The value after solving mixed fraction is 32/10=3.2
What is fraction?A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator. The numerator indicates the number of equal parts that were actually taken, whereas the denominator shows the total number of equal parts in the whole.
What is mixed fraction?The quotient and remainder of a fraction are used to represent it, making it a mixed fraction. For instance, 2 1/3, where 2 is the quotient and 1 is the remainder, is a mixed fraction. A mixed fraction is a combination of a whole number and a recognised fraction.
according to question,
=51/10 - 19/10
=32/10
=3.2
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The value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.
What is mixed fraction?It is a mixed fraction when the remainder and quotient of a fraction are utilised to represent it. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. A whole number and a recognised fraction are combined to form a mixed fraction.
To subtract mixed numbers like 5 1/10 and 1 9/10, you need to convert them to improper fractions first.
5 1/10 can be converted to an improper fraction as follows:
5 1/10 = (5 x 10 + 1)/10 = 51/10
1 9/10 can be converted to an improper fraction as follows:
1 9/10 = (1 x 10 + 9)/10 = 19/10
Now we can subtract the two fractions:
51/10 - 19/10 = (51 - 19)/10 = 32/10
32/10 can be simplified to 16/5 by dividing both the numerator and denominator by the greatest common factor, which is 2.
So, the value of 5 1/10 minus 1 9/10 is 16/5 or 3 1/5.
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Select all statements that are true.
Answers:
A, B, D, E
Nearly everything except choice C is true.
====================================================
Explanation:
Choice A is true because sine = opposite/hypotenuse.Choice B is true as well because cosine = adjacent/hypotenuseTangent is opposite/adjacent. The 4/9 should be 9/4. Therefore, choice C is false. If beta was theta, then tan(theta) = 4/9 would be true.Choice D is true because of the pythagorean theorem a^2+b^2 = c^2.Choice E is true because tan = opposite/adjacent, and the 9 and 4 are in the correct order (see choice C).4 William and his three friends had lunch at a restaurant. They split the bill
equally. The total bill was $34. They left a 15% tip. How much would each person
pay?
9x
omission for?
Answer:
$9.10 per person
Step-by-step explanation:
34 / 4 is 8.50
15% is 2.40, then divided 2.40 by 4 and get 0.60.
0.60 + 8.50 = 9.10 per person
f (t) = Atne(−bt)
The values A, n, and b are the parameters of the function.
This function accurately represents the way a drug interacts in the bloodstream. Studying
this function is essential to doctors and pharmacists because it allows them to administer
dosages of medicine correctly.1
A drug dose is being designed for a 90kg male patient. The amount of the drug in the
patient’s bloodstream after t hours, measured in nanograms per milliliter (ng/ml) is given
by a surge function.
Any positive value of A can be achieved by increasing or decreasing the amount of
medicine given. However, depending on the type of delayed release mechanism selected
there are choices possible for the value of the pair (n,b): The achievable pairs are listed in
the table below.
Delay Type n value b value
Extended 2 0.3
Medium 3 0.5
Rapid 3 0.7
The medical requirements for the treatment are:
• The dose (in ng/ml) may not exceed 100 at any time.
• The dose must fall to be at or below 20 ng/ml by 24 hours.
Within these parameters, the treatment effect will be measured in ng/ml-hours. (1
ng/ml concentration for 1 hour is 1 ng/ml-hour of treatment). The objective is to obtain
the maximum possible treatment effect while ensuring the requirements are met.. For each Delay Type, determine the value of A (dosage amount) that maximizes treat-
ment effect for that Delay Type while meeting medical requirements.
2. Determine which Delay Type (assuming optimal dosage) will maximize treatment ef-
fect.
3. For the Delay Type and dosage level you selected above,
(a) determine the treatment effect over the first 24 hours.
