Answers
Answer:
[tex] {≈225.4 \: m}^{2} [/tex]
[tex] {≈248.2 \: m}^{2} [/tex]
Step-by-step explanation:
(My first few steps are in the photo I've added)
Now, we can find the area of the first cutout:
[tex]s(cutout1) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 114°}{360°} = \frac{36963\pi}{360°} = 102.6\pi[/tex]
We can also find the altitude of the first triangle using trigonometry:
[tex] \sin(∠obd) = \frac{od}{ob} [/tex]
We also need to find AB by using the Pythagorean theorem:
[tex] {ad}^{2} = {ao}^{2} - {od}^{2} = {18}^{2} - {5.56}^{2} = 293.0864[/tex]
[tex]ad > 0[/tex]
[tex]ad = \sqrt{293.0864} ≈ 17.12[/tex]
[tex]ab = 2 \times 17.12 = 34.24[/tex]
[tex]h1 = od = ob \times \sin(∠obd) = 18 \times \sin(18°)≈5.56[/tex]
Then, we can find the area of the 1st triangle:
[tex]s (1triangle)= \frac{1}{2} \times 5.56 \times 34.24 ≈95.19[/tex]
And we can also find the area 1:
[tex]area1 = s(cutout1) - s(triangle1) = 102.6\pi - 95.19≈225.25[/tex]
Now let's do the same thing with the second area:
[tex]s(cutout2) = \frac{\pi \times {r}^{2} \times \alpha }{360°} = \frac{\pi \times {18}^{2} \times 131°}{360°} = \frac{42444\pi}{360°} =117.9 \pi[/tex]
[tex] \sin(∠obe) = \frac{oe}{oc} [/tex]
[tex]h2 = oe = oc \times \sin(∠obe) = 18 \times \sin(24.5°)≈7.46[/tex]
[tex] {be}^{2} = {bo}^{2} - {oe}^{2} = {18}^{2} - {7.46}^{2} = 268.3484[/tex]
[tex]be > 0[/tex]
[tex]be = \sqrt{268.3484} ≈16.38[/tex]
[tex]bc = 2 \times 16.38 = 32.76[/tex]
[tex]s(triangle2) = \frac{1}{2} \times 7.46 \times 32.76 = 122.19[/tex]
[tex]area2 = s(cutout2) - s(triangle2) = 117.9\pi - 122.19≈248.2[/tex]
I don't know if I got this right, though...
The area of the shaded segments in the circle is 422.5 square meters
Calculating the area of the shaded segmentsGiven that
Radius = 18 meters
Angles = 114 degrees and 131 degrees
The area of the shaded segments is the sum of the area of the individual segments and this is calculated as
Segment area = (½) × r² × [(π/180) θ – sin θ]
Using the above, we have
Shaded segments = (½) × 18² × [(114π/180) – sin (114)] + (½) × 18² × [(131π/180) – sin (131)]
Evaluate
Shaded segments = 422.5 square meters
Hence, the shaded segments is 422.5 square meters
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Related Questions
Baldwin received some gift cards for music and movie downloads for his birthday. Using one of them, he downloaded 12 songs and 19 movies, which cost a total of $195. Using another, he purchased 14 songs and 12 movies, which cost a total of $136. How much does each download cost?
Answers
Answer:
165.5
Step-by-step explanation:
Because you have to add them together and then divide
Calculate the measures of center for the data in the dot plot, rounding your answers to the nearest tenths place. Show how you determined your answer. (2 points)
Answers
The values of Mean = 6.3 and Median = 6
Define the term dot plot?A dot plot is a type of data visualization that displays data points as dots on a number line. Each dot represents a single data point and is placed at the corresponding value on the number line.
Here, each dot corresponds to a particular value in the data set, below diagram.
Mean: The mean is calculated by dividing the total value of all the data sets by the total number of data sets.
