The final expression that gives us the cost of x skirts and y hats in pounds is 24x + 15y.
In this case, our variables are x and y, which represent the number of skirts and hats, respectively. Our constants are 24 and 15, which represent the cost of one skirt and one hat, respectively. And our operations are multiplication and addition.
The cost of x skirts is simply the cost of one skirt (which is 24) multiplied by the number of skirts (which is x). So, the expression for the cost of x skirts would be:
24x
Similarly, the cost of y hats is the cost of one hat (which is 15) multiplied by the number of hats (which is y). So, the expression for the cost of y hats would be:
15y
To find the total cost of x skirts and y hats, we simply add the two expressions together. Thus, the expression for the cost in pounds of x skirts and y hats is:
24x + 15y
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A level 0. 95 confidence interval is: a range of values with margin of error ± 0. 95, which is also correct 95% of the time. Any interval with margin of error ± 0. 95. A range of values computed from sample data that will contain the true value of the parameter of interest 95% of the time. A range of values computed from sample data by a method that guarantees that the probability the interval computed contains the parameter of interest is 0. 95
A level 0.95 confidence interval is a range of values computed from sample data that will contain the true value of the parameter of interest 95% of the time. So, the correct answer is C).
A level 0.95 confidence interval is a statistical measure used to estimate the true value of a population parameter based on a sample of data. It provides a range of values that is likely to contain the true value of the parameter with a certain degree of confidence.
The level of confidence, in this case 0.95, means that if the same sampling method and data analysis were repeated multiple times, the resulting confidence intervals would contain the true population parameter in 95% of cases.
The width of the interval, or margin of error, is influenced by factors such as sample size, variability, and level of confidence. So, the correct option is C).
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A rock dropped into a pond and creates a circular area of ripples whose radius increases at a constant rate of 2 feet per second. At what rate is the circular area increasing with respect to time when the radius os exactly 3 feet
The rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the radius is exactly 3 feet.
To solve this problem, we need to use the formula for the area of a circle:
[tex]A = πr^2[/tex],
where A is the area and r is the radius.
We also need to use the chain rule of differentiation because we are dealing with a changing radius over time.
First, we can find the rate of change of the area with respect to time (dA/dt) by differentiating the formula for the area:
dA/dt = 2πr(dr/dt)
where dr/dt is the rate of change of the radius with respect to time, which is given as 2 feet per second in the problem.
Therefore, we can substitute these values into the formula to get:
dA/dt = 2π(3)(2)
dA/dt = 12π
So, the rate of change of the circular area is increasing at a constant rate of 12π square feet per second when the
radius is exactly 3 feet.
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Cuanto es 14 pulgadas en cual es el area aproximada en pulgadas cuadradas
If 14 inches represents the length of a square, then the approximate area of that square would be 196 square inches.
If the 14 inches represents the length of a square, we can calculate the area of the square by multiplying its length by its width. However, since a square has four sides of equal length, we know that its width is also 14 inches. Therefore, the area of the square can be calculated as:
Area = length x width = 14 inches x 14 inches = 196 square inches.
In general, the formula for the area of a rectangle is length x width, while the formula for the area of a circle is πr^2, where r is the radius of the circle.
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Complete question is:
If the 14 inches represents the length of a square. what is the approximate area in square inches.
Paul considers investing $8,000 in three different accounts for 6 years.
Option A: 5% simple interest
Option B: 4.5% interest compounded continuously
Option C: 4.75% interest compounded yearly
After 6 years, Option B, to the nearest dollar, will be worth
$
more than Option A and
$
less than Option C.
linearexponentialquadraticconstant
Option A is a
function while Options B and C are
functions. While the
function gains
value the fastest initially, over time the
functions will gain value faster.
Answer:
Step-by-step explanation:
Option A: 8,000(1+6(0.05))
is equal to 10,400
Option B is 10,479.72
Option C: 8,000(1+0.0475)^6
is equal to 10,568.52
making B about $80 more than A and $89 less than C
mark took 30minutes to finish lunch describe the turn the minute hand made
The turn the minute hand made is about 180 degrees when Mark finished his lunch.