(b) determine the residual treatment effect for time after the first 24 hours
We can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml
How to solveTo determine the optimal dosage amount A for each Delay Type, we need to first define the surge function for each delay type as:
Extended: f(t) = [tex]At^2e^-^0^.^3^t[/tex]
Medium: f(t) = [tex]At^3e^-^0^.^5^t[/tex]
Rapid: f(t) = [tex]At^3e^-^0^.^7^t[/tex]
To find the optimal dosage amount A, we need to maximize the treatment effect while ensuring that the dose does not exceed 100ng/ml at any time and falls to be at or below 20ng/ml by 24 hours.
The treatment effect can be calculated by integrating the surge function over time from 0 to 24 hours and then adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20ng/ml
For the Delay Type and dosage level selected, we can calculate the treatment effect over the first 24 hours by integrating the surge function from 0 to 24 hours.
Then, we can calculate the residual treatment effect for a time after the first 24 hours by adding up the integrals for each subsequent 24-hour period until the residual treatment effect falls to or below 20 ng/ml..
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Determine how many liters a right circular cylindrical tank holds if it is 5 m long and 13 m in diameter.
The tank holds about _____ liters of liquid.
(Round to the nearest thousand as needed.)
The right circular cylindrical tank which is 5 m long and 13 m in diameter holds about 663,325 liters of liquid approximately.
The formula to find the volume of a right cylindrical tank is
V = πr²h, where 'r' is the radius and 'h' is the height.
Given that, the height is 5 m and the diameter is 13 m.
Radius = Diameter/2.
Radius = 13/2 = 6.5 m.
We know that, π = 3.14.
Now, we can substitute the values in the formula.
V = 3.14×(6.5)²×5.
V = 3.14×6.5×6.5×5
V = 663.325 cubic meters.
Now, we have to convert cubic meters into liters.
We need to multiply by 1000 as a thousand liters are in one cubic meter.
663.325×1000 = 663,325.
Therefore, the tank holds about 663,325 liters of liquid approximately.
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Find the surface area of a triangular prism (which has 2 triangular bases and 3 rectangular sides) with the following dimensions:
Base of triangles= 4 in
Height of triangles = 3 in
Length of rectangles = 10 in
Width of rectangles = 5 in
The surface area of the triangular prism is 162 square inches.
What is prism?In geometry, a prism is a three-dimensional solid shape that has two identical, parallel faces (called bases) and rectangular or parallelogram-shaped sides. The sides connect the bases, and their shape determines the type of prism.
To find the surface area of the triangular prism, we need to find the areas of all five faces and add them together.
The area of each triangular base is:
A = (1/2)bh
where b is the length of the base (which is equal to 4 in) and h is the height (which is equal to 3 in).
A = (1/2)(4 in)(3 in) = 6 in²
So the total area of both triangular bases is:
2A = 2(6 in²) = 12 in²
The area of each rectangular side is:
A = lw
where l is the length (which is equal to 10 in) and w is the width (which is equal to 5 in).
A = (10 in)(5 in) = 50 in²
So the total area of all three rectangular sides is:
3A = 3(50 in²) = 150 in²
Therefore, the total surface area of the triangular prism is:
12 in² + 150 in² = 162 in²
Thus, the surface area of the triangular prism is 162 square inches.
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HELP ASAP ASAP PLS PLS ALSO BRAINLIEST
A family recipe calls for sauce and oregano. The table below shows the parts of sauce to oregano used to make the recipe.
Servings Sauce (cups) Oregano (tsp)
4 8 one half
6
At this rate, how much sauce and oregano will be needed to make 6 servings?
The recipe will need 12 cups of sauce and three fourths teaspoons of oregano for 8 servings.
The recipe will need 12 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and 1 teaspoon of oregano for 8 servings.
The recipe will need 10 cups of sauce and three fourths teaspoons of oregano for 8 servings
The amounts needed to make 6 servings are given as follows:
Sauce: 12 servings.Oregano: 3/4 teaspoons.How to obtain the amounts?The needed amounts to make 6 servings of the recipe are obtained applying the proportions in the context of the problem.
