The percentage rate of change per day is approximately 0.1932%.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To represent the number of users on the website after t years, we can use the exponential growth formula:
[tex]N_t = N_0 \times e^{rt}[/tex]
where [tex]N_0[/tex] is the initial number of users, r is the growth rate, and t is the time in years.
Given that [tex]N_0[/tex] = 6300 and the growth rate is 73%, or 0.73, per year,
The function is:
[tex]N_t = 6300 \times e^{0.73t}[/tex]
To find the percentage rate of change per day, we can use the formula:
[tex]r = (e^{0.73/365} - 1) \times 100%[/tex]
where 0.73/365 is the daily growth rate.
Solving for r, we get:
[tex]r = (e^{0.73/365} - 1)[/tex] x 100%
r ≈ 0.1932%
Therefore,
The percentage rate of change per day is approximately 0.1932%.
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Find g(x), where g(x) is the translation 5 units right of f(x)= – 7(x–5)2+3.
g(x) is the translation 5 units right of f(x)= – 7(x–5)²+3.
A function called f(x) accepts an input of "x" and outputs "y". You can write it out as y = f. (x).‘x’ is a variable that represents an input to a function.
To translate a function, we need to replace x with (x-a) in the function f(x) where ‘a’ is the amount of translation.
To translate a function 5 units right, we need to replace x with (x-5) in the function f(x).
So, g(x) = f(x-5) = -7(x-5-5)²+ 3 = -7(x-10)²+ 3.
Therefore, g(x) is the translation 5 units right of f(x)= – 7(x–5)²+3.
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Find the missing side lengths. Leave your answers as radicals in simplest form
Answer:
[tex]u = \frac{2 \sqrt{6} }{3} [/tex]
[tex]v = \frac{ \sqrt{6} }{3} [/tex]
Step-by-step explanation:
Use trigonometry:
[tex] \tan(60°) = \frac{ \sqrt{2} }{v} [/tex]
Use the property of proportion to find v:
[tex]v = \frac{ \sqrt{2} }{ \tan(60°) } = \frac{ \sqrt{2} }{ \sqrt{3} } = \frac{ \sqrt{2} \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } = \frac{ \sqrt{6} }{3} [/tex]
Use the Pythagorean theorem to find u:
[tex] {u}^{2} = {v}^{2} + ( { \sqrt{2} )}^{2} [/tex]
[tex] {u}^{2} = ( { \frac{ \sqrt{6} }{3}) }^{2} + ( { \sqrt{2} )}^{2} = \frac{6}{9} + \frac{2}{1} = \frac{6}{9} + \frac{2 \times 9}{9} = \frac{6}{9} + \frac{18}{9} = \frac{24}{9} = \frac{8}{3} [/tex]
[tex]u > 0[/tex]
[tex]u = \sqrt{ \frac{8}{3} } = \frac{2 \sqrt{6} }{3} [/tex]
Lydia is buying a house and looking at blueprints to make his decision. If each 4 cm on the scale drawing below is equal to 8 feet, what is the area of the living room? The rectangular scale drawing of the living room has a length of 12 centimeters and a width of 12 centimeters.
So the area of the living room on the scale drawing is 334128.48 square centimeters.
What is area?Area is a measure of the size of a two-dimensional surface or region, typically expressed in square units. It is the amount of space inside a flat, enclosed shape or surface, and is calculated by multiplying the length and width of the shape or surface. For example, the area of a rectangle can be calculated by multiplying its length by its width, while the area of a circle can be calculated by multiplying pi (3.14) by the square of its radius. Area is a fundamental concept in mathematics and is used in a wide range of fields, from geometry and physics to engineering and architecture.
Here,
First, we need to determine the actual dimensions of the living room. Since each 4 cm on the scale drawing is equal to 8 feet, we can set up a proportion:
4 cm : 8 feet = 12 cm : x
Solving for x, we get:
x = (12 cm x 8 feet) / 4 cm
= 24 feet
So the actual length and width of the living room are 24 feet and 24 feet, respectively.
