The union and intersection of n sets that are all subsets of the universal set u can be found using bit strings.
Bit strings are a way of representing sets as strings of binary digits. To represent a set, each element is assigned a digit of 0 or 1. A 1 indicates that the element is in the set, while a 0 indicates that the element is not in the set.
The union of the sets is found by combining the bit strings and setting any digit that is 1 in any of the sets to a 1. The intersection is found by comparing the bit strings and setting any digit that is 1 in all of the sets to a 1.
By using bit strings, we can quickly and accurately find the union and intersection of n sets that are all subsets of the universal set u.
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Divya has $45 to spend on movie tickets. If each movie ticket is $14 and he pays $1 in tax, how much money does Divya have left over?
Answer:$30
Step-by-step explanation:
45-14=31
31-1=30
so the answer is 30
hope this helps
7. Write the unknown value that makes this
statement true:
25% of is 10
Answer: 40
Step-by-step explanation:
25/100 x ? = 10
multiply both sides by 100/25
x= 10 x 100/25
x=10
Lily has a box of candies.
5
6
of the candies are pink.
1
2
of the pink candies are round.
What fraction of the candies are pink and round?
Answer:
1/12
Step-by-step explanation:
Out of the total number of candies, 1/2 of the pink candies are round.
To find the fraction of the candies that are pink and round, we need to multiply the fractions representing the proportion of pink candies and the proportion of round candies among the pink candies:
pink candies = 5/6
round candies among the pink ones = 1/5
Therefore, the fraction of candies that are pink and round is:
(5/6) x (1/2) x 1/5 = 1/12
So, 1/12 of the candies are pink and round.
PLEASE HELP - WORTH 20 POINTS! Choose the statement that is true in the diagram below.
Answer:
Step-by-step explanation:
Option 3
the final exam scores in a science class were normally distributed with a mean of 60 and a standard deviation of seven. find the probability that a randomly selected student scored more than 70 on the exam. round your answer to four decimal places.
Answer:
Step-by-step explanation:
We can use the standard normal distribution to solve this problem by standardizing the score.
z = (x - mu) / sigma
Where:
x = 70 (score we are interested in)
mu = 60 (mean score)
sigma = 7 (standard deviation)
z = (70 - 60) / 7 = 1.43
Using a standard normal distribution table or calculator, we can find the probability that z is greater than 1.43. The probability is approximately 0.0764.
Therefore, the probability that a randomly selected student scored more than 70 on the exam is 0.0764 (or about 7.64%).
george flips an unfair coin $7$ times. the coin has a $\frac{1}{4}$ probability of coming up heads and a $\frac{3}{4}$ probability of coming up tails. what is the probability that he flips exactly $2$ tails?
The probability of getting exactly 2 tails in 7 flips of a coin with a probability of tails being 3/4 is 189/16384 or approximately 0.0115.
We can use the binomial distribution formula to solve this problem. Let X be the number of tails that come up in 7 flips of the coin. Then X follows a binomial distribution with n = 7 and p = 3/4 (since the probability of tails is 3/4).
The probability of getting exactly 2 tails is given by:
P(X = 2) = (7 choose 2) * (3/4)^2 * (1/4)^5
= (21 * 9/16 * 1/1024)
= 189/16384
So the probability that George flips exactly 2 tails is 189/16384, or approximately 0.0115.
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zero vertical asymptote removable discontinuity
A zero vertical asymptote removable discontinuity means that there is a zero of the function at the input value where the vertical asymptote would occur,
How to explain the termA zero of a function occurs when the value of the function is zero. A vertical asymptote of a function occurs when the value of the function becomes unbounded (either positive or negative) as the input approaches a certain value.
A removable discontinuity of a function occurs when there is a hole in the graph of the function at a certain input value, but the function can be made continuous at that point by defining its value at that input.
In the case of a zero vertical asymptote removable discontinuity, this means that there is a zero of the function at the input value where the vertical asymptote would occur, and the function can be made continuous at that input value by defining its value to be the value of the function at that input.
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Which equation matches the hanger diagram?
Equations are collections of two or more statements with equal signs.
I must locate the solution that the hanger diagram matches. [tex]3x=4[/tex] is the equation that fits the hanger diagram. Thus, option C is correct.
What is a hanger diagram?The hanger shows a total weight of 7 units on one side that is balanced with 3 equal, unknown weights and a 1-unit weight on the other.
Two or more expressions containing equal signs are called equations. I need to find the equation that corresponds to the hanger diagram. The hanger model is a visual representation of the equation.
Both sides must have the same weight to keep the hanger balanced. Like scales and barbells. There are 3 x on the left side of the hanger and 4 x on the right side.
