The optimal Bayesian classifier is the one that minimizes the probability of misclassification. This can be achieved by choosing the class that has the highest posterior probability given the observed data. In this case, we need to compare the conditional class probabilities P2(t) and P0(I) for each data point and choose the class with the higher probability.
To find the optimal Bayesian classifier, we need to find the values of a and b that define the decision boundary between the two classes. This can be done by setting P2(t) = P0(I) and solving for x:
P2(t) = P0(I)
Pr(Y; = 1|X, = x) = Pr(Y; = 0[Xi = 1)
1 - P2(I) = P2(I)
2P2(I) = 1
P2(I) = 0.5
Now we can solve for x to find the decision boundary:
0.5 = Pr(Y; = 1|X, = x)
0.5 = P2(I)
x = a + b
Therefore, the optimal Bayesian classifier is of the form:
if Xe [a, b] then yi = 1
if Xe [b, a] then yi = 0
where a and b are the values of x that satisfy P2(I) = 0.5.
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Help pls on this problem 100points pleas.
Answer:
2026 to maximize the present value function.
Step-by-step explanation:
To find the year in which the timber should be harvested to maximize the present value function, we need to find the time t that maximizes the present value function A(t). We can begin by finding A(t):
A(t) = V(t)e^(-0.09t)
A(t) = 140,000e^(0.72√t) * e^(-0.09t)
A(t) = 140,000e^(0.72√t - 0.09t)
To maximize A(t), we need to find the critical points of A(t). We can do this by taking the derivative of A(t) and setting it equal to zero:
A'(t) = 140,000(0.36/√t - 0.09)e^(0.72√t - 0.09t) = 0
Simplifying this equation, we get:
0.36/√t - 0.09 = 0
0.36/√t = 0.09
√t = 4
t = 16
Therefore, the critical point of A(t) occurs at t = 16 years.
We can check that this is a maximum by taking the second derivative of A(t) and evaluating it at t = 16:
A''(t) = 140,000(-0.648/t^3 - 0.243/√t + 0.081)e^(0.72√t - 0.09t)
A''(16) = 140,000(-0.648/16^3 - 0.243/4√16 + 0.081)e^(0.72√16 - 0.09(16))
A''(16) ≈ -4,980.4
Since the second derivative is negative, we can conclude that t = 16 years corresponds to a maximum for the present value function A(t).
Therefore, the timber should be harvested in the year 2010 + 16 = 2026 to maximize the present value function.
Answer:
Step-by-step explanation:
whatb you need
In the expression $c \cdot a^b - d$, the values of $a$, $b$, $c$, and $d$ are 0, 1, 2, and 3, although not necessarily in that order. What is the maximum possible value of the result?
The maximum possible value of the result is 8.
How to solve Linear Equations?
We are given the linear equation;
4x - x = 0
From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;
The first step to solving the equation is to; C. add x to both sides
The second step to solving the equation is to; C. cube both sides
Solving the equation for x initially yields; C. two possible values
Checking the solutions shows that; D. none are valid solutions
4x - x + x = 0 + x
4x = x
Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;
(4x)³ = x³
4³x = x³
64x = x³
Divide both sides by x to get;
x² = 64
Take square root of both sides to get;
x = ±√64
x = ±8
Hence, The maximum possible value of the result is 8.
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40 Answer:
Solve the equation by a method of your choice:
x2 - 36 = 0
If there are two solutions, separate the solutions by a comma.
41 Answer:
Solve the equation by a method of your choice:
x2 + 12x + 36 = 0
If there are two solutions, separate the solutions by a comma.
The solution of the equations are
x^2 - 36 = 0
x = 6, -6
The equation x2 + 12x + 36 = 0
x = -6, -6
How to solve the equationsThe equation x^2 - 36 = 0 is solved as follows
x^2 - 36 = 0
x = ±√36
x = 6 or -6
The quadratic equation x^2 + 12x + 36 = 0 is solved as follows
x^2 + 6x + 6x + 36 = 0
x(x + 6) + 6(x + 6) = 0
(x + 6)(x + 6) = 0
hence
x = -6 and -6
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The area of a triangular sail is given by the expression
1
2
bh, where b is the length of the base and h is the height. What is the area of a triangular sail in a model sailboat when b = 12 inches and h = 7 inches?
