Answer: 0
Step-by-step explanation:
Y2 - Y1
________.
X2 - X1
A linear slope means that the Ys are the same and you can't divide by zero.
You have your points (8,7) and (3,7)
Use the template like I have above.
7 - 7
______
3 - 8
which equals....
0
__
-5
I hope that makes sense for you :)
() Find the value of y in the regular dodecagon whose interior angle
has a measure of (17y + 14)º.
The value of y in the regular dodecagon is 8°
What is Dodecagon?
Dodecagon is is a closed figure that has 12 sides and 12 angles. It has 12 vertices, each of which is connected to two sides.
What is Regular Dodecagon?
Regular Dodecagon is has all 12 sides of equal length and all angles of equal measure. It is a 12-sided polygon that is symmetrical.
To find the interior angle ,
= (n - 2)180° where the sides is 12
= (12-2)180°
= 1800°
= 1800/12 = 150°
i.e, each angle of the dodecagon = 150°
To determine this,
17y + 14° = 150°
17y = 150° - 14°
17y = 136°
y = 136°/17
y = 8°
Therefore, the value of y = 8°
Read more about Dodecagon
https://brainly.com/question/9459741
#SPJ1
How can making an experiment single-blind or double-blind help?
A. If an experiment is blinded, the sample will be more representative of the population.
B. If an experiment is blinded, then differences between the control group and the treatment group are exaggerated.
C. If an experiment is blinded, then the sample can be less representative of the population and the data can still be used to make inferences about the population.
D. If an experiment is blinded, then any effect arising from psychological factors should affect all groups equally.
Answer:
D. If an experiment is blinded, then any effect arising from psychological factors should affect all groups equally.
The table shows the number of each color pen in Mrs. Devon's desk drawer. Suppose she selects a pen at random from the drawer. How much greater is the theoretical probability of selecting a black pen than selecting a red or a green pen? Express your answer as a percent. Color Number of Pens Black 9 Blue 6 Green 1 Red 4
Answer:
Step-by-step explanation:
Black = 9, Blue = 6, Green = 1, Red = 4
Pr(Black) = 9/18 = 1/2 = 50%
Pr(Red or Green) = 5/18 = 28%
therefore it is 22% (50-28) more likely that Mrs. Devon will select a black pen than a red or green
Answer:
1. 9+6+1+4=20
Black 9/20 = 0.45 = 45%
Red or green = 5/20 = 0.25= 25%
selecting black is 45-25 = 20%
Completely factor the polynomial 2x³ + 54
Answer:
Step-by-step explanation:
2x³+54=2(x³+27)=2(x³+3³)
a³+b³=(a+b)(a²-ab+b²)
complete it
Each bicycle has 2 wheels. How many wheels do 8 bicycles have?
Answer: 16
Step-by-step explanation:
Since each bicycle has 2 wheels, this means 2 wheels times 8 bicycles. with comes out to 16 wheels
Answer:
16
Step-by-step explanation
If each bicycle has 2 wheels, we would multiply 2 wheels times 8 bicycles and we would get 16 wheels altogether.
let f(x)=|x-3|, g(x)=-(x-4)^(2)-3 and h(x)=-7 find the range
Therefore , the solution of the given problem of range comes out to be the range of the composite function f(g(h(x))) is [0, ∞).
Describe range.By calculating the variable's maximum observed value and subtracting its minimum observed value, the variable range is obtained (minimum). Potential range or finite difference bounds include different steel pricing and various designs. A procedure or action's breadth or scope insight into the maximum or expected range of a weapon's projectile. The number between the minimum and maximum of a list and set is known as its range. You can locate the area by lining up all the numbers.
Here,
The range of a function is the set of all possible output values. Let's consider each function separately:
f(x) = |x-3|
The absolute value of any number is always non-negative, so the range of f(x) is [0, ∞).
g(x) = -(x-4)²-3
The square of any real number is always non-negative, so the range of the function -(x-4)² is (-∞, 0]. Subtracting 3 from this range gives the range of g(x) as (-∞, -3].
h(x) = -7
The output of h(x) is always -7, so the range of h(x) is {-7} (a singleton set containing only the number -7).
