Answer:
Step-by-step explanation:
The team drank a total of 7 x 8 = 56 juice boxes, and there were 29 remaining, so the team opened 56 - 29 = 27 juice boxes.
Since the team only opened a new box after finishing the previous one, the team opened 27 - 1 = 26 boxes of juice in total.
To explain this solution in more detail, we can use basic arithmetic. We know that the mom bought 7 boxes of juice, each containing 8 juice boxes,
so the total number of juice boxes is 7 x 8 = 56. After the team drank all the juice they wanted, there were 29 juice boxes remaining. This means that the team drank 56 - 29 = 27 juice boxes.
Since the team only opened a new box of juice after finishing the previous one, the number of boxes opened will be one less than the total number of juice boxes consumed.
Therefore, the team opened 27 - 1 = 26 boxes of juice in total. It is important to note that this assumes that the team opened all the boxes they consumed and did not drink any juice directly from the remaining boxes.
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Question 10 9 pts Let f(c) = x3 +62? 15x + 3. (a) Compute the first derivative of f f'(x) = (c) On what interval is f increasing? interval of increasing = (d) On what interval is f decreasing? interval of decreasing = **Show work, in detail, on the scrap paper to receive full credit. (b) Compute the second derivative of / L'(x) = (e) On what interval is concave downward? interval of downward concavity = () On what interval is concave upward? interval of upward concavity = **Show work, in detail, on the scrap paper to receive full credit.
(a) The first derivative of f is f'(x) = 3x² - 15.
(b) The second derivative of f is f''(x) = 6x.
(c) f is increasing on the interval (-∞, √5) and decreasing on the interval (√5, ∞).
(d) f is decreasing on the interval (-∞, √5) and increasing on the interval (√5, ∞).
(e) f is concave downward on the interval (-∞, 0) and concave upward on the interval (0, ∞).
(a) To find the first derivative of f, we differentiate each term of the function with respect to x using the power rule. Thus, f'(x) = 3x² - 15.
(b) To find the second derivative of f, we differentiate f'(x) with respect to x. Thus, f''(x) = 6x.
(c) To determine the intervals where f is increasing, we set f'(x) > 0 and solve for x. Thus, 3x² - 15 > 0, which simplifies to x² > 5. Therefore, x is in the interval (-∞, √5) or (√5, ∞). To determine which interval makes f increasing, we can test a point within each interval.
For example, when x = 0, f'(0) = -15, which is negative, so f is decreasing on (-∞, √5). When x = 10, f'(10) = 285, which is positive, so f is increasing on (√5, ∞). Thus, f is increasing on the interval (√5, ∞) and decreasing on the interval (-∞, √5).
(d) To determine the intervals where f is decreasing, we set f'(x) < 0 and solve for x. Thus, 3x² - 15 < 0, which simplifies to x² < 5. Therefore, x is in the interval (-∞, √5) or (√5, ∞). Again, we can test a point within each interval to determine which one makes f decreasing.
For example, when x = 0, f'(0) = -15, which is negative, so f is decreasing on (-∞, √5). When x = 10, f'(10) = 285, which is positive, so f is increasing on (√5, ∞). Thus, f is decreasing on the interval (-∞, √5) and increasing on the interval (√5, ∞).
(e) To determine the intervals of concavity, we examine the sign of the second derivative of f. If f''(x) > 0, then f is concave upward, and if f''(x) < 0, then f is concave downward. If f''(x) = 0, then the concavity changes. Thus, we set f''(x) > 0 and f''(x) < 0 and solve for x. We get f''(x) > 0 when x > 0 and f''(x) < 0 when x < 0.
Therefore, f is concave upward on (0, ∞) and concave downward on (-∞, 0).
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Please help I need it ASAP, also needs to be rounded to the nearest 10th
Answer: AB = 16.4
Step-by-step explanation:
You can use tan x = opposite/adjacent
tan 38 = AB/21
21 tan 38 = AB
AB = 16.4
Determine the equation of the circle graphed below.
