The way that the Great Awakening lead to a new American government is that; The Great Awakening helped the colonists realize they needed their own national religion.
What happened in the period of the great awakening?The Great Awakening was a period in history characterized by religious revival in the US. There were five major Great Awakenings, that occurred between the beginning of 18th and the end of the 20th century. However, the last of the Great Awakenings lasted until the year 2000.
During the years of 1730s and 1740s, it was clear that the English colonies in America went through the Great Awakening which was a religious resurgence. This movement came into play at a period when there was a very huge emphasis on the idea of secular reason and as a result religious zeal had lost its freshness.
The gospel was usually preached by Christian leaders from town to town to stir up interest in Christianity while emphasizing deliverance from sin. The outcome or result was a reinvigorated commitment to religion.
The Great Awakening, in the opinion of many historians, had a profound effect on the American culture as a whole as well as on different Christian denominations.
Read more about Great Awakening at; https://brainly.com/question/10952720
#SPJ1
Help, due tonight at midgnight!
The value of x is given as follows:
x = 14.
What are similar triangles?Similar triangles are triangles that share these two features presented as follows:
Congruent angle measures.Proportional side lengths.Due to the bisection, the two triangles in this problem are similar, hence the equivalent side lengths are given as follows:
x + 2 and 12.24 and 18.The proportional relationship is then given as follows:
(x + 2)/12 = 24/18
Applying cross multiplication, the value of x is obtained as follows:
18(x + 2) = 24 x 12
18x + 36 = 288
x = (288 - 36)/18
x = 14.
More can be learned about similar triangles at brainly.com/question/14285697
#SPJ1
Select all equivialnt expressions from the list
B. 12x-4x+8x
1. 8x+8x
2. 8x-8x
3. 16+x
4. 16x
Answer:
3
Step-by-step explanation:
12x-4x+8x = 16+x
the black population is about a. 25% of the u.s. population b. 20.5% of the u.s. population c. 13.5% of the u.s. population d. 30% of the u.s. population
As per the U.S. population report, the black population is about 13.5% of the total U.S. population.
The black population in the United States refers to the total no people that identify themself as black or African American.
The exact percentage of the black population in the United States can vary based on the source and the methodology used to collect the data, but as of the population report from 2021, it was estimated to be about 13.5% of the total population.
This information can be used to understand the demographic composition of the United States and to help inform decisions about resource allocation, public policy, and other important issues that can affect different populations. it can be also noted that the demographics of a country can change over time, so it is crucial to regularly update this information to ensure that it remains accurate and relevant.
Learn more about U.S. population:
https://brainly.com/question/28538166
#SPJ4
The gateway arch in st. Louis, mo is approximately 630 ft tall. How many u. S. Nickels would be in a stack of the same height? each nickel is 1. 95 mm thick.
The gateway arch in st. Louis, MO is approximately 630 ft tall, the same height of the Nickels would be in a stack is 98474.
Height of Gateway Arch in St. Louis, MO = 630ft tall
We are asked, how many nickels would be in a stack of the same
height when 1 nickel is 1.95 mm thick.
Convert height in ft to mm
1 ft = 304.8 mm
630ft = X
After Cross Multiply,
630ft × 304.8mm/1ft
= 192024 mm.
To find how many nickel would be in a stack of the same height
= Total thickness/ Thickness of 1 US dime
= 192024 mm/1.95mm
= 98473.8
≈98474 nickels
Therefore, the number of nickel that would be in a stack of the same height is 98474.
Learn more about Height problem:
https://brainly.com/question/17438476
#SPJ4
Which is equivalent to (3 √2x³)(√8x³)?
Answer:
Step-by-step explanation: (3 sqrt 2x^3)(sqrt 8x^3) when simplified is 12x^8
The width of a rectangle 4n-9.5 feet and the length is 9.5n+10 feet. Find the perimeter of the rectangle
The perimeter of the rectangle is P = 27n + 1.
What is perimeter?The whole distance encircling a shape is referred to as its perimeter. It is the length of any two-dimensional geometric shape's boundary or outline. Depending on the size, the perimeter of several figures can be the same. Consider a triangle built of an L-length wire, for instance. If all the sides are the same length, the same wire can be used to create a square.
