The slope of the line is 9/13 according to the given line.
What is a slope?The same number is given for every two different points on the same line when the ratio is stated as a quotient ("rise over run"). On a falling line, there is a negative "rise." In a diagram that depicts a roof or a road as a description or a design, the line may be practical as established by a road surveyor.
The steepness, incline, or grade of a line can be approximated by the slope's absolute value. The slope of a line in the plane including the x and y axes is typically symbolized by the letter m and is defined as the difference in the y coordinate by the equivalent difference in the x coordinate between two different places on the line. The following equation encapsulates this:
Slope=rise/run
Rise=y₂-y₁
=-1-(-10)
=9
Run=x₂-x₁
=9-(-4)
=13
Therefore, slope=9/13
Hence, the slope of the line is 9/13.
To know more about slope, visit:
https://brainly.com/question/3605446
#SPJ1
Which of the following statement is true each parallelogram is a square? a) All the rhombuses are squares b) each square is a parallelogram c) each parallelogram is a square d) each trapezium is a parallelogram
The statement is true for parallelogram is a square is a) All the rhombuses are squares.
What are the 4 properties of a rhombus?In a rhombus, the opposing sides are parallel. In a rhombus, the opposing angles are equal. Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals.
What is the rule of rhombus?Diagonals in a rhombus cut each other at right angles. A rhombus' angles are divided by diagonals. One of the most significant characteristics of rhombus diagonals is this. Two adjacent angles added together equal 180°.
To learn more about parallelogram visit:
https://brainly.com/question/19187448
#SPJ4
An ice cream stand uses the expression 2 + 0.5x2+0.5x2, plus, 0, point, 5, x to determine the cost (in dollars) of an ice cream cone that has xxx scoops of ice cream.
How much does an ice cream cone with 555 scoops cost?
\$$dollar sign
Answer:
qwqe
Step-by-step explanation:wqeqwe
Match each number on the left with the correct description of the number on the right.
Answer options on the right may be used more than once.
-10
This is an integer.
This is a rational number, but not an integer.
This is an irrational number.
√5
-5.6
31/
π
The numbers are matched to description as follows
-10 This is an integer
31/π This is an irrational number
√5 This is an irrational number
-5.6 This is a rational number, but not an integer
What is an integer?An integer are whole numbers both positive and negative
hence -10 is an integer
What are rational numbers?A rational number is one that has the form p/q, where p and q are both integers and q is not zero
Rational function means that the equation will be a fraction
-5.6 can be written as a fraction and the decimals can be terminated
Irrational numbers are made up of repeating decimals
Learn more on rational function at:
tps://brainly.com/question/29692995
#SPJ1
how ,any four digit positive integers have property that the product of their digits is 120?
The positive integers that meet the requirement that the product of their digits be 120 are: 1546, 1564, 1456, 1465, 1654, 1645, 6145, 6154, 6451, 6415, 6541, 6514, 4156, 4165, 4561, 4516, 4651, 4615, 5146, 5164, 5461, 5416, 5614, and 5641.
How to identify the integers that meet the requirement?To find the integer numbers that meet the aforementioned requirement that the product of its digits be 120, we must take a positive 4-digit integer number and multiply its digits until obtaining the result of 120.
In this case, the four digits would be 1456. So, we must find all the four-digit numbers that are made up of these numbers, the numbers are shown below:
1546, 1564, 1456, 1465, 1654, 1645, 6145, 6154, 6451, 6415, 6541, 6514, 4156, 4165, 4561, 4516, 4651, 4615, 5146, 5164, 5 4161, and 5 614, and 4
Finally, we can check it with any of the numbers and the result will be 120 because the order of the factors does not change the result.
Learn more about integers in: https://brainly.com/question/1768255
#SPJ1
What is 35 percent of 80? = 28 - Percentage Calculator
The percentage of 35 percent of 80 is 28
Percentage:
In mathematics, a percentage (from Latin: per centum, "by a hundred") is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number (pure number); it has no unit of measurement.
For example, 45% (read as "forty-five per cent") is equal to the fraction
45/100, the ratio 45:55 (or 45:100 when comparing to the total rather than the other portion), or 0.45. Percentages are often used to express a proportionate part of a total.