Answer:
(x-4)^2+(y-1)^2=9
Step-by-step explanation:
diameter = 6
radius = diameter/2 = 3
center (h,k) = (4,1)
standard equation of a circle (x-h)^2 + (y-k)^2=r^2
(x-4)^2+(y-1)^2=9
Which function is increasing and has a domain of (1,infiniti)?
A. F(x) = log(x - 1) + 2
B. F(x) = -log(x - 2) + 1
C. F(x) = -log(x - 1) + 2
D. F(x) = log(x - 2) + 1
The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.
To determine the increasing function with the specified domain, let's analyze each option:
A. F(x) = log(x - 1) + 2
This function is increasing because the logarithm of a positive number is always increasing. The domain is (1, infinity), which matches the requirement.
B. F(x) = -log(x - 2) + 1
This function is decreasing because the negative sign in front of the logarithm inverts the increase. The domain is (2, infinity), which does not match the requirement.
C. F(x) = -log(x - 1) + 2
This function is also decreasing because of the negative sign in front of the logarithm. The domain is (1, infinity), which matches the requirement, but the function is not increasing.
D. F(x) = log(x - 2) + 1
This function is increasing because the logarithm of a positive number is always increasing. However, the domain is (2, infinity), which does not match the requirement.
The function that is increasing and has a domain of (1, infinity) is A. F(x) = log(x - 1) + 2.
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Answer Immeditely Please
Answer:
√429.
Step-by-step explanation:
Triangles BCD and ABC are similar, so corresponding sides are in the same ratio, so:
x/ AC = DC/x
x/39 = 11/x
x^2 = 11*39
x^2 = 429
x = √429
A person was driving their car on an interstate highway
and a rock was kicked up and cracked their windshield
on the passenger side.
The driver wondered if the rock was equally likely to
strike any where on the windshield, what the probability
was that it would have cracked the windshield in his line
of site on the windshield. Determine this probability,
provided that the windshield is a rectangle with the
dimensions 28 inches by 54 inches and his line of site
through the windshield is a rectangle with the
dimensions 30 inches
by 24 inches.
a) 0. 373
b) 0. 139
c) 0. 423
d) 0. 476
There is about a 47.62% or 0.476 chance that the rock hit the windshield in the driver's line of sight. Option D.
To determine the probability that the rock hit the driver's line of sight on the windshield, we need to compare the area of the driver's line of sight rectangle to the total area of the windshield rectangle.
The area of the windshield rectangle is:
A1 = 28 in x 54 in = 1512 sq in
The area of the driver's line of sight rectangle is:
A2 = 30 in x 24 in = 720 sq in
Therefore, the probability that the rock hit the driver's line of sight on the windshield is:
[tex]P= \frac{A2}{A1}= \frac{720 \:sq in}{1512 \:sq in }[/tex] = 0.476 or 47.6%
So, there is about a 47.62% chance that the rock hit the windshield in the driver's line of sight.
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The demand function for an exclusive wool blanket is given byp=D(x)=33-2√x dollars, where x is in thousands of blankets. Findthe level of production for which the demand is elastic
To maximize the company's profit, we need to find the profit function and then differentiate it with respect to the quantities produced by each plant to find the optimal values.
The profit function is given by:
π = TR - TC
where TR is the total revenue and TC is the total cost.
Using the demand function p = 40 - 0.04q, we can express the total revenue as:
TR = p * q = (40 - 0.04q) * q = 40q - 0.04q²
The total cost is the sum of the costs of each plant, so we have:
TC = C1 + C2 = 6.7 + 0.03q1² + 7.9 + 0.04q2² = 14.6 + 0.03q1² + 0.04q2²
Substituting these expressions into the profit function, we get:
π = 40q - 0.04q² - 14.6 - 0.03q1² - 0.04q2²
To find the optimal values of q1 and q2, we differentiate the profit function with respect to each quantity and set the derivatives equal to zero:
∂π/∂q1 = 40 - 0.06q1 - 0.04q2 = 0
∂π/∂q2 = 40 - 0.03q2 - 0.04q1 = 0
Solving these equations, we get:
q1 = 357.14
q2 = 285.71
So each plant should produce 357.14 and 285.71 units of the item, respectively, in order to maximize the company's profit.