You can figure out the total as follows:
0 (1) = 0 4 (3) = 12 5(8) = 40 6(3) = 18
7(1) = 7 8(5) = 40 9(2) = 18 10 (3) = 30
Sum = 0+12+40+18+7+40+18+30 = 165
Number of data set = 26
⇒Mean = 165/26
= 6.346 ≈ 6.3 (nearest tenth place)
⇒Median: The center value in the data collection is known as the median. Since there are 26 data points total, the middle value is located between data points 13 and 14. The median value will be determined by averaging the 13th and 14th data points.
So, the 13th and 14th values both are 6.
Therefore, median = {6+6} ÷ 2 = 12/2 = 6
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Complete Question-
Can someone explain how to find cordinates from slop in graph to find angle
Answers
Answer:
Find the components of the line (x,y)
And then use Tan ^-1(y/x)= Theta or angle
I hope you understand, and I go explain further.
Step-by-step explanation: In "simple terms". Slope is rise/run. Rise is the change in y value, which will equal the length of the opposite side of the right triangle. Run is the change in x value, which is the length of the adjacent side. The trigonometric function Tangent is opposite/adjacent. Use the inverse tangent of the slope to find the angle.
The only catch is that sometimes inverse tangent will give you a negative angle. It is generally not acceptable to provide the angle in a triangle as the negative angle. If you get a negative angle, use the absolute value of the angle.
Help with math problems
Answers
The inequality that has the solutions represented by the graph?
2x - 5 > 3
What is the solution of the inequality?The solution of the inequality represented by the graph is x > 4
The solution of the given inequalities are:
5 - x > 4;
solution: x < 1
2x + 1 ≥ 9;
solution: x ≥ 4
2x - 5 > 3
solution: x > 4
6x - 7 > 5
solution: x > 3
2. Considering the inequality statement given:
n ≤ 3: This is a solution.
If we substitute n with 3, we get 5 + 2(3) ≤ 11, which simplifies to 11 ≤ 11, which is true. And if we substitute n with any number less than 3, the inequality will still hold.
3 ≥ n: This is also a solution.
If we substitute n with 3, we get 5 + 2(3) ≤ 11, which simplifies to 11 ≤ 11, which is true. And if we substitute n with any number greater than 3, the inequality will still hold.
n ≤ 8: This is a solution.
If we substitute n with 8, we get 5 + 2(8) ≤ 11, which simplifies to 21 ≤ 11, which is false. But if we substitute n with any number less than or equal to 8, the inequality will still hold.
3 ≥ n: This is the same as the second representation, so it is also a solution.
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Complete question:
Which inequality has solutions represented by the graph?
5 - x > 4
2x + 1 ≥ 9
2x - 5 > 3
6x - 7 > 5
Consider the inequality Five plus two times a number n is less than or equal to eleven. Indicate whether each representation is or is not a solution.
n ≤ 3
3 ≥ n
n ≤ 8
3 ≥ n
The sides of a triangle are x cm, (x − 4) cm and (x - 8) cm, respectively. If the cosine of the largest angle is, calculate the angles of the triangle.
Answers
the angles of the triangle are approximately 38.24 degrees, 67.53 degrees, and 74.23 degrees.
Step-by-step explanation:
Let's use the Law of Cosines to solve this problem. According to this law, in any triangle with sides of lengths a, b, and c, and angles opposite those sides denoted by A, B, and C, respectively, the following equation holds:
c^2 = a^2 + b^2 - 2ab*cos(C)
We can use this equation to find the cosine of the largest angle, which will allow us to determine the angles of the triangle.
In this case, the largest angle is opposite the longest side, which has a length of (x - 8) cm. So, let's rewrite the Law of Cosines equation in terms of x:
(x - 8)^2 = x^2 + (x - 4)^2 - 2x(x - 4)*cos(C)
Expanding and simplifying this equation gives:
x^2 - 16x + 64 = 2x^2 - 16x + 16 + 2x(x - 4)*cos(C)
Canceling out the common terms and rearranging, we get:
cos(C) = (x^2 + (x - 4)^2 - (x - 8)^2)/(2x(x - 4))
Simplifying the numerator and denominator gives:
cos(C) = (5x - 24)/(2x(x - 4))
Now, we can use a calculator to evaluate the cosine for different values of x and find the values that satisfy the given condition. Specifically, we want the cosine to be negative, since the largest angle of a triangle is always obtuse (greater than 90 degrees).