The area of a triangular sail in a sail model is
in2.
The area of the triangular sail in the sail model is 42 square inches.
According to given information:The area of a triangular sail is given by the formula:
Area = (1/2)bh
where b is the length of the base and h is the height.
Substituting b = 12 inches and h = 7 inches, we get:
Area = (1/2)(12 inches)(7 inches) = 42 square inches
Therefore, the area of the triangular sail in the sail model is 42 square inches.
What is area of triangle ?The area of a triangle is given by the formula:
Area = (1/2) * base * height
where "base" is the length of the base of the triangle and "height" is the height of the triangle perpendicular to the base.
To find the area of a triangle, you simply need to plug in the values of the base and height into the formula and perform the calculation. The resulting value will be the area of the triangle.
Note that the base and height of the triangle must be measured in the same units (e.g., inches, centimeters) in order for the formula to work correctly.
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Answer:
24
Step-by-step explanation:
N/A
a student estimated their mass to be 82.0 kg. upon stepping on the scale at the doctor's office, the actual (accepted) mass of 83.8 kg was recorded. use the formula on page 4 of lab 3v to calculate the % error of the student's estimated mass. remember to take the absolute value in the numerator and to round off to the proper degree of certainty. the unit that should be reported is % (use the symbol, do not type out the word).
The percentage error of the student's estimated mass is 2.15%.
What is the percentage error?The percentage or percent error is the difference between the estimated value and the actual value divided by the actual value, multiplied by 100.
The estimated mass of the student = 82.0 kg
The actual mass of the student = 83.8 kg
Absolute error = Actual Value - Estimated Value
= 1.8 kg (83.8 - 82.0)
Percentage error = Actual Value - Estimated Value /Actual Value x 100
= 2.15% (1.8/83.8 x 100)
Thus, we can conclude that the student's estimate contains a 2.15% error.
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Problems 29,37, and 41
Each year an organization raises money to offer Berkeley College students scholarships. They currently have raised $14,300. This represents 58% of the money they raise. Determine the amount of money the organization will raise in total.
Jamal paints sceneries on canvas and sells them at art auctions. A large painting sells for $45.99 and a small one for $28.99. In six months he sold seven large paintings and four small ones. Calculate how much money Jamal made in six months.
Answer:
Step-by-step explanation: To calculate the total amount of money Jamal made in six months, we need to multiply the number of paintings sold by the price of each painting, and then add the results for the large and small paintings:
7 large paintings * $45.99/large painting = $321.93
4 small paintings * $28.99/small painting = $115.96
Total amount made = $321.93 + $115.96 = $437.89
Therefore, Jamal made $437.89 in six months by selling seven large paintings and four small ones.
I WILL GIVE BRAINLEST (7TH GRADE QUESTION)
Answer:
1. volume= 135
2. prism volume in cubic feet is: 21
3. surface area is 294 ft^2
4. surface area is 430 ft^2
A rectangle that is 9 meters long has an area of 36 square meters what is the perimeter
Answer:
the perimeter of the rectangle is 26 meters.
Step-by-step explanation:
To find the perimeter of the rectangle, we need to know its width. We can find the width by dividing the area by the length:
width = area / length = 36 / 9 = 4 meters
Now we can use the formula for the perimeter of a rectangle:
perimeter = 2(length + width)
Substituting the given values, we get:
perimeter = 2(9 + 4) = 2(13) = 26 meters
Therefore, the perimeter of the rectangle is 26 meters.
PLEASE HURRY
A. Plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane.
B. Find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y). The point (2,0) will go to the ordered pair___.
C. What do you notice about x^2+y^2=4 and x^2+y^2=1? The small circle is a __ of the larger one using the origin as a center and a scale factor of __.
