Graph comparison:
In the image (at the end, below) you can find the function [tex]f (x) = 3^{x}[/tex] and [tex]g(x) = log_{3} x[/tex]
a) Which curve represents the graph of the function f (x)? And g (x)?
b) What is the relationship between f (x) and g (x)?
![Graph Comparison:In The Image (at The End, Below) You Can Find The Function [tex]f (x) = 3^{x}[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/6tPmUJvHJvPHS1YRACEZrMuLRjqop0xU.jpeg)
Answers
9514 1404 393
Answer:
a) left curve: f(x); right curve: g(x)
b) the functions are inverses of each other
Step-by-step explanation:
(a) An exponential function with a base greater than 1 has increasing slope. A log function has decreasing slope. The exponential function is on the left.
__
(b) The base of the exponential is the same as the base of the logarithm, so these functions are inverses of each other. This can be seen in the fact that each is a reflection of the other in the line y=x.
![Graph Comparison:In The Image (at The End, Below) You Can Find The Function [tex]f (x) = 3^{x}[/tex]](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/NSbNaUyweyk7eBNcnGMjzSrBw2H9ryD6.jpeg)
Related Questions
g(x) = 2x
Find g(g(-3))
Answers
Question
Find the third degree polynomial function that has an output of 320 when x = 4, and has zeros 2 and
-8i
Answers
Answer:
[tex]f(x)=2(x-2)(x^2+64)[/tex]
Step-by-step explanation:
A standard polynomial in factored form is given by:
[tex]f(x)=a(x-p)(x-q)...[/tex]
Where p and q are the zeros.
We want to find a third-degree polynomial with zeros x = 2 and x = -8i and equals 320 when x = 4.
First, by the Complex Root Theorem, if x = -8i is a root, then x = 8i must also be a root.
Therefore, we acquire:
[tex]f(x)=a(x-(2))(x-(-8i))(x-(8i))[/tex]
Simplify:
[tex]f(x)=a(x-2)(x+8i)(x-8i)[/tex]
Expand the second and third factors:
[tex]=(x+8i)x+(x+8i)(-8i)\\\\=(x^2+8ix)+(-8ix-64i^2)\\\\=(x^2)+(8ix-8ix)+(-64i^2)\\\\=x^2-64(-1)\\\\ =x^2+64[/tex]
Hence, our function is now:
[tex]f(x)=a(x-2)(x^2+64)[/tex]
It equals 320 when x = 4. Therefore:
[tex]320=a(4-2)(4^2+64)[/tex]
Solve for a. Evaluate:
[tex]320=(2)(80)a[/tex]
So:
[tex]320=160a\Rightarrow a=2[/tex]
Our third-degree polynomial equation is:
[tex]f(x)=2(x-2)(x^2+64)[/tex]
Answer:
f(x)=2(x-2)(x^2+64)
Step-by-step explanation:
can anyone help me with this answer?
Answers
Answer:
6m-2m+12 and 4(m+3)
Step-by-step explanation:
4(m+12)=4m+48❎
3m-m+12=2m+12❎
6m-2m+12=4m+12✅
4(m+3)=4m+12✅
Describe what happens to the exponential function when the value of "k" is
positive. *
Answers
Answer:
Step-by-step explanation:It isn’t. There are really 4 different versions of the exponential function. Positive (like the growth of money invested at 5%), negative (like the US debt constantly becoming more negative), positive decay (like the half life of a radioactive element), or negative decay ( pay half your loan amount in year 1, 1/4 in year two, 1/8 in year three, you in theory will never pay your loan completely but the debt is growing closer to zero.
Krish and Aanya gor to a restaurant for dinner. Their meals total $13.75. The tax is 5%
a. How much tax is added to the bill?
b. Aanya and Krish want to leave a 15% tip based on their bill and tax combined. How much should they leave?
Answers
Answer:
A) $6.87
B) $3.09
Step-by-step explanation:
45633 seconds en heures minutes et seconds
Answers
Find the rate of change
Answers
Answer:
2
Step-by-step explanation:
the rate of change is Rise/ Run
= Δy / Δx
= (y2 – y1) / (x2 – x1)
= (1 - (-1))/(-1 - (-2))
=2/1
=2
Determine which lines, if any, are parallel? Explain.
