Answer:the space is 7 in the text below
Step-by-step explanation:
The most obese countries in the world have obesity rates that range from 11.4% to 74.6%. This data is summarized in the following table.
Percent of Population Obese Number of Countries
11.4–20.45 29
20.45–29.45 12
29.45–38.45 4
38.45–47.45 0
47.45–56.45 3
56.45–65.45 2
65.45–74.45 1
74.45–83.45 1
(a) What is the best estimate of the average obesity percentage for these countries? (Round your answer to two decimal places.)
(b) The United States has an average obesity rate of 33.9%. Is this rate above average or below? (Round your answers to two decimal places.)
Since the average for the United Sates is 33.9%, compared to the average obesity rate of
%, the United States has an obesity rate
% higher than average.
(c) How does the United States compare to other countries? (Assume that the United States is included in the data. Assume the other countries in the range 29.45–38.45 have higher obesity than the United States.)
The United States has an obesity rate higher than about 81% of the other countries listed.
The United States has an obesity rate equal to about 81% of the other countries listed.
The United States has an obesity rate lower than about 50% of the other countries listed.
The United States has an obesity rate higher than about 19% of the other countries listed.
6 out of 11 players played well on the baseball team. What percent is it?.
40.45%
45.45%
51.45%
54.55%
Answer:
Ok, Here is your answer
Step-by-step explanation:
To find the percentage of players who played well on the baseball team, we need to divide the number of players who played well by the total number of players and then multiply by 100.
Number of players who played well = 6
Total number of players = 11
Percentage of players who played well = (6/11) x 100%
= 54.55%
Therefore, the answer is 54.55%. Hence, option D, 54.55%, is the correct answer.
MARK ME AAS BRAINLIESTf(x)=-9x+9 and g(x)=√x+1
Answer:
-5
Step-by-step explanation:
Calculate the surface area of a triangular prism 10.8cm long and having a triangle bar face of dimensions 8.8cm by 5.7cm by 6.8cm
Answer:
268.8
Step-by-step explanation:
Let the sides of the base triangle be:
a = 8.8 cm
b = 5.7 cm
c = 6.8 cm
Let h be the length
h = 10.8 cm
The surface area is given by:
[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}[/tex]
Where
[tex]s = \frac{a + b + c}{2} \\\\= \frac{8.8 + 5.7 + 6.8}{2} \\\\=\frac{21.3}{2} \\\\= 10.65[/tex]
[tex]SA = (a + b + c)*l + 2\sqrt{ s(s - a)(s - b)(s - c)}\\\\= (8.8 + 5.7 + 6.8)*10.8 + 2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\= 21.3*10.8 +2\sqrt{ 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8)}\\\\=230.04 + 2\sqrt{ 10.65(1.85)(4.95)(3.85)}\\\\=230.04 + 2\sqrt{ 375.48}\\\\= 230.04 + 2*19.38\\\\=230.04 +38.76\\\\=268.8[/tex]
Consider the shape of a circle inside a square: 1.3.1 Calculate the area of the circle. eserved r = 5 cm
The area of the circle with a radius of 5 cm is approximately 78.53975 square centimeters.
To calculate the area of a circle, we need to use the formula A = πr², where A represents the area and r represents the radius of the circle. In this case, the given radius is 5 cm.
Plugging the value of the radius into the formula, we get:
A = π(5 cm)²
Simplifying the equation further, we have:
A = π(25 cm²)
Using the value of π (pi) as approximately 3.14159, we can calculate the area:
A ≈ 3.14159 × 25 cm²
A ≈ 78.53975 cm²
It's important to note that the area of a circle is always expressed in square units, as it represents the amount of space enclosed by the circle.
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The ratio of oranges to apples required to make the blend is 5 : 2 the person making the blend has 26 litres of oranges concentrate and 9 litres of apples concentrate. What is the maximum amount of juice blend can he make
The maximum amount of juice blend he can make is 2 blends.
