No because it is not possible to groom 0.2 of an animal.
What is median ?
The value of the middle observation found after the data are arranged in ascending order is referred to as the median of the data. In many cases, it is challenging to take all of the facts into account when representing something, and in these cases, the median is helpful. The median is one of the simple to compute statistical summary metrics. The median is also known as the place average since it uses the data that is in the center of a sequence to determine its value.
To support this, we can also calculate the median and mode of the data set to see if they are close to the mean. The median is the middle value of the sorted data set, which is 8 in this case, and the mode is the most common value, which is also 7 and 8 in this data set. So, the mean, median, and mode are all relatively close to each other, indicating that the data is roughly symmetric around the center.
Based on the given data, the mean of 8.2 animals per day can be considered as a reasonable measure of central tendency.
Hence the answer is No because it is not possible to groom 0.2 of an animal.
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Answer:
Yes, because there is no outliers to skew the data.
Step-by-step explanation:
I did the quiz
 find the formula for an exponential function that passes through (-2,6) and (3,1)
The exponential function that passes through (-2,6) and (3,1) is y = 2.93(0.6988)ˣ
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.
An exponential equation is in the form:
y = abˣ
where a is the initial value and b is the multiplier.
Given that an exponential function that passes through (-2,6) and (3,1). At the point (-2, 6):
6 = a(b)⁻²
a/b² = 6
a = 6b² (1)
At the point (3, 1):
1 = ab³
substitute a = 6b²:
1 = 6b²(b³)
1/6 = b⁵
b = 0.6988
a = 6(0.6988)²
a = 2.93
The exponential function is y = 2.93(0.6988)ˣ
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The graph of a linear function passes through the points (−4,8)
and (6,10)
. What is the rate of change of the function?
ResponsesThe graph of a linear function passes through the points (−4,8)
and (6,10)
. What is the rate of change of the function?
Responses
Answer:
the slop is 2
Step-by-step explanation:
i just calculated it a minute ago
the line passes through -5 ,3 and -2,-3
The line of equation which passes through (-5, 3) and (-2, -3) is 2x+y+7=0.
What is line of equation?A line of equation is an equation that represents a straight line on a coordinate plane.
The Straight line equation is: y = mx + b
Here y is the dependent variable, x is the independent variable, m is the slope of the line, and constant b is the y intercept.
The equation of line is:
[tex]y-y_{1} = \frac{y_{2}-y_{1}}{x_{2}-x_{1}} (x-x_{1} )[/tex]
Given that, ([tex]x_{1}, y_{1}[/tex]) = (-5, 3) and ([tex]x_{2}, y_{2}[/tex]) = (-2, -3)
By putting the values in above equation,
[tex]y-3 = \frac{-3-3}{-2+5} (x+5)\\[/tex]
y-3 = -2x-10
2x+y+7 = 0
Therefore the line equation is 2x+y+7 = 0.
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4(2x + 3) ÷ 5y
From the expression above, provide an example of each of the following: sum, term, product, factor, quotient, and coefficient. If any are not present, write "not present."
Answer:
Sum: not present
Term: 4(2x + 3), 5y
Product: 4 and (2x + 3), 4 and 2x, 4 and 3, 5 and y
Factor: 4, 2x, 3, 5, y
Quotient: (4(2x + 3)) ÷ 5y
Coefficient: 4, 5
Step-by-step explanation:
QUESTION 2
Consider the following argument: If we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the
bookcase, the bookcase collapses. We do not put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of
the bookcase. Hence, the bookcase does not collapse. What is the logical form of this argument?
O a. Modus Ponens
O b. Hypothetical Syllogism
c. Denying the antecedent
d. Modus Tollens
e. Disjunctive Syllogism
Answer:
Modus Tollens
Step-by-step explanation:
Consider the following argument: If we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase, the bookcase collapses. We do not put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase. Hence, the bookcase does not collapse.
The logical form of this argument is Modus Tollens.
Modus Tollens is a mode of argumentation that involves affirming the consequent of a conditional statement. In this argument, the conditional statement is "If we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase, the bookcase collapses." The antecedent of this statement is "we put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase," and the consequent is "the bookcase collapses."
