The P-value for the test is 1.804 and the 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers is [-0.00147, 0.00347].
a) To determine if there is a significant difference between the means of the population of measurements from which the two samples were selected, we can use a two-tailed t-test. We can calculate the t-statistic as follows:
t = (x1 - x2) / sqrt[((s1^2)/n1) + ((s2^2)/n2)]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, and n1 and n2 are the sample sizes.
For this example, the sample means are x1 = 0.266 and x2 = 0.267. The sample standard deviations are s1 = 0.0017 and s2 = 0.0015. The sample sizes are n1 = 12 and n2 = 12.
Plugging these values into the formula, we get:
t = (0.266 - 0.267) / sqrt[((0.0017^2)/12) + ((0.0015^2)/12)] = -0.145
The critical t-value for a two-tailed test at a significance level of 0.05 with 11 degrees of freedom is 2.201. Since our calculated t-value of -0.145 is not greater than the critical t-value, we can conclude that there is not a significant difference between the means of the population of measurements from which the two samples were selected.
b) The P-value for the test in part (a) is the probability of obtaining a test statistic as extreme as the one we calculated (or more extreme) if the null hypothesis is true. We can calculate this probability as follows:
P = 2 * P(t <= -0.145)
where P(t <= -0.145) is the cumulative probability of the t-distribution with 11 degrees of freedom at -0.145.
Using the t-distribution table, the cumulative probability of t at -0.145 is 0.902. Thus, the P-value for the test in part (a) is P = 2 * 0.902 = 1.804.
c) To construct a 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers, we can use the following formula:
CI = [x1 - x2 +/- t(alpha/2, df) * sqrt[((s1^2)/n1) + ((s2^2)/n2)] ]
where x1 and x2 are the sample means, s1 and s2 are the sample standard deviations, n1 and n2 are the sample sizes, and t(alpha/2, df) is the critical t-value for the two-tailed test at a significance level of alpha/2 with df degrees of freedom.
For this example, the sample means are x1 = 0.266 and x2 = 0.267. The sample standard deviations are s1 = 0.0017 and s2 = 0.0015. The sample sizes are n1 = 12 and n2 = 12. The critical t-value for a two-tailed test at a significance level of 0.025 with 11 degrees of freedom is 2.771.
Plugging these values into the formula, we get: CI = [0.266 - 0.267 +/- 2.771 * sqrt[((0.0017^2)/12) + ((0.0015^2)/12)] ] = [-0.00147, 0.00347]
Thus, the 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers is [-0.00147, 0.00347].
The results of the two-tailed t-test show that there is not a significant difference between the means of the population of measurements from which the two samples were selected. The P-value for the test is 1.804 and the 95 percent confidence interval on the difference in mean diameter measurements for the two types of calipers is [-0.00147, 0.00347].
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Deb is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Boston was $225. Now the cost is $300. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?
Answer:
The percent increase for airfares from Hartford to Boston is:
(300 - 225)/225 * 100% = 33.333%
If the airline charges an additional $50 baggage fee with the new ticket price, the percent increase from 300 to 350 is:
(350 - 300)/300 *100% = 16.67%
Z-scores are useful with regard to inferential statistics primarily because they offer a tool by which to determine whether _____. a. a sample is noticeably different from a population. b. a distribution of scores is standardized. c. a distribution of scores is symmetrically shaped. d. an individual is different from a sample.
Z-scores are useful with regard to inferential statistics primarily because they offer a tool by which to determine whether a sample is noticeably different from a population. The answer is A.
Inferential statistics is a branch of statistics that deals with making predictions, generalizations, or inferences about a population based on a sample of data collected from that population.
Z-scores are a measure of the number of standard deviations away from the mean that a particular score lies. By standardizing a distribution of scores, Z-scores allow us to compare scores from different distributions or from different populations. By determining the Z-score of a particular sample, we can determine whether it is noticeably different from a population based on its distance from the population mean.