Putting it all together, the range of the composite function f(g(h(x))) is [0, ∞).
To know more about range visit:
brainly.com/question/28135761
#SPJ1
David's farm produces 12 pounds of Zuccini per acre and 3 pounds of Watermelon per acre
Morgan's farm produces 18 pounds of Zuccini per acre and 6 pounds of Watermelon per acre
David's opportunity cost of producing 1 pound of watermelon is_______
pounds of zucchini, whereas Morgan's opportunity cost of producing 1 pound of watermelon is________
pounds of zucchini. Because David has a _______ opportunity cost of producing watermelon than Morgan, _______ has a comparative advantage in the production of watermelon, and ______ has a comparative advantage in the production of zucchini.
David's opportunity cost of producing 1 pound of watermelon is 4 pounds of zucchini, whereas Morgan's opportunity cost of producing 1 pound of watermelon is 3 pounds of zucchini. Because David has a higher opportunity cost of producing watermelon than Morgan, Morgan has a comparative advantage in the production of watermelon, and David has a comparative advantage in the production of zucchini.
What is opportunity cost?
Opportunity costs are the possible advantages that a person, investor, or company forgoes while deciding between two options. Opportunity costs are by definition invisible, making it simple to ignore them.
The best input combinations to achieve the highest level of output are displayed on the production potential frontier.
The individual who has a lower opportunity cost in output than another individual enjoys a comparative production advantage.
David's watermelon production -
54 units watermelon = 216 units zucchini
1 unit watermelon = 216/54 units zucchini
1 unit watermelon = 4 units zucchini
Morgan's watermelon production -
108 units watermelon = 324 units zucchini
1 unit watermelon = 324/108 units zucchini
1 unit watermelon = 3 units zucchini
Morgan has absolute advantage in production of Zucchini and Morgan has also absolute advantage in production of watermelon.
Therefore, David's opportunity cost of 1 pound of watermelon is 4 pound of Zucchini and Morgan's opportunity cost of 1 pound of watermelon is 3 pound of Zucchini.
To learn more about opportunity cost from the given link
https://brainly.com/question/481029
#SPJ1
suppose the profit function for a company selling x items if a product is given by p(x)=-6x^2+360x-2500.
what is number of units will maximize the company's profit for this product?
what is the maximum profit?
Answer:
$2700
Step-by-step explanation:
The x-coordinate of the vertex can be found using the formula:
x = -b/2a
where a = -6 and b = 360, so we have:
x = -360/(2*(-6)) = 30
Therefore, the company will maximize its profit by selling 30 units of the product.
p(x) = -6x^2 + 360x - 2500
(x = 30 )
p(30) = -6(30)^2 + 360(30) - 2500 = 2700
So, the maximum profit for the company is $2700.
A person invested $13,000, part of the money, x, was placed in a stock that paid 9% annual interest. The rest of the money suffered a 5% loss. Express the total annual income from both investments, I, as a function of x.
The total annual income from both investment is
(14x -65000)/100
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
I = x× 9/100
I = 9x/100
(13000 - x) × 5/100
= (65000-5x)/100
therefore the total amount annual income
= 9x /100 - (65000-5x)/100
= (9x+5x-65000)/100
= (14x - 65000)/100
therefore the total annual income = (14x -65000)/100
learn more about interest from
https://brainly.com/question/2294792
#SPJ1
In a case whereby a person invested $13,000, part of the money, x, was placed in a stock that paid 9% annual interest the total annual income from both investments, I, as a function of x is I= [ 0.14X+12350 ]
How can the total annual income from both investmentsbe expressed?The Amount that was invested =$13,000
Then the Profitable Investment which was givden as 9% can be expressed as = [ X(1.09) ]
Then from the question we can see the Negative Investment, which is -5% and can be expressed as = [ (13,000-X)(1-0.05) ]
The we can sum up as
I= [ X(1.09) ]+ [ (13000-X)(0.95) ]
This can be simplified as
I= [ 1.09X-0.95X+12350 ]
I= [ 0.14X+12350 ]
Learn more about interest at:
https://brainly.com/question/25793394
#SPJ1
CAN SOMEONE HELP WITH THIS QUESTION?✨
The correct sketch is B
What is the liquid range of water?The liquid range of water refers to the temperature range at which water exists as a liquid. At standard atmospheric pressure (1 atm), the liquid range of water is from 0 degrees Celsius to 100 degrees Celsius, or from 32 degrees Fahrenheit to 212 degrees Fahrenheit.
