Answer:
False.
Step-by-step explanation:
It is not possible to create a regular tessellation with a regular heptagon. A regular tessellation refers to a pattern of repeating shapes that completely covers a flat surface without any gaps or overlaps. The only regular polygon shapes that can form regular tessellations are the equilateral triangle, square, and hexagon. Regular heptagons do not have the symmetry necessary to form a repeating pattern that covers a flat surface without gaps or overlaps.
Mrs. Ross the couselor, is helping plan a field at her middle school and is trying to decide what yard games to buy. She randomly surveyed 80 students at lunchtime anf asked about the yard game each one preferref. The results of the survey are shown in the table. Bean bag toss 14 checkers 16 connect 4 28 jenga 14 tic tac toe 8, based on the results in the table, which statement is true? A a student is more likely to prefer tic tac toe or connect 4 than checker or jenga. B a student is four times as likely to prefer connect 4 as tic tac toe. C a student is twice as likely to prefer tic tac toe as checkers. D a student is less likely to prefer checkers or bean bag toss than jenga or tic tac toe.
To determine which statement is true, we need to compare the number of students who prefer each game relative to the total number of students surveyed.
The total number of students surveyed is:
14 + 16 + 28 + 14 + 8 = 80
A) To find the probability of a student preferring tic tac toe or connect 4 versus checker or jenga, we add the number of students who prefer tic tac toe or connect 4:
28 + 8 = 36
And add the number of students who prefer checker or jenga:
14 + 16 + 14 = 44
Therefore, statement A is false.
B) To find the probability of a student preferring connect 4 versus tic tac toe, we divide the number of students who prefer connect 4 by the number of students who prefer tic tac toe:
28/8 = 3.5
Therefore, statement B is false.
C) To find the probability of a student preferring tic tac toe versus checkers, we divide the number of students who prefer tic tac toe by the number of students who prefer checkers:
8/16 = 0.5
Therefore, statement C is true.
D) To find the probability of a student preferring jenga or tic tac toe versus checkers or bean bag toss, we add the number of students who prefer jenga or tic tac toe:
28 + 8 = 36
And add the number of students who prefer checkers or bean bag toss:
14 + 16 = 30
Therefore, statement D is true.
Therefore, the correct answer is option D: a student is less likely to prefer checkers or bean bag toss than jenga or tic tac toe.
Two numerical expressions are equivalent if______________________
Which of the following statements are true about the following expressions?
the expressions- 18-(6*2) or (18+6)*2
1. The two expressions are equivalent
2. The first expression is eight times as large asthe second expression
3. Both expressions are numerical expressions.
The given expressions are not equivalent. They are numerical expressions.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expressions are -18-(6 * 2) or (18 + 6)*2.
If the expressions are equivalent, then they will have the same values.
If they are not equivalent, then they will have different values.
-18-(6 * 2) = -18 - 12 = -30
(18 + 6)*2 = 24 * 2 = 48
Both the expressions are not equivalent.
Hence the expressions are not equivalent.
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A head nurse borrowed 35 syringes from the intensive care unit (ICU). If this was 20% of the ICU's total supply, how many syringes did the ICU have in total?
The total number of syringes that the ICU had is given as follows:
175.
How to obtain the total number of syringes that the ICU had?The total number of syringes that the ICU had is obtained applying the proportions in the context of the problem.
20% of the total supply x is equivalent to 35 syringes, hence the equation is given as follows:
0.2x = 35
Solving the equation, the total number of syringes that the ICU had is given as follows:
x = 35/0.2
x = 175 syringes.
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A binomial experiment consists of 10 trials. The probability of success on trial 3 is 0.34. What is the probability of success on trial 7?
0.85
0.34
0.32
0.56
0.23
0.43
The probability of success on the trial 7 for the given binomial experiment is 0.34.
Binomial experiment - what is it?An experiment utilizing a set number of independent trials with just two results is called a binomial experiment. There are two possible outcomes for these experiments: success and failure. Because of the nature of what is being tested, results in these studies can only ever be successes or failures.
Because there are only a limited number of outcomes that can occur during each trial of a binomial experiment, they are unique from other types of studies. Particularly, there can only ever be one of two outcomes in binomial experiments.
The probability of success and failure of a trial is same for every number of trials.