The percentage of 35 percent of 80 is
= [tex]\frac{35}{100}[/tex]× 80
=28
The percentage of 35 percent of 80 is 28
To learn more about percentage:
https://brainly.com/question/29306119
#SPJ4
If matrix M is of dimension 5 x 3, and matrix N is of dimension 5 x 5 then the dimension of NM is
A₂ₓ₃ matrix and B₃ₓ₄ matrix, The dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.
What are matrices?Matrices represent data in the form of rows and columns in an array form.
Suppose we have two matrices and their multiplication is possible only when the no. of columns in the first matrix is equal to the no. of rows in the second matrix.
Let A₂ₓ₃ matrix and B₃ₓ₄ matrix, Then the dimension of the matrix AB obtained by multiplying A and B will be AB₂ₓ₄.
learn more about matrices here :
https://brainly.com/question/11367104
#SPJ1
.
Please help 25 points, if you please show how you did it that would be very appreciated
The unknown angle measures are 51.5° and 51.5° respectively.
What is an isosceles triangle?
An isosceles triangle in geometry is a triangle with two equal-length sides.
Given, side DE = side EF
Then, ∠D = ∠F
So, the sum of all angles of the triangle = 180°
or, ∠D + ∠E + ∠F = 180°
or, ∠F + 77° + ∠F = 180°
or, 2∠F = 180° - 77°
or, ∠F = 103/2 = 51.5°
And, ∠D = 51.5°
Hence, the unknown angle measures are 51.5° and 51.5° respectively.
To learn more about an isosceles triangle
https://brainly.com/question/29618252
#SPJ1
In Original Source 2, "Development and initial validation of the Hangover Symptoms Scale: Prevalence and correlates of hangover symptoms in college students," one of the questions was how many times respondents had experienced at least one hangover symptom in the past year. Table 3 of the paper (page 1,445) shows that out of all 1,216 respondents, 40% answered that it was two or fewer times. Suppose the researchers are interested in the proportion of the population who would answer that it was two or fewer times. Can they conclude that this population proportion is significantly less than half (50% or 0.5)? Go through the four steps of hypothesis testing for this situation for women only. Use appropriate software or a calculator to find the standard deviation and the test statistic. (Round your standard deviation to three decimal places and your test statistic to two decimal places.) Test Statistic?
Only twice or less, according to 40% of respondents. Suppose the researchers are curious about the percentage of the population that would respond that it was two or less times, in which case the test statistic would be -0.208 and the standard deviation would be 0.048.
H0: The population proportion of women who have experienced two or fewer hangover symptoms in the past year is equal to or greater than 0.5.
Ha: The population proportion of women who have experienced two or fewer hangover symptoms in the past year is less than 0.5.
Set the alpha level
α = 0.05
Calculate the test statistic
n = 618 (women only)
p = 0.4 (from Table 3)
Standard Deviation = sqrt[p*(1-p)/n]
Standard Deviation = sqrt[0.4*(1-0.4)/618]
Standard Deviation = 0.048
Test Statistic = (0.4 - 0.5) / 0.048
Test Statistic = -0.208
Step 4: Make a decision
Since the test statistic (-0.208) is less than the alpha level (0.05), we reject the null hypothesis and conclude that the population proportion of women who have experienced two or fewer hangover symptoms in the past year is less than
Learn more about test statistic here
https://brainly.com/question/14128303
#SPJ4
4
A line segment contained endpoints (-4, -3) and (1, -3). Which of the following is the reflection of the
line segment over the y-axis?
Given the speeds of each runner below, determine who runs the fastest.
\text{Adam runs 13 feet per second.}
Adam runs 13 feet per second.
\text{Stephanie runs 199 feet in 17 seconds.}
Stephanie runs 199 feet in 17 seconds.
\text{Noah runs 1 mile in 592 seconds.}
Noah runs 1 mile in 592 seconds.
\text{Katie runs 878 feet in 1 minute.}
Katie runs 878 feet in 1 minute.
Katie runs fastest among all .
What is the units of conversion ?
Unit of Conversion is a multi-step process involving multiplication or division by a numerical factor.