What is the maximum amount of juice blend can he make?Ratio of oranges to apples required to make the blend = 5 : 2
Quantity of oranges available = 26 litres
Quantity of apples available = 9 litres
Number of blend made with oranges = 26 litres / 5
= 5.2
Approximately to the nearest whole number
= 5
Number of blend made with apples = 9 litres / 2
= 2.5
Approximately to the nearest whole number is
2
Since, the quantity of apple concentrate available can only make 2 blend of juice, it can be concluded that maximum amount of juice blend he can make is 2
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Determine the equation of the midline of the following graph.
Answer:
y = - 3
Step-by-step explanation:
the midline is a horizontal line positioned midway between the maximum and minimum values of the graph.
maximum = - 1 and minimum = - 5
then
(- 1 + (- 5)) ÷ 2 = (- 1 - 5) ÷ 2 = - 6 ÷ 2 = - 3 so equation of midline is
y = - 3
Given A matrix with 2 rows and 2 columns where row 1 is 4 and 4 and row 2 is 2 and 1., what is A–1? A matrix with 2 rows and 2 columns, where row 1 is negative 0.25 and 1 and row 2 is 0.5 and negative 1. A matrix with 2 rows and 2 columns where row 1 is negative 1 and negative 1 and row two is negative 0.5 and negative 0.25. A matrix with 2 rows and 2 columns where row 1 is 0.25 and negative 1 and row 2 is negative 0.5 and 1. A matrix with 2 rows and 2 columns where row 1 is 1 and negative 2 and row 2 is negative 4 and 4.
The matrix[tex]A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.[/tex]
To find the inverse of a matrix, we can use the formula:[tex]A^(-1) = (1/det(A)) * adj(A)[/tex]
Where A^(-1) represents the inverse of matrix A, det(A) is the determinant of A, and adj(A) denotes the adjugate of A.
Given the matrix A with 2 rows and 2 columns:
A = | 4 4 |
| 2 1 |
To find A^(-1), we need to calculate the determinant of A and the adjugate of A.
The determinant of A (det(A)) is calculated as:
det(A) = 4 * 1 - 2 * 4 = -4
The adjugate of A (adj(A)) is obtained by swapping the diagonal elements and changing the sign of the off-diagonal elements:
adj(A) = | 1 -4 |
| -2 4 |
Finally, we can find A^(-1) using the formula mentioned earlier:[tex]A^(-1) = (1/det(A)) * adj(A)A^(-1) = (1/-4) * | 1 -4 |[/tex]
| -2 4 |
Simplifying the expression:
A^(-1) = | -0.25 1 |
| 0.5 -1 |
Therefore, the matrix A^(-1) is a matrix with 2 rows and 2 columns, where row 1 is -0.25 and 1, and row 2 is 0.5 and -1.
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The distance between two cities on a map is 25 inches. The actual distance between the two cities is 300 miles. How many miles would 35 inches be on the map?
Answer:
Step-by-step explanation:
Sure, I can help you with that.
The scale of the map is 300 miles / 25 inches = 12 miles / inch.
Therefore, 35 inches on the map would be 35 * 12 = 420 miles.
Here's the calculation:
Code snippet
scale = actual distance / distance on map
12 miles / inch = 300 miles / 25 inches
35 inches * 12 miles / inch = 420 miles
Use code with caution. Learn more
I hope this helps! Let me know if you have other questions.
A) Find an equation for the line perpendicular to the tangent line to the curve y=x^3-4x+6 at the point (2,6)
-The equation is y=
b) What is the smallest slope on the curve? At what point on the curve does the curve have this slope?
