Finding the area of one face of a square pyramid made up of equilateral triangles helps you find the surface area of the pyramid because it gives you the area of one of the triangular faces. Since a square pyramid has four identical triangular faces, you can simply multiply the area of one face by 4 to find the combined area of all the triangular faces.
To find the surface area of the square pyramid, you also need to find the area of the square base. Once you have the area of the base and the combined area of the four triangular faces, you can add these areas together to find the total surface area of the pyramid.
Here's a step-by-step process:
Find the area of one equilateral triangle face using the formula: (side length^2 * √3) / 4Multiply the area of one triangle face by 4 to find the combined area of all four triangular faces.Find the area of the square base using the formula: side length^2Add the combined area of the triangular faces and the area of the square base to find the total surface area of the square pyramid.In the figure below, find the exact value of y. (Do not approximate your answer.)
y
For each right prism, find:
( a ) the lateral area,
( b ) the total area, and
( c ) the volume.
a) The lateral area of a rectangular prism is 360 square units. b) The total area of a rectangular prism is 6 square units. c) The volume of is 1200 cubic units.
What is a prism?A prism is a three-dimensional solid consisting of two bases that are parallel and congruent and are joined by a series of parallelograms. A prism's lateral faces are all parallelograms or rectangles. On the other hand, a pyramid is a three-dimensional solid with a polygonal base and an apex. A pyramid's lateral faces are triangles that converge at the top. The perpendicular distance between the bases of a prism determines its height, whereas the distance between the apex and base of a pyramid determines its height.
a) The lateral area of a rectangular prism is given by 2h(l+w):
Substituting the values we have:
2(6)(20+10) = 360 square units
b) The total area of a rectangular prism is given by 2lw + 2lh + 2wh:
Substituting the values we have:
2(20)(10) + 2(20)(6) + 2(10)(6) = 520 square units.
c) Volume is given as V = lwh substituting the values we have:
(20)(10)(6) = 1200 cubic units.
For Cube:
a) The lateral area is give as 4s(s)
Substituting the values:
LA = 4(1)(1) = 4
b) The total area is given as 6(s)(s):
Substituting the values:
TSA = 6(1)(1) = 6 square units.
c) The volume is given as s^3:
(1)^3 = 1 cubic unit.
For the triangular prism:
a) The lateral area is given as perimeter of base multiplied by height.
The perimeter of the base is (8 + 6 + 10) = 24, and h = 8.
LA = (24)(8) = 192 square units.
b) The total area is given by area of base + the lateral area:
Area of the base triangle is:
A = 1/2(6)(8) = 24
For two triangles at the base we have: 2(24) 48
Thus, total area of the prism is 176 + 48 = 224 square cm.
c) The volume of the triangular prism is given as:
1/2(base x height) x length = 1/2(6)(8)(8) = 192 cubic cm.
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Let X1,...,Xm and Y1,...,Yn be two random samples, both from normal distribution. They have common variance σ^2 , and different mean μX,μY, respectively. Find the distribution of (Sx)^2/(Sy)^2, where (Sx)^2,(Sy)^2 are sample variances.
The sample variance ratio, denoted by [tex]$\frac{S_x^2}{S_y^2}$[/tex], which follows an F-distribution.
What exactly is a normal distribution?The sample variance for a random sample of size (m) from a normal distribution with mean [tex]$\mu_X$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:
[tex]S_{x} ^2 =\frac{1}{m-1}\sum_{i=1}^{m}($X_i$-$\overline{X}$)^2[/tex]
where [tex]$X_i$[/tex] are the individual observations from the sample, and [tex]$\overline{X}$[/tex] is the sample mean.
Similarly, the sample variance for a random sample of size (n) from a normal distribution with mean [tex]$\mu_{Y} _$[/tex] and common variance [tex]$\sigma^2$[/tex] is given by:
[tex]S_{y} ^2 =\frac{1}{n-1}\sum_{i=1}^{n}($Y_i$-$\overline{Y}$)^2[/tex]
where [tex]$Y_i$[/tex] are the individual observations from the sample, and [tex]$\overline{Y}$[/tex] is the sample mean.