This means that water can exist as a liquid within this temperature range, but if the temperature falls below 0 degrees Celsius or rises above 100 degrees Celsius, it will freeze into a solid or boil into a gas, respectively.
Learn more about water:https://brainly.com/question/28465561
#SPJ1
to determine the reliability of experts who interpret lie detector tests in criminal investigations, a random sample of 280 such cases was studied. the results were
The reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of the random sample of 280 cases that were studied. It is important to look at the overall accuracy of the interpretations, as well as any potential biases or errors that may have affected the results.
To analyze the results, we can look at the number of correct and incorrect interpretations, and calculate the percentage of accurate interpretations. This will give us an overall measure of the reliability of the experts.
We can also look for any potential biases or errors that may have affected the results. For example, we may want to examine whether certain experts were more likely to make accurate interpretations than others, or whether there were any factors that may have influenced the interpretations, such as the type of crime or the suspect's behaviour.
Overall, the reliability of experts who interpret lie detector tests in criminal investigations can be determined by analyzing the results of a random sample of cases and looking for any potential biases or errors that may have affected the results. By doing this, we can gain a better understanding of the accuracy and reliability of these experts and their interpretations.
https://brainly.com/question/30759604
#SPJ1
Volume of a Bird Cage. A company makes rectangular shaped bird cages with height b inches and square bottoms. The volume of these cages is given by the function V b 6 9 b b = 3 2 − + . (i) Find an expression for the length of each side of the square bottom. (ii) Use the function to find the volume of a cage with a height of 18 inches. (iii) Use the remainder theorem to find the volume of a cage with a height of 15 inches
The remainder theorem can be used to determine the volume of a cage with a 15-inch height since b = 15, which results in a volume of 2160 inch3.
what is volume ?The size of an item in 3 directions is the area that is covered by its boundaries. The amount of room an object occupies in three aspects is measured by its height, which is given in cubic inches. A few of illustrations of cubic units are cm3 and in3. On the other perspective, an item's mass is used to measure what more matter it contains. The typical method to ascertain an object's mass is to weigh it, either in pounds or kilograms. Unlike the fundamental equations for the area of a rectangular box, which is length, breadth, and height, the primary equation for volumes is length, width, and height.
given
Height is listed as b and is 18 inches.
B = 18 s= b-3 (from I = 18 - 3 s = 15 as a result.
Therefore, volume
volume of a rectangle = l x b x h V= 18 x 15 x 15 = 4,050 inch3
3) Height = 15 then b = 15 b -15 = 0 if height = 15.
The remaining theorem's definition is:
To get a smaller polynomial and a remainder, we divide a polynomial P(x) by the factor (x - a). The polynomial does not have to contain the factor.
= 2160
The remainder theorem can be used to determine the volume of a cage with a 15-inch height since b = 15, which results in a volume of 2160 inch3.
To know more about volume visit :-
https://brainly.com/question/13338592
#SPJ1
The following table lists numbers in their standard and scientific notations. Fill in the missing values.
The first two have been completed for you as examples.
