On solving the provided question we can say that Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.
What is probability?Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.
Therefore there are 15 bottles that match both requirements (well arranged and Plastic #4).
The sample has 100 bottles in total.
As a result, the likelihood that a randomly chosen bottle is appropriately put AND is a Plastic #4 bottle is:
P(properly positioned and Plastic #4) = the number of bottles that match both requirements. / The sample's total number of bottles
P(properly positioned and Plastic #4) = 15 / 100
P(properly positioned and Plastic #4) = 0.15 or 15%
Based on Sandra's research, there is a 15% probability that a randomly picked bottle is appropriately put AND is a Plastic #4 bottle.
To know more about probability visit:
https://brainly.com/question/11234923
#SPJ1
Consider the following scores. (i) a score of 40 from a distribution with mean 50 and standard deviation 10 (ii) a score of 45 from a distribution with mean 50 and standard deviation 5 How do the two scores compare relative to their respective distributions? They are both 1 standard deviation above their respective means. They are both 1 standard deviation below their respective means. They are both 2 standard deviations below their respective means. The score of 40 is 2 standard deviations below its mean, while the score of 45 is only 1 standard deviation below its mean.
The correct answer is: They are both 1 standard deviation away from their means, but in opposite directions. The first score is 1 standard deviation below mean, while second score is 1 standard deviation above the mean.
What is standard deviation?Standard deviation is a measure of the deviation or spread from the mean (mean) of a set of data values.
More specifically, the standard deviation is calculated by taking the square root of the variance of the data. Variance is the mean square of the difference of each data point from the mean.
The first score of 40 from a distribution with a mean of 50 and a standard deviation of 10 is 1 standard deviation below the mean, because it is (50-40)/10 = -1 standard deviation from the mean.
The second score of 45 from a distribution with a mean of 50 and a standard deviation of 5 is 1 standard deviation above the mean, because it is (45-50)/5 = -1 standard deviation from the mean.
To know more about mean visit:
https://brainly.com/question/16030790
#SPJ1
Which expression is represented by the model below? pleaseeeee help!!! 30 points!!!!
8 orange cost 1.20 workout the cost of twelvel orange
Answer:
9.6$
Step-by-step explanation:
Answer: If 8 oranges cost 1.20, we can use a proportion to find the cost of 12 oranges:
8 oranges / 1.20 = 12 oranges / x
Solving for x, we can cross-multiply and get:
8 oranges * x = 1.20 * 12 oranges
8x = 14.4
x = 1.80
Therefore, 12 oranges would cost 1.80.
20 percent of 30 dvide 100
To find 20 percent of 30, you can multiply 30 by 0.2 (which is the decimal equivalent of 20 percent):
20% of 30 = 0.2 x 30 = 6
So, 20 percent of 30 is 6.
To divide 6 by 100, you can simply move the decimal point two places to the left:
6 ÷ 100 = 0.06
Therefore, if you want to find what is 20% of 30 and then divide that result by 100, the answer is 0.06.
help pls show ur work
Answer:
For #17:
This is a 45-45-90 triangle. Therefore, the missing side length (x) is equal to the other leg of the triangle, which is 6.
For #18:
This is a 30-60-90 triangle. Therefore, the missing side length (m) is equal to the hypotenuse (18) divided by 2, or 9.
For #19:
This is a 30-60-90 triangle. Therefore, the missing side length (y) is equal to the hypotenuse (12) multiplied by the square root of 3, or 12√3.
For #20:
This is a 30-60-90 triangle. Therefore, the missing side length (u) is equal to the short leg (5√3) multiplied by 2, or 10√3.
For #21:
This is not a right triangle because the angles do not add up to 180 degrees.
For #22:
This is a right triangle because the angles add up to 180 degrees and one of the angles is 90 degrees.
Step-by-step explanation:
If a = 18 in, b = 18 in, c = 30 in, and d = 48 in, and the bases of the figure are the shaded regions, what is the lateral surface area of the geometric shape formed by this net?
A.
1,728 sq in
B.
2,808 sq in
C.
1,944 sq in
D.
1,404 sq in
The lateral surface area of the geometric shape formed by the given net is 3,780 sq in.
What is lateral surface area?The lateral surface area is the sum of the areas of the trapezoidal faces and the rectangular faces.
