The intersection of all of those intervals always be a closed interval if it is nonempty
Given that
for an arbitrary collection of closed intervals
the intersection of all of those intervals always be a closed interval if it is nonempty it's true
An arbitrary (finite, countable, or uncountable) intersection of
closed sets is closed.
Let C0 = [0, 1], C1 = [0, 1/3] ∪ [2/3, 1], and
C2 = [0, 1/9] ∪ [2/9, 1/3]∪ [2/3, 7/9] ∪ [8/9, 1]
In general, let
Cn =(1/3 [tex]C_{n-1}[/tex])U(1/3[tex]C_{n-1}[/tex] + 2/3)
Let C = ∩n>1Cn, called Cantor’s middle-third set. Show that C is
a closed set.
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I need help with thi
The length of each diagonal is of: 11 units.
How to obtain the length of each diagonal?The diagonal lengths are defined as follows:
WY = 6x - 7.XZ = 3x + 2.As the figure is a rectangle, the diagonal lengths are the same, and thus the value of x is obtained as follows:
WY = XZ
6x - 7 = 3x + 2
3x = 9
x = 9/3
x = 3.
Hence the diagonal length is given as follows:
XZ = 3(3) + 2 = 9 + 2 = 11 units.
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How many solutions can an absolute value equation have?
An absolute value equation may have one solution, two solutions, or no solutions.
Absolute value means "distance from zero" on a number line. To represent the absolute value of a number, we use a vertical bar on either side of the number.
The absolute value is the distance from zero, It is the non-negative quantity, which defines the number as the distance of the number from zero on the number line.
The absolute value has only one solution when it is compared to 0.
When the absolute value equation is compared with any positive number, then the number of solutions is two.
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Isosceles triangle ABC has AB = AC = 3/6, and a circle with radius 52 is tangent to line AB at B and to line AC at C. What is the area of the circle that passes through vertices A, B, and C ? (A) 24 (B) 25.- (C) 267 (D) 27.01 (E) 28.7
Answer:
Step-by-step explanation:
An isosceles triangle with sides of 3/6, 3/6 and an unknown length, and a circle tangent to the two sides with a given radius can be solved using the Pythagorean theorem, trigonometry and the circle area formula.
We know that the triangle is isosceles, so the angle at point B is congruent to angle at point C, and let's call it x. Now we know that angle BAC = 90- x. Since the circle is tangent to the side AB and AC at B and C respectively, we can use the property of tangents that says that the radius of a circle that is tangent to a line is perpendicular to that line, and we can use the triangle formed by the radius, the side and the angle at that point to apply the Pythagorean theorem.
3/6^2 + r^2 = (3/6/sin(x))^2
r^2 = (3/6)^2 (1/sin^2(x) -1)
Now we can use the area of the circle formula A = πr^2, to find the area of the circle that passes through the vertices A, B, and C:
A = π r^2 = π(3/6)^2 (1/sin^2(x) -1)
Using the values of the problem we get
A = π(3/6)^2 (1/sin^2(90- x) -1) = π(3/6)^2 (1/cos^2(x) -1) = π(52^2) = 2701π = 27.01 (D)
Therefore the area of the circle that passes through vertices A, B, and C is 27.01.
HELPPPPPPPPPPP
YALL AMAZING :))
Answer:
14.8%
Step-by-step explanation:
decrease = -100 * ((final - initial) / initial)
Answer:
14.8%
Step-by-step explanation:
Original fishing pole cost: $54
New fishing pole cost: $46
Using the percentage decrease formula:
[tex]\frac{Original Value - Final Value}{|Original Value|}[/tex] ×100%
Substitute
[tex]\frac{54-46}{|46|}[/tex] ×100%
From this, you should get 14.814814814814814...
Round to nearest tenths.
Final answer: 14.8%
Heeeeeeeeeeeeeeeeeeeelp
Answer:
Step-by-step explanation:
all internal angles in a triangle add to 180 degrees.
77+36=113
180-113=67
we know that the final angle in the triangle is 67 degrees
the left parallel line makes another triangle in the bottom left. we know that one angle is 41 and we just calculated that the other is 67.
