The probability that the average final exam grade of a sample of 45 students selected from this class is between 80 and 83 is approximately 0.0922.
The standard error of the mean is given by the formula: [tex]standard error=standard deviation / \sqrt{sample size}\\\\ = 8.2/\sqrt{45} \\\\ = 1.935[/tex]
Next, we can calculate the Z-scores for 80 and 83:
Z1 = (80 - 79.8) / 1.935 = 0.512
Z2 = (83 - 79.8) / 1.935 = 2.056
Finally, we can use a Z-score table or calculator to find the cumulative probability of a standard normal distribution between Z1 and Z2:
P(80 < Xbar < 83) = P(0.512 < Z < 2.056) = 0.0922
So the probability that the average final exam grade of a sample of 45 students selected from this class is between 80 and 83 is approximately 0.0922.
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you can infer causality from a correlational result, but only when the r value is greater than
Therefore, the r value alone is not enough to infer causality, regardless of its magnitude.
What is correlation coefficient (r value)?The correlation coefficient, also known as the Pearson correlation coefficient or Pearson's r, is a measure of the strength and direction of the linear relationship between two continuous variables. It is expressed as a number between -1 and 1, where -1 indicates a perfect negative correlation (meaning that as one variable increases, the other decreases), 1 indicates a perfect positive correlation (meaning that as one variable increases, the other also increases), and 0 indicates no correlation. The value of the correlation coefficient provides information about how closely the two variables are related, but it does not establish causality.
According to question:The r value alone is not enough to infer causality. A high correlation coefficient suggests a strong relationship between two variables, but causality means that one variable is causing the changes in the other variable and requires a causal mechanism and a demonstration of a temporal relationship between the variables.
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need help asap!!!
Match each expression on the left with an equivalent expression on the right. Not all of the options on the right will be used.
Answer:
100x14 = 1,400
14(10) = 140
361 * 1000 = 361,000
100(361) = 36,100
Area and Perimeter
If a = 5 in and b = 4 in, what is the area of the sketch?
OA. 139 in²
OB.
144 in²
OC. 101.5 in²
OD. 39.5 in²
2a
4b
Note: figure not drawn to scale
Reset
4
Submit
b
The total area of the shape is 165.5 in².
What is the area of the shape?
The total area of the shape is calculated from the area of the trapezium and the area of the base which is rectangle.
Area of the base ( rectangle ) = L x B
where;
L is the length = 4b = 4 x 4 in = 16 inB is the breadth = 2b = 2 x 4 in = 8 inArea of base = 16 in x 8 in = 128 in²
Area of the trapezium = ¹/₂ ( 2a + a ) a
= ¹/₂ ( 3a²)
= ¹/₂ ( 3 x 5²)
= 37.3 in²
Total area = 128 in² + 37.3 in² = 165.5 in²
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Rita goes to the mall. If d is the number of items she bought, the expression 18.82d+22 gives the amount she spent in dollars at one store. Then she spent 20 dollars at another store. Find the expression which represents the amount Rita spent at the mall. Then estimate how much Rita spent if she bought 6 items. PLEASEEEE HELPPPP
The expression which represents the amount Rita spent at the mall is 18.82d + 42. If d = 6, then the total amount spent is $154.92.
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.
Amount spent at one store is given by the expression 18.82d + 22.
Here d is the number of items she bought at that store.
Amount spent at another store = $20
Total amount spent at the mall = 18.82d + 22 + 20 = 18.82d + 42.
If she bought 6 items, d = 6.
Total amount spent = (18.82 × 6) + 42 = $154.92
Hence the required expression to find the total amount is 18.82d + 42. And the total amount spent if the items bought is 6 is $154.92.
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Help please on picture
The image of the translation 3 units right and 2 units down is attached.
What is transformation in geometry?Transformation in geometry is the process of changing the position, size, or shape of a geometric figure or shape. It can include
translations, rotations, reflections, and dilations,Translation in geometry is a transformation that involves moving a figure from one place to another on the coordinate plane, without changing its size or orientation.
The image of a figure after a translation is simply a slide of the original figure along the plane.
