Mathematics College

Hello! I need some assistance with this homework question for precalculus, please?HW Q5

Answers

Answer 1

Explanation:

We were given the function:

[tex]g(x)=-1+4^{x-1}[/tex]

We are to determine its domain, range and horizontal asymptote. This is shown below:

Domain:

[tex]\begin{gathered} g(x)=-1+4^{x-1} \\ 4^{x-1} \\ when:x=-10 \\ 4^{-10-1}=4^{-11} \\ when:x=1 \\ 4^^{1-1}=4^0=1 \\ when:x=20 \\ 4^{20-1}=4^{19} \\ \text{This shows us that the function is valid for every real number. This is written as:} \\ \left\{x|x∈R\right\} \end{gathered}[/tex]

Range:

[tex]\begin{gathered} g(x)=-1+4^{x-1} \\ \begin{equation*} -1+4^{x-1} \end{equation*} \\ when:x=-10 \\ =-1+4^{-10-1}\Rightarrow-1+4^{-11} \\ =-0.9999\approx-1 \\ when:x=1 \\ =-1+4^{1-1}\Rightarrow-1+4^0\Rightarrow-1+1 \\ =0 \\ when:x=5 \\ =-1+4^{5-1}\Rightarrow-1+4^4\Rightarrow-1+256 \\ =255 \\ \text{This shows us that the lowest value of ''y'' is -1. This is written as:} \\ \left\{y|y>−1\right\} \end{gathered}[/tex]

Horizontal asmyptote:

For exponential functions, the equation of the horizontal asymptote is given as:

[tex]y=-1[/tex]

Related Questions

A linear equation written in the form y = mx + b is in ?

Answers

A linear equation is written in the form

[tex]y=mx+b[/tex]

it is the Slope-intercept form

The points −−5, 11 and r, 9 lie on a line with slope 2. Find the missing coordinate r.

Answers

Solution

[tex]\begin{gathered} Let\text{ }(x_1,y_1),\text{ }(x_2,y_2) \\ Let\text{ }m=slope \\ m=\frac{y_2-y_1}{x_2-x_1} \end{gathered}[/tex][tex]\begin{gathered} If(-5,-11)=\text{ }(x_1,y_1),then\text{ }x_1=-5,\text{ }y_1=-11 \\ (r,9)=\text{ }(x_2,y_2),then\text{ }x_2=r,\text{ }y_1=9 \end{gathered}[/tex]

Using the Slope formula written above;

[tex]\begin{gathered} 2=\frac{9-(-11)}{r-(-5)} \\ 2=\frac{20}{r+5} \\ Cross\text{ }multiply \\ 2(r+5)=20 \\ Expansion\text{ }of\text{ }bracket \\ 2r+10=20 \\ 2r=20-10 \\ 2r=10 \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }2 \\ \frac{2r}{2}=\frac{10}{5} \\ r=5 \end{gathered}[/tex]

Therefore, the missing co-ordinate r is 5.

During a baseball game, Diego thought his team would get 4 runs, and they actually got 7 runs. What was Diego's percent error? Make sure to include a percent sign. (Round to two decimal places)

Answers

Answer:

11 percent

Step-by-step explanation:

No idea to explain

which description compass the domains of function a and function be correctly rest of the information in the picture below please answer with the answer choices

Answers

Given:

Function A: f(x) = -3x + 2

And the graph of the function B

We will compare the domains of the functions

Function A is a linear function, the domain of the linear function is all real numbers

Function B: as shown in the figure the graph starts at x = 0 and the function is graphed for all positive real numbers So, Domain is x ≥ 0

So, the answer will be the last option

The domain of function A is the set of real numbers

The domain of function B: x ≥ 0

Kuta Software Infinie Algebra ? Absolute Value Inequalities Salve each inequality and graph its solution. 61 1 laulsis * -36043 3) m-2/

Answers

Prob 22

7 + | 6v + 7| ≤ 60

then

| 6v + 7| ≤ 53

now eliminate lines ||

6v + 7 ≤ 53

and

6v + 7 ≤ - 53,. 6v ≤ -60

Now solve for x

6v ≤ 47,. v≤ 46/6

also

6v ≥ -47,. v≥ -46/6

Then answer is

-10 ≤ v ≤ -46/6

Graph for problem 22

If students only know the radius of a circle, what other measures could they determine? Explain how students would use the radius to find the other parts.