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Suppose you carry out a significance test of h0: μ = 8 versus ha: μ > 8 based on sample size n = 25 and obtain t = 2.15. find the p-value for this test. what conclusion can you draw at the 5% significance level? explain.
a the p-value is 0.02. we reject h0 at the 5% significance level because the p-value 0.02 is less than 0.05.
b the p-value is 0.02. we fail to reject h0 at the 5% significance level because the p-value 0.02 is less than 0.05.
c the p-value is 0.48. we reject h0 at the 5% significance level because the p-value 0.48 is greater than 0.05.
d the p-value is 0.48. we fail to reject h0 at the 5% significance level because the p-value 0.48 is greater than 0.05.
e the p-value is 0.52. we fail to reject h0 at the 5% significance level because the p-value 0.52 is greater than 0.05.
We can draw at the 5% significance level, the p-value is 0.02. we reject h0 at the 5% significance level because the p-value 0.02 is less than 0.05. The correct answer is a.
To find the p-value, we need to find the area to the right of t = 2.15 under the t-distribution curve with 24 degrees of freedom (df = n - 1 = 25 - 1 = 24). Using a t-table or a calculator, we find that the area to the right of t = 2.15 is approximately 0.02.
Since the p-value (0.02) is less than the significance level (0.05), we reject the null hypothesis H0: μ = 8 and conclude that there is sufficient evidence to support the alternative hypothesis Ha: μ > 8 at the 5% significance level. This means that we can say with 95% confidence that the true population mean is greater than 8.
Therefore the correct answer is a.
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A set of 9 books has 5,481 pages.
How many pages would be in each
book, if each book has the same
number of pages.
Answer:
609 pages
Hope this helps!
Step-by-step explanation:
9 books = 5481 pages
1 book = ? pages
9 books ÷ 9 = 1 book so 5481 pages ÷ 9 = 609 pages
1 book has 609 pages.
Robert got home from school at twenty-seven minutes to four in the afternoon. He decided to bake muffins as an after-school snack. The muffins were ready at two minutes to four in the afternoon. How long did it take to prepare and bake the muffins?
Assuming that the muffins were actually ready at two minutes to five in the afternoon, we can determine that it took Robert approximately 38 minutes to prepare and bake the muffins.
To arrive at this conclusion, we can use the following logic:
Robert got home from school at 3:33 PM (twenty-seven minutes before 4:00 PM).
The muffins were ready at 4:58 PM (two minutes before 5:00 PM).
Therefore, the time between when Robert got home and when the muffins were ready is 85 minutes (58 minutes + 27 minutes).
Since Robert decided to bake the muffins immediately upon arriving home, it took him 85 minutes to prepare and bake them.
Of course, this assumes that Robert did not take any breaks or perform other activities during the time between getting home and the muffins being ready. In reality, the actual time it took to prepare and bake the muffins may have been longer or shorter depending on various factors, such as the recipe, equipment used, and Robert's baking experience.
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A random sample of 13 $1 Trifecta tickets at a local racetrack paid a mean amount of $52. 23 with a sample standard deviation of $3. 35. Is there sufficient evidence to conclude that the average Trifecta winnings exceed $50? Use a 10% significance level and assume the distribution is approximately normal.
What is the critical value?
The critical value for the given problem is 1.282.