From the first line of the table, we get the amounts of sauce and oregano per serving are follows:
Sauce: 8/4 = 2 cups.Oregano: 0.5/4 = 1/8 teaspoons per serving.Hence the amounts for six servings are given as follows:
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The exponential function f, represented in the table, can be written as f(x)=axb^x
x l f(x)
0 l 15
1 l 9
Complete the equation for f(x)
The equation for f(x) can be written as f(x)= 15(3/5)ˣ
Define exponential function?An exponential function is a mathematical function of the form f(x) = aˣ, where 'a' is a positive constant and 'x' is any real number. The graph of an exponential function is characterized by a rapid increase or decrease as 'x' increases or decreases, respectively. Exponential functions have many applications in fields such as finance, biology, and physics.
From this table we know this thing that when x=0, y=15
when x=1, y=9
a×b⁰=15⇒ a=15 as b⁰=1
a×b¹=9⇒ ab=9
so b=9/a
b= 9/15⇒3/5
After putting the values we get the result f(x)=15×(3/5)ˣ
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d) If repeats are not allowed, at least one character must be a symbol and characters can be digits, lower- case letters or any of the 5 symbols !$%&*, how many passwords of length 5 can be made?
There are 65,000 possible passwords of length 5 that can be made with no repeats allowed.
What is length?
Length is a measure of distance between two points or the extent of something along its longest dimension. It is one of the basic dimensions in geometry and can be defined as the distance between two points measured in one dimension, typically along a straight line.
Since at least one character must be a symbol, there are 5 choices for the first character. For the remaining four characters, there are 10 choices (0 to 9) for each character if digits are allowed, 26 choices (a to z) for each character if lowercase letters are allowed, and 5 choices for each character if the other symbols are allowed.
Therefore, the total number of passwords of length 5 that can be made, with no repeats allowed and at least one character being a symbol, is:
5 * (10 * 26 * 5 * 5 * 5)
Simplifying the expression, we get:
5 * (13,000)
65,000
Therefore, there are 65,000 possible passwords of length 5 that can be made with no repeats allowed, at least one character being a symbol, and characters being digits, lowercase letters, or any of the 5 symbols !$%&*.
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pls
a golf ball is hit so that it travels a horizontal distance of 440 feet and reaches a maximum height of 190 feet
using your understanding of parametric equations for projectile motion, what is the angle the ball takes off?
The requried, quadratic equation that models the path of the golf ball, is 16.0850t² - 110.560t - 190 = 0 and the angle the ball takes off is 64.4⁰.
The motion of the golf ball can be modeled using two equations, one for the vertical motion and another for the horizontal motion.
The equation for the vertical motion of the ball is given by:
h = V₀t - ¹/₂gt²,
Using the given values, we find that,
V₀ = √(2 x 32.17 x 190) = 110.56 ft/s.
Substituting this value and the value of g into the equation of motion for the vertical direction, we get -190 = 110.56t - ¹/₂(32.17)t², which simplifies to 16.0850t² - 110.560t - 190 = 0.
The equation for the horizontal motion of the ball is given by [tex]x = V_xt[/tex], where x is the horizontal distance traveled, Vx is the initial horizontal velocity, and t is the time. Using the given value of x, we can find Vx as [tex]V_x = 440/t.[/tex]
We can then solve the quadratic equation 16.0850t² - 110.560t - 190 = 0 to find the time t of flight.
Using the formula method, we get t = 8.3 s. Substituting this value into the equation for the horizontal motion, we get [tex]V_x = 440/8.3 = 53.01 ft/s.[/tex]
Finally, we can find the angle of projection θ using the formula tan θ = [tex](V_y) / (V_x)[/tex],
tan θ = (110.56)/(53.01),
which simplifies to tan θ = 2.086. Taking the inverse tangent of both sides, we get θ = tan⁻¹(2.086) = 64.4⁰.
Therefore, the angle at which the ball takes off is 64.4⁰.
