The equation can be used to calculate the average speed at which Yusef drove is (c) r = 130/2.5
How to determine the speed equationThe formula to calculate average speed is:
Average speed = distance traveled / time taken
In this problem, Yusef drove 130 miles in 2.5 hours.
So, we can substitute the values in the formula:
Average speed = 130 miles / 2.5 hours
Simplifying this expression, we get:
Average speed = 52 miles per hour
Therefore, the correct equation to calculate the average speed at which Yusef drove is:
r = 130/2.5 or r = 52
Option C matches this equation, so the answer is C.
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estimate the population in the year 2040
The population in the year 2040 is 31800.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 4 is an equation.
We have,
The exponential equation is y = m[tex]a^t[/tex].
Where t is a variable
Now,
In 2007 (t = 0). the population was 12,000.
y = 12000
This means,
12000 = m[tex]a^0[/tex]
12000 = m
And,
In 2019 (t = 12). the population was 23,000.
y = 23000
23000 = m[tex]a^{23}[/tex]
23000 = 12000 [tex]a^{23}[/tex]
23000/12000 = [tex]a^{23}[/tex]
1.92 = [tex]a^{23}[/tex]
[tex]1.036^{23}[/tex] = [tex]a^{23}[/tex]
a = 1.03
Now,
y = 12000 [tex]1.03^t[/tex]
The population in the year 2040.
i.e
t = 33
y = 12000 x [tex]1.03^{33}[/tex]
y = 12000 x 2.65
y = 31800
Thus,
31800 is the population in the year 2040.
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Hi! Can someone please help me? Please look in the photo
I would appreciate it a lot thanks :)
Answer:
D
Step-by-step explanation:
Count total dots => 30
Amount of dots under x>=5 => 21
21/30 = 7/10 = 70%
PLEASEEE HELP —-> Step 1: Construct a circle through three points not on a line.
a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by
drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and
name the point of intersection of the perpendicular bisectors O. How do you know that point O
is the center of the circle that passes through the three points? (10 points)
Answer:
Step 1: Construct a circle through three points not on a line.
a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by
drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and
name the point of intersection of the perpendicular bisectors O. How do you know that point O
is the center of the circle that passes through the three points?
Answer:
Step-by-step explanation:
To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.
This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:
OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2
Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.
Jaelyn had $150 in the school account and sold tickets for the fundraiser at a cost of $8 per ticket. Erik had $480 in his school account and sold tickets for $6 per ticket. How many tickets had to be sold before both accounts had the same amount of money?
Using equations, they sold 165 tickets before both accounts had the same amount of money.
What is an equation?A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.
Finding the values of the variables that result in the equality is the first step in solving an equation with variables. The variables that must be included in the equation are also known as the unknowns.
Given that, Jaelyn had $150 in the school account and sold tickets for the fundraiser at a cost of $8 per ticket.
and Erik had $480 in his school account and sold tickets for the fundraiser at a cost of $6 per ticket.
Let they sold x tickets and they have the amount in their account is y.
After sold tickets, Jaelyn accounts had the amount is
y = 150 + 8x
After sold tickets, Erik accounts had the amount is
y = 480 + 6x
the amount in their account is same, so we compare both equation to find x
150 + 8x = 480 + 6x
arranging like terms in same side
8x - 6x = 480 - 150
2x = 330
divide both sides by 2 we get,
x = 330/2
x = 165
So, they sold 165 tickets before both accounts had the same amount of money.
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Can someone please help me with this I can’t figure it out
Answer:
69
Step-by-step explanation:
if it bisects that mean both angles are equal which tells us we can just divide the whole angle by 2
angle BOA is 138
so when you divide 138 by 2 you get 69
hope it helped
please mark brainiest
Solve the triangle. Round to the nearest tenth.
In the given triangle, ∠F=29°, d>15 and e<15.
What exactly is a triangle?
Triangles are polygons in geometry that have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is a three-sided polygon. A triangle's three angles added together equals 180°. A single plane contains the triangle. The triangle is classified into six forms based on its sides and angles.