PLEASE HURRY
Answer:
A. Image shows the two circles
B. he ordered point(2, 0) will go to the ordered pair [tex]\mbox{\large \left(\boxed{1}, \boxed{0}\right)}[/tex]'
C. The small circle is a [tex]\boxed{\textsf{copy}}[/tex] of the larger one using the origin as a center and a scale factor of [tex]\boxed{\dfrac{1}{2}}[/tex]
*** I am guessing what word goes into the first box. It should be something that is close to the word copy. The words replica or duplicate could be other choices If you are unable to come up with a choice, post the answer choices as a comment and I can be more specific ***
Step-by-step explanation:
A. Image shows the two circles
B. The larger circle x² + y² = 4 is dilated by a factor of 1/2
The ordered point(2, 0) will go to the ordered pair (2/2, 0/2) = (1,0)
C. What do you notice about the two circles?
They are concentric circles with origin(0, 0) as the center
The small circle is a copy of the larger one using the origin as a center and a scale factor of 1/2
* I do not know what your answer choices are. I have just filled in a term which indicates the relationship.
What is the slop of the line that passes through (7,-4) and (11 -4)
Answer:
The slope of the line that passes through (7,-4) and (11 -4) is 0, since it is a horizontal line.
To find the slope when given two points, use the formula:
y2-y1/x2-x1=m(-4- -4)/(11-7)=0/4=0
So the slope is 0 because 0 is the numerator. If 0 is the denominator, the slope will be undefined.
Hope this helped!
What is the area of this triangle?
Enter your answer in the box.
units?
The area of the triangle DEF shown in the coordinate plane is 6 units².
What is Area of a Triangle?Area of a triangle is defined as the total region bounded by the shape of the triangle.
The formula to calculate the area of a triangle if the base length and height is given is,
Area = [tex]\frac{1}{2}[/tex] × base × height
Given is a triangle in a coordinate plane.
Base of the triangle is the side DE.
Length of DE is the length of the points (1, 1) t0 (1, 4), which is 3 units apart.
Length of base = 3 units
Height of the triangle is the perpendicular length from the vertex opposite base to the base.
That is, the distance from F(-3, 3) to (1, 3), which are 4 units apart.
Height = 4 units.
Area of triangle DEF = [tex]\frac{1}{2}[/tex] × 3 × 4
= 6 units²
Hence the area of the triangle is 6 units².
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Adam is planning
a rectangular patio that will have an area of
16x2 1 20x square feet. The length of the patio
will be x 1 5 feet. Write an expression to
represent the width of the patio.
Answer:
The width of the patio is 15 feet
Step-by-step explanation:
We can start by using the formula for the area of a rectangle:
Area = length x width
In this case, we know that the area of the patio is given by:
16x^2 + 20x square feet
And we also know that the length of the patio is x + 5 feet. So we can substitute these values into the formula to get:
16x^2 + 20x = (x + 5) x width
Simplifying the right-hand side by multiplying x + 5 by width, we get:
16x^2 + 20x = width x^2 + 5x
To solve for the width, we can move all the terms with width to the left-hand side and all the other terms to the right-hand side:
width x^2 - 16x^2 + 20x - 5x = 0
Simplifying the left-hand side by combining like terms, we get:
width x^2 - 16x^2 + 15x = 0
Factoring out x, we get:
x (width x - 16x + 15) = 0
Now we can solve for the width by setting each factor equal to zero and solving for x:
x = 0 or width x - 16x + 15 = 0
Since the length and width of the patio must be positive values, we can disregard the solution x = 0. So we are left with:
width x - 16x + 15 = 0
We can factor this quadratic equation by finding two numbers whose product is 15 and whose sum is -16. These numbers are -1 and -15, so we can write:
(width x - 1)(x - 15) = 0
Setting each factor equal to zero and solving for x, we get:
width x - 1 = 0 or x - 15 = 0
width x = 1 or x = 15
Since the length of the patio is x + 5, which is 20 feet, we know that x = 15 is the correct solution. So we can substitute x = 15 into the expression for the width:
width x = 1, x = 15, so we choose x = 15
width x - 16x + 15 = (15) x - (16)(15) + 15 = 15 feet
Therefore, the width of the patio is 15 feet.