Given that,
n = 10 trials
Success = 0.34
Hence, the probability of success on the trial 7 for the given binomial experiment is 0.34.
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Does anyone know the answer to this?
Answer:
m<B = 58 degrees, m<C = 63 degrees
Step-by-step explanation:
let's find y!
angles B and A are complementary, so they should equal 90
therefore, B + A = 90
substitute
4y + 8y - 6 =90
12y = 96
y=8, and m<B = 8y-6; so m<B = 58
angles C and D are equal because of vertical angles
therefore, C = D
substitute
7x=5x+18
2x=18
x=9
m<C = 7x, so m<C = 63
the cost of a new car is $32,000 it depreciates at a rate of 15% per year . this means that it loses 15% of each value each year
The mathematical function describing the cost of car the next year is →
C{n + 1} = C{n} (1 - 3/20).
What is depreciation rate?The depreciation rate is a rate at which the price of a quantity decreases every year.
Given is that the cost of a new car is $32,000 it depreciates at a rate of 15% per year.
We can understand it as follows.
After one year the cost would be -
{x} = 32000 - {15% of 32000}
{x} = 32000 - 4800
{x} = $27200
After second year the cost would be -
{x} = 27200 - {15% of 27200}
{x} = 27200 - 4080
{x} = $23120
This means that after every year, the value decrease by 15% of what it was a year before. We can write -
C{n + 1} = C{n} - (15/100) C{n}
C{n + 1} = C{n} (1 - 3/20)
Therefore, the mathematical function describing the cost of car the next year is →
C{n + 1} = C{n} (1 - 3/20).
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When I combine 2x and - 10x what should I get?
Answer:
-8x
Step-by-step explanation:
when you combine 2x and -10x,
2x - 10x = -8x
This means that the expression 2x and -10x are combined to form the expression -8x.
17.) passes through X(1,-4), parallel to YZ with Y(5, 2) and Z(-3,-5) helppp please
The equation of the line parallel to the line passing through the points Y(5, 2) and Z(-3,-5) will be y = 7/8x + 4.5.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given that the line is passes through X(1,-4), parallel to YZ with Y(5, 2) and Z(-3,-5).
The equation of the line will be calculated as:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -5 - 2 ) / ( -5 - 3 )
Slope = 7 / 8
The equation will be written as:-
y = 7/8x + c
The slope of the two parallel lines will be the same. The y-intercept of the parallel lines will be,
y = 7/8x + c
1 = (7/8 x -4 ) + c
c = 4.5
The equation will be:-
y = 7 / 8x + 4.5
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Suppose Joan has a fair four-sided die with sides that are numbered 1, 2, 3, and 4.
After she rolls it 2,000 times, she finds that she rolled the number 2 a total of 187 times. Which of the following is true?
A. Joan has provided evidence that calls into question whether or not this is a fair die because the relative frequency of rolling a 2 is quite different than the theoretical probability even after repeating the experiment many times.
B. Joan has demonstrated that this is a fair die, since the relative frequency of rolling a 2 is nearly equal to the theoretical probability.
C. We cannot draw any conclusions from Joan's experience with this die because there is only a very weak link between the relative frequency of an event and the theoretical probability.
D. We cannot draw any conclusions from Joan's experience with this die without also knowing how many times the other numbers appeared.
The true statement is that Joan has provided evidence that calls into question whether or not this is a fair die because the relative frequency of rolling a 2 is quite different than the theoretical probability even after repeating the experiment many times. The answer is A.
The theoretical probability of rolling a 2 on a fair four-sided die is 1/4 or 0.25. If Joan rolled the die 2,000 times, we would expect her to roll a 2 approximately 500 times (0.25 x 2,000 = 500).
However, she only rolled a 2 187 times. The relative frequency of rolling a 2 is 187/2,000, which is 0.0935 or 9.35%. This is quite different from the expected theoretical probability of 25%, which suggests that the die may not be fair.
Joan's experience provides evidence that the die may not be fair. The relative frequency of rolling a 2 is significantly lower than the theoretical probability, indicating that the die may be biased.
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determine the volume of the solid whose base is the region enclosed by the curve and the line . the cross sections perpendicular to the -axis are right isosceles triangles.
The volume of the solid whose base is the region enclosed by the curve and the line is calculated as V = ∫ A(x) dx.
