The depreciation schedule (in dollars) using MACRS for the metal-working lathe is as follows:
Year 1: $1,429.00
Year 2: $2,449.00
Year 3: $1,749.00
Year 4: $1,249.00
Year 5: $893.00
Year 6: $892.00
Year 7: $893.00
What is the MACRS depreciation schedule?The depreciation schedule using the Modified Accelerated Cost Recovery System (MACRS) is prepared as follows:
Given data:
Purchase cost of the metal-working lathe: $38,000
Business use percentage: 90%
Section 179 deduction: $18,000
Special depreciation allowance: 50%
Depreciable basis = Purchase cost - Section 179 deduction
Depreciable basis = $38,000 - $18,000 = $20,000
Special depreciation allowance = $20,000 * 50%
Special depreciation allowance = $10,000
Adjusted depreciable basis = $20,000 - $10,000
Adjusted depreciable basis = $10,000
The recovery period for a metal-working lathe is 7 years.
Using MACRS, the depreciation rates for a 7-year recovery period are as follows:
Year 1: 14.29%
Year 2: 24.49%
Year 3: 17.49%
Year 4: 12.49%
Year 5: 8.93%
Year 6: 8.92%
Year 7: 8.93%
Annual depreciation expense = Adjusted depreciable basis * Depreciation rateYear 1:
Depreciation expense = $10,000 * 14.29% = $1,429.00
Year 2:
Depreciation expense = $10,000 * 24.49% = $2,449.00
Year 3:
Depreciation expense = $10,000 * 17.49% = $1,749.00
Year 4:
Depreciation expense = $10,000 * 12.49% = $1,249.00
Year 5:
Depreciation expense = $10,000 * 8.93% = $893.00
Year 6:
Depreciation expense = $10,000 * 8.92% = $892.00
Year 7:
Depreciation expense = $10,000 * 8.93% = $893.00
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What is the radian measure of a 45 degree angle in a circle of radius 24 ft
To convert from degrees to radians, we use the conversion factor that 180 degrees is equal to π radians (or π/180 radians per degree).
Given that the angle is 45 degrees, we can calculate the radian measure as follows:
Radian measure = (45 degrees) * (π/180 radians per degree)
Radian measure = 45π/180
Simplifying further:
Radian measure = π/4
Therefore, the radian measure of a 45 degree angle is π/4.
A set of data is represented in the stem plot below.
Stem plot with stems of 3, 4, 5, 6, 7, 8, 9. Leaf for stem of 3 is 5. Leaves for stem of 4 are 4, 5. Leaves for stem of 5 are 3, 6. Leaves for stem of 6 are 2, 5. Leaves for stem of 7 are 5, 5, 6. Leaves for stem of 8 are 2, 5. Leaf for stem of 9 is 2.
Key: 3 | 5 = 35
Part A: Find the mean of the data. Show each step of work. (2 points)
Part B: Find the median of the data. Explain how you determined the median. (2 points)
Part C: Find the mode of the data. Explain how you determined the mode. (2 points)
Part D: Compare your values for mean, median, and mode from parts A, B, and C. Which value would best represent the data, and why? Explain using complete sentences. (4 points)
In this dataset, the mean is approximately 65.77, the median is 65, and the mode is 5 and 75.
Part A: Finding the mean of the data:
To find the mean, we need to calculate the average of all the data points.
Step 1: Identify the stems and their corresponding leaves:
3 | 5
4 | 4, 5
5 | 3, 6
6 | 2, 5
7 | 5, 5, 6
8 | 2, 5
9 | 2
Step 2: Assign numerical values to each stem-leaf combination:
3 | 5 = 35
4 | 4 = 44, 5 = 45
5 | 3 = 53, 6 = 56
6 | 2 = 62, 5 = 65
7 | 5 = 75, 5 = 75, 6 = 76
8 | 2 = 82, 5 = 85
9 | 2 = 92
Step 3: Calculate the sum of all the numerical values:
35 + 44 + 45 + 53 + 56 + 62 + 65 + 75 + 75 + 76 + 82 + 85 + 92 = 855
Step 4: Determine the count of all the data points:
The count is the total number of data points, which can be determined by adding up the frequencies of each stem-leaf combination:
1 (stem 3) + 2 (stem 4) + 2 (stem 5) + 2 (stem 6) + 3 (stem 7) + 2 (stem 8) + 1 (stem 9) = 13
Step 5: Calculate the mean by dividing the sum of all values by the count:
Mean = Sum of all values / Count = 855 / 13 = 65.77 (rounded to two decimal places)
The mean of the data is approximately 65.77.
