The median's class interval is 20 hours and 30 minutes. And the average number of hours is thought to be 26.17.
Who defines median?The median is the exact middle value of a dataset after it has been sorted. A measure of central tendency is the distance between the bottom 50% of data and the top 50% of values. The methods for determining the median will vary depending on whether you have an odd or even number of data points.
the class interval that have median.
total is frequency is as -
∑f = 30
median class of corresponds to half of the value
∑th is the value
i.e. 15th value.
least cumulative frequency higher than or equal to 15 is obtained by accumulating frequencies starting at the top.
[tex]2+8+9=19[/tex]
So, corresponds to the class interval = [tex]20 < h\leq 30.[/tex]
Hence, median class is [tex]20 < h\leq 30.[/tex]
Since this is a grouped data we use the midpoint
The median:-
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if y varies jointly as x and the inverse of z and y = -5 and x = -5 and z = 6, find y when x = 5 and z = -8
Step-by-step explanation:
y varies inversely as x=
y= k/xz
-5= k(-5)/6
k= 6
y=6/xz
y=6/5×-8
y= -3/20
( r - 8 ) - ( r + 15 )
Find the Sum or Difference! :)
Answer:
-23
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
Answer:-23 ITS SUPER EASY:0
Step-by-step explanation:
Open up the parenthesis
R - 8 - R - 15
R - R - 8 - 15
-23
11. - a? - 2bc - Icl
if a = -2, b = 3,
and c = -3
problem in the photo
algebra
The value of expression - a² - 2bc - |c| if a = -2, b = 3, and c = -3, is 11.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
Given:
- a² - 2bc - |c|, a = -2, b = 3, and c = -3,
Plug the values of a, b, and c as shown below,
- a² - 2bc - |c| = -(-2)² - 2 × (3) × (-3) - |-3|
- a² - 2bc - |c| = - 4 - 6 × (-3) - 3
- a² - 2bc - |c| = -4 + 18 - 3
- a² - 2bc - |c| = 18 - 7
- a² - 2bc - |c| = 11
Thus, the value of the expression is 11.
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Find the explicit formula for an arithmetic sequence with a common difference of 8 and whose first term is -2.
The explicit formula of the sequence is aₙ = -10 + 8n
How to determine the explicit formula of the sequence?From the question, we have the following sequence that can be used in our computation:
The first term and the common difference
These values of the first term and the common difference are given as
First term = -2
Common difference = 8
The interpretation of the above sequence is that the 8 is added to the previous term to get the current term
Using the above as a guide,
So, we have the following representation
aₙ = aₙ₋₁ + 8
When represented explicitly, we have
aₙ = a + (n - 1) * d
Where
a = -2 and d = 8
Substitute the known values in the above equation, so, we have the following representation
aₙ = -2 + (n - 1) * 8
Evaluate the products
aₙ = -2 + 8n - 8
Evaluate the like terms
aₙ = -10 + 8n
Hence, the explicit formula is aₙ = -10 + 8n
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Match the following factored-form quadratics with their equivalent standard form
The factored quadratic functions with their equivalent standard form are given as follows:
1. e -> x² - 3x - 10 = (x - 5)(x + 2)
2. a -> x² + 7x - 10 = (x + 5)(x + 2).
3. c -> x² - 7x + 10 = (x - 5)(x - 2).
4. d -> x² - 2x - 63 = (x - 9)(x + 7)
5. f -> x² + 2x - 63 = (x + 9)(x - 7).
6. b -> x² + 16x + 63 = (x + 7)(x + 9).
How to factor a quadratic function?A quadratic function is defined as follows:
y = ax² + bx + c.
A quadratic function can be factored as a function of it's roots x* and x**, as follows:
y = a(x - x*)(x - x**).
For item a, the function is given as follows:
y = x² + 7x + 10.
The coefficients are given as follows:
a = 1, b = 7, c = +10.
The discriminant is of:
D = 7² - 4(1)(10)
D = 49 - 40
D = 9.
Hence the first root is of:
x = (-7 - square root of 9)/2
x = -5.
The second root is of:
x = (-7 + square root of 9)/2
x = -2.
Meaning that the factored expression is given as follows:
y = (x + 5)(x - 2).
Matched with the second expression of column A.
The same procedure is followed for the remaining quadratic functions.
