a finite group with an even number of elements contains an even number of elements such that. x inverse = x.
a similar statement for a finite group with an odd number of elements
For a finite group with an even number of elements, we can prove that it contains an even number of elements such that their order is 2.
Let G be a finite group of even order.
We can define t(G) as the set { g ∈ G | g ≠ g − 1 }.
if g ∈ t(G), then g − 1 ∈ t(G), and by definition g − 1 ≠ g.
Now let A = { { g, g − 1 } | g ∈ t (G) }.
Thus we have | t (G) | = ∑ α ∈ A | α | = 2 k for some positive integer k;
in particular, t (G) contains an even number of elements 1.
Hence [tex]x^{-1}=x[/tex]
For a finite group with an odd number of elements, we can prove that it contains an odd number of elements such that their order is 2. For any element in G-{e}, there must be an inverse of that element in G-{e}. Take any element in G-{e}, say b, If bb=e, then the proof is done. If the inverse of b is not itself, then there must be one element in G-{e}, say c, such that bc=e. Because there are an odd number of elements, I keep doing this until I have left with one
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angle bisector theorem
The value of the unknown term in the given triangle that satisfied the relation of angle bisector theorem is 9.
What about angle bisector theorem?
The angle bisector theorem is a fundamental theorem in geometry that relates the lengths of the sides of a triangle to the lengths of the segments formed by the intersection of an angle bisector with the opposite side.
Specifically, the angle bisector theorem states that the length of the segment of the side of a triangle that is opposite to the bisected angle is proportional to the lengths of the other two sides of the triangle. More precisely, if AD is the bisector of angle BAC in triangle ABC, then:
BD/DC = AB/AC
where BD and DC are the lengths of the segments of side BC that are adjacent to point A, and AB and AC are the lengths of the sides opposite to angles B and C, respectively.
This theorem is useful in many geometric constructions and proofs, and can be applied to various problems involving triangles and their properties.
According to the given information:
Using the concept of height and distance we have that,
[tex]tan(y) = \frac{4}{12} \\\\tan(2y) = \frac{2tany}{1-(tany)^{2} }[/tex]
In the given figure of triangle the value of tan(2y) = [tex]\frac{4+x}{12}[/tex]
So, when we correlate all of them we have that
[tex]\frac{2*\frac{4}{12} }{1-(\frac{4}{12}) ^{2} } = \frac{4+x}{12} \\\\x = 5[/tex]
So, the length of the unknown part is 9.
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educational professionals refer to science, technology, engineering and mathematics as the STEM disciplines. A research group reported of 27% of freshmen entering college in a recent year planned to major in a stem discipline. A random sample of 85 freshmen is selected. Use the cumulative normal distribution table as needed. Round your answer to at least four decimal places if necessary
The probability that at most 20 freshmen out of 85 plan to major in STEM is approximately 0.2420.
What is probability?
Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.
We can use the normal distribution to find probabilities related to STEM majors.
Let X be the number of freshmen out of 85 who plan to major in a STEM discipline. We are given that p = 0.27 is the proportion of freshmen who plan to major in STEM.
Then, X follows a binomial distribution with parameters n = 85 and p = 0.27.
The mean of the distribution is given by μ = np = 85 × 0.27 = 22.95.
The standard deviation of the distribution is given by σ = sqrt(np(1-p)) = sqrt(85 × 0.27 × 0.73) ≈ 4.27.
To find the probability that at most 20 freshmen plan to major in STEM, we can use the normal approximation to the binomial distribution:
P(X ≤ 20) ≈ P(Z ≤ (20 - 22.95) / 4.27) ≈ P(Z ≤ -0.697)
Using a standard normal distribution table or calculator, we find that P(Z ≤ -0.697) ≈ 0.2420.
Therefore, the probability that at most 20 freshmen out of 85 plan to major in STEM is approximately 0.2420.