Modus Tollens is used to prove the negation of the consequent by negating the antecedent. In other words, if the consequent is not true, then the antecedent must also not be true. Thus, in this argument, since we know that the bookcase does not collapse, we can conclude that we did not put all thirty-two volumes of the Encyclopedia Britannica on the top shelf of the bookcase.
Therefore, the logical form of this argument is Modus Tollens.
What are the coordinates of X′ for the image of △TUX after dilation with center at (0, 0) and scale factor 4, then applying (x, y) ⟶ (x − 3, y + 1), given T(−7, −6), U(−8, 3), X(2, 1)?
The coordinates of the image of triangle △TUX after dilation with center at (0,0) and scale factor 4, then applying the transformation (x, y) ⟶ (x − 3, y + 1) are T''(25, 25), U''(-35, 13), and X''(5, 5).
What is Dilation with Center?Dilation with center refers to a transformation that involves scaling a geometric shape around a fixed center point. The center of dilation is the fixed point around which the shape is being scaled.
What is Coordinate Geometry?Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes in a coordinate plane. It combines the principles of geometry and algebra, where geometric shapes can be represented using algebraic equations and coordinates.In coordinate geometry, points are located in a two-dimensional plane using a system of Cartesian coordinates, which consists of an x-axis and a y-axis perpendicular to each other.
In the given question,
To find the coordinates of the image of triangle △TUX after dilation with center at (0,0) and scale factor 4, we first need to find the coordinates of the image of each point after the dilation.
The image of a point (x, y) after dilation with center at (0,0) and scale factor 4 can be found by multiplying its coordinates by 4. So:
The image of T(-7, -6) is T'(-74, -64) = (28, 24).
The image of U(-8, 3) is U'(-84, 34) = (-32, 12).
The image of X(2, 1) is X'(24, 14) = (8, 4).
Next, we apply the transformation (x, y) ⟶ (x − 3, y + 1) to find the coordinates of the final image of the triangle.
The image of T' is T'' = (T'x - 3, T'y + 1) = (28 - 3, 24 + 1) = (25, 25).
The image of U' is U'' = (U'x - 3, U'y + 1) = (-32 - 3, 12 + 1) = (-35, 13).
The image of X' is X'' = (X'x - 3, X'y + 1) = (8 - 3, 4 + 1) = (5, 5).
Therefore, the coordinates of the image of triangle △TUX after dilation with center at (0,0) and scale factor 4, then applying the transformation (x, y) ⟶ (x − 3, y + 1) are T''(25, 25), U''(-35, 13), and X''(5, 5).
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can you please solve? thank you
The numeric values for the composite functions are given as follows:
p(q(2)) = 7.q(p(2)) = 3.What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the function rule presented as follows:
(f ∘ g)(x) = f(g(x)).
For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).
Using the definitions of p(x) and q(x) given in this problem, the composite function of p and q is given as follows:
[tex]p(q(x)) = p(\sqrt{x + 2}) = (\sqrt{x + 2})^2 + 3 = x + 2 + 3 = x + 5.[/tex]
Hence the numeric value at x = 2 is given as follows:
2 + 5 = 7.
The composite function of q and p is given as follows:
[tex]q(p(x)) = q(x^2 + 3) = \sqrt{x^2 + 3 + 2} = \sqrt{x^2 + 5}[/tex]
Hence the numeric value at x = 2 is given as follows:
sqrt(2^2 + 5) = sqrt(9) = 3.
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Is there enough information to prove the triangles congruent? If yes, write which pistulate can be used and write a congruence statement for the triangle. If no, write not enough information.
The Congruency Postulates for each of the given triangle are:
1) SAS Congruency
2) AAS Congruency
3) HL Congruency
4) Not enough Information
5) AAS Congruency
How to Identify Congruent Triangles?
There are different congruency postulates such as;
SSS: Side Side Side Congruency
SAS: Side Angle Side Congruency
ASA: Angle Side Angle Congruency
AAS: Angle Angle Side Congruency
HL: Hypotenuse Leg Congruency
1) We are given two triangles with two congruent sides and the included angle and as such it is congruent by SAS Congruency Postulate.