Part B: Finding the median of the data:
To determine the median, we need to arrange the data in ascending order and find the middle value.
Arranging the data in ascending order: 35, 44, 45, 53, 56, 62, 65, 75, 75, 76, 82, 85, 92
There are 13 data points, the median will be the value in the middle. In this case, the middle value is the 7th value, which is 65.
The median of the data is 65.
Part C: Finding the mode of the data:
The mode represents the value(s) that occur with the highest frequency.
From the stem-leaf plot, we can see that the leaves with the highest frequency are 5 and 75. Both of these frequencies occur twice.
The mode of the data is 5 and 75.
Part D: Comparing the mean, median, and mode:
In this dataset, the mean is approximately 65.77, the median is 65, and the mode is 5 and 75.
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− 4 p − ( 5 p − 4 ) ≤ −4p−(5p−4)≤ 7 p + 10 + 3 p 7p+10+3p
Answer:
To solve the inequality −4p − (5p − 4) ≤ 7p + 10 + 3p, we can simplify and isolate the variable p. Let's work through the steps:
Step 1: Distribute the negative sign (-) inside the parentheses:
-4p - 5p + 4 ≤ 7p + 10 + 3p
Simplifying further:
-9p + 4 ≤ 10p + 10
Step 2: Group like terms by adding 9p to both sides of the inequality:
-9p + 9p + 4 ≤ 10p + 9p + 10
Simplifying further:
4 ≤ 19p + 10
Step 3: Subtract 10 from both sides of the inequality:
4 - 10 ≤ 19p + 10 - 10
Simplifying further:
-6 ≤ 19p
Step 4: Divide both sides of the inequality by 19:
-6/19 ≤ 19p/19
Simplifying further:
-6/19 ≤ p
So the solution to the inequality is p ≥ -6/19.
Suppose that the marginal cost function of a handbag manufacturer is
C'(z)=0.046875x² − z + 100
dollars per unit at production level z (where z is measured in units of 100 handbags). Find the total cost of producing 10 additional units if 2 units
are currently being produced.
Total cost of producing the additional units:
Note: Your answer should be a dollar amount and include a dollar sign and be correct to two decimal places.
The total cost of producing the additional units is $767.50.
How to determine the total cost of producing 10 additional units?In order to determine the total cost of producing 10 additional units assuming 2 units are currently being produced, we would have to integrate the marginal cost function for this handbag manufacturer with respect to x, and over the interval [10, 2].
Based on the information provided above, the marginal cost function for this handbag manufacturer is given by this function;
C'(x) = 0.046875x² − x + 100
₂∫¹⁰C'(x)dx = ₂∫¹⁰(0.046875x² − x + 100)dx
₂∫¹⁰C'(x)dx = ₂∫¹⁰(0.046875x²)dx − ₂∫¹⁰(x)dx + ₂∫¹⁰(100)dx
₂∫¹⁰C'(x)dx = 0.046875x³/3|¹⁰₂ - x²/2|¹⁰₂ + 100x|¹⁰₂
₂∫¹⁰C'(x)dx = 0.015625(10³ - 2³) - 1/2(10² - 2²) + 100(10 - 2)
₂∫¹⁰C'(x)dx = 0.015625(1000 - 8) - 0.5(100 - 4) + 100(8)
₂∫¹⁰C'(x)dx = 0.015625(992) - 0.5(96) + 800
₂∫¹⁰C'(x)dx = 15.5 - 48 + 800
₂∫¹⁰C'(x)dx = $767.50
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Fred is buying A New
refrigerator for his
Apartment. His friend has A
4-year-old refrigerator that
he will sell to Fred for only
$200, but the refrigerator
Needs About $350 iN
repairs. The local Appliance
shop hAs A New model for
$615, plus 7% sales tax.
