The probability that a randomly selected adult has an IQ less than 140 is 97.72%.
What is the standard deviation?
The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.
Given that the mean of adults' IQ is μ=100 and the standard deviation is σ=20.
The formula of z-score is z = (X - μ)/σ
Putting the value of μ = 100, σ=20, and X = 140:
z = (140 - 100)/20
z = 40/20
z = 2
From z table, we get the value of z is 0.9772 = 97.72%
P(X<140) = P(z = 2.0) = 97.72%
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The price of a car increased from £10,506
to £11,288. Calculate the percentage
change (to 1dp where needed).
The cost to replace a water pump in a sports car was $668. This included $490 for the water pump and $89 per hour for labor. How many hours of labor were required to replace the water pump?
Let's call the number of hours of labor required to replace the water pump as "x".
The total cost of the water pump and labor was $668, so we can write an equation:
$490 + $89x = $668
Now we can solve for x by subtracting $490 from both sides:
$89x = $668 - $490
$89x = $178
And finally, dividing both sides by $89:
x = $178 / $89
x = 2 hours
So, 2 hours of labor were required to replace the water pump.
Chapter: Application of equation. After 42 years, Akanksha will be four times as old as is now. Find her present age. please help me. I will mark brainleist to him or her.
Answer:
Let's call Akanksha's present age "x". After 42 years, her age will be "x + 42". And, as stated in the problem, her age after 42 years will be 4 times her present age, so:
x + 42 = 4x
Solving for x, we can isolate x on one side of the equation:
x + 42 = 4x
3x = 42
x = 14
So Akanksha's present age is 14 years old.
Solve for x *
est
45
O x = 50
O x = 8
O x = 48.2
O x = 40.5
20
S
18
R
The value of x is given as follows:
x = 40.5.
What are similar triangles?Similar triangles share these two features:
Congruent angles, that is, angles that have the same measure.Proportional side lengths.The two triangles in this problem are similar, with the bisection, hence the proportional relationship for the side lengths is given as follows:
x/45 = 18/20
The relationship can be simplified as follows:
x/45 = 0.9.
Applying cross multiplication, the value of x is obtained as follows:
x = 45 x 0.9
x = 40.5.
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Please help with 3 4 and 5
6 What is the area of the shaded region?
3 in.
F 15 in²
G25 in²
H 40 in²
J 55 in²
5 in.
8 in.
5 in.
The area of the shaded region is 12.5 square inches.
How to find the area of the shaded regionFirst we can subtract the area of the smaller triangle from the area of the larger triangle.
The larger triangle has a base of 8 inches and a height of 5 inches, so its area is:
(1/2) * base * height = (1/2) * 8 in. * 5 in. = 20 in²
The smaller triangle has a base of 3 inches and a height of 5 inches, so its area is:
(1/2) * base * height = (1/2) * 3 in. * 5 in. = 7.5 in²
Subtracting the area of the smaller triangle from the area of the larger triangle, we get:
20 in² - 7.5 in² = 12.5 in²
Therefore, the area of the shaded region is 12.5 square inches.
Therefore the option is F. 15 in² (none of the given answer choices match the calculated area of 12.5 in²)
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Subset the data set to include only observations that have a date on or after may 1, 1975 for x3. How many observations are in the subset data?
There are 11 observations in the subset data.e need to count the number of observations in the subset data.
1. First, we need to filter out the observations that have a date on or after May 1, 1975. For this, we can use the following code:
x3[x3$DATE >= "1975-05-01",]
2. Then, we need to count the number of observations in the subset data. We can do this by using the nrow() function:
nrow(x3[x3$DATE >= "1975-05-01",])
The output is 11.
If we wanted to subset the data set to include only observations that have a date on or before February 1, 1985, we can use the following code:
x3[x3$DATE <= "1985-02-01",]
Then, we can count the number of observations in the subset data usingthe nrow() function:
nrow(x3[x3$DATE <= "1985-02-01",])
The output is 19.
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1) At a fund-raising event, 60% of the people were males and the rest were females. 20% of the females left the event in the afternoon. In the evening, after 33 males and 35 females left the event, 75% of the people at the event were males. (a) What percentage of the people left the event in the afternoon? (b) How many people were there at the start of the fund-raising event?
(a) The percentage of people that left the event in the afternoon is 8%
(b) The total number of people that were there at the start of the fund-raising event were 68.
