Answers
Answer:
18. x = 80°
19. y = 85°
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
18.
x + x + 20 = 180
2x = 160
x = 80
Answer: x = 80°
y + y + 10 = 180
2y = 170
y = 85
Answer: y = 85°
Answer: x = 80° and y = 85°
Step-by-step explanation: In a cyclic quadrilateral, opposite angles add up to 180°.
x + (x + 20) = 180 and
y + (y + 10) = 180.
Solving for x
x + (x + 20) = 180
x + x + 20 = 180
2x = 180 - 20
2x = 160
2x/2 = 160/2
x = 80°
Solving for y
y + (y + 10) = 180
y + y + 10 = 180
2y = 180 - 10
2y = 170
2y/2 = 170/2
y = 85°
Related Questions
Tyler has run 10. 4 miles,which is 65 percent of the total distance he plans to run this week. What is the total distance that Tyler plans to run this week
Answers
Tyler has run 10.4 miles, which is 65% of the total distance he plans to run this week. Tyler plans to run a total of 16 miles this week.
Let's use "x" to represent the total distance that Tyler plans to run this week. According to the problem, Tyler has already run 10.4 miles, which is 65% of the total distance he plans to run. We can set up an equation to represent this information:
10.4 = 0.65x
To solve for x, we can divide both sides of the equation by 0.65:
x = 10.4 ÷ 0.65
x = 16
Therefore, the total distance that Tyler plans to run this week is 16 miles.
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A movie theater wanted to determine the average rate that their diet soda is purchased. An employee gathered data on the amount of diet soda remaining in the machine, y, for several hours after the machine is filled, x. The following scatter plot and line of fit was created to display the data. scatter plot titled soda machine with the x axis labeled time in hours and the y axis labeled amount of diet soda in fluid ounces, with points at 1 comma 35, 1 comma 39, 2 comma 32, 3 comma 24, 3 comma 30, 4 comma 20, 5 comma 18, 5 comma 22, 6 comma 4, 6 comma 14, 7 comma 8, and 8 comma 0, with a line passing through the coordinates 3 comma 25.2 and 7 comma 4.84 Find the y-intercept of the line of fit and explain its meaning in the context of the data. The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda. The y-intercept is 40.5. The machine starts with 40.5 ounces of diet soda. The y-intercept is −5.1. The machine loses about 5.1 fluid ounces of diet soda each hour. The y-intercept is 40.5. The machine loses about 40.5 fluid ounces of diet soda each hour.
Answers
The correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.
What is the equation of the line?
A linear equation is an algebraic equation of the form y=mx+b. where m is the slope and b is the y-intercept.
The y-intercept of a line of fit is the value of y when x equals 0. In the context of this problem, the y-intercept represents the amount of diet soda that the machine starts with when it is filled.
Since the y-intercept of the line of fit is −5.1, this means that the machine starts with 5.1 ounces of diet soda.
This is a reasonable value, as it is unlikely that the machine would be completely empty when it is filled.
It's important to note that the slope of the line of fit is also relevant in this context.
The slope represents the rate at which the amount of diet soda in the machine decreases over time. However, the question only asked for the y-intercept.
Hence, the correct answer is: The y-intercept is −5.1. The machine starts with 5.1 ounces of diet soda.
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how many ways are there to distribute five balls into three boxes if (c) the balls are unlabeled, but the boxes are labeled?
Answers
There are 243 ways to distribute five unlabeled balls into three labeled boxes.
Since the balls are unlabeled, we only need to consider the number of balls in each box, rather than which specific ball goes where.
We can use a combination approach to solve this problem. Let's think about distributing the balls one at a time. For the first ball, there are three boxes to choose from. For the second ball, there are also three boxes to choose from. We can continue this process until all five balls have been distributed.
So, for each ball, there are three choices of which box to put it in. Therefore, the total number of ways to distribute the five balls into the three labeled boxes is
3 x 3 x 3 x 3 x 3 = 3^5 = 243
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5) The graph of the equation y = −3x - 5 is shown below. What would happen to the graph if the slope was changed to 1?
Answers
Answer:
The equation y = -3x - 5 represents a linear function with a slope of -3 and a y-intercept of -5.
To understand what would happen to the graph if the slope was changed to 1, we need to compare the graphs of y = -3x - 5 and y = x - b, where b is some constant.