The translation involves adding 3 units to the x and subtracting 2 units to the y
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I need help with this question. Is due in 5 minutes.
Answer:
x=2
Step-by-step explanation:
not hard at all unless you forgot it XD
a jar contains 6 red marbles numbered 1 to 6 and 10 blue marbles numbered 1 to 10. a marble is drawn at random from the jar. find the probability of the given event. enter all answers as reduced fractions.
The probability of the event a. P(E)3/8 b. P(E)3/8 c. P(E∩F)=11/16 d. P(G∪H)=13/16.
Divide the total number of outcomes by the entire number of different ways an event could happen to arrive at the probability. There are differences between probability and odds. Odds are determined by dividing the probability of a situation happening by the probability that it won't happen. Probability is a metric used to determine how likely an event is to occur. The likelihood that the coin will land with the heads side up is measured using the probability concept when we toss it in the air. Here is an example of how probability is used in everyday life that you probably already know about. Prior to a major outing, we always consult the weather prediction.
There are 16 marbles in total in a jar, 6 of it are red marbles that numbered 1 to 6 and there are 10 blue marbles numbered from 1 to 10
Let red marbles = r, blue marbles = b.
(a) The marble is red.
P(E)3/8
(b) The marble is odd-numbered.
P(F)=1/2
We may utilize the probability of the union of events to determine the likelihood of receiving red and odd-numbered marbles in solutions (a) and (b).
(c) The marble is red or odd-numbered.
P(E∩F)=11/16
(d) The marble is blue and even-numbered.
P(G∪H)=13/16
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The diagonal of a tv screen is 26 inches. the base is 18.8 inches wide. how tall is the tv?
the height of the triangle formed by the diagonal and base of the TV screen.
The height of the TV is approximately 15.6 inches.
(26 inches / √2) = 18.8 inches
(18.8 inches * √2) = 26 inches
Height = (26 inches / 18.8 inches) * 18.8 inches
Height = 15.6 inches
Step 1: Calculate the hypotenuse of the triangle formed by the diagonal and base of the TV screen.
Hypotenuse = diagonal / √2
Hypotenuse = 26 inches / √2
Hypotenuse = 18.8 inches
Step 2: Calculate the diagonal of the triangle formed by the hypotenuse and base of the TV screen.
Diagonal = hypotenuse * √2
Diagonal = 18.8 inches * √2
Diagonal = 26 inches
Step 3: Calculate the height of the triangle formed by the diagonal and base of the TV screen.
Height = diagonal / base
Height = 26 inches / 18.8 inches
Height = 15.6 inches
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a six-lane urban freeway (three lanes in each direction) has a free-flow speed of 55 mi/h. traffic includes 10% trucks and 2% express buses. each truck and express bus displaces 2.0 passenger cars from the traffic stream. if the occupancy of passenger cars is 1.5 people per vehicle, and buses carry an average of 50 people per bus, what is the person-capacity of the freeway (in one direction)? it may be assumed that trucks carry one person (the driver).
The freeway can carry 85 vehicles per hour in one direction.
To calculate the person-capacity of the freeway in one direction, we can use the following formula:
Person-capacity = (Total number of vehicles - (Number of trucks + Number of buses)) × 2.0 × Occupancy × Speed
where,
Total number of vehicles = (Number of trucks + Number of buses) × 0.1
Therefore,
Person-capacity = ((Number of trucks + Number of buses) × 0.1 - (Number of trucks + Number of buses)) × 2.0 × 1.5 × 55 mi/hPerson-capacity = (Number of trucks + Number of buses) × 0.1 × 2.0 × 1.5 × 55 mi/hPerson-capacity = (Number of trucks + Number of buses) × 1.35 × 55 mi/hPerson-capacity = (Number of trucks + Number of buses) × 73.25 mi/hPerson-capacity = 85 people per hourIn conclusion, the freeway can carry 85 people per hour in one direction. This is determined by taking into account the freeway speed, the number of passenger cars, and their occupancy. We can plan accordingly by understanding the freeway's capacity with this calculation.
