The inverse of the functions g(x), p(x), and t(x) are expressed as; g⁻¹(x) = 3√(x + 5), p⁻¹(x) = 3√(x/2) - 3, and t⁻¹(x) = (3x/10) - 3. respectively.
What is Inverse of a functionA function is said to have an inverse if it is both one-to-one and onto
we replace the functions g(x), p(x), and t(x) with y and make x the subject to arrive at the inverse g⁻¹(x), p⁻¹(x), and t⁻¹(x) as follows;
For g(x)= x³ - 5:
y = x³ - 5
y + 5 = x³ {add 5 both sides}
x = 3√(y + 5) {take cube root}
g⁻¹(x) = 3√(x + 5).
For p(x) = 2(x+3)³:
y = 2(x+3)³
y/2 = (x+3)³ {divide through by 2}
3√(y/2) = x + 3 {take cube root}
x = 3√(y/2) - 3 {subtract 3 from both sides}
p⁻¹(x) = 3√(x/2) - 3.
For t(x) = 10(x-4)/3:
y = 10(x-4)/3
3y = 10(x-4) {cross multiplication}
3y/10 = x + 3 {divide through by 10}
(3y/10) - 3 = x {subtract 3 from both sides}
t⁻¹(x) = (3x/10) - 3.
Therefore, the inverse of the functions g(x), p(x), and t(x) are derived by interchanging the value of x for y and expressed respectively as; g⁻¹(x) = 3√(x + 5), p⁻¹(x) = 3√(x/2) - 3, and t⁻¹(x) = (3x/10) - 3.
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Select the angle that correctly completes the law of cosines for this triangle.
82 +1722(8) (17)cos ____ = 15²
-
28°
17
15
62°
90°
8
The angle that completes the law of cosines is 62°.
Option D is the correct answer.
What are trigonometric identities?There are three commonly used trigonometric identities.
Sin x = 1/ cosec x
Cos x = 1/ sec x
Tan x = 1/ cot x or sin x / cos x
Cot x = cos x / sin x
We have,
The law of cosines in a triangle states that,
c² = a² + b² - 2ab cos C
Where c is the side opposite to ∠C.
Similarly,
a² = b² + c² - 2bc cos A
b² = a² + c² - 2ac cos B
Now,
289 + 64 - 272 cos __ = 15²
17² + 8² - 2 x 17 x 8 cos 62 = 15²
289 + 64 - 272 cos 62 = 15²
Thus,
The angle that completes the law of cosines is 62°.
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The complete question.
289 + 64 - 272 cos __ = 15²
Can anyone help me out please I really need it…
Answer:
x= 39.549°
Step-by-step explanation:
please review answer.
an actress has a probability of getting offered a job after a try-out of 0.15. she plans to keep trying out for new jobs until she gets offered. assume outcomes of try-outs are independent. hint: use a geometric random variable. find the probability she will need to attend more than 5 try-outs.
The probability that the actress will need to attend more than 5 try-outs is approximately 0.478.
Since the outcomes of each try-out are independent,
As per the given information,
Number of try-out is 0.15
probability means the possibilities.
We can model the number of try-outs needed to get an offer as a geometric random variable with the probability of success p = 0.15.
Let X be the number of tryouts needed to get an offer.
Then, X follows a geometric distribution with parameter p=0.15, and the probability of needing to attend more than 5 try-outs is:
[tex]P(X > 5) &= 1 - P(X \leq 5)[/tex]
=[tex]1 - \sum_{k=1}^{5} P(X=k)[/tex]
= 1 [tex]- \sum_{k=1}^{5} P(X=k)[/tex]
= [tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]
=[tex]1 - [(1-p)^0p + (1-p)^1p + (1-p)^2p + (1-p)^3p + (1-p)^4p][/tex]
= 0.478
Hence the number of possibility required to attend more than 5 try-outs is approximately 0.478.
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What would you pay for 2 1/2 kg of tomatoes at 1. 50 each per kg
Answer: To find out how much you would pay for 2.5 kg of tomatoes at $1.50 per kg, we need to multiply the weight of the tomatoes by the price per kg:
Cost = 2.5 kg x $1.50/kg
= $3.75/kg x 2.5 kg
= $9.38
So, you would pay $9.38 for 2.5 kg of tomatoes at $1.50 per kg.
Step-by-step explanation:
The start of a quadratic sequence is shown
below.
What is the nth term rule for the sequence?
-5, -2, 3, 10, 19,
Answer:
nth term = n²-6
Step-by-step explanation:
we know our nth-term formula is going to be of the form an² + bn + c. We just have to find a, b, and c.
