Therefore, the value of k for the given function is either k = 1/2 or k = -1/2.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain or range) with the property that each input is related to exactly one output. A function is often represented by an equation, formula, or a graph, and it is used to describe the relationship between two or more variables. Functions are widely used in various fields of mathematics, science, engineering, and economics, and they have many important applications in real life, such as modeling and analyzing complex systems, predicting future outcomes, and solving problems.
Here,
We can use the given table of values for g(x) = f(kx) to find the value of k.
When x = -2, we have g(-2) = f(k(-2))
= f(-2k)
= 1
When x = 2, we have g(2) = f(k(2))
= f(2k)
= 1
From the graph of f(x), we can see that f(-1) = 1 and f(1) = 1.
Therefore, we have the equations:
f(-2k) = 1 (equation 1)
f(2k) = 1 (equation 2)
We can solve for k by using the x-coordinate of the vertex of f(x):
x = -b/2a
= -0/2a
= 0
So, the vertex of f(x) is at (0,0).
Using the vertex form of the quadratic equation, we have:
f(x) = a(x - 0)² + 0
f(x) = ax²
Substituting the point (1,1), we get:
1 = a(1)²
a = 1
Substituting the point (-2,4), we get:
4 = a(-2)²
4 = 4a
a = 1
Substituting the point (2,4), we get:
4 = a(2)²
4 = 4a
a = 1
Therefore, f(x) = x²
Now we can substitute f(x) into equations 1 and 2 to get:
(-2k)² = 1
(2k)² = 1
Solving for k, we get:
k = 1/2 or k = -1/2
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Assume the distribution of IQ scores for adults can be modeled with a normal distribution with a mean score of 100 points and a standard deviation of 10 points. 30% of adults will have an IQ score higher than what value?
Step-by-step explanation:
Use z-score table to find the z-score that corresponds to .7000 ( 70%)
approx .525 s.d. above the mean
.525 * 10 = 5.25 points above 100 = 105.25
For a point to be a solution to a
system of inequalities, the point
must make_ of the
inequalities true.
Answer:
The signs.Step-by-step explanation:
For a point to be a solution to a system of inequalities, the points must make the signs of the inequalities true.
For example, the points must give results like 2<3 or 0>-2, these are true solutions. If the points gives 1>2, then that point is not a solution.
Help me with this 9 math
The height of the cylinder is 4 feet.
How to find the height of a cylinder?The volume of a cylinder can be found as follows;
volume of a cylinder = base area × height
Therefore,
base area = πr²
volume of the cylinder = 48π ft³
base area = 12π ft²
Therefore, let's find the height of the cylinder as follows:
48π = 12π × h
divide both sides of the equation by 12π
h = 48π / 12π
h = 4 ft
Therefore,
height of the cylinder = 4 feet
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Write 8.05 as a mixed number and as an improper fraction.
Given the decimal value 8.05.
First we need to express as a fraction as shown;
8.05 = 805/100
Write in ots simplest form
805/100 = 5 * 161/5*20
805/100 = 161/20
Hence the decimal 8.05 as an improper fraction is 161/20
Express as mixed fraction;
161/20 = [(20*8) + 1]20
161/20 = (20*8)/20 + 1/20
161/20 = 8 + 1/20
161/20 = 8 1/20
Hence the deco
9. Suppose the length and width of the rectangle are doubled. What effect would this have on the perimeter? Justify your
answer.
10. Suppose the length and width of the rectangle are doubled. What effect would this have on the area? Justify your answer.
Since the length and width of the rectangle is doubled, then the perimeter of the rectangle is doubled and the area of the rectangle is fourfold.
Perimeter and area of rectangle:
The general form to calculate Perimeter of a Rectangle
P = 2(a + b);
And Area of Rectangle
A= a × b
where
a refers the length
b refers the width
Given,
Suppose the length and width of the rectangle are doubled.
Here we need to find the effect on the perimeter and the area of the rectangle.
While we looking into the given rectangle,
We have identified that the value of
length = 17 feet,
width = 4 feet
So, the perimeter of rectangle is,
=> P = 2 (17 + 4) = 42
Similarly, the area of the rectangle is
=> A = 17 x 4 = 68
Here we have given that the length and width is doubled, then the value of length is 34 and the width is 8.
Now, the perimeter of the rectangle is,
=> P = 2 (34 + 8) = 84
And the area of the rectangle is,
=> A = 34 x 8 = 272
While we comparing the resulting values we have identified that the perimeter is doubled and the area is fourfold.
