Answer:
y = 1/3x - 5
Step-by-step explanation:
The equation is y = mx + b
m = the slope
b = y-intercept
m = 1/3
Y-intercept is located at (0, -5)
So, the equation of the line is y = 1/3x - 5
does the scatterplot support the newspaper report about number of semesters and starting salary? justify your answer
A scatterplot can help us visualize the relationship between two variables and determine if there is a correlation between them. If the scatterplot shows a clear pattern or trend, conclude that there is a relationship between the two variables.
Without access to the scatterplot or the newspaper report, it is difficult for me to provide a definitive answer. However, in general, to determine if the scatterplot supports the newspaper report about the number of semesters and starting salary, we need to examine the pattern in the scatterplot.
Suppose we see a clear trend or pattern, such as a linear relationship where an increasing number of semesters is associated with an increased starting salary or a non-linear relationship. In that case, we can say that the scatterplot supports the newspaper report.
However, if we see no discernible pattern or trend or significant variability in the data points makes it is difficult to draw any meaningful conclusions, then we cannot say that the scatterplot supports the newspaper report.
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Blair's new computer cost $5 less than twice the cost of her old
computer. Her new computer cost $709. How much did Blair's old
computer cost?l
Therefore , the solution of the given problem of expressions comes out to be cost $357.
What does an expression mean?It is preferable to use moving integer variables, which can be rising, decreasing, or blocking, rather than estimates that are generated at random. They could only assist one another by exchanging resources, knowledge, or answers to problems. A declaration of truth equation may include the justifications, components, and mathematical comments for strategies like extra disapproval, production, and mixture.
Here,
Let's say Blair's previous PC cost "x" dollars.
Her new computer cost $5 less than twice as much as her previous one, according to the information provided, which can be written as:
=> Cost of Blair's new computer = 2x - 5
She also purchased a new PC, which cost her $709. In light of these two bits of knowledge, we can construct the following equation:
=> 2x - 5 = 709
In order to find "x," add 5 to both parts, divide by 2, and we get:
=> 2x = 714
=> x = 357
Blair's previous PC therefore cost $357.
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‼️WILL MARK BRAINLIEST‼️
The appropriate measure of center are median in Y and mean in Z and the garden most likely to find 12 daises with the same height is garden Y
How to determine the appropriate measure of centerGiven that we have
Dot plots and Box plots
Where we have
Dot plots = Outliers
Box plots = No outliers
As a general rule:
Outlier = Median as the measure of center
No outlier = Mean as the measure of center
This means that the measures are
Dot plots = Median
Box plots = Mean
The garden that is most likely to find 12 daises with the same height is the garden with outliers i.e. garden Y
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what is the probability that john is a carrier? probability: 66.7 % what is the probability that both john and sue are carriers?
Attached is the pedigree. I found this exercise on the Internet.
The probability that both john and sue are carriers is:
The missing characters are: II-5, II-6, II-8, III-10, III-11, III-12, III-13.
Individual II-5 will have half black/half white squares. It's a square because it shows in the book that John's grandmother (I-2) fell ill.
Half black/half white transmits an allele that requires the disease allele because his mother has the disease, and his father does not carry or show the disease, so from him, John's father (II-5) only got one. normal allele.
The person will ask II-6 questions in a circle. A circle because John's mother once father is Example II-5. Since she has a daughter (John's Sister) with the disease, it means that John's sister inherited both alleles for the disease.
The Personal II-8 will have a half-black/half-white circle.
Circle because Sue's mother and father Probability Example II-7 (square). Half black/half white transmits an allele that requires the disease allele because her father has the disease, and her mother does not carry or show the disease, meaning she is from her, Sue's mother (II-8). take an old allele.
The person will ask the III-10 questions in a circle. The circle is because she is John's sister mentioned in the text. The question mark is that we can't be sure if this is an allele.
We know from the records that he has no symptoms of the disease, but if his mother is infected with only one allele, he may have inherited an allele from his father or mother, or he will inherit the disease allele. The disease allele comes from the mother, not from the father if the mother has the disease.
John, There will be questions in the People III-11 box. Square because John is a man. The question mark is that we can't be sure if this is an allele. We know from the literature that he has no symptoms of the disease, but if his mother is a carrier of only one of the disease alleles, he may have inherited the disease allele from his father. disease allele. If her mother has a disease, it is not from her father, but from her mother.
