according to the question the actual distance between Chattanooga and Nashville is 133 miles.
What is distance ?Distance is an object's total, aimless movement. Without regard to whether anything has a beginning or an end, distance can be defined as the amount of space that something has traversed. Distance is referred to be the breadth or magnitude of the gap between two locations. It should be highlighted that the distance between two points and the length travelled between the two are not the same thing. The total length of a path connecting two locations counts as the distance travelled. Distance is the distance in reality that a body travels. It also goes by the name "path length." For instance, the length of a path for the thing passing via point O and arriving at position P would be OP = 360 m.
given,
If 1 inch on the map represents 38 miles in reality, then 3.5 inches on the map would represent:
3.5 inches * 38 miles/inch = 133 miles
Therefore, according to the scale on the map, the actual distance between Chattanooga and Nashville is 133 miles.
To know more about distance visit :-
brainly.com/question/29130992
#SPJ1
What is 2^6*2^5 is other exponent?
Answer:
below
Step-by-step explanation:
Yes, there is another exponent.
When you are multiplying exponents, you add the exponents.
So from the equation 2^6 x 2^5, you can keep the 2 the same, as this is the base:
2^11
and add the exponents (6+5)
To check:
2^6=64
2^5=32
64x32=2048
2^11=2048
So, 2^11 is equivalent to your equation. Hope this helps ;)
a continuous random variable x has a uniform distribution between 5 and 25 (inclusive), then p(x = 15) = 0.05. a. true b. false
Answer:
Step-by-step explanation:
The probability of a continuous random variable taking any specific value is always zero, so the statement p(x = 15) = 0.05 is false.
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]
Read more about area
brainly.com/question/2607596
#SPJ1
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.
To learn more about area click on,
https://brainly.com/question/7021400
#SPJ4
Complete question is:
If the 14 inches represents the length of a square. what is the approximate area in square inches.
assume that the hourly cost to operate a commercial airplane follows the normal distribution with a mean of $3,403 per hour and a standard deviation of $398.what is the operating cost for the lowest 2% of the airplanes?
Answer:
$2,611.9.
Step-by-step explanation:
To find the operating cost for the lowest 2% of the airplanes, we need to find the corresponding z-score from the standard normal distribution using a z-table.
Using the formula:
z = (x - μ) / σ
where x is the cost we are interested in, μ is the mean cost, and σ is the standard deviation.
For the lowest 2% of airplanes, the z-score can be found by looking up the area to the left of z in the z-table. This area is 0.02.
Looking up 0.02 in the z-table gives a z-score of approximately -2.05.
So we have:
-2.05 = (x - 3403) / 398
Solving for x, we get:
x = -2.05 * 398 + 3403 = $2,611.9
Therefore, the operating cost for the lowest 2% of the airplanes is approximately $2,611.9.
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.
To learn more about profits click on,
https://brainly.com/question/13534163
#SPJ4
Answer:
A. ) 15,149.72
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.
Learn more about dollar ,
https://brainly.com/question/29846475
#SPJ4
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.
Learn more about Maximum here:
https://brainly.com/question/30693656
#SPJ4
On Ernest Airlines, baggage cannot weigh more than 40 pounds. Devin packed 21 pounds of clothes and four packages which weighed a total of 7 pounds. Write an inequality for this scenario. Then solve and determine the weight that each package must be less
Inequality for this scenario
x ≤ 4.75
So, each package must weigh less than or equal to 4.75 pounds in order for Devin to stay within the weight limit of 40 pounds on Ernest Airlines.
HOW TO SOLVE AN INEQUALITY?Let x be the weight of each package (in pounds).
The inequality for the scenario can be written as:
21 + 4x ≤ 40
This represents the total weight of Devin's clothes (21 pounds) plus the total weight of the four packages (4x pounds) cannot exceed the weight limit of 40 pounds on Ernest Airlines.
To solve for x, we can subtract 21 from both sides of the inequality:
4x ≤ 40 - 21
4x ≤ 19
Finally, we divide both sides by 4 to isolate x:
x ≤ 19 / 4
Let x be the weight of each package (in pounds).
The inequality for the scenario can be written as:
21 + 4x ≤ 40
This represents the total weight of Devin's clothes (21 pounds) plus the total weight of the four packages (4x pounds) cannot exceed the weight limit of 40 pounds on Ernest Airlines.
To solve for x, we can subtract 21 from both sides of the inequality:
4x ≤ 40 - 21
4x ≤ 19
Finally, we divide both sides by 4 to isolate x:
x ≤ 19 / 4
x ≤ 4.75
So, each package must weigh less than or equal to 4.75 pounds in order for Devin to stay within the weight limit of 40 pounds on Ernest Airlines.
To know more about inequality visit,
https://brainly.com/question/30228778
#SPJ1
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:
A(n) ______ design compares different independent variable levels by using homogeneous groups of experimental units.
A blocked design compares different independent variable levels by using homogeneous groups of experimental units.
In this type of experimental design, subjects are divided into homogeneous groups, or blocks, based on similar characteristics or traits. These blocks help to control or account for potential confounding variables that may affect the outcome of the experiment.
By grouping subjects into blocks, researchers can reduce the variability within each group and increase the accuracy of the experimental results. This allows for a more precise comparison of the effects of different levels of the independent variable on the dependent variable. Blocked designs are particularly useful when there are natural groupings within the experimental units or when the variability between units is high.
In summary, a blocked design is a powerful experimental tool that can help researchers account for potential confounding factors and reduce variability among experimental units. By doing so, it enables the accurate comparison of different levels of the independent variable, ultimately leading to more reliable and valid results.
Learn more about Blocked designs here: https://brainly.com/question/29655358
#SPJ11
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.
Find out more on integers at https://brainly.com/question/29050175
#SPJ1
PLEASE HELP I have no idea how to do this.. our teacher hasnt been here all week.. and I have no clue what this is..
solve for the value of V (9v+3)° 60°
The value of v is 13 degrees.
What are supplementary angles?Supplementary angles are a set of given measure of angles which add up to 180 degrees. Thus producing a measure of the sum of angles on a straight line.
To determine the value of v in the given diagram, we have;
60 + (9v + 3) = 180 (sum of angles on a straight line)
So that;
9v + 3 = 1890 - 60
9v + 3 = 120
9v = 120 - 3
= 117
v = 117/ 9
= 13
v = 13^o
The value of v in the question is 13 degrees.
Learn more about supplementary angles at https://brainly.com/question/404323
#SPJ1
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
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:
What is 4.5621 rounded to the nearest tenth?
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.
To learn more about scale click on,
https://brainly.com/question/2897262
#SPJ4
What is the media, mode, range, and mean for 39, 82, 74, 96, 64, 52,74
Find the value of x. If a segment looks like a tangent, it is a tangent.
We got x = 84.50 by using Pythagorean theorem.
What is the Pythagorean theorem in plain English?According to Pythagoras's Theorem, the square of the hypotenuse side in a right-angled triangle is equal to the sum of the squares of the other two sides.Perpendicular, Base, and Hypotenuse are the names of this triangle's three sides.angle of semicircle is always be 90°.
[tex]115^2 = 78^2 + x^2[/tex]
[tex]13225 = 6084 + x^2[/tex]
[tex]x^2 = 13225- 6084[/tex]
[tex]= 7141[/tex]
[tex]x = \sqrt{7141}[/tex]
[tex]x = 84.50[/tex]
Learn more about Pythagorean theorem:
brainly.com/question/14930619
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.
Learn more about area here:
https://brainly.com/question/28470545
#SPJ1
Evaluate (-25)^1/2
Answers:
a) 625
b)-625
c) not a real number
Then the answer is C. not a real number
How to evaluate that?
An exponent of 1/2 is equivalent to the square root, so we can write:
√-25
That is the square root of a negative number, so we will get the complex numbers ±i
Then the answer is C.
Learn abotu complex numbers at.
https://brainly.com/question/10662770
#SPJ1
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
#SPJ1
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.
To know more about time calculation visit:
brainly.com/question/20416068
#SPJ1
The complete question is: "Mark took 30minutes to finish lunch describe the turn the minute hand made when he finished his lunch".
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
To learn more about rate of change
https://brainly.com/question/17214872
#SPJ11
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
Learn more about slope intercept at
https://brainly.com/question/1884491
#SPJ1
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.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ1
The slope at [1,pi/2] from -8x^3/siny
As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.
what is slope ?The slope of a line in mathematics serves as a gauge for how steep it is. Between any two locations on the line, it is the proportion of the shift in the vertical motion (y) to the shift in the horizontal position (x). If we take into account two points on a line, (x1, y1) and (x2, y2), we can use the following formula to get the slope of the line: slope equals (y2 - y1)/. (x2 - x1) . Depending on the line's direction, the inclination can be zero, positive, or negative. A line with a positive slope is moving upward from left to right, whereas one with a negative slope is moving downward.
given
Finding the derivative of the given function with respect to x can be our first step. By applying the quotient rule, we get:
F(x) = 8x 3 sin (y)
[tex][(sin(y))(-24x2)] = f'(x) - (-8x^3) (cos(y))(y')] / (sin(y))^2[/tex]
where the derivative of y with respect to x is denoted by y'.