How to calculate time with angle?To calculate time with angle, you need to know the angle between the hour hand and the minute hand. With that, you can use the formula
θ = 30H - 11/2M
where H is the current hour and M is the current minute.
Once you calculate the angle, you can use the formula
t = θ/30 to find the elapsed time in hours and decimal fractions of an hour.
The minute hand of a clock makes a full revolution (360 degrees) in 60 minutes (1 hour). Therefore, in 30 minutes, the minute hand will turn half the way around the clock face, which is 180 degrees.
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The complete question is: "Mark took 30minutes to finish lunch describe the turn the minute hand made when he finished his lunch".
There are 31 students in a class. Each student was asked how many pets he has at home. The table below summarizes the data.
Based on the data, estimate the probability that a randomly selected student from this class has four or more pets at home. Round your answer to the nearest two decimal places.
Please help :DDD
The estimated probability that a randomly selected student from this class has four or more pets at home is approximately 0.13.
What is probability?Probability is a way to gauge how likely or unlikely something is to happen. Usually, it is stated as a number between 0 and 1, where 0 denotes that an event is impossible and 1 denotes that it is certain to happen.
According to question:Out of the 31 students surveyed, 6 reported having no pets, 8 reported having one pet, 10 reported having two pets, 3 reported having three pets, and a total of 4 (1+2+1) reported having four or more pets.
Thus, the probability that a randomly selected student from this class has four or more pets at home is:
P(four or more pets) = 4/31 ≈ 0.13 (rounded to two decimal places)
Therefore, the estimated probability that a randomly selected student from this class has four or more pets at home is approximately 0.13.
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On a piece of paper graph y = 2x-4 then determine which answers
matches the graph you drew
The graph shown in the equation y = - 2x - 4 is the graph that corresponds to that equation. The answer is option (B).
What is graph?A data structure called a graph is used to show the mathematical connection between two or more objects. It is made up of nodes and edges, where nodes stand in for individual things and edges for the connections between them. In computer science, graphs are used to solve a variety of issues, including finding the shortest path between two points and figuring out whether a graph contains cycles. In addition, social networks, transportation networks, and many other kinds of networks can all be represented using graphs.
Option B's graph is the one that corresponds to the equation y = - 2x - 4.
The following is how the equation is written in slope-intercept form:
It is -2 degrees.
-4 is the intercept.
This shows that the slope of the graph is negative and that the trend line crosses the y axis at a negative four-degree angle.
The only graph with a negative slope and a -4 intercept is the one for option B.
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Complete question attached below,
Which set of fractions is not an example of a reciprocal fractions
Answer:
It can be deduced that the set of fractions that is an example of reciprocal fractions include, 1/2, 3/1, and 1/6.
Step-by-step explanation:
Some whole numbers are not integers
True/False
Some integers are not irrational numbers
True/False
Some whole numbers are irrational
numbers
True/False
All integers are whole numbers
True/False
Answer:
1) False--all whole numbers are integers.
2) False--no integers are irrational numbers.
3) False--no whole numbers are irrational numbers.
4) False--only zero and the positive integers are whole numbers.
I keep on getting the angle wrong even though all the math looks right — does anyone know what went wrong?
The velocity and direction of the jet and the velocity and direction of the wind, expressed as vectors are;
(a) (0. 45)
(b) (450, 0)
(c) (450, 45)
(d) 452
84.3 °E
What is a vector quantity?A vector quantity is one that has both magnitude and direction.