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For the sample data shown in the table below Number of Yes answers Number sampled Group 1 108 150 Group 2 117 180 (F1) What is the best estimate for pl - p2? (F2) Test whether a normal distribution may be used for the distribution of pl - p2 - (F3) Find the standard error of the distribution of pl - p2 (F4) Find a 95% confidence interval for pl - p2
Estimate p1 - p2, test normality, find standard error, and calculate 95% confidence interval.
How to estimate and test p1 - p2, assess normality, find the standard error, and calculate a confidence interval?(F1) The best estimate for p1 - p2 is (108/150) - (117/180).
(F2) To test whether a normal distribution may be used for the distribution of p1 - p2, you can perform a hypothesis test such as the z-test or t-test using the sample proportions.
(F3) The standard error of the distribution of p1 - p2 can be calculated using the formula: sqrt((p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)), where p1 and p2 are the sample proportions and n1 and n2 are the respective sample sizes.
(F4) To find a 95% confidence interval for p1 - p2, you can use the formula: (p1 - p2) ± (z * SE), where z is the critical value corresponding to a 95% confidence level (typically 1.96 for large sample sizes) and SE is the standard error calculated in (F3).
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the window of a room is 20m long and 14m wide. if the carpenter works to put a metallic frame around it which cost Rs.120 per metre, then how much will the metallic frame cost.
Answer:
33,600
Step-by-step explanation:
length=20m
wide=14m
area= 28m²
1m= 28
cost = 120*28= rs33600 per m²
find the area of the following figure. the triangular ends are congruent.
The area of the figure which consists of two congruent triangles and a rectangle is calculated as: 52 cm².
How to Find the Area of a Composite Figure?In the diagram given above, we see a composite figure consisting of two triangles that are congruent, and a rectangle, therefore:
Area of the figure = area of the two triangles + area of rectangle.
The Area of the two triangles:
base = 8 cm²
height = 4.5 cm²
Area of the two triangles = 2(1/2 * base * height) = base * height
Area = 8 * 4.5 = 36 cm²
Area of rectangle = length * width = 4 * 4
= 16 cm²
Total area = 36 + 16 = 52 cm²
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Read the word problem below.
Answer:
Step-by-step explanation:
Number 4if x represent the numbers of pencils per box solve the equation 8x4=196so,she put 4 in each boxAn airplane can seat up to 175 passengers. The airline has already sold 87 tickets for a flight on the airplane. Which graph represents the solution to the inequality that finds the number of tickets the airline can still sell?
Answer:
C
Step-by-step explanation:
The number of tickets the airline still sells will be 88. Then the correct graph is A.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
An airplane can seat up to 175 passengers.
The airline has already sold 87 tickets for a flight on the airplane.
Then the graph represents the solution to the inequality that the number of tickets the airline still sells will be
Let x be the number of the ticket which need to sell. Then the inequality equation will be
x + 87 ≤ 175
x ≤ 175 - 87
x ≤ 88
Thus, the correct option is A.
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141% as a mixed or whole number
Answer:
1 41/100
Step-by-step explanation:
Answer:
141/100 (Already in simplest form). As a mixed number, it is: 1 41/100
Step-by-step explanation:
Expression: a collection of ________, variables, operations, and parentheses
Expression: a collection of numbers, variables, operations, and parentheses.
What are expressions?An algebraic expression consists of unknown variables, numbers and arithmetic operators.
Given a statement,
The blank of the statement will be filled by the word "numbers" because an expression is a combination of numbers, variables and at least one mathematical operation.
Hence, the answer is numbers.
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In State College, PA the average outside temperature during the month of January was 35 degrees F. Calculate the HDD for the month of January.
The HDD for the month of January in State College, PA is 930.
To calculate the HDD (Heating Degree Days) for the month of January in State College, PA, we need to subtract the average daily temperature from 65 degrees Fahrenheit, which is considered the standard temperature for indoor heating.
HDD = 65°F - 35°F
HDD = 30°F
Therefore, the HDD for the month of January in State College, PA is 30 degrees Fahrenheit.
Hi! To calculate the Heating Degree Days (HDD) for the month of January in State College, PA with an average outside temperature of 35 degrees F, follow these steps:
1. Determine the base temperature: In the US, the base temperature is commonly 65 degrees F.
2. Subtract the average temperature from the base temperature: 65 - 35 = 30 degrees.
3. Multiply the difference by the number of days in the month: January has 31 days, so 30 * 31 = 930.
So, the HDD for the month of January in State College, PA is 930.