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When we started here, there were 500 employees. Since then, we have added 35% more employees, so we now have a total of _________ employees
The company now has 675 employees after adding 35% more employees to the initial 500 employees.
What is percentage?A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100.
To calculate the total number of employees after adding 35%, you can multiply the initial number of employees by 1.35:
Total number of employees = 500 x 1.35
Total number of employees = 675
Therefore, the company now has 675 employees after adding 35% more employees to the initial 500 employees.
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A right rectangular prism had a length 2 1/2yd, width 3 1/2yd, and height 1 1/2yd. You use cubes with fractional edge length 1/2yd to find the volume. How many cubes are there for each of the length, width, and height of the prism? Find the volume.
The volume of the rectangular prism is 13.125 cubic yards.
Calculating the number of cubes and the volumeTo find the number of cubes that fit along the length, width, and height of the rectangular prism, we need to divide the length, width, and height by the edge length of each cube, which is 1/2yd.
Along the length: (2 1/2 yd) / (1/2 yd) = 5 cubes
Along the width: (3 1/2 yd) / (1/2 yd) = 7 cubes
Along the height: (1 1/2 yd) / (1/2 yd) = 3 cubes
Therefore, there are 5 cubes along the length, 7 cubes along the width, and 3 cubes along the height of the rectangular prism.
To find the volume of the rectangular prism, we can multiply the length, width, and height:
Volume = (2 1/2 yd) x (3 1/2 yd) x (1 1/2 yd)
Volume = (5/2 yd) x (7/2 yd) x (3/2 yd)
Volume = (13.125 yd^3)
Therefore, the volume of the rectangular prism is 13.125 cubic yards.
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Suppose you roll a special 11-sided die. What is the probability that the number rolled is a "1" OR a "2"?
The probability of rolling a "1" OR a "2" on an 11-sided die is 2/11, or approximately 0.1818.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. Usually, it is stated as a number between 0 and 1, where 0 denotes that an event is impossible and 1 denotes that it is certain to happen.
According to question:The probability of rolling a "1" or a "2" on an 11-sided die can be calculated by adding the probabilities of rolling a "1" and rolling a "2".
Assuming the die is fair (i.e., each face has an equal chance of landing face up), the probability of rolling any particular number is 1/11. Therefore, the probability of rolling a "1" is 1/11, and the probability of rolling a "2" is also 1/11.
To find the probability of rolling a "1" OR a "2", we add the probabilities:
P(rolling a "1" OR a "2") = P(rolling a "1") + P(rolling a "2")
P(rolling a "1" OR a "2") = 1/11 + 1/11
P(rolling a "1" OR a "2") = 2/11
Therefore, the probability of rolling a "1" OR a "2" on an 11-sided die is 2/11, or approximately 0.1818 (rounded to four decimal places).
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Area and perimeter assignment. (9th Grade geometry)
Thus, the perimeter of the shown triangle using the distance formula is found as 13.45 units.
Explain about the perimeter:A path that encircles a region is referred to as a perimeter. Adding the lengths of every one of the sides together is the simplest formula for calculating the perimeter. The word circumference, that only encompasses a circle's perimeter, is used to describe the distance around a circle.
Given that:
coordinates of triangle: A(5,3) , B(1,5) and C(3,0)Perimeter = sum of all sides
Perimeter = AB + BC + CA
Estimate each distance using the distance formula:
d = √(x2 - x1)² + (y2 - y1)²
AB = √(1 - 5)² + (5 - 3)²
AB = √(-4)² + (-2)²
AB = √(16 + 4)
AB = √20
BC = √(3 - 1)² + (0 - 5)²
BC = √(2)² + (-5)²
BC = √(4 + 25)
BC = √29
CA = √(5 - 3)² + (3 - 0)²
CA = √(2)² + (3)²
CA = √(4 + 9)
CA = √13
Perimeter = AB + BC + CA
Perimeter = √20 + √29 + √13
Perimeter = 4.47 + 5.38 + 3.60
Perimeter = 13.45 units.