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A block of wood of mass 150.5g is 6.0cm long 4.2cm thick and 8.6cm high. The density of glass in kg/m3
density = 693.79 kg/[tex]m^3[/tex] (approx)
How to calculate density?The density of the block of wood can be calculated using the formula:
density = mass / volume
To find the volume of the block of wood, we need to multiply its length, width, and height:
volume = length x width x height
volume = 6.0 cm x 4.2 cm x 8.6 cm
volume = 217.08 cm^3
We need to convert the volume to cubic meters and the mass to kilograms to use the density of glass, which is typically given in kg/m^3:
volume = 217.08 cm^3 = 0.00021708 m^3
mass = 150.5 g = 0.1505 kg
Now we can calculate the density of the block of wood:
density = mass / volume
density = 0.1505 kg / 0.00021708 [tex]m^3[/tex]
density = 693.79 kg/[tex]m^3[/tex] (approx)
Keep in mind that the density of wood varies depending on its moisture content and type, but it is typically lower than that of glass, which is between 2500 and 3000 kg/[tex]m^3[/tex].
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The diagram shows a triangle OPQ and a circle with centre O.
The points P and R lie on the circumference of the circle.
The radius of the circle is 6 cm.
The length QR is 14 cm.
The area of triangle OPQ is 25 cm².
Calculate the area of the sector OPR.
The area of the sector OPR is approximately 5.20 cm².
What is an area?
First, we need to find the length of PR. Since O is the center of the circle, we know that OP and OR are both 6 cm long (the radius of the circle). By the triangle inequality, we have:
PR < OP + OR = 6 + 6 = 12
Since QR = 14, we have:
PR > QR - OP - OR = 14 - 6 - 6 = 2
Therefore, 2 cm < PR < 12 cm.
Next, we can use the formula for the area of a sector of a circle:
A = (θ/360)πr²
where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.
To find the central angle θ, we can use the law of cosines:
(PR)² = (OP)² + (OR)² - 2(OP)(OR)cos(θ)
Substituting in the known values, we get:
(PR)² = 6² + 6² - 2(6)(6)cos(θ)
(PR)² = 72 - 72cos(θ)
cos(θ) = (72 - (PR)²)/72
Using the known values, we have:
cos(θ) = (72 - (PR)²)/72 = (72 - x²)/72
where x is the length of PR.
Since OPQ is a triangle, we know its area:
25 = (1/2) base × height
25 = (1/2) QR × OP
25 = (1/2) (14) × 6
25 = 42
Therefore, the height of triangle OPQ is:
height = (2)(25)/QR = (2)(25)/14 = 25/7
The height of the triangle is also the distance from O to the line PQ, which is also the distance from O to the chord PR. Therefore, the area of sector OPR can be calculated as follows:
A = (θ/360)πr² = (θ/360)π(6)²
A = (θ/360)(36π) = (θ/10)π
where θ is the central angle of the sector in degrees. To find θ, we can use the formula:
sin(θ/2) = (PR/2)/r = x/6
Substituting in the known values, we get:
sin(θ/2) = x/6
θ/2 = [tex]sin^{-1}[/tex](x/6)
θ = 2[tex]sin^{-1}[/tex](x/6)
Finally, substituting this value of θ into the formula for the area of the sector, we get:
A = (θ/10)π = [2[tex]sin^{-1}[/tex](x/6)]/10 * π
To find the value of x that gives the area of the sector, we can use trial and error or a numerical solver. Using a calculator, we find that x ≈ 5.5 cm gives an area of the sector of:
A ≈ 5.20 cm²
Therefore, the area of the sector OPR is approximately 5.20 cm².
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Solve for x 1/2x +1/3 = 3/4
Answer:
x = 5/6
Step-by-step explanation:
Combine multiplied terms into a single fraction, Multiply by 1, Find common denominator, Combine fractions with common denominator, Multiply all terms by the same value to eliminate fraction denominators, Cancel multiplied terms that are in the denominator, DistributeMultiply the numbers, Subtract from both sides, and then Simplify the expression.
