It represents the output values, hence the claim that "The notation "f(x)" (f of x) is another means of encoding y-values in a function" is accurate.
What is meant by function?An expression that can be used to define and depict the relationship between two or more variables in a data collection is referred to as a function in mathematics.
In conclusion, this means that a function typically illustrates the link between a data set's input values (x-values or domain) and output values (y-values or range), as well as demonstrating how the components in a table are uniquely paired (mapped).
Generally speaking, the output values (y-values or range) of a data set (function) are displayed on the y-coordinate of a graph, and they are typically denoted by either the notation f(x) or y.
The complete question is:
The notation "f(x)" (f of x) is another way of representing y-values in a function. True or False?
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Explain weather there is a possible transformation of f in the form g(x) =f(x)+k, where k is a constant for which the graph y=g(x) will have no x-intercepts. Enter your answer and your justification in the space provided.
There is a possible translation of the form g(x) = f(x) + k for which the graph y=g(x) will have no x-intercepts.
What is a translation?A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.
The translations are represented as follows:
Left a units: g(x) = f(x + a).Right a units: g(x) = f(x - a).Up a units: g(x) = f(x) + a.Down a units: g(x) = f(x) - a.Hence, for the function to have no x-intercepts, the function must be shifted up as though the minimum value of the function is greater than zero.
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Water flows at a steady rate from a tap.
It takes 40 seconds to fill a 4 litre watering can from the tap
The rate at which the water is now flowing from the tap is 50 cubic centimeters per second.
What is Unit Rate?Unit rate is the amount of one quantity for a unit amount of the other quantity.
In other words it compares 1 unit of some quantity with different amount of another quantity.
Given that,
Time taken to fill the watering can of 4 liter = 40 seconds.
4 liter = 4000 cm³
Time taken to fill the watering can of 4000 cm³ = 40 seconds
Unit rate of flow of water = 4000 / 40 = 100 cm³ / sec
Now the rate at which water flows is halved.
Rate = 100 / 2 = 50 cm³ / sec
Hence the rate of the flow of water now is 50 cubic centimeters per second.
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The complete question is as follow :
Water flows at a steady rate from a tap it takes 40 seconds to fill a 4 liter watering can from the tap. The rate at which water flows is halved.
4litre=4000cm³
Find the rate at which the water is now flowing from the tap. Give your answer in cubic centimeters per second (cm³/s).
one week a shop sold 32 ham, 46 tuna, and 18 cheese sandwiches. The next week, the shop sold 38 ham, 43 tuna, and 24 cheese sandwiches. How many more sandwiches did the shop sell the second week?
Step-by-step explanation:
To get the total amount of sandwiches sold in the first week, we would need to add up all of the ham, tuna, and cheese sandwiches.
32 + 46 + 18 = 96
The shop sold 96 sandwiches in the first week.
To find out how many more sandwiches the store sold in the second week, we will need to add up all of the sandwiches again.
38 + 43 + 24 = 105
The shop sold 105 sandwiches in the second week.
Taking 105, we can subtract 96 from it to get how many more sandwiches the shop sold in week 2.
105 - 96 = 9
The shop sold 9 more sandwiches in the second week.
Can someone please help me with these equations ??
The value for x is 1 or -6. The solution has been obtained by using logarithm.
Describe the logarithm.A logarithm is the power to which a number must be raised in mathematics in order to produce other numbers. It is the most useful way to express really large numbers.
We are given [tex]log_3 \frac{3(2-x)}{x(x+2)} = 0[/tex]
Solving the equation, we get
[tex]log_3 \frac{3(2-x)}{x(x+2)} = 3^0[/tex] (Using the property of log)
On multiplying both sides by x(x+2), we get
[tex]log_3 \frac{3(2-x)}{x(x+2)} x(x+2) = 3^0 x(x+2)[/tex]
⇒3 (2−x) = x(x+2)
⇒ 6 - 3x=x² +2x
= x²+5x-6=0
⇒ x²+6x-x-6=0
⇒ (x+6)(x-1)=0
⇒ x = 1,-6
Hence, the value for x is 1 or -6.