The length of the rectangle is: l = 9.5n+10.
The width of the rectangle is: w = 4n-9.5.
The perimeter of the rectangle is given as:
P = 2(l + w)
P = 2(9.5n + 10 + 4n-9.5)
P = 2(13.5n + 0.5)
P = 27n + 1
Hence, the perimeter of the rectangle is P = 27n + 1.
Learn more about perimeter here:
https://brainly.com/question/6465134
#SPJ1
Alma reads 2 books each week. Which number line best represents the number of weeks it will take her to read at least 28 books?.
Option(c) is the correct answer.
The image is attached below.
According to the question,
Create an inequality from the given details:
( 2x ≥ 28, where x denotes the number of weeks)
Then divide both sides of the inequality by 2, resulting in x ≥ 14, or all values greater than or equal to 14.
Now, choose the number line that shows all numbers greater than or equal to 14 (all the numbers to the right of 14 and including 14, which is indicated by a shaded circle).
Hence, [C} is the correct answer.
Read more about inequality:
https://brainly.com/question/24372553
#SPJ4
A first number plus twice a second number is 10. Twice the first number plus the second totals 14. Find the numbers
Answer:
Below
Step-by-step explanation:
x + 2y = 10 given
2x + y = 14 given multiply this equation by -2 to get :
-4x - 2y = - 28 add to top equation to get
-3x = -18 so x = 6
x + 2y = 10 so y = 2
Manueala scored
−
4
1
2
−4
2
1
minus, 4, start fraction, 1, divided by, 2, end fraction points relative to her season average against the China Dragons. She scored
1
1
2
1
2
1
1, start fraction, 1, divided by, 2, end fraction points relative to her season average against the Canada Moose.
Comparison of Manueala's relative number points:
1 1/2 > - 4 1/2
Manueala scored more points against the China Dragons than against Canada Moose .
The correct answer is A.
What is an inequality?Inequality refers to a relationship that makes a non-equal comparison between two numbers or other mathematical expressions.
Given,
Manueala scores relative to average against China Dragons
= -4 1/2 points
Manueala scores relative to average against Canada Moose
= 1 1/2 points
If Manueala scored x points,
season average against China Dragons is y.
season average against Canada Moose = z
x - y = -4 1/2
x - z = 1 1/2
∵ 1 1/2 > - 4 1/2
∴ x - z > x - y
- z > -y
⇒ z < y
Hence,
Relative scores to both seasons can be written as inequality
1 1/2 > - 4 1/2
Season average against China Dragons is more than season average against Canada Moose.
Learn more about inequality here:
https://brainly.com/question/30228778
#SPJ1
What is the inverse of the function
�
(
�
)
=
−
3
(
�
+
6
)
g(x)=−3(x+6)
what is the equation of a line that passes through point (-2,1) and is perp to y= -5x 2
The equation of the line that passes through (-2,1) and is perpendicular to y = -5x² is y = -10x + 21
The equation of a line is a mathematical representation of the relationship between its x and y values.
In this case, we are given a line that passes through the point (-2,1) and is perpendicular to y = -5x².
To find the equation of this line, we first need to find the slope of the line that is perpendicular to y = -5x².
The slope of a line can be found by finding the derivative of the original equation.
In this case, the derivative of
=> y = -5x² is -10x,
which gives us the slope of -10x.
Since we know that the line passing through (-2,1) is perpendicular to
y = -5x²,
we can use the point-slope form of the equation of a line.
The point-slope form of the equation is given by
=> y - y1 = m(x - x1),
where m is the slope and (x1, y1) is a point on the line.
Plugging in the values, we have
=> y - 1 = -10(x + 2).
We can simplify this equation further by distributing the -10 and combining like terms.
This gives us
=> y - 1 = -10x - 20,
which we can then rearrange to get
=> y = -10x + 21.