For example, if we try x = 10, we get:
cos(C) = (5(10) - 24)/(2(10)(6)) = -0.25
This satisfies the condition, so we can use this value of x to find the angles of the triangle:
Angle opposite x cm side = cos^-1((x^2 + (x - 4)^2 - (x - 8)^2)/(2x(x - 4)))
= cos^-1((10^2 + (10 - 4)^2 - (10 - 8)^2)/(210(10 - 4)))
= cos^-1(7/8)
≈ 38.24 degrees
Angle opposite (x - 4) cm side = cos^-1((x^2 + (x - 8)^2 - (x - 4)^2)/(2x(x - 8)))
= cos^-1((10^2 + (10 - 8)^2 - (10 - 4)^2)/(210(10 - 8)))
= cos^-1(3/8)
≈ 67.53 degrees
Angle opposite (x - 8) cm side = 180 - angle opposite x cm side - angle opposite (x - 4) cm side
= 180 - 38.24 - 67.53
≈ 74.23 degrees
Therefore, the angles of the triangle are approximately 38.24 degrees, 67.53 degrees, an the angles of the triangle are approximately 38.24 degrees, 67.53 degrees, and 74.23 degrees.
I hope this helped
The Louvre Pyramid serves as a entrance to the Louvre Museum in Paris. The base of the pyramid is 35 meters long and the aides are 32 meters long. Classify the triangle on the front of the Louvre Pyramid by the length of its sides and the measure of its angles.
Answers
The triangles on the front of the Louvre Pyramid are all isosceles triangles.
What is Louvre Pyramid?The building acts as a visible reminder of the importance of the museum's Egyptian Antiquities collections.
The Louvre Pyramid: What Makes It Famous?The primary entry point to the Louvre is the I.M. Pei Pyramid, which is situated in the courtyard. The building acts as a visible reminder of the importance of the museum's Egyptian Antiquities collections.
A graph on the right AB = 35 meters {Given}
AE = 32 meters {Given}
Because AE = BE = 32 meters
So <EAB = <ABE By measure,
<EAB=663°
So <ABE=663°.
So <AEB = 180° - LEAB-LABE.
= 180°-66.3° - 66.3° =47.4°
So, ΔABE is an isosceles triangle.
And the four triangles are all isosceles triangles.
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In Exercises 43-46, solve the equ
43. 33x+6=27* +2
Answers
Answer:
43. All real numbers
44. x = 1/4
45. No solution
Step-by-step explanation:
The technique here is two write two expressions with the same base that are equal. Then set the exponents equal and solve for the variable.
43.
[tex] 3^{3x + 6} = 27^{x + 2} [/tex]
[tex] 3^{3x + 6} = (3^3)^{x + 2} [/tex]
[tex] 3^{3x + 6} = 3^{3(x + 2)} [/tex]
[tex] 3^{3x + 6} = 3^{3x + 6} [/tex]
[tex] 3x + 6 = 3x + 6 [/tex]
Answer: all real numbers
44.
[tex] 3^{4x + 3} = 81 [/tex]
[tex] 3^{4x + 3} = 3^4 [/tex]
[tex] 4x + 3 = 4 [/tex]
[tex] 4x = 1 [/tex]
[tex]x = \dfrac{1}{4}[/tex]
45.
[tex] 4^{x + 3} = 2^{2(x + 1)} [/tex]
[tex] (2^2)^{x + 3} = 2^{2(x + 1)} [/tex]
[tex] 2^{2(x + 3)} = 2^{2(x + 1)} [/tex]
[tex] 2(x + 3) = 2(x + 1) [/tex]
[tex] x + 3 = x + 1 [/tex]
[tex] 3 = 1 [/tex]
No solution.