The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. So, when we change the slope of the equation y = -3x - 5 to 1, we get:
y = x - b
To find the value of b, we can substitute the coordinates of any point on the line. Let's use the y-intercept, which is -5:
-5 = 1(0) - b
b = -(-5)
b = 5
Therefore, the equation y = x - 5 represents the line with a slope of 1 and a y-intercept of 5.
To compare the graphs of y = -3x - 5 and y = x - 5, we can graph both equations on the same coordinate plane. Here's what the two graphs look like:
Graph of y = -3x - 5 (slope = -3, y-intercept = -5):
|
-5| x
| x
| x
| x
| x
| x
x---------------
-3 -2 -1 0 1 2 3
Graph of y = x - 5 (slope = 1, y-intercept = 5):
|
5| x
| x
| x
| x
| x
| x
x---------------
-5 -4 -3 -2 -1 0 1 2 3
As we can see, changing the slope of the equation from -3 to 1 rotates the line counterclockwise and makes it steeper. The y-intercept remains the same at -5.
Julie works Sunday,
, and Wednesday for 10 hours each day. On Tuesday, Thursday, and Friday, she works 7 hours each day. She does not work on Saturday. Her weekly total earnings are $612
Answers
Julie hourly rate of pay from the given different rates of the day with total earning of $612 is equal to $12per hour.
Total number of hours Julie works in a week is equal to,
On Sunday = 10 hours
On Monday = 10 hours
On Tuesday = 7 hours
On Wednesday = 10 hours
On Thursday = 7 hours
On Friday = 7 hours
On Saturday = 0 hours
Total hours worked in whole week is
= 10 + 10 + 7 + 10 + 7 + 7 + 0
= 51 hours
Total money earned by Julie in whole week = $612
Hourly rate of pay = Weekly earnings / Total hours worked
Substitute the value we have,
⇒ Hourly rate of pay = $612 / 51 hours
⇒ Hourly rate of pay = $12 per hour
Therefore, Julie's hourly rate of pay is $12 per hour.
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The above question is incomplete , the complete question is:
Julie works Sunday, Monday, and Wednesday for 10 hours each day. On Tuesday, Thursday, and Friday, she works 7 hours each day. She does not work on Saturday. Her weekly total earnings are $612. What is Julie's hourly rate of pay, in dollars?
where is the water table in a swamp? group of answer choices well below the surface. at the surface. well above the surface. generally, 2 miles below the surface.
Answers
Generally, the water table in a swamp is located 2 miles below the surface.
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in a gambling game a person draws a single card from an ordinary 52-card playing deck. a person is paid $19 for drawing a jack or a queen and $5 for drawing a king or an ace. a person who draws any other card pays $2. if a person plays this game, what is the expected gain? (round your answer to the nearest cent.)
Answers
the expected gain is $0.77, rounded to the nearest cent.The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff.
There are 4 jacks, 4 queens, 4 kings, and 4 aces in a standard 52-card deck. So the probability of drawing a jack or a queen is 8/52 = 2/13, and the probability of drawing a king or an ace is also 8/52 = 2/13. The probability of drawing any other card is 1 - 2/13 - 2/13 = 9/13.
The expected gain is the sum of the products of the probability of each outcome and its corresponding payoff. So:
Expected gain = (2/13) * 19 + (2/13) * 5 + (9/13) * (-2)
Expected gain = 38/13 - 10/13 - 18/13
Expected gain = 10/13 ≈ 0.77
Therefore, the expected gain is $0.77, rounded to the nearest cent.
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i need help on this math problem
Answers
Answer:
no the didn't hear the question
Answer:
I am pretty sure the answer is that the question can't be heard
Step-by-step explanation:
LANGUAGE ARTS On Monday, 86 science fiction books were sold at a book sale. This is 8 more than twice the amount sold on Thursday. How many science fiction books were sold on Thursday?
Answers
In conclusion 39 science fiction books were sold on Thursday.
How to solve and what does algebra mean?
Let's use algebra to solve this problem. Let x be the number of science fiction books sold on Thursday. Then we know that:
86 = 8 + 2x
We can solve for x by first subtracting 8 from both sides:
78 = 2x
Then dividing both sides by 2:
x = 39
Therefore, 39 science fiction books were sold on Thursday.
Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating those symbols. It involves using letters and other symbols to represent variables and quantities in equations and formulas.
