To confirm that the solution is correct, we can use the method of substitution. Substitute the solution back into the original differential equation, and if the equation is satisfied, then the solution is correct.
To confirm that the proposed solution is indeed a valid solution to the original equation, we can use the method of substitution. This involves substituting the proposed solution into the original equation and verifying that it satisfies the equation. If the equation holds, then the solution is correct. This method is useful for verifying the correctness of a proposed solution. It can also be used to determine if a proposed solution is the only solution, or if there are other solutions to the equation.
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suppose that y1 and y2 are independent and that both are uniformly distributed on the interval (0,1), and Let U1 and U2 be independent uniform random variables, both on (0,1). Let Y1 = U1U2 and let Y2=U2. (a) Find the joint density of Y1 and Y2.
(b) What is the marginal density for Y1?
a) The joint density of Y1 and Y2 is f(y1, y2) = 1, for 0 ≤ y1, y2 ≤ 1.
b) The marginal density for Y1 is f(y1) = 1, for 0 ≤ y1 ≤ 1.
Explanation:
(a) The joint density of Y1 and Y2 is found by multiplying the two individual densities together. Since Y1 and Y2 are independent, this is simply the product of the two densities.
The density for U1 is the same for all values of U1 on the interval (0,1), which is 1. The density for U2 is also the same for all values of U2 on the interval (0,1), which is also 1.
Therefore, the joint density of Y1 and Y2 is:
f(Y1,Y2) = f(U1U2,U2)
= f(U1) x f(U2)
= 1 x 1
= 1
(b) The marginal density for Y1 is the density of Y1 without regard to Y2. Since Y2 is uniform on (0,1), we can integrate the joint density over the interval (0,1) to obtain the marginal density of Y1:
f(Y1) = ∫f(Y1,Y2)dY2
= ∫1dY2
Y2 = 1
Therefore, the marginal density of Y1 is 1
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MODELING REAL LIFE An obstacle course
needs :
new piece made
in the shape
of a triangular prism
with an equilateral triangle for base. The side length
x (in feet) of the base and
prism are related by
the height y (in feet) of the
the inequality y > 1/2x^2+ 1. The
piece has the following additional constraints.
The height must be no more than 7 feet greater than
the side length of the base.
The side length of the base must be at least foot.
Write and graph a system that represents the situation.
Give one example of a height and side length that the
obstacle course can use.
The solution for the situation is [tex]x[/tex] ∈ [tex][-\sqrt{2(y-1)} , \sqrt{2(y-1)}][/tex] Where y > 1, and the graph is attached below.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
The side length x (in feet) of the base,
the height y (in feet) of the inequality y > 1/2x²+ 1 and y ≤ x,
In solving this inequality, we get,
[tex]x[/tex] ∈ [tex][-\sqrt{2(y-1)} , \sqrt{2(y-1)}][/tex] where y > 1
The graph of the system is attached below.
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The LA Lakers had a PCT of 583 in the 2020-21 season. What does this mean in practical terms?
The meaning when LA Lakers had a PCT of 58.3 in the 2020-21 season is that the percentage of winning is 58.3%.
How to illustrate the percentage?A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.
From the information given, the LA Lakers had a PCT of 58.3 in the 2020-21 season. It should be noted that PCT simply means percentage. Therefore, it denotes 58.3 percent.
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Complete question
The LA Lakers had a PCT of 58.3 in the 2020-21 season. What does this mean in practical terms
Determine the measures of the unknown angles.
Answer:
1.
x = 24
m = 112
z = 44
y = 72
2.
x = 35
Step-by-step explanation:
Number 1
Finding x
- Total angle in a triangle is 180.
- QVS = triangle
180 = ∠Q + ∠V + x
180 = 73 + 83 + x
x = 180 -73 - 83
x = 24
Finding m
- Total angle in a straight line is 180
- RW is a straight line
180 = m + ∠U
180 = m + 68
m = 180 - 68
m = 112
Finding z
- Total angle in a triangle is 180.
- RUS = triangle
180 = m + x + z
180 = 112 + 24 + z
z = 180 - 112 - 24
z = 44
Finding y
- Total angle in a triangle is 180.
- RWT = triangle
180 = z + y + ∠W
180 = 44 + y + 64
y = 180 - 44 - 64
y = 72
Number 2
- Total angle in a triangle is 180.