The area of a trapezoid is given by the formula:
A = (1/2)h(b1 + b2)
where A is the area, h is the height, b1 and b2 are the lengths of the parallel sides.
Area of trapezoid 1 = (1/2)(30 + 18)(48) = 972 sq in
Area of trapezoid 2 = (1/2)(18 + 18)(48) = 864 sq in
The area of each rectangular face is given by the product of the length and the width.
Area of rectangular face 1 = 30 x 18 = 540 sq in
Area of rectangular face 2 = 48 x 18 = 864 sq in
Area of rectangular face 3 = 30 x 18 = 540 sq in
The total lateral surface area is the sum of the areas of all the faces:
Lateral surface area = Area of trapezoid 1 + Area of trapezoid 2 + Area of rectangular face 1 + Area of rectangular face 2 + Area of rectangular face 3
Lateral surface area = 972 + 864 + 540 + 864 + 540
Lateral surface area = 3,780 sq in
Therefore, the lateral surface area of the geometric shape formed by the given net is 3,780 sq in.
To know more about lateral surface area visit,
https://brainly.com/question/31221192
#SPJ1
Malik described the figure shown below. He said, " Ray ST and ray UT form angle STU." Is Malik's description correct? Explain why or why not.
Answer:
If the figure shows two rays ST and UT with a common endpoint U, then Malik's description is correct. When two rays share a common endpoint, they form an angle. The angle formed by rays ST and UT would be angle STU. So, if the figure matches this description, then Malik's statement is correct.
coordinate points: (-5,-3),(-7,-11),(4,-13). give the coordinate of the fourth vertex
The coordinate of the fourth vertex is determined as (13,-23).
What is the coordinate of the fourth vertex?To find the fourth vertex of the parallelogram, we need to use the fact that opposite sides of a parallelogram are parallel and equal in length.
Let's start by finding the vectors for two sides of the parallelogram. We can use the given coordinate points to find the vectors:
Vector AB = (xB - xA, yB - yA) = (-7 - (-5), -11 - (-3)) = (-2, -8)
Vector BC = (xC - xB, yC - yB) = (4 - (-7), -13 - (-11)) = (11, -2)
Since opposite sides of a parallelogram are parallel, we know that these two vectors are parallel.
To find the fourth vertex, we can add the vector AB to the endpoint of vector BC:
Vector CD = Vector BC + Vector AB = (11, -2) + (-2, -8) = (9, -10)
Now we can add this vector to point C to find the coordinates of point D:
Point D = (xC + CDx, yC + CDy) = (4 + 9, -13 - 10) = (13, -23)
Learn more about coordinate points here: https://brainly.com/question/17206319
#SPJ1
a tree casts a shadow that is 20 ft long. Frank is 6 ft tall, and while standing next to the tree he casts a shadow that is 4 ft long. how tall is the tree? and how much taller is the tree than frank?
for the following exercise, consider the following scenario: the weight of a newborn is 11 pounds. the baby gained one-half pound a month for its first year. find the linear function that models the baby's weight, w , as a function of the age of the baby, in months, t .
w(t) = _____
The linear function that models the baby's weight, w, as a function of the age of the baby, in months, t, is equals to the w(t) = 11 + (1/2)t.
The a straight line graph represents linear function. The linear function form is, y = f(x) = a + bx. It has an independent variable and a dependent variable. There is independent and dependent variables are x and y respectively. We have provide a scenario which consists the following informations,
The weight of new born baby = 11 pounds
The weight gained by new born baby in one month = 1/2 pounds
We have to determine a linear function which models the baby's weight (w pounds), as a function of the baby's age, in months (t). From the definition of linear function, we see here weight of baby is an dependent variable and month in first year is independent. So, the linear function of weight of baby is written as w(t) = 11 + (1/2)t , where t represents months in baby's first year. Hence, required function is w(t) = 11 + (1/2)t.
For more information about linear function, visit:
https://brainly.com/question/30339205
#SPJ4
65 POINTS, NEED HELP ASAP!!!
7. True, 8. True, 9 No, because every name had an equal chance of being drawn from the jar, 10. False
What is a probability?Probability is a branch of statistics that deals with the study of random events and their likelihood of occurrence.
