The mean is frequently less than the median when the distribution of the data is skewed to the left. The mean is frequently higher than the median when the distribution is skewed to the right.
What is a histogram?
A histogram is a representation of statistical data that makes use of rectangles to display the frequency of data items in a series of equal-sized numerical intervals. The independent variable is plotted along the horizontal axis and the dependent variable is plotted along the vertical axis in the most popular type of histogram.
Left-skewing histograms: As seen in the example below, some histograms will have a left-skewing distribution. Negatively skewed refers to a distribution that is skewed to the left. There are many instances of this type of distribution on the right side's upper-value cells, while there are few instances on the left side's lower-value cells (left side). When information is gathered from a system with a boundary, such as 100, a skewed distribution, such as 100, can result. In other words, none of the data that was gathered has values greater than 100.
Some histograms will display a distribution that is skewed to the right, as shown below. Positive skewness refers to a distribution that is skewed to the right. Large numbers of occurrences in the lower-value cells (left side) and few in the upper-value cells characterize this type of distribution (right side). When information is gathered from a system with a boundary like zero, the distribution may become skewed. In other words, all the data that was gathered has values that are greater than 0.
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What do u round your answer too if the number is 4.65885
Answer:
4.7
Step-by-step explanation: anything over 5 you round up
Use the graph below to determine the values of x at which the function is not continuous. +1; -1). The order The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or of the list does not matter.
The graph shows the discontinuity of the function at x = -1 and x = 1. Therefore, the values of x at which the function is not continuous are -1 and 1.
The graph shows that at x = -1 and x = 1, the graph has a sharp jump in the value of the function. This means that the function is not continuous at those points, and thus the values of x at which the function is not continuous are -1 and 1. The graph represents a mathematical function, and the concept of continuity is crucial in mathematical analysis. A function is considered continuous at a specific point if the value of the function at that point exists and the limit of the function as the input approaches that point is equal to the value of the function at that point. In this particular graph, the function experiences a sharp increase or decrease in its value at the points x = -1 and x = 1. This sudden change in the function's value indicates that the function is not continuous at these points, meaning that its value does not approach a single limiting value as the input approaches these points. Thus, the points -1 and 1 are the values of x at which the function is not continuous.
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ANSWER QUESTION han or em Using the table of equalities, select the correct conversion factors that indicate the number of feet (ft) in one mile (mi). O O O O O Z dit or 082LA U.S. Metric-U.S. 2.54 cm - l in exact) Some Common Equalities Quantity Metric (SD) Length Im-1000 mm 1 cm - 10 mm 1 - 1000 ml 1 dl - 100 ml 1 ml - Icm Mass 1 kg - 1000 1 - 1000 mg Time 1h 60 min 1 min - 605 I ft 12 in 1 yd - 3 11 I mi - 520 ft Iqt4 cups 19 - 2p Igal - 4 1 lb 16 . Volume 1 km 0.621 mi 946 ml. It IL- 1.0691 popor der Ikg - 2.20 lb 4549 - I b I DON'T KNOW YET
The correct conversion factors to indicate the number of feet in one mile is: 1 mi = 5280 ft.
To convert miles to feet, we must use the equality: 1 mi = 5280 ft.
Using the table of equalities, we can see that 1 mi = 5280 ft, so the correct conversion factor to indicate the number of feet in one mile is 1 mi = 5280 ft.
To convert miles to feet, we use the conversion factor of 1 mile being equal to 5280 feet. This means that for every 1 mile, there are 5280 feet. To convert a specific number of miles to feet, we multiply the number of miles by the conversion factor of 5280 feet/mile. For example, if we want to convert 2 miles to feet, we multiply 2 by 5280 to get 10560 feet. Hence, 2 miles is equal to 10560 feet. This conversion factor can be used to convert any number of miles to feet, as long as we use it consistently and accurately.
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Which given value, if any, is a solution of the equation a + 16 = −30 for a: {–46, –14, 14, 36}?
The value of the equation is -46, the correct option is A.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
Given;
The equation; a+16=-30
Now,
a=-30-16
a=-46
Therefore, the answer of equation will be -46
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a signal is monitored every second start at t= 0 when its value is recorde as an integer an example signal might look like 10 3 25 4 30 2 17
At time t=0 the signal value is 10, then it decreases to 3, increases to 25, decreases to 4, increases to 30, decreases to 2 and then increases to 17.