To determine if there's sufficient evidence that the average Trifecta winnings exceed $50, follow these steps:
1. State the hypotheses:
H0: µ ≤ $50 (null hypothesis)
H1: µ > $50 (alternative hypothesis)
2. Choose the significance level:
α = 0.10
3. Calculate the test statistic (t-score):
t = (sample mean - population mean) / (sample standard deviation / √sample size)
t = ($52.23 - $50) / ($3.35 / √13)
t ≈ 2.15
4. Determine the critical value:
Using a t-distribution table or calculator, find the critical value for a one-tailed test with 12 degrees of freedom (13-1) and α = 0.10. The critical value is 1.282.
5. Compare the test statistic to the critical value:
Since the test statistic (2.15) is greater than the critical value (1.282), we reject the null hypothesis.
In conclusion, there is sufficient evidence to conclude that the average Trifecta winnings exceed $50 at a 10% significance level.
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Complete question:
A random sample of 13 $1 Trifecta tickets at a local racetrack paid a mean amount of $52. 23 with a sample standard deviation of $3. 35. Is there sufficient evidence to conclude that the average Trifecta winnings exceed $50? Use a 10% significance level and assume the distribution is approximately normal.What is the critical value?
Below is attached t-table image:
!!I need help seriouslyyy!!
The average cost per day for the four service is $3.23 per day
What is average cost?Average cost refers to the per-unit cost of production, which is calculated by dividing the total cost of production by the total number of units produced.
Therefore average cost = total cost/ number of unit
total cost = $108
average cost for the three services = $108/3
= $36
total average cost = $36+$54.30
= $90.30
therefore average cost for a day will be average cost for a month over 28day i.e 7days ×4
= 90.30/28
= $3.23 per day
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Solve (d-8) (6d-3) using the box method show work
6d^2 - 51d + 24
that's it
...............................
Can someone explain ._.
The mark-up value percentage is 25 %
Given data ,
The markup amount is the selling price minus the cost price, so:
Markup = $8630 - $6900 = $1730
The markup percentage is the markup amount divided by the cost price, expressed as a percentage:
Markup percentage = (Markup / Cost price) x 100%
Markup percentage = ($1730 / $6900) x 100%
Markup percentage = 0.25 x 100%
Markup percentage = 25%
Hence , the markup percentage is 25%
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Triangle Z Y X is shown with its exterior angles. Point Z extends to point L, point X extends to point N, and point Y extends to point M.
Analyze the diagram to complete the statements.
The m∠MXN is
the m∠YZX.
The m∠LZX is
the m∠ZYX + m∠YXZ.
The m∠MYL is
180° − m∠ZYX.
The completed statements, obtained from the relationship between the exterior angles of a triangle and supplementary angles are;
The m∠MXN is greater than m∠YZX
The m∠LZX is equal to m∠ZYX + m∠YXZ
The m∠MYL is equal to 180° - m∠ZYX
What are supplementary angles?Supplementary angles are angles that form a linear pair and when added together are equivalent to 180°
The exterior angle of a triangle theorem indicates, that we get;
m∠MXN = m∠YZX + m∠ZYX
Therefore; m∠MXN > m∠YZXm∠LZX = m∠ZYX + m∠YXZ∠MYL is a supplementary angle to the angle ∠ZYX
Therefore; m∠MYL + m∠ZYX = 180°
m∠MYL = 180° - m∠ZYXThe completed statements are therefore;
m∠MXN is greater than m∠YZX
m∠LZX equal to m∠ZYX + m∠YXZ
m∠MYL equal to 180° - m∠ZYX
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Domain of the rational function.
(5x^2)/(1-x)
Answer:
(-∞, 1) ∪ (1, ∞)
Step-by-step explanation:
1 - x = 0
-x = -1
x = 1
In interval notation, the domain is (-∞, 1) U (1, ∞)
This wooden frame is made of three planks of wood attached with glue and nails. The wood will be painted with emulsion paint which takes 80ml of paint per metre of wood. Calculate the amount of paint needed to cover all the wood
amount of paint needed to cover all the wood in the frame, we need to first determine the total length of the wood in meters. Let's assume that each plank of wood is 1 meter long, so the total length of wood in the frame is 3 meters.