PLEASE PLEASE HELP ME ASAP
Answers
Answer:
The 2 on the right because they don't cross and they are straight
Step-by-step explanation:
Recently many companies have been experimenting with telecommuting, allowing employees to work at home on their computers. Among other things, telecommuting is supposed to reduce the number of sick days taken. Suppose that at one firm, it is known that over the past few years employees have taken a mean of 5.4 sick days. This year, the firm introduces telecommuting. Management chooses a simple random sample of 80 employees to follow in detail, and at the end of the year, these employees average 4.5 sick days with a standard deviation of 2.7 days.
a) Describe the population in the context of this problem
b) Describe the parameter u in the context of this problem.
c) Describe the sample in the context of this problem.
d) Describe the statistic in the context of this problem
e) The firm would like to know if there is evidence that the true mean number of sick days for all employees of the firm has decreased after telecommuting was introduced. State the hypotheses. Use ?-0.10.
f) Check the assumptions. If you don't know if an assumption is satisfied based on the information provided, then state "We must assume
g) Calculate the test statistic
h) Find the p-value.
i) Make a decision.
j) State the conclusion in terms of the problem.
Answers
Answer:
A.) Population : All employees at a firm
B.) μ = 5.4
C.) Sample : 80 employees at a firm
D.) Sample mean, x bar = 4.5
Step-by-step explanation:
From the question :
E.)
H0: μ ≥ 5.4
H1 : μ < 5.4
F.)
If Pvalue < α ; Reject H0
G.)
Test statistic :
(xbar - μ) ÷ (s/sqrt(n))
(4.5 - 5.4) ÷ (2.7/sqrt(80))
-0.9 ÷ 0.3018691
= - 2.98
H.)
Pvalue fro Zscore calculator, α = 0.10 = 0.002882
I.)
Decision :
0.002882 < 0.10
Since, Pvalue < α ; We reject the Null
J.)
We Can conclude that the true mean number of sick days for all employees of the firm has decreased after telecommuting was introduced
The most popular pizza at Pavone’s Pizza is the 9-inch personal pizza with one topping. What is the area of a pizza with a diameter of 9 inches?
Answers
Answer:
63.62
Step-by-step explanation:
pie X r^2
Please need help thank you
Answers
Fast Answer - 3x10 and 10
Here is a circle. Points A, B, C, and D are drawn, as
well as Segments AD and BC.
D.
What is the area of the circle, in square units?
Answers
A=pi*4^2
A=50.24 square units
Hope it helps
Mookie Betts of the Boston Red Sox had the highest batting average for the 2018 Major League Baseball season. His average was 0.352. So, the likelihood of his getting a hit is 0.352 for each time he bats. Assume he has five times at bat tonight in the Red Sox-Yankee game. a. This is an example of what type of probability
Answers
Answer:
Binomial probability, with [tex]n = 5, p = 0.352[/tex]
Step-by-step explanation:
For each time Mookie Betts went to bat, there were only two possible outcomes. Either he got a base-hit, or he did not. The probability of getting a hit on each at-bat is independent of any other at-bat. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
His average was 0.352.
This means that [tex]p = 0.352[/tex]
Assume he has five times at bat tonight in the Red Sox-Yankees game.
This means that [tex]n = 5[/tex]
a. This is an example of what type of probability
Binomial probability, with [tex]n = 5, p = 0.352[/tex]
what is 18 + (31-19) x 3
Answers
Answer:
18+(93-57)
18+(36)
54
Step-by-step explanation:
Multiply before addition.Using bodmas
An estimated 1.8 million students take on student loans to pay ever-rising tuition and room and board (The New York Times, April 17, 2009). It is also known that the average cumulative debt of recent college graduates is about $22,500. Let the cumulative debt among recent college graduates be normally distributed with a standard deviation of $7,000. Approximately how many recent college graduates have accumulated a student loan of more than $30,000
Answers
Answer:
Approximately 256,140 recent college graduates have accumulated a student loan of more than $30,000.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Average cumulative debt of recent college graduates is about $22,500, standard deviation of $7,000.
This means that [tex]\mu = 22500, \sigma = 7000[/tex]
Proportion more than 30000.
1 subtracted by the pvalue of Z when X = 30000. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30000 - 22500}{7000}[/tex]
[tex]Z = 1.07[/tex]
[tex]Z = 1.07[/tex] has a pvalue of 0.8577
1 - 0.8577 = 0.1423
Approximately how many recent college graduates have accumulated a student loan of more than $30,000?
0.1423 out of 1.8 million.