Given:
Speed of Adam = 13 feet per second
Speed of Stephanie = 199 feet in 17 seconds
Speed of Noah = 1 mile in 592 seconds
Speed of Katie = 878 feet in 1 minute
Now on converting all the units to one single unit,we get
1 mile = 5280 feet
1 minute = 60 seconds
Speed of Adam = 13 feet per second
Speed of Stephanie = 199 feet in 17 seconds
= [tex]\frac{199}{17}[/tex] feet per second
= 11.705 feet per second
Speed of Noah = 1 mile in 592 seconds
= 5280 feet in 592 seconds
= [tex]\frac{5280}{592}[/tex] feet per second
= 8.919 feet per second
Speed of Katie = 878 feet in 1 minute
= 878 feet in 60 seconds
= [tex]\frac{878}{60}[/tex] feet per second
= 14.6333 feet per second
Hence ,Katie runs fastest among all sice its speed is the highest .
Learn more about the units conversion by:
https://brainly.com/question/19420601
#SPJ1
Part 1 of 2
Describe and correct the error a student
made finding the intercepts of the graph
of the line 4x-6y = 12.
1.4(0)-6y = 12
2. 6y=12, so y = 2; the y-intercept is 2.
3.4x-6(0) = 12
4.4x = 12, so x = 3; the x-intercept is 3.
X
UA. In solving for the x-intercept, the student's calculation of x is incorrect. The error occurs in
(Type an integer or a decimal.)
OB In solving for the v-intercent the student substituted 0 for x The student should have suhe
Answer:
The error is when 6y = 12 it will be -6y = 12 and the intercept would be -2.
Step-by-step explanation:
certain kind of sheet metal has, on average, 4 defects per 13 square feet. Assuming a Poisson distribution, find the probability that a 14 square foot metal sheet has at least 5 defects.
Using Poisson distribution to calculate the probability distribution of the event, the probability is 0.2084
What is Probability DistributionProbability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 indicates an impossibility and 1 indicates a certainty.
A probability distribution is a mathematical function that describes the likelihood of a random variable taking on a particular value or set of values. It is used to describe the behavior of random variables, either discrete (e.g. coin flips) or continuous (e.g. temperatures), and is often used in the field of statistics to predict the behavior of a system or process.
Using Poisson distribution;
P(X ≥ 5) = 1 - P(X ≤ 4)
P= 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4))
P= 1 - (e^(-4.615) + (4.615*e^(-4.615))/1! + (4.615^2*e^(-4.615))/2! + (4.615^3*e^(-4.615))/3! + (4.615^4*e^(-4.615))/4!)
P = 0.2084
Learn more on probability distribution here;
https://brainly.com/question/14802212
#SPJ1
a) ( combining like terms)
Simplify (7a + 10b) − (4a − 6b).
b) Simplify the expression. ( combining like terms)
−5x + 8y + 2x − 3y
c) Solve and graph the inequality x - 4 ≤ -1 (the name of the game is ...)
a) Combining like terms (7a + 10b) − (4a − 6b) = 3a + 16b
b) The Simplify expression −5x + 8y + 2x − 3y the answer is -3x + 5y
c) The inequality x - 4 ≤ -1 Graph is given below.
What do you mean by algebraic expression?
When addition, subtraction, multiplication, division, and other mathematical operations are performed on variables and constants, the result is a mathematical statement known as an algebraic expression.
Any combination of terms that have undergone operations like addition, subtraction, multiplication, division, etc. is known as an algebraic expression (or variable expression).
An algebraic expression is composed of various parts.
a) Given expression:
(7a + 10b) - (4a - 6b)
= 7a + 10b - 4a + 6b
On combining like terms we get,
(7a - 4a) + (10b + 6b)
= 3a + 16b
Therefore, (7a + 10b) − (4a − 6b) = 3a + 16b
b) Given expression :
−5x + 8y + 2x − 3y
On combining like terms we get,
-5x + 2x + 8y - 3y
= (-5x + 2x) + (8y - 3y)
= -3x + 5y
therefore, −5x + 8y + 2x − 3y = -3x + 5y
c) Given expression:
x - 4 ≤ -1
⇒ x ≤ -1 + 4
⇒ x ≤ 3
Graph of the function is given below:
To learn more about the algebraic expression from the given link.
https://brainly.com/question/28036476
#SPJ1
Which is always true about a trapezoid?