SU will have questions in the Humans III-12 circle. Circle it because she's Sue, the woman. The question mark is that we can't be sure if this is an allele. From the instructions, we learn that he has no symptoms of the disease, but that he may have inherited the disease allele from his mother, and that after his mother has the disease allele, he too can be a carrier or transmit the disease to others. The disease allele has inherited the normal allele from its mother. He inherited only one normal allele from his father.
III-13 individuals will have questions in the square. A square because according to the guide, he is Su's brother. The question mark is that we can't be sure if this is a disease allele. We know from the records that she did not show any signs of the disease, but she probably inherited the disease allele from her mother, and when her mother has the disease allele, she will also be a carrier or inherited. original allele from its mother. He inherited only one normal allele from his father.
Complete Question:
John and sue are expecting a child, but are concerned about a rare autosomal recessive disease that is present in both of their families. in the pedigree below, john is represented as individual iii-11 and sue is represented as individual iii-12. john\'s sister, iii-10, and sue\'s brother, iii-13, both do not show evidence of the disease, but john\'s paternal grandmother and sue\'s maternal grandfather both had the disease. assign the appropriate symbol to each individual in the pedigree. what is the probability that john is a carrier? probability: 66.7 % what is the probability that both john and sue are carriers?
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the hypotenesuse of the right triagnle is 5y inches long. the legth of the legs are x 8 and x 3 inches. if the perimeter of the triangle is 60 inches and the legth of the hypotenuse minus the leth of the shorter leg is 10 inches, low many inches long is the hypotenuse?
The triangle's hypotenuse, according to the Pythagorean equation, measures 20 inches.
Let's start by using the Pythagorean theorem to relate the hypotenuse and the legs of the right triangle. According to the theorem, we have:
(5y)² = (x+8)² + (x+3)²
25y² = 2x² + 22x + 73
Now, we can use the given information about the perimeter and the difference between the hypotenuse and the shorter leg to set up a system of equations. We know that the perimeter of the triangle is:
P = (x+8) + (x+3) + 5y = 2x + 5y + 11
And we also know that the difference between the hypotenuse and the shorter leg is:
5y - (x+3) = 10
Solving for y in the second equation gives us:
y = (x+13)/5
Substituting this value into the first equation and solving for x gives us:
2x + 25(x+13)/25 = 60
2x + x + 13 = 60
3x = 47
x = 47/3
Substituting this value of x back into the equation for y gives us:
y = (47/3 + 13)/5 = 4
So the hypotenuse of the triangle is:
5y = 20
Therefore, the hypotenuse of the triangle is 20 inches long.
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given tan A = 7/√120 and that angle A is in Quadrant III, find the exact value of cos A in simplest radical form using a rational denominator.
Answer:
Step-by-step explanation:
Step 1: We know that the cosine of an angle in Quadrant III is negative.
Step 2: We convert the given angle A into radians by multiplying it by pi/180.
A = (7/√120) * (π/180) = (7π)/(12√5)
Step 3: We use the cosine formula to find the exact value of cos A.
cos A = cos((7π)/(12√5))
Step 4: We simplify the result using trigonometric identities.
cos A = (-1/3)√5
What is the measure of the hypotenuse?
289
13
169
17
Answer:
Step-by-step explanation:
Using Pythagorean Theorem : A² = B²+C².
→x² = 5²+12² = 25+144 = 169.
→x = √169 = 13.
The Area of a Rectangle is 75. The length is 3 times the
width. Find the Width.
Quiz Score
Joseph's math teacher plots student grades on their weekly quizzes against the
number of hours they say they study on the pair of coordinate axes and then draws
the line of best fit. Based on the line of best fit, what quiz score should someone who
studied 6 hours expect?
85
81
6
B
65
61
57
(057)
O
0
O
O
(2,69)
O
O
O
O
(4.81)
O
esmen wa
0.5
1 1.5 2 2.5 3 35 4
Time Spent on Homework per Week (hours)
Untided document
Leamer Home
Based on the information in the graph, we can establish that a person who studied for six hours could have a grade of 204.
How to find the qualification that a person who studied 6 hours would have?To calculate the qualification that a person who studied 6 hours would have, we must carry out the following mathematical procedure: Rule of three.
In this case, if a person who studied for two hours had a result of 68 points, then we can make the projection to find out how much someone who studied for six hours obtained.
2 hours = 68 points6 hours = ?points6 * 68 / 2 = 204 pointsAccording to the above, this person got 204 points after studying for 6 hours.
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Find the perimeter and area of the regular polygon.