Next, we need to calculate the amount of paint required per meter of wood. The problem states that 80ml of emulsion paint is needed per meter of wood. So, we can multiply 80ml by 3 meters to get the total amount of paint needed for the entire frame.
80ml/meter x 3 meters = 240ml
Therefore, we need 240ml of emulsion paint to cover all the wood in the frame.
It is important to note that this calculation assumes that only one coat of paint will be applied to the wood. If multiple coats are desired, the amount of paint required will need to be adjusted accordingly.
In conclusion, to paint the wooden frame made of three planks of wood attached with glue and nails, we would need 240ml of emulsion paint.
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Solid metal support poles in the form of right cylinders are made out of metal with a
density of 6.3 g/cm³. This metal can be purchased for $0.30 per kilogram. Calculate
the cost of a utility pole with a diameter of 42 cm and a height of 740 cm. Round your
answer to the nearest cent. (Note: the diagram is not drawn to scale)
Answer:Therefore, the cost of a utility pole with a diameter of 42 cm and a height of 740 cm is approximately $1957.43.
Step-by-step explanation:First, we need to calculate the volume of the cylinder-shaped utility pole:
The radius of the pole is half the diameter, so it's 42 cm / 2 = 21 cm.
The height of the pole is 740 cm.
The volume of a cylinder is given by the formula V = πr²h, where π is approximately 3.14, r is the radius, and h is the height.
Substituting the values we have, we get V = 3.14 x 21² x 740 = 1,034,462.4 cm³.
Now we can calculate the mass of the pole:
The density of the metal is 6.3 g/cm³, which means that 1 cm³ of the metal has a mass of 6.3 g.
The volume of the pole is 1,034,462.4 cm³, so its mass is 6.3 x 1,034,462.4 = 6,524,772.72 g.
Next, we convert the mass to kilograms and calculate the cost:
1 kg is equal to 1000 g, so the mass of the pole in kilograms is 6,524,772.72 g / 1000 = 6524.77 kg.
The cost of the metal is $0.30 per kilogram, so the cost of the pole is 6524.77 kg x $0.30/kg = $1957.43.
Help pls. And please actually answer the question
Start with the base graph: y = |x|
Translate the graph one unit to the right: y = |x - 1|
---We use a minus/negative/subtraction sign when dealing with horizontal translations because it is the opposite of the way we want to go. If the translation occurs within parenthesis/absolute value bars, we always do the opposite of what we think we should.
Translate the graph one unit down: y = |x - 1| - 1
---If the translation occurs to the y-value/vertically, we use the expected operation/sign. If the translation occurs outside of parenthesis, we use the same operation/sign as the translation (+ for up, - for down).
Answer: y = |x - 1| - 1
Hope this helps!
Answer:
y=|x-1|-1
Step-by-step explanation:
The function for a v shaped graph is an absolute value function: y=|x|
Subtracting 1 from the absolute value y=|x|, we move the graph 1 unit right of the x axis
Subtracting 1 from the whole equation, y=|x-1|, we move the graph 1 unit down the y axis
So, the equation would be y=|x-1|-1
1. Paula has x cups of food in a container to feed her dogs. She pours 1. 5 cups of food into their bowls. There is now 5. 25 cups left in the container. Which equation would be used to solve this problem?
a. 1. 5 - x = 5. 25
b. 5. 25 - x = 1. 25
c. X - 1. 5= 5. 25
d. X + 1. 5= 5. 25
2. A box of donuts cost $9. You want to send donuts to the local nursing home. Set up an equation to find how many boxes you can send if you have $72.
a. 72 = 9 + b
b. 72 = 9 - b
c. 72 = 9b
d. 72 = 9/b
3. Jordan is purchasing a board to build a bookcase. He wants to divide the board into 1. 75 foot sections and he needs 6 sections. Which equation can be used to solve this problem?
a. B/1. 75 = 6
b. 1. 75b = 6
c. B - 1. 75 = 6
d. B + 1. 75 = 6
The correct option for each individual question is c. X - 1. 5= 5. 25, c. 72 = 9b and B/1.75 = 6.