41+67=108
180-108=72
so now we know that the small triangle in the bottom left has angles of 41,67 and 72.
all straight lines are 180 degrees, and we just figures out that the left side of the left parallel line is 72 degrees. therefore the other side is 108 degrees.
since they are parallel lines, the left angle of both of them on the bottom line is 72, while the right angle is 108.
this means that x=108 degrees
i hope this is right and it helps if it is correct. really sorry if it is wrong. have a good day :)
Ratio of boys to girls is 4:5 what fraction of class is boys
Answer:
The ratio of boys to girls is 4:5, which can be simplified to 4/5.
The fraction of the class that is boys is 4/5 (or 0.8), and the fraction of the class that is girls is 5/9 (or 0.5555).
So, 4/9 of the class is boys.
Use the distributive property to remove the parentheses
(-4+v+4x)(-6)
By distributive property for real numbers, the expression (- 4 + v + 4 · x) · (- 6) is equivalent to the expression 24 - 6 · v - 24 · x.
How to use distributive property
In real algebra, distributive property is an algebraic property where a real number is "distributed" on every term of a sum of real numbers. This property is described below:
c · (a + b) = a · c + b · c
Where a, b, c are real numbers.
Now we proceed to use distributive property in the following case. First, write the entire expression:
(- 4 + v + 4 · x) · (- 6)
Second, apply distributive property:
(- 6) · (- 4) + (- 6) · v + (- 6) · (4 · x)
Third, use associative property:
(- 6) · (- 4) + (- 6) · v + [(- 6) · (4)] · x
Fourth, use sign laws and multiply on each term:
24 - 6 · v - 24 · x
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B. Reviewing Key Terms
Complete each sentence by writing the correct term in the blank.
15. When a bank borrows money from another bank, the interest rate it pays is called the
16. Ownership of more than one bank constitutes a
17. When a bank customer writes a check, the check will go through the process of
M
18. A bank's total assets minus its total liabilities make up its
19. Banks repay loans from the Federal Reserve at a rate of interest called the
The correct term for each term is -
Federal Fund Rate
Bank holding company
Check clearing
Net worth
Discount rate
What is an account?
A certain kind of financial asset or debt that is kept and owned in your name.
When a bank borrows money from another bank, the interest rate it pays is called the Federal Fund Rate.
Ownership of more than one bank constitutes a bank holding company.
When a bank customer writes a check, the check will go through the process of check clearing.
A bank's total assets minus its total liabilities make up its net worth.
Banks repay loans from the Federal Reserve at a rate of interest called the discount rate.
Therefore, these are the key terms used in banking.
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How is shape d different from shapes a, b, and c?
it has 2 pairs of angles with the same
measure.
a
b
)
it has 2 acute angles and 2 obtuse
angles.
it has only 1 pair of parallel sides.
d
it has 0 pairs of perpendicular sides.
done
On solving the provided question, we can say that unlike other shapes, which all have parallel lines, only has one parallel side.
what is parallel lines?Parallel lines in geometry are coplanar infinite lines that don't intersect anywhere. In a given three-dimensional space, parallel planes are those that never cross. Curves with a constant minimum distance between them and no points of contact or intersection are said to be parallel. Two lines that are in the same plane, equally spaced apart, and never intersect are referred to as parallel lines in geometry. Either horizontal or vertical can apply. Parallel lines can be noticed in everyday objects like railroad tracks, rows of notebooks, and pedestrian crossings.
unlike other shapes, which all have parallel sides, only has one parallel side.
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acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. the abc electronics company has just manufactured 2100 write-rewrite cds, and 50 are defective. if 3 of these cds are randomly selected for testing, what is the probability that the entire batch will be accepted?
The probability that the entire batch will be accepted will be 9339
4000-90 = 3910 (non-defective) (non-defective)
If P(first not defective) = 3910/4000 and it is not changed (1 less to choose from and 1 less not defective)
P(second is not flawed if first is flawed) = 3909/3999 If the item is also not replaced (a total of 2 less to choose from and 2 less not defective)
P
(1st and 2nd are not defective, so the third is also not defective)) = 3908/3998
Simply multiply these three fractions to get the answer: 3910(3909>)(3908)) / (4000(3999)(3998)).
=9339
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Zach substitutes the values 32 inches, 20 inches, and 20 inches into the Pythagorean theorem. Explain what Zach is most likely trying to find out.
Zach is trying to find out the hypotenuse value of the right-angle triangle.
What is the right triangle?
A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
The Pythagorean theorem states that "in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides".