To know more about equation here.
https://brainly.com/question/10413253
#SPJ4
Caleb owns two types of dogs. The difference in height of his Yorkshire Terrier and his Great Dane is at least 25 inches. Caleb’s Yorkshire Terrier has a height of 6 ¼ inches. Write and solve an inequality to determine the possible height of the Great Dane. Then interpret the solution
The inequality to determine the height of Great Dane can be expressed as [tex]b-6\frac{1}{4}\geq 25 inches[/tex] and according to that the height of the dog should atleast be 31.25 inches
Let us assume the height of Great Dane as b
if the height of Yorkshire Terrier is 6.25 inches and is atleast 25 inches smaller than Great Dane then the inequality can be represented as
[tex]b-6\frac{1}{4}\geq 25 inches[/tex]
now, on solving this inequality the height of great dane comes out to be atleast 31.25 inches
[tex]b\geq 25+6\frac{1}{4}[/tex] = 31.25 inches
learn more about inequality here:
brainly.com/question/17675534
#SPJ4
Yessica leaves her house on her bicycle to locate a geocache at the same time Zoe leaves her house heading for the same cache. Zoe lives further away than Yessica so she takes her car and travels 12 mph faster than Yessica. Their combined distance traveled is 63 miles. If both women arrive at the geocache site after 90 minutes, find their average speeds
Yessica and Zoe's average speeds are equal to 63 miles/90 minutes, or 0.7 miles/minute.
To solve this problem, we need to use the formula for average speed, which is distance divided by time. We are given the combined distance traveled by both women, which is 63 miles, and the total time they took, which is 90 minutes. We can divide the distance (63 miles) by the time (90 minutes) to get the average speed: 63/90 = 0.7. This means that their average speed was 0.7 miles per minute. This can also be expressed as 42 mph, which is the same as 0.7 miles per minute. To summarize, Yessica and Zoe's average speeds were 0.7 miles per minute or 42 mph.
Learn more about average here
https://brainly.com/question/796053
#SPJ4
WILL MARK THE BRAINLIEST IF CORRECT!
The statement that is true about the graphs include the following: D. both graphs have the same horizontal asymptotes.
What is a horizontal asymptote?In Mathematics, a horizontal asymptote can be defined as a horizontal line (y = b) where the graph of a function approaches the line as the input values (domain or independent value) approach negative infinity (-∞) to positive infinity (∞).
In this context, the line passing through the ordered pair (0, 3) on the graph of this exponential decay function represents a horizontal asymptote and it has an equation of y = -4, as shown in the image attached above.
Read more on horizontal asymptote here: brainly.com/question/14492751
#SPJ1
List five vectors in Span{V1, V2}. Do not make a sketch. V1: [ 7 3 8 ] V2 = [-7 4 0]
List five vectors in Span{V1, V2}. (Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element. Type each answer only once.)
Span{V1, V2} is the set of all vector linear combinations V1 and V2, which contains every vector that can be represented as a vector linear combination of V1 and V2. The five vectors in SpanV1, V2 are as follows:
[7, 3, 8] (V1)
[-7, 4, 0] (V2)
[0, 0, 0] (the zero vector)
[7, 7, 8] (V1 + V2)
[-14, 10, 16] (2V1)
What is vector?A vector is a matrix that has only one row or one column. A row vector is a matrix with only one row. Example Because it only contains one row, the matrix is a row vector. A column vector is a matrix with only one column. If all of the scalars in a matrix are real-valued, it is indicated using uppercase boldface letters, such as A R m n. That is, the matrix exists in a real-valued vector space with m n dimensions. As a result, matrices are just vectors expressed in a two-dimensional table-like format.
Here,
Span{V1, V2} is the set of all linear combinations of vectors V1 and V2, which includes any vector that can be expressed as a linear combination of V1 and V2. The five vectors in Span{V1, V2} are:
[7, 3, 8] (V1)
[-7, 4, 0] (V2)
[0, 0, 0] (the zero vector)
[7, 7, 8] (V1 + V2)
[-14, 10, 16] (2V1)
To know more about vector,
https://brainly.com/question/30202103
#SPJ4
michael and angelo are both artists who can create sculptures or paintings each day. the following table describes their maximum outputs per day. what is michael’s opportunity cost of a sculpture?