So [tex]3x=4[/tex] is an equation that satisfies the given trailer diagram.
So option C is correct. [tex]3x=4[/tex] is the equation that fits the hanger diagram.
From the diagram we have,
Left=x+x+x
Right [tex]=1+1+1+1[/tex]
This gives
Left=[tex]3x[/tex]
Right [tex]=4[/tex]
Therefore, the equation [tex]3x =4[/tex]
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solve the pair of simultaneous equations:(step by step, using factorization method)
y²+2y+11=x
x=5-3y
Answer: (-3,-2)
Step-by-step explanation:
y²+2y+11 = 5-3y
y^2+2y+11-5+3y =0
y^2+5y+6=0
y^2+3y+2y+6=0
y(y+3)+2(y+3)=0
(y+3)(y+2)=0
y= -3, -2
All you do is plug in the x value to the equation
Hope it helps:)
Help please, Which value of x satisfies the equation 7/3(x+9/28)=20
Answer:
Step-by-step explanation:
[tex]\frac{7}{3} (x+\frac{9}{28} )=20[/tex]
[tex]7 (x+\frac{9}{28} )=60[/tex] (multiplied both sides by 3)
[tex]x+\frac{9}{28} =\frac{60}{7}[/tex] (divided both sides by 7)
[tex]x=\frac{60}{7}-\frac{9}{28}=\frac{240}{28}-\frac{9}{28}=\frac{231}{28} =8.25[/tex] (subtracted [tex]\frac{9}{28}[/tex] both sides and solved)
Find the quadratic function
Answer:Get a quadratic function from its roots. Enter the roots and an additional point on the Graph. Mathepower finds the function and sketches the parabola.
Step-by-step explanation:Solve a quadratic equation using the quadratic formula.
Write the quadratic equation in standard form, ax2 + bx + c = 0. Identify the values of a, b, and c.
Write the Quadratic Formula. Then substitute in the values of a, b, and c.
Simplify.
Check the solutions.
a survey of 142 randomly selected students at one college showed that only 82 checked their campus email account on a regular basis. construct a 95% confidence interval for the percentage of students at the college who do not check their email account on a regular basis. round to one decimal place.
Confidence interval for the percentage of students at the college who do not check their email account on a regular basis is 49.6%< P < 65.8%.
The percentage (frequency) of acceptable confidence intervals that include the actual value of the unknown parameter is represented by the confidence level. In other words, a limitless number of independent samples are used to calculate the confidence intervals at the specified degree of assurance. in order for the percentage of the range that includes the parameter's real value to be equal to the confidence level.
We must determine the proportion of achievements to which our problem pertains when calculating confidence intervals for proportions. This value should be used in the computations. Another thing to keep in mind is that the z-value is calculated by dividing the alpha value by two.
x = 82
n = 142
p = x/n = 82/142 = 0.577
Point estimate P = 0.577
1 - P = 1 - 0.577 = 0.423
At 95% confidence level the z is
[tex]\alpha[/tex] = 1 - 95%
= 1 - 0.95
= 0.05
[tex]\alpha[/tex]/2 = 0.025
[tex]z_\alpha _/_2 = 1.96[/tex]
Margin of error E = [tex]z_\alpha _/_2 *\sqrt{\frac{P(1-P)}{n} }[/tex]
= 1.96 x [tex]\sqrt{\frac{0.577(0.423)}{142} }[/tex]
= 0.081
At 95% confidence interval the P is
P - E < P < P + E
0.577 - 0.081 < P < 0.577 + 0.081
0.496 < 0.658.
confidence interval for the percentage of students at the college is 49.6% < P < 65.8%.
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A parking lot was full of different colored cars. There were 12 red cars, 15 blue cars, and 3 green cars. At this rate, how many blue cars will there be if there were 120 total cars?
please help with this!!!
The graph of g can be obtained using a horizontal stretch by a factor of 4 and a vertical translation 3 units up of the graph of f.
What is a translation?In Mathematics, the translation of a graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.
In Mathematics, a horizontal translation to the left is modeled by this mathematical equation g(x) = f(x + N) while a vertical translation to the positive y-direction (upward) is represented by this mathematical expression g(x) = f(x) + N.
Where:
N represents an integer.g(x) and f(x) represent a function.Based on the information provided about the parent function f, a function that represents g(x) is given by:
g(x) = 4f + N
g(x) = 4x + 3
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w(x)= -5(x-8)(x+4)
What is the maximum height that the stone will reach?
