write a rule for $g$g that represents a translation 3 units right and 1 unit up, followed by a horizontal stretch by a factor of 8 of the graph of $f\left(x\right)=\ln x$f(x)=lnx .
Answers
The rule for g(x) is g(x) = ln((x/8) - 3) + 1.
A translation in math moves a shape left or right and/or up or down. The translated shapes look exactly the same size as the original shape, and hence the shapes are congruent to each other. They just have been shifted in one or more directions.
To write a rule for g(x) that represents a translation 3 units right and 1 unit up, followed by a horizontal stretch by a factor of 8 of the graph of f(x) = ln(x), proceed as follows:
1. Translate 3 units right by replacing x with (x - 3) in the original function:
f(x - 3) = ln(x - 3).
2. Translate 1 unit up by adding 1 to the translated function:
f(x - 3) + 1 = ln(x - 3) + 1.
3. Apply a horizontal stretch by a factor of 8 by replacing x with x/8 in the translated function:
f((x/8) - 3) + 1 = ln((x/8) - 3) + 1.
The complete question is:
"What is the rule for g that represents a translation of 3 units to the right and 1 unit up, followed by a horizontal stretch by a factor of 8, applied to the graph of f(x) = ln x?"
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Related Questions
Create an equation that meets the following criteria:
•Contains the variable x on both side of the equation
•Uses at least 2 inverse operations to solve
To receive full points, you must write out your equation and show ALL the steps to solving it to get the correct solution
I’ll give brainlist to the person who follows the instructions to the T
Answers
Answer:
4x+9=x+15
x = 2
Step-by-step explanation:
Let's solve this equation I just made:
4x + 9 = x + 15
Subtract 9 from each side:
4x = x + 6
Subtract x from each side:
3x = 6
Divide each side by 3:
x = 2
The following data was obtained from the entire population in small town of Texas. Individuals were classified into whether they were of normal weight or overweight based on the Body Mass Index (BMI). Cholesterol levels were also measured from every individual and classified as high or low. High cholesterol Low cholesterol Overweight 324 450 Normal weight 368 890 Calculate the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol.
Answers
If the number of people who are overweight and have high cholesterol is 324, the number of people who are overweight and have low cholesterol is 450, the number of people who are normal weight and have high cholesterol is 368, and the number of people who are normal weight and have low cholesterol is 890, then the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol is 46.8%
To find the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol, follow these steps:
Let A be the event of selecting an individual who is overweight and B be the event of selecting an individual who has high cholesterol. The formula for calculating conditional probability, P(A/B) = P(A ∩ B) / P(B), where P(A∩B) represents the probability of the intersection of A and B events and P(B) represents the probability of the occurrence of event B.P(A/B) = P(overweight ∩ high cholesterol) / P(high cholesterol) ⇒P(high cholesterol) = total number of individuals with high cholesterol / Total population= (324 + 368) / (324 + 450 + 368 + 890)= 692 / 2032P (overweight ∩ high cholesterol) = Number of overweight individuals with high cholesterol / Total population= 324 / 2032∴ P(A/B) = P(overweight ∩ high cholesterol) / P(high cholesterol)= 324 / 692= 0.468 = 46.8%Hence, the conditional probability of sampling an individual that is overweight given that the individual has high cholesterol is 46.8%.
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find the midpoint of a segment with endpoints A(3,4) and B(-1,2)
Answers
find the euler equation that represents the relationship between current-period consumption and future-period consumption in the optimum.
Answers
The Euler equation represents the relationship between current-period consumption and future-period consumption in the optimum. It is derived from intertemporal optimization in economics.
In the context of consumption, the Euler equation can be expressed as:
u'(Ct) = β * u'(Ct+1)
where:
- u'(Ct) represents the marginal utility of consumption in the current period,
- Ct represents current-period consumption,
- β is the discount factor representing the individual's time preference,
- u'(Ct+1) represents the marginal utility of consumption in the future period.
This equation states that the marginal utility of consumption in the current period is equal to the discounted marginal utility of consumption in the future period. It implies that individuals make consumption decisions by considering the trade-off between present and future utility.
Note: The Euler equation assumes a constant discount factor and a utility function that is differentiable and strictly concave.
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What is the value of x to the nearest tenth?
In a triangle, acute angle is 28 degree and the obtuse angle is 126 degree. The adjacent side of 28 degree angle is 8. 2 and opposite side is x.