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Sophia owns a small business selling used books. She knows that in the last week 15 customers paid cash, 50 customers used a debit card, and 15 customers used a credit card. Based on these results, express the probability that the next customer will pay with a debit card as a decimal to the nearest hundredth.
The probability that the next person will pay with a debit card is:
P = 0.63
How to find the probability?
We want to find he probability that the next customer will pay with a debit card.
That probability can be estimated as the quotient between the number of customers that paid with debit card and the total number of customers.
We know that:
15 paid in cash.
50 paid with debit card.
15 paid with credit card.
For a total of 15 + 50 + 15 = 80
Then the probability is:
P = 50/80 = 0.63
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Gabriel determined that his total cost would be represented by 2.5x 2y – 2. his sister states that the expression should be x x 0.5x y y – 2. who is correct? explain.
Answer:
Step-by-step explanation:
Hey! the answer is:
They are both correct, since the equations are the same.
Luna and Miles want to start selling baked goods to raise money for their gymnastics team to get new gear. Luna is baking double chocolate brownies with white chocolate chips and is selling them for $5 for each brownie. Miles is making oatmeal raisin cookies because that is his favorite and is selling them for $2 per cookie. Between the two of them they would like to raise $120. Start by defining the variables. Then write an equation in standard form and show your work for writing it in slope intercept form to express the scenario. Identify one possible solution and explain what it means.
An equation in standard form to express the scenario is 5x + 2y = 120.
An equation in slope-intercept form to express the scenario is y = -5x/2 + 60.
One possible solution (x, y) is (10, 35), which means Luna and Miles can sell 10 chocolate brownies and 30 chocolate chips.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would a assign variable to the number of chocolate brownies sold and the number of chocolate brownies sold respectively, and then translate the word problem into a linear equation as follows:
Let the variable x represent the number of chocolate brownies sold.Let the variable y represent the number of chocolate chips sold.Since they are selling chocolate brownies for $5 each and $2 per chocolate chips, with a total revenue of $120, a linear equation in standard form that models the situation is given by:
5x + 2y = 120
In order to write the linear equation in slope-intercept form, we would make y the subject of formula;
2y = -5x + 120
y = -5x/2 + 60
When x = 10, the y-value is given by:
y = -5(10)/2 + 60
y = -25 + 60
y = 35
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The moon orbits the earth at 384,400km. The distance from the earth to the sun is 149,600,00 km. The diameter of the sun is 1,391,000 km. What would the diameter of earth have to be to appear the same size as the sun from the moon?
The diameter of the Earth would need to be approximately 3,548.896 km to appear the same size as the Sun from the Moon.
What is the ratio?A ratio in mathematics is a comparison of two or more numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, while the divisor or number that is dividing is referred to as the consequent.
Let's call the diameter of the Earth "d".
From the Moon, the Earth is at a distance of 384,400 km,
and the Sun is at a distance of 149,600,000 km.
The ratio of the Sun's diameter to its distance from the Moon is
= 1,391,000 km / 149,600,000 km
= 0.00928.
So, to make the Earth appear the same size as the Sun, we need the ratio of the Earth's diameter to its distance from the Moon to be equal to 0.00928.
d / 384,400 km = 0.00928
Solving for d, we get:
d = 384,400 km x 0.00928
= 3,548.896 km
Hence, the diameter of earth should be 3,548.896 km
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a test to measure psychotic tendencies was given to a group of 1,000 potential air force cadets who wished to work in nuclear silos. any cadet who scored at or over 64 would be eliminated. the mean of the test was 52 and the standard deviation was 12. out of the 1,000 cadets how many were accepted?
840 of the 1,000 applicants were accepted to join the air force.
Explain the term psychotic tendencie?A mental health condition called psychosis makes people view or interpret the world in ways that are different from others around them. This could entail delusions or hallucinations.The given data:
Number of potential air force cadets n = 1000.mean = 52Standard deviation: 52 + 12 = 64Thus, selected cadets:
84% of 1,000
As, 84% is the percentile at one of the Standard deviation.
Thus, 840 of the 1,000 applicants were accepted to join the air force.
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the difference of n and 10 is less than 1. how many whole numbers n are there with this characteristic?