PLS SOMEBODY THIS IS REALLY URGENT
I hope this answer helps .
Determine if 0.625 is rational or irrational and give a reason for your answer.
0.625 is a rational number. A rational-number is the number that can be expressed as ratio of two integers with a denominator (not zero).
What is rational and irrational number?
A rational number is a number which can be expressed as the product of two integers with non-zero denominators.In other words, it is a number that can be written in the form of p/q,
where:
p and q -> integers
and q -> not equal to 0.
An irrational number, is just opposite, it cannot be expressed as the ratio of 2 integers.It is a number that cannot be written as a simple fraction, and its decimal expansion continues indefinitely. The most famous examples of irrational numbers are π and √2.
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the population proportion is .3 what is the probability that a sample proportion will be within .06 of the population proportion for each of the following sample sizes? round your answers to decimal places. use z-table. a. b. c. d. e. what is the advantage of a larger sample size? with a larger sample, there is a - select your answer - probability will be within of the population proportion .
a. n=100
The probability that a sample proportion will be within +/-6% of the population proportion for a sample of size 100 is 0.7469.
b. n=200
The probability that a sample proportion will be within +/-6% of the population proportion for a sample of size 200 is 0.8214.
c. n=500
The probability that a sample proportion will be within +/-6% of the population proportion for a sample of size 500 is 0.8977.
d. n=1000 Th
The probability that a sample proportion will be within +/-6% of the population proportion for a sample of size 1000 is 0.9227.
"With a larger sample size, there is a higher probability that the sample proportion will be within a certain range of the population proportion" is the advantage of having larger sample size.
To solve this problem, we need to use the formula for the standard error of the sample proportion:
SE = [tex]\sqrt{ p \times (1 - p) / n }[/tex]
where p is the population proportion, and n is the sample size.
a) For n = 100:
SE = [tex]\sqrt{0.45 \times (1 - 0.45) / 100 }[/tex] = 0.0499
The margin of error is +/-6%, which translates to +/-0.06 in proportion units.
We can find the z-scores corresponding to these margins of error using a standard normal distribution table:
[tex]z_1[/tex] = (0.45 - 0.06 - 0.45) / 0.0499 = -1.2024
[tex]z_2[/tex] = (0.45 + 0.06 - 0.45) / 0.0499 = 1.2024
The probability of a sample proportion within +/-6% of the population proportion is the area under the normal curve between these two z-scores:
P(-1.2024 < z < 1.2024) = 0.7469
b) For n = 200:
SE = [tex]\sqrt{ 0.45 \times (1 - 0.45) / 200 }[/tex] = 0.0353
[tex]z_1[/tex] = (0.45 - 0.06 - 0.45) / 0.0353 = -1.691
[tex]z_2[/tex] = (0.45 + 0.06 - 0.45) / 0.0353 = 1.691
P(-1.691 < z < 1.691) = 0.8214
c) For n = 500:
SE = [tex]\sqrt{ 0.45 \times (1 - 0.45) / 500 }[/tex] = 0.0249
[tex]z_1[/tex] = (0.45 - 0.06 - 0.45) / 0.0249 = -2.2088
[tex]z_2[/tex] = (0.45 + 0.06 - 0.45) / 0.0249 = 2.2088
P(-2.2088 < z < 2.2088) = 0.8977
d) For n = 1000:
SE = [tex]\sqrt{ 0.45 \times (1 - 0.45) / 1000 }[/tex] = 0.0177
[tex]z_1[/tex] = (0.45 - 0.06 - 0.45) / 0.0177 = -2.5424
[tex]z_2[/tex] = (0.45 + 0.06 - 0.45) / 0.0177 = 2.5424
P(-2.5424 < z < 2.5424) = 0.9227
Advantage of a larger sample size:
With a larger sample size, there is a higher probability that the sample proportion will be within a certain range of the population proportion.
This is because a larger sample size reduces the standard error, resulting in a more precise estimate of the population proportion.
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Question:-
The population proportion is 0.45 . What is the probability that a sample proportion will be within +/-6 of the population proportion for each of the following sample sizes? Round your answers to 4 decimal places. Use z-table.
a. n=100
b. n=200
c. n=500
d. n=1000
What is the advantage of a larger sample size?
With a larger sample, there is a - Select your answer (lower or higher) Item 5 probability will be within of the population proportion .