This solid has a base that is defined by a curve and a line, and its cross sections perpendicular to the x-axis are right isosceles triangles. We will use mathematical techniques to find the volume of this solid.
To find the volume of this solid, we need to use calculus. First, we need to determine the equation of the curve that forms the base of the solid. Once we have the equation, we can find the limits of integration that define the boundaries of the base region.
Next, we need to find an expression for the area of a cross section of the solid. We are given that these cross sections are right isosceles triangles. This means that the base and height of each triangle are equal. Let's call this length "a". Then, the area of each cross section is given by
=> A(x) = (1/2) * a²
To find the volume of the solid, we need to integrate the area of each cross section over the range of x values that define the base region. We can write the volume as V = ∫ A(x) dx.
To perform the integration, we need to determine the limits of integration. We can do this by finding the points where the curve intersects the line that defines the base region. Let's call these points (x1, y1) and (x2, y2). Then, the limits of integration are x1 and x2.
Finally, we need to substitute the expression for A(x) into the integral and evaluate it. The final result will give us the volume of the solid.
In summary, to find the volume of this solid, we need to use calculus. We first determine the equation of the curve that forms the base, then find an expression for the area of a cross section, and integrate this expression over the limits of integration that define the base region.
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write a function even count fr : int list -> int that returns the number of even integers found in the input list. the function is required to use (only) forward recursion (no other form of recursion). you may not use any library functions or any problems later in this set.
The answer of given question: That we are using the fact that True is treated as 1 and False as 0 in Python, so the expression (lst[0] % 2 == 0) will evaluate to 1 if the first element of the list is even, and 0 otherwise.
Here's an implementation of the even count function using forward recursion in Python:
python
def even_count_fr(lst: list[int]) -> int:
if not lst:
return 0
else:
return (lst[0] % 2 == 0) + even_count_fr(lst[1:])
This function takes a list of integers as input, and returns the number of even integers found in the list.
The base case for the recursion is when the list is empty, in which case the function returns 0. Otherwise, the function checks if the first element of the list is even, and adds 1 to the result if it is. The function then makes a recursive call to the same function with the tail of the list (i.e., all the elements except the first one), and adds the result of that call to the result from the previous step.
The equation (lst[0]% 2 == 0) will evaluate to 1 if the first entry of the list is even and 0 otherwise. This is because we are exploiting the Python fact that True is considered as 1 and False as 0, respectively.
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If a = 4 units, b = 6 units, and c = 10 units, what is the volume of the three prisms above?
Question Write an equation that you can use to find the value of x . Perimeter of square: 30 m
An equation that helped to find the value of x is 30 = 4x.
The value of x is 7.5mm.
What is the perimeter?A closed shape's perimeter is the sum of the lengths of its outside boundaries. The lengths of all the sides are added to determine the measurement.
Given:
A shape is a square.
And perimeter of the square is 30 mm.
And we know that the sides of the square are equal.
So, the perimeter of the square = 4 x The length of one side.
Substituting all the given values,
we get,
30 = 4x
x = 30/4
x = 7.5 mm
Therefore, x = 7.5 mm.
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a map measuring 21.6 cm by 9 cm is enlarged twice in the ratio 3:5 calculate the final dimensions of the map
Answer:
36cm and 15cm
Step-by-step explanation:
What is a ratio?A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
Divide the dimensions of the map by the given ratio.
3:5 = [tex]\frac{3}{5}[/tex]After the first reduction the dimensions of the new map are:
21.6 ÷ [tex]\frac{3}{5}[/tex] = 369 ÷ [tex]\frac{3}{5}[/tex] = 15Therefore, the new dimensions of the map are 36cm and 15cm.
The final dimensions of the map are 72 cm by 30 cm.
How to find the final dimensions ?If the map is enlarged twice in the ratio 3:5, this means that both the length and the width are multiplied by the same factor. Let the scale factor of the enlargement be x. Then, we have:
x = ( 5 / 3) x 2
x = 10 / 3
To find the final dimensions of the map, we multiply the original dimensions by the scale factor.
Final length = 21.6 cm x ( 10 / 3 ) = 72 cm
Final width = 9 cm x ( 10 / 3 ) = 30 cm
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Rhonda has a USB drive that can hold
8
,
000
,
000
,
000
B
8,000,000,000 B8, comma, 000, comma, 000, comma, 000, start text, space, B, end text.