The direction of the pilot is heading = Due east
The speed of the jet relative to the air = 450 mi/h
The direction of the wind = Due north
Speed of the wind = 45 mi/h
(a) The velocity of the wind expressed as a vector is therefore;
[tex]\vec{v}_w[/tex] = 0·i + 45·j
Which indicates that the vector component form of the velocity of the wind is (0, 45)
(b) The velocity of the jet relative to the wind expressed as a vector therefore is; [tex]\vec{v}_j[/tex] = 450·i + 0·j
Which indicates that the vector form of the velocity of the jet relative to the wind is; (450, 0)
(c) The true velocity of the jet expressed as a vector is the sum of the two vectors, which indicates;
The true velocity of the jet = 0·i + 45·j + 450·i + 0·j = 450·i + 45·j
The vector form of the true velocity of the jet is (450, 45)
(d) The true speed of the jet is the magnitude of the vector of the true velocity of the jet, which is;
Speed = √((450 mi/h)² + (45 mi/h)²) ≈ 452 mi/h
The direction of the jet is the arctangent of the ratio of the components of the vector of the true velocity of the jet
The direction of the jet = arctan(45/450) ≈ 5.7° North = (90 - 5.7)° E = 84.3 °ELearn more on vectors here: https://brainly.com/question/28931875
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Students are making lemonade from a powdered lemon drink mix. Khloe mixes 5
cups of water and 2 teaspoons of powdered lemon mix. Jayden mixes 1 cup of water
and 2 teaspoons of powdered lemon mix. Whose mix will be more lemony?
A Khloe’s mix will be more lemony.
B Jayden's mix will be more lemony.
C The two mixes will be equally lemony.
By the ratio of teaspoons of powdered lemonade mix and cup of water, jayden mix will be more lemony.
What is the ratio?Ratio is a mathematical comparison between two or more quantities, typically expressed as a fraction or a colon (:). It represents the relationship or proportion between the quantities being compared. Ratios are used to describe the relative size or amount of one quantity in relation to another.
According to the given information:
Based on the given information, we can determine that option B, Jayden's mix will be more lemony.
This is because the ratio of powdered lemon mix to water is the same for both Khloe and Jayden, which is 2 teaspoons of powdered lemon mix per cup of water. However, Jayden uses only 1 cup of water, whereas Khloe uses 5 cups of water. Therefore, Jayden's mix will have a higher concentration of powdered lemon mix per cup of water compared to Khloe's mix, making Jayden's mix more lemony in flavor.
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if the toss of a coin comes down heads, you win a dollar. if it comes down tails, you lose fifty cents. how much would you expect to earn after 20 tosses? enter your answer rounded to two decimal places.
The expected value of winning a dollar when the coin comes down heads is:
Earnings from heads = 1 * 0.5 = 0.5
The expected value of losing fifty cents when the coin comes down tails is:
Earnings from tails = -0.5 * 0.5 = -0.25
The expected value of earnings for one toss is:
Earnings per toss = Earnings from heads + Earnings from tails = 0.5 - 0.25 = 0.25
Therefore, the expected earnings for 20 tosses is:
Expected earnings for 20 tosses = 20 * Earnings per toss = 20 * 0.25 = 5
So, you would expect to earn $5 after 20 tosses.
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Kiera had 1 1/3 cups of coffee in the morning and 1 1/4 cups of coffee in the afternoon. She wants to add the fractions 1 1/3+ 1 1/4 to find how much coffee she drank in all.
She can add the whole numbers, but before she can add the fractions she must find the common denominator. Drag and drop the numbers into the boxes to make the statement true.
Picture attached to
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
To add and Kiera found the common denominator is Response area. Before adding the fractions together she wrote the numerator of the first fraction as Response area and the numerator of the second fraction as Response area.
For given problem, The common denominator is 12 and Before adding the fractions the numerator of first fraction was 16 and numerator of second fraction was 15.
What are fractions?The representation of sections or portions of a whole using fractions is common. It consists of Numerator and the denominator reflects the total number of equally sized pieces that make up the whole, whereas the numerator represents the number of components we have.
For example, in the fraction 5/4, 4 is the denominator and 5 is the numerator.
Now for given problem,
Kiera had [tex]1\frac{1}{3}[/tex] cups of coffee in the morning, equivalent to [tex](4/3)[/tex] cups of coffee.