- Total angle in a straight line is 180.
180 = (180 -120) + 85 + x
180 = 60 + 85 + x
x = 180 - 60 - 85
x = 35
Jill is going to make weekly deposits of $100 into an account for 3 years. The account earns 5.2%/a compounded weekly. How much money will she have in her account at the end of 3 years? How much money did she make on this investment?
Answer:
every week jill is going to make 5.20 dollars then you do 5.20 x 1095 days in 3 years = $5694 a year
Step-by-step explanation:
the effectiveness of a blood-pressure drug is being investigated. an experimenter finds that, on average, the reduction in systolic blood pressure is 55.9 for a sample of size 29 and standard deviation 7.4. estimate how much the drug will lower a typical patient's systolic blood pressure (using a 80% confidence level). assume the data is from a normally distributed population.
The tri-linear inequality with the required 80% confidence interval of 54.1 to 57.7 shows the genuine mean value by which the drug decreases the average patient's systolic blood pressure.
A confidence interval expresses the likelihood that a population parameter will fall between a range of values a predetermined percentage of the time. It is the estimate's mean plus or minus the estimate's range of values.
Given the confidence level is 80%, the significance level α=100-80=20% = 0.20. The sample mean [tex]\overline{x}[/tex] is 55.9, the sample standard deviation s is 7.4, and the sample size n is 29.
We are using t-distribution to population standard deviation first. For that first find the degree of freedom and critical value of t.
Degree of freedom,
df = n - 1
df = 29 - 1
df = 28.
The critical value of t calculated from the t-distribution table is,
[tex]\begin{aligned}t_{\text{critical}}&=t_{\alpha/2,df}\\&=t_{0.10,28}\\&=\pm1.3125 \end{aligned}[/tex]
Then, an 80% confidence interval is,
[tex]\begin{aligned}\mu&=\overline{x}\pm\frac{t\cdot s}{\sqrt{n}}\\&=55.9\pm\frac{1.3125\times7.4}{\sqrt{29}}\\&=55.9\pm1.80\end{aligned}[/tex]
Then, the interval is written as
55.9 - 1.80 < μ < 55.9 + 1.80
54.1 < μ < 57.7
The required interval is 54.1 < μ < 57.7.
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Determine which set of side measurements could be used to form a right triangle.
14, 5, 15
O 3, 4, 5
O9, 14, 16
O 5, 2,7
Answer:
3,4,5
Step-by-step explanation:
Because, it is the only pair that fulfill the pythagorean theorem/formula
Pythagorean formula: [tex]c^2 = \sqrt{a^2 + b^2}[/tex]
Where c is the longest side of the triangle, or the hypothenuse, and a and b is the two perpendicular side.
What are some possible solutions for the following inequality? 2f - 8 ≤ 6f + 4
-4.5
-8
-1
4
0
Answer:
Solutions: -1, 4, and 0
Step-by-step explanation:
f= -4.5
2f - 8 ≤ 6f + 4
2 (-4.5) -8 ≤ 6 (-4.5) + 4
-9 - 8 ≤ -27 + 4
-17 ≤ -23
Not True
f= -8
2f - 8 ≤ 6f + 4
2 (-8) - 8 ≤ 6 (-8) + 4
-16 - 8 ≤ -48 + 4
-24 ≤ -44
Not true
f= -1
2f - 8 ≤ 6f + 4
2 (-1) - 8 ≤ 6 (-1) + 4
-2 - 8 ≤ -6 + 4
-10 ≤ -2
True
f= 4
2f - 8 ≤ 6f + 4
2 (4) - 8 ≤ 6 (4) + 4
8-8 ≤ 24 + 4
0 ≤ 28
True
f= 0
2f - 8 ≤ 6f + 4
2 (0) - 8 ≤ 6 (0) + 4
0 - 8 ≤ 0 + 4
-8 ≤ 4
True
for how many integers $n$ between 1 and 1990 is the improper fraction \[\frac{n^2 7}{n 4}\] not in lowest terms? (a) 0 (b) 86 (c) 90 (d) 104 (e) 105
86
Step-by-step explanation:
(15points) Let 21, 22, ..., Ik be linearly independ vectors in a vector space V. If we add a vector Ik+1 to the collection, will we still have a linear independent collection of vectors? Explain. If we delete a vector, say, 2k , from the collection, will we still have a linearly independent collection of vectors? Explain.