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What is the correct equation for a slope of 2 and a y-intercept of -7
Answer:
y=2x-7
Step-by-step explanation:
y=mx+b ==> m is the slope and b is the y-intercept
y=(2)x + (-7) ==> plugin 2 for m=slope and -7 for b = y-intercept
y=2x-7 ==> simplify
is a(b)+a(c) the same as a(b+c)
Answer:
Yes, a(b)+a(c) is the same as a(b+c)
Step-by-step explanation:
a(b)+a(c) is the same as a(b+c). We call it distributive property in math.
What is the use of if __ name __ == '__ main __' in Python?
The use of if__name__ == '__main__' in python is to check whether the current script is being run on its own or being imported somewhere else by combining it with if statement.
Here we need to find the use of if __ name __ == '__ main __' in Python.
Basically, in python the term Allows You to Execute Code When the File Runs as a Script, but Not When It’s Imported as a Module
Here for most practical purposes, this is known as the conditional block that you open with if __name__ == "__main__" as a way to store code that should only run when your file is executed as a script.
Therefore, the function is used as a variable defined for each script that defines whether the script is being run as the main module or it is being run as an imported module.
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How do you check if a trinomial is a perfect square trinomial?
The binomial equation can be squared to provide an expression that is a perfect square trinomial.
what is perfect square ?Perfect squares result from squaring an integer. One such example is the number 81, which is a perfect square since it can be derived by squaring 9: 99=81. 144 is a perfect square since it can be generated by squaring the number 12, which results in 12. 169 is a perfect square since it can be squared to produce the number 13. mathematics-specific language Informally: When an integer (a "whole") number, whether positive, negative, or zero, is multiplied by itself, the result is referred to as a square number, a perfect square, or simply "a square". Accordingly, all square numbers are 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
The binomial equation can be squared to provide an expression that is a perfect square trinomial.
If and only if a trinomial that takes the form ax 2 + bx + c satisfies the requirement b 2 = 4ac is considered to be a perfect square.
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What is the smallest positive integer that is both a multiple of $7$ and a multiple of $4$?
The smallest positive integer that is both multiple of 4 and 7 is 2
What are multiples?In mathematics, multiples are the results of multiplying an integer by a given number.
The given numbers for this problem are 4 and 7. The positive multiples of 4 and 7 will be listed and the first number that appeared in the both multiples s the smallest positive integer that is both a multiple of 7 and a multiple of 4.
The multiples of 4
4 8 12 16 20 24 28 32 36 .......
The multiples of 7:
7 14 21 28 35 42 49 56 63 70 77 84 91 98 .....
The smallest common multiple is 28
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help i have 5 mins left
Answer: c = P - a - 5
Step-by-step explanation:
P= a + 5 + c
P - a - 5= c
PLEASE HELPPP
what is the simplified expression for (picture below)
Answer:
[B] 6²
Step-by-step explanation:
Given:
[tex]\frac{6^4\cdot \:6^3}{6^5}[/tex]
Solve:
Add the exponents - [tex]6^4 \times 6^3=6^7[/tex]
Now we have - [tex]\frac{6^7}{6^5}[/tex]
Exponent Rule: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]
Which means - [tex]\frac{6^7}{6^5}=6^{7-5}[/tex]
Subtract the exponent - [tex]6^2[/tex]
Hence, the answer is [B] 6²
RevyBreeze
A newsletter publisher believes that less than 68% of their readers own a Rolls Royce. Is there sufficient evidence at the 0.02 level to substantiate the publisher's
claim?
State the null and alternative hypotheses for the above scenario.
Null hypothesis (H0): The proportion of newsletter readers who own a Rolls Royce is greater than or equal to 0.68.
Alternative hypothesis (H1): The proportion of newsletter readers who own a Rolls Royce is less than 0.68.
What is the hypothesis?In statistics, hypothesis testing is the process by which an analyst tests an assumption about a population's parameter. Using sample data, hypothesis testing is performed to examine the plausibility of a theory.
In this scenario, we can set up the null and alternative hypotheses as follows:
Null hypothesis (H0): The proportion of newsletter readers who own a Rolls Royce is greater than or equal to 0.68.
Alternative hypothesis (H1): The proportion of newsletter readers who own a Rolls Royce is less than 0.68.
In order to determine if there is sufficient evidence to support the publisher's claim, we would need to conduct a statistical test to determine if the proportion of newsletter readers who own a Rolls-Royce is significantly less than 0.68. The significance level of 0.02 is used to determine the level of evidence required to reject the null hypothesis.
