The five-number summary of the given data 18, 15, 1, 14, 18, 11, 12, 20, 13, 19, 14, 8, 24, 18, 17 is ,
Put the numbers in ascending order 1, 8, 11, 12, 13, 14, 14, 15, 17, 18, 18, 18, 19, 20, 24.The minimum is 1 and the maximum is 24The median is 17Find the Lower quartile = 12 , Upper quartile = 19minimum = 1, Q1 = 12, median = 17, Q3 = 19, and maximum = 24.Your data set's five-number summary offers you a general notion of how it is organised. You will, for instance, have your best value and lowest value (the maximum). The main reason you'll want to locate a five-number summary is to find other valuable statistics, like the interquartile range, also known as the middle fifty, even if it's important in and of itself.
The five number summary includes 5 items:
Step 1: Put your numbers in ascending order (from smallest to largest). For this particular data set, the order is:
1, 8, 11, 12, 13, 14, 14, 15, 17, 18, 18, 18, 19, 20, 24.
Step 2: For your data set, determine the lowest and maximum. This ought to be obvious now that your math is correct.
In the example in step 1, the minimum (the smallest number) is 1 and the maximum (the largest number) is 24.
Step 3: Find the median. The median is the middle number.
median = 17
Step 4: (This is not technically necessary, but it makes Q1 and Q3 easier to find).
(1, 8, 11, 12, 13, 14, 14, 15), 17, (18, 18, 18, 19, 20, 24).
Step 5: Find Q1 and Q3. Q1 can be thought of as a median in the lower half of the data, and Q3 can be thought of as a median for the upper half of data.
(1, 8, 11, 12, 13, 14, 14, 15), 17, (18, 18, 18, 19, 20, 24).
Step 6: Write down your summary found in the above steps.
minimum = 1, Q1 = 12, median = 17, Q3 = 19, and maximum = 24.
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Find the principal value of Arctan (-1.44) to the nearest minute.
Answer: To find the principal value of arctan(-1.44) to the nearest minute, we first need to find the value of arctan(-1.44) in radians.
We can use the arctan function in a mathematical software or calculator to find the result. The value of arctan(-1.44) in radians is approximately -0.8623.
Next, we convert the result from radians to minutes, by multiplying the radians by 180/π and then multiplying the result by 60.
-0.8623 * 180/π * 60 = -50.47 minutes
So the principal value of arctan(-1.44) to the nearest minute is approximately -50 minutes.
Step-by-step explanation:
I’m a lil bit confused please help
Answer:
5000
Step-by-step explanation:
10×16=160
160 Btu?
is 5000
because the closesd value in the graph is 5000
for 160
What is the inverse of a function?
A function for which the domain remains the same, and reciprocal values of the range are used
A function for which the values or the domain and the range are interchanged
A function for which the range remains the same, and reciprocal values of the domain are used
The requried, inverse of a function is a function for which the values or the domain and the range are interchanged. Option C is correct.
What is an inverse function?The inverse of a function is a new function that results from interchanging the input (domain) and output (range) of the original function.
Here,
if f(x) is a function, its inverse function is denoted by f⁻¹(x), and it is defined such that f⁻¹(y) = x, where y = f(x) is the original function.
For example, if f(x) = 2x + 3, the inverse function f⁻¹(x) is found by interchanging x and y, and solving for y:
x = 2y + 3
2y = x - 3
y = (x - 3)/2
Therefore, f⁻¹(x) = (x - 3)/2, and it is the inverse of the original function f(x). Note that the domain and range of the inverse function are interchanged with respect to the original function.
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what is 8 1/6-3 7/12
Answer: 4 7/12
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{8\dfrac{1}{6} - 3 \dfrac{7}{12}}[/tex]
[tex]\mathsf{= \dfrac{8\times6 + 1}{6} - \dfrac{3\times12 + 7}{12}}[/tex]
[tex]\mathsf{= \dfrac{48 + 1}{6} - \dfrac{36 + 7}{12}}[/tex]
[tex]\mathsf{= \dfrac{49}{6} - \dfrac{43}{12}}[/tex]
[tex]\mathsf{= \dfrac{49}{6}\times\dfrac{2}{2} - \dfrac{43}{12}\times\dfrac{1}{1}}[/tex]
[tex]\mathsf{= \dfrac{49\times2}{6\times2} - \dfrac{43\times1}{12\times1}}[/tex]
[tex]\mathsf{= \dfrac{98}{12} - \dfrac{43}{12}}[/tex]
[tex]\mathsf{= \dfrac{98 - 43}{12 - 0}}[/tex]
[tex]\mathsf{= \dfrac{55}{12}\rightarrow 4\dfrac{7}{12}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{4\dfrac{7}{12}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]find the dilated coordinates with the scale factor of 1/5
The dilated coordinates:
D(-7, 0) → D' (-7/5, 0)
E(-7, -5) → E' (-7/5, -1)
F(-2, -5) → F' (-2/5, -1)
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
Given:
Coordinates: D(-7, 0), E(-7, -5), F(-2, -5).