Answers

Radius of the circle : Radius is the distance from the center outwards.

With the help of radius we can determine the following terms:

1. Diameter : Diameter is the twice of radius and it is teh staright line that passes through the center. Expression for the diameter is :

[tex]\text{ Diameter= 2}\times Radius[/tex]

2. Circumference: Circumference of the circle or perimeter of the circle is the measurement of the boundary of the circle. It express as:

[tex]\begin{gathered} \text{ Circumference of Circle=2}\Pi(Radius) \\ \text{ where }\Pi=3.14 \end{gathered}[/tex]

3. Area of Circle: Area of a circle is the region occupied by the circle in a two-dimensional plane. It express as:

[tex]\begin{gathered} \text{ Area of Circle = }\Pi(radius)^2 \\ \text{where : }\Pi=3.14 \end{gathered}[/tex]

4. Center Angle of the Sector: Central angles are subtended by an arc between those two points, and the arc length is the central angle of a circle of radius one. It express as :

[tex]\text{ Central Angle of sector=}\frac{Area\text{ of Sector}}{\Pi(radius)^2}\times360[/tex]

5. Arc length : An arc of a circle is any portion of the circumference of a circle. It express as :

[tex]\text{ Arc Length = }Radius(\text{ Angle Substended by the arc from the centerof crircle)}[/tex]

In the given figure the radius is AO & BO

10. A city has a population of 125,500 in the year 1989. In the year 2007, its population is 109, 185. A. Find the continuous growth/decay rate for this city. Be sure to show all your work.B. If the growth/decay rate continues, find the population of the city in the year 2021.C. In what year will the population of the city reach 97,890? Be sure to show all your work.

Answers

SOLUTION

To solve this question, we will use the compound interest formula.

Which is:

[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ Since\text{ we are dealing with a yearly statistics, n = 1} \end{gathered}[/tex][tex]\begin{gathered} \text{From 1989 to 2007, there is a year difference of 18 years} \\ t=18 \\ A=109,185 \\ P=125,500 \\ We\text{ are looking for the continuous growth rate (r)} \\ \text{Now, we will substitute all these given parameters into the formula } \\ \text{above.} \end{gathered}[/tex][tex]\begin{gathered} 109,185=\text{ 125,500(1-}\frac{r}{100})^{18} \\ \frac{195185}{125500}=\frac{125500}{125500}(1-\frac{r}{100})^{18} \\ 0.87=(1-\frac{r}{100})^{18} \\ \text{take the natural logarithm of both sides:} \\ \ln 0.87=18\ln (1-\frac{r}{100}) \\ -0.1393=18\ln (1-\frac{r}{100}) \\ \frac{-0.1393}{18}=\ln (1-\frac{r}{100})_{}_{}_{}_{}_{} \\ -0.007737=\ln (1-\frac{r}{100}) \\ \end{gathered}[/tex][tex]\begin{gathered} e^{-0.007737}=(1-\frac{r}{100}) \\ 0.9922=1-\frac{r}{100} \\ \frac{r}{100}=1-0.9922 \\ \frac{r}{100}=0.007707 \\ r=100\times0.007707 \\ r=0.771\text{ \%} \end{gathered}[/tex]

The continuous decay rate is 0.771%

Using the same formula:

[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ t=2021-2007=14 \\ P=109,185 \\ n=1 \\ A=\text{?} \\ r=0.771 \\ \text{Substitute all the parameters into the formula above:} \end{gathered}[/tex][tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=109,185(1-\frac{0.771}{100})^{1\times14} \\ A=109,185\times0.89730607 \\ A=97,972.36 \\ A=97,972\text{ (to the nearest person)} \end{gathered}[/tex]

The population of the city in the year 2021 is 97,972.