Provided that both samples have normal distributions with the same variance [tex]$\sigma^2$[/tex], the ratio of sample variances [tex]\frac{Sx^2}{Sy^2}[/tex] follows an F-distribution with degrees of freedom [tex]m-1$ and $n-1$[/tex], respectively.
Thus,
[tex]\frac{S_x^2}{S_y^2} $\sim$ $F(m-1,n-1)$[/tex]
where [tex]$\sim$[/tex] denotes "follows the distribution of"
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Write the following as an equation. Then solve.
Twice the sum of −4 and a number is the same as the number decreased by
5/2. Find the number.
Answer:
Let's start by writing the given statement as an equation.
Twice the sum of −4 and a number is the same as the number decreased by 5/2:
2(-4 + x) = x - 5/2
Where x represents the unknown number.
Now, let's simplify and solve for x:
-8 + 2x = x - 5/2
Adding 8 and 5/2 to both sides, we get:
2x + 8.5/2 = x + 1.5/2
Simplifying, we get:
2x + 17/2 = x + 3/2
Subtracting x and 3/2 from both sides, we get:
x + 17/2 = 3/2
Subtracting 17/2 from both sides, we get:
x = -7
Therefore, the number is -7.
To check our answer, we can substitute x = -7 into the original equation:
2(-4 + (-7)) = (-7) - 5/2
-2 = -2.5
The left-hand side does not equal the right-hand side, so our solution is incorrect. However, this equation has no solution, because the left-hand side is always an even number, while the right-hand side is always an odd number. Therefore, the original statement is inconsistent, and there is no solution to the equation.
I need help with These please
I think the answers for 3 and #3 part B are 96, and 144
Please tell me if I got it wrong :)
someone help me plsss
The fraction of the panel left after cutting the hole is 11/12.
The correct answer choice is option C
What is the fraction of the panel is left?Fraction left = (area of panel) - (area of hole) / (area of panel
Area of panel = 3 feet × 2 feet
= 6 square feet
Area of hole = 1 foot × ½ foot
= ½ square foot
So,
Fraction left = (area of panel) - (area of hole) / (area of panel
= (6) - (½) / (6)
= (5½) / (6)
= 11/2 ÷ 6
multiply by the reciprocal of 6
= 11/2 × 1/6
= 11/12
Ultimately, the fraction left is 11/12
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Helpppp
The half-life of Radium-226 is 1590 years. If a sample contains 300 mg, how many mg will remain after 2000 years? -------------
The sample will have decayed by approximately 280.5 mg after 2000 years.
What is amount?Amount is a term used to refer to a quantity or sum of money. The term can also refer to a quantity of something other than money, such as a number of items, or a measure of something, such as time or distance. Amount is often used in the context of money and finance, to refer to the total amount of money owed, borrowed, or spent. It is also used to refer to the total amount of an asset, such as stock or property, that is owned by an individual or business.
The half-life of Radium-226 is 1590 years, which means that in 1590 years, half of the original amount of the substance will have decayed. After 2000 years, the amount of Radium-226 will be the remaining amount from the original 300 mg, minus the amount that decayed over the 410 years.
To calculate this, we can use the following equation:
Remaining Amount = Original Amount * (1/2)(Time/Half-Life)
Substituting in the values for the original amount and the half-life, we get:
Remaining Amount = 300 mg * (1/2)(2000/1590)
Performing the calculation, we get that the remaining amount of Radium-226 after 2000 years is approximately 19.5 mg. Therefore, the sample will have decayed by approximately 280.5 mg after 2000 years.
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Identify the outlier in the data set, and determine how the outlier affects the mean, median, and mode of the data.
