a. The probability that a person could give up her cell phone would be 0.69.
b. Probability that a person who could give up her cell phone could also give up television would be 0.45
c. The probability that a person who could not give up her ell phone could give up television would be 0.55.
d. Probability of giving up television is higher for people who could not give up their cell phone than for those who could give up their cell phone.
What is probability?
Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.
a. The probability that a person could give up their cell phone is the sum of the probabilities in the "Could Give Up" column: 0.31 + 0.38 = 0.69.
Therefore, The probability that a person could give up her cell phone would be 0.69.
b. The probability that a person who could give up their cell phone could also give up television is the conditional probability of "Could Give Up Television" given "Could Give Up Cellphone." This is calculated by dividing the joint probability of "Could Give Up Television" and "Could Give Up Cellphone" (0.31) by the probability of "Could Give Up Cellphone" (0.69): 0.31 / 0.69 = 0.4493 or approximately 0.45.
c. The probability that a person who could not give up their cell phone could give up television is the conditional probability of "Could Give Up Television" given "Could Not Give Up Cellphone." This is calculated by dividing the joint probability of "Could Give Up Television" and "Could Not Give Up Cellphone" (0.17) by the probability of "Could Not Give Up Cellphone" (0.31): 0.17 / 0.31 = 0.5484 or approximately 0.55.
d. To compare the probabilities of giving up television for people who could or could not give up their cell phone, we need to calculate the conditional probabilities of "Could Give Up Television" given "Could Give Up Cellphone" and "Could Give Up Television" given "Could Not Give Up Cellphone" respectively.
Probability of giving up television if one could give up a cell phone: 0.31 / 0.69 = 0.4493 or approximately 0.45.
Probability of giving up television if one could not give up a cell phone: 0.17 / 0.31 = 0.5484 or approximately 0.55.
The probability of giving up television is higher for people who could not give up their cell phone than for those who could give up their cell phone.
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The amount of time it takes to finish a race might be a function of which of the following?
A. the entry fee of the race
B. the distance of the race
C. the number of people involved in the race
Answer:
b
Step-by-step explanation:
time debends in how long it going to take the longer the race the longer the time
A bookmark is shaped like a rectangle with a semicircle attached at both ends. The rectangle is 15 cm long and 4 cm wide. The diameter of each semicircle is the width of the rectangle. What is the area of bookmark ? Use 3.14 for pie
The area of the bookmark is 72.56 cm².
What is Area of Rectangle?The area of Rectangle is length times of width.
The width of the rectangle is 4 cm, so the diameter of each semicircle is also 4 cm.
Radius of each semicircle is 2 cm.
The area of the rectangle is length x width
= 15 cm x 4 cm
= 60 cm².
The area of each semicircle is (1/2) x π x radius²
= (1/2) x 3.14 x 2² = 6.28 cm².
The total area of the two semicircles is 2 x 6.28 = 12.56 cm².
The total area is 60 cm² + 12.56 cm² = 72.56 cm²
Therefore, the area of the bookmark is 72.56 cm².
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saif made 60 runs in 5 over and anus made 72 runs in 8 over whose performance was better
Saif's performance was better.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
We will compare the run rates of Saif and Anus.
The run rate is the average number of runs scored per over.
Now,
The run rate of Saif.
= 60 / 5
= 12 runs per over
And,
The run rate of Anus
= 72 / 8
= 9 runs per over
Therefore,
Saif's performance was better.
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Nick can invest $10,000 in either one of two annuities. Annuity A has a 6% annual interest rate and requires a starting principal of $9,000, plus annual $100 deposits for the next 10 years. Annuity B has a 12% annual interest rate and requires a starting principal of $9,000, plus annual $200 deposits for the next 5 years.
What is the difference between the final balances of the two annuities?
Answer:
7.95%
An annuity due is an annuity whose payment is due immediately at the beginning of each period. A common example of an annuity due payment is rent, as landlords often require payment upon the start of a new month as opposed to collecting it after the renter has enjoyed the benefits of the apartment for an entire month.