Answer:
(2, 180)
Step-by-step explanation:
w(x)=-5x^2+20x+160
a=-5 b=20
x=-20/2x(-5)
x=2
w(2)=180
2, 180
find the number of ways of arranging N people in a straight line if two particular people must always be separated
The number of ways to arrange N people with A and B separated is given by expression N! - 2*(N-1)! .
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, operators, and functions that are grouped together in a meaningful way. Expressions can be as simple as a single number or variable, or they can be complex and include many different elements. They are used to represent mathematical relationships and operations, and can be evaluated or simplified using mathematical rules and techniques. Examples of expressions include:
3x + 7(2a - b) / (c + 1)sin(x) + cos(y)Now,
Let the two particular people be A and B.
If we place A in a spot, there are N-1 spots left for B to be placed. Once A and B are placed, there are (N-2)! ways to place the remaining people. Therefore, the number of ways to arrange N people with A and B separated is:
(N-1) * (N-2)!
Alternatively, we can find the total number of ways to arrange N people in a line (N!) and subtract the number of ways to arrange them with A and B together.
To find the number of ways to arrange N people with A and B together, we can treat A and B as a single entity, so there are (N-1)! ways to arrange the remaining people with AB together. However, A and B can be arranged in two ways (AB or BA), so we need to multiply (N-1)! by 2.
Therefore, the number of ways to arrange N people with A and B separated is:
N! - 2*(N-1)!
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HI! PLEASE SHOW FULL SOLUTIONS FOR BOTH QUESTIONS AND ONLY ANSWER IF YOU KNOW! NO CALCULUS PLEASE! THAT WOULD BE VERY APPRECIATED!!
Answer:
3) p(2) = 22
4) k = 0
Step-by-step explanation:
Remainder theorem: If the polynomial p(x) is divided by the linear polynomial x -a then the remainder is p(a).
3)p(m) = m⁴ - 2m³ + m² + 12m - 6
p(m) is divided by (m - 2).
m -2 = 0
m = 2. The remainder is p(2)
p(2) = 2⁴ - 2*2³ + 2² + 12*2 - 6
= 16 - 16 + 4 + 24 - 6
= 22
p(2) = 22
4) p(x) = 8x³ + 6x² + x + k
p(x) is divided by (2x + 3).
2x + 3 = 0
2x = -3
[tex]x = \dfrac{-3}{2}[/tex]
[tex]p(\dfrac{-3}{2})=-15[/tex]
[tex]8*(\dfrac{-3}{2})^3+6*(\dfrac{-3}{2})^2-\dfrac{3}{2}+k=-15\\\\\\8*\dfrac{-27}{8}+6*\dfrac{9}{4}-\dfrac{3}{2} + k = -15\\\\\\-27 + \dfrac{27}{2}-\dfrac{3}{2}+k=-15\\\\\\-27 + \dfrac{24}{2}+k=-15\\\\[/tex]
-27 + 12 + k = -15
k = -15 + 27 - 12
k = 0
What is y=-2(x-4)^2+2 in factored form?
The factored form of this quadratic equation is equal to y = -2x² + 16x - 30.
How to determine the factored form of a quadratic equation?In this exercise, you are required to determine the factored form of the given quadratic function that is written in vertex form (standard form).
In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.Based on the information provided above, we have the following quadratic function:
y = -2(x - 4)² + 2
y = -2(x - 4)(x - 4) + 2
y = -2(x² - 4x - 4x + 16) + 2
y = -2(x² - 8x + 16) + 2
y = -2x² + 16x - 32 + 2
y = -2x² + 16x - 30
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of a group of 200 workers, 15 are chosen to participate in a survey about the number of miles they drive to work each week
In this situation, the sample consists of the [ ]workers selected to participate in the survey.
the population consists of [ ] workers.
The sample consists of the 15 workers selected to participate in the survey.
The population consists of 200 workers.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Out of a group of 200 workers, 15 are chosen to participate in a survey about the number of Miles they drive to work each week.. In this situation the samples consist of the 15 workers selected to participate in the survey.The population consist of 200 workers
SAMPLE: This is a representative part of a population on which a research is about the population is administered
POPULATION: This is the large collection of people or objects that is the focus of a scientific query or research. Often times, the logistics involved in reaching the entire population may be unavailable, so a sample is taken
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Compute the design strength for the following double-angle shape: 2L8 times 4 times 3/4, long legs 3/8-in. back-to-back, Fy = 36 ksi; KL is 20 feet for all axes, and there are two intermediate connectors. Use the procedure of AISC Section E4 (a). Do not use the column load tables. Compare the flexural and the flexural-torsional buckling strengths.