Michael's opportunity cost of a sculpture is 2 paintings per sculpture.
According to the table, Michael can produce either 3 sculptures or 6 paintings in a day. Therefore, the opportunity cost of producing one sculpture for Michael is 2 paintings, as he could have produced 2 additional paintings instead of the sculpture.
Opportunity cost represents the trade-off between two options and helps decision makers understand the benefits and drawbacks of different choices. In this case, by choosing to produce a sculpture, Michael is forgoing the opportunity to produce 2 paintings.
To know more about trade-off click on the link below:
https://brainly.com/question/10895386#
#SPJ11
One group of subjects was given an herbal supplement and another group was given a placebo. After one year, the number of illnesses each group had was compared.
answer choices
- Observational Study
- Experiment
The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .
What is Observation and Experiment ?The active gathering of data from a primary source is observation. Observation of living things makes use of the senses. In science, observation can also entail the perception of information and the recording of that information using tools.
Because of ethical considerations or practical limitations, an observational study infers information from a sample to the population even when the researcher has no control over the independent variable.
An experiment is a technique used to confirm or deny a hypothesis, as well as assess the possibility or effectiveness of something that has never been done before. Experiments show what happens when a certain component is modified, which sheds light on cause-and-effect relationships.
The kind of study that was conducted on the subjects who were given suplement and Placebo is termed as Experimental Study .
To learn more about Experimental Study refer to :
https://brainly.com/question/30363686
#SPJ4
24687abc is divisible by 125. what is the sum of the digits of all possible values of ‘a’?
To find the sum of the digits of all possible values of 'a', we need to add the sum of the digits of each value of abc. The sum of the digits for all possible values of a would be 8 + 7 + 15 + ... + 27, which can be calculated further.
The divisibility rule for 125 states that a number is divisible by 125 if the last three digits are divisible by 125. In the case of 24687abc, we know that the last three digits (abc) must be divisible by 125. This means that abc must be a multiple of 125. The smallest multiple of 125 is 125, and the largest is 999, so the possible values of abc are 125, 250, 375, 500, ..., 999.
The sum of the digits of each possible value of a can be calculated by adding the individual digits of each value of abc. For example, for the value 125, the sum of the digits is 1 + 2 + 5 = 8. For the value 250, the sum of the digits is 2 + 5 + 0 = 7. For the value 375, the sum of the digits is 3 + 7 + 5 = 15.
To know more about divisibility rule click on the link below:
https://brainly.com/question/28281492#
#SPJ11
is it possible to choose a random natural number in such a way that every number is equally likely to be chosen? explain why or why not. if not, is it possible for every number have a positive (nonzero) probability of being chosen?
Yes, it is possible to choose a random natural number in such a way that every number is equally likely to be chosen.
Suppose we use a fair die with an infinite number of sides, where each face corresponds to a different natural number, and roll the die to determine the randomly selected number. Here, each natural number has an equal probability of being chosen.
Alternatively, we could use a pseudorandom number generator to generate a sequence of numbers that appear to be randomly distributed and choose one of the numbers in the sequence as the randomly selected natural number. In this case, while the process of generating the numbers is deterministic, the numbers themselves appear to be randomly chosen and each natural number has an equal probability of being chosen.
It is also possible for every number to have a positive (nonzero) probability of being chosen, as long as the probabilities are defined in such a way that they sum up to 1. This can be achieved by using a uniform distribution where each natural number has a positive but nonzero probability of being chosen.
Read more about Probability:
brainly.com/question/24756209
#SPJ4
calculate the double integral. r 3x x2 y2 da, r = [1, 5] × [0, 1]
(2/3) (1-(0)) = 2/3 is the the double integral for the integral. r 3x x2 y2 da, r = [1, 5] × [0, 1].