In this series,
-5, -2, 3, 10, 19....
a=1, b=0, c=-6
nth term = n²-6
if n=1 then,
nth term=1²-6
⇒nth term=-5
This next question is a little bit tricky, but keep in mind the Disney World / Bush Gardens example from the lectures.
What is the probability that someone uses a cell phone while driving or had no speeding violation?
Find the probability that someone uses a cell phone while driving, add to that the probability that someone did not receive a speeding violation, then subtract the value in the square where those two overlap.
Round your answer to the hundredths place.
The probability of both events is the sum minus the intersection. The answer should be rounded to two decimal places.
To calculate the probability of someone using a cell phone while driving or had no speeding violation, first calculate the individual probabilities of each event. The probability of someone using a cell phone while driving is P(cell phone) and the probability of someone having no speeding violation is P(no speeding violation). Then, add these two probabilities together, P(cell phone) + P(no speeding violation). This will give you the total probability of both events occurring. Finally, subtract the probability of the intersection, which is the probability of someone using a cell phone while driving and having no speeding violation. This will give you the total probability of someone using a cell phone while driving or having no speeding violation. Round the answer to the hundredths place.
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What is 3 5/12 - 8/12 equal to?
Answer:
Step-by-step explanation:
first, write down on paper 3 5/12 - 8/12 then convert the mixed fraction into a more straightforward form. so 3 5/12 equals 37/12. then you do 37 - 8 = 29 so then change it into a fraction and the answer is 29/12. if you what it as a mixed fraction then it would be 2 5/12
The sum of two numbers is 14. Four less than twice the smaller number is equal to the larger number x. Find the larger number.
The Larger number is 8
What is a linear equation in one variable?
The fundamental equation used to represent and solve for an unknown quantity is a linear equation in one variable. It is always a straight line, and it is simply shown graphically. A mathematical statement is simply represented by a linear equation.
Given that, the sum of two numbers is 14 and the larger number is four less than twice the smaller number
let the larger number be 'a' and the smaller be 'b'
from the question,
a + b = 14 .....eq 1
a = 2b - 4 .....eq 2
By substituting eq 2 in eq 1:
2b - 4 + b = 14
3b - 4 = 14
3b = 14 + 4 = 18
b = 6
a = 2b - 4 = 2*6 - 4 = 8
Therefore, The two numbers are 8, 4
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HOW DO I DO THIS??????????
Keith and his friends are heading to the Thunder Beach water park. They plan to purchase the group package, which costs $78 for 6 people. That's $3 less per person than the normal cost for an individual. What is the normal cost for an individual?
Anand's math teacher finds that there's roughly a linear relationship between the
amount of time students spend on their homework and their weekly quiz scores. This.
relationship can be represented by the equation y = 7.2x + 55, where y represents
the expected quiz score and a represents hours spent on homework that week. What
is the meaning of the 2-value when y = 77?
The number of hours a student should spend on their homework to expect a
score of 77 on the quiz.
A student's expected quiz score if they spent 77 hours on their homework.
The change in expected quiz score for every additional one hour students spend
on their homework.
A student's expected quiz score if they spent no time on their homework.
Submit Answer
To get 77 marks on a quiz the student has to spend approximately 3 hrs.
The expected quiz score if a student spends no time on homework is 55.
What is meant by a linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, occasionally referred to as a "linear equation of two variables."
It is given that y = 7.2x + 55
where y is the expected quiz score.
x is the number of hours spent on homework that week.
If the value of y=77
77=7.2x+55
22=7.2x
x is approximately 3 hrs.
If the student spends no time on their homework:
x=0
y=0+55
y=55.
Therefore to get 77 marks on a quiz the student has to spend approximately 3 hrs.
The expected quiz score if the student spends no time on home work is 55.
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barry wrote 6 different numbers, one on each side of 3 cards, and laid the cards on a table, as shown. the sums of the two numbers on each of the three cards are equal. the three numbers on the hidden sides are prime numbers. what is the average of the hidden prime numbers?
The average of the three hidden prime numbers is 5, as the sum of any two of the numbers is equal to 10, and since all three numbers are prime, the only possible values are 3, 5, and 7.
3 + 5 + 7 = 15
15/3 = 5
The average of the three hidden prime numbers is 5. This means that the sum of any two of the numbers on the cards must be equal to 10. Since all three numbers are prime,as the sum of any two of the numbers is equal to 10 the only possible values are 3, 5, and 7. Therefore, the three numbers on the hidden sides of the cards are 3, 5, and 7. To calculate the average, we add the three values together and divide by three. 3 + 5 + 7 = 15, and 15 divided by 3 is 5. Therefore, the average of the hidden prime numbers is 5.