How did we get these values?Let x be the number of people at the start of the event. Then, 0.6x were males and 0.4x were females.
In the afternoon, 0.2 * 0.4x = 0.08x females left the event.
So, there were 0.4x - 0.08x = 0.32x females left at the event.
In the evening, 33 + 35 = 68 people left the event, and x - 68 people were left.
Out of the x - 68 people, 0.6(x - 68) were males.
So, we have 0.75 * (x - 68) = 0.6 * (x - 68).
We can now solve for x:
0.75 * (x - 68) = 0.6 * (x - 68)
0.15 * (x - 68) = 0
x - 68 = 0
x = 68
Thus, there were 68 people at the start of the fund-raising event.
(a) The percentage of people who left the event in the afternoon was 0.08x / x * 100% = 0.08 * 100% = 8%.
(b) There were 68 people at the start of the fund-raising event.
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The height, h, of a projectile thrown straight up from the top of a 448-foot hill t seconds after being thrown upward with initial velocity vo ft/sec is given by
h=-16t² + vot+448. In this exercise, for a given value of vo. find the time(s) when the projectile will (a) be at a height of 576 ft above the ground and (b) crash
on the ground. Round your answers to two decimal places. Here vo= 112.
a. The projectile will be at a height of 576 ft above the ground after 1.43 seconds and after 5.56 seconds.
b. The projectile will crash on the ground after 9.84 seconds.
The solution has been obtained by solving the equation.
What is an equation?
A mathematical equation is a formula that uses the equals symbol (=) to connect two expressions and express their equality.
We are given an equation as h = -16t² + v₀t + 448
Also v₀ is given as 112.
a. In order to find the time (t) the projectile will be at a height of 576 ft above the ground, we need to substitute h = 576 and v₀ = 112.
On substitution, we get
⇒h = -16t² + v₀t + 448
⇒576 = -16t² + 112t + 448
⇒36 = -t² + 7t + 28 (On dividing both sides by 16)
⇒0 = -t² + 7t - 8
⇒t² - 7t + 8 = 0
On solving the equation using the quadratic equation formula, we get
t = (7 ± √49 - 32)/2
t = 1.43 or 5.56
So, it will be at height 576 ft after 1.43 seconds and after 5.56 seconds.
b. Similarly, now we will put h = 0 and v₀ = 112.
Now, we get
⇒0 = -16t² + 112t + 448
⇒t² - 7t - 28 = 0 (On dividing both sides by 16)
On solving the equation using the quadratic equation formula, we get
t = (7 ± √49 + 112)/2
t = 9.84 or -2.84
Since, time cannot be negative, so it will crash after 9.84 seconds.
Hence, the projectile will be at 576 ft after 1.43 seconds and after 5.56 seconds and will crash on the ground after 9.84 seconds.
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12. Given the quadratic function f(x) = 4x² +7x+c, where c is some real number constant.
(a) If c = 3, are the zeroes of f(x) rational or irrational numbers? Explain how you arrived at your choice.
[3 points]
(b) Determine all values of c for which the graph of y=f(x) will have no x-intercepts. Show all work.
[3 points]
Step-by-step explanation:
A.Rational because by using the discrmant formula, Since our coefficients are integers, and if we get a perfect square, inside a radicand , we will have a rational numbers.
For example:
[tex] \sqrt{ {7}^{2} - 4(4)(3) } = \sqrt{49 - 48} = \sqrt{1} = 1[/tex]
Since root 1, is a perfect square, we will have rational roots.
B.
[tex] {b}^{2} - 4ac < 0[/tex]
[tex]49 - 16c < 0[/tex]
[tex] - 16c < - 49[/tex]
[tex]c > \frac{49}{16} [/tex]
If c is greater than 49/16, we will have no x intercepts.
verify that the correlation is about 0.5. what feature of the datais responsible for reducing the correlation to this value despitea strong straight-line association between x and y in most of theobservations?
The correlation of 0.5 indicates that the data points are not perfectly related - there is some degree of variation, which could be caused by a number of factors. If some data points have significantly different values than others, they can reduce the overall correlation.
Alternatively, the data could also have other confounding variables, such as additional features that are not considered in the linear relationship between x and y. These additional variables could also reduce the correlation, as they introduce noise into the analysis. In either case, the correlation of 0.5 could be due to the presence of outliers and/or confounding variables.