There are no whole numbers n that satisfy this characteristic
The difference of n and 10 must be a negative number for it to be less than 1, and no whole number can be negative.
Whole numbers are those that can only be represented as integers and don't include any fractional or decimal elements. They also go by the names "counting numbers" or "natural numbers," and they consist of the digits 0 through 9, including 1, 2, 3, 4, 5, 6, 7,, 8, and so on.
A whole number that can be either positive, negative, or zero is known as an integer. A group of integers that are not a fraction or a decimal, such as..., -2, -1, 0, 1, 2,..., are referred to as an integer in mathematics. The natural numbers (1, 2, 3,...), their opposites (-1, -2, -3,...), and zero are all included in the set of integers. Mathematicians employ integers for many various purposes, such as counting, organising, and performing arithmetic operations.
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Given that a line goes through the point (7,-6) and has a slope -4, write an equation in point slope form for the line
Twenty-five sixths times eight ninths
in the final multiple score (fms), pass not advanced (pna) exam points are awarded for what maximum number of exam cycles? a) four
In the final multiple score (fms), pass not advanced (pna) exam points are awarded for five maximum number of exam cycles.
It is a calculation system, primarily practiced by the U.S Navy in order to make sure whether sailors in the pay grade of E-3, E-4, E-5 and E-6 are eligible in order to receive the position of the next pay grade. It consists of six categories such as exam score, performance mark average (PMA), etc.
If sailors score well, they will be awarded with PNA points. In each exam cycle, a sailor can receive a maximum of 3 PNA points, i.e., for a good score, 1.5 PNA points and for a good performance mark average, another 1.5 PNA points will be awarded.
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Complete question: in the final multiple score (fms), pass not advanced (pna) exam points are awarded for what maximum number of exam cycles? a) four, b) five, c) two, d) six
Solve using the quadratic formula :
8x^2-4x+2=0
The solution of the given expression using the quadratic formula is x = 4 + 6.9i ÷ 16 and x = 4 - 6.9i ÷ 16.
What is imaginary number?The complex numbers that are not real are represented by the fictitious unit "i." However, in order to convert complex numbers into their whole real form, we must first determine what the value of the fictitious number i is √-1.
Essentially, it was once thought that there was no difference between real and imaginary numbers in fact. Real numbers and fictitious numbers, however, were distinguished when the complex number entered the scene.
The quadratic formula is given as:
x = -b ± √ b² - 4ac ÷ 2a
In the given equation:
8x^2-4x+2=0
b = -4, a = 8, and c = 2
Substituting the value in the quadratic equation formula we have:
x = -(-4) ± √(-4)² - 4(8)(2) ÷ 2(8)
x = 4 ± √16 - 64 ÷ 16
x = 4 ± √-48 ÷ 16
The negative sign can be replaced by imaginary number (i)^2 hence:
x = 4 ± √48(i)² ÷ 16
x = 4 + 6.9i ÷ 16 and x = 4 - 6.9i ÷ 16
Thus, the solution of the given expression using the quadratic formula is x = 4 + 6.9i ÷ 16 and x = 4 - 6.9i ÷ 16.
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the side length of square a is (2x 1) meters. the side length of square b is 2 meters longer than that of square a. find the difference in the area of the squares.
The difference in the area of the square 'a' and 'b' as per given side-length is equal to 8 ( x + 1 ) square meters.
Side length of square 'a' = (2x + 1) meters
Side length of square 'b' = ( 2x + 1 + 2 ) meters
= ( 2x + 3 ) meters
Area of a square 'a' = ( side length )²
= ( 2x + 1 )²
Area of a square 'b' = ( side length )²
= ( 2x +3 )²
Difference in the area of the squares = ( 2x +3 )² - ( 2x +1 )²
= ( 2x + 3 -2x -1 )( 2x + 3 + 2x + 1 )
= ( 2 ) ( 4x + 4 )
= 8 ( x + 1 )
Therefore, the difference in the area of the given squares is equal to 8 ( x + 1 ) square meters.
The side length of square 'a' is (2x + 1) meters. The side length of square 'b' is 2 meters longer than that of square a. find the difference in the area of the squares.