The area of the living room is then:
Area = length x width
= 24 feet x 24 feet
= 576 square feet
Now, we need to determine the area of the living room on the scale drawing. Since the length and width of the scale drawing are both 12 cm, the area is:
Area = length x width
= 12 cm x 12 cm
= 144 square cm
Finally, we can determine the scale factor for the area by dividing the actual area by the scale area:
Scale factor = actual area / scale area
= 576 square feet / 144 square cm
Since we need the area in square centimeters, we can convert square feet to square centimeters by multiplying by 929.03:
Scale factor = (576 square feet / 144 square cm) x (929.03 square cm/square feet)
= 2324.12
Therefore, the area of the living room on the scale drawing is:
Area = scale area x scale factor
= 144 square cm x 2324.12
= 334128.48 square cm
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72x5/12=blankx5x1/12=blank x 1=360/12=blank
Answer:
Step-by-step explanation:
Starting with 72x5/12:
72x5/12 = (72/12) x 5 (simplifying the fraction)
= 6 x 5
= 30
Now, we have:
30 = ?x5x1/12
Multiplying both sides by 12, we get:
30 x 12 = ? x 5 x 1
360 = ? x 5
Dividing both sides by 5, we get:
72 = ?
Therefore, the missing value is 72.
If agent D was able to reduce their average Handling Time by 10% what would thier average handling time be
The new average handling time for Agent D would be 90% of their original handling time.
What are Percentages?A percentage is a way of expressing a number as a fraction of 100. It is typically represented using the percent sign (%) and is often used to describe the amount or proportion of something in relation to a whole. Percentages are commonly used in a variety of fields, such as finance, mathematics, and statistics.
Let's say the original average handling time for Agent D was "x" units (e.g. seconds, minutes, etc.). If Agent D was able to reduce their average handling time by 10%, their new average handling time would be:
New average handling time = x - 0.1x
Simplifying the expression on the right-hand side:
New average handling time = 0.9x
Therefore, the new average handling time for Agent D would be 90% of their original handling time.
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A company makes two kinds of engineering pencils , Type I and Type II ( deluxe ) . Type I needs 2 min of sanding and 6 min of olishing . Type needs 5 min of sanding and 3 min of polishing . The sander can run no more than 66 hours per week and the olisher can run no more than 73 hours a week . A $ 3 profit is made on Type I and $ 5 profit on Type II . How many of each type be made to maximize profits ?
After solving by linear programming, the business needs create 100 Type I pencils and 80 Type II pencils to increase revenue.
LINEAR PROGRAMMING: WHAT IS IT?
A mathematical method called linear programming is used to maximise a linear objective function under the restrictions of linear equality and inequality. In a mathematical model whose requirements are expressed by linear connections, it is used to identify the best result.
With linear programming, this issue can be resolved.
Please define x as the quantity of Type I pencils produced and y as the quantity of Type II pencils produced.
Profit = 3x + 5y is the formula for the goal function.
2x + 5y 660 are the restrictions (sanding constraint)
(Polishing constraint): x ≥0 y≥ 0; 6x + 3y 730
Under these limitations, we wish to maximize the profit function.
The largest profit comes when x = 100 and y = 80,
with a profit of $740, according to software that can solve linear programming issues or a graphing calculator.
Thus, the business needs create 100 Type I pencils.80pencil for type II
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Are these ratios equivalent?
6 teal sweatshirts to 8 purple sweatshirts
15 teal sweatshirts to 13 purple sweatshirts
True
False
Answer:
False
Step-by-step explanation:
Purple: 13÷8= 1.625
Teal: 15÷6= 2.5
The ratios don't have the same scale factor. Therefore they are not equivalent fractions.
Samantha sells tomatoes at a farmer's market. She uses 15 to 60 gallons of water each week to water her tomato plants. She measured the number of tomatoes produced each week and noticed that the amount of water given to the plants impacts the amount of tomatoes they produce.
What are the domain, independent and dependent variables in this situation?
a.) 15 to 60 gallons of water
b.) gallons of water used
c.) number of tomato plants
d.) number of tomatoes produced
e.) 0 to 60 gallons of water
f.) price per tomato sold
Domain: ?