Answer: They always have one pair of parallel lines.
Step-by-step explanation:
What is a special segment?
The special segments of a triangle are median, altitude, perpendicular bisector, angle bisector, and mid-segment.
What is a special segment?A line segment that establishes a special relationship with the existing segments of a geometrical shape is said to be a special segment.
Using this special segment, we can able to find the other characteristics of the geometry (a triangle or a circle, etc.)
Description about special segments:The special segments in a triangle are:
1) Altitude 2) Median 3) Perpendicular bisector and 4) Angle bisector
Altitude: This line segment whose one end starts at one of the vertexes of the triangle and the other end is perpendicular to the opposite side of the triangle.
The point of intersection of three altitudes of a triangle forms an "Orthocenter".
Median: This line segment whose one end starts at one of the vertexes of a triangle and the other end meets at the midpoint of the opposite side.
The point of intersection of three medians of a triangle forms a "Centroid".
Perpendicular bisectors: These line segments whose ends bisect the two sides of the triangle perpendicularly.
The point of intersection of perpendicular bisectors of a triangle form a "Circumcenter".
Angle bisector: This line segment bisects the angle of the triangle and divides the angle into exactly two halves.
The point of intersection of angle bisectors of a triangle form an "Incenter".
We have one more special segment in a triangle i.e., a midsegment. This line connects two midpoints of opposite sides of a triangle and becomes parallel to the third side.
Learn more about special segments here:
https://brainly.com/question/29548849
#SPJ4
suppose you roll a special 37-sided die. what is the probability that one of the following numbers is rolled? 35, 25, 33, 9, 19
The probability that one of the following numbers is rolled is 0.135.
We are provided a 37 sided dice. Hence, each of the number between 1 to 37 can be rolled. Now, to find the probability of rolling any of these five numbers, we will simply perform the multiplication.
The formula to be used for calculation of probability to roll any one number on the dice -
Probability = number of favourable outcomes ÷ total number of outcomes
Keep the values in formula
Probability = 1/37
Now, for the mentioned five numbers among which any can be rolled, the probability is -
Probability = 5 × (1/37)
Performing multiplication
Probability = 5/37
Performing division
Probability = 0.135
Hence, the probability is 0.135.
Learn more about probability -
https://brainly.com/question/13604758
#SPJ4
The propagation of fatigue cracks in various aircraft parts has been the subject of extensive study in recent years. The accompanying data consists of propagation lives (flight hours/104) to reach a given crack size in fastener holes intended for use in military aircraft. 0.737 0.843 0.871 0.911 0.920 0.932 0.961 1.010 1.039 1.050 1.102 1.120 1.138 1.161 1.241 1.352 (a) Compute and compare the values of the sample mean x and median . (Round your answers to four decimal places.) x = flight hours/104 = flight hours/104 (b) By how much could the largest sample observation be decreased without affecting the value of the median? (Enter your answer to three decimal places.) flight hours/104
On solving the provided question we got to know that, the median value won't change if the greatest sample Observation is decreased to 1.3735.
What is median?One of three ways to gauge central tendency is the median. The center position of a record is specified when describing it. A measure of central tendency is what this is. The mean, median, and mode are the three most frequently used indicators of central tendency.
The sum of all the values is divided by the total number of values, giving the mean value.
[tex]0.736 + 0.863 + 0.865 + 0.913 + 0.915 + 0.937 + 0.983 + 1.001 + 1.011 + 1.064 + 1.109 + 1.132 + 1.140 + 1.153 + 1.253 + 1.397 = 16.472\\16.472 /16 = 1.0295\\1.0295 is the mean value[/tex]
The number near the middle of the point is the median value. At the halfway point, there are two values.
[tex](1.001 + 1.011) / 2 = 1.006\\ 1.006 is the median value.[/tex]
As a result, the median value, which depicts the middle value of the numbers in the result, is less than the mean value, which depicts the real middle value of the numbers if they were equally distributed.