2) We are given two congruent angles and the included side and as such they are congruent by AAS Congruency Postulate.
3) We are given the hypotenuse and leg as congruent and as such we can say that they are congruent by HL Congruency Postulate.
4) We are given two congruent sides and the non-included angle and as such they are not congruent by any congruency postulate.
5) We are given two congruent angles and the non-included side and as such they are congruent by AAS Congruency Postulate.
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Find the measurment of line segement
DE and EF?
The length of the measurements are;
EF = 7. 1 units
DE = 7. 0 units
How to determine the measurementUsing the sine trigonometric identity, we have that;
sin θ = opposite/hypotenuse
Given that;
Opposite side = DE
Hypotenuse = DF
Substitute the values
sin 45 = DE/10
Find the value and substitute
DE = 0. 7071(10)
DE = 7. 0
Using the Pythagorean theorem;
EF² = 10² - 7²
find the square value
EF = √ 51
EF = 7.1
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Which system of inequalities is represented by the graph?
The inequalities that are represented by the given graph are expressed as;
y - x > 0 and y ≥ 1
How to interpret Inequality Graph?Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.
The general form of the equation of a line in slope intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
For the dashed line, shading is above the line, the y-intercept is 0.
Slope is 1. Thus, equation is;
y - x > 0
For the horizontal line, the inequality is expressed as;
y ≥ 1
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Which statement best describes discretionary government spending?
Back
A. A fixed amount of money spent on the same categories every year
B. The money used to pay for Social Security and Medicare
C. A changing amount of money spent on different categories each year
D. Money that you determine how it is spent by the government when you submit your taxes
Select an answer
C. A changing amount of money spent on different categories each year
What is amount?Amount is a term used to describe a quantity of something, typically money. It is often used to refer to the total value of a financial transaction or the sum of multiple payments. Amount can also refer to any other quantifiable measure, such as a number of items, units of time, or a volume or quantity of something.
Discretionary government spending is a type of government spending that is determined each year by the Congress, and typically includes funds for defense, education, infrastructure, and other government programs. The amount of money spent on each category can vary from year to year, making it a type of changing, or discretionary, spending.
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Find x.
X
17
45°
Simplify answer to the simplest form of radical. No decimal.
Check the picture below.
m=-1 b=0 what does y equal
Answer:
-x.
Step-by-step explanation:
1) the equation of the line in slope-interception form is: y=slope*x+interception;
2) according to the graph and data in the condition slope=-1, interception=0, then the requred equation is:
y=-x.
Kristoff needs to fill in the blanks below to factor x2 - 12x + 20. Which of the following is
NOT true about the missing values?
Answer:
c. The numbers must have a sum of 12.
Step-by-step explanation:
Given a polynomial [tex]x^2+cx+d[/tex], in its factored form, [tex](x+a)(x+b)[/tex], the following must be true:
[tex]a + b = c[/tex]
[tex]a \cdot b = d[/tex]
In the given polynomial, we can assign the following values:
[tex]c = -12[/tex]
[tex]d=20[/tex]
Using these values, we can go through the answer choices:
Remember: we are finding the statement that is NOT true.
a) "the numbers must have a product of 20"
If we look at the equation [tex]ab = d[/tex], we can see that this statement is correct; therefore, we should not check it.
b) "the numbers must both be negative"
This is not necessarily true, as a positive plus a negative can still result in a negative; however, in this case, it is true (if we factor, we get a = -2, b = -10).
c) "the numbers must have a sum of 12"
This is false, since c = -12. The numbers (a and b) must add to negative 12, not positive 12; therefore c) is the correct answer.
a) If y = x² - 2, what is the value of y when
x2
x = 3?
b) Some points on the graph of y = x² – 2
have been plotted.
Use your answer to part a) to work out which
of the points A-E is correct.
-3
-2
*1
Y
20-
15-
10+
5-
0
-5+
*1
2
*A
*B
*C
*D
3x Ex
The value of y when x=3 is y=7. Point A on the graph corresponds to x=3 and y=7.