How much sales tax will Fred pay if he buys the new refrigerator?
Fred will pay $43.05 in sales tax if he buys the new refrigerator.
To calculate the sales tax Fred will pay for the new refrigerator, we first need to find the amount of the sales tax.
The cost of the new refrigerator is $615.
To calculate the sales tax, we multiply the cost by the tax rate of 7%:
So, Sales tax = 7% of $615
Sales tax = (7/100) x $615
Sales tax = $43.05
Therefore, Fred will pay $43.05 in sales tax if he buys the new refrigerator.
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Can you help me find x
[tex] \boxed{\rm{Similarity \: shape}}[/tex]
[tex]\begin{aligned} \frac{AB}{DE}&= \frac{BC}{EF}\\ \frac{36}{24}&=\frac{15}{x} \\ x &= \frac{\cancel{^{ \green{2}}24} \times 15}{\cancel{36_{ \green{3}}}} \\ x&= \frac{2 \times 15}{3} \\ x &= \bold{10} \\ \\\small{\blue{\mathfrak{That's \: it \: :)}}} \end{aligned}[/tex]
PLEASE HELP ME ANSWER QUESTIONS 7, 8, 9 AND 10. I REALLY, REALLY NEED THEM
The area under the curve y = x² + 5x + 4 and the x-axis is [tex]1\frac{2}{3}[/tex] square units.
To find the area under the curve y = x² + 5x + 4 and the x-axis, we need to integrate the given function over a specific interval.
We need to find the definite integral of the function over a suitable interval.
Let's find the definite integral of the function from its roots (where the curve intersects the x-axis).
First, let's find the roots of the function by setting y = 0:
x² + 5x + 4 = 0
Factoring the quadratic equation:
(x + 1)(x + 4) = 0
Setting each factor equal to zero:
x + 1 = 0 => x = -1
x + 4 = 0 => x = -4
The roots of the function are x = -1 and x = -4.
To find the area under the curve, we integrate the function from x = -4 to x = -1:
∫[x=-4 to -1] (x² + 5x + 4) dx
Integrating the function:
∫[x=-4 to -1] (x² + 5x + 4) dx = [1/3x³ + (5/2)x² + 4x] from -4 to -1
Substituting the limits:
[1/3(-1)³ + (5/2)(-1)² + 4(-1)] - [1/3(-4)³ + (5/2)(-4)² + 4(-4)]
Simplifying:
[-1/3 + 5/2 - 4] - [-64/3 + 40/2 - 16]
[tex]1\frac{2}{3}[/tex]
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find the perimeter of a rectangle where the width is 2x^2 + 5x-4 and the length is 3x+2
Answer:
The perimeter of the rectangle is P = 4x^2 + 16x - 4.
Step-by-step explanation:
1. L = 3x + 2, W = 2x^2 + 5x - 4
2. P = 2(L + W)
3. P = 2((3x + 2) + (2x^2 + 5x - 4))
4. P = 2(2x^2 + 8x - 2)
5. P = 4x^2 + 16x - 4
(4x-12) + ( 1/2x y -10) for x=4 and y=6
Answer: (4x-12) + ( 1/2x y -10) = 6
Step-by-step explanation:
First, input 4 for x and 6 for y into the equation so it looks like this:
(4(4)-12) + (1/2(4)(6)-10)
Now solve inside the parentheses starting with the first one. 4 * 4 = 16 so the inside of the first parentheses should look like (16 - 12) which equals 4.
For the second set of parentheses, 1/2 * 4 * 6 = 12, so the inside of that parentheses would look like (12 - 10), which equals 2.
At this point, the equation should look like this: (4) + (2). If you add those two together, your answer should be 6.
(02.02 MC)
If trapezoid ABCD was reflected over the y-axis, reflected over the x-axis, and rotated 180°, where would point A′′′ lie?