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Nate sells wooden boxes. He sells 8 small boxes and 3 large boxes. He sells small boxes for $12 each. He sells large boxes for $17 each. What is the most reasonable estimate of the total sale of the wooden boxes?
The most reasonable estimate of the total sale of the wooden boxes would be= $147
How to calculate the total sale of the wooden boxes?The total number of small wooden boxes= 8
The price for the small boxes= $12.
The total price for the small boxes= 12×8 = $96
The total number of larger wooden boxes= 3
The price for the larger boxes= $17
The total price for the larger boxes= 17×3 = $51
The total price for all the boxes = 96+51 =$147
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(20 POINTS) The area of the right triangle shown below is 200 ft^2. The segment XY has a length of 10 ft. Find the length of the hypotenuse. Round to the tenths place if necessary. Show or explain your work. (20 POINTS)
The length of the hypotenuse is given as follows:
41.23 ft.
How to obtain the length of the hypotenuse?The area of a right triangle is given by half the multiplication of the two side lengths of the triangles.
The parameters are given as follows:
Side lengths of 10 and x.Area of 200 ft².Hence the side length x is given as follows:
0.5 x 10x = 200
5x = 200
x = 200/5
x = 40 ft.
Applying the Pythagorean Theorem, the length of the hypotenuse is given as follows:
h² = 10² + 40²
h = sqrt(10² + 40²)
h = 41.23 ft.
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(12.) The population of Michigan is nearly 10,000,000 people as Massachusetts has nearly 6,000,000
people. The number of state representatives is 15 and 10, respectively.
a. Write the equation of the line given the state population and appointed state representatives.
b. What does the slope represent?
c. What does the y-intercept represent?
d. Use your model to predict how many state representatives that the state of New York will be
assigned if they have a population of 19,000,000.
What’s the difference between slope-intercept form and and point slope formula
Point slope form and slope intercept form of a line are y - y₁ = m (x - x₁) and y = mx + c respectively.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.
The point slope form of a line is given by,
y - y₁ = m (x - x₁),
where (x₁, y₁) is a point on the line, m is the slope and (x, y) be any point.
The slope intercept form of a line is given by,
y = mx + c
where m is the slope and c is the y intercept.
y intercept is the point where the line touches the Y axis. x coordinate will be 0 at that point.
The slope intercept form of a line can be found from the point slope by substituting (x₁, y₁) = (0, c)
y - c = m (x - 0)
y - c = mx
y = mx + c
Hence the slope intercept form of a line is y = mx + c and the point slope form is y - y₁ = m (x - x₁).
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If Triangle PQR ~ Triangle VST with a scale factor of 2:5, find the value of x.
The value of x that makes Triangle PQR ~ Triangle VST is 5
How to determine the value of xFrom the question, we have the following parameters that can be used in our computation:
Triangle PQR ~ Triangle VST
Scale = 2 : 5
So, we have the following equivalent ratio
6 : 2x = 15 : 25
So, we have
2x/6 = 25/15
Make x the subject
So, we have the following representation
x = 6 * 25/(15 * 2)
Evaluate the expression
x = 5
Hence, the value is 4
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Complete question
If Triangle PQR ~ Triangle VST with a scale factor of 2:5, find the value of x.
PQ = 6
QR = 2x
VS = 15
ST = 25
Tina is taking her husband and three kids to the movies everyone gets a soda for two hours and $2.50 and a popcorn for $3.50 are two different expressions that will allow Tina to calculate the total cost of the soda and popcorn
Total cost of soda and popcorn for 5 people = $6.00 x 5 = $30.00
How can we prove it ?Yes, two different expressions to calculate the total cost of the soda and popcorn for Tina and her family are:
Expression 1: Total cost of soda = $2.50 x 5 (5 people) = $12.50
Total cost of popcorn = $3.50 x 5 = $17.50
Total cost of soda and popcorn = $12.50 + $17.50 = $30.00
Expression 2: Total cost of soda and popcorn for one person = $2.50 + $3.50 = $6.00
Total cost of soda and popcorn for 5 people = $6.00 x 5 = $30.00
What is ratio ?A ratio is a comparison of two or more values. It is a way of expressing the relationship between two or more quantities in the form of a fraction. The numerator of the fraction represents the first quantity and the denominator represents the second quantity. The ratio can be written in the form of a:b, where a and b are the two quantities being compared.