We will use the same formula:

[tex]\begin{gathered} A=P(1-\frac{r}{100})^{nt} \\ A=97,890 \\ P=125,500 \\ r=0.771 \\ t=\text{?} \\ \text{Substitute all these parameters into the formula above:} \\ \end{gathered}[/tex][tex]\begin{gathered} 97890=125,500(1-\frac{0.771}{100})^t^{} \\ \frac{97890}{125500}=\frac{125500}{125500}(0.99229)^t \\ 0.78=0.99229^t \\ \ln 0.78=t\ln 0.99229 \\ -\frac{0.2485}{\ln 0.99229}=t \\ t=32.101 \\ SO\text{ the year that the population will reach 97,890 will be:} \\ 1989+32.101=2021.101 \\ \text{Which is approximately year 2021.} \end{gathered}[/tex]

Margie uses 36 inches of lace to make one pillow. She makes 24 pillows for the school fair. How many total inches of lace does Margie use on the pillows?

Answers

Margie used a total of 264 inches of lace for the 24 pillows

How to calculate the total inches of lace used ?

Margie used 36 inches of lace for one pillow

She needs to make 24 pillows

The total inches of lace that was used for the 24 pillows can be calculated as follows

= 36 × 24

= 864

Hence Margie used 864 inches of lace for 24 pillows

Answers

The probability that the subject tested negative or did not use marijuana is 145/293.

What is probability?

Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Before we can determine the probability that a certain event will occur, we must first know the total number of outcomes.

As given in the question,

Total positive results are 143 out of which 24 are false, and

total negative results are 150 out of which 5 are false.

We know that,

probability = favorable outcome/ Total outcome

so,

Total outcome = total tests

total tests = 143 + 150

total outcome = 293

and favorable outcome = true negative outcome

true negative outcome = total negative outcome - false negative outcome

true negative outcome = 150 - 5

favorable outcome = 145

Therefore, the probability is equal to 143/293

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2. (02.01 LC)While researching the industry she is interested in, Charlize sees that the average employment rate is 97.3%. How many people, out of every 250, are employed? (1point)24.33O 234.66Ο Ο243.25O 256.93

Answers

EXPLANATION

We can compute the average by multiplying the average by 0.973, as shown follows:

[tex]\text{Amount of people}=250\cdot0.973=243.25[/tex]

In conclusion, the amount of people is equal to 243.25

27. Ava surveys teachers for how long it takes them to drive to school eachmorning. She records each response in the dot plot shown.5 10 15 20 25 30 35 40 45 50 55 60Length of Drive (minutes)Ava considers drives of 55 minutes or more as not typical. Given this,which measure of the entire data set represents the most typicaldriving time?meanrangemedianmean absolute deviation

Answers

EXPLANATION

The measure that represent the most typical driving time is the mean.

Section 5.2-4 Graph the following system of equations and find the solution. Plot the solution on the graph. Enter your answer as (x,y). -2x-3y = 0 x+3y = 3 1 2 3 4 5 -1 -2 -3 -4 -5 1 2 3 4 5 -1 -2 -3 -4 -5 Clear All Draw: LineDot Solution =

Answers

For finding y, we can replace the value of x in any equations.

Solution (-3,2)

Plot graphs

The graph shows the relationship between pounds of grapes, g, and their cost, c.

A graph on a coordinate plane shows cost of grapes on the horizontal axis (c), numbered 2 to 6, and pounds of grapes on the vertical axis (g), numbered 1 to 4. Solid circles are at points (0, 0), (2, 1), (4, 2), (6, 3), and are connected by a solid line.

Use the graph to complete the statements.

For every dollar you spend, you can get
0.5
pounds of grapes.