If we run a test, if the p-value is below 0.02, we can reject the Null hypothesis and conclude that the evidence is sufficient to show that the proportion of newsletter readers who own a Rolls Royce is less than 0.68, and thus the publisher's claim is substantiated.
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What is the first month in which the board will see the cumulative total number of cars shipped to Japan exceeded the cumulative total in Vietnam
The cumulative total in Vietnam j(n) is 23(n-1),cumulative takes into account all data up to the present. In month four, j(n) will be worth more than v(n).
Is the sum the same as the total?The distinction between total and cumulative is that total refers to the entirety of something, whereas cumulative takes into account all data up to the present.
When a new number is added to a series of numbers, the running total is updated by adding the new number's value to the previous running total. Partially sum is another name for it. Running totals serve two distinct objectives.
We take it for granted that you mean that vehicles delivered to Vietnam should be modeled by v(n) = 5 + 11 and those sent to Japan by j(n) = 23(n-1).
In month four, j(n) will be worth more than v(n).
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Dilate line f by a scale factor of 3 with the center of dilation at the origin to create line f'. Where are points A' and B' located after dilation, and how are lines f and f' related ?
O The locations of A' and B' are A' (0, 2) and B' (6, 0); lines f and f' intersect at point A.
O The locations of A' and B' are A' (0, 6) and B' (2, 0); lines f and f' intersect at point B.
O The locations of A' and B' are A' (0, 2) and B' (2, 0); lines f and f' are the same line.
O The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
To explain this using a formula, we can use the dilation formula. This formula states that for any point (x,y) on the original line (f), when dilated with a scale factor of k and the center of dilation is the origin (0,0), the coordinates of the point on the new line (f') would be (kx, ky).
For point A, which has coordinates (2,0) on line f, when dilated with a scale factor of 3 and the center of dilation being the origin, the coordinates of point A' on line f' would be (3 * 2, 3 * 0) = (6, 0).
Similarly, for point B, which has coordinates (0,2) on line f, when dilated with a scale factor of 3 and the center of dilation being the origin, the coordinates of point B' on line f' would be (3 * 0, 3 * 2) = (0, 6).
Since the two lines have the same slope, line f and line f' are parallel.
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The state transportation commission counted cars traveling east and west across a toll bridge. The commission counted 486 cars traveling east and 189 cars traveling west. What percentage of the cars were traveling east?
The percentage of cars traveling east is 28% of the total number of cars.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, The commission counted 486 cars traveling east and 189 cars traveling west.
We know percentage change we'll divide the net amount change by the original amount and multiply it by 100%.
From this concept, the percentage of the cars were traveling east would be
The cars traveling east divided by the total numbers of cars time s100%.
= (189/486 + 189)×100%.
= (189/675)×100%.
= 0.28×100%.
= 28%.
So, 28% of the total cars traveling east.
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It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle
formed by third base, second base, and home plate. What can you conclude about the distance from first base to home plate, and from home plate to third base? Explain using your knowledge of congruent triangles.
Distance between first base to home plate and from home plate to third plate are equal.
Given : It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle formed by the third base to home plate ,and from home plate to third base.
The given situation and distance between first base to home plate and from home plate to third plate are equal.
On Converting the given situation into a geometry problem. So we name the require points.
Let A be the home plate,
B is first base,
C is the second base,
And D is the third base.
Now, we can present a geometrical proof:
Statement and their reasons
(1) BC = CD - ( Given )
(2) AC = AC - ( Reflexive Property )
(3) Δ ACD = Δ ACB - ( SAS Congruence - side angle side)
(4) AD = AB - ( CPCTC - Congruent Parts of Congruent Triangles are Congruent )
Therefore, the gap from 1st base to home plate, and from home plate to 3rd plate are equal.
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Which expression simplifies to
m-2
—— ?
m-1
Customary System Units Metric System Units 1 gallon 3.79 liters 1 quart 0.95 liters 1 pint 0.473 liters 1 cup 0.237 liters Approximately how many centiliters are in 3 quarts
3 quarts is equal to approximately 285 centilitres.
To Calculate this we have:
3 quarts is equal to 3 x 0.95 liters = 2.85 liters.
1 litre is equal to 100 centilitres, so 2.85 litres is equal to 2.85 x 100 = 285 centilitres.
Therefore, 3 quarts is equal to approximately 285 centilitres.