Zach is most likely trying to find the length of the hypotenuse of a right triangle, which is the side opposite the right angle, given the lengths of the other two sides.
In this case, given 32 inches, 20 inches, and 20 inches values, he's trying to find out the hypotenuse value of the right-angle triangle.
Hence, Zach is trying to find out the hypotenuse value of the right-angle triangle.
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in a group of 10 people, each person shakes hands with everyone else once. how many handshakea re there
The possible number of handshakes in a group of 10 people, where each person shakes hands with everyone else once are equal to 45.
Number of people in the group = 10
Each person shakes hands with everyone else once. When n people shake hands with each other, the total number of handshakes = ⁿC₂
where C denotes the combination , is represent an arrangement of objects in different ways without care of order.
Total number of handshakes = ¹⁰C₂
= 10!/2!(10 - 2)! = 10!/2!×8!
= 10×9×8!/(2×1)8!
= (10×9)/2
= 45 handshakes.
In other words, when 10 people are shaking hands, each one will shake hands with 9 others. Then, the total possible number of handshakes in a group = 10 × 9 = 90
(but remember the point that , when A shakes hands with B, B is also shaking hands with A, i.e., we are counting one handshake twice, one from A's side and the other from B's side).
The total number of handshakes in actual way = 90/2 = 45 handshakes. Hence, the total number of handshakes in a group is 45.
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What is the center of the circle?
The circle passes through the pint (-2,3). What is it’s radius?
Answer:
Step-by-step explanation:
Use the formula for circles.
[tex]x^{2} + y^{2} = r^{2}[/tex]
Since we already have the values of x and y in the given problem (-2,3), substitute the values in the fomula.
[tex]x^{2} + y^{2} = r^{2}[/tex]
[tex](-2)^{2} + (3)^{2} = r^{2}[/tex]
[tex]4 + 9 = r^{2}[/tex]
[tex]13 = r^{2}[/tex] (square both sides to get the radius)
[tex]\sqrt{13} = \sqrt{r^{2} }[/tex]
[tex]\sqrt{13} = r[/tex]
Complete the statement with >, < or =.
To complete the given statement, we have;
i. SM > DM
ii. <PQS < <RQS
iii. AS > RM
iv. m<1 = m<2
Properties of sides and angles of a triangles.Any given shape which is bounded by straight side is referred to as a plane shape. Examples include: triangles, rectangle, trapezium, parallelogram etc.
It can be observed in the given question that the shapes have different properties regarding their length of sides and measure of internal angles. Each of the statement can be completed as thus;
1. From triangle SJD,
m<SJM > m<DJM
Then, it can be deduced that;
SM > DM
2. From quadrilateral PQRS,
RS > PS
It can be deduced that;
<PQS < <RQS
3. From triangle AMS, it can be deduced that AS > RM.
4. From quadrilateral ABCD,
AD II BC
Then,
m<1 = m<2 (by alternate angle property)
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the australian official lottery has scratch-off instant lottery tickets that can be purchased for $1. the probability of winning a prize is 1 in 4. (a) mr. urban is feeling lucky one day and decides to purchase 100 of the scratch-off instant lottery tickets. find the probability that fewer than 20 tickets are winners.
In this scenario, the number of winning tickets follows a binomial distribution, since each ticket has a fixed probability of winning (1/4) and the trials (purchasing a ticket) are independent.
The probability that k out of n trials will be successful is given by the binomial probability mass function:
P(k) = (n choose k) * p^k * (1-p)^(n-k)
Where n is the number of trials (100 tickets), k is the number of successful trials (winning tickets), p is the probability of success (1/4), and (n choose k) is the binomial coefficient.
To find the probability that fewer than 20 tickets are winners we have to calculate the probability of getting 0 to 19 winning tickets.
P(x<20) = P(0) + P(1) + P(2) +...+ P(19)
using the above formula we can find the probability of getting k winning tickets
P(x<20) = P(0) + P(1) + P(2) +...+ P(19)
= (100 choose 0) * (1/4)^0 * (3/4)^100 + (100 choose 1) * (1/4)^1 * (3/4)^99 +.... + (100 choose 19) * (1/4)^19 * (3/4)^81
This can be calculated using a calculator or spreadsheet software, however, it's not possible for me to provide you with the exact answer as it involves multiple complex calculations.