Trapezoid formed by ordered pairs A at negative 4, 1, B at negative 3, 2, C at negative 1, 2, D at 0, 1.
(1, −1)
(−4, 1)
(1, 1)
(−4, −1)
The location of point A''' after the three transformations would be (-4, 1).
To determine the location of point A''', we need to apply the three transformations (reflection over the y-axis, reflection over the x-axis, and rotation of 180°) to point A.
When a point is reflected over the y-axis, the x-coordinate is negated while the y-coordinate remains the same.
So, the reflection of point A (-4, 1) over the y-axis would be (4, 1).
When a point is reflected over the x-axis, the y-coordinate is negated while the x-coordinate remains the same. So, the reflection of point (4, 1) over the x-axis would be (4, -1).
When a point is rotated 180°, the x-coordinate and y-coordinate are both negated. So, the rotation of point (4, -1) by 180° would be (-4, 1).
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identify the initial amount a and growth/decay factor b.
y= -2(.5)^x
In the equation [tex]y = -2(0.5)^x[/tex], the initial amount (a) is -2, and the growth/decay factor (b) is 0.5.
In the given equation, [tex]y = -2(0.5)^x[/tex], we can identify the initial amount and the growth/decay factor.
The equation is in the form of exponential decay, as the base (0.5) is between 0 and 1, resulting in the function decreasing as x increases.
The initial amount, denoted as "a," is the coefficient in front of the exponential term. In this case, the initial amount is -2. This means that when x = 0, y = -2.
The growth/decay factor, denoted as "b," is the base of the exponential term. In this equation, the base is 0.5. The value of the base determines how quickly the function decreases or decays.
To summarize:
Initial amount (a) = -2
Growth/decay factor (b) = 0.5
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!!!!!PLEASE HELP 100 POINTS AND WILL MARK BRAINLIEST!!!!!
Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth of a percent (!!!!!SHOW YOUR WORK!!!!!)
A) Inside the Square
B) Outside the Triangle
A square and a traingle are present in a large rectangle with given dimensions in the figure.
Area of the rectangle is :[tex]\qquad\displaystyle \tt \dashrightarrow \: 12 \times 8[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 96 \: \: unit {}^{2} [/tex]
Area of square :[tex]\qquad\displaystyle \tt \dashrightarrow \: 4 \times 4[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 16 \: \: unit {}^{2} [/tex]
Area of triangle :[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: \frac{1}{2} \times 4 \times 5[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 2 \times 5[/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: 10 \: \: unit {}^{2} [/tex]
Problem 1 : Inside the square[ area of square / total area ]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{16}{96} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(inside \: \: the \: \: square) = \frac{1}{6} [/tex]
Problem 2 : Outside the triangle[ total area except area of triangle / total area ]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{96 - 10}{96} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{86 }{96} [/tex]
[tex]\qquad\displaystyle \tt \dashrightarrow \: p(outside \: the \: triangle) = \frac{43}{48} [/tex]
Factor the following and then fill in the blanks. 2x²7x-15 = (2x + )(x- Blank 1: Blank 2:
Answer:
(2x + 3)(x - 5)
Step-by-step explanation:
2x² - 7x - 15
consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 2 × - 15 = - 30 and sum = - 7
the factors are - 10 and + 3
use these factors to split the x- term
2x² - 10x + 3x - 15 ( factor the first/second and third/fourth terms )
= 2x(x - 5) + 3(x - 5) ← factor out (x - 5) from each term
= (2x + 3)(x - 5) ← in factored form
Blank 1 is 3
Blank 2 is 5
50 Points! Multiple choice geometry question. Photo attached. Thank you!
The length of y in the right triangle is 15 units.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The sum of angles in a triangle is 180 degrees.
