Answer:
(-2, -6, -6)
Step-by-step explanation:
The center of the sphere, O, and point A, are located on the same diameter of the sphere, AB. Thus, the line segment joining these two points is the radius of the sphere. Therefore, the length of the line segment, OA = OB = r, where r is the radius of the sphere.
We can find the length of the line segment, OA, using the distance formula:
√((5 - 2)^2 + (1 + 3)^2 + (1 - 5)^2) = √(3^2 + 4^2 + (-4)^2) = √49 = 7
Since OA = OB = 7, the coordinates of B can be found by subtracting the radius, 7, from the x, y, and z-coordinates of point A:
B = (5 - 7, 1 - 7, 1 - 7) = (-2, -6, -6)Therefore, the coordinates of B are (-2, -6, -6).
The large tank begins with 600 gallons of oil. The flow rate is recorded as –4 gallons per minute. After a period of 32 minutes, how much oil has been moved and to which tank?
After a period of 32 minutes 128 gallons of oil is moved from a large tank to a small one.
What is the flow rate?
The quantification of bulk fluid movement is called flow measurement. The mass of a material that moves per unit of time is known as the mass flow rate. The amount of fluid moving per unit of time is known as the volumetric flow rate.
Here, we have
Given that the flow rate is recorded at -4 gallons per minute, which is negative.
It means that the oil is flowing in the small tank.
The rate of flow, r is 4 gallons per minute, here work is oil flowing into a tank
Rate of flow, r = oil flown in a tank/time taken
Given that time, t = 32 minutes
∴ rate of flow × time taken = Oil flown in small tank
⇒ r× t = oil flown in small tank = 4 × 32 = 128 gallons
Hence, after a period of 32 minutes 128 gallons of oil is moved from a large tank to a small one.
To learn more about the flow rate from the given link
https://brainly.com/question/13559135
#SPJ1
Tanya went to the store and bought a box of spaghetti noodles for $4. She also bought x pounds of ground beef for $3.52 per pound. The total amount of money Tanya spent can be represented by the equation 18 = 3.52x + 4. How many pounds of ground beef did Tanya buy?
Answer:
Answer is in the attached photo.
Step-by-step explanation:
SolutionThe solution is in the attached photo, do take note for this question, we will have to make x the subject and solve for x.
What number to the power of three is 500000?
The number that, when raised to the power of three, equals 500000 is approximately 100.
To find this number, we can use the cube root function:
x^3 = 500000
x = cube root of (500000)
x = approximately 100
So, the number that, when raised to the power of three, equals 500000 is approximately 100.
La masse d’un atome est de 1,05•
Answer:La masse d'un atome de cuivre est de 1,05 x 10^-25 kg. Un atome de cuivre comporte 29 électrons. Ces electrons constituent le nuage electronique de l'atome. chaque electron a une masse de 9,11 x 10^-311.
Step-by-step explanation:
Now given your positive test result from test 2, what is doctor b's posterior probability for the hypothesis that you do have cogscitis?
The posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.
With your positive test result from Test 2, we must apply Bayes' theorem to get Doctor B's posterior probability that you have cogscitis, which is:
P(A|B) = P(B|A) * P(A) / P(B)
The following probabilities are known:
P(A) = 0.001 (the population prevalence and previous likelihood of getting cogscitis)
P(B|A) = 0.95 (the possibility of receiving a positive Test 2 result while having cogscitis)
P(B|not A) = 0.10 (the possibility of receiving a positive test result from Test 2 even if you do not have cogscitis)
The law of total probability, which asserts the following, can be used to determine the marginal probability of a positive test result (P(B)):
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
where:
P(not A) = 1 - P(A) = 0.999 (the multiplier of the previous probability of contracting cogscitis)
Substituting the values, we get:
P(B) = 0.95 * 0.001 + 0.10 * 0.999 = 0.1008
The posterior probability of developing cogscitis can now be determined, given a positive test result from Test 2:
P(A|B) = P(B|A) * P(A) / P(B)
= 0.95 * 0.001 / 0.1008
= 0.0094
Therefore, the posterior probability of having cogscitis, given a positive test result from Test 2, is 0.0094 or about 0.94%. This indicates that even though you had a positive Test 2 result, the likelihood that you actually have CNS inflammation is still extremely low less than 1%.