What is graph ?
A graph is a visual representation of data or mathematical functions. Graphs are used to display data in a way that is easy to understand and interpret. There are many types of graphs, including line graphs, bar graphs, pie charts, scatter plots, and more. Each type of graph has its own unique features and is used for different purposes. Graphs are commonly used in many fields, including science, economics, finance, and engineering, among others, to visualize data and communicate information in a clear and concise way.
According to the question:
a) If x = 3, then:
y = x² - 2
y = 3² - 2
y = 9 - 2
y = 7
Therefore, when x = 3, y = 7.
b) From the graph, we can see that the point (3,1) corresponds to x = 3 and y = 1. Therefore, point A is the correct point on the graph that corresponds to x = 3 and y = 7.
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In order to develop a more appealing cheeseburger, a franchise uses taste tests with 8 different buns, 5 different cheeses,2 types of lettuce,and 3 types of tomatoes. If the taste test were done at one restaurant by one tester who takes 10 minutes to eat each burger ,approximately how long would it take the tester to eat all possible cheeseburgers ?
Answer: So it will take 90 hours (which is 3.75 days or 3 days, 18 hours) to eat all the possible cheeseburgers.
Step-by-step explanation:
There are 9 x 6 x 2 x 5 = 540 different cheeseburgers
So...
(540 cheeseburgers)*(10 minutes/1 cheeseburger) = 540 x 10 = 5400 minutes
Convert to hours to get
(5400 min)*(1 hr/60 min) = 5400/60 = 90 hours
Test Prep While working at the school store, John sold a jacket for $40.00 and notebooks for $1.50 each. If he collected $92.50, how many notebooks did he sell?
Answer: 35
Step-by-step explanation:
So we already know he sold $40 worth jacket so lets subtract that from 92.50
92.50-40= 52.5
So he sold $52.5 worth of notebooks
since we know each notebook costs 1.50 all we have to do is divide
52.5 / 1.50 = 35
He sold 35 notebooks
Evaluate the following piece wise function.
Find the values of :
F(-2) =
F(4) =
3F(0) =
10F(14) =
110 is the value of x in function .
What exactly are function and example?
A function is a type of rule that produces one output from one input. This is illustrated by the equation y=x2. You only get one output for y if you enter anything for x.
Considering that x is the input value, we would state that y is a function of x.
f(x) = { 5; x< 1 }
{ -1/2x + 4 ; x≥ 1 }
f(4) = { -1/2 * 4 + 4 }
= { -2 + 4 }
= { 2 }
f( -2) = { -1/2 * -2 + 4 }
= { 1 + 4 }
= 5
3f(0) = { -1/2 * 0 + 4 }
= { 0 + 4}
= 4 * 3 = 12
10f(14) = ( -1/2 * - 14 + 4 )
= 7 + 4
= 10 * 11 = 110
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What is 1500+7y > 4700
Answer:
Step-by-step explanation:
1500+7y > 4700 can be solved algebraically to find the value of y that satisfies the inequality.
First, we need to isolate the variable y on one side of the inequality by subtracting 1500 from both sides:
1500 + 7y - 1500 > 4700 - 1500
Simplifying the left-hand side:
7y > 3200
Finally, we isolate y by dividing both sides by 7:
y > 3200/7
Therefore, the solution to the inequality is y > 457.14 (rounded to two decimal places).
PLEASEEE HURRY 15 POINTS
Joseph wants to buy a tennis racket and some cans of tennis balls.
The tennis racket costs $85
Each can of tennis balls costs $2.50
There is no sales tax
A. 2.50x + 85 < 125
B. 2.50x+85≤125
C. 2.50x+85>125
D. 2.50x+85≥125
Answer:
A. 2.50x + 85 < 125.
Step-by-step explanation:
Let x be the number of cans of tennis balls that Joseph wants to buy.
The total cost of the tennis racket and x cans of tennis balls is:
Cost = 85 + 2.5x
Joseph wants to make sure that he spends less than $125, so we can set up the inequality:
85 + 2.5x < 125
Simplifying this inequality, we get:
2.5x < 40
x < 16
So Joseph can buy at most 15 cans of tennis balls if he wants to spend less than $125.