What do you mean by integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
The double integral can be calculated as:
3x(x²y²) = dxdy
To evaluate this, we first evaluate the inner integral with respect to x, then evaluate the outer integral with respect to y.
y²dy = 2/3y³
evaluated at y=1-(2/3) = 1
So, the final answer is:
(2/3) (1-(0)) = 2/3
To know more about integral visit:
brainly.com/question/1867761
#SPJ4
(2/3) (1-(0)) = 2/3 is the the double integral for the integral. r 3x x2 y2 da, r = [1, 5] × [0, 1].
What do you mean by integration?Integration is a fundamental concept in calculus that deals with finding the area under a curve and calculating the accumulation of values over an interval. Integration can be thought of as the reverse of differentiation, which is the process of finding the rate of change of a function at a given point.
The double integral can be calculated as:
3x(x²y²) = dxdy
To evaluate this, we first evaluate the inner integral with respect to x, then evaluate the outer integral with respect to y.
y²dy = 2/3y³
evaluated at y=1-(2/3) = 1
So, the final answer is:
(2/3) (1-(0)) = 2/3
To know more about integral visit:
brainly.com/question/1867761
#SPJ4
The is ________ the horizontal center line on the coordinate plane (left to right). The _________ is the vertical center line on the coordinate plane. The point where the x and y axis interact, identified by 0 is called the _________
The x-axis is the horizontal center line on the coordinate plane (left to right). The y-axis is the vertical center line on the coordinate plane. The point where the x and y axis interact, identified by 0, is called the origin.
This point is located at coordinates (0,0). The x-axis is usually associated with the horizontal axis in a two-dimensional graph and is typically used to represent different categories of data. The y-axis is associated with the vertical axis and is used to represent a range of values from high to low.
The formula for determining the coordinates of a point is (x,y). The x-coordinate is the distance from the origin on the x-axis and the y-coordinate is the distance from the origin on the y-axis. For example, if a point has an x-coordinate of 4 and a y-coordinate of -3, the coordinates of the point would be (4,-3). To calculate the distance between two points, you can use the distance formula, which is the square root of the sum of the squares of the differences between the x-coordinates and the y-coordinates. For example, if the coordinates of point A are (2,3) and the coordinates+ of point B are (7,1), the distance between A and B would be calculated by taking the square root of (5-2)^2+(1-3)^2, which would equal 5.
Learn more about coordinates here:
https://brainly.com/question/27749090
#SPJ4
13. A company is buying new computers. The company needs no more than 220 desktops and at
least 50 laptops. A total of at least 200 computers must be bought. Write a system of linear
inequalities to represent the constraints of this situation. Let x represent the number of desktops
and let y represent the number of laptops,
The system of linear inequalities to represent the constraints of this situation is x + y ≥ 200, x ≤ 220, y ≥ 50.
This means that the total number of computers (desktop plus laptops) must be at least 200 (x + y ≥ 200). The company needs no more than 220 desktops (x ≤ 220), and at least 50 laptops (y ≥ 50).
The inequality x + y ≥ 200 represents the total number of computers needed, x ≤ 220 represents the maximum number of desktops needed, and y ≥ 50 represents the minimum number of laptops needed. Together, these inequalities represent the constraints of the situation.
For more questions like Desktops click the link below:
https://brainly.com/question/17925522
#SPJ4
(x³ + x² + 3x − 4 ) ÷ (x² + 2x + 1) =
Answer:
To find the quotient of (x³ + x² + 3x - 4) ÷ (x² + 2x + 1), we can use polynomial long division.
The long division would look like this:
x³ + x² + 3x - 4
x² + 2x + 1
x² + x - 4
________
2x - 4
______
0
So, the final answer is:
x³ + x² + 3x - 4 = (x² + x - 4) * (x² + 2x + 1) + 0
Therefore, the result of (x³ + x² + 3x - 4) ÷ (x² + 2x + 1) is x² + x - 4.
Step-by-step explanation:
Question 5 of 10
1.8"
22.8"
15.8"
Which of the following volume measurements is the best estimate for the
figure above? Round each measurement to the nearest whole number to get
your estimate.
OA. 690 in ³
B 330 in ³
The estimated volume of the given cuboid is 736 inch³
The volume of a Cuboid:In geometry, a cuboid is a three-dimensional figure or geometrical shape that has 6 faces, 12 edges, and 8 vertices. The space occupied by the cuboid is known as the Volume of the cuboid.
The dimensions of the cuboid are Length, Width, and Height. The formula for the volume of the cuboid is given by
Volume of cuboid = Length × Width × Height
Here we have
Measurements cuboid are
Length = 22.8 inches
On rounding to a whole number, Lenght = 23 inches
Width = 1.8 inches
On rounding to a whole number, Width = 2 inches
Height = 15.8 inches
On rounding to a whole number, height = 16 inches
As we know
The volume of a cuboid = Length × Width × Height
= 23 inch × 2 inch × 16 inch
= 736 inch³
Therefore,
The estimated volume of the given cuboid is 736 inch³
Learn more about Volume of a Cuboid
https://brainly.com/question/29568631
#SPJ1
Draw a parallelogram with a base of 3cm and a height of 7cm and how to calculate its area?
The area is determined by adding the base and the height.
Parallelogram:
A simple (non-self-intersecting) quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
A parallelogram is a shape with four equal sides that are parallel to one another. A parallelogram's area is determined by multiplying its base by its height. Given that the height is 7 cm and the base is 3 cm, the area would be as follows:
The area is equal to the sum of a base and a height.
Size is 21 cm2
The parallelogram with the specified base and height is shown in the following diagram:
_________
| |
| |
| |
-----------
3cm 7cm
To learn more about parallelograms, refer to the link:brainly.com/question/29147156
#SPJ4
The area is equal to height×base.
height =7cm and base = 3 cm
Area= 21 cm2
A simple (non-self-intersecting) quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
A parallelogram is a shape with four equal sides that are parallel to one another. A parallelogram's area is determined by multiplying its base by its height. Given that the height is 7 cm and the base is 3 cm, the area would be as follows:
The area is equal to height×base.
height =7cm and base = 3 cm
Area= 21 cm2
The parallelogram with the specified base and height is shown in the following diagram:
learn more about parallelogram.
https://brainly.com/question/29147156
#SPJ4
A software company provides specialized resort reservation software that can be tailored to the needs of its customers. The company’s 120 customers pay yearly subscription costs that can vary from customer to customer. The company knows that to be profitable, it needs each customer to be spending at least $23,000 per year, on average. The company selects a random sample of 33 customers and computes a mean of $27,871 and a standard deviation of $309. 10. It performs a hypothesis test and computes a very small p-value. The software company concludes that the mean is greater than $23,000. Was it appropriate for the software company to perform the hypothesis test and make the conclusion that was made?
This hypothesis test can be set up as a one-tailed test, where the null hypothesis is that the mean is equal to $23,000 and the alternative hypothesis is that the mean is greater than $23,000.
The p-value, which is the probability of obtaining a test statistic as extreme or more extreme than the one observed, given that the null hypothesis is true, can then be used to determine whether to reject or fail to reject the null hypothesis.
In this case, if the p-value is very small, it indicates strong evidence against the null hypothesis and in favor of the alternative hypothesis.
This means that it is highly unlikely that the mean subscription cost per customer is equal to $23,000, given the sample data and the assumptions of the test.
Therefore, it is appropriate for the software company to make the conclusion that the mean is greater than $23,000. However, it is important to note that the conclusion should be based on the assumptions of the test being met and the sample being representative of the population of customers.
Additionally, it is always good practice to report the results of the test, including the p-value, the sample mean, the sample standard deviation, and the sample size, to provide context for the conclusion.
To know more about Standard Deviation:
https://brainly.com/question/23907081
#SPJ4
this may indicate a reasonable promotion rate for new and seasoned employees. is this distribution unimodal or bimodal? please explain.
The promotion rate distribution of employees can be either unimodal or bimodal, depending on the company's policies and the type of employees. Understanding the distribution is important for employees as it provides insight into the likelihood of being promoted and the time it may take to reach the desired promotion.
Promotion Rates for Employees: Promotion is a common goal for employees as it is often associated with career advancement, higher salaries, and increased responsibility. The rate at which employees are promoted can vary from company to company, depending on various factors such as the size of the organization, the industry, and the company's policies.
In this context, it is important to understand the distribution of the promotion rates, which can be either unimodal or bimodal. Unimodal Distribution: A unimodal distribution is a type of distribution that has a single peak or mode. This means that the majority of the employees are promoted at a certain rate, and the frequency of promotions decreases as the rate moves away from the mode.
Here you can learn more about distribution unimodal
https://brainly.com/question/28833459#
#SPJ11
rewrite as an exponential equation. =lnx3. rewrite as a logarithmic equation
The exponential equation of ln x = 3 is: x = e^3.
What is exponential function?The formula for an exponential function is f (x) = axe, where x is a variable and an is a constant that serves as the function's base and must be bigger than 0. The transcendental number e, or roughly 2.71828, is the most often used exponential function basis.
The logarithmic function can be written in exponential form as follows:
x = logb(a) ⇔ a = b^x
The two functions can be written in an equivalent form.
The given logarithmic function is ln x = 3.
The exponential equation of ln x = 3 is:
x = e^3
Hence, The exponential equation of ln x = 3 is: x = e^3.
Learn more about exponential function here:
https://brainly.com/question/14355665
#SPJ4
Stephanie recorded the time, in minutes, she took to walk from home to work. {15,16,18,20,21}She also recorded the time, in minutes, she took to walk from work to home. {14,21,21,25,27}Based on the data she collected, what is the best conclusion Stephanie can make?
A. The range of times for walking to work is more than for walking home.
B. The range of times is the same for walking to work and walking home.
C. Stephanie’s walk times are more spread out coming home than going to work.
D. Stephanie’s walk times are more spread out going to work than coming home
If Stephanie recorded the time, in minutes, she took to walk from home to work {15,16,18,20,21} and the time, in minutes, she took to walk from work to home {14,21,21,25,27} the best conclusion Stephanie can make is:
D. Stephanie’s walk times are more spread out going to work than coming home.
The data Stephanie collected shows that the range of times for walking to work is greater than for walking home. The range for walking to work is 15-21 minutes, while the range for walking home is 14-27 minutes. This indicates that Stephanie’s walk times are more spread out going to work than coming home.
This suggests also that Stephanie may be taking a more direct or efficient route when walking home, while she may be taking a more leisurely or meandering route when walking to work. It is possible that this could be due to a variety of factors, such as traffic, terrain, or the presence of stops along the way.
The data also reveals that the average time for walking to work is 18.4 minutes, while the average time for walking home is 20.6 minutes. This indicates that, on average, Stephanie takes slightly longer to walk home than to work.
To know more about walk times, click on the link below:
brainly.com/question/4255437
#SPJ4
Which function has a domain of x greater-than-or-equal-to 5and a range of y less-than-or-equal-to 3?y = startroot x minus 5 endroot + 3y = startroot x + 5 endroot minus 3y = negative startroot x minus 5 endroot + 3y = negative startroot x + 5 endroot minus 3.
Option C has an x larger than or equal to 5 domain and a y less than or equal to 3 range. y = negative Start Root x minus 5 End Root + 3.
What is Domain and Range of Functions?
Let's consider a function y=f(x) where x is a set of values such as f exists. All the values of x are called the domain of f. Similarly, f takes a set of values when x takes values in its domain. All the values f could take is its range. We know the domain and range of f are, respectively x≥5,y≤3. Since all the options contain a square root, we already know the domain will be restricted by the argument of a square root, that is, it must be non-negative. From the given domain, we construct the argument of the square root x≥5 x-5≥0. It corresponds to the argument of a square root that must be non-negative. So our function must contain √x-5. Now about the range, the square root is assumed as positive or zero, and the range is restricted as less or equal to zero, so we operate the inequality for y
y≤3=>0≤3-y=>3-y≥0
Now we can safely say
3-y=√x-5
Or equivalently
y=3√x-5
This corresponds to the option C. written as
y= negative start root x minus 5 end root + 3
To learn more about Domain and Range of Functions refers to:
brainly.com/question/14202749
#SPJ4