To learn more about posterior probability , visit the link below:
https://brainly.com/question/29100510
#SPJ4
help pls, i dont get this
Answer:
Your already got it.
Step-by-step explanation:
I have no explanation for this.
For a classical infinite square-well potential of width a. How does the classical result compare with the quantu
For small particles such as atoms and subatomic particles, quantum mechanics produces more accurate results than classical mechanics. As the particle size decreases, the differences between classical and quantum mechanical results become more pronounced.
The particle in an infinite square well potential is treated as a point particle with well-defined position and momentum in classical mechanics. The classical solution to the infinite square well problem involves a particle bouncing back and forth between the well's walls, its energy being provided by the kinetic energy associated with its motion inside the well.
In quantum mechanics, on the other hand, the particle in an infinite square well potential is treated as a wave function that solves the Schrödinger equation. The probability distribution of the particle's position and momentum inside the well is described by the wave function. The allowed energy levels of the particle are quantized and can be calculated using the problem's boundary conditions.
The following formula gives the classical result for a particle's energy in an infinite square well potential:
[tex]n2*h2/(8ma2) = E n[/tex]
where n is an integer, h is Planck's constant, and m is the particle's mass. According to this formula, energy levels are continuous and can take any value.
The quantum mechanical result for a particle's energy in an infinite square well potential, on the other hand, is given by the formula:
[tex]E n = (n2 * pi2 * h2) / (2ma2).[/tex]
n must be a positive integer. According to this formula, energy levels are quantized and can only take on discrete values.
As a result, the classical result for the energy of a particle in an infinite square well potential differs greatly from the quantum mechanical result. The classical result predicts continuous energy levels, whereas the quantum mechanical result predicts quantized energy levels.
To learn more about quantum mechanics
https://brainly.com/question/11855107
#SPJ4
Hayden use 2.25 cups of water in his lemonade mixture that serves nine people Christian use 3.75 cups of water in his own lemonade mixture that serves 10 people how much more water is in one serving of Christians lemonade.
One serving of Christian's lemonade has 0.125 cups more water than one serving of Hayden's lemonade.
What is lemonade?Lemonade is a sweetened beverage made from lemon juice, water, and sugar. It is typically served cold, and may also include other ingredients such as fruit, herbs, or carbonated water. Lemonade is a popular summer drink that is enjoyed in many parts of the world.
First, we can find the amount of water per serving in Hayden's lemonade by dividing the total amount of water (2.25 cups) by the number of servings (9 people):
Water per serving in Hayden's lemonade = 2.25 cups / 9 = 0.25 cups per serving
Next, we can find the amount of water per serving in Christian's lemonade by dividing the total amount of water (3.75 cups) by the number of servings (10 people):
Water per serving in Christian's lemonade = 3.75 cups / 10 = 0.375 cups per serving
To find how much more water is in one serving of Christian's lemonade compared to one serving of Hayden's lemonade, we can subtract the water per serving in Hayden's lemonade from the water per serving in Christian's lemonade:
Water per serving difference = 0.375 cups per serving - 0.25 cups per serving = 0.125 cups per serving
Therefore, one serving of Christian's lemonade has 0.125 cups more water than one serving of Hayden's lemonade.