Standard Notation
I
Answer:
Hope the picture helps! <3
Step-by-step explanation:
interpolating polynomial. f(x) = ln x
Data points at x = 1, x2 = 4, x3 = 6 and x, = 5 were used to estimate in 2 with a third-order Newton's
Using third-order Newton's interpolating a polynomial the value of f(2) is (25ln(2))/9.
What is the value of f(2)To estimate the value of f(2) using a third-order Newton's interpolating polynomial with the given data points, we first need to calculate the divided differences. The divided differences are defined as:
f[xi] = f(xi) for i = 1, 2, 3
f[x1,x2] = (f[x2] - f[x1]) / (x2 - x1) = (ln(4) - ln(1)) / (4 - 1) = ln(4) / 3
f[x2,x3] = (f[x3] - f[x2]) / (x3 - x2) = (ln(6) - ln(4)) / (6 - 4) = ln(3) / 2
f[x1,x2,x3] = (f[x2,x3] - f[x1,x2]) / (x3 - x1) = ((ln(3) / 2) - (ln(4) / 3)) / (6 - 1) = -0.018
Using these divided differences, we can write the third-order Newton's interpolating polynomial as:
f(x) = f[x1] + f[x1,x2](x - x1) + f[x1,x2,x3](x - x1)(x - x2) + f[x1,x2,x3,x4](x - x1)(x - x2)(x - x3)
Substituting the values of the data points and the divided differences we calculated, we get:
f(x) = ln(1) + ln(4)/3 (x - 1) - 0.018 (x - 1)(x - 4)
Simplifying this expression, we get:
f(x) = ln(1) + (ln(4)/3)x - (11ln(2)/9) + (ln(2)/9)x^2
To estimate f(2), we plug in x = 2:
f(2) = ln(1) + (ln(4)/3)(2) - (11ln(2)/9) + (ln(2)/9)(2)^2
f(2) = 2ln(2) - (11ln(2)/9) + (ln(2)/9)(4)
f(2) = (25ln(2))/9
Learn more interpolating polynomial here;
https://brainly.com/question/26460790
#SPJ1
Ricky says each other fractions below would be to the right of one on a number line do you agree? Question choose yes or no.
A. 3/4
B. 5/4
C. 4/2
D. 1/3
Answer:
Step-by-step explanation:
no because they don't have the same dominator
An electrician fixed 4 bulbs in a room how many rooms can 216 bulbs be fixed by him
Answer:
216÷4=54
Step-by-step explanation:
we have to divide the bulb he fixed in per room by how many he fixes I guess so
Answer: He can fix in a total of 54 rooms which makes 216 bulbs fixed by him.
Step-by-step explanation:
4 bulbs are present in = 1 room
thus, 216 bulbs are present in = 216/4 = 54 rooms
So, he fixes 54 rooms in total
Internal Links: https://brainly.in/app/ask?q=an+electrician+needa+7%2F12+of+a+roll+of+electrical+wire+to+wire+each+room+in+a+house+how+many+rooms+can+be+wired+with+3+whole+1%2F2+rolls+%E2%80%8B&skip=51221553&source=answer-box
please help!
this is due by tonight
Answer:
6
Step-by-step explanation:
The two triangles are similar which means the the two length is parallel
.°., the Length of the smaller triangle=6
Calculate the mean, Variance and Standard deviation of the age of 12 student 16, 17, 18, 16/0.5, 17, 18, 19, 17, 17, 13, 17/½/2 and 16
The mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.
What is Statistic?The statistic is the study of mathematics that deals with relations between comprehensive data.