A triangle is categorised into three categories based on its sides, namely:
Scalene Triangle - Each side has a distinct length.
Isosceles Triangle - A triangle with two sides of equal length and one side of a different length.
Equilateral Triangle - A triangle has three sides that are of the same length.
A triangle is categorised into three categories based on its angles, namely:
Acute Angle Triangle - A triangle with all of its angles smaller than 90°.
Obtuse Angle Triangle - A triangle with one of its angles larger than 90°.
Triangle with a Right Angle - A triangle with one of its angles equal to 90°.
Now
As sum of all angles of triangle=180°
∠F+127°+24°=180°
∠F=180-151
∠F=29°
and In a triangle Largest angle is opposite to largest side and smallest angle is opposite to smallest side.
Then the sides e and d will be as following d>15 and e<15.
hence,
In the given triangle, ∠F=29°, d>15 and e<15.
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Find the area of a rectangle with side lengths 5/8ft. and 1/3 ft.
A. 5/11
B. 1 11/12
C. 6/11
D. 5/24
The area of a rectangle with side lengths 5/8ft. and 1/3 ft is: D. 5/24 ft².
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.W represents the width or base of a rectangle.L represents the length or height of a rectangle.Substituting the given points into the area of rectangle formula, we have the following;
Area of rectangle = 5/8 × 1/3
Area of rectangle = 5/24 square feet.
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carrie is cutting sheets of stickers to put in 4 gift bags Each bag will contain the same number of stickers . if each sheet contains 22 stickers then what is the fewwer number of sheets carrie can use so there are no stickers left over
Carrie is slicing sticker sheets to fit four present bags. There will be an equal quantity of stickers in each bag.
What is fewer number?The word "fewer" is represented by the Greek letter "," which denotes that one thing is less than another. Any number bigger than another is indicated by the sign >. In this case, 6 10 demonstrates that 6 is less than 10. According to this, 6 is less than 10 in size.A rule concerning fewer and less is frequently cited. As an example, "fewer options" and "fewer issues" relate to the quantity or amount among things that are counted, whereas "less time" and "less work" refer to the quantity or amount among things that are measured. Lesser simply indicates "not as many."To learn more about fewer number refer to:
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here are the first four terms of a number sequence 1 5 13 29.
The rule to continue this sequence is mutiply the previous term by 2 then add 3
work out the 5th term of this sequence
Answer:
61
Step-by-step explanation:
using the rule to find the fifth term from the fourth term 29
5th term = 2 × 29 + 3 = 58 + 3 = 61
Given the function g(n) = 2 n4 + 20 n3 + 42n2
Its g-intercept is
Its n intercepts are
The g-intercept of the function g(n) is 0.
The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.
What is a function?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the range), such that each input is related to exactly one output.
To find the g-intercept of a function, we need to determine the value of g when n = 0. So, to find the g-intercept of the function g(n) = 2n⁴+ 20 n³ + 42n², we can simply substitute n = 0 into the function:
g(0) = 2(0)⁴ + 20 (0)³ + 42(0)² = 0
Therefore, the g-intercept of the function g(n) is 0.
To find the n-intercepts of a function, we need to determine the values of n for which g(n) = 0. In other words, we need to solve the equation 2n⁴+ 20 n³ + 42n² = 0.
We can factor out a common factor of 2n² to simplify the equation:
2n²(n² + 10n + 21) = 0
This equation is true when either 2n² = 0 (which implies n = 0), or when n² + 10n + 21 = 0. The quadratic equation n² + 10n + 21 = 0 can be factored as (n + 3)(n + 7) = 0, so its solutions are n = -3 and n = -7.
The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.
Hence,
The g-intercept of the function g(n) is 0.
The n-intercepts of the function g(n) are n = 0, n = -3, and n = -7.
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Express the integral f(x, y, z) dV E as an iterated integral in six different ways, where E is the solid bounded by the given surfaces. Y = x2, z = 0, y + 4z = 16
The integral f(x, y, z) dV E as an iterated integral can be expressed in six different ways, where E is the solid bounded by the given surfaces.