7. True: Sampling bias: unequal chance of selection leading to unrepresentative samples.
8. True: Avoiding bias: random sampling, representative samples, and minimizing nonresponse bias.
9 No, because every name had an equal chance of being drawn from the jar.
10. False: Biased sample: unrepresentative sample due to factors like nonresponse or small sample size.
To know more about probability, visit:
https://brainly.com/question/13604758
#SPJ1
and with a solution pls thanks
Answer:
you didn't say which process to use while solving so I have used graphical method but I hove it's useful
What is the smallest number of cars that can tailgate in a straight line at a football game so that one car is in front of two cars,one car is behind two cars,and one car is in between 2 cars ?
Answer:
The smallest number of cars that can tailgate in a straight line at a football game is 12.
Step-by-step explanation:
Smallest Tailgate Cars Number
This can be determined by using a logic puzzle approach. If one car is in front of four cars, that's 5 cars in total. If one car is behind four cars, that's also 5 cars. And if three cars are between two cars, that's 5 sets of two cars, or 10 cars. The total number of cars is 5 + 5 + 10 = 20.
This logic puzzle approach is not applicable for all problems. It depends on the specific problem and the information provided. For certain types of problems, a different approach or method may be more appropriate. The key is to understand the problem, determine the necessary information, and select the best approach to solve it.
Answer:
3
Step-by-step explanation:
basicly one car will be in the back one in the middle and one in the front. if I'm correct then it should be 3
NO LINKS!!! URGENT HELP PLEASE!!!
Please help me with 3 and 4
Answer:
3. 5.3 ft
4. 4.5 ft
Step-by-step explanation:
3.
Let's call the height of the connection point on the tree "h". We can use trigonometry to relate the angle and the length of the guy wire to "h". Specifically, we can use the sine function:
sine of the angle = opposite / hypotenuse
In this case, the opposite side is the height "h", and the hypotenuse is the length of the guy wire, which is 8 feet. So we have:
sin(42) = h / 8
To solve for "h", we can multiply both sides by 8:
h = 8 sin(42)
Using a calculator, we get:
h ≈ 5.3 feet
So the height of the connection point on the tree is about 5.3 feet, to the nearest tenth of a foot.
4.
The ladder, the wall, and the ground form a right triangle, with the ladder being the hypotenuse. Let's call the height on the wall that the ladder reaches "x". We can use trigonometry to relate the angle and the length of the ladder to "x". Specifically, we can use the sine function:
sine of the angle = opposite / hypotenuse
In this case, the opposite side is the height "x", and the hypotenuse is the length of the ladder, which is 5 meters. So we have:
sin(65) = x / 5
To solve for "x", we can multiply both sides by 5:
x = 5 sin(65)
Using a calculator, we get:
x ≈ 4.5 meters
So the ladder reaches a height of about 4.5 meters on the wall.
what is the value of 63,798 divided by 49?]
Answer:
1302
Step-by-step explanation:
Find the experimental probability that only 1 of
4 children in a family is a boy.
The problem has been simulated by tossing 4
coins (one to represent each child). Let "heads"
represent a boy and "tails" represent a girl. A
sample of 20 coin tosses is shown.
HTHH HTTH TTTT THTT HTHT
HHTT HHHT THHT HTTH TTHH
HTTT HTHT TTHH THTH HTHH
TTHT HTTT HTHT HHHT HHHH
Experimental Probability = [?]%
International Academy of Science. All Rights Reserved.
Q Search
60
File Explorer
Enter
Suppose the current cost of gasoline is $ 2.73 per gallon. Find the current price index number, using the 1975 price 56.7 of cents as the reference value. Question content area bottom Part 1 The current price index number is enter your response here. (Round to one decimal place as needed.)
As a result, this same current price index stands at about 481.2.
What does pricing mean?Amount offered or established as consideration again for sale of a certain item. the quantity of anything that is bought, requested, or bartered for another; also known as the price paid for something.
We may use the following formula to determine a current price index using 1975 price as reference value:
Price index: 100 multiplied by (Current market price / Reference price).
First, we must change the 56.7 cent price from 1975 to current currency:
Reference price is equal to 56.7 cents divided by $1.01 to get $0.567.