Thus, the perimeter of the shown triangle using the distance formula is found as 13.45 units.
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3. vertices at (-8, 4) and (4, 4), foci at (-3, 4) and (-1, 4)
The equation of the ellipse is ((x+2)² / 36) + ((y-4)² / 35.12) = 1
To find the center of the ellipse, we can find the midpoint between the two vertices:
Midpoint = ((-8 + 4)/2, (4 + 4)/2) = (-2, 4)
So the center of the ellipse is (-2, 4).
To find the semi-major axis (a), we can find the distance from the center to one of the vertices:
Distance = √[(-8 - (-2))² + (4 - 4)²] = √36 = 6
So the semi-major axis is 6.
To find the distance between the foci (2c), we can find the distance between the two foci:
Distance = √[(-3 - (-1))² + (4 - 4)²] = 2
So 2c = 2 and c = 1.
Now we can use the relationship between a, b, and c in an ellipse:
c² = a²- b²
(1)² = (6)² - b²
b² = 35
b ≈ 5.92
So the semi-minor axis is approximately 5.92.
Therefore, the equation of the ellipse is ((x+2)² / 36) + ((y-4)² / 35.12) = 1
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Correct question is "vertices at (-8, 4) and (4, 4), foci at (-3, 4) and (-1, 4), find the equation of the ellipse."
The equation -4x + y = 0 relates the
number of pages in a photo album y to
the number of pictures in the album x.
Tell whether the relationship is a direct
variation. Explain your answer.
Recall the general equation for a line in slope-intercept form:
[tex]y=mx+b[/tex]
where:
[tex]\text{y = y-coordinate}[/tex]
[tex]\text{m}=\bold{slope}[/tex]
[tex]\text{x = x-coordinate}[/tex]
[tex]\text{b = y-intercept}[/tex]
In this equation, if you isolate for [tex]y[/tex], you end up with an equation that looks like this:
[tex]-4x+y=0[/tex]
[tex]-4x +4x+y=0+4x[/tex]
[tex]\implies y=4x+0[/tex]
Recall that in direct variation, the graph goes through the origin, (0,0). Since the y-intercept of this equation is 0, this means the graph intersects the origin. Thus, this graph represents direct variation.
If you were to graph the line, you would see the intersection at (0,0):
graph[tex]\{y=4x [-12.66, 12.65, -6.33, 6.33]\}[/tex]
I saw this problem somewhere and tried to solve it, but it didn't work. Here is the problem; Suppose you have a ruler whose length is infinite, to measure a line of length: 3x + 15y = 12y - 45
Write a function and call it ω, and get the line length per ruler with the function
The function ω that gives the length per ruler for the line 3x + 15y = 12y - 45 is:
ω(x) = √(2)
How do we calculate?rewrite the equation of the line as:
3x - 3y = -45
The line has a slope of:
m = 3/3 = 1
We choose two points on the line with integer coordinates:
Point 1: (0, 15)
Point 2: (15, 30)
d = √t((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates of the two points, we get:
d = √((15 - 0)^2 + (30 - 15)^2)
d = √(225 + 225)
d = √t(450)
d = 15√(2)
Length per ruler = (distance between points) / (total length of line)
3x + 15((3/2)x + 15) = 12((3/2)x + 15) - 45
we simplify this equation, we get:
3x + (45/2)x + 225 = (18/2)x + 180 - 45
Combining like terms, we get:
(57/2)x = 0
Solving for x, we get:
x = 0
Substituting this value of x into the expression for the total length of the line, we get:
y = (3/2)x + 15
y = 15
Length per ruler = (15√(2)) / 15
Length per ruler = √(2)
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The compliment of an angle is three times the measurement of the angle. Find the measurement of the larger angle
The greater angle has a 67.5° degree measurement. When two angles' measurements add up to 90°degrees, they are said to be complimentary.
How to calculate the larger angle?Call that angle we're looking for "x" for convenience.