Choose the best approximation of the number of bytes that Rhonda's USB drive can hold.
The best approximation of the number of bytes that Rhonda's USB drive can hold is 8 x [tex]10^9[/tex] B.
What is Scientific Notation?Using scientific notation, one can express extremely big or extremely small values. When a number between 1 and 10 is multiplied by a power of 10, the result is represented in scientific notation.
Given:
We have Rhonda has a USB drive that can hold 8, 000, 000, 000 B.
In Scientific Notation the decimal point should be placed just after one number and the number of extra zeroes raised to power.
Here we have 9 zeroes after 8 then the Scientific Notation is
= 8, 000, 000, 000 B.
= 8 x [tex]10^9[/tex] B
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25 points and will make the brainiest. Please answer each question as soon as possible. Thank you.
The sets of the domain and range of the relation are X = {- 4, - 3, 1, 0} and Y = {- 4, - 1, 0, 3, 4}.
How to determine the domain and range of a relation
In this problem we find a graphic representation of a relation, that is, a construction formed by two sets and its relationships. There is an input set called domain and an output set called range. Domain is represented by all values along the horizontal axis (x-axis) and range is represented by all values along the vertical axis (y-axis).
The points seen in the graph are now listed: (x₁, y₁) = (- 4, 0), (x₂, y₂) = (- 3, - 1), (x₃, y₃) = (1, - 4), (x₄, y₄) = (1, 4) and (x₅, y₅) = (0, 3). The set of the domain is {- 4, - 3, 1, 0} and the set of the range is {- 4, - 1, 0, 3, 4}.
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For a given distribution, the range is 60. Assuming the distribution is bell-shaped, the estimated standard deviation is = ____
Assuming the distribution is bell-shaped, the estimated standard deviation is 10.
Since the range is 60 and the distribution is bell shaped the N or Number will be 6
Thus, to calculate the standard deviation:
60/6 = 10
The standard deviation is a statistic that expresses the degree of variation or dispersion among a set of values. A low standard deviation suggests that values are typically close to the set's mean, whereas a high standard deviation suggests that values are dispersed over a wider range.
None of the standard deviations are "good" or "bad.". They serve as gauges of your data's dispersion. Sometimes, when using ratings scales, we want a wide spread because it shows that the range of the group we are rating is covered by our questions and ratings.
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For one-pair poker hands, why is the number of denominations for the three single cards (12 3) rather than (12 1) (11 1) (10 1)?
The number of denominations for the three single cards is 12 3 because there are 220 possible combinations of three cards from a deck, each combination representing a unique poker hand.
The number of denominations for the three single cards is 12 3 because it is impossible to have a poker hand with only two cards. The two-card hands can contain only one pair or two different cards, and neither of these hands are possible with only two cards. Therefore, the number of possible combinations of three cards is 12 3.
We can calculate this using the combination formula: nCr = n! / r!(n-r)!
For a hand of three cards, n = 12 (there are 12 denominations of cards) and r = 3. Therefore, 12 3 = 12! / 3!(12-3)! = 220. This means there are 220 possible combinations of three cards from a deck, each combination representing a unique poker hand.
The number of denominations for the three single cards is 12 3 because there are 220 possible combinations of three cards from a deck, each combination representing a unique poker hand.
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HELP ME PLEASE ANYONE I NEED HELPP
Step-by-step explanation:
I don't know car stuff, but that looks like its asking you to use the formula:
F1 x r1 = F2 x r2
Therefore, it will be:
175N x 200mm = 160N x 20mm
I hope this helps :)
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given questions.
Listed below are the highest amounts of net worth (in millions of dollars) of all celebrities. What do the results tell us about the population of all celebrities? Based on the nature of the amounts, what can be inferred about their precision?
Look at pic for numbers
Question content area bottom
Part 1
a. Find the mean.
Please don’t answer with the wrong answer! I’m tried of getting it wrong!!
According to the information, the mean of these values would be: 169
How to calculate the mean of this series of numbers?To calculate the mena of this series of numbers we must add all the values and multiply them by the number of values available. In this case, we would have to divide it by 10. The procedure is shown below:
290 + 190 + 175 + 165 + 155 + 155 + 140 + 140 + 140 + 140 = 1,6901,690 / 10 = 169According to the above, the mean of this operation would be 169.