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To calculate the HDD for the month of January in State College, PA, we need to first determine the base temperature. The base temperature is the temperature below which a building needs to be heated in order to maintain a comfortable indoor temperature. In this case, we will use a base temperature of 65 degrees F.
To calculate the HDD, we need to subtract the average daily temperature from the base temperature and sum up the values for each day of the month. If we assume that January has 31 days, we can calculate the HDD as follows:
HDD = (65 - 35) x 31
HDD = 930
So the HDD for the month of January in State College, PA is 930. This means that during the month of January, there were 930 heating degree days, which indicates the amount of heating required to maintain a comfortable indoor temperature. It is important to note that the HDD can vary depending on the base temperature used, so it is important to choose a base temperature that is appropriate for the climate and the building being heated.
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the given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.
The scatterplot with the least squares line provides insights into the relationship between average annual global surface temperature and the years from 2000 to 2015, allowing us to assess trends, strength of correlation, and make predictions within certain limitations.
The scatterplot represents the relationship between the average annual global surface temperature, in degrees Celsius, and the corresponding years from 2000 to 2015. The line drawn on the plot is the least squares line, which is the best fit line that minimizes the overall distance between the observed data points and the line.
The least squares line is determined using a statistical method called linear regression. It calculates the equation of a straight line that represents the trend in the data. This line serves as a mathematical model to estimate the average temperature based on the year.
By analyzing the scatterplot and the least squares line, we can make several observations. Firstly, we can see whether the temperature has been increasing, decreasing, or remaining relatively stable over the given years. If the slope of the line is positive, it indicates a positive correlation, implying that the temperature has been increasing. Conversely, a negative slope suggests a decreasing trend.
Additionally, we can evaluate the strength of the relationship between temperature and time by examining how closely the data points cluster around the line. If the points are closely grouped around the line, it suggests a strong correlation, indicating that the line is a good representation of the data. On the other hand, if the points are more scattered, the correlation may be weaker.
Furthermore, the line can be used to predict the average annual global surface temperature for future years beyond the data range of 2000 to 2015. However, it's important to note that such predictions should be made with caution and considering other factors that may affect global temperatures, such as climate change and natural variability.
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Question
The given scatterplot shows the average annual global surface temperature, in degrees celsius, for each year from 2000 to 2015. the line drawn is the least squares line for the data set.
What is the value of x?
A. 5
B. 2.5
C. 7.5
D. 10
Answer:
x = 5
Step-by-step explanation:
x is to x+5 what x-2 is 70 x+1
x/x+5 = x-2/x+1
x(x+1) = (x-2)(x+5)
x^2+x = x^2+ 5x - 2x - 10
x^2 - x^2 = -x + 5x - 2x - 10
10 = 2x
x = 5
Geometry Suppose that a pizza must fit into a box with a
base that is 12 in. long and 12 in. wide. You can use the
quadratic function A Tr² to find the area of a pizza in
terms of its radius.
a. What values of r make sense for the function?
b. What values of A make sense for the function?
c. Graph the function. Round values of A to the
nearest tenth.
Question 39
The value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
How to determine the Radius of the circle?You should understand that the pizza is fit inside the square box making all circumference of the circle to touch all the sides of the square box
The quadratic function reads
A= πr²
Where A= Area of circle,
π = 22/7
and r= radius of the circle
A= (22/7)*6
Width of the box is 12
Therefore 12/2 = r=6
A= (22*6*6)/7
A=113.1 in²
In conclusion, he value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
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5. are there any conditions in which it would be acceptable to allow skewed variables into a research study? if so, describe these conditions.
The conditions to allow skewed variables are: they are naturally occurring phenomenon that can't be controlled, it serves as control variable, and if it has significant impact on the outcome variable, it may be necessary to include.
Yes, there are certain conditions in which it may be acceptable to allow skewed variables into a research study. One such condition is when the variable is a naturally occurring phenomenon and cannot be manipulated or controlled. In such cases, it may be necessary to include the variable in the study despite its skewed nature.
Another condition is when the skewed variable is not the primary focus of the research, but rather serves as a control variable or confounding variable. In such cases, the focus of the study may be on other variables, and the skewed variable may be included simply to control for its effects on the outcome variable.
Additionally, if the skewed variable is expected to have a significant impact on the outcome variable, it may be necessary to include it in the study despite its skewed nature. In such cases, researchers may use statistical techniques to account for the skewedness and ensure that the results are still valid and reliable.
Overall, while skewed variables can present challenges in research studies, there may be certain conditions in which their inclusion is necessary or acceptable. Researchers should carefully consider these conditions and use appropriate techniques to address any issues related to skewed variables in their studies.