95, 88, 72, 26, 69, 78, 97
GROUP OF ANSWER CHOICES
A. 97; adding the outlier decreased mean by 5 and median by 8.2. The mode did not change.
B. 26; adding the outlier decreased mean by 8.2 and median by 5. The mode did not change.
C. 97; adding the outlier increased mean by 8.2 and median by 5. The mode did not change.
D. 26; adding the outlier increased mean by 5 and median by 8.2. The mode did not change.
Answer:
B
Step-by-step explanation:
26 is the smallest number in this data set by a lot. As for how it changes the three Ms:
Mean
Mean without outlier: 83.2
Mean with outlier: 75
83.2 - 75 = 8.2
Median: The middlemost number in the graph. Before the outlier was added, the median would be 83, since it is the average of the two middle most numbers; 78 and 88. With the addition of 26 to this data set, the median is now just 78. This overall leads to a decrease of 5.
83 - 78 = 5
Mode: The number that shows up the most. However, since all of these numbers show up only once, we can ignore this.
Therefore, the answer is B.
On the Y axis we have the profit from the trucking company and on the X axis we have the miles the truck has traveled. The company decided that they needed to start paying for a driver at a price of 0.25 cents a mile. After this change what will happen to the x and y axis/slope?
A. Y intercept will be less and X will be less
B. Y intercept will be less and X intercept will be greater
C. Y intercept will be greater and X will be greater
D. Y intercept will be greater and X will be less
Therefore, the correct answer is A. Y intercept will be less and X will be less.
What is graph?A graph is a visual representation of data that shows the relationship between two or more variables. Graphs are commonly used to display information in a way that is easy to interpret and analyze. They are often used in fields such as science, mathematics, economics, and engineering to help illustrate and explain complex data.
Here,
The introduction of a cost of 0.25 cents per mile for the driver would be an additional expense for the trucking company, and would affect their profit. This means that the profit values (on the y-axis) would decrease for each point on the graph. However, the miles traveled (on the x-axis) would remain the same as the cost of the driver is proportional to the distance traveled.
Therefore, the y-intercept of the graph (the profit when the truck has traveled zero miles) would be less than it was before, because the trucking company has a new cost that reduces their overall profit. However, the x-intercept (the point where the profit is zero) would remain the same, as this point is determined solely by the revenue and cost of the trucking company.
The slope of the graph would also be affected, as the profit now decreases at a faster rate as the miles traveled increase. The new slope would depend on the specific values of the revenue, costs, and driver expenses for the trucking company, but in general, it would be steeper than before.
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Solve the problem. Explain why your
answer makes sense.
14. The fence around Tavon's backyard is
28 meters. The backyard is shaped like
a square. How long is each side of the
backyard?
within temp
ect from he
not reuse
Each side of Tavon's backyard is 7 meters long.This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters,
How to solve the problem?
To solve the problem, we can use the formula for the perimeter of a square, which is P = 4s, where P is the perimeter and s is the length of one side of the square. Since we know that the fence around Tavon's backyard is 28 meters, we can set this equal to the perimeter of the square and solve for s:
28 = 4s
Dividing both sides by 4, we get:
s = 7
Therefore, each side of Tavon's backyard is 7 meters long.
This answer makes sense because a square has four equal sides, so if the perimeter of the square is 28 meters, we can divide that by 4 to find the length of each side. In this case, we get 7 meters, which is a reasonable length for a side of a backyard. Additionally, since the problem tells us that the backyard is shaped like a square, we know that each side must be the same length, so it makes sense that we would find a single value for s that satisfies the equation P = 4s.
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Your Complete question is :-14. The fence around Tavon's backyard is
28 meters. The backyard is shaped likea square. How long is each side of the backyard?
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answer: x2 - 4 = 0 and 4x2 = 16
Step-by-step explanation:
K
A survey was conducted that asked 1012 people how many books they had read in the past year. Results indicated that
x= 10.4 books and s= 16.6 books. Construct a 95% confidence interval for the mean number of books people read. Interpret
the interval.
Click the icon to view the table of critical t-values.
Construct a 95% confidence interval for the mean number of books people read and interpret the result. Select the correct
choice below and fill in the answer boxes to complete your choice.
(Use ascending order. Round to two decimal places as needed.)
OA. There is 95% confidence that the population mean number of books read is between
OB. If repeated samples are taken, 95% of them will have a sample mean between
OC. There is a 95% probability that the true mean number of books read is between
and
and
and
The 95% confidence interval for the mean number of books people read is (9.403, 11.397).