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the quotient of 9(7y - 15) and 110 - 6y ÷ 4
y = 7
The quotient of the expression,
9(7y - 15) / (110 - 6y ÷ 4) is 18(7y - 15) / (55 - y).
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
We have an expression,
9(7y - 15) / (110 - 6y ÷ 4)
Simplifying,
9(7y - 15) / (110 - 6y ÷ 4),
= 9(7y - 15) x 4 / (110 - 6y)
= 36(7y - 15) / (110 - 6y)
= 18(7y - 15) / (55 - y)
Therefore, the quotient is 18(7y - 15) / (55 - y).
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A tank has a height of 10 feet. The area of the horizontal cross section of the tank at height h feet is given by the function A where A(h) is measured in square feet. The function A is continuous and decreases as h increases. Selected values for Ach) are given in the table. (a) Use a left Riemann sum with the three subintervals indicated to approximate the integral. Indicate correct units of measure. (b) Interpret your answer from part (a). What is being measured?
(C) Is your estimate of the integral in part (a) an overestimate or underestimate of the actual integral?! Justify your answer
So. the left Riemann sum is 23.74 ft^2.
Given the information in the table:
(a) To use a left Riemann sum with three subintervals to approximate the integral of A(h) with respect to h, we need to divide the interval of integration [0,10] into three equal subintervals. The width of each subinterval is (10-0)/3 = 3.33 ft. The left Riemann sum can be calculated as:
(A(0) * 3.33) + (A(2) * 3.33) + (A(5) * 3.33) = (50.3 * 3.33) + (14.4 * 3.33) + (6.5 * 3.33) = 16.80 + 4.78 + 2.16 = 23.74 ft^2
(b) This approximation represents the total area of the horizontal cross section of the tank up to a specific height h.
(c) The Riemann sum is an underestimate of the actual integral. This is because the Riemann sum uses the left endpoint of each subinterval to approximate the area under the curve, but the actual area under the curve is always greater than or equal to the area of the rectangles.
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(2x + 5y = 18)
Consider the system of equations
(3x + 1.5y = 9)
A : Graph to estimate the solution of the system.
Estimated Solution
B: Solve the system by substitution
The solution for the equations (2x + 5y = 18) and (3x + 1.5y = 9) will be x = 1.5 and y = 3.
What is a system of equations?A system of equations in algebra consists of two or more equations and looks for common answers to the equations. "A set of equations satisfied by the same set of variables is called a system of linear equations."
Given that the system of the equations is (2x + 5y = 18) and (3x + 1.5y = 9). The equations by substitution method can be solved as,
(2x + 5y = 18)
(3x + 1.5y = 9)
Rewrite the equation (2x + 5y = 18) as,
x = ( 18 - 5y) / 2
Substitute the value of x in the second equation,
3x + 1.5y = 9
3 ( 18 - 5y) / 2 + 1.5y = 9
( 54 - 15 y) /2 + 1.5y = 9
54 - 15y + 3y = 18
-12y = -54 + 18
-12y = -36
y = 3
The value of x will be calculated as:-
2x + 5y = 18
2x + ( 5x 3 ) = 18
2x + 15 = 18
2x = 3
x = 1.5
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What is the circumference of the circle in terms of π?
circle with a segment drawn from one point on the circle through the center to another point on the circle labeled 7 yards
A. 3.5π yards
B. 7π yards
C. 21.98π yards
D. 49π yards
The circumference of the circle in terms of π is 7π yards. Option B
How to determine the circumference of the circleThe formula for calculating the circumference of a circle is expressed as;
C = 2πr
Given that the parameters are;
C is the circumference of the circleπ is the constant value 3.14 and 22/7r is the radius of the circleThe formula for calculating the radius of a circle is given as;
Radius = d/2
Where; d is the diameter of the circle
From the information given,
Diameter = 7 yards
Radius = 3.5 yards
Now, substitute the value
Circumference = 2× 3. 5 ×π
Multiply the values
Circumference = 7π yards
Thus, the value is 7π yards
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Answer: 7 yards
Step-by-step explanation:
taking into accoutn rules of precendent which of the following parathesized expressions is equivalent
Legal precedent means that a decision on a definite principle or question of law has already been made by a court of higher authority, such as a call or supreme court. below such a decision, lower courts defer to, or adhere to, that prior decision in similar cases.