4x=+2-6
4x=-4
X=-1
For the given cost function
C(x)=12100+800x + x² find:
a) The cost at the production level 1200
b) The average cost at the production level 1200
c) The marginal cost at the production level 1200
d) The production level that will minimize the average cost
e) The minimal average cost
Answers
a) The cost at production level 1200 is not given in the text, b) The average cost at production level 1200 is 2101.75, c) The marginal cost at production level 1200 is 3200, d) The production level that minimizes the average cost is not meaningful as it is outside the domain of production levels, e) The minimal average cost is not meaningful as it cannot be negative.
What is an expression?An expression is a mathematical phrase that can contain variables, constants, and operators (such as addition, subtraction, multiplication, division, and exponentiation) that represent some combination of numbers or other mathematical objects. Expressions can be simple, such as a single number or variable, or complex, such as a series of terms connected by operators. Expressions can be evaluated, simplified, and manipulated using algebraic techniques to solve problems and analyze mathematical relationships.
According to the given information:a) The cost at the production level 1200 is[tex]C(1200) = 12100 + 800(1200) + (1200)^2 = 2522100.[/tex]
b) The average cost at the production level 1200 is [C(1200)]/1200 = 2101.75.
c) The marginal cost at the production level 1200 is the derivative of C(x) with respect to x evaluated at x = 1200. Thus, MC(1200) = 800 + 2(1200) = 3200.
d) The production level that will minimize the average cost is given by the formula x = -b/(2a) where a and b are the coefficients of [tex]x^2[/tex] and x, respectively. Thus, x = -800/(2(1)) = -400. This value is not meaningful, as it is not in the domain of production levels.
e) The minimal average cost is the average cost at the vertex of the parabola given by C(x). The x-coordinate of the vertex is x = -b/(2a) = -800/(2(1)) = -400, and the y-coordinate is C[tex](-b/(2a)) = C(-400) = 12100 + 800(-400) + (-400)^2 = 168900[/tex]. Therefore, the minimal average cost is 168900/(-400) = -422.25. This is not a meaningful answer, as average cost cannot be negative.
Therefore,a) The cost at production level 1200 is not given in the text, b) The average cost at production level 1200 is 2101.75, c) The marginal cost at production level 1200 is 3200, d) The production level that minimizes the average cost is not meaningful as it is outside the domain of production levels, e) The minimal average cost is not meaningful as it cannot be negative.
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31 points
2a) Why wouldn’t a 2x2 area model (2 rows, 2 columns) with 4 smaller areas work to multiply
(x + 3)(2x
4 − 3x
3 − 2x
2 − 4x − 1) ? In your explanation, include a description of how to determine the correct rows
and columns for the area model [be sure to refer to and include the correct number of ‘terms’ and correct dimensions]
2b) Show what the area model SHOULD look like with the
correct lengths and widths labeled. DO NOT MULTIPLY!
2c) Draw an area model to find the ‘total area’ of a rectangle if the length is (x + 8) and the width is (x − 5). Write
your final ‘total area’ as a polynomial in Standard Form.
Final Area:
Answers
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.
b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.
c) The final total area is 2x² - 10x - 15.
What is an area model?An area model is a way to visualize multiplication by breaking up the larger rectangle into smaller rectangles whose areas represent the products of the terms being multiplied. To determine the correct rows and columns for the area model, we count the number of terms in each factor and use that as a guide. For example, if one factor has 3 terms and the other has 4 terms, we would use a 3x⁴ area model, with 3 rows and 4 columns.
a) A 2*2 area model would not work to multiply (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) because this expression has 5 terms, and a 2*2 area model can only accommodate 4 smaller areas.
b) The area model for (x + 3)(2x⁴ − 3x³ − 2x² − 4x − 1) with the correct lengths and widths labeled has been attached below.