Independent variable: ?
Dependent variable: ?
Samantha waters her tomato plants once a week with between 15 and 60 gallons of water.
15 to 60 gallons of water are the domain.Gallons of utilized water is an independent variable.The number of tomatoes produced is a dependent variable.Domain refers to the set of possible values that the independent variable can take. In this case, the domain is the range of possible amounts of water that Samantha can use to water her tomato plants, which is 15 to 60 gallons.
The independent variable is the variable that is being manipulated or controlled by Samantha, which in this case is the amount of water used to water the tomato plants. So, the independent variable is "gallons of water used".
The dependent variable is the variable that is being measured or observed, which in this case is the number of tomatoes produced each week. So, the dependent variable is the "number of tomatoes produced".
Therefore, the answer is:
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Which system of equations represents the graph?
y = 3x - 5 and 2x + 4y = 8
y = 3x - 5 and 4x + 2y = 8
y = 2x - 5 and 4x + 2y = 8
y = 2x - 5 and 2x + 4y = 8
Part B
What is the apparent solution to the system of equations in the graph?
(1, 2)
(2, 1)
(4, 0)
(0, 2)
Part A: The system of equations represented by the graph: y = 3x - 5 and 2x + 4y = 8.
Part B: The solution of the system of equations : (2, 1).
Explain about the system of equations:Determining the significance of the variables employed in a system of equations entails solving the set of equations.
A specific system of equations may have a variety of solutions,
unique responseNo remedythere are several optionsLet's examine three approaches to solving a set of equations, presuming that they are linear equations with two variables.
Method of Substitution Method of EliminationGraphical ApproachFrom the graph shown.
The blue line shows the equation: 2x + 4y = 8
At x =0, y= 2
At y =0, x = 4
Red line shows the equation: y = 3x - 5
At x = 0, y = -5.
Part B: solution to the system of equations.
From the graph, where two lines intersect is the solution of the system of equations.
That is point (2,1).
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The function f(x) = 3x + 13 x + 4 1 is a transformation of the function g(x) = r(x) To make the transformation visible, rewrite the rule for f in the form f(x) = q (x) + d (r) where q, r, and d are polynomials.
The rule for f in the desired form is: f(x) = (3x^2 + 12x + 13r(x) + 52) / (x + 4)
How to rewrite the rule for f in the formTo rewrite the rule for f in the form f(x) = q(x) + d(r), we need to first write g(x) in terms of r(x).
We know that g(x) = r(x) / (x + 4) + 1, so we can rewrite it as:
g(x) = r(x) / (x + 4) + (x + 4) / (x + 4)
g(x) = (r(x) + x + 4) / (x + 4)
Now, we can see that f(x) is a transformation of g(x) with q(x) = 3x and d(r) = 13. So, we can write:
f(x) = q(x) + d(r)
f(x) = 3x + 13(r(x) + x + 4) / (x + 4)
f(x) = (3x(x + 4) + 13r(x) + 52) / (x + 4)
Therefore, the rule for f in the desired form is: f(x) = (3x^2 + 12x + 13r(x) + 52) / (x + 4)
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Solve the systems by graphing.
Y=1/4 x-5
y=-X+4
Answer: (7.2, -3.2)
Step-by-step explanation:
First, we will graph these equations. See attached. One has a y-intercept of -5 and then moves four units right for every unit up (we get this from the slope of 1/4). The other has a y-intercept of 4, and moves right one unit for every unit down (we get this from the slope of -1).
The point of intersection is the solution, this is the point at which both graphed lines cross each other. Our solution is:
(7.2, -3.2) x = 7.2, y = -3.2
HELP ASAP ASAP PLEASE ASAP HELP BRAINLIEST
The histograms display the frequency of temperatures in two different locations in a 30-day period.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 12 above 80 to 89, at 6 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Desert Landing.
A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 16. A shaded bar stops at 2 above 60 to 69, at 4 above 70 to 79, at 9 above 80 to 89, at 9 above 90 to 99, at 4 above 100 to 109, and at 2 above 110 to 119. The graph is titled Temps in Flower Town.