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Yellow cab charges 1.75 flat rate in in addition to $0.75per mile. Leo has no more than $20 to spend on a ride. How many miles can Leo travel without exceeding his limit?
Show steps
Answer:
Step-by-step explanation:
Set x miles Leo can travel, and his cost have to be no more than $20, so
1.75+0.75x =20
0.75x = 20-1.75
0.75x = 18.25
x = 18.25/0.75 = 24.333 miles
Which of the following can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean?
a. The mode
b. percentiles
c. Chebyshev's Theorem
d. The empirical rule - assuming a normal distribusion
Chebyshev's Theorem can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean.
Chebyshev's Theorem is a mathematical theorem that can be used to determine the proportion of data points that fall within a specified number of standard deviation from the mean. It states that for any distribution, no matter what its shape, at least a certain proportion of values will fall within a certain number of standard deviations from the mean. This proportion can be calculated using the formula 1-1/k², where k is the number of standard deviations. For example, if k is 3, then at least 75% of all data points will fall within three standard deviations of the mean. This theorem is particularly useful for distributions that are not normally distributed, since it provides a way to estimate the proportion of data points that fall within a certain range, even if the distribution is not symmetrical. Chebyshev's Theorem is an important tool for data analysis and can be used in a wide variety of contexts.
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Point A is located at (-3, 7) on a
coordinate plane. Which point is located
8 units from Point A?
A. (-3, 8)
B. (8,7)
C. (−3, 1)
D. (-3,-1)
A point that is located 8 units from Point A include the following: D. (-3,-1).
What is a translation?In Mathematics, the translation of a geometric figure to the right simply means adding a digit to the value on the x-coordinate (x-axis) of the pre-image of a function while a geometric figure that is translated downward simply means subtracting a digit from the value on the y-coordinate (y-axis) of the pre-image.
By translating the coordinate of point A vertically downward by 8 units, the coordinates of the image of point A' include the following:
(x, y) → (x, y - 8)
Coordinate of point A = (-3, 7) → Coordinate of point A' (-3, 7 - 8) = (-3, -1)
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Which one is faster pulley with belt or just gears?
In both cases, pulley C is the fastest one since its radius is the smallest one.
Which pulley does rotate faster?
In this problem we find two cases of power transmition, the first example consists in a rigid transmition system formed only by pulleys and the second example consisting in a flexible transmition system formed by belts and pulleys.
Ideally, power is conserved throughout every system and rotational velocity of the pulley is inversely proportional to its radius. We need to determine does rotate faster in each case.
n ∝ 1 / R
Thus, we find the following results:
Case 1: Pulley C is the fastest pulley since it has the smallest radius.
Case 2: Pulley C is the fastest pulley since its has the smallest radius.
RemarkThere is no additional information (i.e. any angular speed of pulley, geometric dimensions in the second case) that may allows us to determine whether if rigid transmition system or a flexible transmition system is faster.
The representation only allows us to determine what pulley is the fastest within a system.
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Can someone help me
The correct statement about the quadratic function is given as follows:
C. The second difference would be constant.
How to model a quadratic function?A quadratic function is modeled as follows:
y = ax² + bx + c.
Then the first difference, which is the first derivative of the quadratic function, is obtained as follows:
y = 2ax + b.
The second difference, which is the second derivative of the quadratic function, is obtained as follows:
y = 2a.
The coefficient a is a constant, hence the second difference would be constant and the correct option is given by option C.
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Figure B is a scaled copy of Figure A. What is the scale factor from Figure A to Figure B?
Answer:
2:1
Step-by-step explanation:
If we examine the two figures we see that the length of each side of Figure B is twice the length of the corresponding side of Figure A
For example side of length 44 in Figure B corresponds to side of length 22 in Figure A
Scale Factor: Final Dimension/Initial Dimension =
Length of Figure B side/Length of Figure A corresponding side
44/22 = 2/1 or 2:1
So the scale factor from A to B is 2 or 2:1
the functions f, g, and h are defined by
f(x)=3x-4, g(x)=x-2, and h(x) = 5x²
find each of the following:
(f + g)(2)
The solution is, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
Given the expressions, f(x)=√x+5, g(x)=3x-7, and h(x)=5x, the answer to f(g(5)) is 8.