In detail, a quart is a unit of measurement in the Customary System Units and is defined as a quarter of a gallon. 1 quart is equal to 0.95 litres. To find out how many centilitres are in 3 quarts, we need to multiply the number of quarts (3) by the conversion factor (0.95 litres per quart). This gives us 2.85 litres. Since 1 litre is equal to 100 centilitres, we can multiply 2.85 litres by 100 to get 285 centilitres. Therefore, 3 quarts is equal to approximately 285 centilitres.
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Graph the following system of equations.
y = 3x + 15
3x + 3y = 9
What is the solution to the system?
There is no solution.
There is one unique solution (-3, 6).
There is one unique solution (0, 15).
There are infinitely many solutions.
Answer:
There is one unique solution (-3, 6)
Step-by-step explanation:
Desmos graphing calculator helps a lot with this stuff
Answer: b) there is only one unique solution (-3, 6)
Step-by-step explanation:
How do you plot a graph step by step?
Plotting a graph step by step is mentioned below.
Define Graph.In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.
What is Bar graph?Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.
There are a few steps to follow when plotting a graph:
Identify the variables in the problem and choose which one to plot on the x-axis and which one to plot on the y-axis.Determine the range of values for each variable. This will help you decide how big to make the scales on the x and y-axis.Choose a scale for each axis. The scale should be such that all the points in the problem can be plotted on the graph. A typical scale is to have equal intervals between each tick mark on the axis.Plot the points on the graph by locating their x-coordinate and y-coordinate on the x-axis and y-axis, respectively, and connecting them with a dot.Draw the x- and y-axes and label them with the appropriate units and ranges. Be sure to include a label on the graph itself so that it's clear what the graph represents.Plot any lines or curves that are also a part of the problem. This could be a line of best fit, a linear regression line, a polynomial function or any other lines or curves that the problem calls for.Once you finished with the line/curve, it is a good practice to give the graph a title and to label the axis with the units used.Lastly, review the graph and ensure that it is accurate and clearly presents the information from the problem.To know more about graph visit:
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Frank is going to plant n vegetable seeds in one garden and 2n +9 vegetable seeds in another. How many seeds is Frank
going to plant?
The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.
What is meant by algebraic expressions?An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).
Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.
Like terms with the same variables are added together.
Let the equation be n + 2n + 9
simplifying the above equation, we get
3n + 9
Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.
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The number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.
What is meant by algebraic expressions?An expression that includes variables, constants, and algebraic operations is known as an algebraic expression in mathematics (addition, subtraction, etc.).
Given that n and (2n + 9) are the seeds that Frank will plant in various gardens, the total number of seeds that Frank will plant can be represented algebraically by combining the two formulas.
Like terms with the same variables are added together.
Let the equation be n + 2n + 9
simplifying the above equation, we get
3n + 9
Therefore, the number of seeds that Frank will plant, expressed in algebraic form, exists 3n + 9.
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Let A, B and C represent distinct non-zero digits. Suppose x is the sum ofall possible 3-digit numbers formed by A, B and C without repetition.Consider the following statements1. The 4-digit least value of x is 1332.2. The 3-digit greatest value of x is 888.Which of the above statements islare correct?
Statement 1 is correct and Statement 2 is not correct.
As A, B and C represent distinct non-zero digits
For least value of x
Let A=1, B=2, C=3
The possible numbers that can be formed using 1,2,3 are 6 {using permutations}
123, 132, 213, 312, 231, 321
x is the sum of all possible 3-digit numbers formed by A, B and C without repetition so
x= 123+ 132+ 213+ 312+ 231+ 321
x=1332
So statement 1 is correct
statement 2 cannot be correct as least value of x is 4-digit so greatest value of x cannot be a three digit number.
The 4-digit least value of x is 1332 so Statement 1 is correct and Statement cannot be correct.
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A grocery tore ha 13%-off ale on all bread. You decide to purchae 6 loave of bread. Let b be the original price of a loaf of bread. Expand the expreion 6(b-0. 13b). Once the expreion i expanded, who do the term repreent
6b - 0.78b it will result after expanding the expression.
What is an expression?A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Any one of the following mathematical operations can be used i.e. addition, subtraction, multiplication, or division.
There are three different expression types:
There is just one arithmetic value that an arithmetic expression may produce.A character expression evaluates to just one character value.One logical value is produced by the evaluation of a logical or relational statement.Let, b represent the original price of a loaf of bread.
Given that,
A grocery store has 13%-off sale on all bread.