Kiera also had[tex]1 \frac{1}{4}[/tex] cups of coffee in the afternoon, equivalent to [tex](5/4)[/tex] cups of coffee.
Now we can add the two fractions together:
[tex](4/3) + (5/4)[/tex]
To find common Denominator;
(LCM) of 3 and 4 is 12
Making denominator of both fraction 12;
[tex](4/3) * (4/4) + (5/4) * (3/3)[/tex]
[tex](16/12) + (15/12)[/tex]
[tex]16/12 + 15/12 = (16 + 15)/12 = 31/12[/tex]
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LOOK AT PHOTO
5x+3> 10
The smallest integer value of x that would be a solution in the inequality would be x = 2.
How to find the smallest integer ?To find the smallest integer value of x that satisfies the inequality 5x + 3 ≥ 10, first solve the inequality for x:
Subtract 3 from both sides:
5x ≥ 7
Divide by 5:
x ≥ 7/5
The inequality states that x must be greater than or equal to 7/5, which is equal to 1.4. Since we are looking for the smallest integer value, we should round up to the next integer, which is 2. Therefore, the smallest integer value of x that satisfies the inequality is x = 2.
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please i need your help for today please i would really appreciate it
Answer:
increasing: x > 0
Step-by-step explanation:
Given a table of function values, you want to know the interval on which the function is increasing.
IncreasingA function is increasing if f(x)-values get larger when x-values get larger. As we go down the table, the x-values get larger.
In the first three lines of the table, the f(x)-values are getting smaller. The function is decreasing on that interval, x < 0.
In the last three lines of the table, the f(x) values are getting larger. The function is increasing on that interval, x > 0.
__
Additional comment
The point (0, 0) represents a minimum. The function is not increasing or decreasing at that point, so the interval of interest is x > 0, not x ≥ 0.
susie has a rectangular garden that is 10 feet by 12 feet she plants flowers in a circular shape with a radius of 4 feet if Susie only wants to fertilize the space outside the flowers how many square feet will she fertilize.
She will fertilize 69.76 square feet outside of the circular flowers.
How many Sq ft will Susie fertilize outside the circular flowers?In order to get the area that she will fertilize outside of the circular flowers, we will calculate area of the entire rectangular garden and the area of the circular flowers.
The area of the rectangular garden is:
[tex]= 10 ft * 12 ft\\= 120 sq ft[/tex]
The area of the circular flowers is:
[tex]= \pi r^2\\= 3.14 * 4^2\\= 50.24 sq ft[/tex]
To find area to be fertilize outside of the circular flowers, we will subtract these area which gives us:
[tex]= 120 sq ft - 50.24 sq ft\\= 69.76 sq ft[/tex]
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What is the solution of the inequality of -0.4x1.2 >0.8 ?
A. x<-5
B. x<-1
C. x<-0.8
d. x>5
Please answer and give out a step-by-step explanation! Thank you :)
Answer:
A. x<-5
Step-by-step explanation:
-0.4x - 1.2 > 0.8
-0.4x > 2
x < -5
So, the answer is A. x<-5
Convert 4.5 x 104 to decimal format.A) 45,000 B) 4,500 C) 0.00045 D) 0.0045 E) 0.000450
After converting [tex]4.5 * 10^4[/tex] to decimal format, one gets 45,000 as an answer. Thus, option (A) is the correct answer.
To convert numbers multiplied by 10 with having an exponent number to decimal format, one first needs to check the sign on the exponent.
If the sign is positive, we must shift the decimal to the right with each power of 10. The exponent indicates the number of zeros added after the number in case no decimal is used.
And if the sign is negative, we have to shift the decimal to the left with each power of 10. One has to divide the number by the number one gets after multiplying 10 by itself as many times as the exponent.
Therefore, to convert [tex]4.5 * 10^4[/tex] to decimal format, we shift the decimal by 4 places and we get 45,000 as the answer.
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What type of triangle 38, 38, and 104
Answer:
A triangle with side lengths of 38, 38, and 104 is an isosceles triangle. This is because it has two sides of equal length (the two sides that are both 38 units long).