For example, if you have 4 apples and 2 bananas, the ratio of apples to bananas can be expressed as 4:2 or 2:1. This means that for every 2 bananas, there are 4 apples. Ratios can also be used to compare values of different units, for example, miles to kilometers or pounds to kilograms.
Ratios are widely used in many fields, including finance, cooking, construction, and physics, to compare and express the relationship between different quantities. They provide a simple and intuitive way to compare values and help to make sense of complex data.
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if e and f are mutually exclusive and p(e)>0 and p(f)>0, which one of the following statements is correct?
Neither statement "E and F are always independent" nor "E and F are always dependent" is correct for mutually exclusive events E and F with positive probabilities p(e)>0 and p(f)>0.
Events that are mutually exclusive cannot occur at the same time. For example, if we have two events E and F such that E represents "rolling a 1 on a fair die" and F represents "rolling a 2 on a fair die", These events cannot occur simultaneously since a 1 and a 2 cannot be rolled.
In probability theory, two events E and F are considered independent if the occurrence of one event has no effect on the probability of the other event occurring. For example, if we have two events E and F such that E represents "rolling a 1 on a fair die" and F represents "rolling a 6 on a fair die", these events are independent because the occurrence of one event (rolling a 1) does not affect the probability of the other event (rolling a 6) occurring.
In the case where events E and F are mutually exclusive, their occurrence does affect each other, as the occurrence of one event makes it impossible for the other event to occur. Therefore, the statement "E and F are always independent" is not correct. Similarly, the statement "E and F are always dependent" is also not correct because dependence is a different concept from mutual exclusiveness.
Therefore, "Neither of the above statements is correct" is the appropriate response.
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The complete question is:
Which of the following statements is correct if e and f are mutually exclusive and p(e)>0 and p(f)>0?
a) E and F are always independent
b) E and F are always dependent
c) Neither of the above statement is correct
5. 315+x=285 -86+20=R+20 d) inte zero. By how many degrees did the temperature drop? The temperature in Kiev was 10 °C below zero. Then it dropped to 24 °C beloy Divis 6. A fish was swimming at 52 m below sea level. It then swam down to 120 m below sea level. How many metres downwards did the fish swim? 7. What us the difference between the elevation of the Dead Sea (-420 m) and Lake Assal (-156 m)? What is the sum of the following temeratures? -10°C: 24 °C -12 °C 8 °C -1 °C ers: ultiplying and dividing integers mis section, you will revise multiplication and division of integers. nt down in intervals of 5 to see happens when you multiply Now start with a negative integer and count up in intervals of 5 as you multiply:
5. The temperature dropped by 10 - (-24) = 34 degrees.
6. The fish swam down 120 - 52 = 68 meters.
7. The difference between the elevation of the Dead Sea and Lake Assal is (-420) - (-156) = 264 meters.
8. The sum of the temperatures is -10 + 24 - 12 + 8 - 1 = 9 degrees Celsius
What is a temperature drop?A temperature drop refers to a decrease in the temperature from one point to another, for example, from a higher temperature to a lower temperature.
It could then be concluded that the correct answers are 34 degrees, 68 meters, 264 meters, and 9 degrees Celsius respectively.
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Determine the area of each composite figure. Round to the nearest tenth if necessary.
The solution is, the area of the given figure is 38.6 ft^2.