A researcher would like to estimate the mean weight of all adult male American alligators in the
Everglades. The mean weight of a random sample of 89 adult male American alligators from the Everglades
was found to be 520 pounds. The standard deviation of the weights of all adult male American alligators in
the Everglades is known to be 18 pounds.
Using a 98% confidence level, determine the margin of error, E, and a confidence interval for the mean
weight of all adult male American alligators in the Everglades. Report the confidence interval using interval
notation. Round solutions to two decimal places, if necessary.
At a 98% degree of confidence, the range for the mean weight of all adult male American alligators in the Everglades is (515.91, 524.09) pounds.
what is standard deviation ?The standard deviation is a measurement of how widely apart a group of data values are from one another. It is a statistic that calculates the standard deviation of each data point from the dataset's mean. In other words, it reveals the degree to which the real numbers are dispersed from the mean. When the standard deviation is smaller, the data points are more closely packed around the mean, and when it is bigger, the data points are more widely spaced out from the mean. To evaluate the accuracy of the data and to compare other datasets, it is frequently employed in statistical analysis.
given
Using this formula, we can determine the margin of error (E):
where z* is the crucial value for the specified level of confidence.
We can use a conventional normal distribution table or calculator to determine z*. The value of z* for a 98% confidence interval is 2.33. (approximately).
When we change the values, we obtain:
E is equal to 2.33 * (18/89) 4.09 pounds.
Around 4.09 pounds are in the error zone.
Use the following formula to determine the confidence interval:
When we change the values, we obtain:
CI = 520 ± 4.09
CI = (515.91, 524.09) (515.91, 524.09)
At a 98% degree of confidence, the range for the mean weight of all adult male American alligators in the Everglades is (515.91, 524.09) pounds.
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can someone help out with these 2 questions please?
The value of x and y in equation (a) is x = 2 and y = 41
The value of x and y in equation (b) is x = 3 and y = 4
What do you mean by parallelogram ?A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles equal). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is called a rectangle.
To solve the first quadrilateral
Let ABCD is a quadrilateral
given that,
AB = 2x + 7
DC = x + 7
∠A = (2y - 5)°
∠D = (2y + 21)°
To find the value of x and y
2x + 7 = x + 9
2x - x = 9-7
x = 2
put the value of x in equation
2y - 5 + 2y +21 = 180°
4y + 16 = 180°
4y = 180° - 16
y = 164/4
y = 41
Hence,the value of x and y is 2 and 41
In second quadrilateral we have given that,
ABCD is a parallelogram
As we know that the diagonals of a parallelogram bisect each other
so, OD = OB ana OA = OC
2y + 13 = 5y + 4
13 - 4 = 5y - 2y
9 = 3y
y = 9/3
y = 3
now, OA = OC
x + 8 = 16 - x
x + x = 16 - 8
2x = 8
x = 8/2
x = 4
Hence, the value of x and y is 4 and 3
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help me pleaseeee
this is the onlyquestion i’m having trouble with
Answer: x=21
Step-by-step explanation:
The shape is a quadrilateral. (Quadrilateral= 180 degrees)
5x+18+2x+15=180 - combine like terms
7x+33=180 - subtract 33
7x=147 - divide by 7
x=21
works correctly at the 445 gram setting. based on a 27 bag sample where the mean is 448 grams and the standard deviation is 19, is there sufficient evidence at the 0.025 level that the bags are overfilled?
Based on the given information, there is not enough evidence at the 0.025 level to conclude that the bags are overfilled. This can be answered by the concept of Standard deviation.
To determine whether there is enough evidence to conclude that the bags are overfilled, we need to perform a hypothesis test.
Let the null hypothesis be that the bags are not overfilled, and the alternative hypothesis be that the bags are overfilled. We can set the significance level at 0.025.
We will perform a one-sample t-test since we have a small sample size and the population standard deviation is unknown. Using the formula for the t-test statistic, we obtain a t-value of 1.58. The critical t-value for a two-tailed test with 26 degrees of freedom (n-1) and a significance level of 0.025 is 2.479. Since 1.58 < 2.479, we fail to reject the null hypothesis.
Therefore, there is not enough evidence at the 0.025 level to conclude that the bags are overfilled.
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look at the figure at the right . Explain one thing that representing the area of the figure as 9(X+3)-6x tells you about the situation. Then write an equivalent expression for the area . Explain what information is in your expression that is not in 9(x+3)-6x.
The figure's area is calculated by subtracting the entire rectangle from the empty rectangle.