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what are the differences between correlation and causation? how do organizations use linear regression. please give some examples. the output for linear regression analysis has multiple numbers. how can we interpret the output? share some hints.
Correlation does not imply causation, but in general, causality suggests correlation. In the corporate world, linear regressions can be used to analyze trends and provide estimates or hypotheses.
Although correlation suggests a relationship between variables, it does not prove that the covariation is due to a direct or causal link between them. However, causality implies a certain kind of link called a causal relationship, which is different from merely inferring a relationship (or circumstances and logical results relationship).
Linear regression is a very powerful measurable technique that may be used to develop experiences on customer behavior, acquiring clients, and factors impacting productivity. Additionally, linear regression can be used to examine an item's evaluation, sales growth, and advertising effectiveness.
The threat can be evaluated based on socioeconomic factors, vehicle characteristics, and driver information. Such an investigation could result in important business decisions being made as a result.
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True or False?
Every rectangle with four congruent sides is a square.
Every rhombus is a quadrilateral.
Every square is a parallelogram.
Every quadrilateral is a square.
Every rectangle with four congruent sides is a square -> True
Every rhombus is a quadrilateral -> True
Every square is a parallelogram -> True
Every quadrilateral is a square -> False.
What is a square?A square is a regular quadrilateral, which means that it has four equal sides and four equal angles. It can also be defined as a rectangle with two equal-length adjacent sides.
here, we have,
we know that,
Every rectangle with four congruent sides is a square -> True
Every rhombus is a quadrilateral -> True
Every square is a parallelogram -> True
Every quadrilateral is a square -> False.
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(4) I'm stuck help me with how to get the equation show all ur steps
The number of solutions for the system of equations is given as follows:
Zero.
How to obtain the solution to the system of equations?The system of equations for this problem is defined as follows:
y = -5/3x + 2.5x + 3y = 12.We want to obtain the graphic solution for the system of equations, hence we obtain the point of intersection of the two equations.
From the image presented at the end of the answer, the two graphs never intersect, and hence the number of solutions to the system of equations is of zero.
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Solve for the value of pp (3p+6)° (4p+7)°
The value of the equation 6 + 3p = 4p + 7 is 1
How to solve the equation?Reorder the terms:
6 + 3p = 7 + 4p
Solving for the value of p by collecting like terms
6 + 3p = 7 + 4p
Move all terms containing p to the left, all other terms to the right.
Add '-4p' to each side of the equation.
-6 + 3p + -4p = -7 + 4p + -4p
Combine like terms: 3p + -4p = -1p
-6 + -1p = -7 + 4p + -4p
Combine like terms: 4p + -4p = 0
-6 + -1p = -7 + 0
-6 + -1p = -7
Add '6' to each side of the equation.
-6 + 6 + -1p = -7 + 6
Combine like terms: -6 + 6 = 0
0 + -1p = -7 + 6
-1p = -7 + 6
Combine like terms: -7 + 6 = -1
-1p = -1
Divide each side by '-1'.
p = 1
Simplifying
p = 1
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nine lines are drawn in a plane. what is the largest possible number of intersections in the plane which at least two of the nine lines intersect
The largest possible number of intersections in a plane with 9 lines is 36, which is achieved when each line intersects with every other line.
The largest possible number of intersections in the plane where at least two of the nine lines intersect is 36. To see why this is the case, consider a construction where each of the nine lines intersects with every other line. In this construction, each line intersects with eight other lines, so the total number of intersections is 9 * 8 / 2 = 36. This construction is possible to achieve in a plane, so 36 is the largest possible number of intersections.
This result can be explained using the formula for counting the number of intersections in a set of n lines. If each line intersects with every other line in the set, the total number of intersections will be equal to n choose 2, or n(n-1)/2, where n is the number of lines. In this case, n=9, so the maximum number of intersections is 9 choose 2 = 9(9-1)/2 = 36.
It is important to note that not all sets of nine lines in a plane will have 36 intersections. The actual number of intersections will depend on the specific configuration of the lines. However, 36 is the largest possible number of intersections for a set of nine lines in a plane.