-The smallest slope on the curve is
-The curve has the smallest slope at the point
c) Find equations for the tangent lines to the curve at the points where the slope of the curve is 8.
a) The equation of the line perpendicular to the tangent line at (2,6) is y = (-1/8)x + 7/4.
b) The smallest slope on the curve is at (-sqrt(4/3), 10 - 4sqrt(4/3)).
c) The tangent lines to the curve where the slope is 8 are y = 8x - 10 and y = 8x + 14.
a) To find the equation of the line perpendicular to the tangent line at the point (2,6), we first need to determine the slope of the tangent line. The derivative of the curve y=x^3-4x+6 is y' = 3x^2 - 4. Evaluating the derivative at x = 2 gives y'(2) = 3(2)^2 - 4 = 8.
Since the line perpendicular to the tangent line has a slope that is the negative reciprocal of the tangent line's slope, the slope of the perpendicular line is -1/8. Using the point-slope form of a linear equation with the given point (2,6), we have y - 6 = (-1/8)(x - 2). Simplifying, we get y = (-1/8)x + 7/4 as the equation of the perpendicular line.
b) To find the smallest slope on the curve, we can take the derivative and set it equal to zero. Differentiating y=x^3-4x+6, we have y' = 3x^2 - 4. Setting y' equal to zero, we get 3x^2 - 4 = 0. Solving for x, we find x = ±sqrt(4/3). The smallest slope occurs at the point where x = -sqrt(4/3) since the curve is concave up at this point. Evaluating y at this x-value, we have y = (-sqrt(4/3))^3 - 4(-sqrt(4/3)) + 6, which simplifies to y = 4 - 4sqrt(4/3) + 6 = 10 - 4sqrt(4/3).
c) To find the equations of the tangent lines where the slope of the curve is 8, we set the derivative equal to 8 and solve for x. 3x^2 - 4 = 8. Simplifying, we get 3x^2 - 12 = 0. Factoring, we have 3(x^2 - 4) = 0, which gives us x = ±2. Evaluating y at these x-values, we find y = 2^3 - 4(2) + 6 = 2 and y = (-2)^3 - 4(-2) + 6 = -2.
Therefore, the equations of the tangent lines to the curve where the slope is 8 are y = 8x - 10 and y = 8x + 14.
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A project has a net present value of Rs. "6172" when discount rate is 9%. What will be the Net present value if discount rate is increased by 12%?
The discount rate is increased by 12%, the new net present value will be approximately Rs. 5514.29.
To determine the net present value (NPV) when the discount rate is increased by 12%, we need to recalculate the NPV using the new discount rate.
Given:
Current NPV = Rs. 6172
Current discount rate = 9%
Increase in discount rate = 12%
To find the new NPV, we can use the formula:
New NPV = Current NPV / (1 + Increase in discount rate)
Calculating the new NPV:
New NPV = 6172 / (1 + 0.12)
New NPV = 6172 / 1.12
New NPV ≈ Rs. 5514.29
Therefore, if the discount rate is increased by 12%, the new net present value will be approximately Rs. 5514.29.
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A woman has a total of $8000 to invest she invest part of the money in the account that pays 11% per year and the rest into account that pays 12% per year if the interest earned in the first year is $910 how much did she invest in each account?
Answer:
Let's assume the woman invested x dollars in the account that pays 11% per year.
Since she invested a total of $8000, the amount invested in the account that pays 12% per year would be (8000 - x) dollars.
Now, let's calculate the interest earned from each investment:
Interest from the 11% account: 0.11x
Interest from the 12% account: 0.12(8000 - x)
According to the given information, the total interest earned in the first year is $910. Therefore, we can set up the following equation:
0.11x + 0.12(8000 - x) = 910
Let's solve this equation to find the value of x:
0.11x + 0.12 * 8000 - 0.12x = 910
0.11x - 0.12x = 910 - 0.12 * 8000
-0.01x = 910 - 960
-0.01x = -50
Dividing both sides by -0.01:
x = (-50) / (-0.01)
x = 5000
Therefore, the woman invested $5000 in the account that pays 11% per year.
The amount invested in the account that pays 12% per year would be 8000 - 5000 = $3000.
So, she invested $5000 in the 11% account and $3000 in the 12% account.
Find the slope-Intercept form of the equation of the line that passes through (-2,-1) and is perpendicular to y + 15 = (x + 10).