Here,
To calculate the mean, variance, and standard deviation of the ages of the 12 students, we first need to find the sum of the ages:
Sum = 16 + 17 + 18 + (16/0.5) + 17 + 18 + 19 + 17 + 17 + 13 + (17/2/2) + 16
= 16 + 17 + 18 + 32 + 17 + 18 + 19 + 17 + 17 + 13 + 4.25 + 16
= 204.25
Mean = Sum / Number of students = 204.25 / 12 ≈ 17.02 years
To calculate the variance, we need to subtract the mean from each age, square the differences, add up the squares, and divide by the number of students minus one:
Variance = [ (16 - 17.02)² + (17 - 17.02)² + ... + (16 - 17.02)² ] / (12 - 1)
= [ 0.16 + 1.96 + ... + 0.16 ] / 11
= 37.41
Finally, we can calculate the standard deviation by taking the square root of the variance:
Standard deviation = √(Variance) ≈ 6.117
Therefore, the mean age of the 12 students is approximately 17.02 years, the variance is 37.41, and the standard deviation is approximately 6.117 years.
Learn more about Statistics here:
https://brainly.com/question/20038903
#SPJ9
Find the area of the figure.
10cm
20cm
6cm
ڈے
A = [? ]cm²
Area of a rectangle = lw
1= length, w = width
Area of a triangle =
b = base, h = height
bh
2
Enter
USE A
Answer:
Step-by-step explanation:
half the base times the height
Determine if the function is even, odd, or neither.
YOU WILL NEED TO SHOW YOUR WORK MANUALLY USING ANY TYPE OF PAPER!
YOU WILL NEED TO UPLOAD YOUR WORK TO THIS QUESTON!
TWO WAYS TO UPLOAD YOUR WORK:
1) USING THE STUDENT CANVAS APP, YOU CAN TAKE A PICTURE AND UPLOAD THE PICTURE TO THIS QUESTION FROM THE APP.
2) YOU CAN TAKE A PICTURE OF YOUR WORK, EMAIL IT TO YOURSELF, SAVE IT TO YOUR COMPUTER, THEN UPLOAD IT TO THIS QUESTION FROM YOUR COMPUTER.
y = x^3 - x + 9
The value of the variable x and y will be 1.5 and -2.5, respectively. Then the value of the expression (x + y) will be negative 1.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
here, we have,
A system of equations is given below.
x = -2y - 3.5 ...1
-5x + 3y = -15 ...2
From equations 1 and 2, then we have
-5(-2y - 3.5) + 3y = -15
10y + 17.5 + 3y = - 15
13y = -32.5
y = - 2.5
Then the value of the variable 'x' is calculated as,
x = - 2(-2.5) - 3.5
x = 5 - 3.5
x = 1.5
Then the value of the expression (x + y) is calculated as,
x + y = 1.5 + (-2.5)
x + y = 1.5 - 2.5
x + y = - 1
More about the solution of the equation link is given below.
brainly.com/question/545403
#SPJ1
what is y2x+x2y? i need answer now
Answer:
are you trying to find the derivative if so the answer will be 0
Step-by-step explanation:
I need the answer to the question.
Step-by-step explanation:
clearly, the price is marked down to $9.60.
so, the 1st and 4th answer options are wrong.
is it marked down by 12% or by 20% ?
the basic price was $12. = 100%
how much are 10% of that ? well, 12/10 = $1.20.
but we marked down by $2.40.
when you compare $1.20 and $2.40, what do to see ?
that the second number is exactly twice the first number.
10%×2 = 20%
therefore, the 3rd answer is correct.
I dont know how to do this someone help me
Answer:
Step-by-step explanation:
We can start by combining the two fractions by finding a common denominator:
sin(a)/(1+cos(a)) + (1+cos(a))/sin(a)
= sin^2(a)/(sin(a)(1+cos(a))) + (1+cos(a))^2/((1+cos(a))sin(a))
= sin^2(a) + (1+cos(a))^2 / (sin(a)(1+cos(a)))^2
= (sin^2(a) + 1 + 2cos(a) + cos^2(a)) / (sin^2(a) + 2sin(a)cos(a) + cos^2(a))
= (2 + 2cos(a)) / (sin(a) + cos(a))^2
= 2(1+cos(a)) / (sin(a) + cos(a))^2
= 2(cos^2(a/2)/sin^2(a/2)) / (sin(a/2) + cos(a/2))^2 (using the half-angle identities)
= 2tan^2(a/2) / (sin(a/2) + cos(a/2))^2
This expression cannot be simplified further without additional information or context.