This is because when g(5) is substituted into f(x) we get f(g(5))=f(3x-7)=√(3x-7)+5. When 5 is substituted for x, this simplifies to f(g(5))=√(-2)+5 which equals 8.
The answer to g(f(78)) is 60. This is because when 78 is substituted into f(x) we get f(78)=√78+5 which simplifies to f(78)=9. When 9 is substituted into g(x) we get g(f(78))=3x-7 which simplifies to g(f(78))=3(9)-7 which equals 60.
Finally, the answer to h(g(f(2))) is 83. This is because when 2 is substituted into f(x) we get f(2)=√2+5 which simplifies to f(2)=3. When 3 is substituted into g(x) we get g(f(2))=3x-7 which simplifies to g(f(2))=3(3)-7 which equals 8. When 8 is substituted into h(x) we get h(g(f(2)))=5x which simplifies to h(g(f(2)))=5(8) which equals 83.
In summary, the answers to f(g(5)), g(f(78)), and h(g(f(2))) are 8, 60, and 83 respectively.
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Circle thermos a) Work out the size of angle AED. b) Work out x.
Answer:
x=2⁰ AED=78⁰
Step-by-step explanation:
180⁰-108⁰= 78⁰
angle AED= 78⁰
108⁰+50⁰= 158⁰
180⁰-158⁰=22⁰
22⁰+78⁰=100⁰
100⁰+ 78⁰=178⁰
180⁰-178⁰= 2⁰
x=2⁰
Nicole has two bags of coins. The first bag contains 5 silver dollars, 4 quarters, and 6 dimes. The second bag contains 2 silver dollars, 3 quarters, and 2 dimes. Nicole is going to let her little brother, Jacob, randomly select and keep 1 coin from each bag. What is the probability that Jacob will choose a silver dollar from each bag?
First, we need to find the probability of Jacob choosing a silver dollar from the first bag and a silver dollar from the second bag.
The probability of choosing a silver dollar from the first bag is 5/15 = 1/3 since there are 5 silver dollars out of a total of 15 coins in the bag.
The probability of choosing a silver dollar from the second bag is 2/7 since there are 2 silver dollars out of a total of 7 coins in the bag.
To find the probability of both events happening (Jacob choosing a silver dollar from each bag), we multiply the probabilities:
(1/3) x (2/7) = 2/21
Therefore, the probability that Jacob will choose a silver dollar from each bag is 2/21.
The DNA molecule comes in the form of a double helix, meaning two helices that wrap around one another. Suppose a single one of the helices has a radius of 7 A (1 angstrom = 10-8 cm) and one full turn of the helix has a height of 33 A. Find the paremetrization r(t) of the helix. r(t) = (7 cos(t), a,b) (Use symbolic notation and fractions where needed.) a = b= Find the arc length L of one full turn of the helix.
The parameterization of the helix is:
[tex]r(t) = (7 cos(t), 7 sin(t), 33/(2*\pi ) * t)[/tex] & the arc length of one full turn of the helix is approximately 147.26 Å
where t is the parameter that varies from 0 to [tex]2\pi[/tex]
In this parameterization, the first two coordinates give the coordinates of a point on a circle of radius 7 that lies in the plane perpendicular to the helix axis, while the third coordinate gives the height of the point along the axis.
To find the arc length L of one full turn of the helix, we use the arc length formula:
[tex]L = ∫_0^(2π) ||r'(t)|| dt[/tex]
where r'(t) is the derivative of r(t) with respect to t, and || || denotes the Euclidean norm.
We have:
[tex]r'(t) = (-7 sin(t), 7 cos(t), 33/(2*pi))and||r'(t)|| = √[(-7 sin(t))^2 + (7 cos(t))^2 + (33/(2pi))^2] = 7√(2 + (33/(2pi))^2)So, we get:L = ∫_0^(2π) 7√(2 + (33/(2pi))^2) dt = 7√(2 + (33/(2pi))^2) * ∫_0^(2π) dt = 14π√(2 + (33/(2*pi))^2)[/tex]
(Note: the symbol "Å" represents angstrom, which is [tex]10^(-10)[/tex] meters, and it is used to express atomic distances.)
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