The commitment of lower courts may be used as precedent for courts of similar jurisdiction, but higher courts are not bound by the resolution of lower courts.
The use of legal precedent helps secure court rulings remain consistent among similar cases. To this end, courts are bound to cling to prior decisions made by a higher court on a same legal matter.
Because a judge is bound by these previously made decisions, this is mentioned to as binding precedent. anew, following the principle of glare decisis, binding precedent promotes the maintenance of answers to legal questions already established.
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Julie is trying to lose weight. She now weighs 180 pounds. Every week for eight weeks, she was able to lose 2 pounds. a. List Julie's weight for each week. b. Write a recursive definition for this sequence.
a. The table for the weekly weight of Julie is illustrated below.
b. The recursive definition for this sequence is y = 180 - 2x.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, Julie is trying to lose weight.
She now weighs 180 pounds and every week for eight weeks, she was able to lose 2 pounds.
The list of her weight every week for eight weeks is,
week 1 = 180 - 2 = 178 pounds.
week 2 = 178 - 2 = 176 pounds.
week 3 = 176 - 2 = 174 pounds.
week 4 = 174 - 2 = 172 pounds.
week 5 = 172 - 2 = 170 pounds.
week 6 = 170 - 2 = 168 pounds.
week 7 = 168 - 2 = 166 pounds.
week 8 = 166 - 2 = 164 pounds.
The equation that represents her weekly weight loss is,
y = 180 - 2x, Where 'x' represents the number of weeks and y represents the final weight.
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PLS HELP Solve for x
In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.
What is an exponent?A number's exponent tells you how long you will need to multiply it in order to get the result. For instance, because 8 is multiplied by itself 3 times, 8 8 8 can be written as 83.
Here, 3 is the "exponent" or "power," which indicates how many times the number 8 is multiplied by itself, and 8 is the "base," which stands for the number being multiplied.
The number of times a number must be multiplied by itself is what a power or exponent, in essence, indicates. The base in this situation can be any integer, fraction, or decimal. Any value, positive or negative, can be assigned to the exponent.
Given
[tex](1/4)^{x-2} = 16[/tex]
[tex](1/4^{x-2}) = 16[/tex]
1 = 16 × [tex]4^{x-2}[/tex]
1 = 16 × [tex](2^2)^{x-2}[/tex]
[tex]$1 = 16 \times \frac{ 2^{2x}}{2^4}[/tex]
[tex]$1 = \frac{ 16 \times2^{2x}}{2^4}[/tex]
[tex]$1 = \frac{ 16 \times2^{2x}}{16}[/tex]
[tex]$1 = 2^{2x}[/tex]
1 = 2²⁽⁰⁾ The only possible exponent that values in 1 is when exponent is 0
1 = 1
x = 0
Thus, In the equation [tex](1/4)^{x-2} = 16[/tex], The value of the exponent x is 0.
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Convert 0.622 0.622 to a fraction in simplest form and a percent.
Answer: 311/500 and 62.22%
Step-by-step explanation:
Fraction: 0.622 = 622/1000 = 311/500
Percent: 0.6222 = 62.22 % (Move decimal 2 places down)
The decimal 0.622 in the form of simplest fraction as 311/500 and in percent is 62.2%.
To convert 0.622 to a fraction in simplest form, write it as follows:
0.622 = 622/1000
Now, simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
622/1000 = (311 × 2)/(500 × 2)
= 311/500
So, 0.622, when expressed as a fraction in simplest form, is 311/500.
To convert 0.622 to a percent, multiply it by 100:
0.622 × 100 = 62.2%
Therefore, 0.622 is equivalent to 311/500 or 62.2%.