What is area of trapezoid?The area of a trapezoid is found using the formula, A = ½ (a + b) h,
where 'a' and 'b' are the bases (parallel sides) and 'h' is the height .
here, we have,
from the given figure , we get,
the trapezoid's,
parallel sides are, 9 ft. & 7ft.
height = 3.6 ft.
so, area = ½ (a + b) h,
i.e. A = 28.8 ft^2
Again, area of the triangle is,
area = 1/2 * base * height
= 1/2 * 7* 2.8
= 9.8
total area = 38.6 ft^2
Hence, The solution is, the area of the given figure is 38.6 ft^2.
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Noah manages a buffet at a local restaurant. He charges $10 for the buffet. On average, 16 customers choose the buffet as their meal every hour. After surveying several customers, Noah has determined that for every $1 increase in the cost of the buffet, the average number of customers who select the buffet will decrease by 2 per hour. The restaurant owner wants the buffet to maintain a minimum revenue of $130 per hour.
Noah wants to model this situation with an inequality and use the model to help him make the best pricing decisions.
Write two expressions for this situation, one representing the cost per customer and the other representing the average number of customers. Assume that x represents the number of $1 increases in the cost of the buffet.
Enter the correct answer in the box. Type the cost expression on the first line and the customer expression on the second line.
The two expressions for this situation, with one representing the cost per customer and the other representing the average number of customers are:
Cost: 10 + x
Customer: 16 - 2x
Inequality: 160 - 4x - 2x² ≥ 130.
How to write two expressions that models this situation?Based on the information provided, we can logically deduce that the amount of money being charged by Noah per buffet is equal to $10. Also, the total number of customers that chose buffet every hour is equal to 16 customers.
For an increase in the cost of buffet by $1, the average number of customers who selected the buffet would decrease by 2 per hour and the minimum revenue per hour is $130.
Therefore, an expression that represents the cost per customer is given by;
Cost: 10 + x
Additionally, an expression that represents the average number of customers;
Customer: 16 - 2x
Lastly, an inequality that would help Noah make the best pricing decisions is as follows;
Revenue = Cost × Customers
(10 + x) × (16 - 2x) ≥ 130
160 - 20x + 16·x - 2x² ≥ 130
160 - 4x - 2x² ≥ 130
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Represent the following sentence as an algebraic expression, where "a number" is the letter x. You do not need to simplify.
4 is multiplied by the difference of 5 and a number.
The solution is, the expression is => 4*(5-x)
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
let, the number is x.
now, when,
4 is multiplied by the difference of 5 and a number.
so, we get,
the expression is => 4*(5-x)
Hence, The solution is, the expression is => 4*(5-x)
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Melanie invests a total of $35,500 in two accounts. The first account earned a rate of return of 12%
(after a year). However, the second account suffered a 4% loss in the same time period. At the end
of one year, the total amount of money gained was $1,300.00. How much was invested into each
account?
$15,500 was invested in the first account
$20,000 was invested in the second account.
Solution
Let's call the amount invested in the first account "x". The amount invested in the second account would be $35,500 - x.
At the end of one year, the first account would have x * 1.12 = x + 0.12x = 1.12x dollars.
And the second account would have (35,500 - x) * 0.96 = 34,320 - 0.96x dollars.
The total amount of money gained at the end of one year would be 1.12x + 34,320 - 0.96x = 35,500 + $1,300 = $36,800.
We can set up an equation to solve for x:
1.12x + 34,320 - 0.96x = $36,800
0.16x = $2,480
x = $15,500
So, $15,500 was invested in the first account, and $35,500 - $15,500 = $20,000 was invested in the second account.
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What is the probability of getting 4 kings when 5 cards are drawn from a standard deck of cards?
The probability of drawing four kings from a standard deck of cards in a single draw is 0.000001515, or 0.001515%.
The probability of drawing four kings from a standard deck of cards is extremely unlikely, as there are only four kings in a standard deck. This means that the probability of drawing four kings in a single draw of five cards is expressed mathematically as:
P(4 kings) = (4C4)*(48C1)/(52C5)
In this equation, 4C4 is the number of ways to select four kings from four kings, 48C1 is the number of ways to select one card of any other rank, and 52C5 is the total number of ways to select five cards from the deck.