Step-by-step explanation:
What is the media, mode, range, and mean for 39, 82, 74, 96, 64, 52,74
For residential drains, a horizontal pipe needs to have a minimum slope of 1/4 inch per foot and a maximum slope of 1/2 inch per foot for waste to drain properly. This means that for every horizontal foot the pipe travels, it should drop between 1/4 and 1/2 inch.
A. Sketch a graph showing a pipe at a minimum slope and a horizontal pipe at a maximum slope.
B. Determine the minimum and maximum angles, to the nearest tenth of a degree, that a pipe can make with the horizontal.
C. Enrico installs a drain pipe that runs a horizontal distance of 172 inches and drops 6 inches from the horizontal. Is the slope of this pipe acceptable? Explain.
A. Here's a sketch of a horizontal pipe at a maximum slope (1/2 inch per foot) and a minimum slope (1/4 inch per foot): / / / / / / / / / / / / / / / / / / /
/ / / / / / / / / / / / / / / / / / /
/ / / / / / / / / / / / / / / / / / /
/ / / / / / / / / / / / / / / / / / /
The pipe on the left has a slope of 1/4 inch per foot, while the pipe on the right has a slope of 1/2 inch per foot.B. To determine the minimum and maximum angles, we need to use trigonometry. If we let the angle that the pipe makes with the horizontal be θ, then we have:Minimum angle: tan(θ) = 1/48 (since 1/4 inch per foot is equivalent to 1 inch of drop over 48 inches of horizontal distance) θ ≈ 1.2 degreesMaximum angle: tan(θ) = 1/24 (since 1/2 inch per foot is equivalent to 1 inch of drop over 24 inches of horizontal distance) θ ≈ 2.4 degreesSo the minimum angle is approximately 1.2 degrees and the maximum angle is approximately 2.4 degrees.C. To determine if the slope of Enrico's pipe is acceptable, we need to calculate the slope of the pipe in inches per foot. Enrico's pipe runs a horizontal distance of 172 inches and drops 6 inches. The slope is:Slope = Drop / Horizontal distance = 6 / 172Slope = 0.0349 inches per inchTo convert this to slope in inches per foot, we multiply by 12:Slope = 0.4188 inches per footSince this slope is between the acceptable range of 1/4 inch per foot and 1/2 inch per foot, Enrico's pipe slope is acceptable.
Correct me if I am wrong
A. Sketch of a pipe at slop 1/4 inch per foot and a horizontal pipe at slope 1/2 inch per foot attached below. B. the minimum and maximum angle are approximately 14.0 degrees and 26.6 degrees, respectively. C. Yes, pipe slope is acceptable according to the given criteria.
B. Determine the minimum and maximum angles:
To find the angle, use the tangent function. The tangent of an angle is equal to the ratio of the height to the horizontal distance travelled.
Minimum angle:
Tangent of the angle= 1/4 inch per foot
Tangent of the angle = 0.25 inches per foot
Minimum angle (in degrees) = arctan(0.25)
Minimum angle ≈ 14.0 degrees
Maximum angle:
Tangent of the angle = 1/2 inch per foot
Tangent of the angle = 0.5 inches per foot
Maximum angle (in degrees) = arctan(0.5)
Maximum angle ≈ 26.6 degrees
C. Enrico's drain pipe:
Horizontal distance travelled = 172 inches
Drop from the horizontal = 6 inches
Slope of the pipe = Drop / Run
Slope of the pipe = 6 / 172
Slope of the pipe ≈ 0.0349 inches per inch
To convert the slope to inches per foot:
Slope = 0.0349 × 12
Slope ≈ 0.4188 inches per foot
Hence, sketch of a pipe at slop 1/4 inch per foot and a horizontal pipe at slope 1/2 inch per foot attached below, the minimum and maximum angle are approximately 14.0 degrees and 26.6 degrees, respectively, and yes, pipe slope is acceptable according to the given criteria.
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What is the value of line 1 and2 in y=mx+b form?Help please!!!