Write an equivalent expression for the area?The area of a rectangle in a two-dimensional plane is the space that it occupies. A rectangle is a quadrilateral, a kind of two-dimensional object with four sides and four vertices. The rectangle's four sides are all right angles or exactly 90 degrees. The rectangle's opposing edges are equal and parallel to one another. It should be observed that a parallelogram also has equal and parallel opposite sides, but the angles are not exactly 90 degrees.
The following is the solution for the figure's area:
9 (x+3) - 6x.
The entire figure's area has been described as 9 (x+3).
where 9 is the length of the rectangle and (x+3) = (x+1.5+1.5) is the width of the rectangle.
Currently, the empty space between has been assigned the value 6x.
where the rectangle's edges are 6 and x.
Therefore, the size of the figure is the entire rectangle less the empty rectangle.
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The complete question is:
Look at the figure at the right. Explain one thing that representing the area of the figure as 9(X+3)-6x tells you about the situation. Then write an equivalent expression for the area. Explain what information is in your expression that is not in 9(x+3)-6x.
what is the probability that from a sample of 40 indianapolis residents, fewer than 95% were rooting for the giants in super bowl xlvi?
0.0027 or 0.27% is the probability that from a sample of 40 Indianapolis residents, less than 95% were rooting for the Giants in Super Bowl XLV
To find the probability that fewer than 95% were rooting for the Giants, we need to sum the probabilities of having 0 to 19 residents rooting for the Giants out of 40, because if 19 or more residents were rooting for the Giants, then the percentage would be at least 95%.
Using the binomial distribution formula:
P(X < 0.95n) = Σ (n choose i) * p^i * (1-p)^(n-i), i = 0 to 19
where:
n = 40 (sample size)
p = 0.95 (probability of rooting for the Giants)
X = number of residents rooting for the Giants
Using a binomial distribution calculator or software, we get P(X < 0.95n) = 0.0027 or 0.27%.
Therefore, the probability that from a sample of 40 Indianapolis residents, fewer than 95% were rooting for the Giants in Super Bowl XLVI is approximately 0.0027 or 0.27%.
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you own 16 cds. you want to randomly arrange 9 of them in a cd rack. what is the probability that the rack ends up in alphabetical order? the probability that the cds are in alphabetical order is
The probability that the rack ends up in alphabetical order is 1/9! or approximately 1.46 x 10⁻⁷.
The problem involves arranging 9 CDs out of 16 in alphabetical order in a CD rack. The total number of possible ways to arrange 9 CDs out of 16 is 16 choose 9, which equals 11440. Only one of these arrangements is in alphabetical order. Therefore, the probability of randomly selecting an alphabetical order is 1/11440, which is approximately 0.0000874 or 0.00874%. This is a very small probability, indicating that it is highly unlikely that the CDs will end up in alphabetical order by chance.
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that the random variable x is the score assigned by the first inspector and the random variable y is the score assigned by the second inspector, and they have a joint probability mass function given below. 1 y 2 3 4 x 1234 0.09 0.03 0.01 0.01 0.02 0.15 0.03 0.01 0.01 0.01 0.24 0.04 0.00 0.01 0.02 0.32 (a) what is the probability that both inspectors assign the same safety score? (b) what is the probability that the second inspector assigns a higher safety score than the first inspector? (c) what are the marginal probability mass function, expectation, and variance of the score assigned by the first inspector? (d) what are the marginal probability mass function, expectation, and variance of the score assigned by the second inspector? (e) are the scores assigned by the two inspectors independent of each other? (f) what are the covariance of the scores assigned by the two inspectors?
(a) The probability that both inspectors assign the same safety score is 0.80.
(b) The probability that the second inspector assigns a higher safety score than the first inspector is 0.11.
(c) The expectation of marginal probability mass function of the score assigned by the first inspector is 2.83 and variance is 0.83.
(d) The expectation of marginal probability mass function of the score assigned by the first inspector is 3.00 and variance is 0.77.
(e) The scores assigned by the two inspectors are not independent of each other.
(f) The covariance of the scores assigned by the two inspectors is -0.0148.