When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
IQR, because Desert Landing is skewed
IQR, because Desert Landing is symmetric
Range, because Flower Town is skewed
Range, because Flower Town is symmetric
The range, on the other hand, is affected by extreme values and may not be a good representation of the spread of the data in these cases.
What is Histogram ?
A histogram is a graphical representation of the distribution of a dataset. It is a way to display the frequency of occurrence of different values or ranges of values in a dataset.
The correct answer is IQR, because it is more robust to outliers and is not affected by extreme values like Range.
Although the question provides information about the shape of the histograms, it does not indicate whether the distributions are symmetric or skewed. Therefore, the choice of IQR over Range is not based on the shape of the data but on the fact that IQR is a more appropriate measure of variability when dealing with skewed data or data with outliers.
In general, the IQR is a better measure of variability than the range when the data is skewed or contains outliers, as it only considers the middle 50% of the data and is not affected by extreme values.
Therefore, The range, on the other hand, is affected by extreme values and may not be a good representation of the spread of the data in these cases.
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What is the linear inequality of the graph below?
The linear inequality for the shaded region with slope -4 is:
[tex]y < -4x + 4[/tex]
What is linear inequality?In mathematics, a linear inequality is an inequality involving a linear function in one or more variables. It describes a region in the coordinate plane that satisfies the inequality.
What is the slope?In mathematics, the slope is a measure of the steepness of a line. It describes how much a line rises or falls as we move from left to right along it.
According to the given information,
To write the linear inequality for the graph passing through points (0,4) and (1,0), we need to find the equation of the line first.
The slope of the line passing through these two points is:
[tex]m = (y_{2} - y_{1} ) / (x_{2} - x_{1})[/tex]
= (0 - 4) / (1 - 0)
= -4
Using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, we can find the equation of the line passing through these two points:
[tex]y = -4x + 4[/tex]
Now, to write the linear inequality for this line, we need to determine which side of the line is shaded. We can use the test point (0,0) to check which side of the line contains the solutions to the inequality.
If we plug in (0,0) into the equation [tex]y = -4x + 4[/tex], we get:
0 = -4(0) + 4
0 = 4
Since 0 is not less than 4, the point (0,0) is not a solution to the inequality. Therefore, we need to shade the side of the line that does not contain the origin (0,0).
The linear inequality for the shaded region is:
[tex]y < -4x + 4[/tex]
So any point below the line [tex]y = -4x + 4[/tex]satisfies this inequality.
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Calculate five-number summary and construct box and whisker plot from the following data: Ans: 30, 40, 50, 60 & 70; No skewed Daily wages (Rs.) 10-30 30-50 50-70 70-90 90-110 110-130 130-150 No. of workers 53 85 56 4 3 21 16 Aus: 10 150-170 2
Five-number summary: Minimum = 30, Q1 = 35, Median = 50, Q3 = 65, Maximum = 70. Bοx and whisker plοt: Bοx spans frοm 35 tο 65 with median at 50, whiskers extend frοm 30 tο 70, nο οutliers.
What are the steps tο calculate five-number summary and cοnstruct a bοx and whisker plοt?Tο find the five-number summary and cοnstruct a bοx and whisker plοt, we need tο first οrganize the given data in ascending οrder:
30, 40, 50, 60, 70
The five-number summary cοnsists οf the minimum value, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum value.
Minimum value: 30
Q1 (first quartile): the median οf the lοwer half οf the data set, which is (30 + 40)/2 = 35
Median (Q2): the middle value οf the data set, which is 50
Q3 (third quartile): the median οf the upper half οf the data set, which is (60 + 70)/2 = 65
Maximum value: 70
Sο, the five-number summary is:
Minimum = 30
Q1 = 35
Median = 50
Q3 = 65
Maximum = 70
To construct a box and whisker plot, we draw a number line that includes the range of the data (from the minimum value to the maximum value), and mark the five-number summary on the number line. Then we draw a box that spans from Q1 to Q3, with a vertical line inside the box at the median (Q2). In addition, we draw "whiskers" from the box to the minimum and maximum values.