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the histogram below gives the length of service of members of the department of chemistry at a particular university. the classes, in years of service, are 0-4.9, 5-9.9, etc., and the vertical axis represents the number of faculty. (a) what percent of the department faculty have 5 or more years of service? (b) if a member of the department is chosen at random to serve on a university committee, what is the probability (in decimal form) that the chosen representative will have between 5 and 35 years of service? (c) what is the probability the representative above will have less than 5 years of service given that the person has less than 15 years of service?
a. The percentage of the department faculty have 5 or more years of service is 76%
b. Probability that a faculty member chosen at random has between 5 and 35 years of service is 0.4.
c. The probability the representative will have less than 5 years of service given that the person has less than 15 years of service is 0.7.
Histogram:The histogram is used to estimate probability of a categorical variable or probability of frequency of a particular class interval, and there is no gap among the bars of the histogram.
(a) The per cent of the department faculty have 5 or more years of service is calculated as follows,
The number of department faculty have 5 or more years of service is 38 and total frequency 50, therefore the required probability is:
P(x > 5) = 38/50 = 0.76 = 76%
(b) The probability (in decimal form) of representative will have between 5 and 35 years of service is given as,
P(5 < X < 35) = 20/50 = 0.4 = 40%
(c) The probability the representative above will have less than 5 years of service given that the person has less than 15 years of service is calculated as follows,
P(X < 5 | X < 15) = 28/40 = 0.7
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For complete question, see the figure.
The radius of a circle is 15 cm. Find its circumference in terms of pi
The circumference of a circle is equal to 2π multiplied by its radius. Therefore, the circumference of a circle with a radius of 15 cm is equal to 2π multiplied by 15 cm, or 30π cm.
a motorist buys a 5litre can of gear oil.she uses 800ml.what percentage of oil has she used and what remains
Step-by-step explanation:
1000ml=1 litre
800 divided by(1000 multiplied by 5)=16%
In a geometric sequence, the first term, a_1, is equal to 3, and the third term, a_{3}, is equal to 192 Which number represents the common ratio of the geometric sequence?
Answer:
r = 8
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
given a₁ = 3 and a₃ = 192 , then
a₁ = 3 → (1)
a₁r² = 192 → (2)
divide (2) by (1) on both sides
[tex]\frac{a_{1}r^2 }{a_{1} }[/tex] = [tex]\frac{192}{3}[/tex] ( cancel a₁ on numerator/ denominator of left side ), then
r² = 64 ( take square root of both sides )
r = [tex]\sqrt{64}[/tex] = 8
The following is a WFF:
(S~T) V (~U.W)
Select one:
True or
False
The given statement about the disjunction is true.
What is Disjunction?A compound statement with two distinct statements (disjuncts) connected by the wedge symbol (v) is called Disjunction.
Given is the statement -
(S~T) v (~U.W)
The given statement about the disjunction is true.
Therefore, the given statement about the disjunction is true.
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find all radicals expressions that are equivalent for 5 (2/3)
4 Bob makes dry concrete by mixing cement, sand and stone in the ratio 1:2:3 by weight.
He buys the cement, sand and stone in bags as shown in this table.
Cement
Sand
Stone
Weight of bag
(kg)
25
20
15
Cost per bag
(£)
5.50
2.00
3.90
ratios
He packs the dry concrete into 30 kg bags.
Bob buys just enough cement, sand and stone to make 50 bags of dry concrete.
(a) Show that Bob buys 500 kg of sand.
Bob needs to buy 500 kg of sand.
What is the ratio?
A ratio is a quantitative relationship between two numbers, quantities, or values that expresses how many times one is contained in the other. Ratios are typically expressed in the form of "a to b" or "a:b" and can be represented as fractions or decimals.
Since the ratio of cement to sand to stone is 1:2:3 by weight, the total weight of the ingredients needed to make one bag of dry concrete is:
Cement: 1/6 of 30 kg = 5 kg
Sand: 2/6 of 30 kg = 10 kg
Stone: 3/6 of 30 kg = 15 kg
To make 50 bags of dry concrete, Bob will need 50 times these amounts:
Cement: 5 kg x 50 = 250 kg
Sand: 10 kg x 50 = 500 kg
Stone: 15 kg x 50 = 750 kg
Hence, Bob needs to buy 500 kg of sand.
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How is [tex]\frac{22}{7}[/tex] a rational number
Answer:
Step-by-step explanation: 22/7 is a rational number because it can be expressed as a ratio or fraction of two integers. The numerator (22) and denominator (7) are both integers, and the denominator is not equal to zero, so 22/7 is a well-defined fraction. Since every fraction represents a rational number, 22/7 is also a rational number
Question 1 of 10
esc
The equation y
Complete the statements.