Ram Borrowed Rs 45000 for 2 years at 10% compound annually. He pais only one third of the principal at the end of 2 years. He paid the remaining principal and interest at the same rate at the end of next 2 years how much amount did he pay at last to clear his debt?
Let's break down the problem into steps to solve it:
Calculate the interest for the first 2 years:
The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.
In this case, P = Rs 45,000, r = 10%, n = 1 (compounded annually), and t = 2 years.
So, A = 45000(1 + 0.1/1)^(1x2) = Rs 59,049
Therefore, the interest for the first 2 years is Rs 59,049 - Rs 45,000 = Rs 14,049
Calculate the remaining principal:
Ram paid one third of the principal at the end of 2 years, which is (1/3) x Rs 45,000 = Rs 15,000.
So, the remaining principal after 2 years is Rs 45,000 - Rs 15,000 = Rs 30,000
Calculate the interest for the next 2 years:
Since Ram paid off the remaining principal and interest at the same rate at the end of the next 2 years, the interest rate will still be 10%.
So, the interest for the next 2 years will be:
A = 30,000(1 + 0.1/1)^(1x2) = Rs 39,690
Therefore, the interest for the next 2 years is Rs 39,690 - Rs 30,000 = Rs 9,690
Calculate the total amount Ram paid at the end of 4 years:
To clear his debt, Ram paid the remaining principal (Rs 30,000) and the interest for the next 2 years (Rs 9,690).
So, the total amount he paid at the end of 4 years is Rs 30,000 + Rs 9,690 = Rs 39,690.
Therefore, Ram paid Rs 39,690 at last to clear his debt.
expand (1+2)^4 using the Pascal Triangle
Answer:
81
Step-by-step explanation:
(1 + 2)⁴
1⁴ + 4(1³ × 2) + 6(1² × 2²) + 4(1 × 2³) + 2⁴
1 + 4(2) + 6(4) + 4(8) + 16
1 + 8 + 24 + 32 + 16
= 81
Pls someone help me.Allen prints a photograph with dimensions as shown. He purchases a 3-inch wide frame for the photo and frame.
The quadratic function representing the area of the photo and the frame is A(x) = 1.7x²+ 16.2x + 36
How to find area of Rectangle ?When calculating a rectangle's area, we multiply the length by the width of the rectangle.
Area of rectangle = length × breadth
To represent the photo and frame area, we need to add the photo area to the frame area. Since the frame is 3 inches wide on all sides, the photo dimensions are reduced by 6 inches in both length and width. Therefore the length of the photo with the frame is (x 6) inches and the width is (1.7 x 6) inches. Thus, the area of the photo and the frame can be represented by a quadratic function:
A(x) = (x 6) (1.7 x 6)
Expanding this expression, we get:
A(x) = 1.7x² + 16.2x + 36
So the quadratic function representing the area of the photo and the frame is A(x) = 1.7x²+ 16.2x + 36
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Select the correct answer.
Residents of four cities are able to vote in an upcoming regional election. A newspaper recently
two candidates. The results of the poll are shown in the two-way frequency table belo
Candidate A Candidate B
Total
Center City
152
198
350
Carsonville
205
266
471
Appleton
260
203
New Thomas
180
138
463
318
Total
797
805
1.602
a survey to gauge support for each of the
Based on the data shown, which of the following statements are true?
I. The two cities with the highest number of respondents both show more support for candidate A.
The number of people who support candidate B in Carsonville is twice the number of people who support candidate B in New
II. Thomas.
III. More residents of Center City responded to the poll than the number who responded from New Thomas
IV. Overall, more residents support candidate A than candidate B.
Options I and II contain claims regarding the two-way frequency table that are accurate.
How to interpret two-way frequency table?We are given the two-way frequency table that shows the newspapers recently conducted survey that gauges support for each of the two candidates.
Let us now analyze the options;
I) The two cities with the highest number of respondents are Carsonville and Appleton and from the table, they both show more support for candidate A and thus this option is true.