We can change x=1 and y=pi/2 in the equation above since we are interested in the slope at the position [1, pi/2].
Due to the fact that cos(pi/2) = 0 and sin(pi/2) = 1, we can write:
[tex]f'(1) = [(1)(-24) (-24) - (-8)(1)(0)(y')] / (1)^2[/tex]
f'(1) = -24 + 0
f'(1) = -24
As a result, the function's slope at [1, pi/2] is [-24] as where the derivative of y with respect to x is denoted by y'.
To know more about slope visit:
https://brainly.com/question/3605446
#SPJ1
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:
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.
Learn more about Decimals:
https://brainly.com/question/28393353
#SPJ4
WILL MARK AS BRAINLEIST!! ASAP PLEASE!!
Question in picture
I have more questions on my account if u can help me out!!
For the region above x + 3y = 9 and below x + 9 = y², we have:
a = 18, b = -9, f(x) = (y² - 9)/3, and g(x) = (9 - x)/3.
For single integration: α = -6, β = 3 and h(y) = [(9 - y²)/3 - (y² - 9)].
What is the area bounded by the curves?To solve this problem, we first need to find the intersection points of the two curves x + 3y = 9 and x + 9 = y². We can do this by solving the system of equations:
x + 3y = 9
x + 9 = y²
Rearranging the first equation, we get:
x = 9 - 3y
Substituting this expression for x into the second equation, we get:
9 - 3y + 9 = y²
Simplifying, we get:
y² - 3y - 18 = 0
Factorizing, we get:
(y - 6)(y + 3) = 0
So the solutions are:
y = 6 or y = -3
Substituting these values of y into the equation x + 3y = 9, we get:
When y = 6, x = -9
When y = -3, x = 18
So the intersection points of the two curves are (-9, 6) and (18, -3).
Now we can find the area between the two curves by splitting it into two regions: the region above the curve x + 3y = 9 and below the curve x + 9 = y², and the region below the curve x + 3y = 9 and above the curve x + 9 = y².
For the region above x + 3y = 9 and below x + 9 = y², we have:
a = 18
b = -9
f(x) = (y² - 9)/3
g(x) = (9 - x)/3
Alternatively, to compute the area between the two curves x + 3y = 9 and x + 9 = y² using a single integral, we need to express the area as a function of y instead of x.
We can rearrange the equations x + 3y = 9 and x + 9 = y² to get:
x = 9 - 3y
x = y² - 9
Setting these two expressions equal to each other, we get:
9 - 3y = y² - 9
Simplifying, we get:
y² + 3y - 18 = 0
Factorizing, we get:
(y + 6)(y - 3) = 0
So the solutions are:
y = -6 or y = 3
Substituting these values of y into the equation x + 3y = 9, we get:
When y = -6, x = 27
When y = 3, x = 0
So the intersection points of the two curves are (27, -6) and (0, 3).
The area between the curves can be expressed as the difference between the integrals of the curves' respective functions with respect to y, since the curves are better expressed in terms of y.
The function representing the curve x + 3y = 9 in terms of y is:
x = 9 - 3y
We can rearrange this equation to get:
y = (9 - x)/3
Substituting x = y² - 9, we get:
y = (9 - y² + 9)/3
Simplifying, we get:
y² + 3y - 18 = 0
This is the same equation we obtained before, so we know that the bounds of integration are -6 and 3.
The function representing the curve x + 9 = y² in terms of y is:
x = y² - 9
Substituting this expression into the formula for the area of a region between two curves, we get:
Area = ∫(y=α)^(y=β) [(9 - y²)/3 - (y² - 9)] dy
Where;
α = -6 and β = 3 are the bounds of integration, and
the integrand [(9 - y²)/3 - (y² - 9)] represents the difference between the y-values of the two curves at a given x-value.
Simplifying the integrand, we get:
Area = ∫(y=-6)^(y=3) (18 - 2y²)/3 dy
Integrating, we get:
Area = [(6y - (2/3)y³)/3] |(y=-6)^(y=3)
Plugging in the limits of integration, we get:
Area = [(18 - 216)/3] - [(-36 + 216)/3]
Simplifying, we get:
Area = 66
Learn more about area of curves here: https://brainly.com/question/30452445
#SPJ1