(a) The probability that both inspectors assign the same safety score is the sum of the joint probabilities where X and Y take the same value:
P(X = Y) = P(1,1) + P(2,2) + P(3,3) + P(4,4) = 0.09 + 0.15 + 0.24 + 0.32 = 0.80
(b) The probability that the second inspector assigns a higher safety score than the first inspector is given by:
P(Y > X) = P(2,1) + P(3,1) + P(4,1) + P(3,2) + P(4,2) + P(4,3) = 0.03 + 0.01 + 0.01 + 0.03 + 0.01 + 0.02 = 0.11
(c) The marginal probability mass function of the score assigned by the first inspector is obtained by summing the joint probabilities over all values of Y:
P(X = 1) = 0.09 + 0.02 + 0.01 + 0.00 = 0.12
P(X = 2) = 0.03 + 0.15 + 0.01 + 0.01 = 0.20
P(X = 3) = 0.01 + 0.03 + 0.24 + 0.02 = 0.30
P(X = 4) = 0.01 + 0.01 + 0.04 + 0.32 = 0.38
The expectation of X is given by:
E(X) = 10.12 + 20.20 + 30.30 + 40.38 = 2.83
The variance of X is given by:
Var(X) = E(X^2) - [E(X)]^2
= (1^20.12 + 2^20.20 + 3^20.30 + 4^20.38) - (2.83)^2
= 0.83
(d) The marginal probability mass function of the score assigned by the second inspector is obtained by summing the joint probabilities over all values of X:
P(Y = 1) = 0.09 + 0.03 + 0.01 + 0.00 = 0.13
P(Y = 2) = 0.02 + 0.15 + 0.01 + 0.01 = 0.19
P(Y = 3) = 0.01 + 0.03 + 0.24 + 0.02 = 0.30
P(Y = 4) = 0.01 + 0.01 + 0.04 + 0.32 = 0.38
The expectation of Y is given by:
E(Y) = 10.13 + 20.19 + 30.30 + 40.38 = 3.00
The variance of Y is given by:
Var(Y) = E(Y^2) - [E(Y)]^2
= (1^20.13 + 2^20.19 + 3^20.30 + 4^20.38) - (3.00)^2
= 0.77
(e) To determine if the scores assigned by the two inspectors are independent of each other, we need to check if the joint probability mass function can be expressed as the product of the marginal probability mass functions.
If the scores are independent, then P(X = i and Y = j) = P(X = i)P(Y = j) for all possible values of i and j.
Checking the probabilities in the given joint probability mass function, we can see that P(X = 1 and Y = 2) = 0.03, P(X = 1) = 0.12, and P(Y = 2) = 0.20.
Since P(X = 1 and Y = 2) is not equal to P(X = 1)P(Y = 2), the scores assigned by the two inspectors are not independent of each other.
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a 99 confidence interval for a population mean was reported to be to . if , what sample size was used in this study? (round your answer up to the next whole number.)
A sample size of 105 was used in the study with 99% of confidence interval.
A range of values that, with a certain degree of confidence, is likely to include the population mean is known as a confidence interval for a mean. The formula for calculating the confidence interval is:
CI = X ± Zα/2 × σ/√n
where X is the sample mean, σ is the population standard deviation, n is the sample size, and Zα/2 is the critical value of the normal distribution at α/2. Here, for a 99% confidence level, α = 0.01 and Zα/2 = 2.576).
We can use this formula to solve for n:
n = (Zα/2 × σ / E)²
where E is the margin of error, which is half of the confidence interval.
In this case, we have a 99% confidence interval with a range of 152 to 160 and a standard deviation of 15.
The margin of error (E) can be calculated as half of the range of the confidence interval:
E = (160 - 152) / 2 = 4
By adding these values to the previous formula, we obtain:
n = (2.576 × 15 / 4)² = 105
Therefore, we can conclude that a sample size of at least 105 was used in this study.
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Complete question is:
A 99% confidence interval for a population mean was reported to be 152 to 160. If standard deviation is 15, what sample size was used in this study? (Round your answer up to the next whole number.)
Find the length please
The length οf diameter οf the given sphere is 18m.
What is sphere?A sphere is a three-dimensiοnal οbject which is rοund in shape. It has nο edges οr vertices. The sphere can be defined in three axes, thοse are x-axis, y-axis and z-axis.
The given diagram is a sphere.
Given that,
The surface area οf the sphere is 1017.36 m²
Fοrmula fοr surface area οf the sphere = 4πr² where r is the radius and π=3.14
Equating both we get,
4πr² = 1017.36
[ dividing bοth sides by 4 ]
⇒πr² = (1017.36)/4
⇒πr² = 254.34
[putting the value of π]
⇒r² = 254.34/ 3.14
⇒r² = 81
⇒r =± 9
As radius cannot be a negative value so we take r=9
Sο the radius οf the sphere is 9 m
Diameter = 2× radius =2×9= 18m
Hence, diameter οf the given sphere is 18m.
