This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.
The local theater fundraiser sold 200 pre-event tickets at $35 each and 50 at-the-door tickets at $40 each to generate a total revenue of $9,375. This can be calculated by multiplying the number of tickets sold by their respective prices: 200 x $35 = $7,000 and 50 x $40 = $2,375.
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In ΔPQR, r = 7.8 cm, q = 6 cm and ∠Q=30°. Find all possible values of ∠R, to the nearest 10th of a degree.
The twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.
What is a triangle?A triangle is a clοsed twο-dimensiοnal geοmetric shape with three straight sides and three angles. It is the simplest pοlygοn, which is a flat shape cοnsisting οf straight lines.
We can use the Law οf Cοsines tο find the length οf side QR:
[tex]c^2 = a^2 + b^2 - 2ab[/tex] cοs(C)
where c is the length οf side QR, a is the length οf side PQ (which is unknοwn), b is the length οf side PR (which is 7.8 cm), and C is the angle οppοsite side c (which is 30°). Substituting the given values, we get:
[tex]QR^2 = PQ^2 + 7.8^2 - 2(PQ)(7.8)cos(30^\circ )[/tex]
[tex]QR^2 = PQ^2 + 60.84 - 7.8PQ[/tex]
Next, we can use the Law οf Sines tο relate the length οf side PQ tο the angle οppοsite it, ∠P:
PQ/sin(30°) = QR/sin(P)
PQ = QR(sin(30°)/sin(P))
Substituting this expressiοn fοr PQ intο the equatiοn fοr [tex]QR^2[/tex] abοve, we get:
[tex]QR^2 = [QR(sin(30^\circ)/sin(P))]^2 + 60.84 - 7.8[QR(sin(30^\circ)/sin(P))][/tex]
Simplifying and rearranging, we get a quadratic equatiοn in terms οf QR:
[tex]QR^2 - 3.9QR + 28.99 = 0[/tex]
Using the quadratic fοrmula, we find that:
QR ≈ 7.466 cm οr QR ≈ 3.866 cm
Since we knοw that QR < PQ + PR = 6 + 7.8 = 13.8, the οnly valid sοlutiοn is QR ≈ 7.466 cm. Therefοre, we have:
[tex]cos(R) = (PQ^2 + QR^2 - PR^2)/(2PQQR)[/tex]
[tex]cos(R) = (PQ^2 + 7.466^2 - 7.8^2)/(2PQ(7.466))[/tex]
[tex]cos(R) = (PQ^2 - 4.928)/[2PQ(7.466)][/tex]
Since cοs(R) ≤ 1, we have:
[tex]PQ^2 - 4.928 ≤ 2PQ(7.466)[/tex]
Sοlving fοr PQ using the quadratic fοrmula, we get:
PQ ≤ 5.474 cm οr PQ ≥ 20.032 cm
Since PQ < PR, the οnly valid sοlutiοn is:
PQ ≈ 5.474 cm
Nοw we can use the Law οf Cοsines again tο find ∠R:
[tex]cos(R) = (PQ^2 + PR^2 - QR^2)/(2PQPR)[/tex]
[tex]cos(R) = (5.474^2 + 7.8^2 - 7.466^2)/(2(5.474)(7.8))[/tex]
cοs(R) ≈ 0.828
R ≈ 33.6° οr R ≈ 326.4°
Therefοre, the twο pοssible values οf ∠R tο the nearest 10th οf a degree are 33.6° and 326.4°.
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if the cycle time is 2 minutes/customer then how many customers are served per hour? multiple choice question. 15 20 30 60
If the cycle time is 2 minutes per customer, 30 customers can be served per hour.
The given cycle time is 2 minutes per customer. To calculate how many customers can be served per hour, we need to calculate the number of minutes in an hour as follows: 60 minutes = 1 hour.
The time taken for each customer is 2 minutes. Therefore, the number of customers that can be served per hour can be calculated as follows:
Number of customers per hour = (60 minutes/hour) ÷ (2 minutes/customer)
Number of customers per hour = 30 customers.
