The logical function that represents the amount of workout Laura does in each week along with her simultaneous increase in workout can be given by Arithmetic Progression.
It is represented as An = A + (n-1)d. Here, A represents the first term, or the amount of workout done in first week, d represents common difference or the difference in workout done in next week to its previous week, n represents the number of terms or the number of weeks for which data is to be calculated and An represents the workout done in nth week.
Arithmetic progression refers to the sequence of numbers such that each succeeding number increases with respect to previous number by fixed/ constant value. Thus, there exists constant amount of difference between each consecutive pair of number.
Since, Laura's workout pattern varies such that the amount of workout she does in one week increases by same amount in next week, so we get an arithmetic progression of her workout pattern.
Hence, her workout pattern can be traced as A, A+d, A+2d, A+3A, ..., An.
Thus, An = A + [(n-1)*d]
A3 = A +[(3-1)*d] = A + [2d] = 20 ...(1)
A9 = A +[(9-1)*d] = A + [8d] = 50 ...(2)
A11 = A +[(11-1)*d] = A + [10d] = 60 ...(3)
Solving equation (1) and (2), we get d = 5 and A = 10.
Thus, we conclude by saying that the function of her exercise routine is given by arithmetic progression and the amount of workout that she increases each week is given by 'd' that is 5 minutes.
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Is -1.5 greater than 2.1
26) Jody earns $8.00 per hour.
Michael earns $10.00 per hour.
They each earn a 2% commission on what they sell.
Jody sold $6000. She worked 30 hours.
Michael sold $5000. He worked 40 hours.
What were each of their earnings for the week?
What was the difference in their earnings?
Jody's weekly earning is $360 and Michael's weekly earning is $500
The difference between their earning is $140
Jody sold $6000
2% commission of $6000 is (2/100)x 6000
Jody's commission is $120
He earns $8 per hour and he worked for 30 hours
= 8 x 30
=$240
Jody's total earning = 240 + 120 = $360
Michael sold $5000
2% commission of $5000 is (2/100)x 5000
Michael's commission is $100
He earns $10 per hour and he worked for 40 hours
= 10 x 40
=$400
Michael's total earning = 400 + 100 = $500
Difference in there earnings= Michael's earning - Jody's earning
= 500- 360
= $140
Therefore, Jody's weekly earning is $360 and Michael's weekly earning is $500
The difference in their earning is $140
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1) 10 3/4 gallons of gas costs $21.50.
What is the cost per gallon
Error Analysis You and a friend are doing math homework together. You have to solve the equation 5x + 4x - 68 = 34 - 8x. Your friend arrives at the incorrect answer x = -2. Find the correct value of x. Then find the error your friend possibly made. X x=0 What possible error could your friend have made to get x = -2? OA. Your friend should have added 68 to each side of the equation, but instead subtracted 68 from the right side. OB. Your friend should have added 8x to each side of the equation, but instead subtracted 8x from the left side. OC. Your friend should have added 5x and 4x to get a sum of 9x, but instead got a sum of 8x.
This is probably what steps your friend took, or something similar.
5x+4x-68 = 34-8x
9x = 34-8x-68
9x = -8x-34
9x+8x = -34
17x = -34
x = -34/17
x = -2
However, the error is when they subtracted 68 from both sides (line 2).
Instead, they should have added 68 to each side to undo the -68 on the left hand side.
----------------------------
Here's what the steps should look like (one variation of it anyway)
5x+4x-68 = 34-8x
9x = 34-8x+68
9x = -8x+102
9x+8x = 102
17x = 102
x = 102/17
x = 6 is the correct value of x
--------------------------
Check:
5x+4x-68 = 34-8x
5*6+4*6-68 = 34-8*6
30+24-68 = 34-48
54-68 = 34-48
-14 = -14
We get the same thing on both sides after replacing each x with 6, so it confirms x = 6 is the solution.
If you were to try x = -2, then you would end up with -86 = 50 which is a false statement. So that rules out x = -2 as a solution.
5 times a number is 36 less than the square of that number. Find the negative solution.
In linear equation , the negative solution is x = -4 .
What is a formula for linear equations?