Answer:
$313.57
Step-by-step explanation:
Compound interests and and compound numbers need:
A base number (starting amount) Multiplier (percentage) And power (time period)This means the original amount is multiplied in the first example by 106%, and the product of that is multiplied by 106%, until its done 10 times for 10 years.
Bank À is best
Run tests can reveal non-random patterns in the time-ordered data. Select 4 patterns that might be seen.
- Points outside limits
- Trend
- Scatter Plot
- Cycles
- Too much dispersion
- Bias
If we run tests that can reveal non random patterns in the time ordered data , then the four patterns that might be seen are : Points outside limits , Trend , Cycles and Bias .
The four patterns that might be seen in run tests which can reveal non-random patterns in time-ordered data are:
(i) Points outside limits: This pattern indicates that the data points fall outside of the control limits and suggests that the process is not in statistical control.
(ii) Trend: This pattern indicates that the data points are moving consistently in a particular direction, either increasing or decreasing over time.
(iii) Cycles: This pattern indicates that the data points are oscillating around a central value over time, with a repeated pattern of highs and lows.
(iv) Bias: This pattern indicates that the data points are consistently above or below the centerline over time, indicating a systematic error or shift in the process.
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Use what you know about zeros of a function and end behavior of a graph to choose the graph that matches the function f(x)=(x-3)(x-1)(x+1).
The graph of the function f(x)=(x-3)(x-1)(x+1) is given by the image presented at the end of the answer.
How to construct the graph of the function?The function for this problem is defined as follows:
f(x)=(x-3)(x-1)(x+1).
The product is written as a product of it's linear factors, hence the x-intercepts are given as follows:
x = 3.x = 1.x = -1.The y-intercept of the function is given as follows:
f(0) = -3(-1)(1) = 3.
The end behavior is given as follows:
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please help
the numbers of hours that you study each day for five days are shown in the table. The mean amount of time that you study each day of the week is 2.5 hours. How many total hours do you study on Friday and Saturday?
The total hours you study on Friday and Saturday is ; 3 hours
It is easy to calculate the Mean of a data table and we do this by Adding up all the numbers, then divide by how many numbers there are.
From the table, we are given number of hours spent for 5 days as;
Sunday = 0.75 hours
Monday = 1.5 hours
Tuesday = 0 hours
Wednesday = 2.5 hours
Thursday = 1 hour
Thus, if average for the week of 7 days is 1.25 and total for Friday and Saturday is x, then we have;
(0.75 + 1.5 + 0 + 2.5 + 1 + x)/7 = 1.25
x + 5.75 = 8.75
x = 8.75 - 5.75
x = 3 hours
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Sketch line where slope should intercept.
The graph of the linear equation is on the image at the end.
How to sketch the linear equation?Here we have the following linear equation:
y = (7/3)*x + 5
To graph that line we need to find two points on the line, to get them, we need to evaluate the line in two different values of x.
if x = 0
y = (7/3)*0 + 5 = 5
if x = 3
y = (7/3)*3 + 5 = 12
Then we have the points (0, 5) and (3, 12)
Now just graph these points and connect them with a line.
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1.
A worker uses 4 gray tiles for every 5 blue tiles that he uses.
If he uses 60 gray tiles, how many blue tiles does he use?
b. If he uses 540 tiles altogether, how many gray tiles does he use?
Answer:
240
Step-by-step explanation:
60/ 4=15
15×5=75
b) 4+5=9
540/9=60
4×60=240
suppose you throw five dice and all outcomes are equally likely. (a) what is the probability that all dice are the same? (in the game of yahtzee, this is known as a yahtzee.) 1/6^5
The probability of getting the same outcome on all five dice is (1/6) x (1/6) x (1/6) x (1/6) x (1/6) = 1/6^5, or approximately 0.00077.
The probability that every one of the five dice show a similar result is equivalent to the probability of obtain a particular result on one pass on, increased by the probability of come by similar result on every one of the leftover four dice.
The probability of obtain a particular result on one pass on is 1/6, since there are six potential results (1, 2, 3, 4, 5, or 6) and they are similarly probable.
In this manner, the probability of obtain similar result on each of the five dice is (1/6) x (1/6) x (1/6) x (1/6) x (1/6) = 1/6^5, or roughly 0.00077.