0.1423*1.8 = 0.25614 million = 256,140
Approximately 256,140 recent college graduates have accumulated a student loan of more than $30,000.
Higher Order Thinking a carpenter plans to extend the length of rectangular desk by 7 feet. Let x represent the desk's original length. The expression 96 + 7) represents the area of the desk surface where 9 is the width, in feet, and () represents the extended length, in feet, of the desk. The carpenter thinks that the area of the extended portion of the desk is 16 square feet Which choice below includes the expanded form of the area expression for the deck's surface and the correct area of the extended portion of the desk's surface?
a. 10x + 16 and 10k square feet
b. 9x+63 and 9x square feet
c. 9x + 7 and 7 square feet
d. 9x + 63 and 63 square feet
Answers
Answer:
d. 9x + 63 and 63 square feet
Step-by-step explanation:
Given
Original
[tex]Length = x[/tex]
[tex]Width = 9[/tex]
Extended
[tex]Length = x + 7[/tex]
[tex]Width = 9[/tex]
[tex]Area = 9(x + 7)[/tex]
Required
Determine an expression and the value of the extended area
First, we calculate the area of the original desk
[tex]A_1 = x * 9[/tex]
[tex]A_1 = 9x[/tex]
From the given parameters, we have:
[tex]Area = 9(x + 7)[/tex] --- area of the new surface
Open bracket
[tex]Area = 9x + 63[/tex]
The area of the new surface is the summation of the area of the original desk and the area of the extended portion (E)
So:
[tex]Area = A_1 + E[/tex]
Make E the subject
[tex]E= Area - A_1[/tex]
[tex]E= 9x + 63 - 9x[/tex]
[tex]E= 63[/tex]
Hence, the area of the extended portion is 63
On a map, the distance of two inches is equal to ten miles. How many
miles does 4 inches represent on the map?
10
20
30
40
Answers
The cost c (in dollars) for the fuel and maintenance of a go-cart is given by c=9x+1500, where x is the number of rides. It costs $34 per ride. How many rides does it take to break even?
Answers
Step-by-step explanation:=x1430
Which of the following equations has a graph in the
xy-plane for which y is always greater than or equal
to -1 ?
A) y = |x| - 2
B) y = x2 - 2
C) y = (x - 2)2
D) y = x3 - 2
Answers
Answer: (x-2)2
Step-by-step explanation:
The required equation is [tex]y=(x-2)^2[/tex]
The correct answer is an option (C)
What is an equation?"It is a mathematical statement which consists of equal symbol between two algebraic expressions."
For given question,
We have been given four equations.
We need to find an equation for which y is always greater than or equal
to -1.
Consider,
A. y = ∣x∣ - 2
We know that the minimum value of ∣x∣ is 0.
So, the minimum value of y becomes -2
Hence, this is not a required equation.
B. [tex]y=x^{2} -2[/tex]
We know that the square of any number is always positive.
The minimum value of [tex]x^{2}[/tex] is 0.
So, the minimum value of y becomes −2
Hence, this is not a required equation.
C. [tex]y=(x-2)^2[/tex]
We know that the square of any number is always positive.
The minimum value of y is zero.
This means, the y value of equation [tex]y=(x-2)^2[/tex] is always greater than -1.
D. [tex]y=x^3-2[/tex]
We know that [tex]x^3[/tex] can go have negative values. This means it may have value that tends to negative infinity.
This means, the y can be less than -1 and this is not a required equation.
Therefore, the required equation is [tex]y=(x-2)^2[/tex]
The correct answer is an option (C)
Learn more about the equation here:
https://brainly.com/question/13170101
#SPJ2
pls help I'll mark the first person brainliest answer all
Answers
Answer:
4
a. 12
b. 8
c. 30
d. 40
Step-by-step explanation:
each exterior = 360/n
30*n=360
divide both side by 30
Answer is 12
The same apply to others to 4d
so first its 4
a. 12
b. 8
c. 30
d. 40
i will try to explain:
each exterior = 360/n
30*n=360
divide both side by 30
Answer is 12
The same apply to others to 4d
A school buys 1,950 pencils. The pencils are sold in boxes, with 30 pencils in each box. If each box costs $4.05, what is the total cost, in dollars, that the school will pay for the pencils?