2x⁴ − 3x³ − 2x² − 4x − 1
+---------------------------------------
x | 2x⁵ -3x⁴ -2x³ -4x² -x
|
3 | 6x⁴ -9x³ -6x² -12x -3
+---------------------------------------
c) To find the total area of a rectangle with length (x + 8) and width (x − 5), we can use an area model with 2 rows and 2 columns. The length (x + 8) corresponds to one dimension of the rectangle, while the width (x − 5) corresponds to the other dimension. The area of each smaller rectangle in the model represents the product of one term from each factor.
x + 8 x - 5
+--------------------
x | x² + 8x x² - 5x
|
-5 | -5x + -40 -5x + 25
+--------------------
The final total area can be found by adding up the areas of the smaller rectangles:
Total area = x² + 8x + x² - 5x - 5x - 40 + 25
= 2x² - 10x - 15
= 2x² - 10x - 15.
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is 0.6263646 irrational?
Answers
Answer:
Step-by-step explanation:
An irrational number is a number that cannot be expressed as a simple fraction. Therefore 0.6263646 is irrational.
Calculate the volume of the triangular prism shown below. Give your answer in cm³. 5 cm 9 cm 11 cm 6 cm
Answers
The volume of the triangular prism is 135 cm³.
To calculate the volume of a triangular prism, we multiply the area of the triangular base by the height of the prism.
Given the dimensions provided:
Base: Length = 5 cm, Width = 9 cm
Height: 6 cm
To find the area of the triangular base, we use the formula for the area of a triangle:
Area = (1/2) * base * height
Substituting the values:
Area = (1/2) * 5 cm * 9 cm
Area = 22.5 cm²
Now, to calculate the volume of the prism, we multiply the area of the base by the height:
Volume = Area * Height
Volume = 22.5 cm² * 6 cm
Volume = 135 cm³
Consequently, the triangular prism has a 135 cm3 volume.
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The salaries did not rise with inflation. The butter is now 25% costlier. By what percentage should a housewife reduce the consumption, so that her expenditure stays the same
Answers
The percentage of reduction in consumption required to keep the same expenditure is 25%.
What is Inflation?Inflation is an economic phenomenon that occurs when the prices of goods and services increase over time.
To find out the percentage of reduction in consumption, we need to calculate the difference between the current and the original prices of the butter.
This can be done by subtracting the original price of the butter from the current price of the butter (25% costlier).
The difference can be expressed as a percentage by dividing the difference by the original price.
Therefore, the percentage of reduction in consumption required to keep the same expenditure is 25%.
This means that a housewife needs to reduce her consumption of butter by 25% in order to keep her expenditure the same.
Thus, the percentage of reduction in consumption required to keep the same expenditure is 25%.
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!!!!!!!!!!!!!!!!!!
she has a gross income of $105500
If she pays $26982
in income tax and $2110
for the Medicare levy, what is her net income?
Answers
Therefore, her net income is $77408.
What is coefficient?A coefficient is a numerical factor that is multiplied by a variable or a term in an algebraic expression. In mathematics, coefficients are commonly used in polynomial functions, where they determine the degree of the polynomial and the specific values of the function.
For example, in the polynomial function[tex]f(x) = 3x^2 + 2x - 1[/tex], the coefficients are 3, 2, and -1. The coefficient 3 is multiplied by the variable. [tex]x^2[/tex], the coefficient 2 is multiplied by the variable x, and the coefficient -1 is the constant term.
Coefficients are also commonly used in statistics, where they are used to describe the relationship between variables in a statistical model. In regression analysis, for example, coefficients are used to represent the slope and intercept of a line that best fits the data.
by the question.
To calculate her net income, we need to subtract the total tax paid from her gross income:
[tex]Net Income = Gross Income - Income Tax - Medicare Levy[/tex]
Substituting the given values, we get:
[tex]Net Income = $105500 - $26982 - $2110[/tex]
[tex]Net Income = $77408[/tex]
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Write 6.384 correct to 1 decimal place
Answers
the answer is 6.4.
solve for x using pythagorean theorem.