For each pound of grapes, you would need $
.

Answers

For every dollar you spend, you can get 0.5 pounds of grapes.

For each pound of grapes, you would need $2.

How to interpret the graph?

From the coordinates of this graph, we can reasonably infer and logically deduce that it models a straight line, shows a proportional relationship and can be represented by using a linear function.

Mathematically, a proportional relationship can be represented by the following equation:

g = kc

Where:

k is the constant of proportionality.g represent the pounds of grapes.c represent the cost of grapes in dollar.

Next, we would determine the constant of proportionality (k) for the data points shown on this graph as follows:

k = g/c

k = 1/2 or 0.5

Therefore, the linear equation is given by g = 0.5c.

For the amount of dollar needed at g = 1, we have:

g = 0.5c

c = g/0.5

c = 1/0.5

c = $2.

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event a is the event that randomly selected students from your school is make event b is the event that randomly selected students from your school owns a bicycle which of the following do we know for certain correctly represents the probability of selecting a male students or selecting a student who owns a bicycle

Answers

The or probability in the context of this problem is represented as follows:

P(A U B).

Or probability

The or probability between two events A and B is the probability that at least one of the events happen.

The symbol of the or probability is given as follows:

In the context of this problem, the events are given as follows:

Event A: a randomly selected student is male.Event B: a randomly selected student owns a bike.

Hence the probability of selecting a male students or selecting a student who owns a bicycle is represented as follows:

P(A or B) = P(A U B).

The other options are as follows:

P(A ∩ B): both male and own bike, representing the intersection operation of the events.P(A): male.P(B): own bike.

Missing information

The complete problem is given by the image at the end of the answer.

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y=-5x+6y=-3x-2x=y= and the grap

Answers

y = -5x + 6 .................1

y = -3x - 2......................1

first equate the two equations to find x and y

-5x + 6 = -3x - 2

-5x +3x = -2 - 6

-2x = -8

x = -8/-2

x = 4

Next substitute x in equation 1

y = 5(4) + 6

y = 20 + 6

y = 26

Graphically,

y = -5x + 6

for x = 0

y = -5 x 0 + 6

y = 6

for y = 0

0 = -5x + 6

5x = 6

x = 6/5

x = 1.2

fiirst plot the coordinate (0,6) and (1.2,0) on the graph for the first equation to get the first straight line.

y = -3x - 2

x = 0

y = -3 x 0 - 2

y = -2

y = 0

0 = -3x - 2

3x = -2

x = -2/3

x = -0.67

plot the coordinate on the graph

solution for this question is (4,26)

In the diagram, RSTU ~ ABC D. Find the ratio of their perimeterA А.24BR18S36TDCThe ratio of their perimeters is

Answers

The ratio of the perimeters of two similar shapes is equal to the ratio of their corresponding sides, then, by taking the top sides of these figures we can express the following ratio

18 : 24

by dividing both numbers by 2, we get:

9 : 12

Dividing by 3:

3 : 4

Then the ratio of their perimeters equals 3 : 4

If Nintendo had sold 12.2 million games in March and they had thought that they had sold 20.9 million how off was there percent error?

Answers

First let's calculate the absolute error by subtracting both values:

[tex]20.9-12.2=8.7[/tex]

So the absolute error is 8.7 millions.

Now, in order to find the percent error, we just need to divide the absolute error by the number of games sold:

[tex]\frac{8.7}{12.2}=0.7131=71.31\text{\%}[/tex]

So the percent error is 71.31%.

Quadrilateral TUVW is a rhombus and m∠SVU=4z+56°. What is the value of z?WTUVS26°z=°Submit

Answers

From the question, we were told:

TUVW is a rhombus

Angle SUV = 4z + 56˚

We are asked to find the value of z.