A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. (b). Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.Let's assume that the number is x
Now according to the question,
When 36 is subtracted from the square of a number, the result is 5 times the number.
x² -36 = 5x
x² -5x -36 = 0
x²- 9x + 4x -36 = 0
x ( x - 9) +4( x - 9 ) = 0
(x-9) ( x + 4 ) = 0
x = 9 , -4
So the negative solution is x = -4
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If the BMI of a person who is 1.9 meters tall is 20 when the person weighs 55 kilograms, what is the constant of variation?
The height is 5.225 meters and the constant of variation will be 10.5
How to calculate the constant?From the information, the BMI of a person who is 1.9 meters tall is 20.
Therefore, the constant of variation when the person has a weight of 55 kilograms will be:
= 20/1.9 = 10.5
The height will be:
= 1.9 × 55/20
= 1.9 × 2.75
= 5.225 meters.
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Consider Line 2, which has the equation: y = = - 1/3x + 14, Give the equation of the line parallel to Line 2 which passes through: (-7,4).
Answer:
x + y = -3.
Step-by-step explanation:
x + y = 2y = -x + 2 - the slope of this line is -1 . The line parallel to it will also have a slope of -1.It also passes through (-7,4) so we havey - 4 = -1(x - -7)y - 4 = -1(x + 7)y - 4 = -x - 7x + y = -3 is the required equation.
Which inequality correctly compares 125%, 0.47, and three and two fifths? 125% < 0.47 < three and two fifths 0.47 < 125% < three and two fifths 0.47 < three and two fifths < 125% three and two fifths < 0.47 < 125%
The inequality that correctly compares the numbers is 0.47 < 125% < three and two fifths
How to determine the inequality that correctly compares the numbers?The numbers are given as:
125%, 0.47, and three and two fifths
Rewrite properly as:
125%, 0.47, and 3.4
Express the percentage as decimal
1.25, 0.47, and 3.4
Reorder the numbers in ascending order
0.47, 1.25 and 3.4
Rewrite as
0.47, 125% and three and two fifths
Include the less than inequality symbol
0.47 < 125% < three and two fifths
Hence, the inequality that correctly compares the numbers is 0.47 < 125% < three and two fifths
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prove that √ 2 - 1 is irrational
Answer:
a+b/2b is an rational no. because LHS is always equal to RHS. therefore our assumption is wrong. hence , 2√2-1 is an irrational number.
Why do we use parenthesis if an interval is infinite on both boundries?
We use parenthesis if an interval is infinite on both boundries in order to exclude end-points .
Square brackets mean the set of all points from a to b .
If we use square brackets , it would mean we are including - infinity and + infinity , which is practically impossible .
When we , use parenthesis only the nos . lying between the two points are taken into consideration , the two points are not included .
So , we use parenthesis to exclude - infinity and + infinity .
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One triangle shown is formed by the tree, its shadow, and a line of sight from the ground to the top of the tree. The other is formed by Manny, his shadow, and a line of sight from the ground to the top of his head. Are the two triangles similar?
The height of the tree is 21 feet if manny stands 512 feet tall, and his shadow is 414 feet long. The tree's shadow extends 17 feet in length.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
The length of Manny's shadow, which is 414 feet long, is 512 feet.
The tree's shadow extends 17 feet.
Here, we'll assume that the height is x.
According to the data given, the calculation is as follows:
414 : 512 = 17 : x
⇒ 414 / 512 = 17 / x
⇒ (414)x = (512)(17)
⇒ x = (512)(17)/(414)
⇒ x =21.02
⇒ x = 21 feet
Therefore, the height of the tree is 21 feet if manny stands 512 feet tall, and his shadow is 414 feet long. The tree's shadow extends 17 feet in length.
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Your question is incomplete, probably the complete question is:
One triangle shown is formed by the tree, its shadow, and a line of sight from the ground to the top of the tree. The other is formed by Manny, his shadow, and a line of sight from the ground to the top of his head. Manny is 512 feet tall, and his shadow is 414 feet long. The shadow of the tree is 17 feet long. How can you determine the height of the tree?
AP Calculus ab question: what is the derivative function, f'(x), using the definition of derivative for : f(x) = 3/(x+1)
Answer:
Solved using 2 different methods, used the definition of derivative aswell.