The box and whisker plot for the given data is as follows:
20 40 60 80 100
|----------|----------|----------|----------|
+-----+
| |
| |
| |
| |
+-----+
The box spans from 35 to 65, with a vertical line inside the box at 50. The whiskers extend from 30 to 70. There are no outliers in the data, so there are no points beyond the whiskers.
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A map has a scale of 1 cm : 275 miles. On the map, the distance between two towns is 3 cm. What is the actual distance between the two towns ?
Answer:
825 miles
Step-by-step explanation:
275 x 3 = 825
Helping in the name of Jesus.
The Griffins bought a $292,000 house. They made a down payment of $48,000 and took out a mortgage for the rest. Over the course of 30 years they
monthly payments of $1462.91 on their mortgage until it was paid off.
Question 13
(a) What was the total amount they ended up paying for the house (including
the down payment and monthly payments)?
$
(b) How much interest did they pay on the mortgage?
$
The Griffins ended up paying a total of $575,647.60 for the house. The Griffins paid a total of $331,647.60 in interest over the 30-year period
What is interest rate?Interest rate refers to the percentage of the principal amount charged by a lender to a borrower for the use of money over a certain period of time.
According to question:(a) The total amount they ended up paying for the house can be calculated by adding the down payment to the total amount paid in monthly mortgage payments over the 30-year period:
Total amount paid = down payment + (monthly payment x number of payments)
Number of payments = 30 years x 12 months/year
= 360
Total amount paid = $48,000 + ($1462.91 x 360)
= $48,000 + $527,647.60
= $575,647.60
Therefore, the Griffins ended up paying a total of $575,647.60 for the house.
(b) The total amount of interest paid on the mortgage can be calculated by subtracting the amount borrowed (i.e., the purchase price minus the down payment) from the total amount paid over the 30-year period:
Total interest paid = total amount paid - amount borrowed
Amount borrowed = $292,000 - $48,000 = $244,000
Total interest paid = $575,647.60 - $244,000 = $331,647.60
Therefore, the Griffins paid a total of $331,647.60 in interest over the 30-year period.
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The sale price of a backpack is $3, it’s 85% off
Answer:
The answer to your question is $2.55
Step-by-step explanation:
85% × $3 = $2.55
With original price $3 and 85% off,
Final price: $0.45
Saved amount: $2.55
I hope this helps and have a wonderful day!
Answer:0.45
Step-by-step explanation:
Purchase Price:
$3
Discount:
(3 x 85)/100 = $2.55
Final Price:
3 - 2.55 = $0.45
Divide the following 11/15by 7/18
Answer:
4567
578९=8877
5790=9766
Answer:
11/15 : 7/18 = 15 / 11 : 18 / 7= 270 / 77
Step-by-step explanation:
You met Jonathan while waiting for your plane in the airport at Brownsville. He is
working in the marketing research department for a company that manufactures
and sells memory chips for microcomputers. He has established the following price-
demand and revenue functions:
P(x) = 75 - 3x
R(x) = x P(x)
Where P(x) is the wholesale price in dollars at which x million chips can be
sold, and R(x) is in millions of dollars. Both functions have a domain 1 ≤ x ≤
20.
a) Jonathan wants to sketch a graph of the revenue function in a rectangular
coordinate system.
b) Jonathan wants to find the value of x that will produce the maximum
revenue. He wants also to find the maximum revenue.
c) Finally, he wants to know the wholesale price per chip that produces the
maximum revenue?
a. The revenue function R(x) = 75x - 3x² graph plotted below.
b. Value of x is 12.5 and maximum revenue produces $468.75
c. Wholesale price/chip that produces the maximum revenue is $37.50
Define the term revenue?A company's or business's revenue is the total amount of money it receives from sales of its products or services over a given time period.