A spherical balloon is being filled with helium at the rate of 9 ft^3/min. How fast is the surface area increasing when the volume is 26 pi ft^3?
A spherical balloon is being filled with helium at the rate of 9 ft^3/min. the surface area of the balloon is increasing at a rate of approximately 37.1 ft^2/min.
What is the surface area?Generally, To find the rate at which the surface area is increasing, we need to use the formula for the surface area of a sphere, which is 4πr^2, where r is the radius of the sphere. We also know that the volume of a sphere is (4/3)πr^3.
Since we know the volume of the balloon, we can set up the following equation:
(4/3)πr^3 = 26*π ft^3
Solving for r, we find that the radius of the sphere is approximately 2.15 ft. Plugging this value back into the formula for the surface area, we find that the surface area of the sphere is approximately 28.9 ft^2.
To find the rate at which the surface area is increasing, we need to find the d/dx surface area formula with respect to time. Since the radius of the sphere is changing at a constant rate (9 ft^3/min), we can use the chain rule to find the d/dx surface area.
The d/dx 4πr^2 with respect to r is 8pir, and the d/dx r with respect to time (which we'll call t) is 9 ft^3/min. Therefore, the d/dx surface area with respect to time is:
(d/dx 4πr^2 with respect to r) * (d/dx r with respect to t) = (8πr) * (9 ft^3/min)
Plugging in the value of r that we found earlier (2.15 ft), we get:
(8π2.15 ft) * (9 ft^3/min) = 37.1 ft^2/min
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the questions in this activity refer back to prelab 0, which would be a good place to look if you need any help. in test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again calculate mean, standard deviation, and standard error. 1)which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?
The most likely statement about the comparison of standard deviation of Test A and Test B is (a) The standard deviations found in Test A and Test B will be about the same .
What is Standard Deviation ?
The term standard deviation is defined as a measure which shows the variation (such as dispersion) from the mean .
it is given that in Test A 100 experimental measurements is taken , and
in Test B 400 experimental measurements is taken .
we know that standard deviation is just square root of average of the square distance of measurements from the mean.
So , it is not affected by the number of experimental measurements .
thus , the standard deviation remain same for both the tests .
Therefore , the correct option is (a) .
The given question is incomplete , the complete question is
In test a, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. in test b, suppose you make 400 experimental measurements of the same quantity and you again .
Which of the following statements is the most likely description of the comparison of the standard deviations found in test a and test b ?
(a) The standard deviations found in Test A and Test B will be about the same
(b) The standard deviation found in Test A will about be twice as big as the standard deviation found in Test B.
(c) The standard deviation found in Test will about be four times as big as the standard deviation found in Test B
(d) The standard deviation found in Test B will about be twice as big as the standard deviation found in Test A .
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Read the following prompt and type your response in the space provided.
Write a real-world problem that could be represented by the inequality.
3x + 6 > 27
Find the perimeter of the figure. If you need to use in your computation, approximate its value as 3.14.
Rectangle topped by a semicircle
10 m
a. 35.57 m
b.
65.40 m
C.
59.70 m.
d. 49.70 m
The total perimeter of the given composite figure is; 74.55 meters
How to find the perimeter of a composite figure?The perimeter of the given figure can be calculated by dividing the figure into two parts : One is semi-circle and second is rectangle.
To find Perimeter of rectangle :
Length of the rectangle = 18 m
Width of the rectangle = 15 m
Perimeter = (2 × Length) + Width
Perimeter = (2 × 18) + 15
Perimeter = 36 + 15
Perimeter = 51 meters
To find perimeter of semi-circle :
Radius of semi-circle = 15/2 = 7.5 m
Perimeter of semi-circle = π × radius
Perimeter = 3.14 × 7.5
Perimeter = 23.55 meter
So, Total Perimeter of the figure = 51 + 23.55
= 74.55 meter
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Please help I've done it but I want to check my answer!