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1) Identify the quadrant in which the point belongs. (-17,-87)
Answer:
It belongs in quadrant 3.
find the order of the group generated by a and b under matrix multiplication (use the convention a^n b^m)
The order of the group generated by a and b under matrix multiplication is a^2b^3.
Start with the identity matrix:
I = [1 0 ; 0 1]
Multiply it by a:
a*I = [1 1; 0 1]
Multiply it by b:
b*a*I = [1 2; 0 1]
Multiply it by a:
a*b*a*I = [2 3; 0 1]
Multiply it by b:
b*a*b*a*I = [2 5; 0 1]
Multiply it by a:
a*b*a*b*a*I = [4 3; 0 1]
Therefore, the order of the group generated by a and b is a^2b^3.
The order of the group generated by a and b under matrix multiplication is a^2b^3.
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A shelf can support 5 5/8 pounds. if a book weights 5/8 of a pound, how many books can the shelf hold?
Answer:
9 books
Step-by-step explanation:
Find the value of z.
X
7
y
N
3
Z =
√[?
Give your answer in simplest form.
Enter
Answer:
z = √30
Step-by-step explanation:
Given similar right triangles with hypotenuse segments marked 3 and 7, you want to know the length of short leg z adjacent to the segment marked 3.
Similar trianglesThe fact that all of these triangles are similar gives rise to some "geometric mean" relationships:
hypotenuse/short side = 10/z = z/3
30 = z² . . . . . . . multiply by 3z
z = √30 . . . . . . take the square root
__
Additional comment
The other two geometric mean relations are ...
x = √(7·10) . . . . . hypotenuse/long side: 10/x=x/7
y = √(7·3) . . . . . . short side/long side: y/7=3/y
The triangles are similar by AA: each has a right angle, and an angle in common with the largest triangle. Triangles similar to the same triangle are similar to each other.
A factory received a shipment of 48 generators, and the vendor who sold the items knows there are 8 generators in the shipment that are defective. Before the receiving foreman accepts the delivery, he samples the shipment, and if too many of the generators in the sample are defective, he will refuse the shipment.
For each of the following, give your responses as reduced fractions.
If a sample of 8 generators is selected, find the probability that all in the sample are defective.
If a sample of 8 generators is selected, find the probability that none in the sample are defective.
Answer: The probability that all generators in a sample of 8 are defective can be calculated by finding the number of ways that 8 defective generators can be selected out of 48 total generators, divided by the total number of ways that any 8 generators can be selected out of 48 total generators.
The number of ways to select 8 defective generators out of 48 total generators is:
C(8,8)*C(40,0) = 1
The total number of ways to select 8 generators out of 48 total generators is:
C(48,8) = 1,907,725
The probability that all generators in a sample of 8 are defective is:
1/1,907,725
If a sample of 8 generators is selected, find the probability that none in the sample are defective.
The number of ways to select 8 non-defective generators out of 48 total generators is:
C(40,8) = 45,765
The total number of ways to select 8 generators out of 48 total generators is:
C(48,8) = 1,907,725
The probability that none in the sample are defective is:
45,765/1,907,725
Both of these are reduced fraction.
If a bottle holding 3 L of milk contains 2 1/2% butterfat how much skin milk must be added to dilute the milk to 2% butterfat
Answer:
You do not need to add any skim milk.
Step-by-step explanation:
Step-by-step explanation:
percentages are represented by hundredths in calculations.
2 1/2% = 2.5% = 0.025
2% = 0.02
we are mixing the 3 L 2.5% milk with x L of 0% milk.
and we are ending up with (3 + x) L of 2% milk.
so, we have
3×0.025 + x×0 = (3 + x)×0.02 = 3×0.02 + 0.02x
3×0.005 = 0.02x
0.015 = 0.02x
x = 0.015/0.02 = 0.75
so, 0.75 L have to be added to dilute the milk to 2%.
three wires are connected at point d, which is located 18 in. below the t-shaped pipe support abc. determine the tension in each wire when a 180-lb cylinder is suspended from point d as shown.