In the formula, we can then enter a current price oil $2.73 / gallon or the case the cost of $0.567 per gallon:
Price index equals ($2.73 | $0.567) x 100 ≈ 481.22
To know more about price visit:
https://brainly.com/question/19091385
#SPJ1
In which of the following scenarios will conducting a paired
-test for means be appropriate? CHECK ALL THAT APPLY.
A. To test if the proportion of low-income families is higher than that of high-income families in British Columbia.
B. To test if there is a difference between the mean number of CD4 T cells in healthy patients and patients with cancer.
C. To test if the mean annual income of Ontarians is higher than that of British Columbians.
D. To test if there is a difference between the mean annual income of husbands and that of their wives in Canada.
E. To test if there is a difference between the mean number of antibodies in patients before surgery and after surgery.
F. To test if there is a difference between the mean annual income of male British Columbians and that of female British Columbians.
G. None of the above
The appropriate scenario to conduct a paired t-test for means is when we have two related samples, and we want to test whether there is a significant difference in the means between the two samples. Hence, B, D, and E are the appropriate responses.
What is a t-test?A t-test is a statistical test used to determine whether two sets of data are significantly different from each other, based on their means. It is a parametric test, meaning it makes certain assumptions about the data, such as that it is normally distributed and that the variances of the two groups being compared are equal.
There are several types of t-tests, including the independent samples t-test, which is used when comparing two groups that are not related to each other, and the paired samples t-test, which is used when comparing two groups that are related or paired, such as before-and-after measurements from the same individuals.
B. To test if there is a difference between the mean number of CD4 T cells in healthy patients and patients with cancer.
D. To test if there is a difference between the mean annual income of husbands and that of their wives in Canada.
E. To test if there is a difference between the mean number of antibodies in patients before surgery and after surgery.
To know more about parametric test, visit:
https://brainly.com/question/30928348
#SPJ1
The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. Create a system of equations to find the smallest number of busses the orchestra can rent.
Let x= the number of busses and y= the number of vans
Create an equation representing the number of vehicles needed.
Preview Change entry mode
Create an equation representing the total number of seats in vehicles for the orchestra members.
The system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
Given that, Six of the orchestra's 111 musicians hold driving licenses for big, multi-passenger vehicles. 25 people can fit on a bus, but renting one is far more expensive. 12 persons can fit in a passenger van.
The system of equations to find the smallest number of busses the orchestra can rent is,
The total number of buses :
b + v ≤ 6
The total number of passengers.
25b + 12v ≥ 111 - - - - (2)
Thus, the system of equations to find the smallest number of buses the orchestra can rent will be b + v ≤ 6 and 25b + 12v ≥ 111.
cos(3x - 180°)=ー√3/2, where 0 < x180°
Since π/18 is greater than 0 and less than π, which is 180° in radians, this value of x satisfies the given range. Therefore, the solution to the equation cos(3x - 180°) = -√3/2, where 0 < x < 180° in radians, is x = π/18.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
cos(3x - 180°) = cos(180° - 3x)
cos(180° - 3x) = -√3/2
-cos(3x) = -√3/2
cos(3x) = √3/2
3x = π/6
x = π/18
Since π/18 is greater than 0 and less than π, which is 180° in radians, this value of x satisfies the given range. Therefore, the solution to the equation cos(3x - 180°) = -√3/2, where 0 < x < 180° in radians, is x = π/18.
To know more about trigonometry visit:
https://brainly.com/question/29002217
#SPJ1
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
Given: T=X=U=Y
Prove: TUV ~ XYZ
The triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.
What is congruent?In mathematics, congruent means that two shapes or objects have the same size and shape. They match exactly when superimposed on each other. Congruence also applies to angles, where two angles are said to be congruent if they are equal in measure. Congruence can also refer to the equality of two expressions, where two expressions are congruent when they have the same value. In other words, congruence is a term used to describe a relationship between two objects or shapes that are exactly the same size and shape.
In order to prove that two triangles are similar, we need to show that their corresponding angles are congruent. Given that angles T, X, and U are all equal, and angles X, U, and Y are all equal, we can therefore conclude that angles T and Y are also equal. This means that triangle TUV is similar to triangle XYZ since two pairs of corresponding angles are congruent. Therefore, TUV ~ XYZ.
To learn more about congruent
https://brainly.com/question/29789999
#SPJ1
The corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write : TUV ~ XYZ
What is congruent?
