The function has an inverse that is also a function is g(x)=2x-3
What is Inverse function?A function that can turn into another function is known as an inverse function or anti function. In other terms, the inverse of a function "f" will take y to x if any function "f" takes x to y. The inverse function is designated by f⁻¹ or F⁻¹ if the function is written by f or F. Here, (-1) should not be confused with an exponent or an inverse.
A function takes in values, applies specific procedures to them, and produces an output. The inverse function works, agrees with the outcome, and returns to the initial function.
The solution in which x and y have been reversed is known as an inverse function.
The vertical line test determines whether a function succeeds or fails when you solve for y once more.
1. Here g(x) = 2x - 3 has inverse x = 2y - 3 which simplifies to;
[tex]y=\frac{x-3}{2}[/tex]
This is a line and is a function;
[tex]y=\frac{x}{2} +\frac{1}{2}[/tex]
2. k(x) = -9x² has the inverse x = -9y² which simplifies to;
[tex]y=\sqrt{x/(-9)}[/tex]
This is a function but only for certain values of x.
3. f(x) = |x+2| is an absolute value function.
Not all absolute value functions have function-based inverses.
4. A function's inverse does not exist for the equation w(x) = -20.
The function therefore has a negative that is also a function, which is
g(x)= 2x – 3.
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the following frequency distribution displays the weekly sales of a certain brand of television at an electronics store. number sold frequency 01-05 12 06-10 5 11-15 5 16-20 5 21-25 25 how many weeks of data are included in this frequency distribution?
There are 52 weeks of data included in this frequency distribution.
The given frequency distribution displays the weekly sales of a certain brand of television at an electronics store.
We need to find the number of weeks of data included in this frequency distribution.From the given data, we can see that the frequency column represents the number of televisions sold per week.
To find the number of weeks of data included, we need to sum up the frequency column. Summing up the frequency column gives us:12 + 5 + 5 + 5 + 25 = 52
Therefore, there are 52 weeks of data included in this frequency distribution.
The given frequency distribution displays the weekly sales of a certain brand of television at an electronics store. We need to find the number of weeks of data included in this frequency distribution.
From the given data, we can see that the frequency column represents the number of televisions sold per week. To find the number of weeks of data included, we need to sum up the frequency column. Summing up the frequency column gives us:
12 + 5 + 5 + 5 + 25 = 52
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suppose the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. based on this information, what interval of prices would we expect at least 95% of new car prices to fall within?
New car prices to fall within is $18,300 - $41,900
Interval of prices would we expect at least 95% of new car prices to fall within Suppose that the average price for new cars has a mean of $30,100, a standard deviation of $5,600 and is normally distributed. Based on this information, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.How to solve the problem? We know that the average price of new cars is $30,100 and the standard deviation is $5,600. The normal distribution has 95% of the data points within two standard deviations of the mean. Therefore, the interval of prices that we would expect at least 95% of new car prices to fall within is given by:Lower limit: $30,100 - 2 × $5,600 = $18,300Upper limit: $30,100 + 2 × $5,600 = $41,900Thus, the interval of prices that we would expect at least 95% of new car prices to fall within is $18,300 - $41,900.
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Attitudes toward school. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. The mean score for U.S. college students is about 115, and the standard deviation is about 30. A teacher who suspects that older students have better attitudes toward school gives the SSHA to 25 students who are at least 30 years of age. Their mean score isAttitudes toward school. The Survey of Study
Habit= 127.8.
(a) Assuming that ? = 30 for the population of older students, carry out a test of
H0: ?= 115
H0: ?> 115
Report the P-value of your test, and state your conclusion clearly.
(b) Your test in part (a) required two important assumptions in addition to the assumption that the value of ? is known. What are they? Which of these assumptions is most important to the validity of your conclusion in part (a)?
(a) To test the hypotheses H0: µ = 115 and H1: µ > 115, we will conduct a one-sample t-test using the given information.
Step 1: Calculate the t-value.
t = (sample mean - population mean) / (standard deviation / √sample size)
t = (127.8 - 115) / (30 / √25)
t = 12.8 / 6
t = 2.13
Step 2: Determine the degrees of freedom (df).
df = sample size - 1
df = 25 - 1
df = 24
Step 3: Find the P-value.