The slope-intercept form of the equation of the line that passes through (-2, -1) and is perpendicular to y + 15 = x + 10 is y = -x - 3.
To find the slope-intercept form of the equation of a line that is perpendicular to a given line, we need to determine the slope of the given line and then find the negative reciprocal of that slope.
The given line equation is y + 15 = x + 10. To rewrite it in slope-intercept form (y = mx + b), we isolate y:
y = x + 10 - 15
y = x - 5.
From this equation, we can see that the slope of the given line is 1.
To find the slope of the line perpendicular to this, we take the negative reciprocal of 1, which is -1.
Now that we have the slope (-1) and a point (-2, -1) that the line passes through, we can use the point-slope form of a line to find the equation.
The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line.
Plugging in the values (-2, -1) and -1 for x1, y1, and m respectively, we get:
y - (-1) = -1(x - (-2))
y + 1 = -1(x + 2)
y + 1 = -x - 2.
To rewrite this equation in slope-intercept form (y = mx + b), we isolate y:
y = -x - 2 - 1
y = -x - 3.
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Select all that apply. Which of the following is included in the table for each unit? A brief quiz A list of all questions from the lessons Description of what you need to know or apply Concepts tested Reference column
The options that apply are:
A. A list of all questions from the lessons
B. Description of what you need to know or apply
C. Concepts tested
D. Reference column.
The options that are typically included in a table for each unit are:
- A list of all questions from the lessons: This helps in organizing and categorizing the questions based on the specific unit or topic.
- Description of what you need to know or apply: This provides an overview or summary of the key concepts, knowledge, or skills that are covered in the unit.
- Concepts tested: This section highlights the specific concepts or skills that will be tested or assessed in relation to the unit. It helps students understand the focus areas and what they need to prioritize in their learning.
- Reference column: This column may include additional information such as page numbers, section titles, or references to specific resources or materials that are relevant to the unit. It serves as a guide for further exploration or reference.
A brief quiz, on the other hand, is not typically included in a table for each unit. Quizzes are usually separate assessments that are administered to evaluate understanding and mastery of the unit's content.
So, the options that apply are:
- A list of all questions from the lessons
- Description of what you need to know or apply
- Concepts tested
- Reference column
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Find the value of an investment of $10,000 for 13 years at an annual interest rate of 3.15% compounded continuously.
Answer:
Step-by-step explanation:
To find the value of an investment compounded continuously, we can use the formula:
A = P * e^(rt)
Where:
A is the final amount
P is the principal amount (initial investment)
e is the mathematical constant approximately equal to 2.71828
r is the annual interest rate (as a decimal)
t is the time period in years
In this case, P = $10,000, r = 0.0315 (3.15% expressed as a decimal), and t = 13.
Plugging in the values into the formula, we get:
A = $10,000 * e^(0.0315 * 13)
Calculating the exponential part:
A = $10,000 * e^(0.4095)
Using a calculator or a math software, we can evaluate e^(0.4095) to get approximately 1.506.
A = $10,000 * 1.506
A ≈ $15,060.
Danny sells food for a company that markets its products to restaurants. He earns 15% commission on his sales. Last month, he sold 16,000 worth of food to restaurants. How much did Danny earn last month?
Answer:
$2,400
Step-by-step explanation:
This is a very simple problem. Simply type the following into a calculator: 0.15*16000, and you should get 2400.
We have to turn the percentage into a decimal less than one because 15% represents 15/100.
Use the following table of index numbers based on the price of a pound of coffee. The index numbers use 2012 as the
base year. If you spent $4.48 for a pound of coffee in 2015, what would the price have been in 2009?
Year
Coffee index
2005
75.3
2012 2013 2014 2015
2006 2007 2008 2009 2010 2011
77.6 81.4 87.1 89.8 93.4 96.2 100.0 103.0 107.1 114.6
***
The price of coffee in 2009 would have been approximately $5.15.