Plugging in the numbers, we get the following equation:
P(4 kings) = (4!)*(48C1)/(52C5)
= (24)*(48C1)/(2598960)
= 0.000001515
Therefore, the probability of drawing four kings from a standard deck of cards in a single draw is 0.000001515, or 0.001515%.
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Enrique and Taylor are 280 feet apart when they start walking toward one another. Taylor walks twice as fast as Enrique, so whenever Enrique travels & feet, Taylor travels 2x feet. Let a represent the number of feet Enrique has traveled since he started walking toward Taylor.(A) Write an expression in terms of a to represent the total number of feet Enrique and Taylor have walked toward one another.(B) Write an expression in terms of a to represent the distance (in feet) between Enrique and Taylor.(C) Let & represent the distance (in feet) between Enrique and Taylor. Write a formula that expresses d in terms of ..
They begin at a distance of 210 feet, hence the distance between them is equal to 210 - 2sx feet
A) Accordingly, if x equals "the number of feet Alan has gone since he started walking toward Victoria," then A) the combined distance (in feet) covered by the two walkers must be 2x, and B) Alan's distance from Victoria must be 210 - 2x.
B) In other words, if Alan and Victoria are walking at the same speed, let's call that speed s, then the total distance each of them has traveled is equal to sx ft (x = the amount of time since they began walking), which equals 2sx ft.
C) They begin at a distance of 210 feet, hence the distance between them is equal to 210 - 2sx feet.
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Give an example of a function f where 0 is in the domain of f,but limx→0 f (x)is undefined.
An example of a function f where 0 is in the domain of f, but limx→0 f(x) is undefined is the piecewise function:
f(x) = x + 45 if x < 0
f(x) = x + 33 if x ≥ 0.
What function has 0 on its domain, such that the limit there is undefined?Remember how the limit works. It only exist if the approach from left and right give the same value.
Then we can define a piecewise function like:
f(x) = x + 45 if x < 0
f(x) = x + 33 if x ≥ 0.
Clearly, 0 belongs to the domain, and the limits are:
[tex]\lim_{x \to 0_-} f(x) = 45\\\\\lim_{x \to 0_+} f(x) = 33[/tex]
These limits are different, thus the limit when x tends to zero is undefined.
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(co 3) consider the following table: age group frequency 18-29 983 30-39 784 40-49 686 50-59 632 60-69 541 70 and over 527 if you created the probability distribution for these data, what would be the probability of 30-39?
The probability of 18-29 is 0.2213 or 22.13%, the probability of 30-39 is 0.1765 or 17.65%.
The probability of 30-39 can be calculated using the following formula:
P(30-39) = Frequency of 30-39 / Total Frequency
P(30-39) = 784 / 4443
P(30-39) = 0.1765
Therefore, the probability of 30-39 is 0.1765 or 17.65%.
To calculate the probability of any age group, the formula is the same. The probability is determined by dividing the frequency of the age group by the total frequency. To calculate the probability of any age group, you must first calculate the total frequency by adding up the frequencies of all the age groups. Then you can use the formula to calculate the probability of any age group.
For instance, to calculate the probability of 18-29, the formula would be:
P(18-29) = Frequency of 18-29 / Total Frequency
P(18-29) = 983 / 4443
P(18-29) = 0.2213
Therefore, the probability of 18-29 is 0.2213 or 22.13%.
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A crew of painters are hired to paint a house. The cost of the pain is estimated to
be $250 and each of the (p) painters will get paid $15 per hour. If the crew of
painters will work a 7 hour day and the job is estimated to take (d) days.
12.)What is the equation to determine the cost of 1 painter per day
13.) What is the cost in dollars per day for painting if the are 5 painters working.
14.) Which expression will represent the total cost of painting the house for the
5 painters working?
a. C-250pd + 775
b.) C=250 + 525d
c. C=250(7)(15) (5)d
d. C= 7d + 285 +5
15.) What is the total cost of 5 painters working for 4 days?