Please help me!!!
Sharon factored the polynomial
x^2 + 81 as (x+9)(x-9)
using the difference of 2 squares method. Her teacher marked her andar wrong. Do you agree or disagree. Write a 1 sentence explaining why you agree or disagree with her teacher. You must write a sentence to earn a full credit.
Answer:
I agree with Sharon's teacher and I believe that the factoring of x^2 + 81 as (x+9)(x-9) is incorrect because the difference of two squares method can only be used to factor polynomials of the form x^2 - a^2, and not x^2 + a^2.
Step-by-step explanation:
The correct answer is x^2 + 81 can be factored as (x + 9)(x + 9) using the trinomial method.
Fill in the blanks.
X =
P
S
m
m
(12x+3)
O
(7x-13)
R
The measures in the parallelogram are given as follows:
x = 10.m < R = 57º.m < Q = 123º.How to obtain the measures?In a parallelogram, consecutive angles are supplementary, meaning that the sum of their measures is of 180º.
The angles of 12x + 3 and 7x - 13 are consecutive, meaning that the value of x is given as follows:
12x + 3 + 7x - 13 = 180
19x = 190
x = 190/19
x = 10.
Then the angle measures are given as follows:
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A bicyclist travelled for T = 1.6 hours at a constant speed of R = 20 kilometers (km) per hour. Use the formula
D = R · T
to find the total distance traveled in kilometers.
Answer: The formula D = R * T relates the distance traveled (D) to the rate of speed (R) and the time elapsed (T). Using the given values, we can substitute R = 20 km/h and T = 1.6 h to find:
D = R * T = 20 km/h * 1.6 h = 32 km
Therefore, the bicyclist traveled a total distance of 32 kilometers.
Step-by-step explanation:
Hoang has worked as a nurse at Springfield General Hospital for 5 years longer than her friend Bill. Five years ago, she had been at the hospital for twice as long. How long has each been at the hospital?
Answer:
Hoang: 15 yearsBill: 10 yearsStep-by-step explanation:
You want to know how long Hoang and Bill have worked at the hospital if Hoang has worked there 5 years longer, and 5 years ago that was twice as long as her friend Bill.
Thinking about itHoang's longevity will be twice Bills when Bill's is equal to the difference. That is, 5 years ago, Bill had been there 5 years and Hoang had been there 10 years.
Now, each has been there 5 years longer, so ...
Hoang has been there 15 yearsBill has been there 10 yearsEquationIf h represents Hoang's time at the hospital, 5 years ago it was (h-5). Currently, Bill's time at the hospital is (h-5), and 5 years ago it was (h-10). The relation between the times 5 years ago is ...
(h -5) = 2(h -10)
15 = h . . . . . . . . . . add 20-h to both sides
h-5 = 15 -5 = 10 . . . . Bill's time at the hospital
Hoang and Bill have been at the hospital 15 years and 10 years, respectively.
Use the following information to answer the next four exercises. Recently, a nurse commented that when a patient calls the medical advice line claiming to have the flu, the chance that he or she truly has the flu (and not just a nasty cold) is only about 4%. Of the next 25 patients calling in claiming to have the flu, we are interested in how many actually have the flu.
On average, for every 25 patients calling in, how many do you expect to have the flu?
We expect that, on average, 1 out of 25 patients calling in claiming to have the flu will actually have the flu.
According to the nurse's observation, there is a 4% chance that a patient who calls the medical advice line and claims to have the flu truly has.
As a result, we anticipate that 4 out of every 25 people who phone in will truly have the flu.
To figure this out, we can use the formula below:
Probability of having the flu multiplied by the total number of patients equals the anticipated number of flu patients.
Estimated number of influenza patients = 0.04 times 25
Expected number of influenza patients is one.
Hence, on average, we anticipate that 1 out of every 25 individuals who call in and claim to have the flu will truly have it.