Kubin Company’s relevant range of production is 12,000 to 16,000 units. When it produces and sells 14,000 units, its average costs per unit are as follows:
Average Cost per Unit
Direct materials $ 7.30
Direct labor $ 4.30
Variable manufacturing overhead $ 1.80
Fixed manufacturing overhead $ 5.30
Fixed selling expense $ 3.80
Fixed administrative expense $ 2.80
Sales commissions $ 1.30
Variable administrative expense $ 0.80
Required:
1. Assume the cost object is units of production:
a. What is the total direct manufacturing cost incurred to make 14,000 units?
b. What is the total indirect manufacturing cost incurred to make 14,000 units?
2. Assume the cost object is the Manufacturing Department and that its total output is 14,000 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department?
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the Manufacturing Department?
3. Assume the cost object is the company’s various sales representatives. Furthermore, assume that the company spent $39,200 of its total fixed selling expense on advertising and the remainder of the total fixed selling expense comprised the fixed portion of the company's sales representatives’ compensation.
a. When the company sells 14,000 units, what is the total direct selling expense that can be readily traced to individual sales representatives?
b. When the company sells 14,000 units, what is the total indirect selling expense that cannot be readily traced to individual sales representatives?
2. Assume the cost object is the Manufacturing Department and that its total output is 14,000 units.
a. How much total manufacturing cost is directly traceable to the Manufacturing Department? (Round per unit values to 2 decimal places.)
b. How much total manufacturing cost is an indirect cost that cannot be easily traced to the Manufacturing Department?
Show less
2a. Direct material cost per unit
2a. Direct labor cost per unit
2a. Variable manufacturing overhead per unit
2a. Fixed manufacturing overhead per unit
2a. Total manufacturing cost per unit $0.00
2a. Number of units produced and sold
2a. Total direct costs $0
2b. Total indirect costs
1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600.
1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200.
2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600.
2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200.
3a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.
3b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.
4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.
4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.
2a. Direct material cost per unit is $7.30.
2a. Direct labor cost per unit is $4.30.
2a. The Variable manufacturing overhead per unit is $1.80.
2a. The Fixed manufacturing overhead per unit is $5.30.
2a. The total manufacturing cost per unit is $18.70 ($13.40 + $5.30)
2a. The number of units produced and sold is 14,000 units.
2a. Total direct costs are $217,000 (14,000 x $13.40 + 14,000 x $2.10).
2b. Total indirect costs are $166,600 (14,000 x $5.30 + 14,000 x $6.60).
Data and Calculations:Relevant production range = 12,000 to 16,000 units
Production and sales units = 14,000 units
Average Cost
per Unit
Direct materials $ 7.30
Direct labor $ 4.30
Variable manufacturing overhead $ 1.80
Direct cost per unit $13.40
Fixed manufacturing overhead $ 5.30
Total manufacturing cost per unit $18.70
Fixed selling expense $ 3.80 $53,200 ($3.80 x 14,000)
Fixed administrative expense $ 2.80 $39,200 ($2.80 x 14,000)
Total fixed costs per unit $6.60 $92,400 ($6.60 x 14,000)
Variable selling and admin:
Sales commissions $ 1.30
Variable administrative expense $ 0.80
Total variable selling and admin per unit = $2.10
1a) The total direct manufacturing cost incurred to make 14,000 units is $187,600 ($13.40 x 14,000).
1b) The total indirect manufacturing cost incurred to make 14,000 units is $74,200 ($5.30 x 14,000).
2a) The total manufacturing cost directly traceable to the Manufacturing Department is $187,600 ($13.40 x 14,000).
2b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department is $74,200 ($5.30 x 14,000).
3) Fixed selling expenses = $53,200 ($3.80 x 14,000)
Advertising expenses = $39,200
Sales Compensation = $14,000 ($53,200 - $39,200)
Sales Commission = $18,200 ($1.30 x 14,000)
Total Salespersons' compensation = $32,200
a) When the company sells 14,000 units, the total direct selling expense, which can be readily traced to individual sales representatives, is $18,200.
b) When the company sells 14,000 units, the total indirect selling expense, which cannot be readily traced to individual sales representatives, is $14,000.
