The Equation of the tangent line is y = 4x - 1.
According to the statement
We have to find that the equation of the tangent of the line.
So, For this purpose, we know that the
Equation of the tangent line can be found using the formula y – y1 = m (x – x1), where m is the slope and (x1, y1) is the coordinate points of the line.
From the given information:
f(x) = 3 X at (1, 3)
Then
The tangent line of a curve y = f(x) is a line that touches the curve at a point (x0, y0). Its slope (m) is found by substituting the point where it is drawn in the derivative f'(x) and its equation is found by using y - y0 = m (x - x0).
From the given it is clear that the slope of the equation is a 3.
Then m = 3
then
y – y1 = m (x – x1)
Substitute the points here
y - 3 = 4(x - 1)
Then
y = 4x - 4 +3
y = 4x - 1.
So, The Equation of the tangent line is y = 4x - 1.
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Greenwood Company manufactures two products—15,000 units of Product Y and 7,000 units of Product Z. The company uses a plantwide overhead rate based on direct labor-hours. It is considering implementing an activity-based costing (ABC) system that allocates all of its manufacturing overhead to four cost pools. The following additional information is available for the company as a whole and for Products Y and Z:
Activity Cost Pool Activity Measure Estimated Overhead Cost Expected Activity
Machining Machine-hours $ 231,000 11,000 MHs
Machine setups Number of setups $ 180,000 300 setups
Production design Number of products $ 94,000 2 products
General factory Direct labor-hours $ 260,000 10,000 DLHs
Activity Measure Product Y Product Z
Machining 9,000 2,000
Number of setups 60 240
Number of products 1 1
Direct labor-hours 9,000 1,000
Product Y would be allocated 20% of the machine setups cost
Product Z would be allocated 80% of the machine setups cost
What is activity-based costing?
Activity-based costing is a costing method where overhead cost of production are allocated based on the cost driver responsible for the overhead rather than using the plantwide overhead rate based on direct labor-hours.
In this case, we need to first of all determine the machine setups cost per per setups, based on the fact there 300 setups for both products Y and Z
machine setup cost per setup=Machine setups cost/Number of setups
Machine setups cost=$180,000
Number of setups=300
machine setup cost per setup=$180,000/300
machine setup cost per setup=$600
Total set up cost for product Y=60*$600=$36000
Total set up cost for product Y as %=$36,000/$180,000=20%
Total set up cost for product Z=240*$600=$144,000
Total set up cost for product Z as %=$144,000/$180,000=80%
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If 2log(x-y)=log x+log y,prove that 2 log(x+y)=log 5+log x+log
Let us understand the properties of Logarithms. In mathematics Logarithms are the inverse of exponential function. In the simplest case, the logarithm counts the number of times same factor in present in a repeated multiplication.
Logarithm of base 10 is also known as common logarithm.Logarithm of base e is called natural logarithm also written as( [tex]ln[/tex])A logarithm of a number 'x' to a base 'y' is defined as:
[tex]log_y^x=z (y > 0)[/tex]
which represents [tex]y^{z} =x[/tex]
According to the properties of Logarithm :
Product Law: [tex]log (a)+log(b)=log(ab)[/tex]Quotient Law: [tex]log (a)-log(b)=log(\frac{a}{b} )[/tex]Power Law: [tex]alog (x)=log(x)^{a}[/tex]Now let us solve the given problem:
[tex]2 log (x-y)=log x+ log y\\or,log(x-y)^2=log(xy)\\or,log(x^2+2xy+y^2)=log(xy)[/tex]
[tex]or,x^{2} +2xy+y^{2}=xy\\[/tex] ( taking anti-logarithms on both sides)
[tex]or,x^{2}+y^{2}=xy+2xy[/tex]
Now let us use the above equation to solve
Left Hand Side:
[tex]2 log(x+y)\\=log(x+y)^2\\=log(x^{2} +2xy+y^{2} )\\=log(x^2+y^2+2xy)\\=log(xy+2xy+2xy)\\=log(5xy)\\=log(5)+log(x)+log(y)[/tex]
=Right Hand side
Hence the statement is proved by using the properties of logarithm.
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Green Sun has net working capital of $400, current assets of $2,315, and inventory of $1,100. �What is the Quick ratio?