The degree that, if added to x, makes x equal 90° degrees is known as the compliment of x.
We now know that 3x, or 3 times x, is the compliment of x.
With this knowledge, we can construct the following equation:
x + 3x = 90°
combining comparable equations;
4x = 90°
x = 22.5°, when both sides are divided by 4.
As a result,
3x = 3(22.5°) = 67.5° degrees is the measurement of the greater angle, which is the complement of x.
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An individual depositing in a non-IRA account has to pay income taxes on the funds deposited and on interest earned in each year but does not have to pay taxes on withdrawals from the account.
Sarah, who is five years from retirement, receives a $10,000 bonus at work. She is trying to decide whether to save this extra income in an IRA account or in a regular savings account. Both accounts earn 8 percent nominal interest, and Sarah is in the 30 percent tax bracket in every year (including her retirement year)
If Sarah invests in the normal savings account, her net value (after taxes) five years from now will be?:
The net value of the $10,000 bonus in a normal savings account after taxes and interest in five years will be $9,181.
What is the net value of Sarah's $10,000 bonus in a normal savings account after taxes and interest in five years?Assuming an 8 percent nominal interest rate and a 30 percent tax bracket, the after-tax return on the normal savings account is 5.6 percent. Thus, after five years, the $10,000 bonus will grow to $14,693.
However, since Sarah is in the 30 percent tax bracket in every year, she will owe taxes on the interest income earned each year. This reduces the after-tax return to 3.92 percent. Therefore, in five years, the $10,000 bonus in the normal savings account will be worth $9,181 after taxes.
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The graph of linear function is shown on the grid
The y-intercept of a graph y=-3.
Here, we have,
Given the graph of a function, the y-intercept is defined as the y-coordinate of the point(s) where the graph crosses the y-axis.
There might be more than one y-intercepts or even none.
The graph provided in the question is a line with a negative slope, i.e., a decreasing line.
Carefully looking it can be determined the graph touches the y-axis in the point (0,-3), thus the y-intercept of the graph is y=-3
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complete question:
The graph of the linear function is shown on the coordinate grid. * 910X -10 What is the y intercept of the graph of the linear function?
HELP QUICKLY PLEASE!!!
What are the x-intercepts of the quadratic function shown?
Answer:
D. 1,0 & -3,0
Step-by-step explanation:
because the two lines pass through points 1,0 and -3,0 at the x-axis
Answer:
your answer is D. 1,0 & -3,0
Step-by-step explanation:
2. Fiona opened a retirement account that has an annual yield of 6%. She is planning on retiring in 20 years.
How much must she deposit into that account each year so that she can have a total of $600,000 by the time
she retires?
Answer:
PMT = $52,023.26
Step-by-step explanation:
To calculate how much Fiona must deposit into her retirement account each year, we can use the formula for annuity payments:
PMT = PV x (r / (1 - (1 + r)^(-n)))
Where:
PMT is the periodic payment
PV is the present value (or desired future value) of the annuity
r is the interest rate per period (in this case, the annual yield of 6% divided by the number of periods per year, which is 1)
n is the total number of periods (in this case, 20 years)
We know that Fiona wants to have a total of $600,000 in her retirement account by the time she retires, so PV = $600,000. We also know that the interest rate per period is 6% / 1 = 0.06, and the total number of periods is 20.
Plugging these values into the formula, we get:
PMT = $600,000 x (0.06 / (1 - (1 + 0.06)^(-20)))
PMT = $600,000 x (0.06 / (1 - 0.312))
PMT = $600,000 x (0.06 / 0.688)
PMT = $52,023.26
Therefore, Fiona would need to deposit approximately $52,023.26 into her retirement account each year for the next 20 years to have a total of $600,000 by the time she retires, assuming the annual yield remains constant at 6%.
Compare and contrast the direct write-off method and the allowance method for bad debts.
At a minimum, please consider the following in your answer:
When is the expense for uncollected accounts receivable recognized under each method?