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On Monday,Jeffery drove 146.3 miles. On Tuesday, he drove 84.13 miles. On Wednesday, he drove 73.02 miles. How many miles did he drive overall?
Answer:
Jeffrey drove a total of 303.43 miles on Monday, Tuesday, and Wednesday.
Step-by-step explanation:
To find the total miles driven by Jeffrey on Monday, Tuesday, and Wednesday, we need to add up the total miles. The total miles driven are 146.3 + 84.13 + 73.02 = 303.43 miles.
2. maria has 3 more than 4 times how much money josh has in savings. if josh has $505, how much does maria have?
Answer:
2023
Step-by-step explanation:
3 + 4x = y
y = 3 + 4(505)
y = 3 + 2020
y = 2023
you leave a 20% tip on your $50 dinner bill . how much was the tip ?
Answer:$10
Step-by-step explanation:
Assume 20% = 0.20
50 x 0.20 = 10
OR
Move the decimal one place to the left for 10 percent, and double it to get 20 percent.
Answer:
Suppose 20% Equals 0.20.
50 x 0.20 = 10
To acquire 10%, move the decimal one position to the left, and to reach 20%, double it.
Step-by-step explanation:
Help me please I don’t know just tell me the answer
Step-by-step explanation:
(e) = number of erasers she had originally.
now she has 38.
so,
A
38 = (e) + 10
B
38 - 10 = (e) + 10 - 10
28 = (e)
she had originally 28 erasers.
describe the possible lengths of the third side of the triangle given the lengths of the other two sides. 9 feet, 16 feet
Answer:
7 ≤ x ≤ 25
Step-by-step explanation:
Triangle Inequality Theorem
The sum of any two sides of a triangle is greater than or equal to the third side:
a + b ≥ cTherefore, the longest side of the triangle is "c".
Let the longest side be "x":
a = 9b = 16Therefore:
9 + 16 ≥ x25 ≥ xLet the longest side be 16:
a = 9c = 16Therefore:
9 + x ≥ 16x ≥ 7As 9 < 16, the longest side cannot be 9.
Therefore, the length of the third side of the triangle, given that the other two sides are 9 ft and 16 ft is greater than or equal to 7, and less than or equal to 25:
7 ≤ x ≤ 2513-45+3+26 = (a) 29 (b) 24 (c)28
answer: none it is -3
help please its very urgent!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
(Thank you!)
Answer:
4x+5 = 13
Step-by-step explanation:
2x-7= 5
Which relation is a function?
The required, relation shown in graphs A and D is functions.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
The curves shown in graphs B and C are not functional, as both graphs consist of only one variable.
While curve shown in graph A and D are function because it shows the relationship between two variables x and y.
Graph A shows, Absolute value function,
Graph D shows the quadratic function.
Thus, the Relation shown in graphs A and D is functions.
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Which expression is equivalent to −3(2x − 8) + 4x?
A -2x - 8
B -2x + 24
C -10x - 8
D -10x + 24
Answer:
The answer is B -2x +24
Step-by-step explanation:
I will show you how I got this answer step by step
-3(2x-8) + 4x
step 1
distribute the -3 through the parentheses
-6x + 24 + 4xstep 2
collect like terms
so -6x+4x = -2x
ANSWER: -2x+24
The expression is equivalent to the given expression is -2x +24
What is an expression?An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.
Given that, is an expression -3(2x-8)+4x, we need to find an expression equal to the given,
Simplifying the expression,
= -3(2x-8) + 4x
= -6x + 24 + 4x
= -6x+4x = -2x
Hence, the expression is equivalent to the given expression is -2x +24
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Evaluate the iterated integral by converting to polar coordinates. 20 sqrt(2x − x2) 0 6 sqrt(x2 + y2) dy dx
The supplied statement states that the iterated integral after being converted to interpolation is 32/3.
What is the definition of an integral?In mathematics, an integral is either a number representing the region beneath a function's graph over a certain interval or just a new function, the reverse of which contains the original mechanism (indefinite integral). To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context. Trigonometric functions of functional and equations are a concept in mathematics. Integral is a derivative of Middle English, Latin integer, and Medieval Latin integralis, each of which mean "making up a whole."
Therefore, the area is,
[tex]R=\left\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \sqrt{2 x-x^2}\right\}[/tex]
So,
[tex]y=\sqrt{2 x-x^2}[/tex]
y² = 2x - x²
x² - 2x + y² = 0
x² - 2x + 1 + y² = 1
(x-1)² + y² = 1
In other words, the area is the middle section of the disk with a radius of 1 and a center at (0,1).