This is the probability of moving a Yahtzee in a solitary throw of five dice, it are similarly prone to expect all results.
The probability of moving a Yahtzee, which is the point at which each of the 5 dice show a similar number, is determined by duplicating the probability of come by a particular result on one bite the dust (1/6) without help from anyone else multiple times. This gives a probability of 1 in 6^5, or roughly 0.00077.
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If a trend line has equation y = 0.0001x + 12, what could you say about the data?
The statement about the data the points appear to be on a straight line
How to determine the statement about the dataFrom the question, we have the following parameters that can be used in our computation:
Equation of a trend line: y = 0.0001x + 12
The above equation is a linear equation
This implies that the data points represented by the equation would appear to be on a straight line
Note that: The points may or may not be on a perfect straight line depending on the correlation value
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Suppose you are given a rectangular prism with dimensions a, b, and c. Which of the following corresponds to the quantity 2a 2c? A. the rate of change of the volume with respect to a B. the rate of change of the volume with respect to b C. the rate of change of the surface area with respect to a D. the rate of change of the surface area with respect to b E. the rate of change of the surface area with respect to c
The quantity 2a 2c corresponds to the rate of change of the surface area with respect to a. So, Correct option is C.
When considering a rectangular prism with dimensions a, b, and c, there are three different measures that we can associate with the dimensions: the length, width, and height. These measures are important in determining both the volume and the surface area of the prism.
In this problem, we are given a quantity 2a 2c and asked to determine which measure of the rectangular prism it corresponds to. We can do this by considering the formulas for the volume and surface area of the prism, and taking the partial derivatives with respect to each of the three dimensions.
The volume of a rectangular prism is given by:
V = abc
Taking the partial derivative of this expression with respect to a, we get:
[tex]\frac {\partial v} {\partial a}[/tex] = bc
This is not equal to 2a 2c, so we can eliminate the possibility of the quantity corresponding to the rate of change of the volume with respect to a.
Taking the partial derivative of the volume with respect to b and c gives:
[tex]\frac {\partial v} {\partial b}[/tex] = ac
[tex]\frac {\partial v} {\partial c}[/tex] = ab
Again, neither of these expressions is equal to 2a 2c, so we can eliminate the possibilities of the quantity corresponding to the rate of change of the volume with respect to b or c.
Next, we can consider the surface area of the prism, which is given by:
A = 2ab + 2ac + 2bc
Taking the partial derivative of this expression with respect to a, we get:
[tex]\frac {\partial v} {\partial a}[/tex] = 2b + 2c
Substituting 2a 2c for 2b + 2c, we get:
[tex]\frac {\partial A} {\partial a}[/tex] = 2a 2c
This is the same expression as the given quantity, so we can conclude that the quantity 2a 2c corresponds to the rate of change of the surface area with respect to a.
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A Gallup poll report revealed that 72% of teens said they seldom or never argue with their friends. Yvonne wonders if this result holds true in her large high school. So she surveys a random sample of 150 students at her school and finds that 96 of them say they rarely or never argue with friends. She uses the data to perform a test of 0:=0.72H0:p=0.72 versus ≠0.72,Ha:p=0.72, where p is the true proportion of teens in Yvonne's school who rarely or never argue with their friends. The test yields a P-value of 0.0291. What conclusion would you make for each of the following significance levels? =0.01α=0.01
We reject the null hypothesis at a significance level of =0.01.
At a significance level of α=0.01, we reject the null hypothesis if the p-value is less than 0.01. In this case, the p-value of 0.0291 is greater than 0.01, so we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the proportion of students in Yvonne's school who rarely or never argue with their friends is significantly different from the national average of 0.72 at a significance level of α=0.01.
In other words, we do not have enough evidence to say that Yvonne's school is significantly different from the national trend of 72% of teens who say they seldom or never argue with their friends.
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PQ = 7x + 13, QR = 10x-2, PR = x + 27 what is the range of x-values
The range of x-values is 1 < x < 21.
What is triangle Inequality?According to triangle inequality theorem, for any given triangle, the sum of two sides of a triangle is always greater than the third side.