There are several marbles of different colours in a bag in front of you. Your job is to select three marbles and record the colour of each marble you chose. In the bag, there are 22 blue marbles, 17 red marbles, 8 yellow marbles and 3 purple marbles. What are the chances of selecting one red marble, one yellow marble and a blue marble?
Assume that once each marble is chosen, it is not returned to the bag.
Answer:
the probability of selecting one red marble, one yellow marble, and a blue marble is 1/52. This can also be expressed as a percentage by dividing the probability by 1 and multiplying by 100%, which gives a probability of approximately 1.9%.
Step-by-step explanation:
In detail please I’m getting graded and can’t find the answer
Answer:
x = 75
y = 15
Step-by-step explanation:
What you need to know to solve this question:
1. Angles in a triangle sum up to 180
2. Angles on a straight line add up to 180
3. A right-angle is 90
4. The triangle illustrated is a right-angle triangle
Solving for x:
According to principle 2:
x + 105 = 180
x = 180 - 105
x = 75
Solving for y:
According to principles 1 and 3:
x + y + 90 = 180
(75) + y + 90 = 180
y = 180 - 90 - 75
y = 15
Kaitlyn went on a diet and lost 8% of her body weight. She now weighs 222 pounds.
What was her original body weight?
To find Kaitlyn's original body weight, we need to determine how much weight she lost and add that amount back to her current weight.
Kaitlyn lost 8% of her body weight, which is equal to 8/100 * 222 pounds = <<8/100*222=17.76>>17.76 pounds.
Therefore, Kaitlyn's original body weight was 222 pounds + 17.76 pounds = <<222+17.76=239.76>>239.76 pounds.
Can someone please help me answer the second part of this question
The compositions of the two given functions are:
g(f(x)) = √(2*x + 29) - 2
f(g(x)) = √(2*x + 25)
How to find the composition of functions?Here we have the two functions:
f(x) = √(2x + 29)
g(x) = x - 2
We want to find the compositions:
f(g(x))
So we just need to evaluate f(x) on g(x), we will get:
f(g(x)) = √(2*g(x) + 29)
Now we can replace g(x) there:
f(g(x)) = √(2*(x - 2) + 29)
f(g(x)) = √(2*x - 2*2 + 29)
f(g(x)) = √(2*x + 25)
The other composition is:
g(f(x)) = f(x) - 2
g(f(x)) = √(2*x + 29) - 2
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Please help me with this question
Answer:
y = -1/2 x - 1
Step-by-step explanation:
A (-2,0)
B (0,-1)
slope = (-1-0)/(0-(-2)
-1/2
y intercept = -1
y = -1/2 x - 1
Answer:
y = e^(-1/2x -1)
Step-by-step explanation:
You want the equation for y(x), which is graphed as a straight line on a semi-log scale.
GraphLet z = ln(x). The graph shows a straight line with a z-intercept of -1 and a slope of "rise"/"run" = -1/2. That means the slope-intercept equation for this line can be written as ...
z = -1/2x -1
EquationUsing z = ln(y), we can find the equation for y by taking antilogs:
ln(y) = -1/2x -1
y = e^(-1/2x -1)
__
Additional comment
The attached graph shows y = f(x) and the line ln(y).
suppose a statistician wishes to test whether a large number of observations follows an exponential distribution with parameter . he wishes to test this hypothesis exactly, and intends that if the observations follow an exponential distribution with a different parameter, the test should reject the null hypothesis given sufficiently many observations. in addition, he wants to have a numeric statistic that he could report and does not want the procedure to involve rounding off observation numbers into bins. which of the following goodness-of-fit tests would be the most appropriate for this purpose? Chi-squared Test O Kolmogorov-Smirnov Test O Kolmogorov-Liliefors Test Quantile-quantile plots
This distribution has no shape parameter as it has only one shape, (i.e., the exponential, and the only parameter it has is the failure rate, \lambda \,\!).
How do you find the parameter of an exponential distribution in R?The exponential distribution can be simulated in R with rexp(n,λ) where λ is the rate parameter. The mean or expected value of an exponential distribution is 1/λ and the standard deviation is also 1/λ. The variance of an exponential distribution is given by 1/λ2.
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Consider exponential functions f and g.
f(x) = 4(5)x
Complete the statements comparing the two functions.
Because the y-intercept of function f is
, it is
the y-intercept of function g.