II) There are 266 supporters of candidate B in Carsonville. While there are 138 supporters of candidate B in New Thomas, we can see that 266 is not twice 138.This choice is untrue.
III) The number of residents that responded from Center city is 350 and we see that this is more than the number of residents that responded from New thomas which is 318 people.
The statement is true.
IV) This is untrue because candidate B has 805 supporters, which is greater than candidate A's 797 supporters. The assertion is thus untrue.
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HELP ASAP
A composite figure is represented in the image.
A four-sided shape with the base side labeled as 21.3 yards. The height is labeled 12.8 yards. A portion of the top from the perpendicular side to a right vertex is labeled 6.4 yards. A portion of the top from the perpendicular side to a left vertex is labeled 14.9 yards.
What is the total area of the figure?
272.64 yd2
231.68 yd2
190.72 yd2
136.32 yd2
the closest answer choice to this value is 372.32 yd2.
How to solve the question?
The given shape is a trapezoid, where the two parallel sides are the base and the top, and the height is the perpendicular distance between them. We can divide this trapezoid into a rectangle and a right triangle, as shown below:
A (bottom B (bottom
left vertex) right vertex)
We can find the length of the top side by adding the portions given on each side of the perpendicular, as follows:
top side = 6.4 yards + 14.9 yards = 21.3 yards (same as the base)
The area of the rectangle (ABCD) is the product of the base (21.3 yards) and the height (12.8 yards):
area of rectangle = 21.3 yards * 12.8 yards = 272.64 square yards
The area of the right triangle (BCD) is half the product of the height (12.8 yards) and the difference between the base and the top (21.3 yards - 6.4 yards = 14.9 yards):
area of triangle = 0.5 * 12.8 yards * 14.9 yards = 95.36 square yards
Therefore, the total area of the figure is the sum of the area of the rectangle and the area of the triangle:
total area = 272.64 square yards + 95.36 square yards = 368 square yards
Therefore, the closest answer choice to this value is 372.32 yd2.
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If the volume of a rectangular prism is 23,504 m3 and it has a height of 16 m, what is the value of B, the area of the base?
Answer:
1,469 [tex]m^{2}[/tex]
Step-by-step explanation:
The volume of a rectangular prism is given by the following:
V = Bh, where B is the area of the base and h is the height.
In this problem, we are given that the volume is 23,504 [tex]m^{3}[/tex] and the height is 16 m.
23,504 [tex]m^{3}[/tex] = B × 16 [tex]m[/tex]
Dividing both sides by 16, we get:
B = 23,504 [tex]m^{3}[/tex] / 16 [tex]m[/tex] = 1,469 [tex]m^{2}[/tex]
Therefore, the value of B, the area of the base, is approximately 1,469 [tex]m^{2}[/tex].
what is the value of the expression shown below when x = 7?
3x(to the power of 2) - 2x + 3
Answer: 430.00
Step-by-step explanation:
So.
3x^2-2x+3.
Replace x with 7
(3·7)^2-(2·7)+3
Multiply within the parenthesis
21^2-14+3
Take care of exponent
441-14+3
Solve the rest.
430
If you did it right, you would get 430 as the end result.
Happy Solving
8 9/14 divided by 12
The value of 8 9/14 divided by 12 is
How to calculate the value of 8 9/14 divided by 12 ?The first step is to convert the mixed fraction to a proper fraction
8 9/14
= 121/14
The next step is to divide the proper fraction by 12
121/14 ÷ 12
= 121/14 × 1/12
= 121/168
= 0.720
Hence the value of 8 9/14 divided by 12 is 0.720
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Kyle always charges the battery of his motorized wheelchair overnight. At the end of each day
he records the distance he traveled and the remaining charge on the battery. The scatter plot
shows the data. The equation of the line of fit is y = -4.2x + 100.
The line of fit y = -4.2x + 100 shows a negative correlation between the distance traveled and the remaining charge on the battery of the motorized wheelchair.