Using a t-table or calculator, find the P-value corresponding to t = 2.13 and df = 24. The P-value is approximately 0.022.
Step 4: State the conclusion.
Since the P-value is less than the commonly used significance level of 0.05, we reject the null hypothesis (H0: µ = 115) and conclude that the mean score for older students is significantly higher than the mean score for the entire population.
(b) The two important assumptions for the t-test are:
1. The sample is randomly selected from the population.
2. The population is normally distributed.
The most important assumption for the validity of the conclusion in part (a) is the normality of the population. If the population is not normally distributed, the results of the t-test may not be valid, and the conclusion may be inaccurate.
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help me please!!!!!!!!!!!!!!!!!!!!!!!!!!!!
A shape's perimeter is calculated by adding the lengths of all of its sides and edges. The V's direction is [tex](-5, -12)[/tex] .
What dimensions are expressed in linear units?The complete length of a shape's boundary is referred to as the perimeter in geometry. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.
We need to know the lengths of all the sides of Fard ZH in order to calculate its perimeter. We can see from the diagram that [tex]ZF = ZD + DF = 24 + 28 = 52[/tex] and [tex]FH = ZG = 30 and ZH = 36.[/tex]
As a result, Fard ZH's perimeter is as follows:
perimeter = [tex]= ZF + FH + ZH + ZG[/tex]
perimeter [tex]= 52 + 30 + 36 + 30[/tex]
perimeter [tex]= 148[/tex]
So the perimeter of Fard ZH is [tex]148[/tex] .
(3) The vector that connects points A and B must be identified in order to determine the direction of V, and it can be written as follows:
[tex]V = (xB - xA, yB - yA)[/tex]
Where xA and yA represent point A's x and y coordinates, and xB and yB represent point B's x and y coordinates.
Plugging in the given values, we get:
[tex]V = (5 - 10, 2 - 14)[/tex]
[tex]V = (-5, -12)[/tex]
Therefore, The V's direction is [tex](-5, -12)[/tex] .
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vhat is the volume of the composite figures
104 ft³
120 ft³
150 ft³
160 ft³
Based on the attached figure, the volume of the composite figure is 408 cm³
Calculating the volume of the figureA composite figure is a three-dimensional shape that is made up of two or more simpler shapes.
To find the volume of a composite figure, you need to break it down into its simpler shapes and then use the appropriate formulas to calculate the volume of each individual shape
The volume of the composite figure is:
Volume = area of base * height
Substituting:
Base area = (14 * 3) + (1/2)(5 + (14-6))(7 - 3) = 68 cm²; height = 6 cm
So, we have
Volume = area of base * height = 68 cm² * 6 cm = 408 cm³
This means that
The volume is 408 cm³
Hence, the volume is 408 cm³
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the australian sheep dog is a breed renowned for its intelligence and work ethic. it is estimated that 45% of adult australian sheep dogs weigh 65 pounds or more. a sample of 12 adult dogs is studied. what is the mean number of dogs who weigh 65 lb or more?
5.4 out of the 12 adult Australian sheep dogs in the sample weigh 65 pounds or more, on average.
We can start by calculating the likelihood that a single adult Australian sheep dog weighs 65 pounds or more using the provided estimate of 45%. If p represents the percentage of adult dogs weighing 65 pounds or more, the following is the result:
p = 0.45
Next, we may calculate the median number of dogs weighing 65 pounds or more using the sample size of 12. If X represents the proportion of dogs in the sample that weigh 65 pounds or more, X will follow a binomial distribution with n = 12 and p = 0.45 as its parameters.
The formula for X's mean or expected value is:
E(X) = np
When we change the values of n and p, we obtain:
E(X) = 12(0.45) = 5.4
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a rod placed up against a wall is sliding down. the distance between the top of the rod and the foot of the wall is decreasing at a rate of 9 inches per second. when this distance is 152 inches, how fast is the distance between the bottom of the rod and the foot of the wall changing? the rod is 172 inches long.
when the distance between the top of the rod and the foot of the wall is 152 inches, the distance between the bottom of the rod and the foot of the wall is decreasing at a rate of approximately 19.08 inches per second.