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Ginny works at the local sneaker shop. She earns $17.50 per hour working there. Her boss offers her a promotion she can either receive a 12.5% hourly raise or $2.50 raise on her rate per hour. Ginny is not sure which choice will make her more money on a weekly basis.
Ginny chooses to take the 12.5% raise. She works 40 hours per week.
How much does she earn after 40 hours ?
Answer:
$787.5
Step-by-step explanation:
first, you have to find how much ginny makes in a week w/o her raise\
17.5*40=700
then, you have to raise it by 12.5%, so her new salary is 112.5% of 17.5
112.5% = 1.125
700*1.125=787.5
a young boy gets into an accident with a parent. they get in a hospital in coma. the doctor looks at the patient and says i cant operate on the patient because thats my young boy. hows this possible? there is a building in the center of town. the building is 43 stories tall, and i am taller than that building. how is this possible? how is a raven like a writing desk?
This riddle does not have any mathematical formula or calculation associated with it.
This is an impossible situation, as it is not possible for a doctor to be the patient's parent. It is also not possible for a person to be taller than a building that is 43 stories tall.
The phrase "How is a raven like a writing desk?" is a riddle posed by Lewis Carroll in his novel Alice's Adventures in Wonderland. The answer to the riddle is "they both have the potential to produce a few notes, though they are very different". This phrase does not have any mathematical formula or calculation associated with it.
This riddle does not have any mathematical formula or calculation associated with it.
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portion of the population of interest that is selected for a study
The surveyor is interested in learning additional information about a segment of the general population. Numerous research projects call for particular interest groups to make decisions in light of their findings. This group of individuals is referred to as a sample.
What Exactly Is a Sample?
An easier-to-manage portion of a bigger group is referred to as a sample. It is a subset of individuals that shares traits with a wider population.
In statistical testing, samples are utilized when population sizes are too vast for all potential participants or observations to be included in the test.
What does a research sample mean?
Sampling is the process of choosing a portion of the target population for a research project.
In the vast majority of research projects, it is impossible to recruit the involvement of the entire population of interest, hence data gathering depends on a smaller group.
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from a survey of 100 college students, a marketing research company found that 80 students owned ipods, 60 owned cars, and 50 owned both cars and ipods. (a) how many students owned either a car or an ipod (but not both)?
how many students owned either a car or an ipod (but not both): =100−90=10
What is union of sets?
Union of two given sets is the littlest set which contains every one of the components of both the sets.
What is intersection of sets?
Intersection of two given sets is the biggest set which contains every one of the components that are normal to both the sets
What is the recipe for union of two sets?
The union of two sets is given by
n(A∪B) = n(A) + n(B) - n(A∩B)
Where,
An and B are the two sets.
∪ is the union
∩ is the intersection.
n(AUB)=n(A)+n(B)−n(A∩B)
=80+60−50
=90
number of students owning a car or an ipod=90
number of students neither car nor stereo =100−90=10
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I NEEEEEEED HELP ASAPPPPP!
Part 1:
The transformation performed from function f to function g are:
Function f is translated to the left 5 units
Function f is translated up to 1 unit.
Part 2:
The transformation performed from function f to function g are:
Function f is translated to the right 3 units
Function f is translated down to 4 units.
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
We will use this concept:
f(x) = f(x - a) when translated a units to the right.
f(x) = f(x + a) when translated a units to the left.
Part 1:
f(x) = (x - 3)³ is tranform to g(x) = (x + 2)³ + 1
Now,
Translating f(x) with 5 units to the left.
f(x) = (x - 3 + 5)³
g(x) = (x + 2)³
Translating f(x) with 1 unit up.
g(x) = (x + 2)³ + 1
Part 2:
f(x) = ∛(x + 1) is tranform to f(x) = ∛(x - 2) - 4
Now,
Translating f(x) with 3 units to the right.
f(x) = ∛(x + 1 - 3)
f(x) = ∛(x - 2)
Translating f(x) with 4 units down.
f(x) = ∛(x - 2) - 4
Thus,
Part 1:
f(x) is translated with 5 units to the left and 1 unit up.
Part 2:
f(x) is translated with 3 units to the right and 4 units down.
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