Both functions
on all intervals of x, but their end behavior is different as x approaches
infinity.
The correct statements regarding the comparisons of the exponential functions are given as follows:
Because the y-intercept of function f is of 4, it is lower than the y-intercept of function g.Both functions are increasing on all intervals of x, however, their end behavior is different as x approaches negative infinity.How to define the exponential functions?The definition of function f(x) is given as follows:
f(x) = 4(5)^x
Meaning that it has an y-intercept and an asymptote given as follows:
y-intercept of 4.asymptote of 0, as when x goes to negative infinity, y goes to zero.From the graph of function g(x), we have that:
The y-intercept is of 5, which is the value that the graph crosses the y-axis.The horizontal asymptote is of y = 2, hence they have different end behavior when x goes to negative infinity.More can be learned about exponential functions at https://brainly.com/question/25537936
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1. 4
2. less than
3. increase
4. negative
Got it right on Edmentum
Function f is represented by an equation in standard form with a = 4 and b = 5. This function is increasing and has a y-intercept of 4. The function approaches 0 as x approaches -∞ and approaches ∞ as x approaches ∞.
Function g crosses the y-axis at (0,5). The function approaches 2 as x approaches -∞ and approaches ∞ as x approaches ∞.
Because the y-intercept of function f is 4, it is less than the y-intercept of function g. Both functions increase on all intervals of x, but their end behavior is different as x approaches negative infinity.
Drag each tile to the correct box. Arrange the steps in the expansion of the binomial (3x + 2y)³ in the correct sequence. 27x³ + (3x)³ + x 9x²2y + 3x2 × 3x × 4y² + 8y³ 2x1 (3x)²2y + 3(3-1) (3x) (2y)² + (2y)³ 21 27x³ +54x²y +36y² + 8y³ ↓
The solution of the algebraic expression (3x + 2y)³ is
[tex]\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]
What is algebraic expression?
Algebraic expression consist of variables and numbers connected with addition, subtraction, multiplication and division.
Now, algebraic expressions are of different types. They are-
Monomial, Binomial and trinomial.
Algebraic expression with only one term is called monomial
Algebraic expression with two terms are called binomial
Algebraic expressions with three terms are called trinomial.
Algebraic expressions with more than three terms are called polynomial.
Based on degree, algebraic expression may be called as linear, quadratic, cubic and so on
Algebraic expression of degree one is called linear
Algebraic expression of degree two is called quadratic
Algebraic expression of degree one is called cubic
The given algebraic expression is (3x + 2y)³
Now,
[tex](3x +2y)^3\\(3x)^3 + 3 \times (3x)^2 \times (2y) + 3 \times 3x \times (2y)^2 + (2y)^3\\27x^3 + 54x^2y + 36xy^2 + 8y^3[/tex]
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Triangle CAT is transformed by a sequence of rigid motions that maps onto triangle DOG. Which three congruency statements would show ASA congruency for these triangles? (select all that apply)
A.∠ A ≅ ∠ T
B.CA ≅ DO
C.AT ≅ OG
D.CT ≅ DG
E.∠ A ≅ ∠ O
F.∠ C ≅ ∠ D
Answer:
B, E and F.-----------------------------
Since the triangles CAT and DOG overlap, their corresponding parts are congruent.
As we are looking for ASA congruency, we need to select two angles and the included side.
Let's review the given options, considering names of triangles and the order of vertices in those names.
A. ∠ A ≅ ∠ T
Incorrect as angles T and A are not corresponding.B. CA ≅ DO
Yes, possible side.C. AT ≅ OG
Yes, possible side.D. CT ≅ DG
Yes, possible side.E. ∠ A ≅ ∠ O
Yes, possible angle.F. ∠ C ≅ ∠ D
Yes, possible angle.So we have corresponding angles A and C and the included side must be AC.
Looking, at the options, we can get ASA with combination of options B, E and F.
Find the value of K
(x+5) is a factor of the Polynomial p(x)
if p(x)=2x³ +7x²+Kx + 20
Therefore the value of K is -11
The two cotton processing companies are producing different products and those are sold out the products one year before. The sold sum of both the two companies salaries are $44,000,000. The sold price of company x is 1000 more than the other. Therefore, find the value of each company's product sold price by framing a linear equation?