a) To sketch a graph of the revenue function R(x), we first need to calculate R(x) using the given formula:
⇒ R(x) = x P(x)
⇒ R(x) = x(75 - 3x)
⇒ R(x) = 75x - 3x²
Now we can plot this function on a rectangular coordinate system. Below is an sketch of the graph.
b) Taking the derivative of R(x) and setting it equal to 0:
⇒ R'(x) = 75 - 6x = 0
⇒ 6x = 75
⇒ x = 12.5
So, x = 12.5 is the value of x that will produce the maximum revenue. To find the maximum revenue, we can substitute x = 12.5 into the revenue function R(x) = x (75 - 3x)
⇒ R(12.5) = 12.5 (75 - 3 (12.5)) = 468.75
⇒ R(12.5) = $ 468.75
Therefore, the maximum revenue is $468.75
c) To find the wholesale price per chip that produces the maximum revenue, we can substitute x = 12.5 into the price function, P(x) = 75 - 3x
⇒ P(12.5) = 75 - 3(12.5)
⇒ P(12.5) = $37.50 per chip
Therefore, the wholesale price per chip that produces the maximum revenue is $37.50.
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Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 2 + sin(x), 0 ≤ x ≤ with n = 8.
The top and lower sums for n =2,4, and 8 and f(x) = 2 +sin(x),0 x are as follows:
n = 2: Upper Sum = 7.85398; Lower sum ≈ 7.85398
n = 4: Upper sum ≈ 6.43917; Lower sum ≈ 6.43917
n = 8: Upper sum ≈ 6.35258; Lower sum ≈ 6.352
It is necessary to first divide the range [0, ] into n subintervals of identical width x, where x = ( - 0)/n = /n, in order to calculate the upper and lower sums for the equations f(x) = 2 + sin(x), 0 x for n = 2, 4, and 8. The endpoints of these subintervals are:
x0 = 0, x1 = Δx, x2 = 2Δx, ..., xn-1 = (n-1)Δx, xn = π.
Then, for each subinterval [xi-1, xi], we can approximate the area under the curve by the area of a rectangle whose height is either the maximum or minimum value of f(x) on that interval. The sum of these areas' overall subintervals gives us the upper and lower sums.
For n = 2:
Subintervals: [0, π/2], [π/2, π]Width of subintervals: Δx = π/2Maximum values of f(x) on each subinterval:[0, π/2]: f(π/2) = 2 + sin(π/2) = 3
[π/2, π]: f(π) = 2 + sin(π) = 2
Minimum values of f(x) on each subinterval:[0, π/2]: f(0) = 2 + sin(0) = 2
[π/2, π]: f(π/2) = 2 + sin(π/2) = 3
Upper sum: (3)(π/2) + (2)(π/2) = 5π/2 ≈ 7.85398Lower sum: (2)(π/2) + (3)(π/2) = 5π/2 ≈ 7.85398For n = 4:
Subintervals: [0, π/4], [π/4, π/2], [π/2, 3π/4], [3π/4, π]Width of subintervals: Δx = π/4Maximum values of f(x) on each subinterval:[0, π/4]: f(π/4) = 2 + sin(π/4) ≈ 2.70711
[π/4, π/2]: f(π/2) = 2 + sin(π/2) = 3
[π/2, 3π/4]: f(3π/4) = 2 + sin(3π/4) ≈ 2.29289
[3π/4, π]: f(π) = 2 + sin(π) = 2
Minimum values of f(x) on each subinterval:[0, π/4]: f(0) = 2 + sin(0) = 2
[π/4, π/2]: f(π/4) = 2 + sin(π/4) ≈ 2.70711
[π/2, 3π/4]: f(π/2) = 2 + sin(π/2) = 3
[3π/4, π]: f(3π/4) = 2 + sin(3π/4) ≈ 2.29289
Upper sum: (2.70711 + 3 + 2.29289)(π/4) ≈ 6.43917Lower sum: (2 + 2.70711 + 3 + 2.29289)(π/4) ≈ 6.43917For n = 8:
Subintervals: [0, π/8], [π/8, π/4], [π/4, 3π/8], [3π/8, π/2], [π/2, 5π/8], [5π/8, 3π/4], [3π/4, 7π/8], [7π/8, π]Width of subintervals: Δx = π/8Maximum values of f(x) on each subinterval:[0, π/8]: f(π/8) = 2 + sin(π/8) ≈ 2.25882
[π/8, π/4]: f(π/4) = 2 + sin(π/4) ≈ 2.70711