From the diagram, we can see that angle SVU is 90˚

So, to get the value of z, we equate the value of SVU to 90˚

4z + 56˚ = 90˚

subtract 56˚ from both sides:

4z + 56 - 56 = 90 - 56

4z = 34

divide both sides by 4 to make z the subject of formula:

z = 34/4

z = 8.5

Which of the following logarithmic expressions have been evaluated correctly?

Answers

Given:

Logarithmic expressions in options.

Required:

Select correct calculated option.

Explanation:

1). ln 1 = 0

2).

[tex]log_29=3.1699250014[/tex]

[tex]log\frac{1}{100}=-2_[/tex]

4).

[tex]log_3(-1)=NaN[/tex]

5).

[tex]log_5\text{ }\frac{1}{125}=-3[/tex]

Answer:

Hence, option A and E are correct.

Sara is 33 years younger than Rolando. The sum of their ages is 105. Select the system of equations if Sara’s age is represented by S and Rolando’s age is represented by R.

Answers

Given:

Sara's age is represented by S and Ronaldo's age is represented by R.

Since,

Sara is 33 years younger than Ronaldo, then;

S= R - 33

Now, the sum of ages of Sara and Ronaldo is 105 then

[tex]R+S=105[/tex]

Hence, from above,

[tex]\begin{gathered} S+R=105 \\ S=R-33 \end{gathered}[/tex]

Therefore, second option is correct.

8You are asked to draw a triangle withside lengths of 10 inches, 7 inches, and2 inches. How many triangles like thiscan you draw?A. OneB. ThreeC. TwoD. Zero

Answers

ANSWER

D. Zero

EXPLANATION

The triangle inequality states that the sum of any two sides of a triangle is greater than the third side,

All these inequalities must be true to be able to form a triangle with the given sides,

[tex]\begin{gathered} 7+10>2\Rightarrow17>2\Rightarrow true \\ 2+10>7\Rightarrow12>7\Rightarrow true \\ 7+2>10\Rightarrow9>10\Rightarrow false \end{gathered}[/tex]

Hence, no triangle can be formed with these side lengths.

144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?

Answers

Problem

144 grapefruits in 4 boxes, How many grapefruits in 100 boxes?

Solution

for this case we can do the following proportional rule:

4/144 = x/100

And solving for x we got:

x= 100 (4/144)= 2.77

So between 2 and 3 grape fruits are expected

the length of a screwdriver is 0.75 cm is how many screws can be placed to the end to make a road that's 18 cm long show yours

Answers

Length of screwdriver = 0.75

Length of road = 18cm

Number of screws that can be placed on a road

[tex]\begin{gathered} =\text{ }\frac{18}{0.75} \\ =\text{ 24} \end{gathered}[/tex]

Given A(-9, -12), B(-2, 2), C(x, 6).and D(-5, -2), find the value ofx so that AB || CD

Answers

[tex]x=-1[/tex]

1) Given these line segments, let's find the slope of them. Let's begin with AB

[tex]m=\frac{2-(-12)}{-2-(-9)}=\frac{14}{-2+9}=\frac{14}{7}=2[/tex]

2) Parallel lines have the same slope, so let's set this slope formula so that we can get the slope m=2. Bearing in mind CD:

[tex]\begin{gathered} 2=\frac{-2-6}{-5-x} \\ 2=\frac{-8}{-5-x} \\ 2(-5-x)=-8 \\ -10-2x=-8 \\ -2x=-8+10 \\ -2x=2 \\ x=-1 \end{gathered}[/tex]

Thus, x=-1

Two liters of soda cost $2.50 how much soda do you get per dollar? round your answer to the nearest hundredth, if necessary.

Answers

If two litters of soda cost $2.50;

Then, a dollar would buy;

[tex]\begin{gathered} =\frac{2}{2.5}\text{litres of soda} \\ =0.80\text{ litres of soda} \end{gathered}[/tex]

Which sequence of transformations will map AABC onto AA' B'C'?A- reflection and translationB- rotation and reflectionC- translation and dilation D- dilation and rotation

Answers

For the given problem, we can observe that the image is bigger than the original diagram.