The side y in the triangle XYZ can be found using trigonometric ratios as follows:
Therefore,
sin 45 = opposite / hypotenuse
opposite sides = y
hypotenuse side = 15√2
sin 45 = y / 15√2
cross multiply
y = 15√2 × sin 45
y = 15√2 × 1 / √2
y = 15 units
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answer:
B. 3188.5 cubic inches.
Step-by-step explanation:
The volume of a cone is calculated using the following formula:
Volume = (1/3) * π * r² * h
Where:
π is the mathematical constant pi, approximately equal to 3.14.r is the radius of the base of the cone.h is the height of the cone.In this problem, we are given that r = 17 inches and S.h = 20 inches.
First we need to find height h.
py using Pythagorous theorem,we get
c²=a²+b²
here c= slight height and a is radius
20²=17²+b²
20²-17²=b²
111=b²
b=√(111)
Plugging these values into the formula, we get:
Volume = ⅓*π* 17² *√(111) = 3188.5 cubic inches
Therefore, the volume of the cone is 3188.5 cubic inches.
how many inches is it from end to end on a bed that is 6 feet long? It is measured in the.
The calculated inches from end to end on the bed is 72 inches
How to determine the inches from end to end on the bedFrom the question, we have the following parameters that can be used in our computation:
Length = 6 feet long
By conversion of units, we have
1 feet = 12 inches
using the above as a guide, we have the following:
Length = 6 * 12 inches long
Evaluate the products
Length = 72 inches long
Hence, the inches from end to end on the bed is 72
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find the unit vector of n=(4,-3)
The unit vector for n = (4, -3) is V = (4/5, -3/5)
How to find the unit vector for the given vector?An unit vector will be a vector that has the same direction than the given one, but a magnitude of 1 unit.
Then we can define the vector V = k*n
Where k > 0 is a real number, then the unit vector is:
V = (4k, -3k)
But notice that this must have a magnitude of 1, then:
1 = √( (4k)² + (-3k)²)
1 = √25k²
1 = 5k
1/5 = k
Then the unit vector is:
V = (4/5, -3/5)
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How many solutions does the system of equations below have? y=-3/4x+1/6
The solution is the point (0, 1/6) y = 1/6
Given the equation y = (-3/4)x + 1/6, which represents a linear equation, there is no "system" of equations involved since there is only one equation.
In this case, the equation is in slope-intercept form (y = mx + b),
where m represents the slope (-3/4) and b represents the y-intercept (1/6).
The slope-intercept form allows us to determine various properties of the equation.
Since there is only one equation, the solution to this equation is a single point on the Cartesian plane.
Each pair of x and y values that satisfy the equation represents a solution.
For example, if we choose x = 0, we can substitute it into the equation to find the corresponding y value:
y = (-3/4)(0) + 1/6
y = 1/6
Therefore, the solution is the point (0, 1/6).
In summary, the given equation has a unique solution, represented by a single point on the Cartesian plane.
Any value of x plugged into the equation will yield a corresponding y value, resulting in a unique point that satisfies the equation.
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Identify the axis of symmetry, vertex, and range for the quadratic function.
Write in exponential form. ln54.60=4
Step-by-step explanation:
ln 54.60 = 4 e^x both sides
e ^ (ln 54.60) = e^4
54.60 = e^4 Done.
The volume of the loading space on a moving truck is 432 cubic feet. The length of the truck is (x+6) feet. The width of the truck is x feet, and
the height is 6 feet. What is the actual length and width of the truck?
Answer:
length=12ft
width=6ft
Step-by-step explanation:
The volume formula is V=lwh.
Plug the values into the equation like this: 432=(x+6)(x)(6)
Divide both sides of the equation by 6: 72=(x+6)(x)
Distribute the x: [tex]72=x^{2} +6x[/tex]
Subtract the 72: [tex]0=x^{2} +6x-72[/tex]
Factor: 0=(x+12)(x-6)
x=-12
x=6
Now, plug in x into the original length and width equations.
length: (6+6)
length=12
width=6
a shade of paint purple berry can be made by mixing red and blue paint in the ratio 5:2. Emma has 30 litres of red paint and 10 litres of blue paint.work out the maximum volume of purple berry that can be made
Answer:The max volume of Purple berry paint is 85
Step-by-step explanation:
Purple = Red + Blue
P = 5 : 2
Simplify 5 : 2 which is 2.5 : 1
P = 30L : 10L
P = (30 x 2.5 ) + (10 x 1)
P = 75 + 10
P = 85 L
In the figure below, S is the center of the circle. Suppose that JK = 20, LM = 3x + 2, SN = 12, and SP = 12. Find the
following.