In this case, we are given that the distance between the top of the rod and the foot of the wall is decreasing at a rate of 9 inches per second. We want to find the rate at which the distance between the bottom of the rod and the foot of the wall is changing.
We can start by using the Pythagorean theorem to relate the three distances involved: the height of the rod (h), the distance between the top of the rod and the foot of the wall (x), and the distance between the bottom of the rod and the foot of the wall (y). Specifically, we have:
[tex]h^2 = x^2 + y^2[/tex]
To find the rate at which y is changing, we can take the derivative of both sides of this equation with respect to time (t), using the chain rule:
2h dh/dt = 2x dx/dt + 2y dy/dt
We are given that dh/dt = -9 inches per second (since h is decreasing). We also know that h = 172 inches and x = 152 inches (when y = 0). Substituting these values and solving for dy/dt, we get:
dy/dt = (h/x) * (dx/dt - (x/y) * dh/dt)
dy/dt = (172/152) * (-9 - (152/y) * 9)
dy/dt = -19.08 inches per second (rounded to two decimal places)
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What is value of x?
Enter your answer in the box.
X =
B
8
A
X+4
12
2x + 1
C
Next ►
We can deduce that X + 4 = 8 by looking at the top row & second column. The X value is therefore 4.
The word "column" has what meaning?an arrangement of written or printed items on a page that are vertical. a vertical part of a printed page divided into two or more equal columns of numbers.
X + 4 corresponds to a value in the second column and top row.
The third row's value is equal to the first column's value plus two.
(Third row, second column) The value is 12 at the bottom right corner.
First row and the first column, top left, represents value as B.
It reads 8, first row, second column, in the upper right corner.
C is the value located on the bottom left (third row, first column).
We can deduce that X + 4 equals 8 from top row & second column. Hence, we can find X:
X plus 4 = 8
When we take 4 away from both sides, you get:
X = 4
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the marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6. what is the probability that a class of 36 has an average midterm mark that is more than 77.83?
The probability that a class of 36 has an average midterm mark that is more than 77.83 is 0.0766. This is because the mean of the normally distributed marks is 78 and the standard deviation is 6. Using the standard normal distribution formula, we can calculate the probability that the average mark of 36 students is more than 77.83.
Standard Normal Distribution Formula: P(x > a) = 1 - P(x < a)
P(x > 77.83) = 1 - P(x < 77.83)
P(x > 77.83) = 1 - 0.9234
P(x > 77.83) = 0.0766
PLEASE HELP ME if you you thank you so much! I need all calculations to receive full credit
Answer:
The television tower is 132 feet high.
Step-by-step explanation:
Let h be the height of the television tower. Set up and solve this proportion.
[tex] \frac{3}{5} = \frac{h}{220} [/tex]
[tex]5h = 660[/tex]
[tex]h = 132[/tex]
solve the inequality -8x < 32 should it be reveresed
The value of x for the given inequality to justify the equation to get the desired result of the equation is x < - 4 .
Define inequality:
In mathematics, inequality refers to a statement that compares two values or expressions, indicating that one value or expression is greater than or less than the other. An inequality can be represented using symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "≠" (not equal to). For example, "2x + 3 > 5" is an inequality that states that the expression "2x + 3" is greater than "5". Inequalities are often used in algebra, calculus, and other branches of mathematics to represent relationships between variables or to solve equations.
What about equation in the relation?
In mathematics, an equation is a statement that asserts the equality of two expressions. An equation consists of two expressions, separated by an equals sign "=" and it states that the value of one expression is equal to the value of the other expression. The expressions in an equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used in many areas of mathematics to describe relationships between variables, to solve problems, and to make predictions. For example, the equation "x + 3 = 7" states that the value of the expression "x + 3" is equal to "7".
According to the given information:
For the following equation we have that,
⇒ - 8x < 32
⇒ -x < [tex]\frac{32}{8}[/tex]
⇒ -x < [tex]4[/tex]
⇒ x < [tex]- 4[/tex]
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This quarter, a local gym has 759 members. That is 65% more than it had last quarter, due to a change in rates. How many members were there last quarter?
Answer:
759=165% of last quarters members so you could divide by 1.65(move the decimal place twice to the left) so you get 460 people were there last quarter
Step-by-step explanation:
match the quadratic equation with the easiest method that could be used to find the solutions.