Therefore, to calculate the design strength of the double-angle shape with the given parameters, the procedure of AISC Section E4 (a) is used to calculate the flexural and flexural-torsional design strength, which can then be compared to determine the highest design strength.
The design strength for the double-angle shape is calculated using the procedure of AISC Section E4 (a).
The given information is: 2L8 times 4 times 3/4, long legs 3/8-in. back-to-back, Fy = 36 ksi; KL is 20 feet for all axes, and there are two intermediate connectors.
To calculate the flexural design strength, the flexural buckling strength is first determined by calculating Euler's critical stress, Fcr, and then multiplying it by the design section modulus.
The Fcr can be calculated using the formula Fcr =[tex]0.658 x SQRT(Fy x KL)[/tex]and the design section modulus can be calculated using the formula [tex]Z = (b x d^2)/6[/tex].
To calculate the flexural-torsional design strength, the flexural-torsional buckling strength is first determined by calculating the effective length, Kx, and then multiplying it by the torsional constant, J. The Kx can be calculated using the formula Kx = 2.6 (L/r) and the torsional constant, J, can be calculated using the formula J = [tex](b d^3)/3.[/tex]
Finally, the flexural design strength and the flexural-torsional design strength can be compared to determine the highest design strength of the double-angle shape.
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Simplify: 76 ÷ 72. 7 3 7 8 7 4 7 12
We can simplify the fraction by dividing both numbers by 4 (or by 2 two times), we will get the equivalent fraction 19/18
How to simplify the quotient?Here we have a quotient (or we can also call it a fraction) which is:
76/72
To simplify any fraction, what you need to do is divide both numerator and denominator by the same number.
For example, if we use 2, we will get:
76/2 = 38
72/2 = 36
then we have the equivalent fraction.
38/36
But we can keep simplifying this, divide by 2 again:
38/2 = 19
36/2 = 18
We get:
19/18
We can't simplify this anymore because 19 is prime.
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Choose the best estimate for the weight of a cantaloupe. Responses A 2 decigrams2 decigrams B 2 kilograms2 kilograms C 2 grams2 grams D 2 milligrams
The best estimate for the weight of a cantaloupe is 2 kilograms (B).
A decigram is 1/10th of a gram, which would be too small of weight for a cantaloupe. 2 grams (C) is also too small for a cantaloupe as it would only be the weight of a few small seeds. 2 milligrams (D) is an extremely small weight, only suitable for a single grain of salt or a tiny insect.
Therefore, 2 kilograms (B) is the most reasonable estimate for the weight of a cantaloupe as it falls within the typical range of cantaloupe weights.
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Complete Question:
Choose the best estimate for the weight of a cantaloupe. Responses
A 2 decigrams
B 2 kilograms
C 2 grams
D 2 milligrams
I am mad confused! I will make you Brainlist if correct and show all steps and I will give a thanks on all your answers
Step-by-step explanation:
The surface area of a rectangular prism can be found by adding the areas of all six of its faces.
In this case, the rectangular prism has side lengths of 3, 6, and 12 feet. So, its faces are:
Top and bottom faces: Each of these faces is a rectangle with side lengths of 3 feet and 6 feet. Therefore, the area of each of these faces is 3 ft * 6 ft = 18 ft². Since there are two of these faces, their combined area is 2 * 18 ft² = 36 ft².
Front and back faces: Each of these faces is a rectangle with side lengths of 3 feet and 12 feet. Therefore, the area of each of these faces is 3 ft * 12 ft = 36 ft². Since there are two of these faces, their combined area is 2 * 36 ft² = 72 ft².
Side faces: Each of these faces is a rectangle with side lengths of 6 feet and 12 feet. Therefore, the area of each of these faces is 6 ft * 12 ft = 72 ft². Since there are two of these faces, their combined area is 2 * 72 ft² = 144 ft².
To find the total surface area, we add the areas of all six faces:
Total surface area = 36 ft² + 72 ft² + 144 ft²
Total surface area = 252 ft²
Therefore, the surface area of the rectangular prism is 252 square feet.
Answer:
Step-by-step explanation:
12*3*2= 72 because there are two rectangles with the same length.
6*3*2= 36 because there are two widths with the same area.
6*12*2= 144 because there are a top and bottom with the same area.
72+36+144= 252
Surface area is 252 ft squared.
What is y'all's teacher teaching y'all!? I learned this two months ago!
What is the volume of the box?
The graph is given below y>x+4 is given below.
Write three points that represent solutions and non-
solutions.