Length of JN = 10
x = 6
Given ,
S is the center of the circle.
JK = 20
LM = 3x + 2
SN = 12
SP = 12
Now ,
SN and SP are perpendicular to the chords JK and LM respectively .
Perpendiculars drawn from the center of circle to the chords bisect chords into two equal halves .
Thus,
JN = JK/2
JN = 10
Now join SJ,
In ΔSJN ,
Apply pythagoras theorem,
SN² + NJ² = SJ²
12² + 10² = SJ²
SJ = 14.52
SJ =Radius of the circle .
Now,
LP = LM/2
LP = 1.5x + 1
Now join SL,
In ΔSLP
SP² + PL² = SL²
SL = SJ (radius of circle)
So,
12² + (1.5x + 1)² = 244
x = 6
Hence the value of x is 6 and JN is 10 .
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answer:
A. 1.78cm².
B. 331.34 square meters.
Step-by-step explanation:
The area of the shaded region in a circle if the radius and central angle is given can be calculated using the following formula:
Area of shaded region = (θ/360) * πr²
Where:
θ is the central angle in degrees. r is the radius of the circle. π is the mathematical constant pi, approximately equal to 3.14.A.
If the radius is 2 meters and the central angle is 51 degrees, then the area of the shaded region is:
Area of shaded region = (51/360)*π*2² = 0.357π m²
≈ 1.78 square meters
Therefore, the area of the shaded region is approximately 1.78square meters.
Therefore, the area of the shaded region is 1.78cm².
B.
If the radius is 12.5 meters and the central angle is 243 degrees, then the area of the shaded region is:
Area of shaded region = (243/360)*π*12.5² = 105.47π m²
≈ 105.47π square meters
Therefore, the area of the shaded region is approximately 331.34 square meters.
you Solve for x:
10
8
12
The value of x in the given figure is 15.
In the given figure
The length of section of chords are given
We have to find the value of x
In order to find the value of x
Apply the intersecting chord theorem,
The intersecting chords theorem, often known as the chord theorem, is a basic geometry statement that defines a relationship between the four line segments formed by two intersecting chords within a circle. It asserts that the products of the line segment lengths on each chord are equal.
Therefore,
From figure we get,
⇒ 10/x = 8/12
⇒ x = 120/8
⇒ x = 15
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im on the final exam for edmentum
The difference between an observational study and an experiment is thatin an observational study, only one group is studied, and in an experiment, two groups are studied.in an observational study, the researchers do not control treatment, and in an experiment, they do.in an experiment, cause-and-effect is analyzed, and in an observational study, it is not.in an experiment, one group is studied over a short period of time, and in an observational study, the group is studied over a longer period of time.
The difference between an observational study and an experiment is that in an observational study, the researchers do not control treatment, and in an experiment, they do
What is observational study and an experiment?In an observational study, it should be noted that the participants are measured or surveyed without any attempt to influence them. *
However the controlled experiment, participants or objects are divided into groups, and one group is given a treatment while the other is not.
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Which of the following correctly order from least to greast 0.75,3/5,70%
Match the system of equations with the number of solutions.
y = 6z+8
y = 6x-4
y = 3x + 2
y + 3x = -7
4z - 2y = 10
2z-y = 5
4z + y = 8
y=-2z+8
No Solution
Answer:
Step-by-step explanation:
The system of equations with no solution is:
y + 3x = -7
4z - 2y = 10
The system of equations with exactly one solution is:
y = 6z+8
y = 6x-4
y = 3x + 2
2z-y = 5
y=-2z+8
The system of equations with infinitely many solutions is:
4z + y = 8
Write a system of linear equations for the graph below. really need lots of help with this!
i also need the y's
Answer:
friend with this information you cannot know the answer you have to say everything says about that mathematical problem