Answer:
Step-by-step explanation: you need to rewrite the formula but with the numbers that are given to you so then you multiply and divide by 2 and BOOM you got your answer
Let f be the function given by f(x)=x/x+2. What are the values of c that satisfy the mean value theorem
The Mean Value Theorem states that if a function f is continuous on the interval [a,b] and differentiable on (a,b), then there exists at least one c in the interval (a,b) such that
f'(c) = (f(b) - f(a)) / (b - a)
For the function f(x) = x/x+2, we can set
f(a) = a/a+2 and f(b) = b/b+2
Therefore, the equation we need to solve is:
(b/b+2 - a/a+2) / (b - a) = c/(c+2)
After rearranging, we get:
(b-a)c + 2(a-b) = 0
Solving this, we find that c = 2(b-a) / (a-b)
Therefore, the values of c that satisfy the Mean Value Theorem for the given function f(x) = x/x+2 are c = 2(b-a) / (a-b).
https://brainly.com/question/30403137
#SPJ1
Use elimination to solve the following system, giving your answers as improper
fractions, if necessary:
If 12x + 9y = 6 and 7x + 6y = −1,
X=
Y=
The solution to the system of equations is x =5 and y = -6
How to solve the system of equationsFrom the question, we have the following parameters that can be used in our computation:
12x + 9y = 6
7x + 6y = −1
Multiply (2) by 1.5
So, we have the following representation
12x + 9y = 6
10.5x + 9y = −1.5
Subtract the equations to eliminate y
1.5x = 7.5
So, we have
x = 5
Recall that
12x + 9y = 6
So, we have
60 + 9y = 6
This gives
9y = -54
Divide
y = -6
SO, the value of y is -6
Read more about equations at
https://brainly.com/question/2972832
#SPJ1
. ΔABC is a right triangle, with ∠C being the right angle. m∠A = 51°, b = 8, find a.
In the given right triangle the length of side a is approximately 9.92 units.
Define the right triangle.A right triangle is a variety of triangles with a 90-degree angle (a right angle). The junction of the triangle's two legs, or the sides that meet at a right angle, creates this angle. The hypotenuse, which is always located opposite the right angle, is the third side of a right triangle.
A key characteristic of right triangles is the Pythagorean theorem, which asserts that the square of the hypotenuse is equal to the sum of the squares of the two legs of a right triangle.
We can use the trigonometric ratios of sine, cosine, and tangent to solve for the missing side of a right triangle. Since we are given the measure of one acute angle and the length of the side opposite that angle, we can use the tangent ratio:
tan A = opposite/adjacent
tan 51° = a/8
Multiplying both sides by 8:
a = 8 tan 51°
Using a calculator, we find that:
a ≈ 9.92
Therefore, the length of side a is approximately 9.92 units.
To know more about the right triangle, visit:
https://brainly.com/question/2217700
#SPJ1
The supplies account has a balance of $1,000 at the beginning of the year and was debited during the year for $2,800, representing the total of supplies purchased during the year. If $750 of supplies are on hand at the end of the year, the supplies expense to be reported on the income statement for the year is
The supplies expense to be reported on the income statement for the year can be calculated using the formula:
Supplies expense = Beginning supplies balance + Supplies purchased during the year - Ending supplies balance
Substituting the given values, we get:
Supplies expense = $1,000 + $2,800 - $750Supplies expense = $3,050Therefore, the supplies expense to be reported on the income statement for the year is $3,050.
~ Zeph
please help me with this one
here is the picture
The value of the composition of functions are
a) f o g ( 5 ) = 1315
b) g o f ( 5 ) = 59
What is Composition of functions?Evaluation of a function at the value of another function is known as Composition of function. A function composition is a process in which two functions, f and g, form a new function, h, in such a way that h(x) = g(f(x)). This signifies that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.