The shape is dilated by the scale factor of 1/5.
The dilation rule:
D(-7, 0) → D' (-7/5, 0)
E(-7, -5) → E' (-7/5, -1)
F(-2, -5) → F' (-2/5, -1)
Hence, the dilated coordinates are given above.
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The complete question:
Find the dilated coordinates with the scale factor of 1/5,
D(-7, 0), E(-7, -5), F(-2, -5).
Mike buys 3 oranges and 1 lemon at the
farmers market. What fraction of his
purchase were oranges?
Mike buys 3 oranges and 1 lemon at the
farmers market. What fraction of his
purchase were oranges?
answer :
3/4
Answer: 3/4
Step-by-step explanation:
there are a total of four purchases and three of them were purchases we can represent this with the fraction 3/4
On the defense of a football team,there are three types of players on the field.What is the probability of picking each type of player at random out of the 11 players
Answer: The probability of picking each type of player at random depends on the number of players of each type on the field. If the number of players of each type is not specified, it is not possible to determine the probability of picking each type of player at random.
Step-by-step explanation:
Which three criteria do binomial experiments meet? There are only two trials. The trials are independent. There are only two outcomes per trial. Each outcome is repeatable. The probability of success is the same for each trial.
The three criteria that binomial experiments meet are :
The trials are independent. There are only two outcomes per trial. The probability of success is the same for each trial.What criteria should binomial experiments meet ?The experiment is referred to as a binomial experiment since there are only two possible output values in a binomial experiment. In the case of binomial experiments, the number of independence variables is fixed.
In the case of binomial experiments, the number of independence variables is fixed. The total number of output values for the binomial experiment is 2. For the binomial experiment, each of the two outputs has a 50% chance of happening—50% for success and 50% for failure.
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Answer:
B. The trials are independent.
C. There are only two outcomes per trial.
E. The probability of success is the same for each trial.
Step-by-step explanation:
and then
B. a survey asking 50 people if they like pizza
C. a survey measuring 50 people to see if they are over 6 feet tall
Why is [tex]0,3^{-1}[/tex] = [tex]\frac{10}{3}[/tex] ?
By the inverse of a number, 0.3⁻¹ = 10/3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The expression is,
⇒ 0.3⁻¹ = 10/3
Now, We can simplify as;
⇒ 0.3⁻¹
⇒ (3/10)⁻¹
⇒ 10/3
Thus, By the inverse of a number, 0.3⁻¹ = 10/3
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A business development manager discusses international steel production and economic development at a conference. He passes out this graphic and asks for comments. Which comment about the data is most accurate? Japan’s production has increased and shows no signs of decreasing. China’s steel production is increasing while its major competitors’ production is declining. By 2009, China’s tons of steel produced per US million ($) GDP was 50, about 10 tons less than Japan’s all-time high. At 50 tons of steel produced per US million ($) GDP, China has the highest steel production of all producers shown as of 2009.
The most accurate comment about the graph data is: "China's steel production is increasing while its major competitors' production is declining."
A graph is what?Academics are using graphs to logically chart or graphically depict events or quantities. A graph point is a common way to depict how different things interact. The non-linear storage structure known as a graph is made up of nodes, also referred to as vertices, and lines. Glue ought to be used to connect the edges, also known as nodes , respectively. (4.5).
Here,
The most accurate comment about the data is: "China's steel production is increasing while its major competitors' production is declining."
This is because the graph shows that China's steel production has been steadily increasing since the early 2000s, while the steel production of other major producers such as Japan, the United States, and Germany has been declining or stagnant. This trend is particularly evident after the global financial crisis of 2008-2009.
While it is true that Japan's steel production has increased and shows no signs of decreasing, this comment does not address the overall trend of declining steel production among major producers.
The other two comments are not accurate. The statement "By 2009, China’s tons of steel produced per US million ($) GDP was 50, about 10 tons less than Japan’s all-time high" is not supported by the graph, as there is no information about tons of steel produced per US million ($) GDP on the graph.