However, the question asks for the correct inequality, and the inequality that correctly represents this situation is:
2.50x + 85 < 125
Therefore, your answer is gonna be A. 2.50x + 85 < 125.
Answer: "B"
Step-by-step explanation:
Joseph wants to buy some tennis balls. Which costs 2.50$ and tennis racket costs 85$
then, 2.50x+85<125
i need help with question 5
Let U represent the set of people in a certain community who were asked if they subscribe to an information source.
Let D ={ x ∈ U | x subscribes to The Daily Informer }
and
N ={ x ∈ U | x subscribes to News Magazine }
(Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to exactly one of the two news sources given.
a) N ∪ D
b) ( N ∩ D )c
c) ( N c ∩ D ) ∪ ( N ∩ D c )
d) ( N c ∪ D ) ∩ ( N ∪ D c )
e) N c ∩ D
( N c ∩ D ) ∪ ( N ∩ D c ) This set represents the people surveyed who subscribe to exactly one of the two news sources given.
What is surveyed?Surveyed means to gather information or feedback from a specific group of people through interviews, questionnaires, or other methods of data collection. Surveying can be used to gain insights into opinions, attitudes, and behaviors of a certain population or group. Surveying helps to provide information on topics such as public opinion, market research, and customer needs.
It is a combination of two sets, the first being the set of people surveyed who do not subscribe to The Daily Informer but subscribe to News Magazine, and the second being the set of people surveyed who subscribe to The Daily Informer but not to News Magazine.
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Perform the following conversion:
2,748 yd to km
Using the unitary method and the conversion factor, we found the value of 2748 yards in km as 2.512 km.
What is meant by the unitary method?The unitary method is a strategy for problem-solving that involves first determining the value of a single unit and then multiplying that value to determine the required value. Therefore, the goal of this method is to establish values in relation to a single unit. Always write the things that need to be calculated on the right side and the things that are known on the left side to simplify things. The unitary approach must be applied whenever we need to determine the ratio of one quantity to another.
We are given the length as 2748 yards.
Now, this is to be converted to km.
This can be done using the unitary method.
The unitary method uses the single unit's value to find the value of multiple units.
But first, we must find the conversion factor.
1 yard = 0.000914 km
So the value of 2748 yards in km is
2748 * 0.000914 = 2.512 km
Therefore using the unitary method and the conversion factor, we found the value of 2748 yards in km as 2.512 km.
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Huntington’s disease is a genetic disorder that doesn’t appear until the middle adult years. Because of this, many victims of the disease have children before they know they are sick. Their children have a one-in-two chance of developing the disease.
Of the next 10 children born to couples where one of the parents has the disease, what is the probability that exactly 5 of them will get Huntington’s disease?
What is the probability that exactly 7 of the ten will get Huntington’s disease?
The probability of exactly 5 out of the next 10 children getting Huntington's disease is 0.2461, and the probability of exactly 7 getting the disease is 0.1172.
What is the probability?
Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.
This problem can be solved using the probability , where we have a fixed number of trials (10 children) and a fixed probability of success (one-in-two chance of getting the disease).
The probability of getting exactly k successes in n trials, each with probability p of success, is given by the binomial probability formula:
P(k) = (n choose k) * [tex]p^k * (1-p)^{(n-k)[/tex]
where (n choose k) is the binomial coefficient, which represents the number of ways to choose k items out of a set of n.
For this problem, we have n = 10, p = 1/2 (since the children have a one-in-two chance of getting the disease), and we want to find P(5) and P(7).
P(5) = (10 choose 5) * ([tex]1/2)^5 * (1/2)^{(10-5)} = 0.2461[/tex] (rounded to four decimal places)
P(7) = (10 choose 7) * [tex](1/2)^7 * (1/2)^{(10-7)} = 0.1172[/tex] (rounded to four decimal places)
Hence, The probability of exactly 5 out of the next 10 children getting Huntington's disease is 0.2461, and the probability of exactly 7 getting the disease is 0.1172.