Why is the direct write-off method not considered to follow generally accepted accounting
The direct write-off method and the allowance method are two different ways of accounting for uncollectible accounts receivable.
How do we explain?When an account is found to be uncollectible, the direct write-off method records the expense for uncollected accounts receivable. This approach involves simply writing off the uncollectible account as a bad debt expense and deducting the outstanding quantity from the accounts receivable total.
Despite being quite easy to understand and basic, this method does not adhere to generally accepted accounting principles (GAAP) because it does not match expenses to the time period during which income was generated.
In contrast, the allowance approach establishes an allowance for doubtful accounts contra-asset account and estimates the amount of uncollectible accounts before recognizing the expense for uncollected accounts receivable.
This allowance account is used to lower the balance of accounts receivable to the anticipated amount of collection. Instead of when the account is found to be uncollectible, the expense is recognized at the time the estimate is made. Because it matches the expense to the time period in which the revenue was received, this method is thought to be more accurate than the direct write-off method.
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Please help thank you
Answer:
(-2)
Step-by-step explanation:
just do -2 x-3 x than + 13 and than you will get - 2
answer ASAP pls with as as much detail in how to complete it as possible :))
An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1150, determine the probability that the mean tariff rate of 600 randomly selected railroad-car shipments of ethanol will be within $90 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.
Therefore, the probability that the mean tariff rate of 600 randomly selected railroad-car shipments of ethanol will be within $90 of the mean tariff rate of all railroad-car shipments of ethanol is approximately 0.9732 or 97.32%.
What is probability?Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability theory is widely used in many fields, including mathematics, statistics, physics, engineering, economics, and social sciences. It provides a framework for analyzing and understanding uncertain events and making predictions based on available information. Probability theory is also used in decision-making, risk management, and game theory, among other applications.
Here,
Let μ be the mean tariff rate of all railroad-car shipments of ethanol, and let x be the mean tariff rate of a random sample of 600 railroad-car shipments of ethanol. We want to find the probability that x will be within $90 of μ.
The standard error of the mean (SE) can be calculated as:
SE = σ / √(n)
where σ is the standard deviation of the population, n is the sample size.
Substituting the given values, we get:
SE = 1150 / √(600)
≈ 47.03
The probability that x will be within $90 of μ can be calculated by standardizing x using the standard error and the z-score formula:
z = (x - μ) / SE
z = ($90) / 47.03
≈ 1.915
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 1.915 is approximately 0.9732.
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5You can form a right triangle by cutting a _______ in half diagonally.
You can form a right triangle by cutting a square in half diagonally.
A square is a quadrilateral with four equal sides and four right angles. When a square is cut in half diagonally, it forms two congruent right triangles. The two halves of the square, which are the two legs of the right triangle, are equal in length.
The diagonal of the square, which is the hypotenuse of the right triangle, can be found using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse).
Therefore, in a right triangle formed by cutting a square in half diagonally, the length of the hypotenuse can be found by taking the square root of the sum of the squares of the lengths of the two legs.
In summary, cutting a square in half diagonally allows us to form two congruent right triangles with equal leg lengths, making it a suitable shape to form a right triangle.
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Please help me. Giving brainliest to whoever answers it!!!
The algebraic expression that represents the age of Ethan's dad is 4a - 5
How to represent the situation as an algebraic expression?Let's start by defining a variable to represent Ethan's age. We'll call this variable "a".
According to the problem, Ethan's dad is five years younger than four times Ethan's age. So, if we multiply Ethan's age by 4 and then subtract 5 years, we'll have the age of Ethan's dad.
Algebraically, we can represent this as:
4a - 5
Therefore, the algebraic expression that represents the age of Ethan's dad is 4a - 5.
Solve the equation [tex]3\frac{2}{3} x=2\frac{2}{5}[/tex]?Solve for x by simplifying both sides of the equation and isolating the variable.