Answer:
3:5.7
Step-by-step explanation:
please Mark me as
Answer:
its not a accurate questions
cant be answered
Step-by-step explanation:
Write the number described by
I ten 16 ones.
Answer:
26
Step-by-step explanation:
10 + 26 = 26
Answer:
26
Step-by-step explanation:
1 × 10 + 16 × 1 = 10 + 16 = 26
I WILL GIVE BRAINLYIST Which number is prime? Choose each correct answer. 41 41 42 42 43 43 44 44 45 45 46 46 47. THIS IS MULTIPLE ANSWER.
Answer:
It is 41, 43, 47! :D
Step-by-step explanation:
how much of an alloy that is 40% copper should be mixed with 400 ounces of an alloy that is 70% copper in order to get an alloy that is 60% copper
The mixture requires 200 ounces of 40% alloy.
What is defined as the mixture?A mixture is a physical combination of two or more substances that retain their identities and are blended as solutions, suspensions, or colloids.
An alloy is a metallic substance made up of two or more elements that can exist as a compound or a solution. Alloy components are typically items, though carbon, a nonmetal, is a necessary component of steel.x = amount of 40% copper
400 = amount of 70% copper
x + 400 = total amount of copper = amount of 60% copper
Set a correctly weighted mixture of x and 300 equal to the a weighted (x+300), in which the weights are decimal percentages;
40% is 0.4, 70% is 0.7, and60% is 0.60.4x + 0.7(400) = 0.6(x + 400)
Solve for x:
0.4x + 280 = 0.6x + 240
0.2x = 40
x = 200
x = 200 ounces of 40% copper.
Therefore, the amount of 40% alloy needed for the mixture is 200 ounces.
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14. Explain how you can use multiplication to
find the quotient. Then evaluate the
expression.3/5 divided 3/15
Answer:
You can flip the second fraction and multiply the fractions so 3/5 * 15/3 = 3
Step-by-step explanation:
Suppose that you're designing a concrete patio. The patio will have height of 6 inches (1/2 foot) and have a rectangular base with a perimeter of 70 feet. If you have 138 cubic feet of concrete, what are the dimensions of the concrete patio?
The dimensions of the concrete patio should be 23ft x 12ft x 0.5feet.
What are the dimensions of an object?Since a rectangle is two-dimensional, while a cube is three-dimensional, the dimensions of the concrete patio include its length, width, and height or thickness.
Data and Calculations:The quantity of concrete required = 138ft³
The perimeter of the patio = 70 feet
Height = 6 inches or 1/2 foot or 0.5 ft
Perimeter = 2(L + W)
70 = 2(L + W)
L + W = 35 (70/2)
The possibilities for the length and width include 20 and 15, 25 and 10, and lastly, 23 and 12, which are also the two pair factors of 276.
Let L = 23 (the length is always longer than the width)
W = 12 (35 - 23)
Check:
Volume of concrete = 138ft³
Area = 276ft² (138ft³/0.5ft)
Two pair factors of 276 are 92 and 3, 46 and 6, 23 and 12, 2 and 138, and 1 and 276.
Given also that (23 + 12)2 = 70 (perimeter)
The dimensions that meet the two requirements are:
Length = 23 feet
Width = 12 feet
and Height = 0.5 feet
= 23 x 12 x 0.5 = 138
Thus, the dimensions of the concrete patio should be 23ft x 12ft x 0.5feet.
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Which function graph represents the following scenario?
The number of students per classroom can be represented by the equation y = 22x.
Question 9 options:
Answer:
The third graph
Step-by-step explanation:
We can immediately eliminate the 1st and last graphs because they are decreasing, not increasing. It wouldn't make sense that the more classrooms there are, the fewer students. Y = 22x would be increasing in the graph.
Let's plug some x values into the equation first, to see where our points are at.
Plug 1 into x
Y = 22(1)
Y= 22
(1,22)
Plug 2 into x
Y = 22(2)
Y = 44
(2,44)
Plug 3 into x
Y = 22(3)
Y = 66
(3,66)
Plug 4 into x
Y = 22(4)
Y = 88
(4,88)
The second graph matches the coordinates, so it works, but it isn't a complete function graph. A function graph needs a line drawn through the points. The second graph isn't your answer.
Let's look at the third graph. The coordinates also match up with the graph and it has a line drawn through the points. It's an accurate function graph representing this scenario. Therefore, the third graph is your answer.