Given:
We have three sides of Triangle as
PQ = 7x + 13, QR = 10x-2, PR = x + 27.
So, PQ + QR > PR
(7x + 13) + (10x - 2) > x + 27, which simplifies to x > 1
and, PQ + PR > QR
(7x + 13) + (x + 27) > 10x - 2, which simplifies to x < 21
and, QR + PR > PQ
(10x - 2) + (x + 27) > 7x + 13, which simplifies to x > -3
So, the Range of sides is 1 < x < 21.
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cans collected each day was
1. The eighth grade class at Robison Middle School is holding a canned food drive. The number of
45, 21, 3, 15, 32, 97, 68, 27, 29, and 52. Explain how to find the interquartile range of cans
collected each day.
The interquartile range, IQR=31.
What is interquartile range?
Interquartile range is a measure of statistical dispersion, which is the spread of the data. The interquartile range is calculated by the difference between the upper and lower quartile. The formula for the interquartile range is given below
[tex]IQR=Q_3-Q_1[/tex]
The given data : 45, 21, 3, 15, 32, 97, 68, 27, 29, 52.
Arrange in ascending order,
3, 15, 21, 27 , 29 ,32 , 45 , 52 , 68 , 97
By dividing in to 2 partition as lower half and upper half from let to right.
Lower half = 3, 15, 21, 27 , 29
Upper half = 32 , 45 , 52 , 68 , 97
Lower Quartile[tex]Q_{1}[/tex] = Median of Lower half of data
⇒[tex]Q_{1}[/tex]= 21 (Median is the middle most term)
Upper Quartile[tex]Q_{3}[/tex] = Median of Lower half of data.
⇒[tex]Q_{3}[/tex]=52 (Median is the middle most term)
Interquartile range = [tex]IQR=Q_3-Q_1[/tex]
= 52-21
= 31
Hence, the interquartile range IQ=31.
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The heights of the 228 men who filled out Survey 1 last semester follow the normal curve fairly closely with an average of about 70.5" and a SD of about 2.5 ".
What percent of the students are over 71.5 "?
Do the problem in steps
First convert 71.5 " to a z score.0.40 tries 0/5In the problem above you were given the height and asked to find the percentile. Now, you'll be going in the opposite direction-- you'll be given the percentile (placement on the normal curve) and asked to find the height. In both cases the first step is to find the z-score.
If someone is in the 92 th percentile in height (i.e., is taller than 92 % of the other males in the class), let's work on finding his height. First we'll find the z score.
(Do NOT look up the z score for Area= 92 % on the table b/c the Areas given on the table are MIDDLE areas. 92 th percentile means 92 % to the LEFT, and 8 % in the right tail.)
What is the Z-score corresponding to the middle area?(If the middle area falls between two lines on the table, you may use the closest one. Put Z-score in blank below.)
Now change the z score to a height. (Remember the z score tells how many SD's the value is from the average. So a z score of 2 means the person is 2 SDs above average which would be 2*(2.5") + 70.5".)
What is his height?
The male in the 92nd percentile in height would be 73.75 inches tall.
To find the z-score corresponding to the 92nd percentile, we need to find the value on the standard normal curve such that 92% of the area is to the left of that value.
Using the standard normal table, we can find the z-score closest to 0.92 which is 1.75.
Now that we have the z-score, we can use the following formula to find the height:
height = z-score * standard deviation + average height
So, using the given values of average height (70.5") and standard deviation (2.5"):
height = 1.75 * 2.5 + 70.5
height = 73.75"
Therefore, a male in the 92nd percentile in height would be 73.75 inches tall.
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Two buckets, each with a different volume of water, start leaking water at the same time, but at different rates. Assume the volumes are changing linearly.
The difference between the starting volumes is 200 milliliters, the first bucket has the larger volume.
What is the difference between the starting volumes?We know that the volumes can be modeled by linear equations, and remember that a general linear equation is:
y = a*x + b
Where a is the slope and b is the initial value.