12. The cost of 1 painter per day is
C = 15 * 7 hours
13. cost in dollars per day for painting if the are 5 painters working is $525
14. The expression will represent the total cost of painting the house for the 5 painters working is C = 250 + 525d
15. the total cost of 5 painters working for 4 days is $2350
How to solve for the cost12. The workers are to work for 7 hours in a day and the pay for each worker at 1 hour is 15 dollars.
The cost of 1 painter per day is
C = 15 * 7 hours
C = $105
13. If 1 person is 105 dollars, then 5 painters would be 105 * 5
= $525
14. The expression that would tell us the total cost of painting the house is cost of paint + cost of 5 painters * number of days
cost of paint = $250
cost of 5 painters = $525
hence
C=250 + 525d
15. The total cost of 5 workers in 4 days is
C=250 + 525 * 4
C = 250 + 2100
C = $2350
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Madison has this equation. Find the y-value when x = -3.
*
[tex]y=0.5x^{2} +4[/tex]
Based on Madison's equation, the y-value is equal to 8.5.
How to find the y-value?In Mathematics, a function is typically used for uniquely mapping an independent value (input variable or domain) to a dependent value (range or output variable).
In order to use the given function to determine the value of y (y-value), we would have to substitute the values of x (x-value or domain) into the function and then evaluate as follows;
y = 0.5x² + 4
y = 0.5(-3)² + 4
y = 0.5(9) + 4
y = 4.5 + 4
y = 8.5.
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Holly bought a magazine subscription for 8 months. She paid $28. Holly wanted to find the price, p, of the subscription each month. She created the model shown to find the price
Therefore , the solution of the given problem of unitary method comes out to be $3.5 is the average price.
What exactly is a unitary method?After calculating the size of a small slice, multiply the quantity by two to complete a task using the unitary technique. Simply expression, the unit variable technique works to separate a coded item from a certain group or collection of groups. For instance, 40 pens would cost Rs. 400 (or 400 pounds, $1.01). It's possible that one country will have total control over the method employed to do this. Almost every living creature has a distinctive quality.
Here,
Given :
subscription for 8 months
She paid $28 and Holly wanted to find the price, p
Price for one month is :
=> 28/8
=> $3.5
Therefore , the solution of the given problem of unitary method comes out to be $3.5 is the average price.
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The complete question is "Holly bought a magazine subscription for a year. She paid $27. Holly wanted to find the price, p, of the subscription each month. She created the model shown to help find this price. 27 р |р |р |р |р |р |р |р | Р | Р |р | p What was the price of the subscription each month? F $39.00 G $2.25 H $324.00 3 $22.50"
Learn before you teach Select an adult at random. Define events A: person
has earned a college degree, and T: person has chosen teaching as his or her
career. Rank the following probabilities from smallest to largest. Explain your
reasoning.
P(A) P(T) P(AT) P(TA)
The order of the probabilities from smallest to largest is P(T) < P(T|A) < P(A) < P(A|T).
A represents the event "Person earned a college degree"
T represents the event "Person's career is teaching"
P(A) represents the probability of event A (Person earned a college degree)
P(T) represents the probability of event T (Person's career is teaching)
P(T|A) represents the conditional probability of event T given event A (Probability of a degree holder being a professional teacher)
P(A|T) represents the conditional probability of event A given event T (Probability of a teaching career being held by a degree holder)
It is a universal fact that all teachers have a college degree, so:
P(A|T) > P(A) as having a college degree is a necessary condition for being a teacher
P(T|A) < P(A) as not all degree holders choose to become teachers
P(T|A) > P(T) as a smaller number of degree holders become teachers compared to the total number of teachers
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there are 22 cherry trees in vince's orchard, and he wants to plant more. it takes him an hour to plant each tree. let h represent the number of hours vince spent planting and c represent the total number of cherry trees he will have. find the value of c when h
When h = 4, Vince will have 26 cherry trees in his orchard.