Solutions
Non-Soultions
Answer:
Solutions: (-5, 1), (-10, 1), (-10, 5)
Non-solutions: (0, 4), (5, 4), (10, 4)
Step-by-step explanation:
Solutions are in the shaded area. Non-solutions are in the non-shaded area and on the dashed line.
Solutions: (-5, 1), (-10, 1), (-10, 5)
Non-solutions: (0, 4), (5, 4), (10, 4)
Find the area of the figure.
7 cm
11 cm
8 cm
The area is ? square centimeters.
pls help I'll mark brainlisest
Answer:
Area of the figure=126.5cm²
Step-by-step explanation:
As we can see based on the shape of the figure, we can divide it into a;
→ Triangle
→ Rectangle
Formulas that we need are;
⇒ Area of triangle =1/2×base×height
⇒ Area of rectangle =length × width
Let's solve the area of the triangle first;
Area of triangle =1/2 × base × heightArea of triangle=1/2 × 11cm × 7cmArea of triangle=38.5cm²Then the area of the rectangle;
Area of rectangle =length × widthArea of rectangle =11cm × 8cmArea of rectangle =88cm²Finally, we add the triangle and rectangle together-
Area of Triangle + Area of Rectangle = 38.5cm²+88cm²
Area of the figure=126.5cm²
RevyBreeze
why mean absolute deviation is a better approach to handle outliers in a data than standard deviation
Mean absolute deviation (MAD) is sometimes considered a better approach to handle outliers in a data set than standard deviation because it is less sensitive to extreme values.
The reason for this is that MAD uses absolute differences between each data point and the median of the data set, rather than the squared differences used by standard deviation.
In a data set with extreme values, such as outliers, the squared differences used by standard deviation can significantly inflate the value, leading to a higher estimate of the overall variability in the data. MAD, on the other hand, uses absolute differences, which are not affected by the sign of the difference and thus are less affected by extreme values. Therefore, MAD can be a better measure of variability in a data set that includes outliers.
However, it is important to note that MAD also has some limitations. It is less widely used and less familiar to many analysts than standard deviation, and it has a more complex formula that can be harder to interpret. Additionally, MAD is not as efficient as standard deviation when the underlying distribution is normal, meaning it requires a larger sample size to achieve the same level of precision as standard deviation. Ultimately, the choice between MAD and standard deviation depends on the specific characteristics of the data set and the goals of the analysis.
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Cielo's rectangular prism shaped swimming pool has a
side of length 8 yards, width of 6-yards and height of 3
yards. What is the total volume of the pool?
a) 36 yd³
b) 144 yd³
c) 1008 yd³
d) 156 yd³
The total volume of the pool is 156 yd³. Option D
How to determine the volumeFirst, to determine the volume, we need to note the properties of a rectangular prism.
It has 6 faces, 12 edges and 8 vertices.The base and side are always rectangles.It also has three dimensions, that is, length width and height.Pairs of opposite faces are identical or equal.The formula for volume of a rectangular prism is;
Volume = lwh
Given that;
l is the length.w is the width.h is the height.Now, substitute the value
Volume = 8 × 3 × 13/2
Volume = 312/2
Volume = 156 yd³
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Please Help! I don't understand this question!
Therefore, the inverse of f(x) is not a function, as it fails the vertical line test.
How does a mathematical function appear?One output is produced for one input by a function, a form of rule. The formula y=x2 serves as an illustration of this. A single output for y results from any input for x. Given that x is the input value, it is appropriate to say that y is a function of x.
We can determine if the inverse of f(x) = 8x² + 27 is a function by finding the inverse and checking if it passes the vertical line test.
To find the inverse, we first replace f(x) with y:
y = 8x² + 27
Next, we swap the roles of x and y:
x = 8y² + 27
Solving for y gives:
8y² = x - 27
y² = (x - 27)/8
y = ±√((x - 27)/8)
Notice that we have a ± sign in front of the square root, which means that for each x value, we have two possible y values.
Therefore, the inverse of f(x) is not a function, as it fails the vertical line test.
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the capacity of a dump truck is listed by the manufacturer as 10 yd3. a construction site requires the removal of 170 m3 of dirt, and the contractor has three identical trucks. how many trips will each need to make?
Trips will each need to make 6 trips.
Given
Capacity = 10yd³
Dirts = 170 m³
Trucks = 4
Required
Count the trips made by each truck.
To determine how much dirt is in each truck, divide the amount of soil by 4.
Each Truck = 170/4 m³
Each Truck = 42.5 m³
Divide the portion of each truck by capacity of each truck to get the number of trip
Trip = Each Truck / 10yd³
Convert m³ to yd³
Trip = 55.587875/10
Trip = 5.5587875
Approximate:
Trip = 6
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