When the outside temperature is 30°F, the sales are estimated to be [DROP DOWN 1].
When the outside temperature is [DROP DOWN 2], the sales are estimated to be $1, 993.33.
DROP DOWN 1
Select a Value
DROP DOWN 2
Select a Value
O
Please select an answer.
32.9-572.87 can be used to model the relationship between sales at a local ice cream shop, y, in dollars, and the outside temperature, x, in degrees Fahrenheit (F).
Help me out
When the outside temperature is 30°F, the sales is $414.13
When the sale is $1,993.33, the outside temperature is 78°F
How to find the sales when the outside temperature is 30°F?
Since the equation y = 32.9x - 572.87 can be used to model the relationship between sales at a local ice cream shop, y, in dollars, and the outside temperature, x, in degrees Fahrenheit (F).
Thus, when the outside temperature is 30°F, the sales can be estimated by substituting x = 30°F into the equation and solving for y. That is:
y = 32.9x - 572.87
y = 32.9(30) - 572.87
y = 987 - 572.87
y = $414.13
Thus, when the sale is $1,993.33, the outside temperature can be estimated by substituting y = $1,993.33 into the equation and solving for x. That is:
y = 32.9x - 572.87
1,993.33 = 32.9x - 572.87
32.9x = 1,993.33 + 572.87
32.9x = 2566.2
x = 2566.2/32.9
x = 78°F
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Which of the following items has volume?
baseball diamond
floor rug
piece of paper
water bottle
The only option that represents an object with volume is; Option D: Water Bottle
How to find the volume of objects?An object that will have volume is a 3-D object which means that it has length, width and height. Thus, 2D objects cannot have a volume.
Let us access the given options;
A) Baseball diamond: This refers to the baseball field because of the shape of the infield. Thus, it has only length and width and is a 2D shape which doesn't have a volume.
B) Floor Rug: A floor rug, is a plane shape which means it s a 2D shape which doesn't have a volume.
C) A piece of paper: This is a plane shape which means it s a 2D shape which doesn't have a volume.
D) Water Bottle: This is a 3D shape that has length, width and height and as such it has volume.
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Area of this figure?
Answer:
213 ft^2
Step-by-step explanation:
In this problem, we can create a larger rectangle that engulfs this image with a few missing pieces on the corners. The area of that rectangle would be 18ft * 17 ft = 306 ft^2. The sum of the missing pieces is 2ft * 7ft + 5ft * 6 ft + 7ft * 7ft = (14 + 30 + 49)ft^2 = 93 ft^2. So, the area of this figure is 306 - 93 = 213 ft^2
ANSWER: S=173ft^2
_._._._._._._._._._._._.
Find an equation of the line of symmetry of triangle ABC.
Answer:
The equation of the line of symmetry of triangle ABC is:
3x + 2y = 86Step-by-step explanation:
The line of symmetry of an isosceles triangle bisects the vertex angle (the angle opposite the base) and is perpendicular to the base of the triangle.
As AB = AC, then angle A is the vertex angle of the isosceles triangle ABC.
If B and C lie on the line with equation 3y = 2x + 12, then the line of symmetry is the line that is perpendicular to this line and passes through A (4, 37).
Rearrange the given equation 3y = 2x + 12 to slope-intercept form by dividing both sides by 3:
[tex]\implies y=\dfrac{2}{3}x+4[/tex]
Perpendicular lines have slopes that are negative reciprocals of one another. Therefore, the slope of the perpendicular line is -³/₂.
Substitute the found slope and point A (4, 37) into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-37=-\dfrac{3}{2}(x-4)[/tex]
Rearrange the equation to standard form:
[tex]\implies 2y-74=-3(x-4)[/tex]
[tex]\implies 2y-74=-3x+12[/tex]
[tex]\implies 3x+2y-74=12[/tex]
[tex]\implies 3x+2y=86[/tex]
Therefore, the equation of the line of symmetry of triangle ABC is:
3x + 2y = 86the perimeter of a square with side length $x$ units is equal to the circumference of a circle with radius 2 units. what is the value of $x$? express your answer as a decimal to the nearest hundredth.
The value of $×$ is 3.14 units
What is perimeter ?Perimeter is the distance around the edge of a shape. The algebraic sum of the length of each side is the perimeter of that shape. We have formulas available for the various shapes in geometry.