At time t=0 the signal value is 10. This is the starting point for monitoring the signal every second. After one second, the signal value decreases to 3. After another second, the signal value increases to 25. After another second, the signal value decreases to 4. After another second, the signal value increases to 30. After another second, the signal value decreases to 2. Finally, after the last second, the signal value increases to 17. As the signal is monitored every second, it is possible to track its changes over time. This example signal had some fluctuation, with both increases and decreases in the value. It started at 10, decreased to 3, then increased to 25, decreased to 4, increased to 30, decreased to 2, and then increased to 17. This example shows how a signal can fluctuate over time, and how its value can change with each second that passes.
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Jamal owns a small business selling bagels. He knows that in the last week 77 customers paid cash, 27 customers used a debit card, and 21 customers used a credit card.
If next week, he is expecting 400 customers, about how many would you expect to pay with a credit card? Round your answer to the nearest whole number.
Rounded to the nearest whole number, we would expect about 68 customers to pay with a credit card next week.
What is a whole number?A whole number is a positive integer that does not have a fractional or decimal part. Whole numbers are the numbers we use for counting and for representing quantities that are not fractions or decimals. The set of whole numbers includes 0, 1, 2, 3, 4, 5, 6, and so on, with no limit on how high the numbers can go. Whole numbers do not include negative numbers or numbers with fractional or decimal parts.
According to the given informationTo estimate the number of customers who will pay with a credit card next week, we can use the proportion of customers who paid with a credit card last week.
The total number of customers who paid with cash or a debit card is 77 + 27 = 104.
So the proportion of customers who paid with a credit card is 21/(104+21) = 0.1688 (rounded to four decimal places).
To estimate the number of customers who will pay with a credit card next week, we can multiply the expected total number of customers by this proportion:
0.1688 x 400 = 67.52
Rounded to the nearest whole number, we would expect about 68 customers to pay with a credit card next week.
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HELP ME PLEASE
12. A business records its net profits for the week by subtracting the operating costs from
the revenue. The function P(x)=(125x)-(40x+1,200) represents the profits for one
week, where x is the number of products sold.
Which statement is true?
a) The slope of the function is 85, and it represents the change in net profit per product
sold.
b) The slope of the function is 85, and it represents the initial operating costs of the
business.
c) The slope of the function is 125, and it represents the change in net profit per product
sold.
d) The slope of the function is 125; and it represents the initial operating costs of the
business.
The correct statement regarding the linear function is given as follows:
a) The slope of the function is 85, and it represents the change in net profit per product sold.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
The slope m represents the rate of change of the output variable relative to the input variable.The intercept b represents the initial value assumed by the output variable.The function for this problem is given as follows:
P(x) = 125x - (40x + 1200).
In slope-intercept format, it is obtained as follows:
P(x) = 125x - 40x - 1200
P(x) = 85x - 1200.
Hence the slope is of 85, representing the rate of change, and option a is the correct option.
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14/32 Marks
Round the following numbers to 1 significant figure:
a) 25637
b) £2.51
c)
9877m
The following values, when rounded to one significant figure in accordance with the stated statement, are 3*10⁴, 3, and 1*10⁴ m.
Give an example of a notable figure?True figures are the number of digits that increase a value's accuracy, often a measurement. Starting with the first semi-digit, we count actual numbers. All the decimal places to the right of the next non-zero digit after the calculation are significant. The number 0.0079800, for instance, includes five significant digits. If a measurement includes the noughts to the side of the last non-zero digit, they are all significant.
As stated in the preceding sentence:
a). 25637 ≈ 3*10⁴
b). 2.51 ≈ 3
c). 9877m ≈ 10000m = 1*10⁴m
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Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the 30 of the lower 48 states, the percentage loss of wetlands per state is as follows.How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.)How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.)
The stem-and-leaf plot of the given data is attached. The correct options regarding percentage distribution, the distribution skewness, and gaps within the data are A, E, and F.