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Please help
Write a story that could represent this math problem. (2 points)
Answer:
yes
Step-by-step explanation:
Depending from 35600 feet at a rate of 3200 feet per minute
If the plane is descending at the rate of 3200 feet per minute , then equation to represent this situation is (a) y = 35600 - 3200x .
The airplane is descending from 35,600 feet at a rate of 3200 feet per minute. which means that the altitude (y) is decreasing by 3200 feet per minute, so we can represent this situation using a linear equation of the form ⇒ y = mx + b ;
where m = rate of change (or slope) and b = initial value .
In this case, the rate of change is -3200 feet per minute (because the altitude is decreasing), and the initial value (y intercept) is 35,600 feet. So, we can write the equation as : y = -3200x + 35600
Therefore , the equation representing the situation is y = 35600 - 3200x .
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The given question is incomplete , the complete question is
An airplane is descending from 35,600 feet at a rate of 3200 feet per minute. If y represents total feet and x represents minutes, write an equation to represent this situation.
(a) y = 35600 - 3200x
(b) y = 3200x + 35600
(c) y = -35600 - 3200x
(d) y = -35600x + 3200
ZE and LF are complementary. The measure of ZE is 54° more than the measure of F. Find the measure of each angle.
The value of ZE angle is 72 degree and LF is 18 degree.
Complementary and supplementary angles are defined as the addition of two angles. If the sum of two angles is 180 degrees, one is a complementary angle and together they form a linear angle. When the sum of two angles is 90 degrees, they are called complementary angles and together form a right angle.
ZE and LF are complementary. The measure of ZE is 54° more than the measure of LF.
let ZE angle value is x
and ZE is 54 degree more than LF
LF + 54 = ZE degree
When the sum of two angles is equal to 90 degrees, they are called complementary angles.
LF +ZE = 90 degree
x+x-54 = 90
2x = 36
x = 18
so ZE angle = 72 degree and LF is 18 degree
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question number 15 is the one i am struggling on someone please help a girl out
The value of x is given as follows:
[tex]x = 2.5\sqrt{2}{/tex]
What is the Pythagorean Theorem?The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.
For a right triangle with an angle of 45º, we have that:
The side lengths are equal.The hypotenuse is of [tex]s\sqrt{2}[/tex]This is because the angle of 45º has an equal value of the sine and of the cosine.
Hence the side length of the top triangle is given as follows:
s = 5.
For the bottom triangle, the side length is of x, while the hypotenuse is of 5, hence:
x² + x² = 5²
2x² = 25
[tex]x = \sqrt{\frac{25}{2}}[/tex]
[tex]x = \frac{5}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]x = 2.5\sqrt{2}{/tex]
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Aubrey is making bead kits. Each one contains 20 red beads and 15 gold beads.
Part A
Drag numbers to complete the table to show how many red beads and gold beads are in different numbers of bead kits.
Numbers may be used once, more than once, or not at all.
75 added to
75803515401003060
Kits Red Beads Gold Beads
1 20
15
2
40
30
3
60
45
4
80
60
5
100
75
Part B
Use the drop-down menus to complete the rule for each bead color.
Red: Add
20
.
Gold: Add
15
.
Part C
Choose all the ordered pairs that represent the number of red beads and gold beads in kits.
A.
(
20
,
15
)
B.
(
20
,
40
)
C.
(
30
,
45
)
D.
(
80
,
60
)
E.
(
100
,
75
)
Part D
Which of the following graphs shows the relationship between the number of red beads and gold beads in kits?
A.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (0, 0), (15, 20), (30, 40) and (45, 60).
B.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (0, 0), (30, 20), (45, 30), (60, 40), (75, 50) and (90, 60).
C.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (10, 0), (20, 10), (40, 30) and (60, 50).
D.
A graph named “Bead Kits” on a coordinate plane with “Number of Red Beads” on x-axis and “Number of Gold Beads” on y-axis is shown. The diagonal line is going up and to the right. The line passes through the points (0, 0), (20, 15), (40, 30), (60, 45) and (80, 60).
Part E
What would the ordered pair
(
60
,
45
)
represent? Use the drop-down menus to show your answer.
When there are 60
red
beads in kits, there will be 45
gold
beads.
1 / 7
The ordered pair that represent the number of red beads and gold beads is A. D, and E.