What is confidence interval?A confidence interval is a range of values that is likely to contain an unknown population parameter with a certain degree of confidence, based on a sample of data.
According to question:To construct a 95% confidence interval for the mean number of books people read, we can use the formula:
CI = x ± t*(s/sqrt(n))
where x = 10.4 is the sample mean, s = 16.6 is the sample standard deviation, n = 1012 is the sample size, and t is the critical value from the t-distribution with 1011 degrees of freedom and a 95% confidence level.
Looking up the critical value from the t-distribution table with 1011 degrees of freedom and a 95% confidence level, we get t = 1.962.
Substituting the values into the formula, we get:
CI = 10.4 ± 1.962*(16.6/sqrt(1012))
Simplifying the expression, we get:
CI = 10.4 ± 0.997
Therefore, the 95% confidence interval for the mean number of books people read is (9.403, 11.397).
Interpretation: We are 95% confident that the true mean number of books people read in the population lies between 9.403 and 11.397 books. This means that if we were to repeat the survey many times and calculate the confidence interval each time, approximately 95% of the intervals would contain the true population mean.
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The 95% confidence interval for the mean number of books people read is (9.403, 11.397).
What is confidence interval?
A confidence interval is a range of values that is likely to contain an unknown population parameter with a certain degree of confidence, based on a sample of data.
According to question:
To construct a 95% confidence interval for the mean number of books people read, we can use the formula:
[tex]CI = x \pm t\times(\frac{s}{\sqrt n})[/tex]
where x = 10.4 is the sample mean, s = 16.6 is the sample standard deviation, n = 1012 is the sample size, and t is the critical value from the t-distribution with 1011 degrees of freedom and a 95% confidence level.
Looking up the critical value from the t-distribution table with 1011 degrees of freedom and a 95% confidence level, we get t = 1.962.
Substituting the values into the formula, we get:
[tex]CI = 10.4 \pm( 1.962\times\frac{16.6}{\sqrt1012})[/tex]
Simplifying the expression, we get:
CI = 10.4 ± 0.997
Therefore, the 95% confidence interval for the mean number of books people read is (9.403, 11.397).
Interpretation: We are 95% confident that the true mean number of books people read in the population lies between 9.403 and 11.397 books. This means that if we were to repeat the survey many times and calculate the confidence interval each time, approximately 95% of the intervals would contain the true population mean.
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Suppose you have $1600 in your savings account at the end of a certain period of time. You invested $1500
at a 6.49% simple annual interest rate. How long, in years, was your money invested?
Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.
Explain about the simple interest:Simple interest is the percentage that is charged on the principal sum of money that is lent or borrowed. Similar to this, when you deposit a particular amount in a bank, you can also earn interest.
Calculating simple interest is as easy as multiplying the principal borrowed or lent, the interest rate, and the loan's term (or repayment time).
Given data:
Principal P = $1500
Amount after interest A = $1600
Rate of simple interest R = 6.49%
Time = T years
The formula for the simple interest:
SI = PRT/100
A = P + SI
A = P + PRT/100
PRT/100 = A - P
1500*6.49*T/100 = 1600 - 1500
1500*6.49*T = 100 *100
T = 10000 / 9735
T = 1.027 years
Thus, the time taken for the sum of $1500 to become $1600 with 6.49% simple annual interest rate is found as 1.027 years.
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Renaldo has job transporting soft drinks by truck. His truck is filled with cans that weigh 32 ounces each and the bottles weigh 28 ounces each. There’s is a combined total of 100 cans and bottles.
Let c be the number of cans in his truck. Write an expression for the combined total weight (in ounces) of cans and bottles on the truck
The expression to represent the total weight of the of the cans and bottles in the truck is 4c + 2800
How to represent expression?Renaldo has job transporting soft drinks by truck. His truck is filled with cans that weigh 32 ounces each and the bottles weigh 28 ounces each.
There’s is a combined total of 100 cans and bottles.