To express the integral as an iterated integral, we need to determine the limits of integration for each variable.
First, we can find the limits of integration for z The plane z = 0 is the xy-plane, and the plane y + 4z = 16 can be rewritten as z = (16 - y)/4. So the limits of integration for z are 0 to (16 - y)/4.
Next, we can find the limits of integration for y The surface y = x^2 bounds the solid from below in the y direction, and the plane y + 4z = 16 bounds the solid from above in the y direction. So the limits of integration for y are x^2 to 16 - 4z.
Finally, we can find the limits of integration for x There are no explicit surfaces that bound the solid in the x direction, so we can use the limits of integration for y to determine the limits of integration for x.
With these limits of integration, we can express the integral in six different ways over dz dy dx:
∫∫∫E f(x, y, z) dV = ∫0^(16/4) ∫x^2^(16 - 4z) ∫0^g(x, y) f(x, y, z) dz dy dx
where g(x, y) = (16 - y)/4
∫∫∫E f(x, y, z) dV = ∫x^2^4 ∫0^16-4z ∫0^g(x, y) f(x, y, z) dz dx dy
where g(x, y) = (16 - y)/4
∫∫∫E f(x, y, z) dV = ∫x^2^4 ∫0^g(x, y) ∫0^(16 - 4z) f(x, y, z) dz dy dx
where g(x, y) = 16 - 4z
∫∫∫E f(x, y, z) dV = ∫0^4 ∫x^(1/2)^4 ∫0^g(x, y) f(x, y, z) dy dx dz
where g(x, y) = (16 - 4z)
∫∫∫E f(x, y, z) dV = ∫0^(16/4) ∫0^(16 - 4z) ∫y^(1/2)^4 f(x, y, z) dy dz dx
∫∫∫E f(x, y, z) dV = ∫0^4 ∫x^(1/2)^4 ∫0^(16 - 4z) f(x, y, z) dz dy dx
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A 14-foot ladder is set up 4 feet from the base of a building. How far up the building does the ladder reach? round your answer to the nearest tenth of a foot.
The height that a ladder reaches is determined by the length of the ladder and its distance from the base of the building.
The ladder can be thought of as the hypotenuse of a right triangle, with the height that the ladder reaches up the building being one of the other sides and the distance of the ladder from the building being the other side.
So, the formula for the height that a ladder reaches can be expressed as:
Height =
Where "Ladder Length" is the length of the ladder, and "Distance from Base" is the distance of the ladder from the building.
Using this formula, we can calculate the height that the 14-foot ladder reaches when set up 4 feet from the base of the building:
Height = ([tex]14^2 - 4^2)^0.5[/tex]
= [tex](196 - 16)^0.5[/tex]
= [tex]180^0.5[/tex]
= 13.416407864
Rounding to the nearest tenth of a foot, the height the ladder reaches is 13.4 feet.
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PLEASEEE HELP —-> Step 1: Construct a circle through three points not on a line.
a) Points D, E, and F are not in a line. To construct a circle through points D, E, and F, begin by
drawing line segments DE and EF. Then construct the perpendicular bisectors of DE and EF, and
name the point of intersection of the perpendicular bisectors O. How do you know that point O
is the center of the circle that passes through the three points? (10 points)
Answer:
Step-by-step explanation:
To show that point O is the center of the circle that passes through points D, E, and F, we can use the property of perpendicular bisectors. The perpendicular bisectors of two chords of a circle bisect the chord and pass through the center of the circle. Since the perpendicular bisectors of DE and EF intersect at point O, it follows that O must be the center of the circle that passes through points D, E, and F.
This property can also be proven using the Pythagorean theorem. Let the radius of the circle be r and let the midpoints of DE and EF be M1 and M2, respectively. Then, OM1 = OM2 = r, and the distance between M1 and M2 is equal to the distance between D and F. By the Pythagorean theorem, the sum of the squares of the sides of a right triangle is equal to the square of the hypotenuse, so we have:
OM1^2 + (M1M2)^2 = r^2 + r^2 = 2r^2
Since OM1^2 + (M1M2)^2 is equal to 2r^2, it follows that the distance between M1 and M2 is equal to the diameter of the circle. This means that M1 and M2 are the midpoints of the diameter of the circle, so they must both lie on the circumference of the circle. This, in turn, means that O is the center of the circle that passes through points D, E, and F.