The tension in each wire when a 180-lb cylinder is suspended from point d is 52.8
The term tension is defined as the tensile load in the wire as it is continuously fed between the wire guides that are used to keep the wire straight between said guides.
While we looking into the following diagram we have identified that the following values are known.
Here the width is 180 lb.
And the distance between the two wires on all the sides is 22 inches, 24 inches and 18 inches.
Then the tension is calculated as,
=> (22 x 24 x 18)/180
=> 9504/180
=> 52.8
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A certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces. A model for the cost C (in dollars) of a first class mailing that weighs x ounces is given below. C(x) = 0.37 0 ≤ x ≤ 1 0.48 1 < x ≤ 2 0.59 2 < x ≤ 3 0.7 3 < x ≤ 3.5 A.) At what values is the function not continuous? B.) Find the cost of mailing a 1.6-ounce letter.
For the given function C(x) = 0.37 + (x - 1)0.11 the cost of mailing a 1.6-ounce letter is $0.436
The term function in math is defined as a relation between a set of inputs having one output each.
Here we have given that certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces.
Let us consider that the term C refers that cost in dollars of a first class mailing and x refers the weight in ounces.
The the function for the given situation is written as,
=> C(x) = 0.37 + (x - 1)0.11
Here we have given that we need to find the cost of mailing a 1.6-ounce letter which defines that the value of x is 1.6, then the cost is calculated as,
=> C(x) = 0.37 + (1.6 - 1) 0.11
=> C(x) = 0.37 + 0.066
=> C(x) = 0.436.
Complete Question:
A certain mailing service's first class mail rates are $0.37 for the first ounce and $0.11 for each additional ounce or fraction thereof up to 3.5 ounces. Find the function of the situation and the cost of mailing a 1.6-ounce letter.
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At a factory, Jin assembles 12 parts each minute. He has assembled 156 parts when Summer starts on the line, assembling at a pace of 15 parts per minute. If their assembly rates continue, will summer ever catch up to jin? When?
I need the substitution and elimination method
If their assembly rates continue, based on an equation, Summer will catch up with Jin in 52 minutes.
What is an equation?An equation refers to a statement claiming the equality of two or more mathematical expressions.
Using the equation sign (=) mathematicians show that expressions are equal or equivalent.
Jin's assembling rate per minute = 12 parts
Summer's assembling rate per minute = 15 parts
The number of parts already assembled by Jin before Summer started = 156 parts
Let the minutes used by Jin or Summer = n
The total parts assembled by Jin in n minutes = 156 + 12n
The total parts assembled by Summer in n minutes = 15n
For Summer to catch up to Jin, 15n = 156 + 12n
Grouping like terms:
15n - 12n = 156
3n = 156
n = 52
Thus, in 52 minutes, the number of assembly parts by Summer will equal Jin's.
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Scientists use drones with digital cameras to help them identify plants, predict, flooding, and construct 3-D maps of different landscapes. A team of scientists is using two drones to map a region. The heights of the drones are represented by the equations given, where x is the number of minutes since the drones were released by the scientists and y is the height in meters.
Equation for Drone A / y = 8x + 5
Equation for Drone B / y = 6x + 25
A : Solve the system of equations.
B : What does the solution tell you about the drones?
8th Grade Math Book - Don't Know What Brand.
The solution of the system of equations is given by the ordered pair (10, 85).
The solution tells us that the height of both Drone A and Drone B would be the same after 10 minutes.
How to solve the system of equations?In this scenario, heights of drones are represented by the following system of equations:
y = 8x + 5 .......equation 1.
y = 6x + 25 .......equation 2.
where:
x represents the number of minutes since the drones were released by the scientists.y represents the height the drones of in meters.By equating equation 1 and equation 2, number of minutes since the drones were released can be calculated as follows;
8x + 5 = 6x + 25
8x - 6x = 25 - 5
2x = 20
x = 20/2
x = 10 minutes.
Next, we would determine the height when x = 10 minutes:
y = 8(10) + 5
y = 80 + 5
y = 85 meters.