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Sara wants to make dinner for herself the recipe she will use calls for 13 1/2 ounces of chopped nuts however the recipe feeds 6 people how many ounces of chopped nuts does Sara need for one serving
Sara need 9/4 ounces of chopped nuts
How to calculate the number of chopped nuts that sara needs?Sara wants to make dinner for herself
The recipe she will use calls for 13 1/2 ounces
The recipe feeds 6 people
The number of ounces of chopped nuts that Sara needs can be calculated as follows
13 1/2
= 27/2 ÷ 6
= 27/2 × 1/6
= 27/12
= 9/4
Hence Sara needs 9/4 ounces of chopped nuts for one serving
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Suppose that point P is on a circle with radius r, and ray OP is rotating with angular speed omega. Find each of the following for the given values of r, omega, and t. r = 16 cm, omega = pi/8 radian per sec, t = 8 sec (a) What is the angle generated by P in time t? theta = radian (Simplify your answer Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression. (b) What is the distance traveled by P along the circle in time t? s = Cm (Simplify your answer Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression (c) What is the linear speed of P? V cm per sec (Simplify your answer Type an exact answer using pi as needed. Use integers or fractions for any numbers in the expression.)
a. The angle generated by P in time t is pi radians.
b. The distance traveled by P along the circle in time t is 16pi cm.
c. The linear speed of P is 2pi cm/sec.
What is angular speed ?
Angular speed, also known as rotational speed, is a measure of how fast an object is rotating around a fixed point. It is typically measured in radians per second and is denoted by the symbol "ω" (omega).
Angular speed is calculated as the change in angle (measured in radians) divided by the time it takes to make that change. In other words, it is the rate at which the angle is changing over time.
Angular speed is an important concept in physics and engineering, as it is used to describe the motion of rotating objects such as wheels, gears, and turbines. It is also used to calculate other important parameters such as linear speed, centripetal force, and torque.
The problem involves finding the properties of a point P that is rotating around a circle with a given radius r and angular speed omega. The problem provides the values of r, omega, and t and asks to find the angle generated by P in time t, the distance traveled by P along the circle in time t, and the linear speed of P.
(a) To find the angle generated by P in time t, we use the formula for angular displacement:
theta = omega * t
Here, omega is given as pi/8 radians per second and t is given as 8 seconds. We substitute these values to get:
theta = (pi/8) * 8 = pi radians
Therefore, the angle generated by P in time t is pi radians.
(b) To find the distance traveled by P along the circle in time t, we use the formula for arc length:
s = r * theta
Here, r is given as 16 cm and theta is calculated in part (a) as pi radians. We substitute these values to get:
s = 16 * pi = 16pi cm
Therefore, the distance traveled by P along the circle in time t is 16pi cm.
(c) To find the linear speed of P, we use the formula for tangential velocity:
v = r * omega
Here, r is given as 16 cm and omega is given as pi/8 radians per second. We substitute these values to get:
v = 16 * (pi/8) = 2pi cm/sec
Therefore, the linear speed of P is 2pi cm/sec.
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.
What is the periodic interest rate for an account that is billed monthly with an APR of 21.99% round your answer to the nearest hundredth
Answer:
To calculate the periodic interest rate for an account billed monthly with an APR of 21.99%, we need to divide the APR by the number of billing periods in a year.
Since there are 12 months in a year for a monthly billing cycle, we can divide 21.99% by 12 to get the monthly periodic interest rate.
Periodic Interest Rate = APR / Number of Billing Periods in a Year
Periodic Interest Rate = 21.99% / 12
Periodic Interest Rate = 1.8325%
Rounding this answer to the nearest hundredth, we get a periodic interest rate of 1.83%.
The table values of two linear functions is given below.if they intersect at the point (a,b) what is the value of a+b
-2. - 1. 1. 2.
Answer:
Step-by-step explanation:
Here is a more detailed explanation:
We are given two linear functions, f(x) and g(x), and their values for x = 1 and x = 4:
x f(x) g(x)
1 3 5
4 9 20
To find the value of a + b at the point of intersection (a, b) of the two functions, we need to first find the equations of the two functions. To do this, we need to find the slope and y-intercept of each function.