If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
For the first bucket we have the points (1, 2900), (10, 2000), then the slope is:
a = (2000 - 2900)/(10 - 1) = -900/9 = -100
So we can write:
y = -100*x + b
To find the value of b, we can replace the value of one of the points in the equation. I will use the first point (1, 2900)
2900 = -100*1 + b
2900 + 100 = b
3000 = b
Now for the other bucket, we have the points (1, 2725) and (10, 2050), so the slope is:
a = (2725 - 2050)/(10 - 1) = -75
So this line is:
y = -75*x + b
Again, replacing the values of one of the points we will get:
2725 = -75*1 + b
2725 + 75 = b
2800 = b
Then the difference in the starting volumes is:
3000 - 2800 = 200
The first bucket has 200 milliliters more.
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Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a deviation of 15.
The shaded area is 0.2525
The IQ score of the adult is 110.05.
What is Normal Distribution?A normal distribution in statistics is defined as the type of continuous probability distribution where the data are arranged in a symmetrical bell shaped graph.
Given that,
Area to the right of a normally distributed graph is 0.2525.
From the standard table, z score for the area given is 0.67.
z = 0.67
We have the formula,
z = (x - μ) / σ
Given Mean, μ = 100 and standard deviation, σ = 15
0.67 = (x - 100) / 15
x - 100 = 10.05
x = 110.05
Hence the indicated IQ score is 110.05.
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The ratio of Green Apple shampoo is 1 fl oz shampoo to 18 fl oz water. How much shampoo is needed to fill a one-gallon container?
Approximately 7.11 fluid ounces of shampoo to fill a one-gallon container.
How to find out how much shampoo is needed to fill a one-gallon container?One gallon is equal to 128 fluid ounces.
The ratio of shampoo to water is 1:18. This means for every 1 fl oz of shampoo, we need 18 fl oz of water.
To find out how much shampoo is needed to fill a one-gallon container, we need to set up a proportion:
1 fl oz shampoo / 18 fl oz water = X fl oz shampoo / 128 fl oz water
To solve for X, we can cross-multiply:
18 fl oz water * X fl oz shampoo = 1 fl oz shampoo * 128 fl oz water
18X = 128
X = 7.11 fl oz shampoo
So, we need approximately 7.11 fluid ounces of shampoo to fill a one-gallon container.
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given the following list of prices (in thousands of dollars) of randomly selected trucks at a car dealership, find the median. 20,46,19,14,42,26,33 provide your answer below: $$median
The median of the randomly selected list of prices of trucks will be 26 thousands dollars.
To find the median , first we need to arrange the list in either ascending form or descending form. Let us arrange the list in ascending form :
List before sorting : 20,46,19,14,42,26,33
List after sorting it in ascending form : 14,19,20,26,33,42,46
Here, the number of observations is 7 which is odd. So, The formula to find the median term from a given number of "Odd" observations in a set is :
⇒ {(n+1) / 2}th term (where n is the number of observations in a set)
⇒({7+1}/2)
⇒8/2
⇒4th term
Therefore, the 4th term in our list of prices of trucks is the median which is 26 thousand dollars
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- A local college will construct a 2-floor building next
year. Each of the 5 classrooms on the 1st floor will
have 20 seats, and each of the 8 classrooms on the
2nd floor will have 35 seats. To comply with the 2010
ADA standard, what is the fewest total number of
wheelchair spaces needed in the 13 classrooms?
F. 4
G. 6
H. 11
J. 13
K. 21
Answer:
According to the 2010 ADA standard, the number of wheelchair spaces required in a classroom depends on the total number of seats in the classroom. Specifically, 1 wheelchair space is required for the first 25 seats, and an additional wheelchair space is required for each 25 seats thereafter.
For the 5 classrooms on the 1st floor, there are a total of 5 x 20 = 100 seats. Therefore, we need 1 wheelchair space for the first 25 seats, and 1 additional wheelchair space for the next 25 seats. So in total, we need 2 wheelchair spaces for the 1st floor classrooms.
For the 8 classrooms on the 2nd floor, there are a total of 8 x 35 = 280 seats. Therefore, we need 1 wheelchair space for the first 25 seats in each classroom, and an additional wheelchair space for the next 25 seats. This means that each classroom needs 2 wheelchair spaces. So in total, we need 8 x 2 = 16 wheelchair spaces for the 2nd floor classrooms.