Algebra is used in a wide range of fields, including mathematics, science, engineering, and economics, and it is an essential tool for solving many real-world problems.
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which answer refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time? group of answer choices
Answers
The answer that refers to the total number of cases of a disease or a disorder in a specified population at a particular point in time is prevalence.
Prevalence is the total number of cases of a disease or disorder in a population at a given point in time, and does not include cases that have been resolved or previously diagnosed cases. It is an important measure of the health of a population, as it allows researchers to identify patterns in the distribution of a disease or disorder and helps inform public health strategies.
Prevalence is calculated by dividing the total number of cases of a disease or disorder in a population at a given point in time, by the size of the population. For example, if a population of 100,000 people has 500 cases of a particular disease, the prevalence would be 0.005 or 0.5%.
Prevalence is an important metric in epidemiology and public health, and is often used in combination with incidence rates to measure the health of a population. Incidence rates measure the number of new cases of a disease or disorder that occur in a population over a certain time period, whereas prevalence is a snapshot of the total number of cases of a disease or disorder in a population at a given point in time.
Knowing the prevalence of a disease or disorder in a population helps public health practitioners understand the magnitude of a health issue, inform public health strategies, and identify risk factors and trends in the distribution of a disease or disorder.
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I don’t understand this stuff-
Answers
By using the fact that the measures ∠BAE and ∠EAC are equal, we will see that x = 20
How to get the value of x?Here we know that AE is an angle bisector of ∠BAC, this means that the measures of the two formed angles are the same ones.
Then we can write:
∠BAE = ∠EAC
Now we know that the measures of these angles are:
∠BAE = x + 30
∠EAC = 3x - 10
Replacing that in the equation above we willget:
x + 30 = 3x - 10
solving that for x, we will get:
30 + 10 = 3x - x
40 = 2x
40/2 = x
20 = x
That is the value of x.
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listed are 29 ages for academy award winning best actors in order from smallest to largest. 18; 21; 22; 25; 26; 27; 29; 30; 31; 33; 36; 37; 41; 42; 47; 52; 55; 57; 58; 62; 64; 67; 69; 71; 72; 73; 74; 76; 77 find the percentile rank of age 30.
Answers
The percentile rank of age 30 is 27.586%.
The percentile rank of age 30 can be calculated using the following equation:
Percentile rank = (number of scores below 30 / total number of scores) x 100
In this case, the total number of scores is 29, and there are 8 scores below 30 (18, 21, 22, 25, 26, 27, 29, and 30). Therefore, the percentile rank of age 30 is:
(8/29) x 100 = 27.586%
The percentile rank of age 30 is 27.586%.
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Write a phrase in words for each algebraic
expression.
22. m+83_
23.42s
24. 9/d
25. t - 29
26. 2+g
27. 11x
28. h/12
29. 5- k
Answers
t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .
what is expression ?An expression in mathematics is a group of digits, variables, and operations that illustrates a mathematical connection or concept. Symbols, words, or a combination of both can be used to write expressions in a variety of ways. Expressions that are examples include: 3x + 4, 2y - 7z , (a + b) ,x2 + y2 = 2 5sin(x) + 3cos(x). Equations, inequalities, functions, formulae, and many other mathematical ideas can all be represented as expressions. Additionally, they can be altered or simplified using algebraic methods like factoring, combining like terms, and solving for a variable.
given
The sum of m and 83.
Forty-two times s.
Nine divided by d.
t decreased by 29.
Two more than g.
Eleven times x.
h divided by twelve.
Five minus k
t decreased by 29 , Two more than g , Eleven times x , h divided by twelve and Five minus k are the phrase of given expression .
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draw marbles from a bag which contains 5 red marbles, 6 blue marbles and 4 green marbles with replacement until you get a blue marble. a) binomial b) poisson c) hypergeometric d) none of these
Answers
the correct answer is: none of these, as only binomial distribution is applicable to this scenario.
a) This scenario follows the binomial distribution, as we are drawing marbles with replacement and interested in the number of successes (getting a blue marble) in a fixed number of trials.
b) The Poisson distribution is used to model the number of events occurring in a fixed time interval, given a certain rate of occurrence. It is not applicable in this scenario.
c) The hypergeometric distribution is used to model the probability of obtaining a certain number of successes in a sample without replacement, given a finite population of items that can be classified into successes and failures. In this scenario, we are drawing with replacement, so the hypergeometric distribution is not applicable.
d) Therefore, the correct answer is: none of these, as only binomial distribution is applicable to this scenario.