Their difference is that 1.0295 - 1.006 = 0.0235
1.397 observations make up the biggest sample. It may be made smaller by taking the number and removing the difference between the mean and median.
Consequently, there is a 0.0235-point difference between the mean and median.
Therefore;
[tex]1.397 - 0.0235 = 1.3735[/tex]
The median value won't change if the greatest sample Observation is decreased to 1.3735.
To know more about median visit:
https://brainly.com/question/28060453
#SPJ4
Please help...........
Answer:
98
Step-by-step explanation:
a. kira
b. lyric
c. they traveled at the same speed
Answer:
they ran the same speed as each other c
find the area of a circle with a radius of 13 inches use 3.14 for pi do not round your answer
The area is:
530.66 in^2Explanation:
To find the circle's area, use the formula [tex]\sf{A=\pi r^2}[/tex].
where:
A = area;
π = 3.14 (pi);
r = radius
Diagram:
[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 13\ in}\end{picture}[/tex]
Plug in the data:
[tex]\sf{A=3.14\times13^2}[/tex][tex]\sf{A=3.14\times169}[/tex][tex]\sf{A=530.66\:in^2}[/tex]
Of the 1500 trains leaving a train station one day, 1290 left within 5 minutes
Of the scheduled time. What percentage of the trains left within 5 minutes
of the scheduled time?
Answer:
55
Step-by-step explanation:
Question 4
The graph of f(x) is shown below.
What is the value of f(-3)?
(1) 6
2) 2
(3)-2
(4) -4
The value of the function instance, f (-3) as required to be determined according to the graph of f (x) as in the attached image is; -4.
What is the value of the function instance; f (-3)?It follows from the task content that the value of the function instance; f (-3) is to be determined according to the attached graph.
By observation; when a vertical line; x = -3 is drawn; it follows that the line passes through and intersects the lines; y = -1 and y = -4.
However, there's an open circle at; y = -1 which indicates that; -1 is not in the range of f (x).
Ultimately, the value of the function instance; f (-3) as required to be determined is; Choice 4; -4.
Read more on function graphs;
https://brainly.com/question/17089414
#SPJ1
The plot below shows the mass of each of 999 puppies in a litter.
A line plot labeled mass of puppies in pounds
shows, moving left to right, labeled tick marks at zero, one-fourth, one-half, three-fourths, and one.There is an unlabeled tick mark between each labeled tick mark. Dots are plotted as follows: 1 dot above one-fourth; 1 dot above one-half; 4 dots above the tick after one-half, and 3 dots above three-fourths.
A line plot labeled mass of puppies in pounds shows, moving left to right, labeled tick marks at zero, one-fourth, one-half, three-fourths, and one.There is an unlabeled tick mark between each labeled tick mark. Dots are plotted as follows: 1 dot above one-fourth; 1 dot above one-half; 4 dots above the tick after one-half, and 3 dots above three-fourths.
How many times as great is the mass of the heaviest puppy than the mass of the lightest puppy?
All measurements are rounded to the nearest \dfrac18
8
1
start fraction, 1, divided by, 8, end fraction pound.
The mass of the heaviest puppy is three times greater than the mass of the lightest puppy.
What is shown by the dot plot?The number of dots for each input of the dot plot shows the number of times that each measure appears in the data-set.
For example, two dots means that the measure appears twice in the data-set.
From the description of the dot plot, the masses are given as follows:
1/4, 1/2, 1/2, 1/2, 1/2, 3/4, 3/4, 3/4.
Then the masses of the lightest and of the heaviest puppy are given as follows:
Lightest: 1/4.Heaviest: 3/4.The ratio of these masses is given as follows:
3/4/(1/4) = 3/4 x 4 = 3.
(division of fractions, the numerator is multiplied by the inverse of the denominator).
More can be learned about dot plots at https://brainly.com/question/24309209
#SPJ1
find the slope of the line that passes through 0.6 and 20.14
Answer:
here this should help you
Twice my hat size is 3 times my shoe size. If my hat size is 18 more than my shoe size, then the sum of my hat size and shoe size together is:
A) 36 B) 54 C) 90 D) 108
What is the least 3-digit odd sum of two prime numbers
A) 101 B) 103 C) 105 D) 107
What is the greatest possible product of the ones digits of 4 numbers
A) 9 B) 105 C) 945 D) 6561
Please give a detailed and simple explanation please!