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64. Use a graph to estimate the critical numbers of f(x)=| x^3-3x^2+2| correct to one decimal place.
The critical numbers of f (x) = | x³ -3x² + 2| is, x = 0 and x = 2.
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).
Given that;
The function is,
⇒ f (x) = | x³ -3x² + 2|
Now, We know that;
⇒ All the critical points are find as;
⇒ f '(x) = 0
⇒ 3x² - 6x = 0
⇒ 3x(x - 2) = 0
⇒ x = 0
⇒ x = 2
Thus, The critical numbers of f (x) = | x³ -3x² + 2| is, x = 0 and x = 2.
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What would 73,412 be rounded to the nearest thousand
Zachary purchased a computer for $1,300 on a payment plan. Two months after he purchased the computer, his balance was $1,090. Seven months after he purchased the computer, his balance was $565. What is an equation that models the balance y after x months?
The equation ______ models the balance y after x months.
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer.)
Answer:
[tex]y=-105x+1300[/tex]
Step-by-step explanation:
Define the variables:
Let x be the number of months after Zachary purchased a computer.Let y be the balance of the payment plan (in dollars).Given information:
Purchase price of the computer = $1,300Balance = $1,090 after 2 months.Balance = $565 after 7 months.Therefore:
x = 0, y = 1300x = 2, y = 1090x = 7, y = 565[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Determine if the equation is linear by calculating the slope between each pair of (x, y) points:
[tex]\implies \text{Slope}\;(m)=\dfrac{565-1090}{7-2}=-105[/tex]
[tex]\implies \text{Slope}\;(m)=\dfrac{1090-1300}{2-0}=-105[/tex]
As the slope is the same, the equation is linear.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The initial purchase price of the computer was $1,300. So when x = 0, y = 1300. Therefore, the y-intercept is 1300.
We have already calculated the slope as -105.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:
[tex]y=-105x+1300[/tex]
Kelly can run 1/2 mile in 3 minutes. How far does
Kelly run in 1 minute if he runs at the same pace the
entire time?
Kelly can run 1/2 mile in 3 minutes. 1/6 mile Kelly run in 1 minute if he runs at the same pace the entire time.
What makes anything a mile?The word "mile" is derived from the Latin "mille passus," which means "one thousand paces." The English Parliament established the Mile at eight furlongs (one furlong is 660 feet) in 1592. A mile is a unit of measurement that is standardised as exactly 1609.344 metres by the International agreement in 1959. A mile is exactly equivalent to 5280 feet, or 1760 yards.
Kelly can run 1/2 mile in 3 minutes so the ratio is 1/2 mile per 3 minutes
= [tex]\frac{\frac{1}{2} }{3}[/tex]
For transforming 3 to 1 we need to divide by 3 because we have to keep the ratio value, we have to divide also the numerator by 3 :
= [tex]\frac{\frac{1}{2} }{3} \times \frac{\frac{1}{3} }{\frac{1}{3}}[/tex]
[tex]= \frac{\frac{1}{2} \times \frac{1}{3} }{3 \times \frac{1}{3} }[/tex]
= 1/6 / 1
= 1/6
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At a music store, Rita got a $12 discount on an item originally priced at $48. What percent discount did she get?
Answer:
a $12 discount like what is it soupoust to be
Lourdes can buy 3-packs of paper for $10.50, or she can buy 4-packs of paper for $13.50. She wants to buy 12 packs of paper. How much more will she spend if she buys only 3-packs of paper
Lourdes will spend an amount of $1.50 more if she buys only 3-packs of paper.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions.
If Lourdes buys only 3-packs of paper, she will need to buy 12 / 3 = 4 sets of paper.
At $10.50 per set, this will cost her 4 x $10.50 = $42.
If Lourdes buys only 4-packs of paper, she will need to buy 12 / 4 = 3 sets of paper.
At $13.50 per set, this will cost her 3 x $13.50 = $40.50.
So, Lourdes will spend $42 - $40.50 = $1.50 more if she buys only 3-packs of paper.
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find p if (p, 2p+1) is solution of 11x-2y=5
Answer:
p = 1
Step-by-step explanation:
since (p, 2p + 1) is a solution then it makes the equation true.
substitute x = p and y = 2p + 1 into the equation and solve for p
11p - 2(2p + 1) = 5 ← distribute parenthesis and simplify left side
11p - 4p - 2 = 5
7p - 2 = 5 ( add 2 to both sides )
7p = 7 ( divide both sides by 7 )
p = 1
Please help me out! Just put these in order from the picture below.