To know more beverage visit:
brainly.com/question/20302225
#SPJ1
Need some helppp on this question will give 20 points
[tex]\cfrac{\sqrt[3]{27xy^3}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{\sqrt[3]{3^3 xy^3}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{(3^3 xy^3)^{\frac{1}{3}}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{3^{3\cdot \frac{1}{3}}x^{\frac{1}{3}}y^{3\cdot \frac{1}{3}}}{5x^{\frac{4}{3}}y^2}\implies \cfrac{3x^{\frac{1}{3}}y}{5x^{\frac{4}{3}}y^2}[/tex]
[tex]\cfrac{3}{5}\cdot \cfrac{x^{\frac{1}{3}}y}{x^{\frac{4}{3}}y^2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}}yx^{-\frac{4}{3}}y^{-2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}}x^{-\frac{4}{3}}yy^{-2}\implies \cfrac{3}{5}\cdot x^{\frac{1}{3}-\frac{4}{3}} y^{1-2} \\\\\\ ~\hfill {\Large \begin{array}{llll} \stackrel{a ~~~~ b ~~ ~~ c}{0.6 x^{-1}y^{-1}} \end{array}}~\hfill[/tex]
Find the value of x.
6x
60°
Answer:
Step-by-step explanation:
If you are implying that the equation is "6x = 60"
Divide both sides by 6 to get just x by itself, then you'd have your answer.
X = 10
g hich is more affected by extreme observations, the mean or median? and how about the standard deviation or iqr? mean, standard deviation mean, iqr median, standard deviation median, iqr
The combinations that are more affected by extreme observations are mean and standard deviation, while the combinations that are less affected are median and IQR.
The mean is more affected by extreme observations, because it takes into account the value of every observation in the data set, whereas the median only considers the middle value(s) and is therefore less sensitive to extreme values.
The standard deviation is more affected by extreme observations, because it takes into account the difference between each observation and the mean of the data set. A single extreme value can have a large impact on the mean, and therefore on the standard deviation.
On the other hand, the interquartile range (IQR) is less affected by extreme observations, because it only considers the range of the middle 50% of the data. The median and IQR are often used together to describe a data set that has extreme values or is not normally distributed.
To learn more about standard deviation please click on below link
https://brainly.com/question/23907081
#SPJ4
Sam asked 15 of his friends what they thought about the pizza they just had, is this a random or biased sample
The sample taken by Sam is Biased sampling.
What is Random sample?A subset of a population is chosen at random in a basic random sampling. Each person in the population has an exact equal probability of getting chosen using this sampling technique.
Given:
Sam asked 15 of his friends what they thought about the pizza they just had.
Sam here chooses his friend that means the people are selective already.
He already chooses the people which were known to him.
So, the selection here is biased sample.
Learn more about Random sampling here:
https://brainly.com/question/29852583
#SPJ1
Help,It's due in like 25 minutes! I know that these might be a lot of questions, but I really need help but I'll give you five points for each picture question. So that means I'll give you 25 points.
Using the table of measurement, 0.4970969 is equivalent to 800 meters
What is unit of measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. To convert a mile measurement to a centimeter measurement, multiply the length by the conversion ratio.
1 inch = 2.54 centimeters
1 foot = 0.3048 meters
1 mile = 1.60 kilometers
Recall that 1 mile is 1609.344 meters
Therefore, the equivalence is 800/1609.344
Therefore 800 meters is equivalent to 0.4970969 miles
Learn more about meters and miles on https://brainly.com/question/29018717
#SPJ1
based on your knowledge of the two data sets described below, would you expect a scatter plot describing the two data sets to have a positive, a negative, or no correlation? hourly pay and total number of sick days allowed
Based on your knowledge of the two data sets described below, would you expect a scatter plot describing the two data sets to have a no correlation.
Based on my knowledge, I would not expect there to be a strong correlation between hourly pay and total number of sick days allowed. These two variables are not directly related to each other and there is no clear reason to expect a positive or negative correlation between them. Therefore, I would expect the scatter plot to show no correlation between the two variables. However, it's worth noting that without actually seeing the data, it's difficult to definitively determine whether there is any correlation present.
To learn more about correlation here:
https://brainly.com/question/28898177
#SPJ4
Ashton just launched a new business page on social media. After one month, she has
35 followers. She decides to take a course that promises to triple her number of
followers each month for 6 months. After 7 months, how many followers will Ashton
have if this is true?