1. The equation of the line in graph 1 in slope-intercept form is
y = (2/3)x + 2/3.
2. The equation of the line in graph 2 is
y = (1/3)x + 4/3.
How to find the equation of the linea. To find the equation of the line passing through (3, 4) and (0, 2) (points obtained from the graph) in slope-intercept form, we need to first find the slope of the line.
slope = (y2 - y1) / (x2 - x1)
Substituting the given values, we get:
slope = (2 - 4) / (0 - 3) = -2 / (-3) = 2/3
The point-slope form of the equation of a line passing through a point (x1, y1) with slope m is given by:
y - y1 = m(x - x1)
y - 4 = (2/3)(x - 3)
y = (2/3)x + 2/3
b. points obtained from the graph (-3, 1) and (-6, 0)
slope = (y2 - y1) / (x2 - x1)
slope = (0 - 1) / (-6 - (-3)) = -1 / (-3) = 1/3
y - y1 = m(x - x1)
y - 1 = (1/3)(x - (-3))
y = (1/3)x + 4/3
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Korey is planning to open a comic book store. In his first year of operation, Korey expects to average $1,000 of profit each month. He then expects profits to increase by 6% each year for the next 4 years. How much does Korey expect to make in profits in his fifth year of operation? A = P (1 r) superscript t a. $15,149.72 b. $16,058.71 c. $31,120.46 d. $32,987.69
Korey expect to make in profits in his fifth year of operation is $15,149.72. So, the correct answer is option A) $15,149.72.
To calculate Korey's expected profits in his fifth year of operation, we need to consider the expected growth rate of profits over the next four years.
Korey expects profits to increase by 6% each year for the next four years. To calculate his expected profits for each of the next four years, we can use the following formula:
Profit = Previous year's profit + (Previous year's profit x growth rate)
Using this formula, we can calculate Korey's expected profits for each of the next four years:
Year 1: $12,000 (average monthly profit of $1,000)
Year 2: $12,720 ($12,000 + ($12,000 x 0.06))
Year 3: $13,478.40 ($12,720 + ($12,720 x 0.06))
Year 4: $14,278.30 ($13,478.40 + ($13,478.40 x 0.06))
To calculate his expected profits in the fifth year, we can use the same formula:
Year 5: $15,149.72 ($14,278.30 + ($14,278.30 x 0.06))
Therefore, the correct answer is option A) $15,149.72.
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Answer:
A. ) 15,149.72
what are the major differences between vertical and horizontal text sets? hypothesize and explain an example of a situation where one type of text set may be more beneficial than the other.
Answer: Vertical text sets are arranged in columns from top to bottom, while horizontal text sets are arranged in rows from left to right. The major differences between the two include:
Readability: Vertical text sets may be more difficult to read for individuals who are accustomed to reading horizontally, while horizontal text sets may be more natural for them to read.
Space utilization: Vertical text sets can utilize space more efficiently, especially in situations where vertical space is available, such as in tall and narrow posters or banners. Horizontal text sets, on the other hand, can utilize space more efficiently in situations where horizontal space is available, such as in wide-screen displays or landscape-oriented documents.
Cultural conventions: In some cultures, such as Japan and China, vertical text sets are traditionally used for writing, while in other cultures, such as the United States, horizontal text sets are the norm. Thus, the use of one or the other may depend on cultural context.
One situation where vertical text sets may be more beneficial is in designing a tall and narrow billboard. In this case, a horizontal text set may be difficult to read from afar, while a vertical text set can make use of the available space and be easily read from a distance. On the other hand, in designing a website, horizontal text sets may be more beneficial as they can utilize the full width of the screen and provide more space for additional content.
Step-by-step explanation:
PLEASE HELP!! 14 POINTS
The total revenue for a bluetooth speaker (in dollars) is given by R(x)=35x−0. 01x2 where x is the number of units sold. What is the average rate of change in revenue as the number of bluetooth speakers sold increases from 20 to 40 units?