A stem and leaf plot refers to a technique used to to present and organize quantitative data (discrete or continuous) in a graphical format. It is displayed as table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit). A stem and leaf plot can be used to visualize the shape of a distribution. The stem and leaf plot of the given data regarding the percentage loss of wetlands in the lower states is attached.
Based on the plot, it can be seen that:
Most of the percentages lie between 20% to 60%, hence the percentage distributions are concentrated from 20% to 60%. The majority of the percentage loss of wetlands are concentrated in the center with few observations slightly scattered to the right tail. Hence, the data is fairly symmetric, perhaps slightly skewed to the right. None of the states have percentage loss of wetlands which lie between 10% to 19%. Hence, there is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands.Note: The question is incomplete. The complete question probably is: Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the lower 48 states, the percentage loss of wetlands per state is given. i) Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) ii). How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.) A) The percentages are concentrated from 20% to 60%. B) ii. The percentages are concentrated from 60% to 90%. C) There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands. D) These data are strongly skewed left. E) These data are fairly symmetric, perhaps slightly skewed right. F) There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands. G) There are no gaps in the data.
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How many miles?? Please help me
Answer:
33 miles
Step-by-step explanation:
You will use the Pythagoras' theorem ([tex]a^2+b^2=c^2[/tex])
Laura to her parents house is 'a', Her parents house to her grandparents house is 'c'
[tex]a^2+b^2=c^2\\c^2-a^2=b^2\\65^2-56^2=b^2\\4225-3136=b^2\\1089=b^2\\b=\sqrt{1089} \\b=33[/tex]
Laura is 33 miles from her grandparents house
solve for the given variable
3(m + 7) =
Answer: 3m + 21
Step-by-step explanation:
evaluate the following. give your answers as exact fractions. 2 x2−4 dx −2 =
The exact fractions. 2 x2−4 dx −2 = 10.6666
What is Fractions?
Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom
[tex]\int\limits^2_2 {|x^{2} -4|} \, dx[/tex]
Eliminate absolutes
[tex]|x^{2} -4| : -2\leq x\leq 2[/tex]
without absolutes is
[tex]\int\limits^2_2 {x^{2} +4} \, dx \\\int\limits^2_2 {-x^{2} } \, dx +\int\limits^2_2 {4} \, dx \\[/tex]
=(-x³/3 )²₋₂ +4x )-₂²
=(-1/3 ) ( 8+8) +4(2+2)
= -16/3 +16
=32/3
= 10.6666
So the exact fraction is [tex]\int\limits^2_2 {|x^{2} -4|} \, dx[/tex]
=10.6666
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find the first six terms of the sequence an=n^2-1
The first six terms of the given sequence are 0, 3, 8, 15, 24, 35
What are sequences?A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.
Given is a formula for a sequence aₙ = n²-1, we need to find the first six terms of the sequence,
Put n = 1 for first term,
a₁ = 1²-1
= 0
Put n = 2, for second term,
a₂ = 2²-1
= 3
Put n = 3, for third term,
a₃ = 3²-1
= 8
Put n = 4, for fourth term,
a₄ = 4²-1
= 15
Put n = 5, for fifth term,
a₅ = 5²-1
= 24
Put n = 6, for sixth term,
a₆ = 6²-1
= 35
Hence, the first six terms of the given sequence are 0, 3, 8, 15, 24, 35
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A road sign in the shape of a triangle has two interior angles that have the same measure as shown.
What is the measure of the third interior angle?
Answer: A: 120
Step-by-step explanation:
When adding all sides of a triangle it should always equal 180 degrees so by adding 30+30=60 after you do 180-60=120 or the proper way is 30+30+x=180
60+x=180
-60 -60
x=120
suppose that limx→6f(x)=15 and limx→6g(x)=−1. find the following limits. a.limx→6[f(x)g(x)]
limx→6[f(x)g(x)] = limx→6f(x) * limx→6g(x). Since limx→6f(x) = 15 and limx→6g(x) = -1, then limx→6[f(x)g(x)] = 15 * (-1) = -15. This means that the limit of the product of the two functions is -15.