Answer:
Q1. The sum of your hat size and shoe size is 54.
Q2. The correct answer is 101.
Q3. The correct answer is 6561.
Step-by-step explanation:
Q1. Let's call the size of your hat H and the size of your shoe S. You can set up the following equation based on the given information:
H = 2S
H = S + 18
Substituting the first equation into the second equation, we get:
2S = S + 18
S = 18
Then, substituting this value back into the first equation, we get:
H = 2S
H = 2 * 18
H = 36
The sum of your hat size and shoe size is S + H = 18 + 36 = 54.
Q2. The least 3-digit odd sum of two prime numbers is 101, which can be achieved by adding the two prime numbers 2 and 99. Both 2 and 99 are prime numbers, and their sum is 101, which is a 3-digit odd number.
Q3. The greatest possible product of the ones digits of 4 numbers is 6561, which can be achieved by choosing the numbers 9901, 9911, 9921, and 9931. The ones digits of these numbers are 1, 1, 1, and 1, respectively, and their product is 6561.
()
Complete the table using the given rules. Then, compare pattern A to pattern B.
() Pattern A
◄) subtract 20
Pattern B
() subtract 4
100
20
Which statement is true?
Each term in pattern B is 80 less than the corresponding term in pattern A.
Each term in pattern B can be found by dividing the corresponding term in
pattern A by 5.
Answer:
100; 80, 60, 4020; 16, 12, 8dividing by 5Step-by-step explanation:
You want to fill a table using the given rules, then describe the relationship between the table values.
Pattern AStarting with 100, you want to subtract 20 to get next terms:
100
100 -20 = 80
80 -20 = 60
60 -20 = 40
The next terms are 80, 60, 40.
Pattern BStarting with 20, you want to subtract 4 to get next terms:
20
20 -4 = 16
16 -4 = 12
12 -4 = 8
The next terms are 16, 12, 8.
RelationshipLooking at second terms, we can determine which description is true:
80 -80 = 0 ≠ 16 . . . . . the description "subtract 80" fails
80/5 = 16 . . . . . . . . . . the description "divide by 5" works
Each term in pattern B can be found by dividing the corresponding term in pattern A by 5.
suppose annual salaries for sales associates from a particular store have a mean of $32,500 and a standard deviation of $2,500
. a. Calculate and interpret the z-score for a sales associate who makes $36,000.
b. Use Chebyshev's theorem to calculate the percentage of sales associates with salaries between $26,250 and $38,750
. c. Suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. Use the empirical rule to calculate the percentage of sales associates with salaries between $27,500 and $37,500.
d. Use the empirical rule to determine the percentage of sales associates with salaries less than $27,500. e. Still suppose that the distribution of annual salaries for sales associates at this store is bell-shaped. A sales associate makes $42,000. Should this salary be considered an outlier? Explain.
a) The z-score for a sales associate who makes $36,000 is 1.4
b) The percentage of sales associates with salaries between $26,250 and $38,750 is 84%
c) The percentage of sales associates with salaries between $27,500 and $37,500 is 95.4%
d) The percentage of sales associates with salaries less than $27,500 is 2.3%
e) Yes, the salary of $42000 should be considered as outlier.
Given,
Mean, [tex]\mu[/tex]=32500
Standard deviation, [tex]\sigma[/tex]=2500
a)
[tex]z=\frac{x-\mu}{\sigma}\\\\z=\frac{36000-32500}{2500}=1.40[/tex]
The sales associate who makes 36000 is 1.4 standard deviation above the mean salary.
b)
As per chebyshev's theorem, [tex](1-\frac{1}{k^2})[/tex] of the observations fall within k standard deviation of the mean, i.e. within [tex]\mu\pm k\sigma[/tex]
[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{26250-32500}{2500}=-2.50\\\\z_2=\frac{x_2-\mu}{\sigma}\\\\z_2=\frac{38750-32500}{2500}=2.50[/tex]
Hence, we need to find proportion of observations within [tex]\mu\pm2.5\sigma[/tex]
k=2.5
[tex](1-\frac{1}{k^2})=1-\frac{1}{2.5^2}=0.84=84\%[/tex]
Hence, 84% of sales associates have salaries between 26250 and 38750.