Therefore, the total number of wheelchair spaces needed in all 13 classrooms is 2 + 16 = 18.
However, it's important to note that the question asks for the "fewest total number" of wheelchair spaces needed. Since we can't have a fraction of a wheelchair space, we need to round up to the nearest whole number. Therefore, the answer is 18 rounded up to the nearest whole number, which is 19.
So the correct answer is not one of the options given. The closest option is K. 21, but that is too high.
A potato head comes with 12 noses, 20 sets of eyes, 5 lips, and 30 accessories. How many arrangements can be made with 1 of each piece?
The number of different arrangements is 36,000
How many arrangements can be made with 1 of each piece?This is equivalent to the total number of combinations, it is given by the product between the numbers of options.
The numbers of options are:
12 for the noses
20 for the eyes
5 for the lips
30 accessories.
Then the number of different arrangements is:
N = 12*20*5*30 = 36,000
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Let me knowwww aspapppppp!!!!
The inequality 2x - 3y < 7 represents the given graph, which is the correct option (B).
What is inequality?Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.
As per option (B), we have
2x - 3y < 7
Subtract 2x from both sides of the inequality:
-3y < 7 - 2x
Divide both sides of the inequality by -3.
y > (7 - 2x) / (-3)
y > (2/3)x - (7/3)
This represents a region in the coordinate plane that is above the line y = (2/3)x - (7/3).
Thus, the inequality 2x - 3y < 7 illustrates the given graph as shown.
Therefore, the correct answer is an option (B) 2x - 3y < 7.
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wich valule of X makes the equation 3x+5=4x+3 true.
Answer:
x=2
Step-by-step explanation:
We will begin by subtracting both sides by 3
3x+2=4x
We will then subtract both sides by 3x since 3x and 4x are like terms
2=x OR x=2
Hope this helps!
Find the following probabilities based on a standard normal variable Z. Use Table 1. (Round your answers to 4 decimal places.)
a. P(Z > 0.74) b. P(Z ≤ −1.92) c. P(0 ≤ Z ≤ 1.62) d. P(−0.90 ≤ Z ≤ 2.94)
a. 0.7787; b. 0.0228; c. 0.7453; d. 0.9793. The probabilities are found by looking up the Z-value in Table 1 and finding the corresponding probability.
a. To find the probability that Z is greater than 0.74, we look up 0.74 in Table 1 and find the corresponding probability. The probability that Z is greater than 0.74 is 0.7787, which is the area to the right of the Z-value in the table.
b. To find the probability that Z is less than or equal to −1.92, we look up −1.92 in Table 1 and find the corresponding probability. The probability that Z is less than or equal to −1.92 is 0.0228, which is the area to the left of the Z-value in the table.
c. To find the probability that Z is between 0 and 1.62, we look up 0 and 1.62 in Table 1 and find the corresponding probabilities. The probability that Z is between 0 and 1.62 is 0.7453, which is the area between the two Z-values in the table.
d. To find the probability that Z is between −0.90 and 2.94, we look up −0.90 and 2.94 in Table 1 and find the corresponding probabilities. The probability that Z is between −0.90 and 2.
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Answer this one question
Answer:
3(m-7)
Step-by-step explanation:
because 3 times the quantity: m-7
Answer:
6. 3 times the quantity m minus 7
O 3(m – 7)Step-by-step explanation:
You're welcome.
he probability distribution of x, the number of defective tires on a randomly selected automobile checked at a certain inspection station, is given in the following table.
x 0 1 2 3 4
p(x) .55 .16 .07 .06 .16
(a) Calculate the mean value of x.
?x =
(b) What is the probability that x exceeds its mean value?
P (x > ?x) =
(A) The mean value of x is 1.12.
(B) The probability that x exceeds its mean value is 0.22.
The first answer is:
(a) To calculate the mean value of x, we multiply each possible value of x by its corresponding probability and add up the products. Mathematically, we can write:
x = (0 * 0.55) + (1 * 0.16) + (2 * 0.07) + (3 * 0.06) + (4 * 0.16)
x = 0 + 0.16 + 0.14 + 0.18 + 0.64
x = 1.12
Therefore, the mean value of x is 1.12.