We can use the limit laws of product to solve this limit.
limx→6[f(x)g(x)] = limx→6f(x) * limx→6g(x)
= 15 * (-1)
= -15
To solve this limit, we can use the limit laws of product. By the limit laws of product, the limit of a product is equal to the product of two limits. Therefore, limx→6[f(x)g(x)] = limx→6f(x) * limx→6g(x). Since limx→6f(x) = 15 and limx→6g(x) = -1, then limx→6[f(x)g(x)] = 15 * (-1) = -15. This means that the limit of the product of the two functions is -15.
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which best describes how to determine the transitive closure by arithmetic operations on the adjacency matrix?
A. Compute A^(n-1)
B. Compute A^n
C. Compute A^0 + A^1 + ... + A^(n-1) where + is standard addition (integers)
D. Compute A^0 + A^1 + ... + A^(n-1) where + is boolean addition (true/false)
E. Compute A^1 + A^2 + ... + A^n where + is standard addition (integers)
F. Compute A^1 + A^2 + ... + A^n where + is boolean addition (true/false)
The transitive closure by arithmetic operations on the adjacency matrix is Compute A⁰ + A¹ + ... + A⁽ⁿ⁻¹⁾ where + is standard addition (integers)
The transitive closure of a graph is the set of all possible paths from one vertex to another in the graph.
The best method to determine the transitive closure by arithmetic operations on the adjacency matrix is C.
Compute
=> A⁰ + A¹ + ... + A⁽ⁿ⁻¹⁾
where + is standard addition (integers).
The standard addition of integers is used because we are counting the number of paths between each vertex.
In this method, we start by computing A⁰, which is simply the adjacency matrix itself.
A¹ gives us the number of paths between each vertex that are one step long. A² gives us the number of paths between each vertex that are two steps long, and so on. We continue this process until we have computed
=> A⁽ⁿ⁻¹⁾
where n is the number of vertices in the graph.
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Determine the independent and dependent variable from the following situation. Quincy was given 3 video games for his new game system. Every month he saves enough to get 2 more video games.
what is the dependent variable and what is the independent variable.
The dependent variable is the number of games and the independent variable is the number of months.
How to identify the independent and dependent variables?We know that Quincy was given 3 video games for his new game system and every month he saves enough to get 2 more video games.
Then the two variables are the number of months and the number of games.
We know that he starts with 3 games and each month he adds 2 more, then we can write the relation:
y = 3 + 2*x
Where y is the number of games and x the number of months.
Then the independent variable is the number of months, and the dependent variable (which depends on the other one) is the number of games.
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The base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in². The slant height of the pyramid is 6 in.
What is the surface area of the pyramid?
The total surface area of the triangular pyramid is 170.4 inches².
What is Surface Area?The area of a three dimensional object on it's outer surface is called the surface area of the object.
A triangular pyramid has a triangular base and three triangular faces.
Given that, base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in².
Area of the base = 62.4 inches²
Slant height = 6 inches
Length of edge of each of the three triangular faces = 12 inches
Area of a triangular face = [tex]\frac{1}{2}[/tex] × 12 × 6 = 36 inches²
Area of three triangular faces = 3 × 36 inches² = 108 inches²
Total surface area = 108 inches² + 62.4 inches² = 170.4 inches²
Hence 170.4 inches² is the total surface area of the pyramid.
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Can someone please help me here? Thank you!
Peter is a product manager earning a semi-monthly salary of P5,500. He is given commission of 2. 5% on his own sales and an override of 0. 5% on his men's sales. His men are entitled to a 3. 75% commission on their own sales and basic semi-monthly salary of P4,000. Peter and his men are given
transportation allowance of P2,000 per month. Compute the gross earnings of Peter and each of his men.
Peter's gross semi-monthly earnings are P7,717.5 and each of his men's gross semi-monthly earnings are P6,150.
To calculate Peter's gross earnings,
We need to find the commission he earns on his own sales and the override commission he earns on his men's sales.
Peter's Commission on his own sales:
2.5% of P5,500 = P137.5
Peter's Override Commission on his men's sales:
0.5% of (number of men * P4,000) = 0.5% of (number of men * 4000)
Let's assume he has 4 men.
Then the total override commission would be:
0.5% * 4 * 4000 = P80
So Peter's gross semi-monthly earnings would be:
P5,500 + P137.5 + P80 + P2,000 = P7,717.5
To calculate the gross earnings of each of Peter's men, we need to find their basic semi-monthly salary, their commission on their own sales, and their transportation allowance.