The quadratic equation with the easiest method that could be used to find the solutions:
5x² + 24x + 21 = 0 :: Factoring
x² + 4x + 27 = 0 :: Completing the Square
x² + 8x + 15 = 0 :: Factoring
-3x² = -5x + 8 :: Dividing by x and simplifying gives Quadratic Formula
What is equation?An equation is a mathematical statement that uses an equal sign to show that two expressions are equal. It contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The goal of an equation is to solve for the variable(s) that make the equation true.
Here,
The easiest method to find the solutions of a quadratic equation depends on the form of the equation and the tools available. Here are some common methods and when they are typically used:
Zero Product Property/Factoring: This method is used when the quadratic equation can be factored into two linear factors, each of which equals zero.
Square Root Property: This method is used when the quadratic equation is in the form of x² = a, where a is a positive number. For example, the equation x² = 9 can be solved using the Square Root Property: take the square root of both sides and remember to include both the positive and negative roots, giving x = ±3.
Completing the Square: This method is used when the quadratic equation is in the form of x² + bx + c = 0, where b and c are constants. Completing the square involves adding and subtracting a constant term to both sides of the equation to create a perfect square trinomial, which can then be factored and solved using the Square Root Property.
Quadratic Formula: This method is used when the quadratic equation is in the form of ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. The Quadratic Formula is x = (-b ± √(b² - 4ac)) / 2a.
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A boutique wants to determine how the amount of time a customer spends browsing in the store affects the amount the customer spends. 2 1 The equation of the regression line is Y - 2+0.98 40 30 . A browsing time of 17 minutes is found to result in an amount spent of 40.3 dollars. What is the predicted amount spent? Ex: 7.9 dollars 20 . 10 Where is the observed value in relation to the regression line? Pick 0 10 20 40 50 dollars Pick Browsing time in minutes) A browsing time of 14 minutes is found to result in a amount spent of 10.84 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? A browsing time of 28 minutes is found to result in a amount spent of 27.2 dollars. What is the predicted amount spent? Where is the observed value in relation to the regression line? dollars ✓ Pick above below 2 on Check Next
EXPLANTION:
1. For a browsing time of 17 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X, where X is the browsing time in minutes.
Step-by-step:
Y = 2 + 0.98(17)
Y = 2 + 16.66
Y = 18.66 dollars
The observed value (40.3 dollars) is above the regression line, as it is higher than the predicted amount spent (18.66 dollars).
2. For a browsing time of 14 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X.
Step-by-step:
Y = 2 + 0.98(14)
Y = 2 + 13.72
Y = 15.72 dollars
The observed value (10.84 dollars) is below the regression line, as it is lower than the predicted amount spent (15.72 dollars).
3. For a browsing time of 28 minutes, the predicted amount spent can be calculated using the equation of the regression line:
Y = 2 + 0.98X.
Step-by-step:
Y = 2 + 0.98(28)
Y = 2 + 27.44
Y = 29.44 dollars
The observed value (27.2 dollars) is below the regression line, as it is lower than the predicted amount spent (29.44 dollars).
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Help me find the slope of the line for each one it’s ok if you don’t know all of them
Answer:
1. 1/2
2. -4/1
3. 1/1
Step-by-step explanation:
Answer:
1 y=2/1+2
2 y=.25x+3
3 y=x-2
Step-by-step explanation:
Step-by-step
y=mx+b
1. 2
2. .25
3. 1
PLEASE HELP!!
Solve and explain
Answer:
Step-by-step explanation:
holy mocacrise
You must find the sum of the volume of the square prism and the square pyramid.
Enter the letter of the answer.
The sum of the volume of the square prism and the square pyramid is 672 cubic inches.
What is prism ?
A prism is a three-dimensional geometric shape that has two identical, parallel polygonal bases and rectangular sides that connect the bases. The sides are perpendicular to the bases and their shape depends on the shape of the base. For example, if the base is a square, the prism is called a square prism. If the base is a rectangle, the prism is called a rectangular prism. The height of the prism is the perpendicular distance between the bases.