Answers
1950/30=65 boxes
Cost of 1 box is =4.05
The cost of 65 boxes=4*65=263.5
Principle $1950 rate 4 1/2% time 9
Answers
Answer:
Interest = [tex] \boxed{\$ 789.75} [/tex]
Explanation:
Interest [I] = principle × rate × time [prt]
______________________________
x% = x/100
a b/c = a + (b/c) = (ac + b) / c
______________________
I = prt
I = ($1,950)(4 ½%)(9)
I = ($1,950)(0.045)(9)
I = ($87.75)(9)
I = ($789.75)
I = $789.75
work out the circumference of this circle
give your answer in terms of pi and state its units
14cm
Answers
Answer:
43.96
Step-by-step explanation:
Well, the first step is finding out the diameter. And then the basic outline is d x 3.14. So I simply just punched in 14 x 3.14 in my calculator.
Answer:
14π cm
Step-by-step explanation:
Circumference of the circle
= 2πr
= 2π(14/2)
= 14π cm
Eric's Dad asks him to figure out the tax on the meal his family just finished eating at their favorite restaurant. The total bill was 57.60 the tax is 7.5%. what is the amount of tax they will pay for this meal?
Answers
Answer:
7.5 percent of 57.60 is 4.32
I hope this helps. :D
2. Write a polynomial function of least degree with rational coefficients so that P(x)=0 has the given root.
4 - 5i
Answers
Answer:
p(x) = x^2 - 8x + 41
Step-by-step explanation:
If a polynomial with rational coefficients has a complex root, then the roots come in complex conjugate pairs. If the polynomial we need to find has the root 4 - 5i, then it must also have its complex conjugate 4 + 5i as a root.
p(x) = [x - (4 - 5i)][x - (4 + 5i)]
p(x) = [(x - 4) + 5i][(x - 4) - 5i]
Now it's a difference of two squares.
p(x) = (x - 4)^2 - (5i)^2
p(x) = x^2 - 8x + 16 + 25
p(x) = x^2 - 8x + 41
PEASE HELP DUE IN 5 MINUTES I WILL MARK YOU BRAINLIST
Find the area of a regular hexagon with side length of 3 ft. Round your answer to the nearest tenth
7.8 ft2
11.7 ft2
23.4 ft2
40.5 ft2
Answers
23.4 ft2
Step-by-step explanation:
jvuctctctcrxrxrxrxrxr
Can someone please give me the answer I will mark u brilliant
Answers
Answer:
p = 16.8
[tex] r \geqslant 5.5[/tex]
Step-by-step explanation:
12)
p + 2.1 = 18.9
p = 18.9 - 2.1
p = 16.8
13)
[tex]r \geqslant 5.5[/tex]
Ecologists wanted to estimate the mean biomass (amount of vegetation) of a certain forested region. The ecologists divided the region into plots measuring 1 square meter each, and they selected a random sample of 9 plots. The mean biomass of the 9 plots was 4.3 kilograms per square meter (kg/m2) and the standard deviation was 1.5 kg/m2 . Assuming all conditions for inference are met, which of the following is a 95 percent confidence interval for the population mean biomass, in kg/m2?
A) 4.3±1.96 (underroot 1.5/3).
B) 4.3±1.96 (1.5/3).
C) 4.3 ± 2.306 (underroot 1.5/9).
D) 4.3±2.3064 (1.5/9).
E) 4.3+2.30/15 (1.5/3).
Answers
Answer:
[tex]4.3 \pm 2.306\frac{1.5}{\sqrt{9}}[/tex], option c
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 9 - 1 = 8
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 8 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.306
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.306\frac{1.5}{\sqrt{9}}[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
Confidence interval:
The confidence interval is the sample mean plus/minus the margin of error. So
[tex]4.3 \pm 2.306\frac{1.5}{\sqrt{9}}[/tex]
The correct answer is given by option c.
I will mark u brainalist
Answers
Answer:
C
Step-by-step explanation:
The cost of 5 notebooks (5x)
Less than (<)
The cost of 3 notebooks (3x)
Plus a 2 dollar pen (2)
All together: 5x < 3x + 2
Matches with the given expression.
Maggie picked 2/5 basket of strawberries and Sally picked 2/4. How much more did Sally pick?
Answers
Answer:
Step-by-step explanation:
2/5 = 0.4
2/4 = 0.5
0.5 - 0.4 = 0.1
Sally picked 1/10 of a basket more than Maggie picked
Answer:
1 this could change depending on how many berries are in each basket
Step-by-step explanation:
2/5 = 0.4
2/4 = 0.5