Given data ,
Let the value of the the function be f ( x ) = x² + 6x
Let the value of the function g ( x ) = x + 4
Now , the composition of functions is given by
f o g ( 5 ) is given by
g ( 5 ) = 5 + 4 = 9
So , the value of f ( 9 ) = ( 9 )² + 6 ( 9 ) = 81 + 54 = 135
Therefore , the value of f o g ( 5 ) = 135
Now , the composition of functions is given by
g o f ( 5 ) is given by
f ( 5 ) = ( 5 )² + 6 ( 5 ) = 25 + 30 = 55
Now , the value of g ( 55 ) = 55 + 4 = 59
Therefore , the value of g o f ( 5 ) = 59
Hence , the composition of functions are solved
To learn more about composition of functions click :
https://brainly.com/question/17673639
#SPJ1
The cost of packing a box of chocolates is given by 1/4 x2, where x is the number of chocolates (a box can never have fewer than 3 chocolates). If the weight of a box of chocolates is given by x + 2, what is the cost of packaging per weight unit?
Using the unitary method, we found that the cost of packing the unit weight of the chocolate box is [tex]\frac{x^2}{4(x+2)}[/tex] , for x ≥ 3.
What is meant by the unitary method?
The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, and then multiplying that value to determine the required value. Recognizing the units and values is crucial when using the unitary technique to a problem.
Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.
The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
Given,
The cost of packing a box of chocolates = 1/4 * x²
where x = Number of chocolates and x ≥ 3 for one box.
Weight of a box of chocolates = x + 2
We are asked to find the cost of packing 1 unit weight of chocolates.
This can be found using the unitary method.
Cost of unit weight = Cost of packing a whole box / Total weight of the box.
= (1/4 * x²) / (x + 2)
= [tex]\frac{x^2}{4(x+2)}[/tex] , for x ≥ 3
Now in the figure below, we are given four options.
On solving the first option we get the above equation as follows.
[tex]\frac{1}{4} x - \frac{1}{2} + \frac{1}{x+2}[/tex]
Taking LCM and making the same denominator for all.
[tex]\frac{x(x+2) - 2(x+2) +4 }{4(x+2)} = \frac{x^2+2x-2x-4+4}{4(x+2)} = \frac{x^2}{4(x+2)}[/tex]
Therefore using the unitary method, we found that the cost of packing the unit weight of the chocolate box is [tex]\frac{x^2}{4(x+2)}[/tex] , for x ≥ 3.
To learn more about the unitary method, follow the link.
https://brainly.com/question/24587372
#SPJ1
Creating two groups of cards with the SAME SUM using as many cards as possible using card numbers 1, 2, 5, 8, -4, and -2
Therefore , the solution of the given problem of unitary method comes out to be we have successfully created two groups of cards with the same sum.
A unitary method is precisely what?After determining the dimensions of one tiny slice, multiply the sum by two to complete a work using unitary procedure. The unit variable methodology, which just requires an expression, can be used to distinguish a coded unit from a certain group or set of groups. 40 pens, for example, might cost Rs. 4,000, which would be equal to $1.01 and 4000 pounds. It's possible that one country will have total control over the method employed to do this. Virtually every living creature has a distinctive quality.
Here,
We can create two groups of cards with the same sum as follows:
Group 1: 1, 2, 5, 8, -4
Group 2: -2, -4, 5, 8, 2
To check that the two groups have the same sum, we can add up the values of each group:
Group 1 sum: 1 + 2 + 5 + 8 - 4 = 12
Group 2 sum: -2 - 4 + 5 + 8 + 2 = 9
We can see that the sum of Group 1 is 12, and the sum of Group 2 is 9. However, we want the sums to be the same. We can make them the same by adding 3 to the sum of Group 2, which gives:
Group 1 sum: 12
Group 2 sum: 12
Therefore, we have successfully created two groups of cards with the same sum, using as many cards as possible from the given set of card numbers.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1