Have a lovely day! :)
Answer: the 2nd graph is what i got right on the test
Step-by-step explanation:
Please list the intercepts I need help!
Answer:
{(5,1),(5,0),(1,0),(0,-3),(-3,0),(-4,-3),(2,5)}
Step-by-step explanation:
This is all I could get from the cropped out picture of the graph
The following data are an example of what type of regression?
x
1
2
3
4
5
6
O A. Exponential
OB. Quadratic
O C. Linear
OD. None of the above
y
10,960
10,808
10,904
11,286
11,876
12,553
Answer:
linear
Step-by-step explanation:
because they're are all in a vertical vay
Can you please help me
help me please FIJDJSHEHE
Answer: 0
Step-by-step explanation:
because -2+-1 is -3. then -3+0 is just -3. lastly -3+1 = -2 and -2 + 2 = 0
Dependent events can best be described as
two or more events that have the same probabilities.
two or more events that do not have the same probabilities.
a group of events whose later outcomes are not affected by previous outcomes.
a group of events whose later outcomes are affected by previous outcomes.
.
Option D is the right choice. Dependent events can best be described as group of events whose later outcomes are affected by previous outcomes.
We are aware of two instances. If the occurrence of one result influences the occurrence of the other outcome, then events A and B are said to be dependent.
For instance,
If we pull the first marble without replacing it from a bag containing 5 blue marbles, 2 red marbles, and 3 green marbles.
The sketching of a blue marble first, followed by a green marble, is an instance of a dependent event.
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Answer:
d on edge
Step-by-step explanation:
There are 10 marbles. What is the probability of drawing two yellow marbles if the first one is not placed back into the bag before the second draw?
Answer: 1/10
Step-by-step explanation:
2 lines intersect. A line with points A, B, D intersects a line with points E, B, C at point B, forming 4 angles.
In the diagram, which angles are vertical angles? Select two options.
The angles that are vertical angles are:
<EBD and <ABC
<ABE and <CBD
What are Vertical Angles?When two straight lines intersect at a point, they form two pairs of angles that are directly vertically opposite each other. These pairs of angles are called the vertical angles.
Given the image below that shows two lines intersecting at point B, they form two pairs of angles that are directly vertically opposite each other, which are:
<EBD and <ABC
<ABE and <CBD
These two pairs of angles are called vertical angles.
Therefore, the angles that are vertical angles are:
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Find the 50th percentile from the following sorted list of 34 data
128 134 144 146 153
190
207 209
220
221
237
256
263 265
271
273
283
324 350
371
389 401 416 417
422
424 443 444
448 466
486
487 490 500
50th percentile =
Enter an integer or decimal number [more..]
Question Help: Message instructor
The 50th percentile value is 303.5.
What is a percentile?
A percentile is a term used in statistics to express how a score compares to other scores in the same set. While there is technically no standard definition of percentile, it's typically communicated as the percentage of values that fall below a particular value in a set of data scores.
Percentiles are commonly used to report values from norm-referenced tests (in which the average is determined by comparing a set of results in the same group) as the percentages of scores that fall below those of the average of the set.
For calculation we have to add all the given numbers.
(128+134+144+146+153+190+207+209+220+221+237+256+263+265+271+273+283+324+350+371+389+401+416+417+422+424+443+444+448+466+486+487+490+500) divided by 34
hence 50th percentile is 303.5
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HELP I DONT UNDERSTAND MY MATH HOMEWORK AND I HAVE 3 PAGES OF IT
Lynn's track team practices for 3 weeks before their first meet. The coach wants them to get in a total of 720 minutes of practice time before the first meet. If the track team meets every Monday, Wednesday, and Friday for 70 minutes, will they have enough practice time before the first meet? Explain.
Answer:
No
Step-by-step explanation:
By the time they meet at their first meet, they would have practiced for 630 minutes total.
70*3=210
If they meet every three days each week for 70 mins each day then I would have to multiply the answer to learn how many minutes they gain each week.
210*3=630
If they have 210 mins per week and they only meet 3 times before the first meet, they will have only met for a total of 630 mins.
Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time. How many weeks does it take to empty the lake? Express your answer as a fraction reduced to lowest terms, if needed.