A linear equation is an algebraic equation with simply a constant and a first-order (linear) component of the form y=mx+b, where m is the slope and b is the y-intercept. The above is sometimes referred to as a "linear equation with two variables," where y and x are the variables.
If it takes Vince an hour to plant each tree, and h represents the number of hours Vince spent planting, then the total number of cherry trees he will have is given by the equation:
c = 22 + h
So when h = 4, the value of c can be found by substituting h = 4 into the equation:
c = 22 + 4 = 26.
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Recall that a bank manager has developed a new system to reduce the time customers spend waiting to be served by tellers during peak business hours. The mean time during peak business hours under the current system is roughly 9 to 10 minutes. The bank manager hopes that the new system will have a mean waiting time that is less than six minutes. The mean of the sample of 100 bank customer waiting times in Table 1.8 is 5.46. If we let u denote the mean of all possible bank customer waiting times using the new system and assume that the standard deviation equals 2.47:
(a) Calculate 95 percent and 99 percent confidence intervals for u.
(b) Using the 95 percent confidence interval, can the bank manager be 95 percent confident that u is less than six minutes? Explain.
(c) Using the 99 percent confidence interval, can the bank manager be 99 percent confident that u is less than six minutes? Explain.
(d) Based on your answers to parts b and c, how convinced are you that the new mean waiting time is less than six minutes?
z is the z-score for the desired confidence level. For 95 percent confidence, z = 1.96 and for 99 percent confidence, z = 2.58.
(a) To calculate the 95 percent and 99 percent confidence intervals for u, we can use the formula:
mean ± z*(standard deviation/sqrt(sample size))
Plugging in the values, we get:
95 percent confidence interval: 5.46 ± 1.96*(2.47/sqrt(100)) = 5.46 ± 0.39
99 percent confidence interval: 5.46 ± 2.58*(2.47/sqrt(100)) = 5.46 ± 0.52
(b) For the 95 percent confidence interval, the interval is 5.46 ± 0.39, which means that we can be 95 percent confident that the true mean waiting time u is between 5.07 and 5.85 minutes. Since 6 minutes falls outside this interval, we cannot be 95 percent confident that u is less than 6 minutes.
(c) For the 99 percent confidence interval, the interval is 5.46 ± 0.52, which means that we can be 99 percent confident that the true mean waiting time u is between 4.94 and 5.98 minutes. Since 6 minutes falls outside this interval, we cannot be 99 percent confident that u is less than 6 minutes.
(d) Based on the results of the 95 percent and 99 percent confidence intervals, we can conclude that there is not enough evidence to be confident that the new mean waiting time is less than six minutes.
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Determine whether the data set is a population or a sample. Explain your reasoning The grades of 5 students in a classroom of 30 Choose the correct answer below. O A. Population, because it is a subset of all students in the class O B. Sample, because it is a collection of grades for all students in the classroom, but there are other classrooms ° O C. Sample, because the collection of 5 students' grades is a subset of all students in the class. O D. Population, because it is a collection of grades for all students in the classroom
The data set is a sample, because the collection of 5 students' grades is a subset of all students in the class. This is indicated by choice "C."
The grades of 5 students in a class of 30 represent only a portion of the total data and do not include all of the grades in the class. Thus, it is a sample and not a population. A sample is a part of the population that is selected for analysis. In this case, the grades of 5 students are a subset of the grades of all students in the classroom, which is the population. A sample is used to make inferences about the population, and the results from the sample are used to estimate the characteristics of the population. However, the sample is not representative of the entire population, so the results from the sample may not reflect the true characteristics of the population. This is why it is important to use a random sample that is representative of the population to ensure accurate results.
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or At the end of the year, cars made in the current year are marked down to make room for next year's models. One particular model has a sale price of $13,065, which is 25% less than it sold for when it was new. What was the original price of the vehicle?
The original price of the car is $17420
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100.