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Determine if the expression 1 is a polynomial or not. If it is a polynomial,
state the type and degree of the polynomial.
Polynomials consist of variables, constants and exponents.
(6x - 1)/ 6x is not a polynomial.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The expression is given as:
⇒ (6x - 1)/ 6x
Hence, We can Split the expression as;
⇒ (6x - 1)/ 6x
⇒ 6x/6x - 1/ 6x
⇒ 1 - 1/6x
Simplify as;
⇒ 1 - (1/6)x⁻¹
Thus, The smallest exponent of a polynomial is 0.
And, The above expression has a negative exponent of x.
Hence, The expression is not a polynomial.
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4x+3y= -15 , 24y = 24x +48
I need m & b for both. Also the graphing
The slope m of the first equation is [tex]-\frac{4}{3}\\[/tex] and the y-intercept b is -5 and slope m of the second equation is 1 and the y-intercept b is 2.
What is equation of line?The formula for a straight line is y=mx+b where c is the height at which the line intersects the y-axis, also known as the y-intercept, and m is the gradient.
According to question:To find the slope-intercept form of the equations and their graphs, we need to solve for y in each equation.
[tex]$$4x+3y=-15$$$$3y=-4x-15$$[/tex]
[tex]$y=-\frac{4}{3}x-5$[/tex]
So the slope m of the first equation is [tex]-\frac{4}{3}\\[/tex] and the y-intercept b is -5.
For the second equation,
24y=24x+48
y=x+2
So the slope m of the second equation is 1 and the y-intercept b is 2.
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Suppose a brewery has a filling machine that fills 12-ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.23 ounces and a standard deviation of 0.04 ounce. The company is interested in reducing the amount of extra beer that is poured into the 12 ounce bottles. The company is seeking to identify the highest 1.5% of the fill amounts poured by this machine. For what fill amount are they searching? Round to the nearest thousandth.
The company is searching for a fill amount of 12.305 ounces to identify the highest 1.5% of fill amounts poured by the filling machine.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given mean of 12.23 ounces and a standard deviation of 0.04 ounces.
To find the fill amount for the highest 1.5% of the fill amounts
we need to find the z-score corresponding to the 98.5th percentile
Using a standard normal distribution table or calculator, we find that the z-score corresponding to the 98.5th percentile is 1.81.
The formula for converting a z-score to a raw score is:
x = μ + zσ
where x is the raw score we want to find, μ is the mean, z is the z-score, and σ is the standard deviation.
x = 12.23 + 1.81(0.04)
x = 12.305 ounces
Therefore, the company is searching for a fill amount of 12.305 ounces to identify the highest 1.5% of fill amounts poured by the filling machine.
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To create a modified box plot for a data set, determine the outliers of the data set and the smallest and largest numbers in the data set that are not outliers. Next, determine the median of the first half of the data set, the median of the entire data set, and the median of the second half of the data set.
What are the values that are needed to create a modified box plot for this data set?
19, 15, 22, 35, 16, 22, 4, 22, 24, 16, 17, 21
Enter your answers in the blanks in order from least to greatest.
Smallest number in the data set that is not an outlier is 15, Median of the first half is 17, Median of the entire data set is 20.5. Median of the second half is 22. Largest number in the data set that is not an outlier is 35.
Give a short note on Median?In statistics, the median is a measure of central tendency that represents the middle value in a dataset. To find the median, the data must first be sorted in ascending or descending order. If the dataset contains an odd number of values, the median is the middle value. If the dataset contains an even number of values, the median is the average of the two middle values.
The median is a useful measure of central tendency in datasets that are skewed or have outliers, as it is less sensitive to extreme values than the mean. It is also useful in datasets with non-numeric values, such as rankings or survey responses.
To create a modified box plot, we need the following values:
The smallest number in the data set that is not an outlier: 15The median of the first half of the data set: 17The median of the entire data set: 20.5The median of the second half of the data set: 22The largest number in the data set that is not an outlier: 35So the values needed to create a modified box plot for this data set are: 15, 17, 20.5, 22, 35.