How to determine the price of coffee in 2009To find the price of coffee in 2009, we need to use the index number for that year. According to the table, the index number for 2009 is 103.0.
We can set up a proportion to solve for the price in 2009:
Price in 2015 / Index in 2015 = Price in 2009 / Index in 2009
Let's denote the price in 2009 as x:
$4.48 / 89.8 = x / 103.0
Now we can solve for x:
x = ($4.48 / 89.8) * 103.0
x ≈ $5.15
Therefore, the price of coffee in 2009 would have been approximately $5.15.
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What is the area of the square that measures 3.1 m on each side
The area of the square with a side length of 3.1 meters is 9.61 square meters.
To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.
Area of a square = side length × side length
Substituting the given side length into the formula:
Area = 3.1 m × 3.1 m
To perform the calculation:
Area = 9.61 m²
It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.
Remember, to find the area of any square, you simply need to multiply the length of one side by itself.
The area of the square with a side length of 3.1 meters is 9.61 square meters.
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Jori has 7 boxes of books, with each box holding the same number of books. He has 126 books in all. How many books are there per box?
Answer: There will be a total of 18 books per box.
Step-by-step explanation:
Here,
Total number of boxes = 7
Total number of books = 126
Let n be the total number of books per boxes.
Now,
n = 126 / 7 = 18
Therefore, the total number of books per boxes is 18.
Enter the number that belongs in the green box
Using the Law of Cosines with angle 103° and adjacent sides 9 and 6, the remaining side is approximately 12.26 units long.
To find the remaining sides of the triangle, we can use the Law of Cosines. Let's assume that the angle of 103 degrees is opposite side c, and the adjacent sides are a = 9 and b = 6.
The Law of Cosines states:
[tex]c^2 = a^2 + b^2[/tex] - 2ab * cos(C)
Plugging in the known values:
[tex]c^2 = 9^2 + 6^2[/tex] - 2 * 9 * 6 * cos(103°)
Simplifying the equation:
[tex]c^2[/tex] = 81 + 36 - 108 * cos(103°)
Now we need to evaluate cos(103°).
Using a scientific calculator or trigonometric table, we find that cos(103°) ≈ -0.3090.
Substituting the value of cos(103°) back into the equation:
[tex]c^2[/tex] = 81 + 36 - 108 * (-0.3090)
Simplifying further:
[tex]c^2[/tex] = 117 + 33.2724
[tex]c^2[/tex]≈ 150.2724
Taking the square root of both sides:
c ≈ √150.2724
c ≈ 12.26
Therefore, the remaining side (opposite the angle of 103 degrees) is approximately 12.26 units long.
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How do I do 9 2/3 - 6 3/4?
Answer:
35/12
Step-by-step explanation:
9 2/3 = 29 / 3
6 3/4 = 27 / 4
We have to find the common denominator. In this case, it is 12
29/3 x 4/4 = 116/12
27/4 x 3/3 = 81/12
Now we can subtract both fractions.
116/12 - 81/12 = 35/12
So, the answer is 35/12
Answer:
35/12 or 2 11/12
Step-by-step explanation:
9 2/3 = 29/3
6 3/4 = 27/4
29/3 - 27/4 = 35/12
Please Solve, Thank you!
Answer:
(-3,7)
Step-by-step explanation:
[tex]3 > -x > -7[/tex] is the same as [tex]-3 < x < 7[/tex] when we divide everything by -1 and flip the signs. Therefore, the interval would be [tex](-3,7)[/tex].
In testing a new drug, researchers found that 6% of all patients using it will have a mild side effect. A random sample of 11 patients using the drug is selected.
(i) Find the probability that none will have this mild side effect.
(ii) Find the probability that at least one will have this mild side effect.
(i) The probability that none of the 11 patients will have the mild side effect can be calculated using the binomial distribution.
In this case, the probability of an individual patient having the side effect is 6% or 0.06, and the probability of not having the side effect is 1 - 0.06 = 0.94.