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The position of a particle moving in a straight line is given by the following equation: x= 2.0−3.6t+1.1t
2
. Note that x is in meters and t is in seconds. What is the average velocity of the particle over the interval t=1.0 s to t=3.0 s?
The average velocity of the particle over the interval from t=1.0 s to t=3.0 s is -2.8 m/s.
The average velocity of an object is defined as the change in its position divided by the change in time. In this case, we need to find the change in position between t=1.0 s and t=3.0 s.
Given the equation for the position of the particle, x = 2.0 - 3.6t + 1.1t^2, we can calculate the position at t=1.0 s and t=3.0 s by substituting the values:
At t=1.0 s:
x = 2.0 - 3.6(1.0) + 1.1(1.0)^2 = -0.5 meters
At t=3.0 s:
x = 2.0 - 3.6(3.0) + 1.1(3.0)^2 = -20.1 meters
The change in position (Δx) over the interval is then:
Δx = (-20.1) - (-0.5) = -19.6 meters
The change in time (Δt) is 3.0 s - 1.0 s = 2.0 s.
Therefore, the average velocity (v) is given by:
v = Δx / Δt = (-19.6 meters) / (2.0 s) = -9.8 m/s
Hence, the average velocity of the particle over the interval from t=1.0 s to t=3.0 s is -9.8 m/s.
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Plz help with the math question
Answer:
the answer is 20
Find the lateral area of a regular prism with height h if the base is a square with side 2 cm and h=125mm (sorry help again :,)
the lateral area of the given regular prism is 100 square centimeters.
Given:
Base of the prism is a square with a side of 2 cm.
Height of the prism is 125 mm.
First, let's convert the height to centimeters since the base side length is given in centimeters:
125 mm = 12.5 cm (as there are 10 mm in 1 cm).
The lateral area of a prism can be calculated by multiplying the perimeter of the base by the height. Since the base of the prism is a square, the perimeter is given by 4 times the length of one side.
Perimeter of the base = 4 * side length
Substituting the given side length:
Perimeter of the base = 4 * 2 cm = 8 cm
Now, we can calculate the lateral area:
Lateral area = Perimeter of the base * Height
Lateral area = 8 cm * 12.5 cm
Lateral area = 100 cm²
Therefore, the lateral area of the given regular prism is 100 square centimeters.
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Pan Asia Mining Co.'s stock (Ticker: PAMC) is trading at $16.25 . The company's stock is expected to pay a year-end dividend of $0.78 that is expected to grow at a certain rate, • The stock's expected rate of return is 7.80%. Based on the information just given, what will be Robert's forecast of PAMC's growth rate? 4.50% 0 7.75% 3.00% 2.49% Which of the following statements accurately describes the relationship between earnings and dividends when all other factors are held constant? Long-run earnings growth occurs primarily because firms pay dividends to reward their shareholders for investing in the company. Growth in earnings requires growth in dividends. Retaining a higher percentage of earnings will result in a higher growth rate.
Retaining a higher percentage of earnings can result in a higher growth rate by providing more capital for reinvestment and fueling business expansion.
The formula for the Gordon Growth Model is as follows:
Expected Growth Rate = (Dividend / Stock Price) + Rate of Return
In this case, the dividend is given as $0.78, and the stock price is $16.25. The rate of return is stated as 7.80%. Plugging these values into the formula, we get:
Expected Growth Rate = (0.78 / 16.25) + 0.078 = 0.048 + 0.078 = 0.126
Converting this to a percentage, the expected growth rate is 12.6%. Therefore, Robert's forecast of PAMC's growth rate would be 12.6%.
The growth in earnings can contribute to the growth in dividends. Long-run earnings growth can result from various factors such as increased sales, cost management, innovation, and market expansion.
In terms of retaining a higher percentage of earnings, it can indeed result in a higher growth rate. When a company retains a higher portion of its earnings, it has more capital available for reinvestment into the business. This can be used for research and development, acquisitions, expanding operations, and other initiatives that can fuel growth. By retaining more earnings, a company can generate higher profits, which can ultimately lead to an increased growth rate.
To summarize, the relationship between earnings and dividends is that dividends are typically paid out of earnings, and growth in earnings can contribute to the growth in dividends. However, long-run earnings growth occurs due to various factors beyond just paying dividends.
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At the movies, a couple bought 2 medium drinks and a large popcorn for
$8.50. At the same theater, a family bought 3 medium drinks and 2 large
popcorns for a total of $15.00. What is the cost of a medium drink?