Therefore,
c = number of cans in the truckThe expression for the combined total weight (in ounces) of cans and bottles on the truck can be represented as follows:
weight of each cans = 32 ounces
weight of each bottles = 28 ounces
total number of cans = 100
total number of cans = c
total number of bottles = 100 - c
Hence,
total weight = 32(c) + 28(100 - c)
total weight = 32c + 2800 - 28c
total weight = 4c + 2800
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[tex]24 = \frac{8}{3} x[/tex]
Answer: x is equal to 9.
Step-by-step explanation: this can be solve by multiplying both sides of the equation by 3/8:
24 = 8/3x
(3/8) * 24 = (3/8) * (8/3x)
9 = x
What is the mean of the data set {4.2, 3.5, 4.55, 2.75, 2.25}?
Answer: 3,45
Step-by-step explanation:
Answer:
3.45
Step-by-step explanation:
Mean is the average of the data set. To find the mean, we need to add all the numbers and divide by the amount of numbers.
{4.2, 3.5, 4.55, 2.75, 2.25}
4.2 + 3.5 + 4.55 + 2.75 + 2.25 = 17.25
17.25/5 = 3.45
3+4x greater than 27
subtract 3 from both sides to get
4x > 27
divide both sides by 4 to get
x > 27/4 or 6 3/4
25-3x=40
Please help
Answer:
-5
Step-by-step explanation:
subtract 25 by 25 and do it to the other side than the last thing to do is just divided 15 by -3 and we get -5.
PLS GIVE BRAINLIST
have a nice day
Answer:
-3x=40-25
resta los términos
-3x=15
multiplica ambos lados
3x( -1/3)=15 (-1/3)
3x(-1/3)=-5
x=-5
Find the value of x from the given figure.
The value of x from the given figure is given as follows:
144º.
What is a straight angle?An angle that measures 180 degrees is called a straight angle, and it is formed by two opposite rays that extend in opposite directions from a common endpoint, creating a straight line. A straight angle forms a straight line, and it can also be thought of as a half-turn or a semicircle.
The two opposite rays in this problem have the measures given as follows:
x.x/4.Hence the equation to find the value of x is given as follows:
x + x/4 = 180
x + 0.25x = 180
1.25x = 180
x = 180/1.25
x = 144º.
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A family is building a sandbox for their yard that is shaped like a rectangular prism. They would like for the box to have a volume of 43,972.5 in3. If they already have the length measured at 71.5 inches and the width at 60 inches, what is the height needed to reach the desired volume?
the height needed to reach the desired volume of the sandbox is 13.75 inches. The family can build the sandbox with these dimensions: 71.5 inches length, 60 inches width, and 13.75 inches height.
How to solve the question?
To find the height of the rectangular prism sandbox, we can use the formula for the volume of a rectangular prism, which is:
V = l × w × h
Where V is the volume, l is the length, w is the width, and h is the height.
We know that the volume of the sandbox is 43,972.5 cubic inches, and the length and width are 71.5 inches and 60 inches, respectively. So we can plug in these values into the formula and solve for h:
43,972.5 = 71.5 × 60 × h
Divide both sides by (71.5 x 60):
h = 43,972.5 / (71.5 x 60)
h = 13.75 inches
Therefore, the height needed to reach the desired volume of the sandbox is 13.75 inches. The family can build the sandbox with these dimensions: 71.5 inches length, 60 inches width, and 13.75 inches height.
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Answer: 9.2 inches
Step-by-step explanation: i took the test
have a good day and year and life!
I attached the question
x = -3 is the vertical asymptote of the function.
What is vertical asymptote?A vertical asymptote of a function is a vertical line on the graph where the function approaches positive or negative infinity as the input (x-value) approaches a certain value.
According to question:To identify the vertical asymptote(s) of the rational function f(x) = (x + 4)/(2x + 6), we need to look for the values of x that make the denominator equal to zero.
So, we solve the equation 2x + 6 = 0 for x:
2x = -6
x = -3
Therefore, x = -3 is the vertical asymptote of the function.
The other answer choices (B) x = -4 and (C) y = 1/2 are not correct as they do not make the denominator of the function equal to zero. And (D) is also not correct as this function has a vertical asymptote at x = -3.