3
Step-by-step explanation:
35 times 3.sub
Give m || n, find the value of x and y
(3x+5). (8x+10)
The value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.
What do you mean by Expression?
In mathematics, an expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions can be combined and simplified to solve problems, find relationships, and evaluate the truth of statements. For example, the expression "3 + 4" is a simple expression that represents the value 7 when evaluated.
Expressions can also be more complex, involving multiple operations, variables, and functions. For example, the expression "2x + 3y - z" is a more complex expression that involves three variables and three different operations.
Given the expression (3x + 5)(8x + 10), to find the value of x and y, we have to multiply the two expressions inside the parentheses and simplify the result.
Multiplication of the expressions:
(3x + 5)(8x + 10) = 24x^2 + 76x + 50
So, the value of x and y are not specified, but the result of the multiplication is 24x^2 + 76x + 50.
Learn more about mathematical expression
https://brainly.com/question/30350742
#SPJ1
Please find the missing side length using trig
Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex] => AC = [tex]\sqrt{115}[/tex]
What is the Pythagorean theorem?Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.
Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.
Here, in this triangle by Pythagorean theorem
[tex]A^2 = B ^2 + c^2[/tex]
AC = [tex]\sqrt{14^2- 9^2}[/tex]
AC = [tex]\sqrt{196- 81}[/tex]
Ac = [tex]\sqrt{115}[/tex]
Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.
Learn more about Pythagorean here:
https://brainly.com/question/24252852
#SPJ4
question 3 a highschool teacher in new york wants to know how students in her class did on their last test. the teacher asks the 10 students sitting in the front row to state their latest test score. she concludes from their report that the class did extremely well. what is the population and what is the sample? a. population: all of the students in the highschool sample: the 10 students selected from the front row b. population: all highschool students within the country sample: all of the students who took the test c. population: all of the students in the class sample: the 10 students selected from the front row d. population: highschool students in new york sample: the students in the class who took the test
The population and the sample is option a population: all of the students in the high school sample: the 10 students selected from the front row
In this scenario, the population refers to the entire group of students that the teacher is interested in studying. The population could be all students in the high school, all high school students within the country, all students in the class, or high school students in New York, depending on the research question.
A sample, on the other hand, is a smaller subset of the population that is actually observed or measured. The teacher selected 10 students from the front row as the sample for her study.
It's important to note that the accuracy of the conclusions drawn from a sample depends on how well the sample represents the population. In this case, the teacher may have concluded that the class did extremely well based on the scores reported by the 10 students in the front row. However, it's possible that the front row students are not representative of the entire class or the entire population, which could lead to inaccurate conclusions.
To know more about population here.
https://brainly.com/question/27991860
#SPJ4
For each value of u, determine whether it is a solution to us 10.
u
8
4
10
13
Is it a solution?
Yes
O
No
X
Ś
For the given inequality, the values of u are:
u = 8 is a solution.u = 4 is a solution.u = 10 is a solution.u = 13 is not a solution.Which values of u are solutions of the inequality?We want to see which ones of the values are solutions of the inequality:
u ≤ 10
So u can be smaller than 10, or equal to 10.
For example, for the irst case u = 8.
8 ≤ 10
This is true, because 8 is smaller than 10.
Then:
u = 8 is a solution.
u = 4 is a solution.
u = 10 is a solution.
u = 13 is not a solution.
Learn more about inequalities at:
https://brainly.com/question/24372553
#SPJ1
The expression (3^8/2)(3^8/4) can be rewritten as 3 where k is a constant. What is the value of k?
The solution of the expression for the value of k is [tex]\dfrac{8}{3^{15}}[/tex].
What is an expression?Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication and division.
The given expression is,
[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]
The given expression will be solved as below,
[tex]\dfrac{3^8}{2}\times \dfrac{3^8}{4}\times k = 3[/tex]
Apply the properties of exponents which say that the number with the same base its exponents will be added.