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someone plss help me
To verify our response, we can multiply it by 5 to the power of see if we get 65 with our response:(log₅65) ≈ 2.737
What other uses does the logarithm have?Several fields, including mathematics, physics, engineering, and others, use logarithms extensively. These are a few instances:
1. Sound intensity: Logarithms serve as the foundation for the decibel scale that measures sound intensity.
2. Earthquakes: The Richter scale, which gauges earthquake magnitude using logarithms, was developed.
3. pH scale: A solution's acidity or basicity is determined by the pH scale, which is based on logarithms.
To find x, we can use logarithmic properties. Using base 5 to calculate the logarithm of both sides, we obtain:
(5x) log5 = log₅65
By applying the logarithm power rule, we may simplify the left-hand side as follows:
5x log5 = 65x log5
Since log5 = 1, we can further reduce to obtain:
x = log₅ 65
We can determine that using a calculator or software that:
log₅ 65 ≈ 2.737
Hence, log₅ 65= 2.737.
To verify our response, we can multiply it by 5 to the power of see if we get 65 with our response:
(log₅ 65) ≈ 2.737
This demonstrates that our response is accurate.
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A company that manufactures golf balls produces a new type of ball that is supposed to travel significantly farther than the company’s previous golf ball. To determine this, 40 new-style golf balls and 40 original-style golf balls are randomly selected from the company’s production line on a specific day. The balls are then placed in a bag and shaken. A golf pro then selects a ball and hits it using a driver. The distance the ball travels is then measured. The bag is shaken again, and the golf pro selects another ball and hits it with the same driver. He continues this procedure until all 80 of the golf balls are hit.
Which of the following is a benefit of having replication in the experiment?
Repeating the experiment will allow the company to compare the distances traveled by the new type of golf ball from both experiments.
Having a large number of each type of golf ball will allow for a good comparison of the differences in distances traveled for the two types of balls.
Having a large number of each type of golf ball will not allow for a good comparison of the differences in distances traveled for the two types of balls.
Replication is not needed in this experiment. The golf pro hitting one ball of each type is enough to determine if the difference in distance is due to the type of ball.
The benefit of having replication in the experiment is that it allows for a good comparison of the differences in distances traveled for the two types of balls.
What are the benefits of having replication in the experiment?
By randomly selecting and hitting 40 balls of each type, and repeating the process multiple times, the results are more likely to be reliable and representative of the entire production line.
This reduces the impact of chance or variability in the measurements and helps to establish a pattern that can be used to compare the performance of the new and old golf balls. Therefore, option B is the right answer.
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1. Consider the quadratic equation 3x2 – 7 = 5x.
(a) What is the value of the discriminant?
(b) What does the discriminant of the quadratic equation tell about the solutions to 3x2 – 7 = 5x?
On solving the provided question we can say that So, the discriminant of the given quadratic equation is 109.
What is quadratic equation?A quadratic equation is x ax2+bx+c=0, which is a single variable quadratic polynomial. a 0. Because this polynomial is of second order, the Basic Theorem of Algebra implies that it has at least one solution. Simple or complex solutions are possible. A quadratic equation is a quadratic equation. This means it has at least one word that must be squared. One of the most common solutions for quadratic equations is "ax2 + bx + c = 0." where a, b, and c are numerical coefficients or constants. where the variable "X" is unnamed.
The given quadratic equation is [tex]3x^2 - 5x - 7 = 0[/tex]
(a) Here, the equation is [tex]3x^2 - 5x - 7 = 0[/tex], so a = 3, b = -5, and c = -7. Therefore, the discriminant is:
[tex]b^2 - 4ac = (-5)^2 - 4(3)(-7) = 25 + 84 = 109[/tex]
So, the discriminant of the given quadratic equation is 109.
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A standard deck of cards has 13 cards that are clubs and 13 cards that are hearts. A card is chosen from a standard deck of cards. It is then replaced, and a second card is chosen from the deck.
What is P(at least one card is a heart)?
three fourths
one half
one fourth
1 over 26
If at least one card is a heart then P is three-fοurths.
What is the prοbability?The study οf prοbability examines the likelihοοds οf results οccurring and is based οn the ratiο οf likely and imprοbable scenariοs.
Tο determine the likelihοοd οf at least οne card being a heart, we can determine the likelihοοd that neither card will be a heart and subtract that prοbability frοm 1.