A. 4. 8
B. 7. 7
C. 8. 8
D. 14. 1
Answers
Answer:
8.8
Step-by-step explanation:
jus did da math
How do you find the midpoint of a line segment with a ratio?
Answers
The midpoint of the given line segment can be determined by using the formula ( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ] .
As given in the question,
Let the two endpoints of the given line segment be A(x₁ , y₁) and B(x₂ ,y₂).
As per midpoint concept it divides the given line segment in the equal ratio.
let the given line segment AB divided in the equal ratio of n : n
Consider the coordinates of the required mid point be ( x , y ) :
using midpoint formula we have :
( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ]
If the point divides the given line segment in the ratio 2 : 2
The required midpoint is given by
(x ,y ) = [ (2x₁ + 2x₂ )/2(2) , (2y₁ + 2y₂ )/2(2)]
= [ (x₁ + x₂ )/2 ) , (y₁ + y₂ )/2 ]
Therefore, the required midpoint which divides the given line segment into equal parts is ( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ].
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4. The Conner family has created a budget for their $3,000 monthly income. Based on the budget below, which statement is not true? RENT FOOD UTILITIES CAR INSURANCE SAVINGS AMOUNT (5) $900 $550 $200 $300 $450 $600
F. the car accounts for 10% of the budget
G. the rent and savings account for more than 50% of the budget
H. savings accounts for 20% of the budget
J. insurance accounts for 15% of the budget
Answers
Answer:
i have the same question
Step-by-step explanation:
i have the same question
a drawing class was assigned a final project where students had to choose one art medium and one genre. the professor kept track of the types of projects submitted. portrait landscape acrylic paint 3 4 oil paint 2 2 what is the probability that a randomly selected student used acrylic paint given that the student chose to create a portrait? simplify any fractions.
Answers
The probability that a randomly selected student used acrylic paint given that the student chose to create a portrait is 3/5 or 60%.
To find the probability that a randomly selected student used acrylic paint given that the student chose to create a portrait, you can use the conditional probability formula:
P(Acrylic Paint | Portrait) = P(Acrylic Paint and Portrait) / P(Portrait)
From the given data:
- There were 3 students who used acrylic paint and created a portrait.
- There were a total of 5 students who created a portrait (3 with acrylic paint and 2 with oil paint).
So, the probability calculation would be:
P(Acrylic Paint | Portrait) = (3/5) / (5/5) = 3/5
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A block of ice in the shape of a cube melts uniformly maintaining its shape. The volume of a cube given a side length is given by the formula V = S^3. At the moment S = 2 inches, the volume of the cube is decreasing at a rate of 5 cubic inches per minute. What is the rate of change of the side length of the cube with respect to time, in inches per minute, at the moment when S = 2 inches?
Answers
Answer:
Ds/dt = 1,25 in/minute
Step-by-step explanation:
s is side of the cube
V(c) = s³
Differentiation on both sides of the equation with respect to time.
DV(c) / dt = 2*s* Ds/dt (1)
In that equation:
s = 2
DV(c) /dt = 5
By subtitution in equation (1)
5 = 2*s*Ds/dt
2*2*Ds/dt = 5
Ds/dt = 5/4 Ds/dt = 1,25 in/minute
The rate of change of the side length of the cube with respect to time, in inches per minute, at the moment when S = 2 inches is \(\dfrac{5}{12} \: \rm in^3/min\)
How to calculate the instantaneous rate of growth of a function?Suppose that a function is defined as;
\(y = f(x)\)
Then, suppose that we want to know the instantaneous rate of the growth of the function with respect to the change in x, then its instantaneous rate is given as:
\(\dfrac{dy}{dx} = \dfrac{d(f(x))}{dx}\)
Let the rate of change of volume V with respect to time t is given by:
\(\dfrac{dV}{dt}\)
And let the rate of change of volume S with respect to time t is given by:
\(\dfrac{dS}{dt}\)
The relation between V and S is \(V = S^3\). Using this value, and the chain rule of differentiation, we get:
\(\dfrac{dV}{dt} = \dfrac{dS^3}{dt} = 3S^2\dfrac{dS}{dt} = 3S^2\dfrac{dS}{dt}\\\\\dfrac{dS}{dt} = \dfrac{1}{3S^2} \dfrac{dV}{dt}\)
At S = 2, we are given that: \(\dfrac{dV}{dt} = 5 \: \rm in^3/min\)
Putting these values in the equation for rate of S, we get:
\(\dfrac{dS}{dt} = \dfrac{1}{3S^2} \dfrac{dV}{dt}\\\\\dfrac{dS}{dt} = \dfrac{1}{3(2)^2}\times 5 = \dfrac{5}{12} \: \rm in^3/min\)
Thus, the rate of change of the side length of the cube with respect to time, in inches per minute, at the moment when S = 2 inches is \(\dfrac{5}{12} \: \rm in^3/min\)
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The exam scores (out of 100 points) for all students taking an introductory Statistics course are used to construct the following boxplot. Box plot About 25% of the students scores exceeded
Answers
About 75% of the students' scores exceeded the score mentioned in the boxplot.