The number of weeks that it takes to empty the lake is; 350/11 weeks
How to solve fraction problems?We are told that Officials begin to release water from a full man-made lake at a rate that would empty the lake in 14 weeks, but a river that can fill the lake in 25 weeks is replenishing the lake at the same time.
Let w = number of weeks required to empty the lake
let the completed job = 1 (an empty lake)
Thus;
w/14 - w/25 = 1
Multiply through by 350 to get;
25w - 14w = 350
11w = 350
w = 350/11 weeks
Thus, the number of weeks that it takes to empty the lake is; 350/11 weeks
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PLEASE HELP ME
An article claimed the state's typical price of a gallon of gasoline is $2.69. The prices from 5 gas stations surveyed were $2.79, $2.99, $2.69, $2.89, and $2.69.
According to this data, what is wrong with the article's statement?
This statement in the article is wrong because $2.69 is not the mean price ($2.81)
How to determine what is wrong with the data?The prices from 5 gas stations surveyed are given as:
$2.79, $2.99, $2.69, $2.89, and $2.69.
There are no outliers in the dataset
So, the dataset can be summarized by the mean
The mean is
Mean = Sum/Count
So, we have
Mean = ($2.79+ $2.99+ $2.69+ $2.89+$2.69)/5
Evaluate
Mean = 2.81
The article quoted $2.69 as the typical price
This statement in the article is wrong because $2.69 is not the mean price ($2.81)
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i need help this is due tomorrow
Given the following graphs of f(x) and g(x), find the value of lim x->7 f(g(x)) in simplest form.
The limit of the composite function is given as follows:
lim x->7 f(g(x)) = 2.
What is a limit?A limit is given by the value of function f(x) as x tends to a value.
From the graph of g(x), we have that the lateral limits at x = 7 are given as follows:
[tex]\lim_{x \rightarrow 7^-} = \lim_{x \rightarrow 7^+} = -2[/tex]
Hence:
lim x->7 f(g(x)) = f(lim x->7 g(x)) = f(-2).
Looking at the graph of f(x), we have that:
f(-2) = 2.
Hence:
lim x->7 f(g(x)) = 2.
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A ball is thrown up on the surface of a moon. It’s height above the lunar surface (in feet) after ‘t’ seconds is given by the formula
h =592t - 16/7t^2
Find the time that the ball reaches its maximum height.
Step-by-step explanation:
we get the points with extreme values as the 0 points of the first derivative of the function.
h'(t) = 592 - 32/7 t = 0
592 = 32/7 t
4144 = 32t
t = 129.5 seconds
so, it will reach its max. height after 129.5 seconds.
The time that the ball reaches its maximum height is 129.5 seconds.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The height above the lunar surface (in feet) after ‘t’ seconds is given by the formula;
⇒ h =592t - 16/7t²
Now,
We have to find the derivative of above formula and equate to zero for the maximum time as;
⇒ h =592t - 16/7t²
⇒ h' =592 - 16/7 × 2t = 0
⇒ 592 - 32/7 t = 0
⇒ 32/7 t = 592
⇒ 32t = 592 × 7
⇒ 32t = 4,144
⇒ t = 4,144/32
⇒ t = 129.5 seconds.
Thus, The time that the ball reaches its maximum height is 129.5 seconds.
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For a rectangle with a perimeter of 20 cm, the width of the rectangle is one-third its length. Use an equation to find the length and width of the rectangle.
Answer:
Step 1. The perimeter P means adding up all four sides of a rectangle.
Step 2. Let w be the width
Step 3. Let 3w be the length since the width is one-third the length
Step 4. Then P=w+w+3w+3w=8w=20 since the perimeter P is 20 cm.
Step 5. Solving the equation in Step 4 leads to the following steps
Divide by 8 to both sides of the equation
8w%2F8=20%2F8
w=5%2F2 and 3w=15/2 and P=2(5/2+15/2)=20 which is a true statement.
Step 6. ANSWER: The width is 5/2 cm.
Step-by-step explanation:
I hope the above steps and explanation were helpful.
The tank for a car holds 20 gallons . The gasoline gauge shows the tank is 2/3 full. How much gas is still in the tank? Give your answer as a whole number or as a mixed fraction reduced to lowest terms.