c)
As per empirical rule for a bell shaped distribution:
68.3% of the observations fall within 1 standard deviation of the mean i.e. within [tex]\mu\pm 1\sigma[/tex]95.4% of the observations fall within 2 standard deviation of the mean i.e. within [tex]\mu\pm 2\sigma[/tex]99.7% of the observations fall within 3 standard deviation of the mean i.e. within [tex]\mu\pm 3\sigma[/tex][tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{27500-32500}{2500}=-2\\\\z_2=\frac{x_2-\mu}{\sigma}\\\\z_2=\frac{37500-32500}{2500}=2[/tex]
Hence, we need to find the proportion of observations within \mu \pm 2\sigma
As per empirical rule, 95.4% of the observations fall within 2 standard deviation of the mean .i.e within [tex]\mu \pm 2\simga[/tex] .Therefore, percentage of sales associates with salaries between 27500 and 37500=95.4%
d)
[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{27500-32500}{2500}=-2[/tex]
Percentage of sales associates with salaries less than 27500 will be equal to the area under the normal curve to the left z=-2
As per empirical rule 95.4% of the observations fall within 2 standard deviation of the mean
Therefore, the percentage of sales associates with salaries less than 27500 : [tex]\frac{100-95.4}{2}=2.3\%[/tex]
e)
[tex]z_1=\frac{x_1-\mu}{\sigma}\\\\z_1=\frac{42000-32500}{2500}=3.8[/tex]
A z-value greater than 3 is considered as an outlier.
Hence, the salary of 42000 should be considered as outlier.
To learn more about chebyshev's theorem refer here
https://brainly.com/question/28482338
#SPJ4
a thief uses a bag of sand to replace a gold statue that sits on a weight-sensitive, alarmed pedestal. the bag of sand and the statue have exactly the same volume, 1.90 ll. (assume that the mass of the bag is negligible.) part a calculate the mass of each object. (densityofgold
4.65 kg the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)
Given that,
A gold statue that is perched on a pedestal with a weight-sensitive alarm is replaced by a thief using a bag of sand. The statue and the bag of sand have the exact same volume, 1.55 L.
We have to calculate the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)
We know that,
Mass of gold = Volume × Density
= 1.55×1000 cc × 19.3
= 29915 grams
= 29.915 Kg
Mass of sand = 1.55×1000×3
= 4650g
= 4.65 Kg
Volume = 1.55 L
= 1.55 × 1000 cc
= 1550 cc
Mass = Volume × Density
Mass of gold = 1550 × 19.3
= 29915 grams
= 29.915 kg
Mass of sand = 1550 × 3
= 4650 grams
= 4.65 kg
Therefore, 4.65 kg the mass of each item (assuming the bag's mass is negligible). (Sand density is 3.00 g/cm3, while the density of gold is 19.3 g/cm3)
To learn more about mass visit: https://brainly.com/question/16940422
#SPJ4
What is the estimated product of 8.78 and 12.356 as a whole number
Answer: 108
Step-by-step explanation:
8.78x12.356=108.48568 so the estimate would be 108
If other factors are held constant, which set of sample characteristics is most likely to lead a researcher to reject a null hypothesis stating that µ = 80? a. M = 85 and s2 = 9 b. M = 90 and s2 = 9 c. M = 85 and s2 = 18 d. M = 90 and s2 = 18
If other factors are held constant, which set of sample characteristics is most likely to lead a researcher to reject a null hypothesis stating that µ = 80 then s2 = 18 and C. M = 85
The standard deviation (s2) is a measure of the variability of the sample data, while the mean (M) is a measure of the central tendency. The higher the mean and the higher the standard deviation, the more likely it is that the null hypothesis will be rejected. Therefore, the set of sample characteristics that is most likely to lead to a rejection of the null hypothesis is M = 85 and s2 = 18.
Learn more about null hypothesis here
https://brainly.com/question/28920252
#SPJ4