[π/4, 3π/8]: f(3π/8) = 2 + sin(3π/8) ≈ 2.96593
[3π/8, π/2]: f(π/2) = 2 + sin(π/2) = 3
[π/2, 5π/8]: f(5π/8) = 2 + sin(5π/8) ≈ 2.96593
[5π/8, 3π/4]: f(3π/4) = 2 + sin(3π/4) ≈ 2.70711
[3π/4, 7π/8]: f(7π/8) = 2 + sin(7π/8) ≈ 2.25882
[7π/8, π]: f(π) = 2 + sin(π) = 2
Minimum values of f(x) on each subinterval:[0, π/8]: f(0) = 2 + sin(0) = 2
[π/8, π/4]: f(π/8) = 2 + sin(π/8) ≈ 2.25882
[π/4, 3π/8]: f(π/4) = 2 + sin(π/4) ≈ 2.70711
[3π/8, π/2]: f(3π/8) = 2 + sin(3π/8) ≈ 2.96593
[π/2, 5π/8]: f(π/2) = 2 + sin(π/2) = 3
[5π/8, 3π/4]: f(5π/8) = 2 + sin(5π/8) ≈ 2.96593
[3π/4, 7π/8]: f(3π/4) = 2 + sin(3π/4) ≈ 2.70711
[7π/8, π]: f(7π/8) = 2 + sin(7π/8) ≈ 2.25882
Upper sum: (2.25882 + 2.70711 + 2.96593 + 3 + 2.96593 + 2.70711 + 2.25882 + 2)(π/8) ≈ 6.35258Lower sum: (2 + 2.25882 + 2.70711 + 2.96593 + 3 + 2.96593 + 2.70711 + 2.25882)(π/8) ≈ 6.352The complete question is:-
Unless specified, all approximating rectangles are assumed to have the same width. Evaluate the upper and lower sums for f(x) = 2 + sin(x),0 ≤ x ≤ π with n = 2, 4, and 8.
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Jake and Steve are calculating the volume of a triangular prism. Who calculated the volume incorrectly? What is the student's error?
Answer: Jake solved it incorrectly.
Step-by-step explanation: His equation was supposed to be (7/2*35/2) *18
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which equation is represented by the graph?
The graph represents the equation with option C, tan x/2.
What is graph?A graph is a structure that resembles a collection of objects in discrete mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each set of connected vertices is referred to as an edge.
Here,
The graph of the function tan(x/2) represents the tangent of half of the angle x in radians.
The tangent function has vertical asymptotes at odd multiples of π/2, which means that the function is undefined at those points. Therefore, the graph has vertical asymptotes at x = π/2, 3π/2, 5π/2, ....
The function also has zeros at even multiples of π, which occur when tan(x/2) = 0. This happens when x/2 = kπ where k is an integer, so x = 2kπ.
Between each pair of vertical asymptotes, the function oscillates between positive and negative infinity. The function is positive in the intervals (2kπ, (2k+1)π) and negative in the intervals ((2k-1)π, 2kπ) for all integers k.
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Write a paragraph proof of the Triangle Proportionality Theorem.
(Theorem 8.6)
__ __
Given: BD || AE
Prove: BA/CB = DE/CD
The Triangle Proportionality Theorem, also known as the Side Splitter Theorem, states that if a line is parallel to one side of a triangle, then it divides the other two sides proportionally.
Triangle Proportionality Theorem:
To prove this theorem, we begin by drawing a ΔABC with a line DE parallel to side AB. We then draw lines BD and CE, which intersect the parallel line DE at points F and G, respectively. By the properties of parallel lines, we know that ∠ADE and ∠ABD are congruent, and ∠AED and ∠ADB are congruent. Similarly, ∠CDE and ∠BDC are congruent, and ∠CED and ∠DCB are congruent.