This means that the amount by which the price of bread was reduced would be
13/100 × b = 0.13 × b = 0.13b
The new price for the loaf of bread would be: b - 0.13b
you decide to purchase 6 loaves of bread. The expression would be:
6(b - 0.13b)
Expanding the expression, it becomes: 6b - 0.78b
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which answer is this
A.43
B.38
C.61
D.81
Answer:
81
Step-by-step explanation:
by corresponding angles from angle ABC
Jill and beth are sisters. Jill is 1/3 of beth's age. Let b represent beth's age.Write an algebraic expression to show jill's age.
The algebraic expression to show Jill's age will be;
Jill = 1/3 x b
What is an Algebraic Expression?Algebraic expressions are the mathematical statements that are derived when operations such as addition, subtraction, multiplication, division, etc. are operated upon on variables and constants.
There are different parts of an algebraic expression and they are; Variables - a symbol that doesn't have a fixed value is called a variable. It can take any value assigned to it.
Constants - a symbol that has a fixed numerical value is called a constant. All numbers are constants.
Terms - A term is a variable alone (or) a constant alone (or) it can be a combination of variables and constants and the operation of multiplication or division with it.
Coefficients - the numbers that are multiplying the variables are called coefficients.
Beth's age = b
Jill's age = 1/3 of Beth's age
Jill's age = 1/3 x b
Jill's age = 1/3b
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what's the equation of a line in slope-intercept form of a line that has a slope of -6 and contains (3,-4)
HELP ME PLEASE!!!!!!
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{3}) \implies y +4= -6 (x -3) \\\\\\ y+4=-6x+18\implies {\Large \begin{array}{llll} y=-6x+14 \end{array}}[/tex]
How to read linear equations?
To read a linear equation, first, identify the constants and the variable, then determine the coefficient of the variable.
A linear equation is an equation that contains two variables and can be written in the form of ax + b = 0, where 'a' and 'b' are constants and 'x' is the variable. This coefficient will indicate how the variable is related to the constants. Then, solve the equation by isolating the variable to determine its value.
To read a linear equation, start by identifying the constants and the variable. The constant is the numerical value that is not connected to the variable. For example, in the equation "2x + 4 = 0", the constants are '2' and '4'. The variable is the letter that represents the values that can change. In this equation, the variable is 'x'.
Next, determine the coefficient of the variable. The coefficient is the numerical value in front of the variable. It represents how the variable is related to the constants. In this example, the coefficient of 'x' is '2'. This means that the value of 'x' will be twice as much as the constants.
Once the constants, variables, and coefficients have been identified, the equation can be solved.
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6. If ON = x^2 - 10, LM = -2x + 5, NM = 3x + 21 and OL = 4y + 18, find the values of x and y
given that LMNO is a parallelogram.
(show work)
Given that ON = [tex]x^{2}[/tex] - 10; LM = -2x + 5; NM = 3x + 21; and OL = 4y + 18; with x and y values of [tex]\sqrt{10}[/tex] and -4.5, respectively.
What is the values of x and y ?ON = [tex]x^{2}[/tex] - 10 ⇒ [tex]x^2[/tex] = 10 ⇒ x =[tex]\sqrt{10}[/tex]
OL = 4y + 18 ⇒ 4y =-18 ⇒ y = -18/4 ⇒ -4.5 .
The issue at hand is here A parallelogram of O N M L is nm. Suppose ON = [tex]x^{2}[/tex] - 10 or LM = -2x + 5. Here, we must determine what X's value is. then look up N M N O L. Due to the parallelogram shape of ONA male, there are four.
Since N M is equal to the opposing sides of a parallelogram and an e parallelogram, we can express that as follows. due to the parallelogram's equal opposite sides. We can therefore write [tex]x^{2}[/tex] - 10 where N M = O L. that is four, -2x + 5, and. Change the two sides of the equation, then write four. Nine times X is equivalent to [tex]x^{2}[/tex] - 10.
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How do you find angles with AAA?
AAA triangles are impossible to solve further since there is nothing to show us the size.
The AAA triangle is a triangle in which all three angles are given, and the triangle is said to be similar to another triangle if any two of its three angles are equal to any two of its three angles.
Knowing only angle-angle-angle (AAA) is insufficient because it can result in triangles that are similar but not congruent.
There are four shortcuts that can be used to check whether two triangles are congruent.
You don't need to be familiar with all of the six corresponding parts, which include three angles and three sides.
When a triangle's three angles are known but not its sides, the answer is "AAA."
Since there is no information to indicate size, AAA triangles are impossible to solve further. We know their shape but not their size.
Hence, the AAA triangles are not solvable or difficult to find angles.
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