4a) The total manufacturing cost directly traceable to the Manufacturing Department per unit is $13.40.
4b) The total manufacturing cost, which is an indirect cost, that cannot be easily traced to the Manufacturing Department per unit is $5.30.
2a. Direct material cost per unit is $7.30.
2a. Direct labor cost per unit is $4.30.
2a. The Variable manufacturing overhead per unit is $1.80.
2a. The Fixed manufacturing overhead per unit is $5.30.
2a. The total manufacturing cost per unit is $18.70 ($13.40 + $5.30)
2a. The number of units produced and sold is 14,000 units.
2a. Total direct costs are $217,000 (14,000 x $13.40 + 14,000 x $2.10).
2b. Total indirect costs are $166,600 (14,000 x $5.30 + 14,000 x $6.60).
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Please show me how to solve this: Katie and Tara are making crafts for their school's craft fair. For every 7 Tara makes, Katie makes 9. If they made a total of 240 crafts, how many did each girl
make?
Answer:
Tara makes 7x =7*15 = 105 crafts and Katie made 9x = 9*15 = 135 crafts.
Step-by-step explanation:
Crafts tara and katie make resoectively are in the ratiob 7:9. Let's say 7x and 9x.
Now,
7x + 9x = 240
so, x = 240/16
so, x = 15
Help! Quadratic Word Problems!
Answer:
Step-by-step explanation:
Which statements accurately describe the function f(x) = 3(√18)x? Select three options.
The domain is all real numbers.
The range is y > 3.
The initial value is 3.
The initial value is 9.
The simplified base is 3√2.
Answer:
The domain is all real numbers.
The initial value is 3.
The simplified base is 3√2.
The statements accurately describe the function f(x) = 3(√18)x are:
The domain is all real numbers.
The initial value is 3.
The simplified base is 3√2.
What is Function?A function is an expression that illustrates the connection between two or more variables and numbers. A function defined by several subfunctions, each of which is applicable to a distinct interval in the domain, is said to be piecewise.
We have function,
f(x) = 3√18 x
now, simplifying the function we get
f(x) = 3 (3√2)x
f(x) = 9x√2
So, we can conclude that.
The domain is all real numbers.
The initial value is 3.
The simplified base is 3√2.
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Solve the equation -2 =
k=
k+7
3
[tex]{ \orange{ \tt{k = 1}}}[/tex]
Step-by-step explanation:
-2 = k+7/3
cross multiply 3 with -2 then,
-6 = k+7 (OR) k+7 = -6.
k = -6+7
k = 1.
Simplify (2.8 × 10−9) − (6.9 × 10−8). Write the final answer in scientific notation.
−6.62 × 10−9
−6.62 × 10−8
−4.1 × 10−1
−4.1 × 101
The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
(2.8 × 10⁻⁹) − (6.9 × 10⁻⁸)
Making the exponents to be similar gives:
(2.8 × 10⁻⁹) − (69 × 10⁻⁹)
Simplifying gives:
-6.62 * 10⁻⁸
The solution to the expression (2.8 × 10⁻⁹) − (6.9 × 10⁻⁸) gives -6.62 * 10⁻⁸
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help i have no clue how to do this pls help
Answer:
4
Step-by-step explanation:
the sequence is like [tex]1^{2}[/tex],[tex]2^{2} ,4^{2},8^{2} ,16^{2} ,32^{2}[/tex]
IS 303 2022 Summer Packet for Incoming
Ms. Hamilton wants to put a decorative iron fence (rather like Winnie's in Tuck Everlasting)
around her yard. The yard is a perfect rectangle: its length is 24.75 feet and its width is 12.75
feet. Home Depot charges $50 a yard for iron fencing.
66.) How many feet of fencing does Ms. Hamilton need to buy?
67.) What do you call the distance around a rectangle?
Math in the Real World (Leave in packet)
68.) Write a detailed explanation of at least 3 ways that you used math this summer (other
completing this packet). How did these skills help you be successful in the real world? W
skills do you hope to develop this year in math?
66) The number of feet of fencing that Ms. Hamilton needs to buy is 75 feet.
67) The distance around a rectangle is called a perimeter.