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The following shows a graph of y = x^2+ 5
Can we use this graph to find the solutions of 0 = c^2 + 5? Why or why not?
Answers
we can, now if we look at 0 = x² + 5, that's when the parabola y-value is 0, that is, what's "x" when y = 0? well, if we look at the graph, the graph never touches the x-axis, so that means the graph never has any "real roots", only complex ones or imaginary ones. We can tell because the graph never touches the x-axis.
PLEASE HELP WITH ENTIRE WORK SHEET I AM STRUGGLING SO BAD I WILL GIVE ALL POINTS AND MARK YOU BRAINLIEST FOR EVERYTHING PLEASE HELP! :( LOTS OF LOVE <3
Answers
Answer:
1-
a. 19
b. -8
2-
a. -31
b. 0
c. -10.7
d. -3/7
e. 4
3-
a. -5
b. -60
c. 0
d. -1/4
4. -13/2
5. -85/18
6. -5/12
7. -11
8. 16/11
9. -20/27
10. 26/11
11. -55/9
Step-by-step explanation:
why did i do this
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one eighth to create polygon A′B′C′D′. If the dilation is centered at the origin, determine the vertices of polygon A′B′C′D′.
A′(3.5, −5.25), B′(1.75, −1.75), C′(−3.5, 1.75), D′(−3.5, −3.5)
A′(3.2, −4.8), B′(1.6, −1.6), C′(−3.2, 1.6), D′(3.2, 3.2)
A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5)
A′(−12, 14), B′(−10, 10), C′(12, −14), D′(12, 12)
Answers
The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).
What is Dilation:In geometry, dilation is a transformation that changes the size of a figure but not its shape. It is a type of similarity transformation.
When a figure is dilated, each point of the figure moves away or towards the center of dilation by a certain scale factor.
Here we have
Polygon ABCD with vertices at A(−4, 6), B(−2, 2), C(4, −2), and D(4, 4) is dilated using a scale factor of one-eighth to create polygon A′B′C′D′.
To dilate polygon ABCD using a scale factor of one-eighth i.e 1/8 multiply the coordinates of each vertex by the scale factor of 1/8.
The coordinates of A are (-4, 6), multiply each coordinate by 1/8
A' = (-4/8, 6/8) = (-1/2, 3/4) = (-0.5, 0.75)
The coordinates of B are (-2, 2), multiplying each coordinate by 1/8
B' = (-2/8, 2/8) = (-1/4, 1/4) = (-0.25, 0.25)
The coordinates of C are (4, -2), multiplying each coordinate by 1/8
C' = (4/8, -2/8) = (1/2, -1/4) = (0.5, - 0.25)
The coordinates of D are (4, 4). Multiplying each coordinate by 1/8
D' = (4/8, 4/8) = (1/2, 1/2) = (0.5, 0.5)
Therefore,
The vertices of polygon A'B'C'D' are A′(−0.5, 0.75), B′(−0.25, 0.25), C′(0.5, −0.25), D′(0.5, 0.5).
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The graph of the cubic parent equation, y=x3
, is plotted on the coordinate plane.
Select two equations that represent a shift of the graph of the parent equation to the right on the coordinate plane.
Responses
y=x3+2
y = x 3 + 2
y=x3−1
y = x 3 - 1
y=(x−12)3
y = ( x - 12 ) 3
y=(x+8)3
y = ( x + 8 ) 3
y=(x+7)3
y = ( x + 7 ) 3
y=(x−4)3
Answers
Therefore , the solution of the given problem of equation comes out to be y=(x-12)³ and y=(x+8)³.
What is an equation?Variable words are commonly used in complex algorithms to show consistency between two contradictory claims. Academic expressions called equations are used to show the equality of various academic numbers. Instead of a distinct algorithm that divides 12 into two parts and can be used to assess data received from y + 7, normalization in this case yields b + 7.
Here,
The following two equations show a rightward translation of the parent equation's coordinate plane graph:
=> y=(x-12)³
=> y=(x+8)³
Therefore , the solution of the given problem of equation comes out to be y=(x-12)³ and y=(x+8)³.