Congruent is a term used in geometry to describe two figures or objects that have the same shape and size. In other words, if two figures are congruent, they are identical in every way, except that they may be oriented differently or located in different positions in space.
To prove that TUV ~ XYZ, we need to show that the two triangles are similar, which means that their corresponding angles are congruent and their corresponding sides are in proportion.
Given that T=X=U=Y, we can conclude that angle TUV and angle XYZ are congruent, and angle TVU and angle YXZ are also congruent. These two angles are the corresponding angles that are congruent in the two triangles.
To show that the corresponding sides are in proportion, we need to compare the ratios of the corresponding side lengths. We can start by comparing the ratio of the lengths of TU and XY:
TU / XY = (TU / TX) * (TX / XY) (by the transitive property of equality)
TU / TX = 1 (because T = X)
TX / XY = 1 (because U = Y)
Therefore, TU / XY = 1 * 1 = 1.
Similarly, we can compare the ratio of UV and YZ:
UV / YZ = (UV / UY) * (UY / YZ) (by the transitive property of equality)
UV / UY = 1 (because U = Y)
UY / YZ = 1 (because T = X)
Therefore, UV / YZ = 1 * 1 = 1.
Therefore, the corresponding angles are congruent and the corresponding sides are in proportion, we can conclude that the two triangles are similar, and we can write:
TUV ~ XYZ
To know more about congruent and given link below-
https://brainly.com/question/12413243
#SPJ1
From a circular card sheet of radius 14 cm, two circles of radius 3.5 cm and a rectangle of length 3 cm and breadth 1cm are removed. (as shown in the adjoining figure). Find the area of the remaining sheet. (show working too)
The area of remaining sheet is 536 cm²
Since, we know that the area of circle [tex]=\pi \times r^2[/tex]
Area of bigger circle [tex]=\dfrac{22}{7} \times14\times14[/tex]
[tex]=44\times14[/tex]
[tex]=616 \ \text{cm}^2[/tex]
Thus, the area of bigger circle is 616 cm²
Similar way, the area of 2 smaller circles [tex]=2\pi r^2[/tex]
[tex]=2\times\dfrac{22}{7} \times3.5\times3.5[/tex]
[tex]=44\times0.5\times0.5[/tex]
[tex]=77 \ \text{cm}^2[/tex]
Thus, the area of 2 smaller circle is 77 cm²
[tex]\text{Area of rectangle}=\text{Length}\times\text{Breadth}[/tex]
[tex]=3\times1=3 \ \text{cm}^2[/tex]
Thus, the area of rectangle is 3 cm²
Now, remaining area of sheet = Area of bigger circle − Area of both smaller circle − Area of rectangle
[tex]=616-77-3=536 \ \text{cm}^2[/tex]
Hence, area of remaining sheet is 536 cm²
Triangles CDE and NOP are similar.
The lengths of CD and NO are 53 inches and 212 inches.
DE is 106 inches long and NP is 318 inches. Find OP and CE.
Answer:
OP = 424: CE = 79,5
Step-by-step explanation:
I added a photo of my solution
48. Graph the vertical line x = -2. Then name its intercept.
Answer:
There is no y intercept because the graph does not cross the y axis.
The x intercept is (-2,0)
Step-by-step explanation:
Helping in the name of Jesus.
I need help with all 3 task
The volume of the cylinders are;
1. 602. 88 cm³
2. 56.52 cm³
3. 141. 3 cm³
How to determine the volumeThe formula for calculating the volume of an open cylinder is expressed as;
V = πr²h
Such that the parameters are;
V is the volume of the cylinder.r is the value of the radius.h is the height of the cylinder.Then, we have;
Substitute the values
1. Volume = 3.14 × 4² × 12
Multiply the values after finding the square
Volume = 602. 88 cm³
2. Substitute the values
Inner radius, r = 2cm
Volume =3.14 × 1.5 ² × 8
Multiply the values, we get;
Volume = 56.52 cm³
3. Substitute the values
Inner radius = 2cm
Volume = 3.14 × 3² × 5
Multiply the values
Volume = 141. 3 cm³
Learn about open cylinders at: https://brainly.in/question/36146634
#SPJ1
The image shows line p
Ethan and Rylee hiked 5 13/15 miles. In one day, Gianna hiked 3 3/4 times as far as Ethan and Rylee hike. How far did she hike?
Answer: 22 miles in one day
Step-by-step explanation:
To find how far Gianna hiked, we first need to convert the mixed number for Ethan and Rylee's hike into an improper fraction, and then multiply it by 3 3/4 to find the distance Gianna hiked.
Ethan and Rylee's hike (5 13/15):
(15 * 5) + 13 = 88
So, they hiked 88/15 miles.
Now, let's convert the mixed number 3 3/4 into an improper fraction:
(4 * 3) + 3 = 15
So, 3 3/4 = 15/4.
Next, we'll multiply the two improper fractions together:
(88/15) * (15/4) = (88 * 15) / (15 * 4) = 1320 / 60
Now, simplify the fraction:
1320 ÷ 60 = 22
So, Gianna hiked 22 miles in one day.
7. Gretchen makes pillows using *
15 yards of fabric per pillow.
She has 814 yards of fabric. What
is the greatest number of pillows
Gretchen can make?
O A 4
OB 5
C 6
OD 8
A pair of linear equations is shown: y = −3x + 5 y = x + 2 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1. On a graph, find the point of intersection of two lines; the first line has y-intercept = −3 and slope = 5, and the second line has y-intercept = 1 and slope = 2. On a graph, find the point of intersection of two lines; the first line has y-intercept = −5 and slope = 3, and the second line has y-intercept = −2 and slope = −1. On a graph, find the point of intersection of two lines; the first line has y-intercept = 3 and slope = −5, and the second line has y-intercept = −1 and slope = −2.
Answer:
The best explanation for the steps to solve the pair of equations graphically is:
On a graph, find the point of intersection of two lines; the first line has y-intercept = 5 and slope = −3, and the second line has y-intercept = 2 and slope = 1.
To solve the pair of equations graphically, you need to plot the two lines on the same coordinate plane and find the point where they intersect. To do this, you can use the slope-intercept form of the equations, which gives the y-intercept and the slope of each line. The y-intercept is the value of y when x equals 0, and the slope represents how steep the line is. Once you have graphed the two lines, the point where they intersect is the solution to the system of equations. In this case, the intersection point can be found by solving the system of equations, which is (x, y) = (2, -1).
Please help me. With problem 11 here
The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.
What is expression ?An expression is a mathematical phrase that can contain numbers, variables, operators, and sometimes functions. Expressions are used to represent or calculate values, and they can be simple or complex. For example, "2 + 3" is a simple expression that can be evaluated to give the value 5, while "3x + 2y - 4" is a more complex expression that contains variables and can only be evaluated if values are assigned to the variables. Expressions can also be combined to form more complex expressions using operators like addition, subtraction, multiplication, and division.
According to the given information:To find the inverse function of g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)), we can follow these steps:
Step 1: Replace g(x) with y, so that the function becomes g'(x) = -y.
Step 2: Solve the equation for y in terms of x: y = - g'(x) = - (sqrt(x) + 6)/(1 - sqrt(x)).
Step 3: Interchange x and y: x = - (sqrt(y) + 6)/(1 - sqrt(y)).
Step 4: Solve for y in terms of x:
[tex]x = - (sqrt(y) + 6)/(1 - sqrt(y))\\x(1 - sqrt(y)) = -sqrt(y) - 6\\x - x sqrt(y) = -sqrt(y) - 6\\x + 6 = (x + 1) sqrt(y)\\(x + 6)/(x + 1) = sqrt(y)\\[/tex]
[tex]y = [ (x + 6)/(x + 1) ]^2[/tex]
Therefore, the inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is:g^-1(x) = [ (x + 6)/(x + 1) ]^2[/tex]
Note that this function is defined for all x except x = 1, where the original function g(x) is not defined. Therefore, g(x) is not invertible at x = 1.
Therefore, The inverse function of [tex]g'(x)=- g(x) = (sqrt(x) + 6)/(1 - sqrt(x)) is g^-1(x) = [ (x + 6)/(x + 1) ]^2.[/tex] However, the function is not invertible at x = 1 where g(x) is not defined.
To know more about expression visit :
https://brainly.com/question/1859113
#SPJ1