According to the question:
First, let's calculate the volume of the square prism:
The formula for the volume of a square prism is V = lwh, where l is the length, w is the width, and h is the height.
In this case, the length (l) and width (w) of the prism are both equal to a, which is 10 inches, and the height (h) is 6 inches. So, we have:
V_prism = lwh = 10 x 10 x 6 = 600 cubic inches
Next, let's calculate the volume of the square pyramid:
The formula for the volume of a square pyramid is V = (1/3)Bh, where B is the area of the base and h is the height.
In this case, the base of the pyramid is a square with side length b, which is 6 inches, so the area of the base is:
[tex]B = b^2 = 6^2 = 36 square inches[/tex]
The height of the pyramid is also 6 inches, so we have:
V_pyramid = (1/3)Bh = (1/3) x 36 x 6 = 72 cubic inches
Finally, the total volume is the sum of the volumes of the prism and pyramid:
V_total = V_prism + V_pyramid = 600 + 72 = 672 cubic inches
Therefore, the sum of the volume of the square prism and the square pyramid is 672 cubic inches.
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Select the statements that are true for the graph of y=(x+2)^2+4
The true statements for the graph of y=(x+2)²2+4 are:, The vertex of the parabola is at the point (-2, 4)., The graph opens upwards, since the coefficient of the squared term is positive., The y-intercept of the graph is at the point (0, 9)., The x-coordinate of the vertex is -2, which is also the axis of symmetry of the parabola., The graph is a parabola, which is a U-shaped curve.
What is graph?
In mathematics, a graph is a visual representation of a set of points, called vertices or nodes, that are connected by lines or curves, called edges. Graphs are used to model relationships between objects or to represent data in a visual way.
In the context of coordinate geometry, a graph is a visual representation of a function or relation, which shows the relationship between the input values (x-axis) and output values (y-axis). The graph is typically a set of points plotted on a Cartesian plane, where each point represents a unique input-output pair.
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Complete Question:
Select the statements that are true for the graph of y = (x+2)²2 + 4.
a) The vertex of the parabola is (-2, 4).
b) The parabola opens upward.
c) The y-intercept of the parabola is 4.
d) The x-intercepts of the parabola are (-4, 0) and (0, 0).
e) The axis of symmetry of the parabola is a vertical line through x = -2.
fatouma is lifting wieghts over a 10 week training period . every week , she lifts 2 kg more than she lift the previous week . during the tenth week she lifts 120 kg . what mass did she lift during the week
Fatouma lifted 1 kg during the first week and 120 kg during the tenth week. Fatouma lifted 120 kg in 10 weeks, increasing by 2 kg each week.
What is linear equation ?Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0
Say the mass Fatouma lifted during the first week "x". According to the problem, she increases the weight she lifts by 2 kg every week. So, the mass of second week is "x + 2" kg, during the third week is "x + 4" kg, and so on.
Since there are 10 weeks of training, the mass she lifted during the 10th week is:
x + (10 - 1) × 2 = x + 18
We also know that during the 10th week, she lifted 120 kg. So, we can set up an equation:
x + 18 = 120
Solving for x, we get:
x = 102
Thus, Fatouma lifted 102 kg during the first week of training.
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explain the difference between cardinality and join type. describe why one-to-many cardinality is often handled using a one-to-one join.
The difference between cardinality and join type is that cardinality describes the relationship between two data tables, while join type is the specific method used to combine the two tables.
Cardinality defines the maximum number of records that can exist in one table for a relationship with another table. Cardinality can be either one-to-one, one-to-many, or many-to-many.
A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. For example, a customer can have multiple orders. In this situation, a one-to-one join type is often used because it is the most efficient way to retrieve the related data. This is because one-to-one join type only requires that one record be searched, while a one-to-many join type would require that multiple records be searched in order to find the related records. Additionally, a one-to-one join type ensures that no duplicate records will be returned in the result.
In summary, cardinality describes the relationship between two tables while join type is the specific method used to combine the two tables. A one-to-many cardinality relationship is when one record in one table can be related to multiple records in another table. To efficiently retrieve the related data, a one-to-one join type is often used. This is because it only requires that one record be searched and it ensures that no duplicate records will be returned in the result.