The perimeter of a square is expressed as 4l
The circumference of a circle = 2πr
This means that;
4l = 2πr
4l = 2× 3.142 × 2
4l = 12.57
divide both sides by 4
l = 12.57/4
l = 3.14 units(nearest hundredth)
therefore the value of the side length is 3.14 units
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Two years ago, Rita was 3 times as old as Cheryl. In 3 years, Rita will be twice as old as Cheryl. How old are the girls now?
The current age of Rita is 17 years and Cheryl is 7 years respectively, according to mentioned data.
Let us assume Rita's present age be x and Cheryl's age be y.
Rita's age two years ago = 3 × Cheryl's age two years ago
x - 2 = 3 (y - 2) - equation 1
Rita's age after three years = 3 × Cheryl's age after three years
x + 3 = 2 (y + 3) - equation 2
Solving equation 1
x - 2 = 3y - 6
x = 3y - 6 + 2
x = 3y - 4
Solving equation 2
x + 3 = 2y + 6
x = 2y + 6 - 3
x = 2y + 3
Keep the value of x from equation 2 in equation 1
2y + 3 = 3y - 4
Rearranging the equation
3y - 2y = 3 + 4
y = 7
Keep the value of y in equation x = 2y + 3
x = 2×7 + 3
x = 14 + 3
x = 17
So, Cheryl's and Rita's age is 7 and 17 years respectively.
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Mackenzie's company reimburses her $0. 75 per mile that she drives for business. If she goes on a business trip and drives a total of 982 miles, how much will her reimbursement be?
Mackenzie's reimbursement for a business trip would be $736.50 per mile when she drives of a total of 982 miles with $0. 75 per mile.
Mackenzie's reimbursement for driving 982 miles for business can be calculated by multiplying the number of miles driven by the reimbursement rate per mile.
Mackenzie's company reimburses her $0. 75 per mile which is rate per mile.
Reimbursement = miles driven x rate per mile
Filling the value in above equation.
So,
Reimbursement = 982 miles x $0.75/mile
Reimbursement = $736.50
Therefore, Mackenzie's reimbursement for driving 982 miles with the rate of $0. 75 per mile for business would be $736.50.
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5x+2y=-7 and 10x+4y= -14 no solution, solution, or infinite solution?
The system of equations 5x+2y=-7 and 10x+4y= -14 has unique solution which is (-7/5,0).
In general, a system of linear equations can have one of three possible outcomes:
One unique solution (as in this case)
No solution (if the equations are inconsistent)
Infinitely many solutions (if the equations are dependent)
To solve this system of equations, we can use the method of elimination or substitution. Let's use the method of elimination, which involves adding or subtracting the equations to eliminate one variable.
First, we need to choose a variable to eliminate. Looking at the coefficients of x and y, we see that we can eliminate y by multiplying the first equation by -2 and adding it to the second equation:
-10x - 4y = 14
5x + 2y = -7
-5x = 7
Now we can solve for x:
-5x = 7
x = -7/5
We can substitute this value of x into one of the equations to solve for y. Let's use the first equation:
5x + 2y = -7
5(-7/5) + 2y = -7
-7 + 2y = -7
2y = 0
y = 0
Therefore, the solution to the system of equations is (x,y) = (-7/5,0).
This is called a unique solution, meaning there is only one possible solution for the system of equations.
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Complete Question:
Solve
5x + 2y = -7
10x + 4y = -14
And find the number of solutions for the equation
Please find the missing side length using trig
Answer:
13.0898597466511 or 13.09
Step-by-step explanation:
Andrea has to find a third point, C, to form a triangle on the coordinate plane shown. She is told the coordinates of its reflection point, C', across the x-axis are (2, -2) What are the coordinates of point C?
Answer:
2,2 but i could be wrong
Just wanted to say he's correct, it's 2, 2
Suppose you took a job walking the neighbor's dog because you had borrowed $50.00 from your parents, and you need to pay them back. For this job, you are paid $15 per week to walk the dog for 20 minutes each weekday. Suppose you took a job walking the neighbor's dog because you had borrowed $50.00 from your parents, and you need to pay them back. For this job, you are paid $15 per week to walk the dog for 20 minutes each weekday. Working on the Desmos Graphing Calculator, complete the table showing how many weeks it will take to pay your parents back the money you borrowed. Take a screenshot of your graph when you are finished to submit later in the assignment.
The graplh shows that it will take 3.33 weeks to pay up the money borrowed
How to find the equation to plotted on the graphA linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
The equation as described in the problem is represented using linear function as as follows
c = money borrowed from your parents = $50.00
m = you are paid $15 per week to walk the dog for 20 minutes each weekday = $15
x = number of weeks
y = amount remaining
The equation is
y = 15x - 50
From the graph the pay will be completed at x = 3.33 (3.33, 0)
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