Ms. Howard spent 1/3 of her monthly salary on groceries and I/4 of it on entertainment. She spent 2/5 of the remainder on transportation. She then had $270 left. Find Ms. Howard’s salary
Ms. Howard's salary would be $360. Below, you will learn how to solve the problem.
Ms. Howard's salary can be found by first calculating the amount of money spent on groceries, entertainment, and transportation. 1/3 of her monthly salary was spent on groceries, so that would be $(1/3)x where x is her salary, 1/4 of her monthly salary was spent on entertainment, so that would be $(1/4)x. 2/5 of the remaining amount was spent on transportation, which is $(2/5)(x-(1/3)x-(1/4)x).
Ms. Howard then had $270 left, so we can set up the equation:
$(1/3)x + $(1/4)x + $(2/5)(x-(1/3)x-(1/4)x) = 270
Solving for x, Ms. Howard's salary would be $360.
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based on the effect size conventions, d = 0.60 is a
Based on effect size conventions, d = 0.60 is considered a moderate effect size. It is a standardized measure that quantifies the magnitude of the difference or relationship between two groups or variables.
It provides a standardized way to compare the strength of effects across different studies or contexts. Effect size conventions vary across disciplines and research areas, but a commonly used benchmark is Cohen's d. In this convention, an effect size of d = 0.20 is considered small, d = 0.50 is considered medium or moderate, and d = 0.80 is considered large.
Therefore, with a value of d = 0.60, the effect size is considered moderate according to this convention. It indicates a meaningful and noticeable difference or relationship between the groups or variables being studied, but not as strong as a large effect size would suggest.
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A study examines scores on an employment test and job performance sik months later. This study is most likely attempting to establish a. criterion validity b. face validity c. reliability d. construct validity 11. In the study by Korn, Davis, and Davis, it was determined that department chairs rated B. F. Skinner higher on their "all time" list than historians did. The study featured a(n)scale of measurement. a. nominal b. ordinal c. interval d. ratio
The study is most likely attempting to establish is Criterion validity and the study featured a(n) scale of measurement is Ordinal scale.
10). The study is most likely attempting to establish is: By criterion validity.
Criterion validity measures how well one measure predicts the outcome for another measure.
Here, we are judging how well the scores on the employment test predict the performance of the person.
Nominal Scale: This scale is used to assign labels to variables that have no numerical values.
For eg : Gender (male and female) , colour (brown blue black white)
Ordinal scale: It matters how the values are arranged, but it makes no difference how much they differ.
For eg: 1: Food applications rated from 1 to 5, 5 being the best. If a app is rated as 2 and other is rated as 4 does not mean the later is twice as good as the first.
Interval scale: An interval scale is a numerical scale where the order and size of the difference between the numbers are known. Absolute zero does not indicate absence in an interval scale, it only means there is no value.
For eg: Temperature in degree Celsius. If T1=5o Celsius and T2=15o Celsius this means is a temperature difference of 10o , but with T3=0o does not mean there is no temperature.
Ratio scale: The ratio scale is another numerical scale where the order and size of the difference between the values are known, and where absolute zero denotes the absence of values.
For eg: Salary of people
11). The study featured a(n)scale of measurement is: By ordinal scale
We will rank the chairs on a scale where order counts and the size of the difference is not particularly significant.
Hence, for 10th the option A is correct and for 11th the option B is correct.
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Help please!
The numbers are 152° and 28°
Answer:
62
Step-by-step explanation:
152-90= 62
Question 12 (5 points)
Find the value x in the figure below and write your answer below.
Answer:
48
Step-by-step explanation:
Solve the system using elimination
2x - 3v = - 19
5x+2v = - 19
Answer:
x = -5
v = 3
Step-by-step explanation:
2x - 3v = -19
3v = 2x + 19
v = (2/3)x + (19/3)
5x + 2((2/3)x + (19/3)) = -19
5x + (4/3)x + (38/3) = -19
(19/3)x = -95/3
x = -5
2(-5) - 3v = -19
-3v = -9
v = 3
i need help what is 7h+1−h+4?
Answer:
6h+5
Step-by-step explanation:
7h-h=6h
1+4=5
Hope this helps :)
Answer:
6h + 5 is the correct answer
Step-by-step explanation:
7h + 1 - h + 4
7h + 1 + 4 - h
7h + 5 - h
6h + 5
hope this helped!
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What is "seven less than a number cubed"?
Answer:
n³ - 7
Step-by-step explanation:
number = n
because 7 is less then the number cubed it's being subtracted by n³