Region R's polar coordinates are
x = r cos∅, y = r sin∅
So,
[tex]y=\sqrt{2 x-x^2}[/tex]
y² = 2x - x²
x² + y² = 2x
r² = 2r cos∅
r = 2 cos∅
The polar coordinates of the sphere of integration as,
[tex]R=\left\{(r, \theta) \mid 0 \leq \theta \leq \frac{\pi}{2}, 0 \leq r \leq 2 \cos \theta\right\}[/tex]
The provided integral then becomes,
[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r \cdot r d r d \theta \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r^2 d r d \theta \\= & \int_0^{\frac{\pi}{2}} 6\left(\frac{r^3}{3}\right)_0^{2 \cos \theta} d \theta\end{aligned}[/tex]
[tex]\begin{aligned}& =\int_0^{\frac{\pi}{2}} 2\left(8 \cos ^3 \theta-0\right) d \theta \\& =16 \int_0^{\frac{\pi}{2}} \cos ^2 \theta \cdot \cos \theta d \theta \\& =16 \int_0^{\frac{\pi}{2}}\left(1-\sin ^2 \theta\right) \cdot \cos \theta d \theta\end{aligned}[/tex]
Let u = sin∅ then du = cos ∅ d∅
If ∅ = 0 then u = 0 and if ∅ = π/2 then u = 1.
The above integral thus becomes,
[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & 16 \int_0^1\left(1-u^2\right) d u \\= & 16\left(u-\frac{u^3}{3}\right)_0^1 \\= & 16\left(1-\frac{1}{3}\right)\end{aligned}[/tex]
= 32/3
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consider the following bet. you toss two coins. if both of them come up heads, you win and get $10. otherwise you lose and have to pay $2. would you take this bet?
I would recommend taking this bet, as the expected value of the bet is Positive.
The expected value of a bet is the sum of the product of each possible outcome and its corresponding probability. In this case, the probability of getting two heads is 0.25, and the payout for that outcome is $10. The probability of not getting two heads is 0.75, and the payout for that outcome is -$2. When you multiply each outcome by its corresponding probability and sum them together, the expected value of the bet is $1.0. Because the expected value of the bet is positive, it is a good bet to take. It is more likely that you will gain money .
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Solve for X, Leave in simplest radical
Answer:
32
Step-by-step explanation:
[tex]8\sqrt{3}[/tex] is opposite to the 60 degree angle
The side opposite to the 60 degree angle = [tex]\sqrt{3}[/tex] times the side opposite to the 30 degree angle.
Side opposite to the 30 degree angle = 8
Leg opposite to the 30 degree angle theorem states that the side opposite to the 30 degree angle is half of the hypotenuse.
Hypotenuse = 16
In the big triangle, 16 is the side opposite to the 30 degree angle, which means it is half of the hypotenuse (big triangle).
Hypotenuse of the big triangle = x = 32
Hope this helps :)
Have a great day!
Which number produces an irrational number when multiplied to 0.5?
Answer: Root 16 = 4, 4*1/2= 2
1/3*1/2= 1/6 r5/9*1/2= 5/18
Root 3 = 1.73205...*1/2= 0.866025...
Root 3 is the answer
For what values of x is the equation 34+x4=1 true?
Answer:
true
Step-by-step explanation:
i had the same question on a quiz.
The value of x for the equation 34+x4=1 is [tex]\frac{-33}{ 4}[/tex]
As we have [tex]34+4x=1[/tex]
Subtracting [tex]34[/tex] from both sides we get
[tex]4x=1-34[/tex]
[tex]4x=-33[/tex]
Dividing with [tex]4[/tex] both sides
we get the answer [tex]x=\frac{-33}{4}[/tex]
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Melanie babysits for $14 per hour.
If she earned $91 last week,
how many hours did she work?
Define the variable. Write and
solve the equation.
Answer:
Equation is 14h = 91
It solves to h = 6.5
===========================================
Work Shown:
h = number of hours worked
14h = amount earned at $14 per hour
14h = 91 is the equation
To solve this equation, divide both sides by 14.
14h = 91
14h/14 = 91/14
h = 6.5
She worked 6.5 hours last week.