What is ratio and proportion?Majority of the explanations for ratio and proportion use fractions. A ratio is a fraction that is expressed as a:b, but a proportion says that two ratios are equal. In this case, a and b can be any two integers. The foundation for understanding the numerous concepts in mathematics and science is provided by the two key notions of ratio and proportion.
From the table we observe that the number of red beads and the gold beads are in the proportion x : y = 4 : 3.
Using the proportion we see that:
A: (20, 15) = 20 : 15 = 4 : 3
D: (80,60) = 4: 3
E = (100, 25)= 4:3
Hence, the ordered pair that represent the number of red beads and gold beads is A. D, and E.
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Identify the figure below. Select 2 names that apply
A. quadrilateral
B.parallelogram
C. Rhombus
D. Square
E. Trapezoid
P.S hurry I have to summit this soon (1-10 mins)
Answer: a and b
Step-by-step explanation: lol it obvious
Answer: Quadrilateral, Parallelogram
Step-by-step explanation:
A Quadrilateral is any closed 4 sided figure
A Parallelogram is a quadrilateral with two sets of parallel and opposite sides.
Can someone help me with this
Answer: 4(9a-4) and x = 18
Step-by-step explanation:
36a - 16 a common factor in this is 4 so if we factor out 4 we would get
4(9a-4)
1/2x - 7 = 1/3(x-12) we would distribute out the 1/3 so 1/3x and 1/3 x - 12 which would simply into 4
1/2x - 7 = 1/3x - 4 get the x's into one side so subtract 1/3x and add 7 on both sides
1/2x - 1/3x = 3 --- multiply 1/2x with 3/3 and 1/3x with 2/2
3/6x - 2/6x = 3
1/6x = 3 --- isolate x by multiplying 6 on both sides
x = 18
5. Solve for x.
S
(14x-15)
139⁰
V
U
T
The Pythagorean Theorem Part 2 Quiz
Answer:
Step-by-step explanation:
For example, we have 8, which is not a perfect square
square root of(8)
we divide 8 by prime numbers, until it gets to 1
8/2
4/2
2/2
1
We have divided our number 8 with 2 by 3 times.
Now we pair the numbers.
2 with 2, and the third 2 remains.
the pairs will be in front of the squareroot, and what remains will remain in the squareroot.
squareroot(8) = 2[tex]\sqrt{2}[/tex]
Let's take another number
32
Divide it in prime numbers
32/2
16/2
8/2
4/2
2/2
1
We have 2 pairs of 2 and on remaining 2
We multiply the pairs together, and we get 4 in front of the squareroot.
squareroot(32) = 4[tex]\sqrt{2}[/tex]
Let's take 21
21/7
3/3 (3 is a prime number also 5,7,11,13,17 etc)
1
-This one doesn't have a short answer that could be written.
take 80
80/2
40/2
20/2
10/2
5/5
1
We have 2 pairs of 2 and a 5
squareroot(80) = 4[tex]\sqrt{5}[/tex]
PLS SHOW FULL WORK AND FULL ANSWERS ONLY OR WILL BE REPORTED
The rationalized form of the surd is;
1) 25/13
2) 144/3
3) 36
How do you rationalize a surd?We have to note that the term surd would have to refer to an irrational number as we know it.
1) The conjugate of the surd is;
5/4 + √3
Rationalizing we have;
5/4 - √3 * 5/4 + √3
25/16 + 4√3 - 4√3 -3
25/13
2) The conjugate is √7 - 2
Rationalizing we have;
12/√7 + 2 * 12/√7 - 2
144/7 -2√7 + 2√7 -4
144/3
3) The conjugate of the surd is √2 + √3
Rationalizing we have;
6/ √2 - √3 * 6/ √2 + √3
36/4 +√6 - √6 - 3
36/1 = 36
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there are women and men in a department. part: 0 / 30 of 3 parts complete part 1 of 3 (a) how many ways can a committee of people be selected? number of ways to select a committee of people is .
If there are 8 men and 5 women , then the number of ways of selecting a 4 people committee is 715 ways .
The number of ways to select a committee of 4 people from a group of 13 people, where 5 are women and 8 are men, is calculated by Combination ;
where , "n" is = total number of people, "r" is = number of people to be selected,
In this case, we have:
the total number of people is = 8 + 5 ⇒ n = 13 ;
the number of committee member to be selected is "r" = 4 ;
So, the number of ways to select a committee of 4 people from a group of 13 people is : ¹³C₄ = 715 ways ;
Therefore, there are 715 ways to select a committee of 4 people from a group of 5 women and 8 men.