Answers
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{\sqrt{257}}\\ a=\stackrel{adjacent}{x}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ (\sqrt{257})^2= (x)^2 + (15)^2\implies 257=x^2 + 225 \\\\\\ 32=x^2\implies \sqrt{32}=x\implies 4\sqrt{2}=x\implies 5.66\approx x[/tex]
What is the missing width of the object below, if the volume is 352 cubic meters? 8 and 11 m
Answers
Answer: 4
Step-by-step explanation: 8x11=88.
352=88x
x=352/88
x=4
Check:
11x8x4=352
"2 Ans" is the answer. Is the answer correct? If not, why? What's the Correct answer?
Answers
The formula for Py(Y) = ∑P y,z (y, z) for z ∈ Z is consistent with the third Axiom of the probability measure.
The Relationship between the Formula for Discrete Random Variables and the Third Axiom of Probability MeasureThe third Axiom of the probability measure states that the sum of probabilities of all possible outcomes of an event is equal to 1. In the context of two discrete random variables Y and Z, this axiom means that the sum of probabilities of all possible pairs (y, z) is equal to 1.
The formula PY(Y) = ∑P y,z (y, z) for z ∈ Z is related to this axiom because it represents the probability of the random variable Y taking on a specific value y, regardless of the value of Z. The summation is taken over all possible values of z in Z, and P y,z (y, z) represents the joint probability of Y and Z taking on the specific values (y, z).
Since the sum of probabilities of all possible pairs (y, z) is equal to 1, the sum of probabilities of all possible values of Y, represented by PY(Y), must also be equal to 1.
Therefore, the formula for PY(Y) is consistent with the third Axiom of the probability measure.
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Find the area of the shaded region on numbers 3-5
Answers
The area of the shaded region is,
(3) 100.28 sq. unit
(4) 72 sq.m
(5) 49.09 sq.m
What is the area?
The area of an object is the amount of room it occupies in two dimensions. It is the calculation of how many unit squares entirely encircle the area of a closed figure.
The accepted measure of area is the square unit, which is frequently expressed as square inches, square feet, etc. Most shapes and objects have edges and angles.
(3)
To calculate the area of the semi-circle having a radius of 3 cm,
[tex]A_1=\frac{1}{2} \pi r^2\\A_1=\frac{1}{2} \pi(3)^2\\A_1=14.14 \ \ sq. \ cm[/tex]
To calculate the area of the rectangle having a width of 12 cm and a height of 6 cm,
[tex]A_2=l*w\\A_2=12*6\\A_2=72 \ sq.cm[/tex]
To calculate the area of the semi-circle having a radius of 3 cm,
[tex]A_3=\frac{1}{2} \pi (3)^2\\A_3=14.14[/tex]
The shaded region's size was calculated using
[tex]A=A_1+A_2+A_3\\A=14.14+72+14.14\\A=100.28 \ \ sq.cm[/tex]
(4)
To calculate the area of the rectangle having a width of 13 m and a height of 8 m,
[tex]A_1=l*w\\A_1=13*8\\A_1=104 \ sq.m[/tex]
To calculate the area of an unshaded triangle,
[tex]A_2=\frac{1}{2} *b*h\\A_2=\frac{1}{2} *8*8\\\\A_2=32 \ sq.m[/tex]
The shaded region's size is thus,
[tex]A=A_1-A_2\\A=104-32\\A=72 \ sq.m[/tex]
(5)
The shaded region's size was calculated using
[tex]A=Area \ of \ circle-Area \ of \ square\\A=\pi (6)^2-(8)^2\\A=36\pi -64\\A=49.09 \ sq.m[/tex]
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Convert 41 divided by 2 day.
to an
hour
Answers
41/2 days is equivalent tο 492 hοurs.
What is divisiοn?Divisiοn is an arithmetic οperatiοn that invοlves splitting a quantity intο equal parts οr determining hοw many times οne quantity is cοntained within anοther. It is cοmmοnly denοted by the symbοl ÷ οr /, and can be written as a fractiοn οr as a ratiο.