Answer:
1) {2,0,-2}
2) {1,-3,1}
3) {1,3,5}
4) {0,1,2}
What is the equation of the function that is graphed as line a?
y = 4 x - 3
y = - 1/4 x + 3
y = 1/4x + 3
y = -4 x - 3
Answer:
y = 4x - 3
Step-by-step explanation:
y = mx + b
The m is the slope and the b is the y-intercept.
The slope is 4. If you start at the point (0,-3) and go up 4 units and then 1 unit to the right, you will be back on the line at point (2,4) The slope is the rise over the run. The rise is 4 and the run is 1. 4/1 = 4.
The slope (m) is 4.
The y-intercept is where the line crosses the y axis. It crosses at (0,-3)
The y-intercept (b) is -3
Plug 4 in for m and -3 in for b
y = mx + b
y = 4x -3
Answer:
[tex]y = 4x - 3[/tex]
Step-by-step explanation:
we need to find out the equation of the function that is graphed. From the given graph we can see that the line passes through points (0,-3) and (2,5) . So we can find out the slope of the line as ,
[tex]\implies m =\dfrac{y_2-y_2}{x_2-x_1}=\tan\theta\\[/tex]
[tex]\implies m =\dfrac{-3-5}{0-2} \\[/tex]
[tex]\implies m =\dfrac{-8}{-2} \\[/tex]
[tex]\implies \mathfrak{ m = 4 }\\[/tex]
Now we may use point slope form of the line to find out the equation of the line as,
[tex]\implies y - y_1 = m(x-x_1) \\[/tex]
[tex]\implies y -(-3) = 4(x-0) \\[/tex]
[tex]\implies y +3 = 4x\\[/tex]
[tex]\implies \underline{\underline{ y = 4x -3}} \\[/tex]
And we are done!
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Write the correct domain and range of the relation. {(-4,-4),(-1,3),(0,5),(3,9)}
Answer:
domain: {-4, -1, 0, 3}range: {-4, 3, 5, 9}Step-by-step explanation:
You want the domain and range of the relation {(-4,-4),(-1,3),(0,5),(3,9)}.
DomainThe domain is the set of first numbers of the ordered pairs:
{-4, -1, 0, 3}
RangeThe range is the set of second numbers of the ordered pairs:
{-4, 3, 5, 9}
Answer:
Domain: {-4, -1, 0, 3}
Range: {-4, 3, 5, 9}
Step-by-step explanation:
The Domain is the number that is on the x-axis.
The Range is the number on the y-axis.
Its quite simple. Hope this HELPED! HAVE A GOOD DAY AND NIGHT!!!!!!!!!!
The graph below is the function f(x)
The required answers are:
lim f(x) = -1
1-2-
lim f(x) = -1
1+2+
lim f(x) = -3
r2
f(2) = -3
How to solve thisGiven image has a graph of the function f(x)
To find [tex]\lim_{x\rightarrow 2^-}f(x), lim f(2) 12+, lim f(x) 12 and f(2)[/tex]
We have from the image of the graph the function f(x) is a discontinuous function with x=2 is the point of discontinuity.
Now from the graph the value of f(x) at x=2 i.e. f(2) = -3 as the graph has a bold dot at y=-3.
Next [tex]\lim_{x\rightarrow 2^-}f(x)=\lim_{x\rightarrow 2^+}f(x)=-1[/tex] as in the graph of f(x) it has a small circle at y = -1.
As f(2) = -3 so [tex]\lim_{x\rightarrow 2}f(x)=f(2)=-3[/tex]
Thus the required answers are
lim f(x) = -1
1-2-
lim f(x) = -1
1+2+
lim f(x) = -3
r2
f(2) = -3
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Determine the domain for the interval of decrease.
d
Distance (km)
60
50
40
30
20
10
8 9 10 11 12 1 2 3 4
am
noon
p.m.
Time of the day
A2≤x≤5
B8≤x≤ 10
3≤x≤5
Answer:
The domain for the interval of decrease is 3 ≤ x ≤ 5
Andrew wins 4 fencing bouts for every 3 that he loses. If he had 35 bouts during the last year, how many bouts did he win?
The number of bouts that Andrew won during the last would be = 20 bouts.