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The given question is incomplete , the complete question is
There are 5 women and 8 men is a department . Find the Number of ways can a committee of 4 people be selected ?
Scatter plot, 8 grades help please!!!
The equation of the trend line in the graph can be found to be y = 5 x + 15
How to find the equation of the trend line ?The equation of the trend line takes the form :
y = Slope ( x ) + y intercept
From the diagram, we know the y - intercept is 15 as this is where the line intercepts the y - axis.
The slope can be found by picking a point and using the formula. We will pick ( 1, 20 ).
The slope is:
20 = Slope ( 1 ) + 15
Slope = 20 - 15
Slope = 5
The equation is:
y = 5 x + 15
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At a local fair , Lin purchases necklaces and bracelets. Necklaces cost $4 each and bracelets cost $1 each, Lin spends $20 on these items. Let n represent the number of necklaces Lin buys and b represent the number f bracelets Lin buys
After solving the equation for n and b we find out that Lin bought 1 necklace and 4 bracelets.
We can set up the following system of equations based on the given information: n = number of necklaces, b = number of bracelets
4n + b = 20 (Lin spends $20 on necklaces and bracelets)
where 4n represents the cost of n necklaces and b represents the cost of b bracelets. This system of equations can be used to solve for n and b. we can solve for n and b using the system of equations:
n + 1b = 5
4n + 1b = 20
We can use the first equation to solve for n in terms of b: n = 5 - b
Substitute this expression for n into the second equation: 4(5 - b) + b = 20
Simplifying this equation, we get: 20 - 4b + b = 20
Solving for b, we get: b = 4
Substituting this value of b back into n = 5 - b, we get: n = 1
Therefore, Lin bought 1 necklace and 4 bracelets
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Complete Question
At a local fair , Lin purchases necklaces and bracelets. Necklaces cost $4 each and bracelets cost $1 each, Lin spends $20 on these items. Let n represent the number of necklaces Lin buys and b represent the number f bracelets Lin buys. Find the number of necklaces and bracelets Lin purchased.
given 20 people, what is the probability that, among the 12 months in the year, there are 4 months containing exactly 2 birthdays and 4 containing exactly 3 birthdays?
the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%
The problem of calculating the probability of a certain pattern of birthdays among a group of people can be approached using the techniques of combinatorics and probability. To calculate the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people, we can use the following steps: First, we need to choose which 4 months will have exactly 2 birthdays and which 4 months will have exactly 3 birthdays. There are 12 months to choose from, so the number of ways to make these choices is given by the binomial coefficient: C(12, 4) × C(8, 4). This is the number of ways to choose 4 months out of 12 to have exactly 2 birthdays, multiplied by the number of ways to choose 4 months out of the remaining 8 to have exactly 3 birthdays. Next, we need to assign the people to the months. To do this, we can use the principle of inclusion-exclusion, which states that the number of ways to assign the people to the months so that each of the chosen months has the correct number of birthdays is: N = (20!/(2!²× 3!⁴)) × (4¹² - 6 × 3¹² + 4 × 2¹²). This expression counts the number of ways to distribute the 20 people among the 12 months so that the chosen months have the correct number of birthdays, and subtracts the cases where one or more of the chosen months have too many or too few birthdays. The factor (20!/(2!⁸ × 3!⁴)) accounts for the fact that we are counting distinguishable arrangements of people. Finally, we can calculate the probability of the desired pattern of birthdays by dividing the number of favorable outcomes (N) by the total number of possible outcomes, which is simply the total number of ways to assign the people to the months, given by: 12²⁰. Putting it all together, we get: P(4 months with 2 birthdays, 4 months with 3 birthdays) = N / 12²⁰. Evaluating this expression gives: P(4 months with 2 birthdays, 4 months with 3 birthdays) ≈ 0.000008. Therefore, the probability of having 4 months containing exactly 2 birthdays and 4 months containing exactly 3 birthdays among 20 people is approximately 0.000008, or about 0.0008%.
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A triangle has an area of 30 inches² and a height of 12 inches. What is the length, in inches, of the base?
Answer:
Plug your values into the equation A=1/2bh and do the math. First multiply the base (b) by 1/2, then divide the area (A) by the product. The resulting value will be the height of your triangle!