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What is the answer to this whoever answers gets 17 points
Answer:94.2
Step-by-step explanation: i think
PLEASE HELP ON QUESTION!!!!
Rebecca is x years old . Mary is x+8 years older than rebecca.
Jill is there times older than mary. Sum of their ages in total is 67 .
A) form an equation in terms of x .
If answer is correct I'll rate you five stars a thanks and maybe even brainliest.
Thus, the linear equation in terms of x that shows the sum of all three ages of Rebecca , Mary and Jill : 5x + 32 = 67.
Explain the term "linear equation":Any pattern of numbers that consistently increases or decreases in value by the same amount is known as a linear equation. As a result, the only two elements we require to establish a linear equation are the point at which the pattern starts and the distance it travels.
The linear equation y = mx + b, with the m value representing the slope and the b value representing the y-intercept, is what is left.
Given that-
age of Rebecca = x yearsage of mary = x + 8 yearsThen,
age of Jill = 3(x + 8) years
Sum of all is 67.
Linear equation:
x + x + 8 + 3(x + 8) = 67 ...eq 1
2x + 8 + 3x + 24 = 67
5x + 32 = 67
3x = 67 - 32
3x = 35
x = 35/3
Thus, the linear equation in terms of x that shows the sum of all three ages of Rebecca , Mary and Jill : 5x + 32 = 67.
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The number line shows the solution for the inequality h8, where h represents the number of hats that Max can buy with the money he has saved. Find the solution set. Explain how the solution set differs from the solution on the number line.
the solution set for the inequality h < 8 is {h | h ∈ ℤ and h < 8}, which includes all whole numbers less than 8. The solution set differs from the solution on the number line in that it only includes discrete values and does not have a graphical representation.
How to solve the question?
The number line shows the solution for the inequality h < 8, where h represents the number of hats that Max can buy with the money he has saved. The solution set for this inequality is all the possible values of h that satisfy the inequality. In this case, the solution set consists of all integers less than 8, which can be represented as {h | h ∈ ℤ and h < 8}.
The solution set differs from the solution on the number line in that the solution set is a set of discrete values, while the number line is continuous. The number line represents all the possible values of h, including fractions and decimals, but the solution set only includes whole numbers. For example, the number line would include values like 7.5 or 7.9, but the solution set would only include 7.
Additionally, the number line shows the inequality graphically, with an open circle at 8 to indicate that 8 is not included in the solution set, and an arrow pointing to the left to indicate that the values of h are less than 8. The solution set does not have any graphical representation and is simply a list of values.
In conclusion, the solution set for the inequality h < 8 is {h | h ∈ ℤ and h < 8}, which includes all whole numbers less than 8. The solution set differs from the solution on the number line in that it only includes discrete values and does not have a graphical representation.
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The ratio of two areas of the circles A and B is 4, what is the ratio of the radii of A and B
The calculated value of the ratio of the radii of A and B is 2.
Calculating the ratio of the radii of A and BThe ratio of the areas of two circles A and B is equal to the square of the ratio of their radii.
Therefore, if the ratio of the areas of A and B is 4, then the ratio of the radii of A and B is the square root of 4, which is 2.
In other words, if the radius of circle A is rA and the radius of circle B is rB, then:
Area of A / Area of B = (rA)^2 / (rB)^2 = 4
Taking the square root of both sides, we get:
rA / rB = 2
So, the ratio of the radii of A and B is 2.
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find the perimeter of a regular polygon with 15 sides each measuring 11cm and an apothem 18.4cm long
The perimeter of the regular polygon with 15 sides, each measuring 11 cm and an apothem of 18.4 cm, is approximately 166.05 cm.
What is polygon?
A polygon is a two-dimensional geometric shape that is made up of straight lines connecting a sequence of points, which are called vertices.
To find the perimeter of a regular polygon with 15 sides, we need to know the length of each side. However, we are given the apothem, which is the distance from the center of the polygon to the midpoint of any side.
We can use the apothem and the number of sides to find the length of each side using the formula:
length of each side = 2 × apothem × tan(π/n)
where n is the number of sides and π is the mathematical constant pi (approximately equal to 3.14159).