In a boxplot, the box represents the interquartile range (IQR), which contains the middle 50% of the data. The lower whisker extends to the minimum value within 1.5 times the IQR below the first quartile (Q1), and the upper whisker extends to the maximum value within 1.5 times the IQR above the third quartile (Q3).
Since the boxplot does not provide specific numerical values, we can infer that the mentioned score lies within the upper whisker, which represents the top 25% of the data. Therefore, about 75% of the students' scores exceeded this score.
It's important to note that without the actual values or specific percentiles, we can only estimate the percentage based on the visual representation of the boxplot. The exact percentage may vary depending on the scale and distribution of the data. To obtain a more precise estimate, additional information such as the quartiles or a histogram of the scores would be needed.
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15 POINTS! (sorry this question deserves way more than 15 points but it's all I have rn) BE A ANGEL AND HELP ME PLEASE, AND THANK YOU I LOVE YOU SM IF YOU DO I APPRERCIATE YOU!!!
1. What is the range of the function y = x^2?
a. all real numbers
b. x ≥ 0
c. y ≥ 0
2. In which quadrants is the ordinate positive?
a. I and II
b. II and III
c. I and IV
3. Which of the following ordered pairs lies on the graph of h(x) = -2x^2?
a. (1, -4)
b. (1, -2)
c. (1, 4)
4. Select all of the following points that lie on the graph of f(x) = 7 - 3x.
(-2, 1) (-1, 10) (0, 7) (1, 5) (2, 1)
5. The set of independent variables of a function is the
a. domain
b. range
c. relation
6. If h(x) = 5 for the function h(x) = 2x + 1, what is the value of x?
a. 2
b. 11
c. 12
7. Find f(6) if f(x) = x^2 ÷ 3 + x.
a. 4
b. 10
c. 18
8. (-3, 5) is located in _____.
a. Quadrant I
b. Quadrant II
c. Quadrant III
d. Quadrant IV
Answers
Answer:
i know number 8 is B but that's all sorry
Step-by-step explanation:
Solve by factoring.
f(x) = x^2 + 7x + 12
Answers
Help , what is the measure of p
Answers
Answer:
Step-by-step explanation:
let angle p be x
x+27=56 degree (sum of two opposite interior angle is equal to the exterior angle formed)
x=56-27
x=29 degree
therefore p is 29 degree.
A bucket contains 3 3/4 gallons of water. If Ariana adds 5 gallons more, how many gallons will there be in all?
Answers
Total:-
\(\\ \tt\hookrightarrow 3\dfrac{3}{4}+5\)
\(\\ \tt\hookrightarrow \dfrac{15}{4}+5\)
\(\\ \tt\hookrightarrow \dfrac{15+20}{4}\)
\(\\ \tt\hookrightarrow 35/4\)
\(\\ \tt\hookrightarrow 8\dfrac{3}{4}gallons\)
\(\large{|\underline{\mathtt{\red{G}\blue{i}\orange{v}\pink{e}\blue{n}\purple{}\green{}\red{↯}\blue{}\orange{}}}}\)
1 bucket contains 3 3/4 gallons of water
\(\large{|\underline{\mathtt{\red{T}\blue{o}\orange{\:}\pink{F}\blue{i}\purple{n}\green{d}\red{↯}\blue{}\orange{}}}}\)
Total amount of water after adding 5 gallons to it =?