A distribution of all sample means or sample variances that could be obtained in samples of a given size from the same population is called
Answer:
sampling distribution
Step-by-step explanation:
:)
Help me with this question….
Answer:c
Step-by-step explanation:
A bag with 12 marbles has 12 blue marbles,a marble is chosen from the bag,What's the probability is blue
100%, If 12 of all 12 marbles are blue, its 100%
Andre pidió prestado al prestado al banco un capital de 350,000 por lo cual el banco le cobrará un 6%de interés mensual cuánto debe pagar por un mes de interés
Andre borrowed 350,000 from the bank and the bank will charge him 6% interest per month. To calculate the amount he has to pay for one month of interest, we can use the following formula:
Interest = Capital * Interest rate
In this case, the capital is 350,000 and the interest rate is 6%. So, we can plug in the values:
Interest = 350,000 * 0.06
Interest = 21,000
Therefore, Andre has to pay 21,000 for one month of interest.
The following information is known about a loan time equals seven years interest rate equals 6% interest equals 840 $.00 what was the principal on a loan
Answer:
$2,000
Step-by-step explanation:
Interest = Principal x Rate x Time
840 = .06(7)p
840 = 0.42p
p = 2000
The length of the dashed line in the circle
The length of the dotted line would be 7.922 ft.
What is the diameter of the circle?
The diameter of a circle is the distance across the circle through its center. It is equal to twice the length of the radius, which is the distance from the center of the circle to any point on the circle.
In mathematical terms, if d represents the diameter of a circle, and r represents its radius, we have the formula:
d = 2r
In the given circle, for finding the inner diameter we have to remove the thickness of the circle from outer diameter, we get
q = 17.708 - 4.893 - 4.893
By solving this, we get
q = 7.922
Hence, the length of the dotted line would be 7.922 ft.
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Graph the line with the equation
Answer:
See below
Step-by-step explanation:
You should just use a graphing calculator or an online graphing site to do this
If you were to do this manually on a graph sheet, here is how you proceed
Given line is
y = -x - 4
We need to find 2 points to plot a straight line
Choose x = 0 ==> y = - 0 - 4 = -4
So (0, - 4) is one point
Choose another value for x. x = -4 is a good point
At x = - 4, y = -(-4) - 4 = 0
So (-4, 0) is another point.
Plot these two points on the graph and draw a straight line through those points
The attached graph shows this all
If x=3. what is y=?
Y=
X: -3 0 3 6
Y: -5 -4 -3 -3
Answer:
Step-by-step explanation:
y = -3
The graph of f(x)=sin(x) is transformed to a new function g(x), by reflecting it over the x-axis and shifting it 2 units up. What is the equation of the new function g(x)?
On solving the provided question we can say that here trigonometry y = Asin(Bx + C)+D
What exactly is trigonometry?Trigonometry is a branch of mathematics that studies the relationship between triangle side lengths and angles. From the use of geometry in astronomical study, the area first appeared in the Hellenistic era, around the third century BC. Exact methods is a branch of mathematics that deals with specific trigonometric functions and how they can be used in calculations. In trigonometry, there are six popular trigonometric functions. Their names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of the properties of triangles, particularly right triangles. However, the study of geometry is the characteristics of all geometric figures.
(x)=sin(x) consider y = Asin(Bx + C)+D adjusts the amplitude of the function (how high or low it is).
if you want to
B determines how many full wavelengths will occur during a certain time period, and C determines the phase shift (left/right on the axis) (positive values will shift left)
The vertical shift, or D, is up or down. For example, a +3 would move the entire function up 3 units.
In your situation, the amplitude is 4 since you wish to stretch vertically.