1. Total food = poured food + remaining food
Keep the values in formula
x = 1.5 + 5.25
Rearranging the equation
x - 1.5 = 5.25
Thus, correct option is c. X - 1. 5= 5. 25
2. Cost of one box × number of boxes = total cost
9 × number of boxes = 72
Let us represent the number of boxes as b. So,
9b = 72
Hence, correct option is c. 72 = 9b.
3. Length of each section × number of sections = total length of bookcase sections
Let us represent total length of bookcase sections as B
1.75 × 6 = B
Rearranging the equation
B/1.75 = 6
So, the correct option is a. B/1. 75 = 6.
Thus, correct option are c. X - 1. 5= 5. 25, c. 72 = 9b and B/1.75 = 6.
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The thickness of paper manufactured at a manufacturing company is roughly symmetrical with a mean of 0. 0039 inch and a standard deviation of about 0. 00001 inch. A marketing manager wants to divide the values of the thickness of paper by 0. 0001 to make the values easier to manage.
What are the mean and standard deviation of the thickness of paper after dividing by 0. 0001?
The mean is ?
inch.
The standard deviation is ?
inch
The mean of the thickness of paper is 39 inches, and the standard deviation is 0.1 inches.
To find the mean and standard deviation of the thickness of paper after dividing by 0.0001, you should follow these steps:
1. Divide the mean by 0.0001:
Mean after dividing = 0.0039 inches / 0.0001
Mean after dividing = 39 inches
2. Divide the standard deviation by 0.0001:
Standard deviation after dividing = 0.00001 inches / 0.0001
Standard deviation after dividing = 0.1 inches
The mean of the thickness of paper after dividing by 0.0001 is 39 inches, and the standard deviation is 0.1 inches.
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Please upload a picture of a piece of paper with the problem worked out, and draw the graph for extra points, there will be 6 of these, so go to my profile and find the rest, and do the same, for extra points. solve this one using the elimination method.
The solution to this system of equations are x = -5 and y = 8.
How to solve these system of linear equations?In order to determine the solution to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
x + y = 3 .........equation 1.
x - 3y = -29 .........equation 2.
By subtracting equation 2 from equation 1, we have:
(x - x) + (y - (-3y) = 3 - (-29)
y + 3y = 3 + 29
4y = 32
y = 32/4 = 8
x = 3 - y
x = 3 - 8
x = -5
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Question 2 of 10
What are the dimensions of AB?
A. 3x2
B. 3x3
C. 2x3
D. 2 x 2
Answer:
Based on the image, we can see that matrix A is a 3x2 matrix, and matrix B is a 2x3 matrix. In order to multiply matrices A and B, the number of columns in matrix A must match the number of rows in matrix B.
Since matrix A has 2 columns and matrix B has 2 rows, we can multiply them together, resulting in a 3x3 matrix. Therefore, the answer is B. The dimensions of AB are 3x3.
I DONT NEED BRAINLEST JUST STAY FUN AND SAFEAns. (c) 2X3
Dimension of matrix is given by row x column
The circumstances if the base of the cone is 12π cm. If the volume of the cone is 96π, what is the height
Answer:8
Step-by-step explanation:
The figure shows the graphs of the functions y=f(x) and y=g(x). If g(x)=kf(x), what is the value of k? Enter your answer in the box given.
The value of k is -2
Let a line passes through the point [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. Thus the equation of line can be given as,
[tex](y -y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]......Eq.(1)
We have the information from the graph:
The graph of f(x) and g(x) are given in the problem.