68) What are the instances of the use of Maths skills?The use of Mathematics skills is all-encompassing. Every activity involves some mathematical calculations and the use of mathematical operations, like additions, subtractions, divisions, and multiplication.
When you visit a Merchandise Store, you undertake some mathematical activities by computing how much is needed and the balance you will get. Future projections depend on maths skills.
For instance, budgeting how much it costs you weekly to maintain your hairstyle also involves maths skills.
As you return to school after the summer breaks, you decide how much savings you must spend. It is maths. Any time calculations are involved, it requires maths.
Data and Calculations:Length of the yard = 24.75 feet
Width of the yard = 12.75 feet
Perimeter of the yard = 75 feet (24.75 + 12.75)2
Charges for a yard of iron fencing = $50 per yard
3 feet = 1 yard
75 feet = 25 yards (75/3)
The cost of 25 yards = $1,250
Thus, Ms. Hamilton will need to spend $1,250 on this decorative iron fence project.
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William needs a box to hold his golf ball collection. He found a box that can fit 8 layers with 14 balls in each layer. How many golf balls cab this box hold
The box will be able to hold 112 balls
How to calculate the number of balls the box will hold ?Williams needs a golf box to hold his collection of balls
He discovered that 8 layers can fit in a box and each of these 8 layers can hold 14 balls
Therefore the number of golf balls the box can hold can be calculated as follows
= 8 × 14
= 112
Hence the box can hold 112 balls
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Copy and complete the table of values for
y = -2x² + 4x + 9.
What numbers replace A and B?
Answer:
Below in bold.
Step-by-step explanation:
A = value of y when x = -1:
A = -2(-1)^2 + 4(-1) + 9
= -2*1 - 4 + 9
= -2 - 4 + 9
= 3.
B = value of y when x = 2:
B = -2(2)^2 + 4(2) + 9
= -2*4 + 8 + 9
= - 8 + 8 + 9
= 9.
Which of the following would represent three consecutive integers if X is the first integer? Check all that apply 
Every day a new puzzle is downloaded into Ken's account. Right now, there are 27 puzzles in his account. The function N ( d ) = 27 + d represents the relation between the number of puzzles, N , and the time, d , measured in days.
Answer:
What's the question?
Step-by-step explanation:
Whats 21 - 20 x 2? (Hint: the most used number and the last number)
Answer:
-19Step-by-step explanation:
Whats 21 - 20 x 2?
remember PEMDAS21 - 20 x 2 =
21 - 40 =
-19
Answer correctly and I’ll give brainlest
Answer: division property of equality
Step-by-step explanation:
A rectangle's width is 6 feet less than its length. Write a quadratic function
that expresses the rectangle's area in terms of its length.
A. A(1)=1²-61
B. A(7)=7w
c. A(1)=12+61
D.A(7)=1-6
Answer:
A. A(l) = l² -6l
Step-by-step explanation:
You want a quadratic function for the area of a rectangle whose width is 6 feet less than its length.
Rectangle areaLet l (ell) represent the length of the rectangle in feet. Then the width will be 6 feet less, or (l -6). The area is the product of length and width:
A = LW
A(l) = l(l -6)
A(l) = l² -6l . . . . . . use the distributive property to eliminate parentheses
a shelf contains 8 novels, 5 biographies, and 2 dictionaries. jane will select one book of each type. how many different ways can this be done?
X^2+7x=8 find the solutions
The value of x is 1 and -8.
To solve this problem we need to understand the concept of quadratic equation.
To solve Quadratic equation we need to understand the concept of equation which says the factor of the product of coefficient of [tex]x^{2}[/tex] and constant must on adding or substracting give the coefficient of x.
Here the equation is [tex]x^{2} +7x-8=0[/tex]
The product of coefficient is 8. The factors of 8 is 8 and 1 which gives 7 on substracting.
Now,
[tex]x^{2} +8x-x-8=0[/tex]
⇒[tex]x(x+8)-1(x+8)=0\\[/tex]
⇒[tex](x-1)(x+8)=0[/tex]
∴ x=1,-8.
So, the required values of x is 1 and -8.
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show ur work you will get brainlest and 30 points if your right THANK YOU!!
I hope this pictures help