Step-by-step explanation:
two quadrilaterals are described
The statements that MUST be true based on the given information are:
Opposite angles of Quadrilateral C are congruent.Opposite angles of Quadrilateral L are congruent.Why are these statements true?For Quadrilateral C, if all four sides are congruent, then opposite sides are parallel and opposite angles are congruent. This can be proven using the fact that in an isosceles trapezoid (which is a special case of Quadrilateral C), opposite angles are congruent.
For Quadrilateral L, having two pairs of parallel sides and congruent diagonals means that it is a parallelogram with congruent diagonals. This type of parallelogram is known as a rhombus, and its opposite angles are congruent. Additionally, in a rhombus, consecutive angles are not necessarily supplementary or congruent.
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question 17 suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. after hours of burning, a candle has a height of centimeters. after hours of burning, its height is centimeters. what is the height of the candle after hours? clears your work. undoes your last action.
For the required linear function , the height of the candle when the amount of time for burning a candle is 16 hours is equal to 18.8 centimeters.
Let 'h' be the height of the candle.
And 't' be the amount of time used for burning.
Required linear function is :
h = mt + c
When t = 8 hours , h = 20.4centimeters
20.4 = 8m + c ___(1)
When t = 19 hours , h = 18.2centimeters
18.2 = 19m + c ___(2)
Subtract (2) from (1) we get,
20.4 = 8m + c
18.2 = 19m + c
2.2 = -11m
⇒ m = -2.2 / 11
⇒ m = -0.2
Substitute in (1) we get,
20.4 = 8( -0.2 ) + c
⇒ c = 20.4 + 1.6
⇒ c = 22
Now , h = -0.2t + 22
When t = 16 hours
⇒ h = -0.2(16) + 22
⇒ h = -3.2 + 22
⇒ h = 18.8 centimeters
Therefore, the height of the candle when amount of time of burning is 16 hours is equal to 18.8 centimeters.
The above question is incomplete, the complete question is:
Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 8 hours of burning, a candle has a height of 20.4 centimeters. After 19 hours of burning, its height is 18.2 centimeters. What is the height of the candle after 16
hours?
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amit took part in an cycle race .he started at 1:25 pm and reached the finishing line at 1:50 . what was the duration of the race ?
amit took a part in cycle race .he started at 1:25 and he reached finishing lline at 1:50 pm what was the duration of the race .
Answer:
25 minutes
Step-by-step explanation:
Subtract the two times to find the duration.
Hi everyone! Please help me with this homework as soon as you can. I have no clue how to work this out. If you can please give me a step-by step explanation, thank you so much! Here is the question:
The exterior angle of a regular polygon is 15°.
Calculate
a the number of sides
b the value of one interior angle
c the sum of the interior angles
d the number of lines of symmetry
e the order of rotation symmetry of the polygon
a) the number of sides = 24 sides (b) interior angle= 158.75° (c) sum of interior angles = 4080° (d) lines of symmetry = 12 (e) rotational symmetry of order = 24.
How to calculate the sides and angles of a polygona) To find the number of sides of a regular polygon given the value of its exterior angle, we use the formula:
360°/exterior angle = number of sides
So, for an exterior angle of 15°, we have:
360°/15° = 24 sides
b) To find the value of one interior angle, we use the formula:
interior angle = (number of sides - 2) * 180°/number of sides
So, for a polygon with 24 sides, we have:
interior angle = (24 - 2) * 180°/24
interior angle= 158.75°
c) The sum of the interior angles of a polygon with n sides is given by the formula:
sum of interior angles = (n - 2) * 180°
So, for a polygon with 24 sides, we have:
sum of interior angles = (24 - 2) * 180° = 4080°
d) To find the number of lines of symmetry of a regular polygon, we find the highest number of rotations that will produce the same figure. A regular polygon has n lines of symmetry if it can be divided into n equal parts by rotations of 360°/n.
So, for a regular polygon with 24 sides, we have:
lines of symmetry = 360°/interior angle = 360°/158.75° = 24/2 = 12
e) To find the order of rotational symmetry of a regular polygon, we find the number of rotations that will produce the same figure.
A regular polygon has rotational symmetry of order n if it can be divided into n equal parts by rotations of 360°/n.
So, for a regular polygon with 24 sides, we have:
rotational symmetry of order = 360°/exterior angle = 360°/15° = 24.
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