Therefore, the number of customers that can be served per hour is 30, according to the given cycle time of 2 minutes per customer.
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DUE TOMORROW PLEASE HELP WELL WRITTEN ANSWERS ONLY!!!!!!
Here is the graph of a function describing the relationship between the height y, in feet, of the tip of a windmill blade and the angle of rotation Θ made by the blade. Describe the windmill.
However, it is important to note that without additional information about the function and the windmill itself, further conclusions about its design and performance cannot be made.
Hi! I'd be happy to help you describe the windmill based on the provided graph.The graph of the function represents the relationship between the height (y) of the tip of a windmill blade and the angle of rotation (Θ) made by the blade. This function is periodic, indicating that the windmill blade follows a repetitive motion as it rotates.
The height of the blade tip varies sinusoidally with respect to the angle of rotation, suggesting that the windmill has a circular or rotational motion. The amplitude of the function gives the length of the windmill blade, while the period of the function represents a full rotation (360 degrees) of the windmill blade.
In summary, the windmill has a rotational motion, with the height of the blade tip following a sinusoidal pattern. The length of the windmill blade and the time it takes to complete a full rotation can be determined by analyzing the amplitude and period of the function.
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A particle of mass 1. 2 kg is moving with speed of 8 ms inn a straight line on a horizontal table. A resistance force is app. Lied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, ao that F=0,3v^2
The speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2[/tex], or 19.2 N.
A particle of mass 1.2 kg is moving with a speed of 8 m/s in a straight line on a horizontal table. A resistance force is applied to the particle in the direction of the motion. The magnitude of the force is proportional to the square of the speed, such that [tex]F=0.3v^2[/tex]
The force of resistance is an opposing force that acts to reduce the speed of the particle. As the particle moves faster, the resistance force increases. The force is proportional to the square of the speed, meaning that if the speed doubles, the force is multiplied by four. The force is also in the same direction as the motion, meaning that it will reduce the speed of the particle.
The equation for the force of resistance is [tex]F=0.3v^2[/tex], where v is the speed of the particle. Therefore, if the speed of the particle is 8 m/s, the force of resistance is [tex]0.3(8)^2,[/tex] or 19.2 N. This means that the force of resistance acting on the particle is 19.2 N.
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Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle B?
Kathy had 20 dollars to spend on 3 gifts. She spent 10 7/10
dollars on gift A and 6 2/5 dollars on gift B. How much money did she have left for gift C?
If Kathy had $20 to spend on 3 gifts and she spent $10⁷/₁₀ on Gift A and $6²/₅ on Gift B, the (balance) amount left for Gift C is $3.89.
How is the balance determined?The balance can be determined using subtraction operation.
Subtraction operation is one of the four basic mathematical operations, including addition, multiplication, and division.
Subtraction operation involves the minuend ($20), the subtrahends ($10.07 and $6.04), giving a difference or balance of $3.89.
The total spending budget that Kathy has = $20
The number of gifts to buy = 3
The amount spent on Gift A = $10.07 ($10⁷/₁₀)
The amount spent on Gift B = $6.04 ($6²/₅)
The amount left for Gift C = $3.89 ($20 - $10.07 - $6.04).
Thus, after spending on Gifts A and B, the amount left for Gift C is determined using subtraction operation as $3.89.
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In terms of the water lily population change, the value 3.915 represents: the value 1.106 represents:
The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x.
In the given regression equation y = 3.915(1.106)x:
The value 3.915 represents the y-intercept or the predicted value of y when x=0. In the context of the water lily population change, this value could represent the initial population of water lilies or the minimum population that can sustain in the given environment.The value 1.106 represents the slope of the regression line or the rate of change of y with respect to x. In the context of the water lily population change, this value could represent the rate at which the water lily population increases or decreases with respect to some independent variable x, such as time or environmental factors.Learn more about slope here https://brainly.com/question/19131126
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If the width and length of a rectangle is 3 by 8 what is the width and length actually if the width is 10. 5
The new length of the rectangle is approximately 2.29 units. We use the formula for the area of a rectangle to solve for the new length, given the new width.