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Find the unknown measurement of the following cuboid
length=10cm
Height=8cm
Volume=440cm,Fibd the breadth
Answer:
5.5cm
Step-by-step explanation:
The volume of a cuboid is given by
V = lbh
where l is the length
b is the breadth
h is the height.
We know that
V = lbh = 440 cm^3
Given l = 10 cm, h = 8 cm
So, we can find b by substituting these values in the above equation
440 = 10 * b * 8
Solving for b, we get:
b = 440 / (10*8)
b = 5.5cm
So, the breadth of the cuboid is 5.5 cm.
A block of mass 2.20 kg is placed against a horizontal spring of constant k = 895 N/m and pushed so the spring compresses by 0.0750 m.
(a)
What is the elastic potential energy of the block-spring system (in J)?
J
(b)
If the block is now released and the surface is frictionless, calculate the block's speed (in m/s) after leaving the spring.
m/s
a) The block-spring system has an elastic potential energy equal to 2.517 joule.
b) The block has speed of approximately 1.513 meters per second.
How to analyze a spring-block system
In this problem we must analyze the energy and kinematics of spring-block system with no irreversibilites (no friction). Part A - Elastic potential energy is determined when spring is entirely deformed:
U = (1 / 2) · k · x²
Where:
k - Spring constant, in newtons per meter.x - Spring deformation, in meters.U - Elastic potential energy, in joule.If we know that k = 895 N / m and x = 0.0750 m, then the elastic potential energy of the block-spring system is;
U = (1 / 2) · (895 N / m) · (0.0750 m)²
U = 2.517 J
The elastic potential energy of block-spring system is 2.517 joule.
Part B - And the speed can be determined by principle of energy conservation and work-energy theorem:
K = U
Where K is translational kinetic energy, in joules.
(1 / 2) · m · v² = U
v² = 2 · U / m
v = √(2 · U / m)
If we know that U = 2.517 J and m = 2.20 kg, then the speed of the block is:
v = √[2 · (2.517 J) / (2.20 kg)]
v ≈ 1.513 m / s
The speed of the block after leaving the spring is approximately 1.513 meters per second.
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1.) A husband 3 years older than his wife. The Sum of their ages is 73 years. Calculate the difference between the square of their ages.
Answer:
The difference between the square of their ages is 219----------------------------
Let the husband's age be h and wife's age be w.
The difference of their age is 3 and sum is 73:
h - w = 3h + w = 73The difference between the squares is:
h² - w² = Difference of squares(h + w)(h - w) = Identity for difference of squares73*3 = Substitute219 AnswerAnswer:
219
Step-by-step explanation:
H-W=3
H+W =73
2H=76
H=38
W=35
38² -35² = 219
True or False: The purchase cost of fixtures can become tax-deductible.
The purchase cost of fixtures can become tax deductible is referred to as a true statement.
What is Taxation?This is referred to as the imposition of compulsory levies on individuals or entities by governments in other to fund government spending and various public expenditures.
Office fixtures such as furniture would typically be considered a long-term asset because it isn't typically replaced on a yearly basis which is why they are not deductible from a business's taxable income. However in a scenario where the fixtures start going through the process of depreciation, amortization or depletion then it becomes tax deductible.
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how does sleep deprivation affect your ability to drive? a recent study measured the effects on 19 professional drivers. each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. the treatments were assigned in random order. in each session, performance was measured on a variety of tasks including a driving simulation. use key terms from this module to identify the following values for this study this experiment.
The independent variable in this study is sleep deprivation, as the study aims to investigate the effects of sleep deprivation on the ability to drive.
This study is an experimental study that measures the effects of sleep deprivation on the ability to drive. The sample size is 19 professional drivers, and the study uses a within-subjects design as each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order, meaning that each driver has an equal chance of being assigned to either the sleep deprivation or normal sleep condition. The outcome variable in this study is performance on a variety of tasks, including a driving simulation. The independent variable in this study is sleep deprivation, as the study aims to investigate the effects of sleep deprivation on the ability to drive.