\(\large\underline{\underline{\maltese{\purple{\pmb{\sf{\: Solution :-}}}}}}\)
Here, To find the total amount of water in the bucket after ariana added 5 gallons to it. We need to add 5 to the given amount of water present in the bucket...\( \sf \: 3 \frac{3}{4} + 5\)
\( \sf \: \frac{15}{4} + 5\)
\( \sf \: \frac{15}{4} + 5\)
\( \sf \: 5\frac{15}{4} \)
\( \sf \: \frac{35}{4} \)
➪ Therefore, She will have 35/4 gallons of water in all...~
What can u multiply by 8.6
then divide by two to get
32.25
Answers
Answer:
umm
Step-by-step explanation:
32.25*2=64.50
64.50/8.6=7.5
so the answer is yes
What is the value of x?
Enter your answer as the correct value, like this: 42
If your answer is a fraction, such as 314, enter it like this: 3/14
Answers
Answer:
1/6
Step-by-step explanation:
First, we'll simplify the inside portion of the question.
\(\frac{3^{3/4}}{3^{3/8}} =3^{3/4-3/8}=3^{3/8}\\\)
Next, we are raising this to the 4/9 power.
\((3^{3/8})^{4/9} = 3^{(3/8) * (4/9)} = 3^{1/6}\)
Thus, x = 1/6.
.Suppose there is a coin. You assume that the probability of head is 0.5 (null hypothesis, H0). Your friend assumes the probability of head is greater than 0.5 (alternative hypothesis, H1). For the purpose of hypothesis testing (H0 versus H1), the coin is tossed 10,000 times independently, and the head occurred 5,002 times.
1.) Using the dbinom function, calculate the probability of this outcome. (Round your answer to three decimal places.
2.) We meet the mutually exclusive condition since no case influences any other case.
True
False
Answers
The probability of observing 5,002 heads out of 10,000 tosses, assuming a probability of 0.5 for each toss, is calculated using the binomial distribution as P(X = 5,002) = dbinom(5,002, 10,000, 0.5) (rounding to three decimal places). The statement "We meet the mutually exclusive condition since no case influences any other case" is false. The independence of coin tosses does not guarantee that the outcomes are mutually exclusive, as getting a head on one toss does not prevent getting a head on another toss.
To calculate the probability of observing 5,002 heads out of 10,000 tosses, assuming a probability of 0.5 for each toss, we can use the binomial distribution. The probability can be calculated using the dbinom function in R or similar software. Assuming the tosses are independent, the probability is:
P(X = 5,002) = dbinom(5,002, 10,000, 0.5)
False. The statement "We meet the mutually exclusive condition since no case influences any other case" is not necessarily true. The independence of the coin tosses does not automatically guarantee that the outcomes are mutually exclusive. Mutually exclusive events are those that cannot occur at the same time. In this case, getting a head on one toss does not prevent getting a head on another toss, so the outcomes are not mutually exclusive.
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It takes a team of 9 builders 10 days to build a wall. How many extra days will it take a team of 5 builders to build the same wall? Assume that all builders are working at the same rate. Optional working Answ extra days
Answers
Please help!! Need this turned in!! In the picture!!
Answers
Answer:
I hope this helps please name me brainliest
Step-by-step explanation:
which ordered pair is a solution to the system of inequalities? help pls
Answers
Answer:
A
Step-by-step explanation:
I got this answer hope it work.
A country has 33 parks that allow camping and 101 parks that have
playgrounds. Of those, 16 parks both allow camping and have
playgrounds. The country has a total of 346 parks.
What is the probability of randomly selecting a park that allows
camping or has a playground? Write your answer as a fraction.
Answers
Answer:
134:346 Add the 33 to 101 to get first number, then total number of parks 346 is the second number, they may end up wanting you to to reduce the fraction.67:143
The sum of a number and 4
Answers
take that number than 'n' {I didn't use x or y for a reason}
n +4 = 4n
Step-by-step explanation:
Brainiest pls
Does anyone know what f(x)=-5x-1 when f(-7) i need help with this please.
Answers
Answer:
f(-7) = 34
Step-by-step explanation:
If f(x) = -5x - 1, then . . .
f(x) = -5x - 1
f(-7) = -5(-7) - 1
= 35 - 1
= 34
. . . because in f(-7), the (-7) is the x-value you're supposed to use to find the value of the function.