Additionally, you want to move it right three units. C = -3 (always the opposite of the direction you wish to go) (always the opposite of the direction you want to go)
g(x) = 4sin(x - 3)
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To find 15+32,
Kayla adds the ones.
Then she adds the tens.
Then she adds the ones and tens.
5+2=7
1+3=4
7+4=11
Do you agree with Kayla? Yes or No.
Explain by showing your thinking using drawings, numbers, or
words.
Answer:
no
Step-by-step explanation:
15+32 you would first add the tens
5+2=7
then the ones
1+3 =4
you're answer would then be 47 as the ones come before the tens
Circles and please answers please just need help Thank you so much
The area of the shaded region is given as follows:
As = 324(2π - 1) in².
What is the area of the shaded region?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr².
For this problem, the circle has a radius of [tex]18\sqrt{2}[/tex], as the radius is the diagonal of the square, hence the area is given as follows:
A = π x [tex](18\sqrt{2})²[/tex]
A = 648π in².
The area of a square of side length s is given by the square of the side length, hence the area of the square is given as follows:
A = 18²
A = 324 in².
Hence the area of the shaded region is given as follows:
As = 648π - 324
As = 324(2π - 1) in².
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Solve the equation in the complex number system. X^2+x+8=0
(Simplify your answer. Type an exact answer, using radicals and i as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.)
Answer:
Step-by-step explanation:
here's a step-by-step explanation with more detail:
The equation X^2 + X + 8 = 0 can be solved using the Quadratic Formula:
X = (-b ± √(b^2 - 4ac)) / 2a,
where a = 1, b = 1, and c = 8.
Plugging in the values, we get:
X = (-1 ± √(1^2 - 4 * 1 * 8)) / 2 * 1
X = (-1 ± √(-31)) / 2
Since the square root of a negative number is not a real number, the solution to the equation must be expressed using complex numbers. In this case, the square root of -31 can be expressed as the imaginary unit i times the square root of 31.
X = (-1 ± i * √31) / 2
So, the two solutions to the equation are:
X = (-1 + i * √31) / 2 and X = (-1 - i * √31) / 2
And these are the two solutions expressed in terms of the imaginary unit i.
A sign in the shape of a circle has a radius of 15 cm. What is the area of the sign? Use 3.14 for pi.
Answer:
The area of the sign is 706.5 cm^2.
Step-by-step explanation:
We know,
The formula of area of a circle,
A = πr^26
Here A is area and r is radius.
Here we have radius is 15 cm, so we can put the values in the above equation and find the area,
A = π * 15^2
A = 3.14 * 225
A = 706.5
The area of the sign is 706.5 cm^2.
Find the distance the point P(3, 1, 7), is to the plane through the three points
Q(5, 0, 3), R(0, -1, 7), and S(7, 5, 0).
The distance between the point P and the plane through the points Q, R, and S is 60/23.
How did we get the value?The distance of a point P(x1, y1, z1) from a plane that passes through the points Q(x2, y2, z2), R(x3, y3, z3), and S(x4, y4, z4) can be found using the following formula:
d = |(A * x1 + B * y1 + C * z1 + D) / sqrt(A^2 + B^2 + C^2)|
Where A, B, and C are the coefficients of the plane's normal vector and D is the constant term in the equation of the plane. The normal vector can be found by taking the cross product of the vectors Q-R and Q-S:
n = (Q-R) x (Q-S)
The coefficients of the normal vector can be found using the following equations:
A = n1
B = n2
C = n3
D = -(A * x2 + B * y2 + C * z2)
Substituting the values of Q, R, and S, we have:
Q-R = (5-0, 0-(-1), 3-7) = (5, 1, -4)
Q-S = (7-5, 5-0, 0-3) = (2, 5, -3)
The cross product of Q-R and Q-S is:
n = (1 * -3 - 5 * -4, -3 * 5 - 2 * -4, -2 * 1 - 5 * 5) = (-23, 29, 17)
So,
A = -23
B = 29
C = 17
D = -(A * x2 + B * y2 + C * z2) = -(-23 * 5 + 29 * 0 + 17 * 3) = -109
Finally, substituting the values of x1, y1, and z1:
d = |(A * x1 + B * y1 + C * z1 + D) / √(A^2 + B^2 + C^2)|
= |(-23 * 3 + 29 * 1 + 17 * 7 + -109) / √(-23^2 + 29^2 + 17^2)|
= |(-69 + 29 + 119 -109) / √(-23^2 + 29^2 + 17^2)|
= |60 / √(-23^2 + 29^2 + 17^2)|
= |60 / √(529)|
= 60 / 23
So the distance between the point P and the plane through the points Q, R, and S is 60/23.