(b). P (x >? x) = P (x > 1.12)
To find this probability, we need to add up the probabilities of all values of x that are greater than 1.12. From the table, we can see that the probabilities for x = 3 and x = 4 are both greater than 1.12. Therefore, we can write:
P (x > 1.12) = P (x = 3) + P (x = 4)
P (x > 1.12) = 0.06 + 0.16
P (x > 1.12) = 0.22
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Indentify any vertical asymptotes and holes of f(x)= x^2+6x+9/x^2-9
The vertical asymptote of the function [tex]f(x) = \frac{x^2 + 6x + 9}{x^2 - 9}[/tex] is at x = 3.
What is an asymptote?Asymptote is a line or curve that serves as the boundary of another line or curve in mathematics.
Given, A function [tex]f(x) = \frac{x^2 + 6x + 9}{x^2 - 9}[/tex].
Factoring the numerator and the denominator we have,
[tex]f(x) = \frac{(x+3)(x+3)}{(x+3)(x-3)}[/tex]
Now, The holes of the function are at [tex]f(x) = \frac{(x+3)}{(x-3)}[/tex], x + 3 = 0, x = - 3.
And the asymptote of the function is at x - 3 = 0, x = 3.
Therefore, The asymptote will be a dotted vertical line at x = 3.
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Find the negation for the following formula: Vx €Z[p(x) ^ q(x)] O Jxez[ p(x) v q(x)] O Jxez[~ p(x) ^ q(x)] O Vxez[ p(x) v q(x)] O for allxelement of straight integer numbers open square brackets tilde p left parenthesis x right parenthesis logical or tilde q left parenthesis X right parenthesis close square brackets
The negation for the formula is Jxez[~p(x) v ~q(x)] ^ Vxez[~p(x) ^ ~q(x)] ^ Vxez[p(x) v ~q(x)]
Negation is a concept used in mathematics to express the opposite or contradictory statement of a given formula.
To find the negation of this formula, we need to apply De Morgan's laws, which state that the negation of a logical conjunction (and) is a logical disjunction (or) with the negation of each of the operands, and vice versa.
First, let's apply De Morgan's laws to the first expression in the formula:
~[Vx €Z[p(x) ^ q(x)]]
The negation of "for all x in Z, p(x) and q(x)" is "there exists x in Z such that ~(p(x) and q(x))," which can be expressed as:
Jxez[~p(x) v ~q(x)]
Now, let's apply De Morgan's laws to the second expression in the formula:
=> ~[Jx €Z[p(x) v q(x)]]
The negation of "there exists x in Z such that p(x) or q(x)" is "for all x in Z, ~(p(x) or q(x))," which can be expressed as:
=> Vxez[~p(x) ^ ~q(x)]
Finally, let's apply De Morgan's laws to the third expression in the formula:
~[Jx €Z[~p(x) ^ q(x)]]
The negation of "there exists x in Z such that not p(x) and q(x)" is "for all x in Z, ~(not p(x) and q(x))," which can be expressed as:
Vxez[p(x) v ~q(x)]
Putting these three expressions together, we get the negation of the original formula as:
=> Jxez[~p(x) v ~q(x)] ^ Vxez[~p(x) ^ ~q(x)] ^ Vxez[p(x) v ~q(x)]
In this case, the original formula involved three functions (p(x), q(x), and logical operators) that were negated using De Morgan's laws to obtain the final expression.
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Find the distance between A and B
Answer:
[tex]C. \ \sqrt{58}.[/tex]
Step-by-step explanation:
1) coordinates of the given points are: A[-3;2] and B[4;-1];
2) the required distance can be calculated using the next formula:
[tex]d=\sqrt{(X_A-X_B)^2+(Y_A-Y_B)^2} ;[/tex]
3) according to the folmula above the required distance is:
[tex]d=\sqrt{(-3-4)^2+(2--1)^2} =\sqrt{49+9} =\sqrt{58} .[/tex]