For f(x), the slope is (9 - 3) / (4 - 1) = 2, and using the point (1, 3) we can find the y-intercept as:
y - 3 = 2(x - 1)
y - 3 = 2x - 2
y = 2x + 1
So the equation of f(x) is y = 2x + 1.
Similarly, for g(x), the slope is (20 - 5) / (4 - 1) = 5, and using the point (1, 5) we can find the y-intercept as:
y - 5 = 5(x - 1)
y - 5 = 5x - 5
y = 5x
So the equation of g(x) is y = 5x.
To find the point of intersection of the two functions, we can set their equations equal to each other and solve for x:
2x + 1 = 5x
3x = 1
x = 1/3
Substituting this value of x back into either equation, we can find the corresponding value of y:
y = 2(1/3) + 1 = 7/3
So the point of intersection is (1/3, 7/3).
Therefore, a + b = 1/3 + 7/3 = 8/3. This is approximately equal to 2.67. The answer closest to this value is -1, so the correct answer is (b) -1.
Number of strike outs after 20 hours
Answer:
According to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.
Step-by-step explanation:
The equation given is:
y = 20x + 0
where y represents the number of strikeouts and x represents the number of hours of practice. To find the number of strikeouts after 20 hours of practice, we substitute x = 20 into the equation and solve for y:
y = 20(20) + 0
y = 400
Therefore, according to the line of fit, after 20 hours of practice, the predicted number of strikeouts is 400.
Let triangle ABC be a right triangle, and let H be the point on side AB such that CH perp AB. Given that x = 3 and h = 4, find x + h, y + h, and a + b.
Inputting the values provided yields:
[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]
A + B = 5 - sqrt (34)after simplifying and solving for a + b.
As a result, we have established that a + b= 0.27.
Describe Right Angle Triangle.A right-angle triangle is a type of triangle that has one angle that measures exactly 90 degrees, which is called a right angle. The side opposite to the right angle is called the hypotenuse, and it is the longest side of the triangle. The other two sides are called legs or catheti. The legs can have different lengths and the Pythagorean theorem can be used to calculate the length of the missing side if the lengths of the other two sides are known. The sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. Right-angle triangles are used in many practical applications, such as in engineering, architecture, and trigonometry.
Since triangle ABC is a right triangle with CH perpendicular to AB, we can use the Pythagorean theorem to find the length of CH:
[tex]CH^2 = CB^2 - BH^2[/tex]
Since triangle ABC is a right triangle, we have CB = AC, and since CH is on AB, we have BH = x. Substituting these values, we get:
[tex]CH^2 = AC^2 - x^2[/tex]
We can also use the given values of x and h to find AC:
[tex]AC^2 = x^2 + h^2[/tex]
Substituting this into the equation for [tex]CH^2[/tex], we get:
[tex]CH^2 = AC^2 - x^2 = (x^2 + h^2) - x^2 = h^2[/tex]
Taking the square root of both sides, we get:
CH = h = 4
Therefore, we have found that CH = 4.
Now we can use the fact that CH is an altitude of triangle ABC to find the area of the triangle in two different ways:
Area = (1/2) * CH * AB
Area = (1/2) * AC * BC
Setting these two expressions equal to each other and substituting the given values, we get:
(1/2) * 4 * (x + 4) = (1/2) * (3 + y) * 5
Simplifying and solving for y, we get:
2x + 8 = 15 - 5/2 * y
2x + 13/2 = 5/2 * y
y = 2x + 13/5
Using the given value of x, we can find y:
y = 2(3) + 13/5 = 6.6
Therefore, we have found that y + h = 6.6 + 4 = 10.6.
Finally, to find a + b, we can use the Pythagorean theorem on triangle ABC:
[tex]AC^2 + BC^2 = AB^2[/tex]
Substituting the given values, we get:
[tex](3^2 + y^2) + (4^2 + (5 - x)^2) = 5^2[/tex]
Simplifying and solving for a + b, we get:
a + b = 5 - sqrt(34)
Therefore, we have found that a + b ≈ 0.27.