[tex]\dfrac{3^{16}}{8}\times k = 3[/tex]
Now cross-multiply the number 3 by the ratio of 8 and the 3¹⁶ and solve for the value of k,
[tex]k = \dfrac{8}{3^{15}}[/tex]
Therefore, the value of k will be calculated as the ratio [tex]\dfrac{8}{3^{15}}[/tex].
To know more about an expression follow
https://brainly.com/question/11145952
#SPJ1
What is the area of this figure? Please show your work.
Answer:
112.13 square mm
Step-by-step explanation:
Decompose the composite figure into familiar shapes. One such decomposition is shown in the attached figure
There are four familiar shapes
A semicircle and 3 rectangles
The diameter of the semicircle = 6 mm and therefore its radius is 3mm
Area of the semicircle = 1/2 x area of circle = 1/2 x π x 3²
= 1/2 x 3.14 x 9
= 14.13 square mm
The rectangle below the semi circle has height 5 mm and width 10 mm
Area of this rectangle= 5 x 10 = 50 square mm
The rectangle at the bottom left has width = 6 mm and height = 7mm
Area of this rectangle = 6 x 7 = 42 square mm
The bottom right rectangle has width 2 mm and height 3 mm
Area of this rectangle = 2 x 3 = 6 square mm
Area of the three rectangles = 50 + 42 + 6 = 98 square mm
Total area of composite figure
= Area of 3 rectangles + Area of semicircle
= 98 + 14.13
= 112.13 square mm
a box contains 12 balls of which some are red in colour. if 6 more red balls are put in the box and a ball is drawn at random the probability of drawing a red ball doubles than what it was before. find the number of red balls in the bag.
We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added.
Let's assume that there are initially "x" red balls in the box. This means that there are (12 - x) non-red balls in the box.
When 6 more red balls are added, the total number of red balls becomes (x + 6), and the total number of balls in the box becomes (12 + 6) = 18.
We are told that the probability of drawing a red ball doubles when an extra 6 red balls are added. This means that the probability of drawing a red ball before the extra balls were added was:
P(red) = x / 12
And the probability of drawing a red ball after the extra balls were added is:
P(red) = (x + 6) / 18
We are also told that the second probability is twice the first:
(x + 6) / 18 = 2 * (x / 12)
Simplifying this equation, we get:
(x + 6) / 9 = x / 6
Multiplying both sides by 18, we get:
2(x + 6) = 3x
Expanding the left-hand side, we get:
2x + 12 = 3x
Subtracting 2x from both sides, we get:
12 = x
Therefore, there are initially 12 red balls in the box.
To learn more about probability please click on below link
https://brainly.com/question/11234923
#SPJ4
the lengths of human pregnancies (gestation) can be modeled by a bell-shaped distribution with mean 266 days and standard deviation 16 days. a certain pregnancy had a z-score of -2.5 (negative 2.5). how many days did this pregnancy last?
If a certain pregnancy had a z-score of -2.5 with mean 266 days and standard deviation 16 days , the pregnancy lasted 230 days.
We know that the length of human pregnancies can be modeled by a normal distribution with a mean of 266 days and a standard deviation of 16 days.
We are also given that a certain pregnancy had a z-score of -2.5. The z-score is a measure of how many standard deviations a data point is away from the mean. A negative z-score means that the data point is below the mean.
We can use the formula for converting a z-score to an actual value in a normal distribution:
z = (x - mu) / sigma
where z is the z-score, x is the actual value we want to find, mu is the mean, and sigma is the standard deviation.
Plugging in the given values, we get:
-2.5 = (x - 266) / 16
Solving for x, we get:
x = (-2.5 * 16) + 266 = 230
To learn more about z-score click on,
https://brainly.com/question/19547491
#SPJ4
1. Simplify the following ratios: 1.1 30:45 1.4 350:400 1.7 600 g: 4 kg 1.2 1.5 1.8 65:91 12 cm: 1m 21:750 ml 1.3 1.6 120:132:144- 3 km: 50 m
The simplified ratios are shown below:
What is Ratio?A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.