Given that, a sale price of $13,065, which is 25% less than it sold for when it was new,
We need to find the original price of the vehicle,
Let the original price be x,
x - 25% of x = 13065
x(1-25%) = 13065
x(75/100) = 13065
x = 13065 × 100 / 75
x = 100 × 174.2
x = 17420
Hence, the original price of the car is $17420
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help please
answer 13 only
The required expected value of the pointer landing on the blue is 9.4 times.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
here,
From the table,
Frequency of blue color = 14
Total outcome = 75
Probability of landing on blue = P(b) = 14 / 75
Now,
The spinner is spun 50 times,
The expected value of the color blue is given as,
E(b) = n × P(b)
E(b) = 50 × 14/75
E(b) = 9.4 times
Thus, the required expected value of the pointer landing on the blue is 9.4 times.
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Identify each of the following as examples of (1) attribute (qualitative) or (2) numerical (quantitative) variables: a. The breaking strength of a given type of string. b. The hair color of children auditioning for the musical Annie. c. The number of stop signs in towns of fewer than 500 people. d. Whether or not a faucet is defective. e. The number of questions answered correctly on a standardized test. f. The length of time required to answer a telephone call at a certain real estate office
The number of questions answered correctly on a standardized test and the length of time required to answer a telephone call at a certain real estate office are all numerical (quantitative) variables.
a. The breaking strength of a given type of string. Numerical (quantitative)
b. The hair color of children auditioning for the musical Annie. Attribute (qualitative)
c. The number of stop signs in towns of fewer than 500 people. Numerical (quantitative)
d. Whether or not a faucet is defective. Attribute (qualitative)
e. The number of questions answered correctly on a standardized test. Numerical (quantitative)
f. The length of time required to answer a telephone call at a certain real estate office. Numerical (quantitative)
For example, if a standardized test had 10 questions, and a student answered 7 correctly, the numerical (quantitative) variable for the number of questions answered correctly would be calculated with the formula: 7/10 = 0.7 or 70%. The length of time required to answer a telephone call at a certain real estate office can also be calculated numerically (quantitatively) by taking the total time of the call and dividing it by the number of calls. For instance, if the total time of 10 telephone calls was 80 minutes, the numerical (quantitative) variable for the length of time required to answer a telephone call would be calculated with the formula: 80/10 = 8 minutes.
Based on the examples given, the breaking strength of a given type of string, the number of stop signs in towns of fewer than 500 people, the number of questions answered correctly on a standardized test and the length of time required to answer a telephone call at a certain real estate office are all numerical (quantitative) variables, while the hair color of children auditioning for the musical Annie and whether or not a faucet is defective are attribute (qualitative) variables.
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Compare using<>=
1/3×5/7 ⭕️ 2/5+4/4
The comparison is
1/3×5/7 < 2/5+4/4
What is Inequality?Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.
Given:
1/3×5/7 ⭕️ 2/5+4/4
we solve the quantities one by one
1/3×5/7
= 5/ 21
and, 2/5+4/4
= 28/20
= 7/5
So, 1/3×5/7 ⭕️ 2/5+4/4
5/21 ⭕️ 7/5
25/105 < 174/105.
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Can someone help me please I don’t get this
[tex]\begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ \stackrel{\textit{we'll be using this one}}{log_a a^x = x}\qquad \qquad a^{log_a x}=x \end{array} \\\\[-0.35em] ~\dotfill\\\\ ~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 140\\ P=\textit{original amount deposited}\dotfill & \$70\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &5 \end{cases}[/tex]
[tex]140 = 70e^{\frac{r}{100}\cdot 5} \implies \cfrac{140}{70}=e^{\frac{r}{20}}\implies 2=e^{\frac{r}{20}}\implies \log_e(2)=\log_e\left( e^{\frac{r}{20}} \right) \\\\\\ \log_e(2)=\cfrac{r}{20}\implies \ln(2)=\cfrac{r}{20}\implies 20\ln(2)=r\implies \boxed{13.86\approx r}[/tex]