We knοw that there are 24 hοurs in day therefοre,
Tο cοnvert 41/2 days tο hοurs, we can use the fact that there are 24 hοurs in οne day:
41/2 days x 24 hοurs/day = 41 x 12 = 492 hοurs
Therefοre, 41/2 days is equal tο 492 hοurs.
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OAB is a minor sector of the circle below. The
circumference of the circle is 65 cm.
Calculate the length of the minor arc AB.
Give your answer in centimetres (cm) and give any
decimal answers to 1 d.p.
A+
72°
circumference = 65 cm
B
cm
Answers
After answering the provided question, we can conclude that Therefore, circle the length of the minor arc AB is approximately 50.9 cm.
What is circle?A circle appears to be an a double component that is defined as the collection of all points in a jet that are equidistant out from hub. A circle is typically depicted with a capital "O" for the centre and a bottom end "r" for the radius, which represents the distance from where it started to any point on the circle. The formula 2r gives the girth (the distance from the center of the circle), where (pi) seems to be a proportionality steady roughly equal to 3.14159. The formula r2 computes the circumference of a circle, which is the quantity of space inside the circle. To calculate the length of the minor arc AB, we need to first find the central angle that it subtends.
C = 2πr
r = C/(2π)
r = 65/(2π) ≈ 10.34 cm
angle = (arc length / radius) x (180/π)
ADB = 360° - AOB
ADB = 360° - 72° = 288°
angle ADB = (arc length AB / 10.34) x (180/π) = 288°
arc length AB = (288° x 10.34 cm x π) / 180 ≈ 50.9 cm
Therefore, the length of the minor arc AB is approximately 50.9 cm.
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Answer this now please
Answers
The answer is 8.6+(-6.1). This is because addition and subtraction are inverse operations.
What is subtraction?Subtraction that involves taking one number away from another. It is the inverse of addition and is represented by the minus sign (-).
This means that when you add two numbers and then subtract the same amount, the result is the same as just adding the two numbers.
Similarly, when you subtract two numbers and then add the same amount, the result is the same as just subtracting the two numbers.
Therefore, 6.1+8.6 is equivalent to 8.6+(-6.1).
Using mathematical notation, we can represent this expression as 6.1+8.6 = 8.6+(-6.1).
To add and subtract the numbers, we can use the traditional column method.
First, we write out 6.1+8.6 as 6.1 - (-8.6). Then, we add the numbers in each column, starting with the ones column:
Ones column: 1+6=7
Tens column: 8-8=0
And our answer is 7,0. We can also write this as 8.6+(-6.1) to show that the two expressions are equivalent.
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When Sally was 10 years old, she was 140 cm tall. Two years later, her height had increased by 10%. Find Sally's height when she was 12 years old.
Answers
Answer: 154cm
Step-by-step explanation:
10% of 140 is 14
add that 10% to get 154
(100 points)
A bakery is making cupcakes using a cylindrical mold. The cupcake mold has a diameter of 3.5 centimeters and is 7 centimeters tall. Which of the following shows a correct method to calculate the amount of cupcake batter needed to fill the mold all the way to the top? Use 3.14 for π.
V = (3.14)(3.5)2(7)
V = (3.14)(7)2(3.5)
V = (3.14)(7)2(1.75)
V = (3.14)(1.75)2(7)
Answers
Answer:
for making cupcakes we need to determine its volume first
that would be πr²h for a cylinder
hence your answer is
V = (3.14)(1.75)^2(7)
V = (3.14)(1.75)^2(7)
A of apples has a mass of 4 kg. The average mass of each apple is 1/8 . How many apples are in the bag?
Answers
Answer:
There are 32 apples in the bag.
Step-by-step explanation:
To find the number of apples in the bag, we can use the formula:
number of apples = total mass of apples / average mass of each apple
Given that the bag of apples has a mass of 4 kg, and the average mass of each apple is 1/8 kg, we can substitute these values into the formula to get:
number of apples = 4 kg / (1/8) kg/apple
Simplifying the right-hand side by dividing 4 kg by (1/8) kg/apple, we get:
number of apples = 4 kg * 8/apple = 32 apples
Therefore, there are 32 apples in the bag.