If the width and length of a rectangle are 3 and 8, respectively, and the width is increased to 10.5, we can calculate the new length of the rectangle using the formula for the area of a rectangle, which is length multiplied by width.
The original area of the rectangle is 3 x 8 = 24 square units. If we increase the width to 10.5, the new area of the rectangle becomes: 10.5 x length = 24 Solving for the length, we get: length = 24/10.5 = 2.29 (rounded to two decimal places)
It's important to note that changing one dimension of a rectangle can affect the other dimension, especially if we want to maintain the same area.
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A circle with radius of 2 cm sits inside a circle with of 4 cm
Answer:
Diameter is equal to twice the radius. Given, radius is 4 cm. Diameter = 2(4) = 8 cm. Hence, diameter of the circle with radius as 4 cm is 8 cm.
Step-by-step explanation:
please
give brianliest
Answer: Area = 0
Step-by-step explanation:
((2*2)*3.14)-(4*3.14) = 0
WILL GIVE BRIANLIAT TO BEST ABWWER
The graph of an exponential of the form y = ab contains the points (2, 60) and (4, 960). What are the values of a and b
Answer:
(15/4)4^x
Step-by-step explanation:
Substituting the x and y values of the first point, we get:
y = ab
60 = ab^(2)
Substituting the x and y values of the second point, we get:
y = ab
960 = ab^(4)
Now we can solve for a and b by eliminating one of the variables. One way to do this is to divide the second equation by the first equation:
960/60 = (ab^(4))/(ab^(2))
16 = b^(2)
Taking the square root of both sides, we get:
b = ±4
Since an exponential function can only have positive values for b, we choose b = 4. Now we can solve for a by substituting b = 4 into one of the original equations:
60 = a(4^(2))
60 = 16a
a = 60/16
a = 15/4
Therefore, the values of a and b are a = 15/4 and b = 4, and the exponential function is y = (15/4)4^x.
rotate 270 degrees…what are the coordinates of B
PLS HELP
Answer:
8;-2
Step-by-step explanation:
8 is the x axis and -2 is the y axis
Answer:
Step-by-step explanation:
List the three classifications of fundamental skull shapes and indicate the number of degrees of angulation (formed by the petrous pyramids and the midsagittal plane) for each classification.
The three classifications of fundamental skull shapes are: +
BrachycephalicMesocephalicDolichocephalicThe number of degrees of angulation (formed by the petrous pyramids and the midsagittal plane) for each classification is 45, 30, and 15 degrees, respectively.
What is a Skull?The skull is a bony structure that supports the face and protects the brain. There are several different skull shapes, which can be classified into three main categories based on their length and width: brachycephalic, mesocephalic, and dolichocephalic.
Brachycephalic: A short, wide skull shape. The petrous pyramids are angled at 45 degrees to the mid-sagittal plane.Mesocephalic: A skull shape that is neither short nor long, with a medium width. The petrous pyramids are angled at 30 degrees to the mid-sagittal plane.Dolichocephalic: A long, narrow skull shape. The petrous pyramids are angled at 15 degrees to the mid-sagittal plane.To know more about the "skull shape": https://brainly.com/question/1463216
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For the given figure, can you conclude mlln? Explain.
help please image attached
The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines.
Describe Inequality?An inequality is a mathematical statement that compares two quantities or expressions using inequality symbols such as "<" (less than), ">" (greater than), "<=" (less than or equal to), ">=" (greater than or equal to), or "!=" (not equal to).
Inequalities can involve variables or constants, and can be expressed in one variable or multiple variables. The solution to an inequality is the set of values that satisfy the inequality.
For example, the inequality 2x + 3 > 7 is true for values of x that are greater than 2, since if we substitute x = 2, we get 2(2) + 3 = 7, which is not greater than 7. On the other hand, if we substitute x = 3, we get 2(3) + 3 = 9, which is greater than 7, so the inequality is true for x > 2.
Inequalities have many applications in mathematics and other fields, such as economics, physics, and engineering. They are used to represent constraints in optimization problems, to model relationships between variables, and to describe ranges of possible values for a quantity or variable.
To determine the double inequalities that define the shaded region, we need to find the equations of the two boundary lines that form the sides of the shaded region.
The two vertical lines are x=-4 and x=3. The two horizontal lines are y=1 and y=6.
The shaded region is enclosed by these four lines, so the double inequalities that define it are:
-4 ≤ x ≤ 3 and 1 ≤ y ≤ 6
The first inequality -4 ≤ x ≤ 3 represents the values of x that fall between the two vertical lines, while the second inequality 1 ≤ y ≤ 6 represents the values of y that fall between the two horizontal lines. Together, they define the rectangular shaded region with vertices (-4,1), (-4,6), (3,6), and (3,1).
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A softball base is 15 inches long and 15 inches wide. How long is the diagonal? Leave your answer as a
simplified radical.
15 in
15 in
Length of diagonal =
I've been waiting to order your cupcakes all day!
I'll have 4 Nom-Nom-Nom cupcakes -- that's
80% of my order. The rest of the order are Wow.
Using fraction, the total number of cupcakes is obtained to be 5.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
If 4 cupcakes represent 80% of the order, then we can use proportional reasoning to find the total number of cupcakes.
Specifically, if x is the total number of cupcakes, then we can write -
4/x = 80/100
where the left-hand side represents the fraction of the order that is Nom-Nom-Nom cupcakes, and the right-hand side represents the percentage of the order that is Nom-Nom-Nom cupcakes.
Solving for x, we get -
x = 4 / (80/100) = 5
So the total number of cupcakes is 5. Since 4 of them are Nom-Nom-Nom cupcakes, the remaining 1 cupcake must be a Wow cupcake.
Therefore, in total there are 5 cupcakes.
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I've been waiting to order your cupcakes all day! I'll have 4 Nom-Nom-Nom cupcakes -- that's 80% of my order. The rest of the order are Wow.
Find the total number of cupcakes.
Help Please
m-6=50
i need to find the value of m
please urgent
Answer:
m = 50 + 6
m= 56
lol easy ques
This one is easy. All you have to do is add 6 to both sides to get the value of m
m-6=50
m=50+6
m=56
4in 5in 6in 6in 8in 7in triangular prism surface area
the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
To calculate the surface area of a triangular prism, you need to find the area of each of the faces and add them up.
First, let's find the area of the two triangular faces. To do this, we need to find the base and height of each triangle. Since the prism is isosceles, the base of each triangle is 6 inches (the length of one of the sides of the equilateral triangle). The height of each triangle can be found using the Pythagorean theorem. We have two sides of the triangle: 4 inches and 5 inches. Using the Pythagorean theorem, we can find the height:
[tex]h^2 = 5^2 - 4^2\\h^2 = 25 - 16\\h^2 = 9\\h = 3[/tex]
So the height of each triangular face is 3 inches. Now we can find the area of each triangular face:
Area of one triangular face = (1/2) x base x height
= (1/2) x 6 x 3
= 9 square inches
Since there are two triangular faces, the total area of the triangular faces is:
Total area of triangular faces = 2 x 9 = 18 square inches
Next, let's find the area of the three rectangular faces. We have two rectangles with sides of 6 inches by 8 inches, and one rectangle with sides of 4 inches by 8 inches. The area of each rectangular face is:
Area of rectangular face = length x width
So the area of the rectangular faces are:
Area of rectangular face 1 = 6 x 8 = 48 square inches
Area of rectangular face 2 = 6 x 8 = 48 square inches
Area of rectangular face 3 = 4 x 8 = 32 square inches
Therefore, the total surface area of the triangular prism is:
Total surface area = 18 + 48 + 48 + 32 = 146 square inches
So the surface area of the given triangular prism with sides of 4in, 5in, 6in, 6in, 8in, and 7in is 146 square inches.
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A rectangular photograph is 8 inches by 10 inches. It will be put into a rectangular frame that is 2 inches wide on all sides. What is the area of the photograph when it is put into the
frame?
Answer:
the area of the photograph when it is put into the frame is 80 square inches, and the area of the frame is 88 square inches.
Step-by-step explanation:
Answer: 36 inches(2)
Step-by-step explanation:
alexis puts dimes and quarters aside for the parking meter. she has a total of 20 coins and they are worth $3.80. how many quarters does alexis have?
Alexis has 12 quarters and 8 dimes.
Let's use d to represent the number of dimes and q to represent the number of quarters. We know that Alexis has a total of 20 coins, so d + q = 20.
We also know that the value of these coins is $3.80. Since dimes are worth $0.10 and quarters are worth $0.25, we can write an equation for the total value in cents:
10d + 25q = 380
To make things easier, let's divide both sides of the equation by 5:
2d + 5q = 76
Now we can use the first equation to solve for d in terms of q:
d + q = 20
d = 20 - q
Substituting this into the second equation gives:
2(20 - q) + 5q = 76
Expanding the parentheses and simplifying, we get:
40 - 2q + 5q = 76
3q = 36
q = 12
Therefore, Alexis has 12 quarters. We can check this by plugging q back into the first equation to find that she has 8 dimes as well:
d + q = 20
d + 12 = 20
d = 8
The total value of 12 quarters and 8 dimes is:
12 quarters x $0.25 per quarter + 8 dimes x $0.10 per dime = $3.00 + $0.80 = $3.80
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Jaxon invested $710 in an account paying an interest rate of 8\tfrac{7}{8}8 8 7 % compounded quarterly. Jason invested $710 in an account paying an interest rate of 8\tfrac{5}{8}8 8 5 % compounded continuously. After 8 years, how much more money would Jaxon have in his account than Jason, to the nearest dollar?
Answer:
I attached your answer along with an explanation
Step-by-step explanation:
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A plane ticket to Barcelona cost £175 the price decreases by 6% work out the new price of the plane ticket
Answer:
£164.50
Step-by-step explanation:
If the discount is 6%, then the discounted price is 94% of the original price.
95% of £175 = 0.94 × £175 = £164.50
the sum of the numbers (20cba)16 and (a02)16 is ( (click to select) )16 and their product is ( (click to select) )16.
To solve this problem, we need to convert the hexadecimal numbers (20cba)16 and (a02)16 to decimal form, add them together, and then convert the result back to hexadecimal form.
(20cba)16 = 2x16^4 + 12x16^3 + 11x16^2 + 10x16^1 = 131402
(a02)16 = 10x16^2 + 0x16^1 + 2x16^0 = 256
Adding the two decimal numbers together gives us:
131402 + 256 = 131658
To convert this decimal number back to hexadecimal form, we can use the repeated division method.
131658 / 16 = 8228 remainder 10 (A)
8228 / 16 = 514 remainders 4 (4)
514 / 16 = 32 remainder 2 (2)
32 / 16 = 2 remainder 0
2 / 16 = 0 remainder 2
Therefore, (20cba)16 + (a02)16 = (131658)10 = (2002A)16.
To find their product, we can multiply the two decimal numbers together and then convert the result to hexadecimal form.
131402 x 256 = 33559552
Converting this decimal number to hexadecimal form gives us:
33559552 / 16 = 2097472 remainder 0
2097472 / 16 = 131092 remainder 0
131092 / 16 = 8193 remainder 4 (4)
8193 / 16 = 512 remainders 1 (1)
512 / 16 = 32 remainder 0
32 / 16 = 2 remainder 0
2 / 16 = 0 remainder 2
Therefore, the product of (20cba)16 and (a02)16 is (33559552)10 = (2011004)16.
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Can someone please help me these questions are due tn
Answer:
$10.98
Step-by-step explanation:
$10.98
0.06 x 183 = $10.98
The following statement should determine if x is not greater than 20. Explain what is wrong with it and write the correction. if (!x > 20)
The student's original statement has an issue in the way the "not" operator is used. The "not" operator (!) is negating the entire expression, including the variable 'x', rather than just the inequality. This leads to incorrect evaluation.
To correctly determine if x is not greater than 20, you should use the "less than or equal to" (<=) operator instead. Here is the corrected statement:
if (x <= 20)
This statement will be true if x is less than or equal to 20, which is the intended condition.
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The student enrollement of a high school was 1350 in 2012 and increases 9% each year. What is the estimated enrollment in 2022
The estimated enrollment of a high school in 2022 is approximately 2775 students.
To calculate the estimated enrollment in 2022, we need to use the formula for compound interest:
A =[tex]P(1 + r)^t[/tex]
where:
A = final amount (enrollment in 2022)
P = initial amount (enrollment in 2012)
r = annual interest rate (increase rate)
t = number of years (10)
We know that P = 1350 and r = 0.09 (9%). We can plug these values into the formula:
A = [tex]1350(1 + 0.09)^{10[/tex]
A = [tex]1350(1.09)^{10[/tex]
A = 2774.92
Therefore, the estimated enrollment in 2022 is approximately 2775 students.
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as a television executive, you have been given 24 shows to choose from to run during your prime time slots each week. if you have to choose 16 shows to run on your network, how many ways can you choose which shows to pick up?
As per the combination concept, there are 735,471 ways to choose 16 shows from a set of 24.
To find the number of ways to choose 16 shows from a set of 24, we can use the formula for combinations, which is:
ⁿCₓ = n! / x!(n-x)!
Where n is the total number of objects in the set (in this case, 24), and x is the number of objects we want to choose (in this case, 16). The exclamation mark (!) denotes the factorial function, which means multiplying the number by all positive integers less than itself.
Plugging in the numbers, we get:
²⁴C₁₆ = 24! / 16!(24-16)! = 735471
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Use ABC to write the indicated trigonometric ratio
Sin B=
Answer:
b/c
Step-by-step explanation:
sin B = opp/hyp
sin B = b/c
How would you solve for m<ACD
The measure of angle ACD is approximately 109.5 degrees.
What are parallel lines ?
Parallel lines can be defined in which the lines which are equidistant to each other and they never intersect.
To solve for m<ACD, we can use the fact that the sum of the angles in a triangle is 180 degrees.
We can start by finding the measure of angle ACD, which is opposite to the known side length of 10 units. Using the Law of Cosines, we have:
cos(ACD) = (AD * AD + CD * CD - 100) / (2 * AD * CD)
We know that AD = 8 units and CD = 6 units, so plugging in these values, we get:
cos(ACD) = (64 + 36 - 100) / (2 * 8 * 6) = -1/3
Since -1/3 is negative, we know that angle ACD is obtuse, meaning it measures between 90 and 180 degrees. Therefore, we can take the inverse cosine of -1/3 to find its measure:
cos(ACD) = (-1/3) ≈ 109.5 degrees
Therefore, the measure of angle ACD is approximately 109.5 degrees.
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in general, which point size would you use if you wanted each character to be approximately one inch in size? a.) 1 pt b.) 72 pts c.) 24 pts d.) 36 pts
If you want each character to be approximately one inch in size, you would use a point size of 72 pts.
Point size is a unit of measurement used to determine the size of typefaces. It represents the height of the characters in a font. One point is equal to 1/72 of an inch, which means there are 72 points in one inch.
Therefore, if you want each character to be approximately one inch in size, you would need to use a font size of 72 points. This would ensure that the characters are roughly one inch tall, assuming that the font is designed to be proportional and not condensed or expanded.
Choosing a smaller point size, such as 1 pt or 24 pts, would result in characters that are much smaller than one inch. Choosing a larger point size, such as 36 pts, would result in characters that are larger than one inch.
Therefore the correct answer is option b.) 72 pts.
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