex]x_{i}^{2}[/tex] + b [tex]y_{i}^{2}[/tex] - 1) = 0

We can simplify these equations by defining the following sums:

Sxx = ∑[tex]x_{i}^{4}[/tex]

Syy = ∑[tex]y_{i}^{4}[/tex]

Sxy = ∑[tex]x_{i}^{2}y_{i}^{2}[/tex]

Sx = ∑[tex]x_{i}^{2}[/tex]

Sy = ∑[tex]y_{i}^{2}[/tex]

Using these sums, we can rewrite the partial derivatives as:

∂f/∂a = 2(aSx² + bSxy² - Sx)

∂f/∂b = 2(aSxy² + bSy² - Sy)

Setting these equal to zero and solving for a and b, we get:

a = (SySx - Sxy²) / (SxSyy - Sxy²)

b = (SxSy - Sxy²) / (SxSyy - Sxy²)

Plugging in the values for Sxx, Syy, Sxy, Sx, and Sy, we get:

a = 0.7205

b = 0.5369

Therefore, the optimal values of (a,b) that minimize the error function f(a,b) are approximately (0.7205, 0.5369).

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If your starting salary is $50,000 and you receive a 4% increase at the end of
every year, what is the total amount, in dollars, you will earn over the first 16
years that you work?
Round your answer to the nearest whole dollar, and express your answer
without using commas.
Answer here
SUBMIT

Answers

Answer:

Total amount of becomes after 16 year is $93649 .

100 Points! Algebra question. Only looking for an answer to B. Please show as much work as possible. Thank you! Photo attached.

Answers

The quotient of functions f(x) and g(x) is given as follows:

(f/g)(x) = (x + 4)/(x - 3).

How to obtain the quotient function?

The quotient function of f(x) and g(x) is given by the division of function f(x) by function g(x), as follows:

(f/g)(x) = f(x)/g(x)

The functions for this problem are given as follows:

f(x) = x² + 7x + 12.g(x) = x² - 9.

The functions can be factored as follows:

f(x) = (x + 4)(x + 3) -> according to it's roots.f(x) = (x + 3)(x - 3) -> subtraction of perfect squares.

The term (x + 3) is common to both numerator and denominator, hence it is simplified and the quotient function is given as follows:

(f/g)(x) = (x + 4)/(x - 3).

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[5 (8^1/3 + 27^1/3)^3]^1/4 simplify

Answers

Answer

Solution

[5 (8^1/3 + 27^1/3)^3]^1/4

= [5 ((2^3)^1/3) + (3^3)^1/3)^3]^1/4

= [5((2+3)^3)1/4

= (5×5^3)^1/4

= (5^4)^1/4

= 5

I need help, I’m struggling with 3 and 4 can someone help me

Answers

Answer:

3 and 4 ==> see work below

[tex]5. \quad\quad f^{-1}(x) = x^{1/7}[/tex]

[tex]6. \quad\quad f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]

Step-by-step explanation:

Definition of inverse functions

If f and g are inverse functions, then f(x) = y if and only if g(y) = x

Or, in other words
If f(g(x)) = (g(f(x)) = x
then f and g are inverse functions

We have f(x) = x + 4 and g(x) = x - 4

To find f(g(x)), substitute g(x) = x - 4 wherever there is an x term in f(x)

f(g(x)) = g(x) + 4

= x - 4 + 4 = x

g(f(x)) = f(x) - 4

= x + 4 - 4 =x

Hence f(x) and g(x) are inverse functions

[tex]f(x) = \dfrac{1}{4}x^3\\\\g(x) = (4x)^{1/3}[/tex]

[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\\\\end{aligned}[/tex]

[tex]\begin{aligned}(g(x))^3 &= \left((4x)^{1/3} \right)^3 \\& = (4x)^{\frac{1}{3} \cdot 3}\\& = 4x\end{aligned}[/tex]

Therefore

[tex]\\\begin{aligned}f(g(x)) &= \dfrac{1}{4} (g(x))^3\\&= \dfrac{1}{4} \cdot 4x\\&= x\\\end{aligned}[/tex]

[tex]\begin{aligned}g\left(f(x)\right) & = \left(4f(x)\right)^{1/3}\\&= \left(4 \cdot \dfrac{1}{4}x^3\right)^{1/3}\\& = \left(x^3\right)^{1/3}\\& =x& \end{aligned}[/tex]

So f(x) and g(x) are inverse functions

[tex]\text{Given $f(x) = x^7 $ we are asked to find inverse $f^{-1}(x)$}[/tex]

[tex]\rm{Let \: y = f(x) = x^7}\\[/tex]

Interchange x and y:
[tex]x = y^7[/tex]

Solve for y:
[tex]y = x^{1/7}[/tex]

The right hand side is the inverse function of f(x)

[tex]f^{-1}(x) = x^{1/7}[/tex]

Q6
[tex]\rm{Given \;f(x) = -\dfrac{2}{5}x^3 \:find\:the\:inverse,\;f^{-1}(x)}[/tex]

Using the same procedure as for Q5

[tex]y=-\dfrac{2}{5}x^3\\\\x=-\dfrac{2}{5}y^3\\\\\text{Solve for y}\\[/tex]

[tex]y^3=-\dfrac{5x}{2}[/tex]

[tex]y=-\left(\dfrac{5x}{2}\right)^{1/3}\\\\\\\text{Inverse of $f(x)$ is $f^{-1}(x) = -\left(\dfrac{5x}{2}\right)^{1/3}$}\\\text{We can also write this as $-\sqrt[3]{\frac{5x}{2}}$ }\\[/tex]

You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.

Answers

In a case wehereby you have $12,000 to invest and want to keep your money invested for 8 years the investment option that will earn you the most money is c.4.175% compounded annually

What is investment compounded annually?

When an investment is compounded annually, it means that the interest earned on the investment is added to the principal amount once a year, and the interest is then calculated on the new total amount for the next year.

For example, if you invest $12,000 at an annual interest rate of 8%, compounded annually, at the end of the first year you will earn the interest of ( $12,000 x 8%) = $960

Then new total amount after one year will be $12,000 + $960 = $12 960 ,

This process will continue for each year of the investment and the formula to calculate the future value (FV) of an investment compounded annually is: FV = P(1 + r)^n

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complete quesation:

You have $12,000 to invest and want to keep your money invested for 8 years. You are considering the following investment options. Choose the investment option that will earn you the most money.

3.99% compounded monthly

4% compounded quarterly

4.175% compounded annually

4.2% simple interest

The line plots represent data collected on the travel times to school from two groups of 15 students.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.

A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.

Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.

Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16

Answers

The correct option regarding which bus has the least spread among the travel times is given as follows: Bus 14, with an IQR of 6.

How to solve

The interquartile range is a better measure of spread compared to the range of a data-set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed by the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed by the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.'

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Hence Bus 14 is the more consistent bus, due to the lower IQR.