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suppose you are one of 19 people at a dinner party. Find the probability that at least one of the other guests has the same birthday as you and that some pair of guests share the same birthday assume there are 365 days in the year
The probability that at least one other guest shares your birthday is approximately?
The probability that some pair of guests share the same birthday is approximately?
The solution is 0.3486 or 34.86%, chance that exactly one other guest has the same birthday as you.
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
here, we have,
For each guest, the probability that they share a birthday with you is 1 in 365. Aside from you, there are 499 guests.
Therefore, this problem can be modeled by a binomial probability model with probability of success 1/365.
The probability of exactly 1 success in 499 trials is given by:
P(x=1) = 0.3486
There is a 0.3486 or 34.86% chance that exactly one other guest has the same birthday as you.
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What is your monthly take-home pay if your take-home pay is calculated as 20 hours per week at $11.66 per hour with 27% deducted for taxes and insurance?
Round intermediate calculations and the final answer to the nearest cent; use 365 days in a year.
Your monthly take-home pay is $
The monthly take-home pay is ¢ 68094. The solution has been obtained by using arithmetic operations.
What are arithmetic operations?
The term "arithmetic operations" refers to four basic mathematical operations that can be used to express any real number. Addition, subtraction, multiplication, and division are the four operations.
We are given that take-home pay is calculated as 20 hours per week at $11.66 per hour with 27% deducted for taxes and insurance.
Considering 365 days in a year, there are 52 weeks in year and 4 weeks in a month.
In a week there are 20 hours
So, in 4 weeks, there will be 80 hours
Take - home pay before deductions = 80 * $11.66 = $932.8
Take - home pay after deductions = $932.8 - 27% of $932.8 = $680.94
This is equal to ¢ 68094.
Hence, the monthly take-home pay is ¢ 68094.
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A deli is trying out new labels for their cylindrical-shaped wheels of cheese. The label covers the entire wheel except the circular top and bottom.
If the wheel has a radius of 30 centimeters and a height of 20 centimeters, how many square centimeters of the wheel does the label cover? (Approximate using pi equals 22 over 7)
792,000 over 7 square centimeters
66,000 over 7 square centimeters
26,400 over 7 square centimeters
2,640 over 7 square centimeters
The label covers approximately 4,800 square centimetres of the wheel of cheese.
What is the lateral surface area of a cylinder?
The lateral surface area of a cylinder can be found using the formula:
L = 2πrh
where L is the lateral surface area, r is the radius of the cylinder, and h is the height of the cylinder.
In this case, we need to find the lateral surface area of the wheel of cheese, so we can use the given radius of 30 centimetres and height of 20 centimeters to calculate:
L = 2 x (22/7) x 30 x 20
L = 4,800 square centimetres
This is the total surface area of the cylindrical-shaped wheel of cheese. However, the label does not cover the circular top and bottom, so we need to subtract their areas from the total surface area to find the area covered by the label.
The area of a circle can be found using the formula:
A = πr²
where A is the area of the circle, and r is the radius of the circle.
In this case, we have two circles (top and bottom), so the total area of the circles that are not covered by the label is:
2 x (22/7) x 30²
= 56,400/7 square centimeters
Subtracting this from the total surface area, we get:
4,800 - 56,400/7
= 33,600/7 square centimeters
= 4,800 square centimeters (rounded to the nearest whole number)
Therefore, the label covers approximately 4,800 square centimeters of the wheel of cheese.
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