The slope of the line is -4.2, which means that for every one unit increase in distance traveled, the remaining charge on the battery decreases by 4.2 units.
The y-intercept of the line is 100, which means that when the distance traveled is zero, the remaining charge on the battery is 100.
The line of fit can be used to make predictions about the remaining charge on the battery for a given distance traveled.
Based on the scatter plot, we can see that there is a negative correlation between the distance traveled and the remaining charge on the battery. As the distance traveled increases, the remaining charge on the battery decreases.
Overall, the line of fit provides a way to estimate the remaining charge on the battery for a given distance traveled based on the data shown in the scatter plot.
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Completar la siguiente oración.
• El costo marginal es la derivada de la función........
.
A) Utilidad.
B Ingreso.
C) Costo.
D Demanda.
The marginal cost is the derivative of the cost function.
Option C is the correct answer.
What is marginal cost?Marginal cost is the additional cost incurred by a firm or producer when producing one more unit of a good or service.
It is the cost of producing an additional unit of output.
We have,
Marginal cost is a concept in economics that describes the additional cost of producing one additional unit of output.
It is calculated as the derivative of the total cost function with respect to the quantity produced.
In other words, if the total cost function is represented as C(q), where q is the quantity of output produced, then the marginal cost (MC) function is given by:
MC(q) = dC(q) / dq
The derivative represents the rate of change of the cost function with respect to the quantity produced, which gives the additional cost of producing one more unit of output.
For example, if a company produces 100 units of a product at a total cost of $1000, and then produces 101 units of the same product at a total cost of $1020, the marginal cost of producing the 101st unit is $20, which is the difference in cost between producing 100 units and producing 101 units.
Thus,
The marginal cost is the derivative of the cost function.
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The complete question.
Complete the following sentence.
The marginal cost is the derivative of the ________ function.
A) Utility.
B Income.
C) Cost.
D Demand.
((30/180)*2.80 + (40/180)*11.20
Answer:
0.47?
Step-by-step explanation:
I don’t understand how to do FOIL with this
2x – 3)(2x + 7)
Answer:
[tex]4x^2[/tex]+8x-21
Step-by-step explanation:
First foil 2x to 2x to get [tex]4x^{2}[/tex].
Then, foil 2x to 7 to get 14x.
Then, foil -3 to 2x to get -6x.
Then, foil -3 to 7 to get -21.
After doing all of that, you will get [tex]4x^2[/tex]+14x-6x-21.
Simplify it, so your final answer is [tex]4x^2[/tex]+8x-21
Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
please I will give point please help
can someone be kind enough to help me
Answer:
-9 < m - 12
Step-by-step explanation:
When you multiply or divide an inequality by a negative number, you flip the inequality sign.
Helping in the name of Jesus.
I want to plant 45 rose plants, 81 lily plants and 63 chilli plants in my garden. If I put the same number of plants in each row and each row has only one type of plant, what is the greatest number of plants I can put in one row?
The greatest number of plants that can be put in one row is 315. We can have 45 rows of roses, 27 rows of lilies, or 21 rows of chili plants, each with 315 plants in a row.
How to find the the greatest number of plants I can put in one rowTo find the greatest number of plants that can be put in one row, we need to find the greatest common factor (GCF) of 45, 81, and 63.
First, we can find the prime factorization of each number:
45 = 3 x 3 x 5
81 = 3 x 3 x 3 x 3
63 = 3 x 3 x 7
Then, we can identify the common factors:
The factors of 45 are 3 and 5
The factors of 81 are 3 and 3
The factors of 63 are 3 and 3
The greatest common factor is the product of the common factors raised to their lowest power:
GCF = 3^2 x 5 x 7 = 315
Therefore, the greatest number of plants that can be put in one row is 315. We can have 45 rows of roses, 27 rows of lilies, or 21 rows of chili plants, each with 315 plants in a row.
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Determine whether KM || JN. Explain or show work.