Thus, The independent variable in this study is sleep deprivation, as the study aims to investigate the effects of sleep deprivation on the ability to drive.
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find parametric equations for the line. (use the parameter t.)the line through (5, 5, 0) and perpendicular to both i j and j kx(t), y(t), z(t)
The parametric equations for the line are:
x(t) = 5 + t, y(t) = 5 - t and z(t) = t
Given that the line through (5, 5, 0) and perpendicular to both i + j and j + k
We know that the symmetric form of the equation of the line is given by,
[tex]\frac{x-x_1}{a} =\frac{y-y_1}{b} =\frac{z-z_1}{c} =t[/tex]
Let us assume that x₁ = 5, y₁ = 5 and z₁ = 0
Evaluating the product of ( i + j) and ( j + k ) we get,
( i + j) × ( j + k )
= i - j + k
The value of a = 1, b = -1 and c = 1.
Substitute all the values in the above equation we get,
[tex]\frac{x-x_1}{a} =\frac{y-y_1}{b} =\frac{z-z_1}{c} =t[/tex]
[tex]\frac{x-5}{1} =\frac{y-5}{-1} =\frac{z-0}{1} =t[/tex]
so, the parametric form of the equation would be,
x(t) = x₁ + at
x(t) = 5 + (1)t
x(t) = 5 + t
y(t) = y₁ + bt
y(t) = 5 + (-1)t
y(t) = 5 - t
And z(t) = z₁ + ct
z(t) = 0 + (1)t
z(t) = t
Thus, the parametric equations: x(t) = 5 + t, y(t) = 5 - t and z(t) = t
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The complete question is:
Find parametric equations and symmetric equations for the line. (Use the parameter t.) The line through (5, 5, 0) and perpendicular to both i + j and j + k
x(t), y(t), z(t) = ?
Candice and Joel each wrote a proof for the statement: If m ∠ DOX = m ∠ BOX , then m ∠ AOX = m ∠ COX . Diagram shows two lines, AB and CD, intersecting at point O. Ray OX extends between rays OA and OC. Candice's Proof Statements Reasons 1. m ∠ AOX ≠ m ∠ COX 1. by supposition 2. ∠ AOD ≅ ∠ COB 2. vertical angles theorem 3. m ∠ AOD = m ∠ COB 3. definition of congruence 4. m ∠ AOD + m ∠ AOX ≠ m ∠ COB + m ∠ COX 4. additional property of equality 5. m ∠ AOX ≠ m ∠ COX 5. angle addition postulate Joel's Proof Statements Reasons 1. m ∠ DOX = m ∠ BOX 1. given 2. m ∠ AOD + m ∠ AOX = m ∠ COB + m ∠ COX 2. angle addition postulate 3. ∠ AOD ≅ ∠ COB 3. vertical angles theorem 4. m ∠ AOD = m ∠ COB 4. definition of congruence 5. m ∠ AOX = m ∠ COX 5. subtraction property of equality What type of proofs did they use? Candice's proof is because . Joe's proof is because .
Both Candice and Joel used a proof by contradiction.
What is the proof about?Candice began her proof by assuming the statement was false (by supposition) and then used the vertical angles theorem, definition of congruence, and additional property of equality to arrive at a contradiction.
By demonstating that assuming a proposition to be false results in a contradiction, proof by contradiction establishes the truth or validity of a proposition in logic.
Joel began his proof by assuming the statement was true and used the angle addition postulate, vertical angles theorem, definition of congruence, and subtraction property of equality to arrive at a conclusion that the statement was true.
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what is property
if VW+WY=ZY, and VW + WY=XZ, then XZ=ZY
The property if VW+WY=ZY, and VW + WY=XZ, then XZ=ZY is referred to as a transitive property.
What is a Transitive property?This states that “if two quantities are equal to the third quantity, then we can say that all the quantities are equal to each other”.
A good example of its application can be seen here which is if x = y, and y = 7, then x must equal 7 which when observed in what was given above corresponds with this type of property and is therefore the reason why it was chosen as the correct choice.
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