The equation given is,
g(x) = k × f(x)
We have to find the value of k and also find the equation of f(x) and g(x).
The line y = f(x) lies on the points, (2,1) and (0,-3). Thus the equation of this line is,
Plug all the values in eq.(1)
[tex](y -(-3))=\frac{-3-1}{0-2}(x-0)[/tex]
[tex]y+3=\frac{-4}{-2}x[/tex]
y + 3 = 2x
y = 2x -3
So, it can be written as:
f(x) = 2x -3
The line y = f(x) lies on the points, (0,6) and (2,-2). Thus the equation of this line is,
[tex](y -6)=\frac{-2-6}{2-0}(x-0)[/tex]
[tex](y-6)=\frac{-8}{2}x[/tex]
(y- 6) = -4x
y = -4x + 6
It can be written as:
g(x) = -4x + 6
The equation given in the problem is:
g(x) = k × f(x)
Put all the values in above given equation:
-4x + 6 = k(2x - 3)
-2(2x - 3) = k × (2x - 3)
Compare the value of k :
k = -2
Hence, The value of k = -2
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For complete question, to see the attachment:
The weekly demand for wireless mice manufactured by Insignia Consumer Electronic
Products group is given by
p(x) = -0.005x + 60, where p denotes the unit price in dollars and x denotes the quantity demanded. The weekly cost
function associated with producing these wireless mice is given by
C(x) = -0.001x^2 + 18x + 4000
Where C(x) denotes the total cost in dollars incurred in pressing x wireless mice (a) Find the production level that will yield a maximum revenue for the manufacturer. What will
be maximum revenue? What price the company needs to charge at that level? (b) Find the production level that will yield a maximum profit for the manufacturer. What will be
maximum profit? What price the company needs to charge at that level?
The production level that will yield maximum revenue is 6000 units, the maximum revenue is $180,000, and the price the company needs to charge at that level is $30. The production level that will yield maximum profit is 5250 units, the maximum profit is $59,250, and the price the company needs to charge at that level is $37.25.
To find the production level that will yield maximum revenue, we need to determine the quantity demanded that maximizes the revenue. The revenue function is given by
R(x) = xp(x) = x(-0.005x + 60) = -0.005x^2 + 60x
To find the maximum value of R(x), we need to take the derivative of R(x) and set it equal to zero
R'(x) = -0.01x + 60 = 0
x = 6000
So the production level that will yield maximum revenue is 6000 units.
To find the maximum revenue, we can plug this value into the revenue function
R(6000) = -0.005(6000)^2 + 60(6000) = $180,000
To find the price the company needs to charge at that level, we can plug the production level into the demand function
p(6000) = -0.005(6000) + 60 = $30
To find the production level that will yield maximum profit, we need to determine the quantity that maximizes the profit function. The profit function is given by
P(x) = R(x) - C(x) = -0.005x^2 + 60x - (-0.001x^2 + 18x + 4000) = -0.004x^2 + 42x - 4000
To find the maximum value of P(x), we need to take the derivative of P(x) and set it equal to zero
P'(x) = -0.008x + 42 = 0
x = 5250
So the production level that will yield maximum profit is 5250 units.
To find the maximum profit, we can plug this value into the profit function
P(5250) = -0.004(5250)^2 + 42(5250) - 4000 = $59,250
To find the price the company needs to charge at that level, we can plug the production level into the demand function
p(5250) = -0.005(5250) + 60 = $37.25
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The inventory at the end of the year was understated by $14,750:
(A) Did the error cause an overstatement or an understatement of the gross profit for the year? Why?
(B) Which items on the balance sheet at the end of the year were overstated or understated as a result of the error?
The error caused an understatement of the gross profit for the year, as the cost of goods sold was overstated by $14,750.
The error in inventory caused an understatement of the inventory value on the balance sheet, which in turn caused an overstatement of the cost of goods sold. This is because the cost of goods sold is calculated by subtracting the cost of the ending inventory from the cost of goods available for sale.