The final value of company x sold price is; $22,000,500
The final value of company y sold price is; $21,999,500
How to solve Linear equation word problems?Let the amount of sold out products in company x and company y be denoted by a
Now, we are told that sum of both the two companies salaries are $44,000,000.
Now, the sold price of company x is 1000 more than the other.
Thus;
Sold price of company y = y
Sold price of company x = 1000 + y
Thus;
1000 + y + y = 44000000
1000 + 2y = 44000000
2y = 44000000 - 1000
2y = 43,999,000
y = 43,999,000/2
y = $21,999,500
Thus;
Sold price of company x = $21,999,500 + $1000 = $22,000,500
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Count the average-case number of + operations performed by the following pseudocode segment. Assume that all possible data sets are equally likely. (Round your answer to two decimal places.) Preconditions: X = {X1, X2, X3, X4,X5} = {10, 20, 30, 40, 50, 60}, where x1 < x2 < X3 < X4 < X5. teo ir 1 while t < 101 do rtet + Xi Liri + 1
Count the average-case number of + operations performed by the following pseudocode segment. The average-case number of + operations performed is 6.67.
The pseudocode segment is a while loop that runs from t=0 to t=101. For each iteration, it adds Xi to the value of the variable liri. Since the preconditions list X as a set of five integers (10, 20, 30, 40, 50, 60) in increasing order, the variable Xi will take on each of these values in turn. Thus, the loop will perform + operations six times (once for each value of Xi). The average-case number of + operations performed is 6.67 (6 operations in total divided by the number of iterations, i.e. 101).
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Over 18 days, Sophia rode her bike an average of 12 miles each day.
What is the total number of miles she biked?
Enter your answer as a number like this: 42
The total Number of miles she biked, was 216.
In the given question, over 18 days, Sophia rode her bike an average of 12 miles each day.
We have to find the total number of miles she biked.
As we know that average is the sum of all numbers divide by total numbers.
As from the question, there is a total average of 18 days.
So the total number of days is 18.
The average distance of her bike for one day is 12 miles.
So we have to find the total number of miles that she biked.
We can find the total number of miles by multiplying the total number of days with the average speed of one day. So;
Total Number of Distance = Total Days × Average Speed of One Day
Total Number of Distance = 18 × 12
Total Number of Distance = 216 miles.
So, the total Number of Distance she biked, was 216 miles.
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Most insurance companies will replace a vehicle any time an estimated repair exceeds 80% of the "blue-book" value of the vehicle. Michelle's insurance company paid 9100$ for repairs on her car after an accident. What can be concluded about the blue-book value of the car?
What is the inverse of the function below?
f(x) = x/3 -2
O A. f1(x) = 2(x+3)
O B. f¹(x) = 3(x+2)
O c. f¹(x) = 3(x - 2)
OD. f¹(x) = 2(x-3)
Answer:
f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]
Step-by-step explanation:
The first step to finding the inverse of a function is to let [tex]y=f(x)[/tex].
This would mean [tex]y=\frac{x}{3}-2[/tex].
Then we swap [tex]x[/tex] and [tex]y[/tex] in the formula.
[tex]x = \frac{y}{3} -2[/tex]
Then rearrange for [tex]y[/tex]:
[tex]x=\frac{y}{3}-2 \\\\x+2=\frac{y}{3}\\\\3(x+2)=y[/tex]
This new equation of [tex]y[/tex] is the inverse function.
f⁻¹ [tex](x)[/tex] = [tex]3(x+2)[/tex]
Graph the solution to this inequality on the number line. 2/3z > 4/5
The solution to the inequality, 2/3z > 4/5, is calculated as z > 1.2. See attachment for the graph of the solution.
How to Solve and Graph the Solution to an Inequality?The solution to an inequality is determined by finding he value of the variable in the inequality that will make it true.
Given the inequality, 2/3z > 4/5, isolate the variable z to one side to determine its value:
2/3z > 4/5 [given]
Multiply both sides by 3/2:
2/3z × 3/2 > 4/5 × 3/2
z > (4 × 3) / (5 × 2)
z > 12 / 10
Simplify further:
z > 6/5
z > 1.2
The solution is z > 1.2. The graph of the solution is shown in the image that is given in the attachment below.
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