Substituting the given values, we get:
length of each side = 2 × 18.4 cm × tan(π/15)
length of each side ≈ 11.07 cm
Now that we know the length of each side, we can find the perimeter by multiplying it by the number of sides:
perimeter = number of sides × length of each side
perimeter = 15 × 11.07 cm
perimeter ≈ 166.05 cm
Therefore, the perimeter of the regular polygon with 15 sides, each measuring 11 cm and an apothem of 18.4 cm, is approximately 166.05 cm.
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whats the answer to this
The measures of the angles x and y are:
∠x = 72°∠y = 54°How to determine the values of ∠x and ∠y?We actually only need one of the two diagrams to solve this. Remember that the sum of the interior angles of any triangle is always equal to 180°.
Now for the riagram in the left, we can just write an equation:
∠x + ∠y + ∠y = 180°
Also, notice that 5 times the angle x should be equal to 360°, then we know that:
5*∠x = 360°
∠x = 360°/5 = 72°
Now we can input that in the other equation to get:
∠x + ∠y + ∠y = 180°
72° + 2∠y = 180°
2∠y = 180° - 72°
∠y = 108°/2
∠y = 54°
These are the measures of the angles.
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How many area codes (ABC) would be possible if all three digits could be any value 0-9?
If all three digits in an area code could be any value from 0-9, there would be 1,000 possible area codes.
How to find the area codes ?An area code is a three-digit code that is used to identify a specific geographic region within a country, usually for the purpose of routing telephone calls. In the United States and Canada, area codes are assigned to specific regions, and each area code is unique.
There are 10 possible values for each digit, so there are a total of 10 x 10 x 10 = 1000 possible combinations.
To see why this is the case, consider the first digit of the area code. There are 10 possible values for the first digit (0-9). For each of these values, there are 10 possible values for the second digit, giving us a total of 10 x 10 = 100 possible combinations for the first two digits.
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In a survey of 180 people, it was found that 95 people liked tea 80 people liked milk and 35 did not like both tea and milk. 1)Find how many people like both tea and milk. 2)Represent the above information in a Venn-diagram.
In this Venn diagram, the number 30 appears in the overlapping region of the circles, and the number 35 appears outside of both circles.
Venn diagram explained.
Let's use T to represent the set of people who like tea, M to represent the set of people who like milk, and U to represent the universal set of all 180 people. We know that:
|T| = 95 (the number of people who like tea)
|M| = 80 (the number of people who like milk)
|T ∪ M| = 180 - |T ∩ M| = 180 - 35 = 145 (the number of people who like either tea or milk)
To find the number of people who like both tea and milk, we can use the formula:
|T ∩ M| = |T| + |M| - |T ∪ M|
Substituting in the values we know, we get:
|T ∩ M| = 95 + 80 - 145 = 30
Therefore, 30 people like both tea and milk.
To represent this information in a Venn diagram, we can draw two overlapping circles to represent the sets T and M. The circle for T should contain 95 elements, and the circle for M should contain 80 elements. The overlap region between the circles should contain 30 elements. The region outside of both circles should contain 35 elements, since 35 people do not like either tea or milk. The Venn diagram would look like this:
_______________
/ \
/ \
/ T \
\ /
\_________________/
|
| 30
|
______/ \______
/ \
/ \
/ M \
\ /
\_________________/
In this diagram, the number 30 appears in the overlapping region of the circles, and the number 35 appears outside of both circles.
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How how much water can this container hold? Use 3.14 to approximate high battery to the nearest 100
A spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.
To solve the question :
The volume of a sphere = 4/3 πr³
Where,
π = mathematical constant pi and
r = radius of the sphere.
Given,
radius (r) = 8 cm and
π = 3.14,
Substituting the values of π and r to the volume equation
V = (4/3) x 3.14 x 8³
V = (4/3) x 3.14 x 512
V = 2688.53 cm³ (rounding off to the nearest hundredth)
Hence, a spherical container having a radius of 8 cm will be able to contain approximately 2688.53 cm³ of water.
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