The probability that none of the 11 patients will have the side effect can be calculated as:
P(X = 0) = (0.94)^11 ≈ 0.5147
So, the probability that none of the patients will have the mild side effect is approximately 0.5147 or 51.47%.
(ii) The probability that at least one patient will have the mild side effect can be calculated as the complement of the probability that none of the patients will have the side effect.
In other words, it is 1 minus the probability of none of the patients having the side effect.
P(at least one patient has the side effect) = 1 - P(X = 0) = 1 - 0.5147 ≈ 0.4853
So, the probability that at least one patient will have the mild side effect is approximately 0.4853 or 48.53%.
(i) To find the probability that none of the patients will have the mild side effect, we use the binomial distribution formula.
The probability of success (having the side effect) is given as 0.06, and the probability of failure (not having the side effect) is 1 - 0.06 = 0.94.
We raise the probability of not having the side effect to the power of the number of trials (11 patients) to find the probability that none of them will have the side effect.
(ii) To find the probability that at least one patient will have the mild side effect, we use the complement rule.
The complement of none of the patients having the side effect is at least one patient having the side effect.
By subtracting the probability of none of the patients having the side effect from 1, we find the probability of at least one patient having the side effect.
These probabilities are important in assessing the likelihood of experiencing the mild side effect when using the new drug.
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discrete mathematics
A. The relation R is reflexive. B. This relation is not symmetric. C. The relation R is neither an equivalence relation nor a partial ordering relation on the set N = {1, 2, 3, 4, ...}.
Di. R is not a partial ordering relation, a Hasse diagram cannot be drawn. ii. There are no equivalence classes to find.
How did we arrive at these assertions?To determine whether the relation R is an equivalence relation or a partial ordering relation on the set N = {1, 2, 3, 4, ...}, examine its properties.
a. Reflexivity:
For a relation to be reflexive, every element in the set should be related to itself. In the given definition of R, we have x = y¹, where y¹ represents the first power of y. Since any number raised to the power of 1 is equal to itself, the relation R is reflexive.
b. Symmetry:
For a relation to be symmetric, if x is related to y, then y should also be related to x. In the given definition of R, we have x = y¹. This relation is not symmetric because if x = 2 and y = 3, then x = y¹ is not satisfied.
c. Transitivity:
For a relation to be transitive, if x is related to y and y is related to z, then x should be related to z. In the given definition of R, we have x = y¹. This relation is not transitive because if x = 2, y = 3, and z = 4, then x = y¹ and y = z¹ are satisfied, but x = z¹ is not satisfied.
Based on the above analysis, we can conclude that the relation R is neither an equivalence relation nor a partial ordering relation on the set N = {1, 2, 3, 4, ...}.
d. Since the relation R is neither an equivalence relation nor a partial ordering relation on the set N = {1, 2, 3, 4, ...}, the Hasse diagram cannot be drawn, as it is applicable only for partial ordering relations.
i. Given that R is not a partial ordering relation, a Hasse diagram cannot be drawn.
ii. Since R is not an equivalence relation, there are no equivalence classes to find. Equivalence classes are relevant only for equivalence relations, where elements are grouped together based on their equivalence under the relation.
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The midpoint of segment AB is M(-2,2). If A is located at (-5,7) find the coordinates of the endpoint B
Answer:
B (1, -3)
Step-by-step explanation:
Step 1: Use the midpoint formula to find the coordinates of the endpoint:
Normally, we find the midpoint of a segment using the midpoint formula, which is given by:
M = (x1 + x2) / 2, (y1 + y2) / 2, where
M is the midpoint,(x1, y1) are one endpoint on the segment,and (x2, y2) are the other endpoint of the segment.Since we're solving for the coordinates of an endpoint, we can allow (-5, 7) to be our (x1, y1) point and plug in (-2, 2) for M to find (x2, y2), the coordinates of the endpoint B:
x-coordinate of B:
x-coordinate of midpoint = (x1 + x2) / 2
(-2 = (-5 + x2) / 2) * 2
(-4 = -5 + x2) + 5
1 = x2
Thus, the x-coordinate of the endpoint B is 1.
y-coordinate of B:
y-coordinate of midpoint = (y1 + y2) / 2
(2 = (7 + x2) / 2) * 2
(4 = 7 + x2) -7
-3 = y2
Thus, the y-coordinate of the endpoint B is -3.