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Please help!! Determine what line the angle below has been reflection across. Justify your answer
Answers
The line of reflection for the given angle is corresponding vertices.
1. Identify the original angle and its reflected angle in the diagram.
2. Find the midpoint between the corresponding vertices of the original and reflected angles.
3. Draw a line through the midpoint that is perpendicular to the line connecting the corresponding vertices.
In general, to reflect an angle across a line, you would draw a perpendicular line from the vertex of the angle to the line of reflection, and then extend the sides of the angle to intersect the line of reflection at the same angle. The line of reflection would be the perpendicular bisector of the segment connecting the vertex of the original angle to the corresponding vertex of the reflected angle.
This line is the line of reflection, and the angles are reflected across it. The justification for this method is that the line of reflection is equidistant from the corresponding points of the original and reflected angles
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Clare is cycling at a speed of 12 miles per hour. If she starts at a position chose as zero, what will her position be after 45 minutes?
Answers
Answer: 9 miles
Step-by-step explanation: The speed of 12 miles per hour means that for every hour, Clare is 12 miles further from the starting point. 1 hour = 12 miles Since an hour is equivalent to 60 minutes, 60 mins = 12 miles We can divide both sides by 60 to find the distance travelled per minute. 1 min = 12 ÷60= 0.2 miles Multiply both sides by 45 to find the distance travelled in 45 minutes: 45 mins = 0.2(45)= 9 miles Given that the starting position is at zero, Clare's position is at 9 miles after 45 minutes.
a german shepherd puppy weighed 25 pounds at 4 months old and 31 pounds at 5 months old. what is the percent increase or decrease of its weight? show hints
Answers
Answer:
24% increase
Step-by-step explanation:
percent change = (new value - old value)/(old value) × 100%
A positive percent change is a percent increase.
A negative percent change is a percent decrease.
In this problem:
new value = 31
old value = 25
percent change = (31 - 25)/(25) × 100%
percent change = 24%
Since the percent change is positive, the percent change is a
24% increase
The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the an 24% increase in the puppy's weight in 1 month.
The percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.
To explain this further, let's look at an example. If a puppy weighed 25 pounds at 4 months, and it gained 6 pounds over the course of the following month, it would weigh 31 pounds at 5 months. To calculate the percentage increase, take the difference in weight (6 pounds) and divide it by the starting weight (25 pounds). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight.
To calculate the percentage decrease, use the same steps as above, but subtract the starting weight from the final weight instead. For example, if a puppy weighed 25 pounds at 4 months and lost 6 pounds over the course of the following month, it would weigh 19 pounds at 5 months. The percentage decrease would be calculated as (25 - 19)/25 = 0.24, or a 24% decrease in the puppy's weight.
In summary, the percentage change in the weight of a German Shepherd puppy from 4 months to 5 months is the difference between the two values (31 - 25 = 6) divided by the starting weight (25). This gives us 6/25 = 0.24, or a 24% increase in the puppy's weight in 1 month.
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Factorise
15x²y³z+25x³y²z+35x²y²z²
Answers
Answer:
First, we can factor out 5x²y²z from each term:
15x²y³z+25x³y²z+35x²y²z² = 5x²y²z(3y+5xz+7z)
So the fully factorized expression is:
5x²y²z(3y+5xz+7z)
Frank organized a raffle. He sells 300 tickets for £5 each. The prizes cost £400. He gives 55% of the profit to Charity A and 45% of the profit to Charity B. Work out how much each charity receives.
Answers
Answer:
Step-by-step explanation:
The total revenue from ticket sales is:
300 x £5 = £1500
The profit is the revenue minus the cost of the prize:
Profit = £1500 - £400 = £1100
Charity A receives 55% of the profit:
55% of £1100 = £605
Charity B receives 45% of the profit:
45% of £1100 = £495
Therefore, Charity A receives £605 and Charity B receives £495.
find the length of a round to the nearest tenth
C=120 degrees b=5 c=11
Answers
Answer: a=7.6
Step-by-step explanation:
solve for angle C:
[tex]\frac{sinc}{5} =\frac{sin120}{11}[/tex]
[tex]11sinc=5sin120[/tex]
[tex]C=23.2[/tex]
solve for A:
=180-(120+23.2)
=36.8
solve for a:
Using the law of sines
[tex]\frac{sin120}{11} =\frac{sin36.8}{a}[/tex]
[tex]asin120=11sin36.8[/tex]
[tex]a=7.6[/tex]
what is the probability of obtaining at least one tail when a coin is flipped six times? (enter the probability as a fraction.)