Therefore, an understatement of the ending inventory leads to an overstatement of the cost of goods sold, which ultimately results in an understatement of the gross profit. None of the other items on the balance sheet are directly affected by the error in inventory.
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Analyzing Solution Sets to Linear Equations with the Variable on Both Sides
2x + 5 = 3 + 2(x + 1)
Answer: it will need to be rewritten so that the variable is only on one side of the equation
Step-by-step explanation:f the equation contains fractions, you may elect to multiply both sides of the equation by the least common denominator
A particle moves along the x-axis so that its position at time t>0 is given by
X(t) = (t^2 - 9)/(3t^2 + 8)
A) show that the velocity of the particle at time this given by v(t) = 70t/(3t^2 + 8)^2
B) is the particle moving toward the origin or away from the originator time t = 2? Give a reason for your answer.
C) The acceleration of the particle is given by £(t). Write an expression for £(t), and find the value of £(2).
D) What position does the particle approach as t approaches infinity?
The velocity of the particle at time t is given by [tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
The expression for the acceleration of the particle is a(t) [tex]= (210t^2 + 1120)/(3t^2+8)^3.[/tex]
A) To find the velocity of the particle, we need to take the derivative of its position with respect to time:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
[tex]v(t) = dX/dt = [(2t)(3t^2+8) - (t^2-9)(6t)]/(3t^2+8)^2[/tex]
[tex]v(t) = (6t^3 + 16t - 6t^3 + 54t)/(3t^2 + 8)^2[/tex]
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
Therefore, the velocity of the particle at time t is given by[tex]v(t) = 70t/(3t^2 + 8)^2.[/tex]
B) To determine whether the particle is moving toward or away from the origin at time t = 2, we need to examine the sign of the velocity v(2). Plugging t = 2 into the expression for v(t), we get:
[tex]v(2) = 70(2)/((3(2)^2 + 8)^2) = 280/169[/tex]
Since v(2) is positive, the particle is moving away from the origin at time t = 2.
C) The acceleration of the particle is given by the derivative of its velocity with respect to time:
[tex]v(t) = 70t/(3t^2 + 8)^2[/tex]
[tex]a(t) = dv/dt = (70(3t^2+8)^2 - 2(70t)(2t)(3t^2+8))/(3t^2+8)^4[/tex]
[tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]
Therefore, the expression for the acceleration of the particle is [tex]a(t) = (210t^2 + 1120)/(3t^2+8)^3[/tex]. To find the value of a(2), we plug in [tex]t = 2:a(2) = (210(2)^2 + 1120)/(3(2)^2+8)^3 = 175/677[/tex]
D) To find the position that the particle approaches as t approaches infinity, we examine the behavior of X(t) as t gets very large. We can do this by looking at the leading term of the numerator and denominator of X(t) as t approaches infinity:
[tex]X(t) = (t^2 - 9)/(3t^2 + 8)[/tex]
As t approaches infinity, the numerator is dominated by the t^2 term, and the denominator is dominated by the 3t^2 term. Therefore, as t approaches infinity, X(t) approaches:
[tex]X(infinity) = t^2/3t^2 = 1/3[/tex]
So the particle approaches the point x = 1/3 as t approaches infinity.
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Please Answer ASAP! PLEEEASE
Answer Fully Please And Fill IN THe Blanks!
also you will get allot of points
It is a fifth order polynomial
The constant term is -7
The leading term is [tex]x^5/7[/tex]
The coefficient of the leading term is [tex]1/7[/tex]
What is the leading term of a polynomial?The term with the highest degree—i.e., the term with the largest power of the variable—is the leading term. The leading coefficient is the leading term's coefficient.
We frequently rearrange polynomials so that the powers are descending or ascending because of the definition of the "leading" term. We can see that the leading term in the expression here is [tex]x^5/7[/tex].
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