Thus, the coordinates of the endpoint B are (1, -3).
10.) Find the surface area of this cone shaped megaphone. Use 3.14 for
pi. (Assume it is a solid)
2.25 ft slant hight
1.2 ft diameter
Image in the solid 6 in by 6 in
Options for answers are
5.3 ft
5.4 ft
53 ft
54ft
Answer:
5.4 ft²
Step-by-step explanation:
To find the surface area of the cone-shaped megaphone, use the surface area of a cone formula.
[tex]\boxed{\begin{minipage}{7cm}\underline{Surface area of a cone}\\\\$S.A.=\pi r^2+\pi rl$\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius of the circular base.\\ \phantom{ww}$\bullet$ $l$ is the slant height of the cone.\\\end{minipage}}[/tex]
The radius of a circle is half its diameter.
Therefore, if the diameter of the cone's circular base is 1.2 ft, then its radius is r = 0.6 ft.
Given values:
r = 0.6 ftl = 2.25 ftπ ≈ 3.14Substitute the values into the formula and solve:
[tex]\begin{aligned}\textsf{Surface area}&=3.14 \cdot0.6^2+3.14 \cdot 0.6 \cdot 2.25\\&=3.14 \cdot 0.36+3.14 \cdot 0.6 \cdot 2.25\\&=1.1304+1.884 \cdot 2.25\\&=1.1304+4.239\\&=5.3694\\&=5.4\; \sf ft^2\;(nearest\;tenth)\end{aligned}[/tex]
Therefore, the surface area of the cone-shaped megaphone is 5.4 ft² (rounded to the nearest tenth).
Noa was walking in the forest and measured the circumference of two trees that he found. The first tree measured 37 and StartFraction 5 over 8 EndFraction inches around, and the second tree measured 45 and one-third inches around. Noa wanted to find the difference of the circumferences of the two trees. He recorded his steps in the table.
Steps
Noa’s work
Step 1
45 and one-third minus 37 and StartFraction 5 over 8 EndFraction
Step 2
45 and StartFraction 8 over 24 EndFraction minus 37 and StartFraction 15 over 24 EndFraction
Step 3
44 and StartFraction 32 over 24 EndFraction minus 37 and StartFraction 15 over 24 EndFraction
Step 4
44 and StartFraction 32 over 24 EndFraction minus 37 and StartFraction 15 over 24 EndFraction = 8 and StartFraction 17 over 24 EndFraction
In which step did Noa first make an error?
Step 1
Step 2
Step 3
Step 4
Answer:step 4
Step-by-step explanation: I just took the test pookies
Find the area of the triangle.
3 9
A
5
B
?] units²
The area of the triangle is 47.91 units²
How to find the area of the triangle?When all three sides of the triangle are known we can use Heron's formula. Consider the triangle ABC with sides a, b, and c has shown in the image.
Heron’s formula is:
Area =√s(s−a)(s−b)(s−c)
where,
a, b, c are the side length of the triangle
s is the semi-perimeter. s = (a+b+c)/2
In this case:
Using the knowledge of the radius of a circle. We can say:
a = BC = 3 + 9 = 12 units
b = AC = 5 + 3 = 8 units
c = AB = 5 + 9 = 14 units
s = (a+b+c)/2
s = (12+8+14)/2
s = 34/2
s = 17 units
Area = √s(s−a)(s−b)(s−c)
Area = √17(17−12)(17−8)(17−14)
Area = √17(5)(9)(3)
Area = √2295
Area = 47.91 units²
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