We can then use the properties of similar triangles to show that ΔADE and ΔABC are similar, as are ΔCDE and ΔACB. This means that the ratios of corresponding side lengths are equal:
BA/DE = CA/CE and CB/DE = AB/BD
We can then substitute CA - BA for CB in the first equation, and BD for AB in the second equation:
BA/DE = (CA - BA)/CE and CB/DE = BD/(CA - BA)
Cross-multiplying both equations, we obtain:
BA * CE = DE * (CA - BA) and CB * DE = BD * (CA - BA)
Adding the two equations, we get:
BA * CE + CB * DE = (DE + CE) * CA
Dividing both sides by CB * DE, we obtain:
BA/CB = (DE + CE)/CE * CA/DE = DE/CD
Thus, we have proven the Triangle Proportionality Theorem.
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A flag-shaped like an equilateral triangular has a perimeter of 45 inches. What is the length of each side of the flag?
Answer: 15 inches
Step-by-step explanation:
An equilateral triangle has three equal sides, so if the perimeter of the triangle is 45 inches, then each side must be 45 inches divided by 3, which gives us:
45 in ÷ 3 = 15 in
Therefore, the length of each side of the flag is 15 inches.
A dealer selling an automobile for $18,340 offers a $500 rebate. What is the percent markdown (to the nearest tenth of a percent)?
Answer:
The selling price of the automobile after the $500 rebate is:
$18,340 - $500 = $17,840
The markdown is the difference between the original selling price and the selling price after the rebate, expressed as a percentage of the original selling price. The markdown can be calculated as follows:
Markdown = [(Original Price - Discounted Price) / Original Price] × 100%
Markdown = [(18,340 - 17,840) / 18,340] × 100%
Markdown = (500 / 18,340) × 100%
Markdown ≈ 2.72%
Rounding to the nearest tenth of a percent, the percent markdown is approximately 2.7%.
Suppose that A and B are independent events such that P (A) - 0.10 and P (B) - 0.60.
Find P(A n B) and P (A U B).
Answer:
Step-by-step explanation:
Since A and B are independent events, we can use the formula:
P(A ∩ B) = P(A) x P(B)
P(A ∩ B) = 0.10 x 0.60
P(A ∩ B) = 0.06
So the probability of both events A and B occurring is 0.06.
To find P(A U B), we can use the formula:
P(A U B) = P(A) + P(B) - P(A ∩ B)
P(A U B) = 0.10 + 0.60 - 0.06
P(A U B) = 0.64
Therefore, the probability of either A or B occurring (or both) is 0.64.
On thurday, lisa had 5$ in her bank account. she went to target to purchase stickers for her class. each pack of stickers cost 2$
write an inequality that represents s, the number of stickers purchased that resulted in her account ending in -10.
What lis the length of bc?
Answer: C (23)
Step-by-step explanation:
Since the triangle is isosceles, BA = BC
x + 17 = 2x -6
x = 23
Answer:
C(23)
Step-by-step explanation:
Since line AB = line BC
x+17=2x-6, by collecting like terms x=23
Help with math problems
Answer:
1) option A
2) p > 34
Step-by-step explanation:
1) Inequality: 7 ≤ n + 5
Subtract 5 from both sides,
7 - 5 ≤ n +5 - 5
2 ≤ n
The value of n is all values greater than or equal to 2.
So, the answer is option A.
2) Inequality: 16 + p > 50
Solution:
Subtract 16 from both sides,
16 - 16 + p > 50 - 16
p > 34
This answer in a fraction
The experimental probability that the next student will register for German is 9/79.
What is probability?
To find the experimental probability that the next student will register for German, we need to divide the number of students who have registered for German by the total number of students who have registered so far:
P(German) = number of students who have registered for German / total number of students who have registered
P(German) = 108 / (108 + 360 + 21 + 459) [Adding all the students who registered for each language]
P(German) = 108 / 948
P(German) = 9/79
Therefore, the experimental probability that the next student will register for German is 9/79.
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