The segments KM and JN are parallel because the ratio LK : KJ = LM : MN are equivalent
Determining whether KM || JNfrom the question, we have the following parameters that can be used in our computation:
The triangle
To determining whether KM || JN, we make use of the following ratio
LK : KJ = LM : MN
Substitute the known values in the above equation, so, we have the following representation
8 : 5 = 12 : 7.5
Express as fraction
5/8 = 7.5/12
Simplify
So, we have
0.625 = 0.625
This means that KM || JN
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Find the missing side lengths. Leaves your answers as radical in simplest form
Answer:
v = 2√2
u = 4
Step-by-step explanation:
Use trigonometry:
[tex] \tan(45°) = \frac{v}{2 \sqrt{2} } [/tex]
Cross-multiply to find v:
[tex]v = 2 \sqrt{2} \times \tan(45°) = 2 \sqrt{2} \times 1 = 2 \sqrt{2} [/tex]
Use the Pythagorean theorem to find u:
[tex] {u}^{2} = {v}^{2} + ( {2 \sqrt{2} )}^{2} [/tex]
[tex] {u}^{2} = ( {2 \sqrt{2}) }^{2} + ({2 \sqrt{2}) }^{2} = 4 \times 2 + 4 \times 2 = 8 + 8 = 16[/tex]
[tex]u > 0[/tex]
[tex]u = \sqrt{16} = 4[/tex]
john bought 151 pounds of peaches if each peach weighs 5/8ths of a pound how many peaches are there?
Answer:
I think 241.6 is you answer
Step-by-step explanation:
I hope I helped! to get the answer first you have to convert 5/8 into a whole number but 5/8 can never be a whole number so make it a decimal which equals to 0.625 then divide 151 / 0.625 and you should get 241.6 as your answer
In the table below, which value is a marginal frequency?
A. 23
B. 46
C. 81
D. 135
The second row and second column's frequency, C. 81, is a marginal frequency (the column total for the second column).
how can we describe frequency distribution ?The frequency distribution statistics method identifies the frequency with which a given value or variety of values exists in a data set. The process is dividing the data into intervals, or "bins," and counting a number of values that fall within every bin.
A graph, such as a statistic or a frequency polygon, can be used to show the frequency distribution. The table displays the categories or intervals as well as the frequency or count for each interval.
The y-axis on the graph represents frequencies, while the x-axis represents intervals. The bars or polygons on the graph reflect the count or % of data within every interval.
given
The totals for each row and column make up the marginal frequencies in the table.
The frequencies for each category in the first variable are represented by the row totals, while the frequencies in the second variable are represented by the column totals.
In order to choose a marginal frequency from the available options:
A. The frequency of 23, which is not a marginal frequency, is in the first row and first column.
B. 46 is not a marginal frequency; it is the frequency in the first row and second column.
The second row and second column's frequency, C. 81, is a marginal frequency (the column total for the second column).
D. A marginal frequency is represented by the frequency in the second row and third column (the column total for the third column).
Options C and D therefore have negligible frequencies.
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Which of the following is NOT equal to the "ratio of 3 to 4?
A. 3:4
B. 3÷4
C. 3x4
D. 3/4
Answer:
C. 3 x 4
There's not really a way to explain it. If you still have questions, I would recommend asking your teacher or someone you can trust.
the answer choices are a. 5599ft B.8049 ft C.12822ft D.16098ft
Option B is the correct option for the total area of the shape which is approximate 8049 ft².
Define the term Isosceles triangle?An isosceles triangle is a polygon with three sides, where two of the sides have equal length.