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the vertices of a triangle are A(8,-24) B(8,-8) C(16,-8). If the triangle is dilated by a scale factor of 1/4 what will be the coordinates of C
After the triangle is dilated by a scale factor of 1/4, the coordinates of point C' are (10, -14).
How to find the coordinates ?We can use the following formula to find the coordinates of point C' after the triangle has been dilated by a scale factor of 1/4:
C' = (1/4)(C - center) + center
where C denotes the original coordinate of point C and centre denotes the dilation center (which is not specified in the problem).
However, because this is the most common choice and is not explicitly stated, we can assume that the center of dilation is the midpoint of line segment AB. Line segment AB's midpoint is:
((8+8)/2, (-24-8)/2) = (8, -16)
So, in the formula, we can substitute this value for Centre:
C' = (1/4)(C - (8, -16)) + (8, -16)
All that remains is to plug in the coordinates of point C and simplify:
C' = (1/4)((16, -8) - (8, -16)) + (8, -16)
= (1/4)(8, 8) + (8, -16)
= (2, 2) + (8, -16)
= (10, -14)
As a result, the coordinates of point C' after the triangle has been dilated by a factor of 1/4 are (10, -14).
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Psychologists are concerned that ____ personality tests are not easy to interpret and do not always produce consistent results because they are not standardized.
Psychologists have raised concerns about the accuracy and validity of ____ personality tests, as they are not standardized. This means that the same test administered to two different people can yield different results, making it difficult to interpret. Moreover, results may be inconsistent, meaning the same test administered at different times could produce different results. This lack of consistency can lead to inaccurate interpretations and can render the tests less useful. Furthermore, there is a lack of standardization of criteria and methodologies used to evaluate personality tests, which could lead to misinterpretations of results.
In order to address these issues, it is important to use standardized personality tests, which are tested and validated to ensure consistent and accurate results. This will ensure that the tests yield consistent results and can be interpreted accurately.
Additionally, researchers must adhere to established guidelines and criteria to ensure that the results are reliable and valid. This will enable professionals to confidently use the tests and make accurate interpretations of the results.
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justin recently drove to visit his parents who live 420 miles away. on his way there his average speed was 24 miles per hour faster than on his way home (he ran into some bad weather). if justin spent a total of 12 hours driving, find the two rates (in mph). round your answer to two decimal places, if needed.
Justin's speed on his way to his parents' house was 42 mph. Therefore, his speed on his way back home was 18 mph slower, or 18 mph.
Let's use x mph to represent the pace at which Justin was travelling to his parents' house. Then, as he travelled 24 mph slower owing to the terrible weather, his speed on the way back would be (x - 24) mph.
By dividing the distance he drove by his speed, one may determine how long it took Justin to drive to his parents' house, or:
Time is a function of both speed and distance.
Similar to how long it would take Justin to drive back home:
Time is a function of distance and speed (x - 24)
Justin drove for a total of 12 hours, so we can construct the following equation:
420/x + 420/(x-24) = 12
By multiplying both sides of the equation by x(x-24), we may simplify the equation and find the value of x. After some algebraic fiddling, we arrive at:
[tex]x^2 - 24x - 840 = 0[/tex]
We can find the value of x by using the quadratic formula:
[tex]x = (24 +- \sqrt{(242 + 41840)}) / 2[/tex] or x = -18
We can determine that Justin was travelling at a speed of 42 mph as he made his way to his parents' home because the speed cannot be negative. Thus, he travelled at a speed of 18 mph less on the way back home.
We can confirm the following to see if the solution is accurate:
420/42 + 420/18 = 10 + 23.33 = 33.33
Justin did, in fact, drive for a total of 12 hours, proving that our answer is accurate.
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the radius of a right circular cone is increasing at a rate of 1.6 in/s while its height is decreasing at a rate of 2.5 in/s. at what rate is the volume of the cone changing when the radius is 136 in. and the height is 110 in.?
When the radius is 136 in. and the height is 110 in., the volume of the cone is changing at a rate of 109.76 in³/s.