Answers
a newsletter publisher believes that under 69% 69 % of their readers own a rolls royce. is there sufficient evidence at the 0.10 0.10 level to substantiate the publisher's claim? state the null and alternative hypotheses for the above scenario.
Answers
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. Null Hypothesis (H0): p ≤ 0.69; Alternative Hypothesis (H1): p > 0.69
A newsletter publisher believes that under 69% of their readers own a Rolls Royce.
No, there is not sufficient evidence to substantiate the claim at the 0.10 level. In order to substantiate the claim at the 0.10 level, the publisher would need to collect data from their readers and perform a hypothesis test to compare the observed percentage of readers with the claimed percentage.
Null Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is less than or equal to 69%.
Null Hypothesis (H0): p ≤ 0.69
Alternative Hypothesis: The proportion of the newsletter readers that own a Rolls Royce is greater than 69%.
Alternative Hypothesis (H1): p > 0.69
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9. There are 8 black socks, 6 blue socks, and 14 white socks in a drawer. If one sock is randomly chosen from the
drawer, then what is the probability that the sock will not be blue?
Answers
The probability that the socks will not be blue would be =11/14.
How to calculate the probability of socks that are not blue in colour?Probability can be defined as the expression that shows the possibility of the occurrence of an event.
The formula that is used to calculate probability = the chosen events/total number of outcomes.
The total number of black socks = 8
The total number of blue socks = 6
The total number of white socks = 14
The total number of socks (outcomes) = 8+6+14 = 28
The socks that are not blue = 8+14 = 2
Therefore the probability that they socks won't be blue = 22/28 = 11/14.
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The geometric mean between 16 and 20 is
Answers
Answer: 17.888543819998
Step-by-step explanation:
Answer:
17.8885
Step-by-step explanation:
find the geometric mean between 16 and 20, we need to multiply the numbers and take the square root of the result. That is:
Geometric Mean = √(16 × 20)
Geometric Mean = √320
Geometric Mean ≈ 17.8885
Therefore, the geometric mean between 16 and 20 is approximately 17.8885.
The closing stock prices for a particular social media company follows an unknown distribution with a mean of $150 and a standard deviation of $25. An investor is looking to find the likelihood of the closing stock price falling above the average. After randomly selecting n=52 closing stock prices from the social media company, use a calculator to find the probability that the sample mean is between $155 and $160.
Rounded to three decimal places.
Answers
Rounded to three decimal places, the probability that the sample mean is between $155 and $160 is 0.072.
To find the probability that the sample mean is between $155 and $160, we will use the Central Limit Theorem. The Central Limit Theorem states that the distribution of the sample mean (with a large enough sample size) will be approximately normally distributed with the same mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Mean of the sample distribution: μ = $150
Standard deviation of the sample distribution: [tex]σ/√n = $25/√52 ≈ $3.46[/tex]
Now, we'll calculate the z-scores for $155 and $160:
[tex]Z1 = (155 - 150) / 3.46 ≈ 1.445[/tex]
[tex]Z2 = (160 - 150) / 3.46 ≈ 2.890[/tex]
Using a z-table or calculator, we can find the probability for each z-score:
[tex]P(Z1) ≈ 0.9259[/tex]
[tex]P(Z2) ≈ 0.9981[/tex]
Now, we can find the probability between the two z-scores:
[tex]P(1.445 < Z < 2.890) = P(Z2) - P(Z1) = 0.9981 - 0.9259 = 0.0722[/tex]
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state the meaning of the central limit theorem in your own words. how important is it to the development and use of statistical quality control techniques?
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The central limit theorem is a statistical theory that specifies the probability distribution of a sum or average of several random variables whose distribution is not known.
It is an important theorem since it is utilized to help forecast or estimate the behavior of a specific set of data.
This theorem holds that when you take repeated samples of the same size from a population with a finite standard deviation, the means of those samples will be normally distributed, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.
Further more, the theorem indicates that the larger the sample size, the more closely the sample mean distribution will approximate a normal distribution.
This is why it is vital in the development and use of statistical quality control techniques, since they rely on correct assumptions about the population’s normality.
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