Suppose the equal sides of Isosceles triangle is 'a',
so we can say that by Isosceles triangle rule: 70 = a√2
or side of Isosceles triangle (a) = 35√2 ft (by Pythagoras theorem)
Area of isosceles triangle (A₁) = [tex]\frac{1}{2}[/tex] × (Side of Isosceles triangle)²
= [tex]\frac{1}{2}[/tex] × (35√2)² = 1225 ft²
Area of two square (A₂) = 2 × a × a
= 2 × 35√2 × 35√2 = 4900 ft²
Area of quadrant circle (A₃) = (πr²)/4
= 3.14 × (35√2)² × (1/4) = 1923.25 ft²
Total area of the shape = A₁ + A₂ + A₃
= 1225 + 4900 + 1923.25 = 8048.25 ft²
Therefore, the total area of the shape is approximate 8049 ft²
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Find the surface area of a cylinder with a height of 7in and a base radius of 2in . Use the value 3.14 for π, , and do not do any rounding. Be sure to include the correct unit.
Answer:
Step-by-step explanation:
Find the surface area of a cylinder with a height of 7in and a bass radius of 2in. Use the value 3.14 for π, , and do not do any rounding.
A=2πrh+2πr2=2·π·2·7+2·π·2²=
not rounded 113.09734
Rounded 113.1
Can someone please solve step by step. I'm having trouble understanding.
A multiple choice test consists of five questions, each of which has four choices. Each
question has exactly one correct answer. How many ways are there to fill out the answer sheet so that four answers are correct and one is incorrect?
Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024.
What is possible way?It involves finding the most efficient and effective solution to a problem by exploring multiple options and assessing the pros and cons of each.
This can be found by calculating the number of possible ways to fill out the answer sheet.
Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024..
To explain why this is happening, it is helpful to look at an example. Let's say the five questions are A, B, C, D, and E.
If a person wants to fill out the answer sheet so that four answers are correct and one is incorrect, they can either choose the correct answer for four of the questions, and then choose an incorrect answer for the fifth question, or they can choose the incorrect answer for four of the questions, and then choose the correct answer for the fifth question.
In terms of calculating the number of ways to fill out the answer sheet, this means that for each of the five questions, there are four possible ways to answer (four choices for each question). This means that there are 4
The answer to this question is 1024. This can be found by calculating the number of possible ways to fill out the answer sheet. Since there are four choices for each question, the total number of ways to fill out the answer sheet is 4⁵, or 4x4x4x4x4, which is equal to 1024.
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Suppose you just received a shipment of fourteen televisions. Two of the televisions are defective. If two televisions are randomly selected, compute the probability that both televisions work. What is the probability at least one of the two televisions does not work.
The probability that both televisions work is ___
Answer: The probability that both televisions work is approximately 0.746, or 74.6%.
Step-by-step explanation:
To calculate the probability that both televisions work, we need to find the probability of selecting a working television, and then multiply that by the probability of selecting another working television from the remaining televisions.
Since 2 out of the 14 televisions are defective, that means there are 12 working televisions out of 14. So the probability of selecting a working television on the first draw is 12/14.
After the first television is selected, there will be 13 televisions left, with 11 working televisions. So the probability of selecting a second working television is 11/13.
Therefore, the probability that both televisions work is:
(12/14) x (11/13) = 0.746
So the probability that both televisions work is approximately 0.746, or 74.6%.
To calculate the probability that at least one of the two televisions does not work, we can use the complement rule. The complement of the event "both televisions work" is the event "at least one television does not work."
So, the probability that at least one television does not work is:
1 - 0.746 = 0.254
So the probability that at least one television does not work is approximately 0.254, or 25.4%.
Answer:
0.60, 0.40
Step-by-step explanation:
The probability that a television works is 11/14. The probability that a television is
defective is 3/14.
The probability that the first TV works and the second works is
[tex]\frac{11}{14}[/tex]×[tex]\frac{10}{13}[/tex]
(If the first selected TV works, the total number of televisions left is 13, and the
the number of working TV is 10).
Answer: 0.60.
The event that at least one of the two televisions does not work is the
opposite of the event ‘both TV work’. So the probability of at least one of the
two televisions does not work is
1- Pr (both works)= 1 − 11/14 ∙ 10/13 = 0.40.
Answer: 0.40.