Given:
We have ratios
1. 30: 45
= 30/45
= 2 /3
2. 350 : 400
= 350/400
= 7/8
3. 600g : 4 Kg
= 600 / 4000
= 6/ 40
= 3/20
4. 65:91
= 5 / 7
5. 12 cm : 1 m
= 12 / 100
= 3 /25
6. 3 Km: 50 m
= 3000 / 50
= 60
Learn more about ratio here:
https://brainly.com/question/13419413
#SPJ9
Heidi contributes 11% of her monthly salary towards her 401(k) and her employer matches her contribution up to 6% of her salary. If the interest rate of her 401(k) is 6.25% compounded monthly and her monthly salary is $3,250, determine the amount in her account after 15 years. Round to the nearest cent.
Answer:
The amount that will be in Heidi’s account after 15 years is option A. $164,146.52.What is Future Value?It can be calculated using the formula for calculating the Future Value (FV) of an Ordinary Annuity as follows:FV = M (((1 + r)^n - 1) / r)Where;FV = Future value of the amount need to findM = total monthly contribution which is Heidi’s monthly contribution of 11% of her monthly salary + Employer monthly contribution of 6% of Heidi’s monthly salary can be calculated as;= (11% of Heidi’s monthly salary + 6.25% of Heidi’s monthly salary) = (11% of $3,250) + (6.25% x $3,250) = $552.50r = Monthly interest rate= Annual interest rate of 401(k) / 12 = 6.25% / 12 = 0.0625 / 12 r = 0.00520833333333333n = number of months = Number of years x 12 = 15 x 12 n= 180Substituting all the values into equation (1), we have;FV = $552.50 (((1 + 0.00520833333333333)^180 - 1) / 0.00520833333333333)FV = $552.50 x 297.097770863934FV = $164,146.518402324Rounding to the nearest cent, we get;FV = $164,146.52Therefore, the amount that will be in Heidi’s account after 15 years is option A. $164,146.52.
Step-by-step explanation:
.
This year 116 kangaroos were adopted from a shelter. This is 24 fewer than twice the number that were adopted last year. Write an equation that you can use to find the number of pets adopted last year?
Answer:
70
Step-by-step explanation:
Let x be the number of kangaroos adopted last year.
Twice the number adopted last year is 2x.
So, the number adopted this year is 2x - 24.
Equating this to the given number of kangaroos adopted this year, we have:
2x - 24 = 116
Adding 24 to both sides, we get:
2x = 140
Dividing both sides by 2, we get:
x = 70
So, the number of kangaroos adopted last year was 70.
From a position 3.5 m above ground level in a building, an an observer measures the angle of elevation of the top of a flagpole to be 48°, and the angle of depression of the foot of the flagpole to be 35°
. a. How far away from the flagpole is the building?
b. How tall is the flagpole?
a. The flagpole is 5 feet away from the building.
b. The height of the flagpole is 8 feet.
What are trigonometric ratios in terms of a right-angle triangle?We know a right-angled triangle has three sides they are -: Hypotenuse,
Opposite and Adjacent.
We can remember SOH CAH TOA which is,
sin = opposite/hypotenuse, cos = adjecen/hypotenuse and
tan = opposite/adjacent.
The distance from the building to the flagpole is,
tan35° = 3.5/x.
x = 3.5/0.7.
x = 5 feet.
Now, tan48° = x/5.
x = 5/1.11.
x = 4.5 feet.
Therefore, The height of the flagpole is 4.5 + 3.5 = 8 feet.
learn more about trig ratios here :
https://brainly.com/question/14977354
#SPJ9
Please help with the attached question.
A. The functions are not inverse of each other.
B. The domain of the composition using interval notation is (-∞, ∞)
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
A. To show that two functions are inverses of each other, we need to show that their compositions are equal to the identity function, which is denoted as f(x) = x.
That is, we need to show that:
(f ∘ g)(x) = x
(g ∘ f)(x) = x
where ∘ denotes function composition.