The amount of gas in the tank is 13 1/3 gallons
How to calculate the amount of gas in the tank ?The tank of the car holds 20 gallons of gas
The gasoline gauge shows 2/3 full
The amount of gas left in the tank can be calculated as follows
= 2/3 × 20
= 40/3
= 13 1/3
Hence there are 13 1/3 gallons of fuel left in the tank
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According to Chapter 3: Shop Layout, in a scene shop, sheet lumber (such as lauan, plywood, masonite, and MDF) is commonly stored flat in an area that is at least _________________.
Group of answer choices
4'x6'
8'x8'
4'x8'
6'x10'
Shop Layout, in a scene shop, sheet lumber (such as lauan, plywood, masonite, and MDF) is commonly stored flat in an area that is at least C. 4'x8'.
What is the size (area) of sheet lumber?The most common size (area) for sheet lumber is 4 x 8 feet, about 32ft² or 2.97m².
Other areas that sheet lumber can occupy include 2 x 2 feet, 2 x 4 feet, 4 x 4 feet, and 4 x 10 feet.
This implies that sheet lumber does not usually come in the following sizes: 4'x6', 8'x8', and 6'x10'.
Data and Calculations:Length of sheet lumber = 8 feet
Width of sheet lumber = 4 feet
Area of sheet lumber = 32 ft² (8 x 4)
Thus, according to Shop Layout, in a scene shop, sheet lumber (such as lauan, plywood, masonite, and MDF) is commonly stored flat in an area that is at least C. 4'x8'.
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Lita Lopez started Biz Consulting, a new business, and completed the following transactions during its first year of operations. Lita Lopez invested $70,000 cash and equipment valued at $10,000 in the company in exchange for its common stock. The company purchased a building for $40,000 cash. The company purchased equipment for $15,000 cash. The company purchased $1,200 of supplies and $1,700 of equipment on credit. The company paid $500 cash for advertising expenses. The company completed a financial plan for a client and billed that client $2,800 for the service. The company designed a financial plan for another client and immediately collected a $4,000 cash fee. The company paid $3,275 cash in dividends to the owner (sole shareholder). The company received $1,800 cash as partial payment from the client described in transaction f. The company made a partial payment of $700 cash on the equipment purchased in transaction d. The company paid $1,800 cash for the secretary's wages for this period. Required:
1. The effects of each transaction on the individual items of the accounting equation are as follows:
Cash $70,000 + (40,000) + (15,000) + (500) + 4,000 + (3,275) + 1,800 + (700) + (1,800) = $14,525
Accounts Receivable $2,800 - 1,800 = $1,000
Office Supplies $1,200
Equipment $10,000 + 15,000 + 1,700 = $26,700
Office Suites $40,000
Accounts Payable $1,200 + $1,700 + (700) = $2,200
Capital–L. Lopez $70,000 + 10,000 = $80,000
Dividends $3,275
Revenues $2,800 + 4,000 = $6,800
Advertising Expenses $500
Wages Expense $1,800
Total $2,300
2. The company's Net income is $4,500.
Data and Calculations:Net income = Revenue - Expenses
= $2,300 ($6,800 - $2,300).
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Question Completion:1. Use additions and subtractions within the table to show the dollar effects of each transaction on individual items of the accounting equation.
2. Determine the company’s net income.
Jada cuts a strip of paper into 5 equal parts. Each part is 7/5 inches long. How long was the strip of paper?
The length of the strip of paper is 7 inches.
How to calculate the value?From the information, Jada cuts a strip of paper into 5 equal parts and each part is 7/5 inches long.
Therefore, the length of the strip will be:
= 7/5 × 5
= 7 inches.
The length is 7 inches.
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An article claimed the state's typical price of a gallon of gasoline is $2.69. The prices from 5 gas stations surveyed were $2.79, $2.99, $2.69, $2.89, and $2.69.
According to this data, what is wrong with the article's statement?
The typical average price of gasoline should be $2.81 and not $2.69 because $2.69 is not the average of the sampled prices.
What is the mean of the sample?
We are given the prices of a gallon of gasoline from 5 gas stations surveyed as; $2.79, $2.99, $2.69, $2.89, and $2.69.
Thus, to calculate the mean, we will use the formula;
Mean = ∑x/n
Mean = (2.79 + 2.99 + 2.69 + 2.89 + 2.69)/5
Mean = 14.05/5
Mean = $2.81
Thus, the typical average price of gasoline should be $2.81 and not $2.69
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