The average rate of change in revenue as the number of bluetooth speakers sold increases from 20 to 40 units is $34.50 per unit.
To find the average rate of change in revenue, we need to calculate the change in revenue over the change in units sold.
First, let's calculate the revenue for 20 and 40 units sold:
R(20) = 35(20) - 0.01(20)^2 = $670
R(40) = 35(40) - 0.01(40)^2 = $1360
Now we can calculate the change in revenue:
ΔR = R(40) - R(20) = $1360 - $670 = $690
And the change in units sold:
Δx = 40 - 20 = 20
Finally, we can calculate the average rate of change in revenue:
ΔR/Δx = $690/20 = $34.50
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Find the area of the shaded region for each composite figure.
The area of the shaded region is 192 m².
We have,
(g)
The shaded region.
= Area of the rectangle - Area of the triangle
So,
Length = 16 m
Width = 18 m
Area of the rectangle.
= 16 x 18
= 288 m²
And,
Base² + 16² = 20²
Base² = 400 - 256
Base = √144 = 12
So,
Area of the triangle.
= 1/2 x base x height
= 1/2 x 12 x 16
= 96
Now,
The shaded region.
= Area of the rectangle - Area of the triangle
= 288 - 96
= 192 m²
Thus,
The area of the shaded region is 192 m².
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Sorry about the bad quality
Answer:
(x) = (-19/9)(x + 3)^2 + 5
Step-by-step explanation:f(x) = a(x - h)^2 + k
where (h, k) represents the vertex of the parabola. Given that the vertex is (-3, 5), we can plug in these values into the vertex form equation:
f(x) = a(x - (-3))^2 + 5
which simplifies to:
f(x) = a(x + 3)^2 + 5
Now, we know that the function passes through the point (0, -14). We can plug in these values into the equation and solve for 'a':
-14 = a(0 + 3)^2 + 5
-14 = 9a + 5
Subtracting 5 from both sides:
-19 = 9a
Dividing both sides by 9:
a = -19/9
6. age of his son by A two-digit number is such that the sum of the digits is 13 and the product of the digits is 40. Find the number.
7 A two-digit number is less than 6 times the sum of its digits by 1. The difference between the digit is 1. Find the number.
Answer:
6.
solution:
8+5=13
8×5=40
Choose an appropriate scale for the replica so that it will fit on a 8.5-by-11am j
To ensure that the replica will fit on an 8.5-by-11-inch paper, we need to choose a scale that will result in dimensions that are smaller than or equal to 8.5 inches by 11 inches.
Choosing an appropriate scale for a replica depends on the size of the original object and the desired size of the replica. To fit a replica on an 8.5-by-11-inch paper, we need to determine the maximum size that the replica can be while still fitting on the paper.
One common method for determining the appropriate scale is to measure the dimensions of the original object and then divide them by the desired size of the replica. For example, if the original object is 20 inches wide and we want to create a replica that is 8 inches wide, the scale would be 20/8, or 2.5.
In order to fit the replica on an 8.5-by-11-inch paper, we need to make sure that the dimensions of the replica are smaller than or equal to 8.5 inches by 11 inches.
We can use the scale factor to determine the maximum dimensions of the replica. For example, if the scale factor is 2.5 and we want the replica to be 8 inches wide, the maximum height of the replica would be 8/2.5, or 3.2 inches.
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Val needs to find the area enclosed by the figure. The figure is made by attaching semicircles to each side of a 58-m-by-58-m square. Val says the area is 1917.48 m. Find the area enclosed by the figure. Use 3.14 for π. What error might Val have made?
The area that is enclosed by the figure which is being observed by Val would be = 3,364m²
How to calculate the area of the given figure?To calculate the area of the enclosed figure, the area of 2 circles and a square should be calculated and added together.
The area of a circle = πr²
r = 58/2 = 49
area = 3.14×49×49
= 7539.14×2
= 15078.28m
Area of the enclosed region = 58×58 = 3,364m²
Therefore, Val is wrong with the area of he calculated.
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