Answer:
Step-by-step explanation:
It is simple by averaging formula as follows
Total mass/average mass = Total apples
4/(1/8)= 32 Apples
The cost of renting a chain saw is $3.90 per hour plus $6.50 for a can of gas. Find the cost of using the chain saw for 7.5 hours. Explanation and Answer
Answers
Answer:
$35.75
Step-by-step explanation:
$6.50 + $3.90(7.5) = $6.50 + $29.25 = $35.75
A survey of 53 randomly selected homeowners finds that they spend a mean of $66 per month on home maintenance. Construct a 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners. Assume that the population standard deviation is $11 per month. Round to the nearest cent. What is the Lower and Upper end point?
Answers
The 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners is (62.49,69.51). So, the Lower and Upper end point are 62.49, 69.51 respectively.
We have a survey of 53 randomly selected homeowners. So,
Sample size, n = 53
Mean spend of home maintenance, μ
= $66 per month
Standard deviations, σ = $ 11 per month
We have to determine the Lower and Upper end point or bound of confidence interval. First we calculate the Z score for 98% of confidence interval. The level of significance, α = 0.02 and α/2 = 0.01, so using distribution table [tex]z_{ \frac{\alpha}{2}} = 2.326[/tex]
Now, Margin of error , [tex]MOE = z_{\frac{\alpha}{2}} ( \frac{\sigma }{\sqrt{}n}) [/tex]
[tex] = 2.326 ( \frac{11}{ \sqrt{}53 })[/tex]
=> E = 3.51
At 98% confidence interval estimate of the population mean is, [tex]\bar x - E < \mu < \bar x + E[/tex]
[tex]66 - 3.51 < \mu < 66 + 3.51[/tex]
=> 62.49 < μ < 69.51
Therefore, Lower end point or bound
= 62.49 and Upper end point or bound
= 69.51.
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2sinx-1 = 0 (Solve with the inverse domain)
Answers
Answer:x = π/6 + 2πn , 5π/6 + 2πn, for any integer n
Profit is defined as total revenue minus total cost. The profit function of a company that manufactures and sells x units of a product is given by P(x)= R(x)-C(x), where
Prepresents the company's profits, R represents the company's revenue, and C represents the company's cost. If a company sells a calculator for $11, its revenue
function is R(x)=11x. The cost of each calculator manufactured is $8. In addition, it renewed its lease on the plant, so its weekly fixed costs are $1220.
(a) Determine the profit function. (b) Determine and interpret P(800)
Answers
Answer:
a.) P(x)= 3x - 1120
b.) make $1,180 profit in 1 week by selling 800 calculators
Step-by-step explanation:
a.) P(x)=R(x)-C(x)
R(x)=11x; C(x)=8x + 1220 assuming they are asking for profit in a week
P(x)= 3x - 1220
b.) P(800) = 3(800) -1220 = 1180
C(x)= 20+4000x+0.09x^2
A. Find the marginal cost function
Use it to estimate how fast the cost is increasing when x=4
Answers
The marginal cost function is $ 4000.72.
What is the marginal cost function?
The overall costs involved in producing an additional good are what is referred to as the marginal cost. Hence, it can be evaluated by changes in the costs associated with each extra unit. Marginal Cost is calculated as Total Expenditure Change / Unit Production Change.
Here, we have
Given: C(x) = 20+4000x+0.09x²
We have to find the marginal cost function.
We differentiate the given function and we get
C(x) = 20+4000x+0.09x²
C'(x) = 4000 + 2×0.09x
To determine how fast the cost is increasing when x=4.
C'(4) = 4000 + 2×0.09(4)
C'(4) = 4000.72
Hence, the marginal cost function is $ 4000.72.
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How many pounds are in 25 tons
Answers
There are 2,000 pounds in one ton. Therefore, to convert 25 tons to pounds, we can multiply 25 by 2,000:
25 tons x 2,000 pounds/ton = 50,000 pounds
So there are 50,000 pounds in 25 tons.