How to calculate the number of bouts won?The number of fencing bouts that Andrew won = 4
The number of bouts he losses every 4 wins = 3 bouts
The total number of bouts he is having this year = 35 bouts.
The number of bouts he won amongst the number that he lost would be calculated as;
= 4+3 = 7
= 4/7 × 35/1
= 4× 5 = 20 bouts.
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You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $85.00, two for $83.00 each, and in general the group rate per room is found by taking $2 off the base of $85 for each extra room rented.
(c) Find a formula for a function R = R(n) that gives the total revenue from renting rooms to a convention host.
(d) Use functional notation to show the total revenue from renting a block of 9 rooms to a group. Calculate the value.
The formula for a function R = R(n) is R(n) = n(85 - 2n) and the total revenue for 9 room is $603
How to determine the formula for a function R = R(n)From the question, we have the following parameters that can be used in our computation:
Base fee = $85.00
Rate = $2 off
Using the above as a guide, we have the following:
R(n) = n(85 - 2n)
Where n is the number of rooms
The value of block of 9 roomsThis means that
n = 9
So, the notation is
R(9)
The value is
R(9) = 9 *(85 - 2 * 9)\
R(9) = 603
Hence, the value is $603
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Prove that the value of the expression (3/5x^2-0.4cy-1.5y+1)-(y^2-2/5xy+0.6x^2) does not depend on x
Therefore, we have proved that the value of the expression
(3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.
Expression: What is it?In mathematics, addition, multiplication, and division are necessary. They result in the following when combined: An equation, some data, and a mathematical function Values, parameters, and mathematical operations like additions, subtractions, multiplications, and divisions can all be found in a declaration of fact. Different phrases and words can be compared and evaluated.
Here,
To prove that the value of the expression doesn't depend on x, we need to show that the x-term disappears when we simplify the expression.
Starting with:
(3/5x² - 0.4cy - 1.5y + 1) - (y² - 2/5xy + 0.6x²)
Distributing the negative sign in the second set of parentheses:
3/5x² - 0.4cy - 1.5y + 1 - y² + 2/5xy - 0.6x²
Rearranging the terms by collecting like terms, we get:
(3/5 - 0.6)x² + (2/5y - 0.4c)y - y²- 1.5y + 1
Simplifying further, we get:
(-0.1)x² + (0.4y - 0.4c)y - (y² + 1.5y - 1)
Notice that there is no x-term in the final expression, which means that the value of the expression doesn't depend on x.
Therefore, we have proved that the value of the expression (3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.
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Solve the formula for the indicated variable.
Z=m+mwg for m
m=
(Simplify your answer.)
The value for variable m in equation Z = m + mwg is m = Z - mwg.
What are variables?
The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.
The equation is given as -
Z = m + mwg
To get the value for variable m, subtract mwg from Z and take it to left-hand side.
Z - mwg = m
Reverse the equation and get it in right form -
The equation obtained is -
m = Z - mwg
Therefore, the value is m = Z - mwg .
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suppose 5x^{2} +5x+xy=4 and y(4)=-24. Find y^'(4) by implicit differentiation.
Your answer:
if 5x² +5x+xy=4 then the value of y'(4) is -21/4
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
The given expression is 5x² +5x+xy=4
Five times of x square plus five times of x plus x times of y equal to four.
Differentiate with respect to x.
10x+5+y(x)+xy'(x)
if x=4
10(4)+5+y(4)+4y'(4)=0
40+5-24+4y'(4)=0
21+4y'(4)=0
4y'(4)=-21
Divide both sides by 4
y'(4)=-21/4
Hence, if 5x² +5x+xy=4 then the value of y'(4) is -21/4
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how to get the volume of a rectangular pyramid
Answer:
length x width x height divided by 3
A salesperson earned a commission of
$806.59
last week on gross sales of
$5880
. If returns and allowances were 11.5% of gross sales, what is his rate of commission based on net sales?
Using percentages we know that the rate of commission of the salesperson based on the net sales is 15.5%.
What are percentages?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and sometimes "pc" is also used, the percent symbol, "%," is frequently used to indicate it.
A % is a number without boundaries and without a standard measurement.
So, calculate as follows:
5880/100 * 11.5 = 676.2
Now,
5880 - 676.2 = 5,203.8
Now, calculate the percentage as follows:
806.59/5,203.8 * 100
15.5%
Therefore, using percentages we know that the rate of commission of the salesperson based on the net sales is 15.5%.
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Can somebody help me please
93,101,109,117,125,133,141,149,157,165