The volume of a right circular cone is given by the formula V = (1/3)*πr²h, where r is the radius and h is the height. Thus, when the radius is increasing at a rate of 1.6 in/s and the height is decreasing at a rate of 2.5 in/s, the rate of change of the volume (dV/dt) is given by:
dV/dt = (1/3)*π(1.6r + 2.5h)
Substituting r = 136 in. and h = 110 in., we get
dV/dt = (1/3)*π(216 + 275) = 109.76 in³/s
Therefore, when the radius is 136 in. and the height is 110 in., the volume of the cone is changing at a rate of 109.76 in³/s.
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Answer this question. I will give brainlist.
The given diagram represents a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.
The given diagram represents a right circular cylinder with a height of 10 meters and a radius of 7 meters, which means the base of the cylinder is a circle with a radius of 7 meters. The equation of the circle is (x - 0)² + (y - 0)² = 7², where (0, 0) is the center of the circle.
The cylinder has been sliced by a plane that is parallel to the base and 4 meters from the center of the cylinder. This means the distance between the center of the cylinder and the plane is 4 meters.
Mathematically, the equation of the ellipse can be written as (x - 0)²/4² + (y - 0)²/5² = 1, where the center of the ellipse is (0, 0), and the semi-major axis is 5 meters and the semi-minor axis is 4 meters.
So, the given diagram described as a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², sliced by a plane parallel to the base and 4 meters from the center of the cylinder, resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.
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Triangle ABC is graphed.
Answer: 2+2
Step-by-step explanation: easy thanks :)
How do you solve the equation x=1.8x+32
One way to do this is to subtract 1.8x from both sides of the equation, which gives:
x - 1.8x = 32
Simplifying the left-hand side, we get:
-0.8x = 32
To solve for x, we can divide both sides of the equation by -0.8:
x = 32 / (-0.8)
Simplifying, we get:
x = -40
Use a calculator to find M Angle B to the nearest 10th.
Answer:
60.3°
Step-by-step explanation:
You want the measure of angle B in right triangle ABC with leg BC = 8 and leg AC = 14.
TangentThe tangent relation is ...
Tan = Opposite/Adjacent
Applying this to the given triangle, we have ...
tan(B) = 14/8
The arctangent function gives you the angle from the tangent.
B = arctan(14/8) ≈ 60.3°
The measure of angle B is about 60.3°.
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the perimeter of the bottom of a rectangular swimming pool is 60 meters. the area is 221 square meters. what are the dimensions of the pool?
The dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).
The perimeter of the bottom of a rectangular swimming pool is 60 meters, and the area is 221 square meters.
To find the dimensions of the pool, we can use the formula P = 2(l + w) where P is the perimeter and l and w are the length and width of the pool respectively. We can rearrange this formula to solve for either l or w, so we'll solve for l.
2(l + w) = 60
2l + 2w = 60
2l = 60 - 2w
l = (60 - 2w)/2
Now, we can use the formula A = l*w to solve for w.
221 = l*w
221 = (60 - 2w)/2 * w
221 = (60w - 2w^2)/2
442 = 60w - 2w^2
2w^2 - 60w + 442 = 0
Using the quadratic formula, we get w = 16.45 or 7.55.
Now that we know the width, we can use the formula l = (60 - 2w)/2 to find the length. For w = 16.45, l = 21.55, and for w = 7.55, l = 28.45.
Therefore, the dimensions of the pool are either (21.55, 16.45) or (28.45, 7.55).
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WILL MARK AS BRAINLEIST!! PLEASE QUICKLY
Find a point e satisfying the conclusion of the Mean Value Theorem for the function f(x) = x^-8 on the interval [1, 5].
c =
The point c satisfying the conclusion of the Mean Value Theorem for the function f(x) = x^-8 on the interval [1, 5] is: c = 1.4697
How to solve mean value theorem?The conclusion of the Mean Value Theorem says that there is a number
c in the interval (1, 5) such that:
f'(c) = (f(5) - f(1))/(5 - 1)
We are given the function f(x) = x⁻⁸
Thus:
f(1) = 1⁻⁸ = 1
f(5) = 5⁻⁸ = 0.00000256
Thus:
f'(c) = (0.00000256 - 1)/4
= -0.25
f'(c) = -8x⁻⁹
Thus:
-8c⁻⁹ = -0.25
c⁻⁹ = 0.25/8
c⁻⁹ = 0.03125
c = 0.03125^(-1/9)
c = 1.4697
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