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Answer:
4, 15, 16, 17, 19, 21, 22
Step-by-step explanation:
Find also the projection of b = (0,3,0) onto a3 = (2
3
,−
1
3
,
2
3
), and add the three projections. Why is P = a1a
T
1 +a2a
T
2 +a3a
T
3
equal to
Addition of the 3 projections will be: (-2.268, 0.168, -1.536)
What do you mean by a matrix?A matrix is a rectangular array of values that are defined for addition, subtraction, and multiplication among other mathematical operations. The number of rows and columns in a matrix, also known as the order of the matrix, defines the size of the matrix. The order of a matrix with 6 rows and 4 columns is shown when written as a 6 4 and read as 6 by 4.
To find the projection of b onto a3, we use the projection formula:
proj a3(b) = (b dot a3 / [tex]||a3||^2[/tex]) * a3
where "dot" represents the dot product and "|| ||" represents the magnitude or norm.
We first find the dot product:
b dot a3 = (0)(23) + (3)(-13) + (0)(23) = -39
Next, we find the norm of a3:
[tex]||a3||^2 = (23)^2 + (-13)^2 + (23)^2 = 1388[/tex]
Using these values, we can compute the projection:
proj a3(b) = (-39 / 1388) * (23, -13, 23) = (-0.768, 0.436, -0.768)
Similarly, we can find the projections of b onto a1 and a2:
proj a1(b) = (-3 / 14) * (2, 4, 4) = (-3/7, -6/7, -6/7)
proj a2(b) = (3 / 18) * (-3, 3, 0) = (-1/2, 1/2, 0)
Finally, we add the three projections:
(-3/7, -6/7, -6/7) + (-1/2, 1/2, 0) + (-0.768, 0.436, -0.768) = (-2.268, 0.168, -1.536)
To see why P = a1aT1 +a2aT2 +a3aT3, we note that each projection can be written in matrix form:
proj_a1(b) = a1(aT1b)
proj_a2(b) = a2(aT2b)
proj_a3(b) = a3(aT3b)
where aT represents the transpose of a. Using these expressions, we can write:
P = a1(aT1b) + a2(aT2b) + a3(aT3b)
= [a1 a2 a3] [aT1b aT2b aT3b] (by distributing the dot product)
= [a1 a2 a3] [b] (since the aT's are row vectors that multiply with b to form a scalar)
= abT
where abT is the outer product of a and b, which is a matrix. This matrix is the projection matrix that projects vectors onto the subspace spanned by the columns of A.
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-
The sum of a number times 7 and 29 is at most − 26.
Use the variable b for the unknown number.
Using the variable b for the unknown number, we have the expression 7b + 29 ≤ - 26.
What is a variable?In algebra, a variable is a symbol (typically a letter) used to represent an unknowable numerical value in an equation. The variables x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s are frequently used (arc length).
The sum of a number times 7 and 29 is at most -26 .
The inequality in the mathematical form will be written as below:-
7b + 29 ≤ -26.
Therefore, the inequality will be written as 7b + 29 ≤ - 26.
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You run around the perimeter of a baseball field at a rate of at least 10 feet per second. Which of the following are possible amounts of time that it takes you to run around the baseball field?
Any amount of time greater than or equal to 85 to 90 seconds is a possible amount of time it takes to run around the baseball field at a rate of at least 10 feet per second.
What is area of circle ?
For calculating the amount of space occupied by a circular field or plot, use the area of the circle formula. If you already have a plot that needs fencing, using the area formula will allow you to determine how much fencing is needed. Or, if you need to purchase a tablecloth, how much cloth would be required to completely cover it?
In order to solve such problems, the concepts of area and perimeter are introduced in mathematics. But the question of "does a circle have volume?" is one that most people frequently ask. "No" is the response. A circle has no volume because it is a two-dimensional shape. It only has a perimeter and an area.
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Complete Question:
You run around the perimeter of a baseball field at a rate of at least 10 feet per second. Which of the following are possible amounts of time that it takes you to run around the baseball field?
85 seconds
90 seconds
95 seconds
100 seconds