First, we'll find the composition (f ∘ g)(x):
(f ∘ g)(x) = f(g(x))
= f(9x+1)
= (9x+1) - 3
= 9x - 2
Next, we'll find the composition (g ∘ f)(x):
(g ∘ f)(x) = g(f(x))
= g(x-3)
= 9(x-3) + 1
= 9x - 26
Since (f ∘ g)(x) ≠ x and (g ∘ f)(x) ≠ x, the functions f(x) and g(x) are not inverses of each other.
B. To find the domain of (f ∘ g)(x), we need to ensure that the input to g(x) is within its domain, which it is for all real numbers. To find the domain of (g ∘ f)(x), we need to ensure that the input to f(x) is within its domain, which it is for all real numbers.
Therefore, the domains of (f ∘ g)(x) and (g ∘ f)(x) are both all real numbers, and we can express this using interval notation as:
Domain of (f ∘ g)(x) and (g ∘ f)(x):
(-∞, ∞)
To know more about Functions check:
https://brainly.com/question/5975436
#SPJ9
which equation represents the amount of money lydia spent of apples and bananas? which equation represents the amount of money ari spent on apples and bananas?
Equation represents the amount of money lydia spent of apples and bananas is 5x + 3y = 8.50. Equation represents the amount of money ari spent on apples and bananas is 3x + 2y = 5.25.
Let x be the cost per pound of apples, and let y be the cost per pound of bananas. Then, the system of equations representing the given situation is:
5x + 3y = 8.50 (Equation 1)
3x + 2y = 5.25 (Equation 2)
Equation 1 represents the amount of money Lydia spent on 5 pounds of apples and 3 pounds of bananas. It shows that the total cost of the apples and bananas that Lydia bought is $8.50. To find the cost per pound of each fruit, we need to solve for x and y.
Equation 2 represents the amount of money Ari spent on 3 pounds of apples and 2 pounds of bananas. It shows that the total cost of the apples and bananas that Ari bought is $5.25. To find the cost per pound of each fruit, we need to solve for x and y.
To solve for x and y, we can use the method of substitution or elimination. Once we find the values of x and y, we can substitute them back into Equation 1 or Equation 2 to find the cost of each fruit for Lydia and Ari.
In summary, the given situation can be represented by a system of two equations. Equation 1 represents the amount of money Lydia spent on apples and bananas, and Equation 2 represents the amount of money Ari spent on apples and bananas. To find the cost per pound of each fruit, we need to solve for x and y using substitution or elimination.
To learn more about equations click on,
https://brainly.com/question/2966111
#SPJ4
Complete question is:
Lydia buys 5 pounds of apples and 3 pounds of bananas for a total of $8.50. Ari buys 3 pounds of apples and 2 pounds of bananas for a total of $5.25. Determine a system of equations that represents the given the situation. Let x be cost per pound of apples and let y be the cost per pound of bananas. Which equation represents the amount of money Lydia spent of apples and bananas? Which equation represents the amount of money Ari spent on apples and bananas?
Lines AAA, BBB, and CCC show proportional relationships. Which line has a constant of proportionality between yyy and xxx of \dfrac{5}{4} 4 5 start fraction, 5, divided by, 4, end fraction?
If lines A, B and C shows proportional relationships, then the line A has a constant of proportionality between y and x is 5
Given the line A, B and C
The constant of proportionality is the ratio of the y coordinates to the x coordinate
k = y /x
Where k is the constant of proportionality
Consider the line A
One point on the line = (1, 5)
Constant of proportionality K = 5/1
= 5
Consider the line B
One point on the line = (3, 5)
Constant of proportionality k = 5/3
Consider the line C
One point on the line = (7, 5)
Constant of proportionality = 5/7
Therefore, the line A has the constant of proportionality of 5
Learn more about constant of proportionality here
brainly.com/question/29126727
#SPJ4
The given question is incomplete, the complete question is
Lines A, B, and C show proportional relationships. Which line has a constant of proportionality between y and x of 5?