Decide which of the following statements are always true. (a) Argz
1
z
2
=Argz
1
+Argz
2
if z
1
=0,z
2
=0. (b) Arg
z
ˉ
=−Argz if z is not a real number. (c) Arg(z
1
/z
2
)=Argz
1
−Argz
2
if z
1
=0,z
2
=0. (d) argz=Argz+2πk,k=0,±1,±2,…, if z
=0.
Answers
The statement (d) is always true: argz = Argz + 2πk, where k = 0, ±1, ±2, ... , if z ≠ 0.
The argument of a non-zero complex number z, denoted as argz, represents the angle between the positive real axis and the line connecting the origin to the point representing z in the complex plane. The principal value of the argument, denoted as Argz, is the value of argz that lies within the range (-π, π]. The statement (d) asserts that any argument of z can be obtained by adding a multiple of 2π to the principal value. This is true because adding 2π to the principal value results in rotating the complex number z by a full circle in the complex plane, which does not change its argument. Adding further multiples of 2π repeats the rotation, again preserving the argument. Therefore, (d) holds for all non-zero complex numbers.
The other statements (a), (b), and (c) are not always true.
(a) Argz1z2 = Argz1 + Argz2 is not always true when z1 and z2 are non-zero complex numbers. The principal values of Argz1 and Argz2 lie within the range (-π, π], and their sum may exceed this range. Therefore, the equality does not hold in general.
(b) Argz bar = -Argz is not always true when z is not a real number. The complex conjugate of a non-real complex number z, denoted as zbar, has the same magnitude but the opposite argument. The principal value of the argument changes sign under conjugation, but the equality -Argz = Argz bar does not hold for all non-real complex numbers.
(c) Arg(z1/z2) = Argz1 - Argz2 is not always true when z1 and z2 are non-zero complex numbers. The argument of a complex division is obtained by subtracting the argument of the denominator from the argument of the numerator. However, the principal values of Argz1 and Argz2 lie within the range (-π, π], and their difference may exceed this range. Therefore, the equality does not hold in general.
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Identify whether each equation has one solution, infinitely many solutions, or no solution.
2.3x - 7 = -7
3x = 5 + 3x
4(10 - x) = 40 - 4x
-7 + x = - (x + 7)
Answers
Answer:
1 solution
No solution
Infinitely many solutions
1 solution
Step-by-step explanation:
2.3x - 7 = -7
2.3x = 0
x = 0
1 solution
3x = 5 + 3x
0 = 5
No solution
4(10 - x) = 40 - 4x
40 - 4x = 40 - 4x
Infinitely many solutions
-7 + x = -(x + 7)
-7 + x = -x - 7
2x = 0
x = 0
1 solution
Answer:
he is right
Step-by-step explanation:
Mrs. Archer is doing a painting project with her art class. She uses a large jug with 28.5 ounces of blue paint to fill 6 smaller bottles. If she divides the paint evenly, how much paint will be in each bottle?
Answers
Answer:
4.75
Step-by-step explanation:
Divide 28.5 evenly with 6 because thee are 6 bottles. Then you receive 4.75
Hope this helps
Which value of x satisfies the equation below? 1/2 (3x + 17) = 1/6 (8x-10)
Choice answers:
A. -61
B -55
C. -41
D-35
Answers
What are the lower (Q1) and upper quartiles (Q3) for the following scores?
3,5,5,5,6,8,9,10,11,13,13,14,15,17,18,20
A. Q1 = 5 and Q3 = 15
B. Q1 = 5 and Q3 = 14.5
C. Q1 = 5.5 and Q3 = 15
D. Q1 = 5.5 and Q3 = 14.5
Answers
if the probability that a particular event occurs is 7/10, what are the odds favoring the event not occurring? express your answer in the form a:b.
Answers
For the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to
7 : 3.
As given in the question,
Probability of any particular event occurring is equal to 7 /10
Probability of any particular event not occurring is = 1- (7/10)
= (10 -7) /10
= 3/10
Probability of the odds favoring the events which are not occurring
= (7 /10) / (3/10)
= ( 7 × 10) / (3 × 10)
= 7 /3
Odds favoring the events which are not occurring in the form a: b
= 7 : 3
Therefore, for the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to 7 : 3.
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A rectangular prism has a length of 12 feet, a width of 6 feet, and a height of 2 feet. What is the volume of the prism? Enter your answer in the box. Ft³
Answers
Answer:
144
Step-by-step explanation: