Determine f –1(x) if f of x is equal to the quantity x plus 2 end quantity over the quantity x minus 3 end quantity where x ≠ 3.
f inverse of x is equal to the quantity x minus 3 end quantity over the quantity x plus 2 end quantity
b
f inverse of x is equal to the quantity x minus 2 end quantity over the quantity x plus 3 end quantity
c
f inverse of x is equal to the quantity x minus 1 end quantity over the quantity 3 times x plus 2 end quantity
d
f inverse of x is equal to the quantity 3 times x plus 2 end quantity over the quantity x minus 1 end quantity
Answers
The inverse function of f(x) = (x + 2)/(x - 3) is given as follows:
\(f^{-1}(x) = \frac{3x + 2}{x - 1}\)
How to obtain the inverse function?The function in this problem is defined as follows:
f(x) = (x + 2)/(x - 3).
Using the notation y = f(x), it is given as follows:
y = (x + 2)/(x - 3).
To obtain the inverse, the first step is exchanging the variables x and y, as follows:
x = (y + 2)/(y - 3).
Now the variable y must be isolated to obtain the inverse function, as follows:
xy - 3x = y + 2
xy - y = 3x + 2
y(x - 1) = 3x + 2
y = (3x + 2)/(x - 1).
Hence the inverse function is given by:
\(f^{-1}(x) = \frac{3x + 2}{x - 1}\)
Meaning that the fourth option is correct.
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Related Questions
Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months. Month 2 3 4 5 Sales 924 91
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Bryant Industries uses forecasting to estimate the number of orders that will be placed by their customers. The table below gives the sales figures for the last four months.Month2345Sales92491942004There are different forecasting techniques used by companies like Bryant Industries to predict future sales.
One of the most widely used methods is the time-series method. This method is particularly useful when the demand for a product or service changes over time and when there are no external factors that affect the sales. In this case, we can use a time-series method called the moving average to estimate future sales. The moving average is a time-series method that uses the average of past sales data to estimate future sales. It is particularly useful when there are no external factors that affect the sales. In this case, we can use a 3-month moving average to estimate future sales. The 3-month moving average is calculated as follows: (924 + 919 + 420) / 3 = 754.33. This means that we can expect sales of around 754 units next month. The moving average method is easy to use and is a good way to get a quick estimate of future sales. However, it has some limitations. For example, it does not take into account external factors that may affect sales, such as changes in the economy or in consumer behavior.
In conclusion, Bryant Industries can use the moving average method to estimate future sales. However, they should also consider other factors that may affect sales, such as changes in the economy or in consumer behavior. By doing so, they can make more accurate forecasts and improve their overall performance.
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Solve.
please and thank you!
Answers
Answer:
Step-by-step explanation:
2(x+3)/3 + 3(x-6)/2=1-x
2x+6/3 + 3x-18/2=1-x
2(2x+6)/3 + 3(3x-18)=6-6x
4x+12+9x-54=6-6x
13x-49=6-6x
13x+6x=6+42
19x/19=48/19
x=49/19
suppose that the slope parameter in a simple linear regression model is β1 = 3.52. what does this suggest about the nature of the relationship between x and y?
Answers
A slope parameter of β1 = 3.52 in a simple linear regression model suggests that there is a positive and direct relationship between the independent variable (x) and the dependent variable (y).
Specifically, for every one unit increase in the independent variable (x), the dependent variable (y) is expected to increase by an average of 3.52 units. This indicates a positive linear association between x and y, implying that as x increases, y tends to increase as well.
The magnitude of the slope parameter (3.52) also indicates the steepness of the relationship. A larger slope suggests a stronger relationship, indicating that the change in y for a given change in x is relatively large.
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700 +[700 * .075 * 5]
Answers
Answer:
962.5
Step-by-step explanation:
It could also be 1925/2 or 962 1/2.
![700 +[700 * .075 * 5]](https://i5t5.c14.e2-1.dev/h-images-qa/answers/attachments/vdX4l2qAxaAOUIYYx6H4AiK1OCAjlKa3.png)
help meeee mathhh eeeekl
Answers
Answer:
75,000
Step-by-step explanation:
I wish I were those kids
What is the area, in square centimeters, of the trapezoid below?
8.5 cm
7.5 cm
15.7 cm
Answers
Answer:
90.75 cm^2
Step-by-step explanation:
The area of a trapezoid is given by
A = 1/2 ( b1+b2) *h
where b1 and b2 are the lengths of the bases and h is the height
A = 1/2(8.5+ 15.7) * 7.5
1/2 (24.2) 7.5
90.75 cm^2
A teacher has a large container of blue, red, and green beads. she reports to the students that the proportion of blue beads in the container is 0.30. the students feel the proportion of blue beads is lower than 0.30. a student randomly selects 60 beads and finds that 12 of the beads are blue. the p-value for the test of the hypotheses, h0:p=0.30 and ha:p<0.30, is 0.045. what is the correct interpretation of this value?
a. there is a 4.5% chance the proportion of blue beads in the container is 0.3.
b. assuming the true proportion of blue beads in the container is 0.30, there is a 4.5% probability that the null hypothesis is true.
c. assuming the true proportion of blue beads in the container is 0.30, there is a 4.5% probability that the sample proportion would be 0.20 or less by chance alone.
d. assuming the true proportion of blue beads in the container is less than 0.30, there is a 4.5% probability that the sample proportion would be 0.20 or less by chance alone.
Answers
The correct interpretation of this value is, assuming the true proportion of blue beads in the container is 0.30, there is a 4.5% probability that the sample proportion would be 0.20 or less by chance alone. ( Option - C is correct )
The null hypothesis is that there are 0.30 blue beads in the container, and the alternative hypothesis is that there are 0.045 blue beads in the container.
Define a null hypothesis:It should be mentioned that the null hypothesis is merely a stastical theory that contends that the variables provided in the data set have no link to one another.
A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the "null," it is represented as H0.
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
According to the information provided, there are 0.30 of blue beads in the container. The null hypothesis in this situation is that there are 0.30 blue beads in the container, and the alternative hypothesis is that there are 0.045 blue beads in the container.
Therefore,
The correct interpretation of this value is, assuming the true proportion of blue beads in the container is 0.30, there is a 4.5% probability that the sample proportion would be 0.20 or less by chance alone. ( Option - C is correct )
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0
1
2.
3
у
8
1
-6
-13
What is an equation that describes the relationship?
Answers
Step-by-step explanation:
that only know
Suppose two mortgage companies compare the ratio of the monthly mortgage payment to the total monthly income as their metric. Suppose 0.3 is the ideal metric for the debt-to-income ratio for Company A, and 0.28 is the ideal metric for the debt-to-income ratio for Company B. Provided the target mortgage payment is the same for either company, then which of these mortgage companies requires a greater monthly income? Explain.
Answers
Answer:
the 0.28 company
Step-by-step explanation:
0.28 is smaller than 0.3 and 0.28 still costs the same amount of money as 0.3
Company A requires a greater monthly income since its ideal debt-to-income ratio (0.3) results in a higher portion of income allocated to the mortgage payment compared to Company B's ideal ratio of 0.28.
Company A's ideal metric for the debt-to-income ratio is 0.3, which means the monthly mortgage payment should be 30% of the total monthly income. Similarly, Company B's ideal metric is 0.28, which means the monthly mortgage payment should be 28% of the total monthly income.
Since the target mortgage payment is the same for both companies, the company with the smaller ideal metric (0.28 for Company B) requires a greater monthly income to meet that target. This is because a smaller ratio (0.28) of the mortgage payment to the total income implies that the mortgage payment is a larger portion of the income, requiring a higher income to maintain the same payment amount.
In other words, Company B's requirement of keeping the debt-to-income ratio lower means that the mortgage payment should be a smaller fraction of the total monthly income. As a result, to keep the mortgage payment constant, a higher income is needed to achieve the smaller debt-to-income ratio of 0.28 compared to Company A's debt-to-income ratio of 0.3.
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To solve 2x=8 you need to divide by what number?
PLEASEEEE HELP
Answers
Answer:
divide by 2
Step-by-step explanation:
to find x you must divide 8 by 2.
Answer:
you divide 8 by 2
Step-by-step explanation:
To isolate the variable, x you need to divide by 2 on both sides so it cancels out the 2 on 2x and will divide 8 by 2=4
helps it is hard only people that do math
Answers
Answer:
d) 1/x^15
Step-by-step explanation:
first, you would multiply the exponents
(x^3)^-5
x^-15
second, in order for it to be simplified, you can not have a negative exponent, so you will move x^15 to the denominator.
1/x^15
Answer: Answer is D
Step-by-step explanation:
please mark me branlest
please help me with these!! it will help a lot!
Answers
D) 8.25
E) 12
F) 13.5
G) 26
H) 28
What is the area of the region enclosed by the graphs of f(x)= x – 2x2 and g(s) = -5x? A 17 / 16 3 20 C 9 E 36
Answers
To find the area of the region enclosed by the graphs of f(x) = x - 2x^2 and g(x) = -5x, we need to find the points where the two graphs intersect and then use those points to find the area of the region between the two graphs.
An explanation graph is what?
A graph is a representation of the relationship between two variables that are normally measured along one of a pair of axes at right angles.
We can find the points of intersection by setting the two functions equal to each other and solving for x:
x - 2x^2 = -5x
2x^2 + 5x - x = 0
2x(x+5) -1(x+5) = 0
(2x-1)(x+5) = 0
x = 1/2 or x = -5
The solution x = -5 is extraneous as it does not give a valid value for the x-coordinate of the point of intersection.
So, x = 1/2 is the valid solution.
So the two graphs intersect at (1/2, 1/4)
Now, we can find the area of the region enclosed by the two graphs by finding the definite integral of the function f(x) - g(x) with respect to x, where the definite integral is taken between the points of intersection x= -5 and x=1/2
So, the definite integral of (x-2x^2)-(-5x) with respect to x, between x = -5 and x =1/2 is:
∫[(x-2x^2)-(-5x)]dx = ∫(x-2x^2+5x)dx = ∫(3x-2x^2)dx between -5 and 1/2
= [x^2-2/3x^3] between -5 and 1/2
= (1/2)^2 - 2/3(1/2)^3 - (-5)^2 + 2/3(-5)^3
= 1/4 - 2/24 - 25 + 2/3*125/27
= 1/4 - 1/12 + 5/3
= (12-3+40)/12 = 49/12
So the area of the region enclosed by the graphs is 49/12 square units.
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You randomly select one card from a 52-card deck. Find the probability of selecting the 2 of hearts or the 4 of clubs.
Answers
The probability of selecting the 2 of hearts or the 4 of clubs from a 52-card deck is 51/2652.
The probability of selecting the 2 of hearts is 1/52 since there is only one 2 of hearts in the deck, and the probability of selecting the 4 of clubs is also 1/52 since there is only one 4 of clubs in the deck.
To calculate the probability of selecting either card, we add the probabilities: 1/52 + 1/52 = 2/52.
However, since we have counted the probability of selecting both cards (2 of hearts and 4 of clubs) twice, we need to subtract the probability of selecting both cards, which is 1/52 x 1/51 (probability of selecting the 2 of hearts and then the 4 of clubs without replacement).
Therefore, the final probability is (2/52) - (1/52 x 1/51) = 1/26 - 1/2652 = 51/2652.
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A continuous iv is infusing at the rate of 15 gtt/min. the drop factor is 10 gtt/ml. how many milliliters will infuse over 1 1 2hours?
Answers
Over a period of 1.5 hours, a continuous IV infusion at a rate of 15 gtt/min (with a drop factor of 10 gtt/ml) will result in 135 milliliters being infused.
To calculate the number of milliliters that will infuse over 1.5 hours, we need to convert the infusion rate from drops per minute to milliliters per hour.
Infusion rate: 15 gtt/min
Drop factor: 10 gtt/ml
First, we can calculate the infusion rate in milliliters per minute:
Infusion rate (ml/min) = Infusion rate (gtt/min) / Drop factor (gtt/ml)
Infusion rate (ml/min) = 15 gtt/min / 10 gtt/ml = 1.5 ml/min
Next, we can convert the infusion rate to milliliters per hour:
Infusion rate (ml/hour) = Infusion rate (ml/min) × 60 min/hour
Infusion rate (ml/hour) = 1.5 ml/min × 60 min/hour = 90 ml/hour
Finally, we can calculate the total volume that will infuse over 1.5 hours:
Volume (ml) = Infusion rate (ml/hour) × Time (hours)
Volume (ml) = 90 ml/hour × 1.5 hours = 135 ml
Therefore, 135 milliliters will infuse over 1.5 hours.
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Solve the following equation algebraically:
-16 = 16x^2 How many solutions does this equation have? Explain.
a. -1=x^2: One solution because only -1 will satisfy the equation.
b. -1=x^2: No real solution because there is no real number that, when squared, produces -1.
C. 1=x^2: Two solutions because the square root of 1 is positive 1 and negative 1.
d. 1=-x^2: One solution because only -1 will satisfy the equation.
Answers
1=x²: two solutions because the square root of 1 is positive 1 and negative 1
Answer:
B. -1 = x^2; No real solution because there is no real number that, when squared, produces -1
Step-by-step explanation:
3/4 - 1/8 how much is it? help me please
Answers
Answer:5/8
Step-by-step explanation:
\(\begin{gathered} \boxed{ \sf \frac{3}{4} - \frac{1}{8}} = \\ \\ \sf \frac{8 \div 4 \times 3 - 8 \div 8 \times 1}{8} = \\ \\ \sf\frac{6 - 1}{8} = \\ \\ \sf \boxed{ \sf\frac{5}{8}} \end{gathered}\)
Therefore, the result of this subtraction of fractions is five eighths.
How to subtract unlike fractions:
Heterogeneous fractions are fractions that have different denominators.
To subtract heterogeneous fractions we follow these steps:
We find the common denominator, which is the least common multiple of the denominators. We divide the common denominator by the other denominator and multiply by the numerator.We will write the above results as numerators with the subtraction sign between them.We subtract the numerators.We simplify the result if possible.The Alpha.the variables, quantitative or qualitative, whose effect on a response variable is of interest are called __________.
Answers
The variables, quantitative or qualitative, whose effect on a response variable is of interest are called explanatory variables or predictor variables.
In a study or experiment, the response variable, also known as the dependent variable, is the main outcome being measured or observed. The explanatory variables, on the other hand, are the factors that may influence or explain changes in the response variable.
Explanatory variables can be of two types: quantitative, which represent numerical data, or qualitative, which represent categorical data. The relationship between the explanatory variables and the response variable can be studied using statistical methods, such as regression analysis or analysis of variance (ANOVA). By understanding the relationship between these variables, researchers can make informed decisions and predictions about the behavior of the response variable in various conditions.
In conclusion, explanatory variables play a vital role in helping to analyze and interpret data in studies and experiments, as they help determine the potential causes or influences on the response variable of interest.
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I need help answering this question!!! will give brainliest
Answers
The vertical distance travelled at 5 seconds is 12 meters
How to estimate the vertical distance travelledFrom the question, we have the following parameters that can be used in our computation:
The graph
The time of travel is given as
Time = 5 seconds
From the graph, the corresponding distance to 5 seconds 12 meters
This means that
Time = 5 seconds at distance = 12 meters
Hence, the vertical distance travelled is 12 meters
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The package of tissues has 180 pieces of tissues. We know that 10% of tissues are blue, 25% of the package are pink tissues, and the rest are white. How many pieces were blue and how many were pink tissue in the package?
Answers
18 are blue
180 - 25% = 45
45 are pink
18 + (-2) + (-7) = ?
please explain how you got your answer :)
i'll give brainliest
Answers
Answer:
9
Step-by-step explanation:
18+-2+-7
16+-7
9
Because - and - makes plus
Solve for MRS
y= 24 - (4(square root of x))
Answers
The Marginal Rate of Substitution (MRS) for the given function is equal to -2/sqrt(x). To find the Marginal Rate of Substitution (MRS), we need to take the derivative of the given function with respect to x.
Given: y = 24 - 4(sqrt(x))
Step 1: Differentiate the function y with respect to x.
dy/dx = d/dx(24 - 4(sqrt(x)))
Step 2: Differentiate each term separately using the power rule and chain rule.
dy/dx = 0 - 4(1/2)(x^(-1/2))(1)
Step 3: Simplify the derivative.
dy/dx = -2(x^(-1/2))
Step 4: Rewrite the derivative in terms of MRS.
MRS = dy/dx = -2/sqrt(x)
Therefore, the Marginal Rate of Substitution (MRS) for the given function y = 24 - 4(sqrt(x)) is -2/sqrt(x).
The negative sign indicates that the MRS is inversely related to x, which means as x increases, the MRS decreases. The value of MRS represents the rate at which a consumer is willing to substitute y (the dependent variable) for an incremental change in x (the independent variable). In this case, as x increases, the consumer is willing to substitute less y for the additional units of x.
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In AON networks, a(n) __________ is a point where one or more lines (arrows) begin or terminate, commonly used for depicting an event or activity.
Answers
In AON networks, "node" is a point where one or more lines (arrows) begin or terminate, commonly used for depicting an event or activity.
What is Activity-on-Node (AON) diagram?Scheduling logic diagrams of the most fundamental kind. Any activity on the schedule that has no float; Total Float = 0; is considered a critical activity.
Between the project's start and finish, there are vital activity(s) that must be completed continuously. This is known as the critical path.
The importance of AON diagram are-
Because it helps identify the essential path, the arrow diagram is crucial for the project timeline. The critical route is used to determine the most effective schedule while still achieving the objectives required for a project to be successful. The critical path indicates the longest time of every dependent task.It is possible to organize tasks and determine not only when they must be finished but also which ones must be performed and which ones can be skipped while still reaching the project's goals and objectives by creating a schedule. An arrow diagram is essential because of this. It results in the project's ideal schedule.To know more about the AOA and AON networks, here
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please help with this question and give detailed explanation!! thank you!!
Answers
Answer:
\(-\sqrt{2}\)Step-by-step explanation:
Make the following operations:
a² + b² = 6aba² + 2ab + b² = 8ab(a + b)² = 8aba + b = \(2\sqrt{2ab}\)and
a² + b² = 6aba² - 2ab + b² = 4ab(a - b)² = 4aba - b = \(-2\sqrt{ab}\), since a < bThe required value is:
\(\cfrac{a+b}{a-b} =\cfrac{2\sqrt{2ab} }{-2\sqrt{ab} } =-\sqrt{2}\)Answer:
\(\dfrac{a+b}{a-b}=-\sqrt{2}\)
Step-by-step explanation:
Given:
\(a^2+b^2=6ab\)
\(0 < a < b\)
Add 2ab to both sides of the given equation:
\(\implies a^2+b^2+2ab=6ab+2ab\)
\(\implies a^2+2ab+b^2=8ab\)
Factor the left side:
\(\implies (a+b)^2=8ab\)
Subtract 2ab from both sides of the given equation:
\(\implies a^2+b^2-2ab=6ab-2ab\)
\(\implies a^2-2ab+b^2=4ab\)
Factor the left side:
\(\implies (a-b)^2=4ab\)
Therefore:
\(\implies \dfrac{(a+b)^2}{(a-b)^2}=\dfrac{8ab}{4ab}\)
\(\implies \dfrac{(a+b)^2}{(a-b)^2}=2\)
\(\textsf{Apply exponent rule} \quad \dfrac{a^c}{b^c}=\left(\dfrac{a}{b}\right)^c:\)
\(\implies \left(\dfrac{a+b}{a-b}\right)^2=2\)
Square root both sides:
\(\implies \sqrt{\left(\dfrac{a+b}{a-b}\right)^2}=\sqrt{2}\)
\(\implies \dfrac{a+b}{a-b}=\pm\sqrt{2}\)
As 0 < a < b then:
a + b > 0a - b < 0Therefore:
\(\implies \dfrac{a+b}{a-b}=\dfrac{+}{-}=-\)
So:
\(\implies \dfrac{a+b}{a-b}=-\sqrt{2}\)
find the slope of the line
Answers
Answer:
Slope = 4
Step-by-step explanation:
Consider two set of point through which the line passes.
Let it be ( 0, 4 ) and ( -1 , 0)
Find slope .
\(Slope = \frac{rise}{run } = \frac{y_2 - y_ 1 }{x_2 - x_1} , \ where \ \ (x_1 , y_1) = (0, 4 ) \ and \ (x_2, y _ 2) = ( -1 , 0 )\)
\(Slope = \frac{0-4}{-1-0} = \frac{-4}{-1} = 4\)
Which of the following is the correct expression, in scientific notation, of the number 37,500 ? \( 3.75 \times 10^{3} \) \( 3.75 \times 10^{-3} \) 37,500 \( 3.75 \times 10^{4} \)
Answers
Answer: 3750
Step-by-step explanation:
An object is moving at a speed of 2 centimeters ever 7 seconds. express this speed in meters per week.
Answers
The speed of the object is 12121 m per week.
What does it mean to do speed?
“Speed” is a street name for various stimulant drugs that teens, young adults and others use to feel more alert and focused, and in some cases, to feel high. Some people also use various forms of speed to reduce their appetite. Types of speed include: Amphetamines (used to treat ADHD, narcolepsy, and depression)The object is moving at a speed of 2 centimeters every 7 seconds.
We need to find the speed in m per week.
2 cm = 0.02 m
1 week = 604800 s
7 s = \(1.65 * 10^{-6} week\)
Speed = distance/time
So,
\(v = \frac{0.02 m}{1.65 * 10^{-6 } week}\)
\(v = 12121.21 m/ week\)
or v = 12121 m/ week
So, the speed of the object is 12121 m per week.
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(1 point) A phone-in poll conducted by a newspaper reported that 72% of those who called in liked ''real TV''. (a) The number 72% is a A. population. B. sample. C. parameter. D. statistic. (b) The unknown true percentage of American citizens who like ''real TV'' is a A. sample. B. statistic. C. parameter. D. population.\
Answers
(a) The number 72% is a D. statistic.
(b) The unknown true percentage of American citizens who like ''real TV'' is a C. parameter.
How to know about the state of the number 72%?It is related to statistics and parameters.
(a) The number 72% is a statistic because it represents a summary measure of the sample of individuals who participated in the phone-in poll.
A statistic is a numerical value calculated from a sample of data, and it is used to make inferences about the population from which the sample was drawn.
How to know about the unknown true percentage of American citizens who like ''real TV''?(b) The unknown true percentage of American citizens who like ''real TV'' is a parameter.
A parameter is a numerical characteristic of a population, such as a mean, proportion, or standard deviation, and it is typically unknown and estimated from sample data.
In this case, the percentage of all American citizens who like ''real TV'' is unknown and cannot be directly observed, so it is considered a parameter.
The phone-in poll only represents a sample of individuals who called in to the newspaper and cannot be used to estimate the parameter for the entire population.
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Given f(x) = 3. + 1, solve for when f(3) = 7.
Answers
Answer:
The question is incomplete
find the area under the standard normal curve over the interval specified below to the right of z=3
Answers
The standard normal curve, also known as the standard normal distribution or the z-distribution, is a specific probability distribution that follows a bell-shaped curve. The area under the standard normal curve to the right of z = 3 is approximately 0.0013.
For the area under the standard normal curve to the right of z = 3, we need to calculate the cumulative probability from z = 3 to positive infinity.
The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. It is a symmetric bell-shaped curve that represents the distribution of standard scores or z-scores.
Using statistical tables or software, we can find the cumulative probability associated with z = 3, which represents the area under the curve to the left of z = 3.
The cumulative probability for z = 3 is approximately 0.9987.
For the area to the right of z = 3, we subtract the cumulative probability from 1.
Therefore, the area to the right of z = 3 is approximately 1 - 0.9987 = 0.0013.
In conclusion, the area under the standard normal curve to the right of z = 3 is approximately 0.0013.
This means that the probability of randomly selecting a value from the standard normal distribution that is greater than 3 is approximately 0.0013 or 0.13%.
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