We can also observe that the image is rotated counterclockwise.

Hence, the sequence of transformation that maps triangle ABC onto triangle A'B'C' is a dilation and a rotation.

Answer: Option D

Hey everybody! Can somebody help me solve this problem? I don't need a big explanation just the answer and a brief explanation on how you get it! Look at photo for problem.

Answers

Given the ordered pairs:

(-12, -16), (-3, -4), (0, 0), (9, 12)

Let's say that the first coordinate corresponds to x, and the second one corresponds to y. Then, the constant of variation k relates x and y as:

[tex]y=k\cdot x[/tex]

Using the ordered pairs:

[tex]\begin{gathered} -16=-12k\Rightarrow k=\frac{4}{3} \\ -4=-3k\Rightarrow k=\frac{4}{3} \\ 0=0\cdot k\text{ (this means that it is correct)} \\ 12=9k\Rightarrow k=\frac{4}{3} \end{gathered}[/tex]

We conclude that the constant of variation is:

[tex]k=\frac{4}{3}[/tex]

Which answer choice shows 3.002 written in expanded form?A) 3 + 0.2B) 3 + 0.02C) 3 + 0.002D) 3+ 0.0002

Answers

SOLUTION

We want to know which answer choice shows 3.002 written in expanded form

To do this let us subtract 3.002 from 3, we have

We got 0.002

So the expanded form is

[tex]3+0.002[/tex]

Hence the correct answer is option C

Corbie earns $2750 paid once a month after taxes.
James gets paid every other week for tutoring at the
local library, and his smallest paycheck in the past six
months was $280.
Their monthly rent for their home is $925 and their most
expensive month for combined utilities last year cost
$325. Their smartphones cost $180 per month. They
spend $120 per week on groceries, $45 per week on
gas,and $620 per month for their car's payment,
insurance, and maintenance savings. James spends
$600 per semester (twice a year) for college tuition.
They each give themselves a $100 per week allowance
for personal expenses such as clothes, haircuts, dining
out, and entertainment.
Calculate their prorated monthly amounts, their monthly
totals, and their cash flow.

Answers

1. Corbie and James' total prorated monthly incomes are Corbie's $2,750 and James' $606.

2. Their combined monthly totals are:

Income = $3,356.

Expenses = $3,111.

3. Their monthly net cash flow is $245.

What is the net cash flow?

The net cash flow is the cash surplus after paying all operating costs.

The net cash flow for Corbie and James is the difference between their total earnings per month and their total expenses per month.

For some income and expenses, there is a proration. Since 52 weeks make up the typical year, each month is considered 4.33 weeks.

1 year = 52 weeks

1 month = 4.33 weeks (52/12)

Monthly Income:

Corbie = $2,750

James = $606 ($280 x 26/52 x 4.333)

Total income = $3,356

Monthly Expenses:

Rent = $925

Utilities = $325

Phones = $180

Groceries = $520 ($120 x 4.33)

Gas = $195 ($45 x 4.33)

Tuition = $100 ($600 x 2)/12

Incidentals = $866 (200 x 4.33)

Total expenses = $3,111

Net Cash Flow = $245 ($3,356 - $3,111)

Thus, whereas, Corbie and James earn a combined and prorated monthly income of $3,356, their total monthly expenses of $3,111 leave them with a net cash flow of $245.

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a lampshade has a radius of 9in what is the circumference of the top of the shade use 3.4 to approximate Pi round your answer to the nearest whole number

Answers

The top of the lampshade is circular in shape

[tex]\begin{gathered} \text{The circumference of a circle = 2}\pi r \\ \text{where }\pi=3.14,\text{ r= radius of the circle} \\ \text{The radius , r=9 in} \\ \text{Circumference = 2 x 3.14 x }9 \\ \text{Circumference = }56.52\text{ in} \end{gathered}[/tex]

The circumference of the top of the shade is 56.52 inches

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