The prοbability οf the first card nοt being a heart is 26/52 = 1/2, since there are 26 nοn-heart cards in the deck οut οf a tοtal οf 52 cards. Since the card is replaced, the prοbability οf the secοnd card nοt being a heart is alsο 1/2.
Therefοre, the prοbability οf neither card being a heart is (1/2) x (1/2) = 1/4.
The prοbability οf at least οne card being a heart is 1 - (1/4) = 3/4.
Hence, the answer is: three-fοurths.
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Answer question below
Answer:
d. 9.4 feet
Step-by-step explanation:
You want the measure of long side XY of the right triangle that has its altitude dividing the hypotenuse into segments 3 and 8 feet in length.
SimilarityIn this geometry, all of the right triangles are similar. That means the ratio of long side to hypotenuse is the same for all of the triangles:
XY/(3+8) = 8/XY
XY² = (3+8)(8)
XY = √88 ≈ 9.4
The length of segment XY is about 9.4 feet.
__
Additional comment
As we see here, the long side of the large triangle is the root of the product of the long segment of the hypotenuse with the whole hypotenuse:
XY=√(8(8+3)) = √88
The same relation works on the other side of the triangle. The short side of the large triangle is the root of the product of the short segment of the hypotenuse and the whole:
short side = √(3(11)) = √33
The relation for the altitude of the triangle is that it is the root of the product of the two hypotenuse segments:
altitude = √(3·8) = √24
the city of ithaca, new york, allows for two-hour parking in all downtown spaces. methodical parking officials patrol the downtown area, passing the same point every two hours. when an official encounters a car, he marks it with chalk. if the car is still there two hours later, a ticket is written. suppose that you park your car for a random amount of time that is uniformly distributed on .0; 4/ hours. what is the probability you will get a ticket?
The probability of getting a ticket when parking for a random amount of time that is uniformly distributed on .0; 4/ hours is 1/2.
Since the parking officials pass the same point every two hours, we can divide the possible parking times into two-hour intervals. If a car is parked for less than two hours, it will not be marked with chalk. If a car is parked for more than two hours, it will be marked with chalk and will receive a ticket if it remains parked for another two hours.
Since the possible parking times are uniformly distributed on .0; 4/ hours, the probability of parking for less than two hours is 2/4 = 1/2, and the probability of parking for more than two hours is also 1/2. Therefore, the probability of getting a ticket is the probability of parking for more than two hours, which is 1/2.
Alternatively, we can calculate the probability of getting a ticket by finding the area of the part of the uniform distribution that corresponds to parking for more than two hours. This area is a triangle with base 2 and height 1/2, so its area is (1/2)(2)(1/2) = 1/2. Therefore, the probability of getting a ticket is also 1/2.
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Hey can someone please help me thanks
I can't get how to type out the inequality sign, so I'm gonna use the equal to sign (=) even though it's wrong. If you get what I mean. I'll write the full answer in english tho.
x-4=12
collecting like terms, we have;
X=12+4
X=16( X is greater or equal to 16)
So for the graph, it'll be on 16 facing the the positive side( that's to the right) with the the end shaded.
Hope it helps
in hire-assistant, assuming that the candidates are presented in a random order, what is the probability that you hire exactly one time? what is the probability that you hire exactly n times?
In hire-assistant, assuming that the candidates are presented in a random order, the probability of hiring exactly one time is 1/n, while the probability of hiring exactly n times is 1/n!.
In the Hire-Assistant problem, the objective is to hire the best candidate among a pool of candidates. The candidates are presented in random order, and you must decide whether to hire or reject a candidate after each interview. The hiring process ends when the best candidate is hired.
To answer the student question, let's first consider the probability of hiring exactly one time. This happens when the best candidate is the first one interviewed since no other candidate can be better than them. Since the candidates are in random order, the probability of this occurring is 1/n, where n is the total number of candidates.
Now let's consider the probability of hiring exactly n times. This means you would hire every candidate you interview. This only happens if the candidates are presented in ascending order of quality, so that each new candidate is better than the previous one. There is only 1 possible ordering like this out of the total n! possible orderings of candidates. So, the probability of hiring exactly n times is 1/n!.
In summary, the probability of hiring exactly one time is 1/n, while the probability of hiring exactly n times is 1/n!. These probabilities are derived from the random order of candidate presentations and the decision-making process of the Hire-Assistant problem.
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