[tex]3\frac{2}{3}x=2\frac{2}{5}[/tex]
Convert mixed numbers to improper fraction :
[tex]3\frac{2}{3} =\frac{11}{3}[/tex]
[tex]\frac{11}{3}x=2\frac{2}{5}[/tex]
Convert mixed numbers to improper fractions:
[tex]2\frac{2}{5} = \frac{12}{5}[/tex]
[tex]\frac{11}{3}x=\frac{12}{5}[/tex]
Multiply both sides by 3
[tex]11x=\frac{36}{5}[/tex]
Divide both sides by 11
[tex]x=\frac{36}{55}[/tex]
Therefore, [tex]3\frac{2}{3} x=2\frac{2}{5}[/tex] = [tex]x=\frac{36}{55}[/tex]
Steve sold 252 fruit baskets for the fundraiser. Therefore, we can find how many baskets Evie sold by using the ratio of her sales to Steve's sales, which is given as 25 baskets for each 100 baskets Steve sold.
We can set up a proportion to solve for the number of baskets Evie sold:
25/100 = x/252
Here, x represents the number of fruit baskets Evie sold.
To solve for x, we can cross-multiply and simplify:
25 * 252 = 100 * x
6300 = 100x
x = 63
Therefore, Evie sold 63 fruit baskets for the fundraiser.
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9x7x9x9x7x9 (I tried the answer 9^4 x 7^2 and it’s not correct
Answer:
321489
Step-by-step explanation:
look at the picture below
Part a: Ratios of side = 1:3 ; Ratios of Area of base = 1: 9 ; Ratios of volume = 1: 27.
Part b: volume of medium box = 5832 cu. in .
Explain about the shape of cube:A solid shape comprising six square faces is called a cube. Because every square face has the identical side length, each face is the same size. A cube has 8 vertices and 12 edges. An intersection of three cube edges is called to as a vertex.
Given data:
volume of cubical box = 216 cu. in.Let each side of the box be 'x'.Formula for the volume of cube :
V = side³
216 = x³
x = ∛216
x = 6 in.
Part A: length, with and height of cube is triples.
new side = 3*old side
new side = 3x
Ratios of side:
new side / old side = x / 3x = 1/3
new side : old side = 1:3
Area of base = side²
Ratios of Area of base:
new area / old area = x² / (3x)²
new area / old are = x² / 9x² = 1/9
new area : old are = 1: 9
Ratios of volume:
new vol / old vol = x³ / (3x³)
new vol / old vol = x³ / 27x³ = 1/27
new vol : old vol = 1:27
Part b: volume of medium box:
V = (3x)³
V = (3*6)³
V = (18)³
V = 5832 cu. in
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I need help with this math
A right triangular pyramid has a height of 14 yards. Its base has a leg that is 8 yd. The volume of the pyramid is 168 cubic yd. The other leg of the base is ___ yd.
Therefore , the solution of the given problem of volume comes out to be the other leg of the right triangular pyramid's base is 3 yards long.
What does volume actually mean?A three-dimensional object's volume, which is expressed in cubic units, indicates how much space it takes up. The indications for cubic measurements are litre and in3. However, you have to be cognizant of an object's volume in order to calculate its dimensions. Converting an object's weight into metric units like iii . and kilogrammes is a standard technique.
Here,
Let's use "x" yards to represent the other leg of the right triangle pyramid's base.
A pyramid's volume can be calculated using the following equation: => Volume = (1/3) * Base Area * Height
In this instance, we are informed that the pyramid has a volume of 168 cubic yards and a height of 14 yards.
=> 168 = (1/3) * 14 * base area
The base area can be estimated as (8 * x)/2 = 4x because we know that one leg of the base is 8 yards long and the other leg is designated as "x" yards.
=> 168 = (1/3) * 4x * 14
=> 168 = (4/3)x * 14
=> 168 = (4/3) * 14x
=> 168 = 56x
=> x = 168/56
=> x = 3
Therefore, the other leg of the right triangular pyramid's base is 3 yards long.
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