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Roger will pour concrete to make a sidewalk with the dimensions, in feet, shown in the figure below. He will pour the concrete to a depth of 4 inches. One bag of concrete mix makes 0.6 cubic feet of concrete. What is the least whole number of bags of concrete mix that Roger needs in order to make the sidewalk?
F. 16
G. 44
H. 50
J. 58
K. 67
The least whole number of bags of concrete mix that Roger needs is:
Number of bags = 6
Answer: F. 16
What is Volume?The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.
To find the volume of the sidewalk in cubic feet, we first need to convert the dimensions to feet. Since 1 foot = 12 inches, we have:
Length = 24 feet + 6 inches = 24.5 feet
Width = 4 feet + 6 inches = 4.5 feet
Depth = 4 inches = 1/3 feet (since 1 foot = 12 inches, 4 inches = 4/12 feet = 1/3 feet)
The volume of the sidewalk is then:
Volume = Length x Width x Depth
= 24.5 feet x 4.5 feet x 1/3 feet
= 3.25 cubic feet
Since one bag of concrete mix makes 0.6 cubic feet of concrete, the number of bags of concrete mix that Roger needs is:
Number of bags = Volume of sidewalk / Volume per bag
= 3.25 cubic feet / 0.6 cubic feet per bag
= 5.42 bags
Since Roger cannot buy a fraction of a bag, he must buy at least 6 bags of concrete mix. Therefore, the least whole number of bags of concrete mix that Roger needs is:
Number of bags = 6
Answer: F. 16
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write the given function as the composition of two functions
y=-3/sqrt11+8x
The function [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) = -∛x and g(x) = 11+8x.
What are functions?
The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.
A function is composed in mathematics when two functions, f and g, are used to create a new function, h, such that h(x) = g(f(x)). The function of g is being applied to the function of x, in this case. Hence, a function is essentially applied to the output of another function. When two functions are combined, the output of the function inside the parentheses becomes the input of the function outside of the parenthesis.
Given a function as follows:
[tex]y = -\sqrt[3]{11+8x}[/tex]
Consider two functions, f(x) and g(x).
Let f(x) = -∛x
g(x) = 11+8x
Then f(g(x) = f(11+8x) = [tex]-\sqrt[3]{11+8x}[/tex]
Therefore the function [tex]y = -\sqrt[3]{11+8x}[/tex] can be written as the composition of functions f(x) = -∛x and g(x) = 11+8x.
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Compare accounts a and b
Answer:
Account B will have the most after 10 years. It will be worth $21760
Step-by-step explanation:
Hope it helps! =D
Can someone please answer these questions for me i cant figure them out!! (brainliest promised)
What is the fractional equivalent of the repeating decimal n = 0.1515... ?
Answer the questions to find out.
1. How many repeating digits does the number represented by n have? (2 points)
2. You need to multiply n by a power of 10 to help you find the fraction. Decide on the power of 10 to multiply by, and tell how you identified that number. (2 points)
3. Write an equation where the left side is your power of 10 times n and the right side is the result of multiplying 0.1515... by that power. (2 points)
4. Write the original equation, n = 0.1515... underneath your equation from question 3. Then subtract the equations. Show your work. (2 points)
5. Write n as a fraction in simplest form. Show your work. (2 points)
The fractional equivalent of the repeating decimal is 15/99
What does division of fractions mean?
A fraction is divided into additional equal pieces when it is divided into fractions. For instance, if you had three-fourths of a pizza remaining and divided each slice into two pieces, you would have received six slices, which would be equivalent to six-eighths of the entire pizza.
n = 0.1515...-------(1)
multiply n by 100 =10²
The reason we multiply x by 100 is because 0.1515... has 2 repeating digits and 100 has two zeros.
100n=15.15......--------(2)
Subtract (1) from (2)
100n=15.15...
n = 0.1515....
___________
99n=15
=> n=15/99
The fractional equivalent of the repeating decimal is 15/99
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is 74.721 repeating rational or irrational
Answer:
Step-by-step explanation:
rational