Each man's basic semi-monthly salary: P4,000
Each man's Commission on their own sales will be:
3.75% * P4,000 = P150
So each man's gross semi-monthly earnings would be:
P4,000 + P150 + P2,000 = P6,150
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The note C, D, E, F, G, A, and B are to be ued to form an ordered five-note muical logo. In how many way can thi be done under the following circumtance?
No note can be repeated. Note can be repeated. Note can be repeated, but all the note cannot be the ame
Note can be repeated, but all the note cannot be the same to form an ordered five-note musical logo.
What is meant by musical notes?A note in music is a symbol for a musical sound. In musical notation, notes can stand in for the pitch and duration of a sound. A pitch class can also be represented by a note.The fundamental units of a lot of written music are notes: discrete representations of musical occurrences that make it easier to perform, understand, and analyze music.Both general and specific meanings of the word note are possible; for example, one could say that "the piece 'Happy Birthday to You' begins with two notes having the same pitch" or "the composition begins with two repeats of the same note." In the first instance, the term "note" refers to a particular musical event; in the second, it designates a group of occurrences that all have the same pitch.Learn more about musical notes refer to :
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What is the geometric relation between the vectors v and w if vw =-||v|| ||w|| ?
The geometric relation between the vectors v and w are:
The vectors are in the same direction.
Now, According to the question:
Geometrical Interpretation of Scalar Product
From the scalar product formula, we have a.b = |a| |b| cos θ = |a| proj→b(→a) proj b → ( a → ) , that is, the scalar product of vectors a and b is equal to the magnitude of vector a times the projection of a onto vector b.
Vectors describe movement with both direction and magnitude. They can be added or subtracted to produce resultant vectors. The scalar product can be used to find the angle between vectors.
Now, vw =-||v|| ||w||
a.b = |a| |b| cos θ = |a| proj→b(→a) proj b → ( a → )
vw =-||v|| ||w|| cos θ = |v| proj →w(→v) proj w → ( v → )
Hence, The vectors are in the same direction.
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How do you convert from kJ to J?
A joule is one unit of energy, while a kilojoule is 1000 joules.
What is the kJ to J formula?KJ x 1,000 = J.
It would be simple to calculate if you had a calculator, but you can get the same answer by simply shifting the decimal point 3 places to the left and adding any necessary zeros.A megaJoule (MJ) is 1,000,000 Joules, whereas a kiloJoule (kJ) is 1000 Joules. The Watt, which is a measure of power, is a comparable unit (energy per unit time). Energy units can be created by multiplying power units by seconds (s), hours (h), or years (yr).A joule is one unit of energy, while a kilojoule is 1000 joules.To learn more about joule refer to:
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A free bu ervice operate throughout the day around Brelney City Centre. The bu tart from the Railway Station, then top ucceively at the Catle, the Shopping Centre, the Park and the Stadium, before returning to the Railway Station. The journey time for each ection of the circuit i 5 minute. The firt departure of the day from the Railway Station i at 09:15. Each time the bu arrive back at the Railway Station it wait for 10 minute before etting off again. Bart will be the driver for the firt 4 circuit tomorrow. At what time will Bart arrive back at the Railway Station for the final time tomorrow?
A 11:25
B 11:35
C 11:45
D 11:55
At B: 11:35 Bart will arrive back at the Railway Station for the final time
Let's call the number of circuits Bart completes "n".
Each circuit takes 5 minutes to travel between each stop and 5 stops in total, so each circuit takes 5 * 5 = 25 minutes.
The bus waits 10 minutes at the Railway Station between each circuit, so the total time for each circuit is 25 + 10 = 35 minutes.
Bart will complete 4 circuits, so the total time he spends on the bus tomorrow is 4 * 35 minutes = 140 minutes.
The first departure of the day from the Railway Station is at 09:15, so after 140 minutes of travel, Bart will arrive back at the Railway Station at 09:15 + 140 minutes = 11:35.
Therefore, the answer is B) 11:35.
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Molly is helping her younger sister run a lemonade stand. They earn $2 for each cup of lemonade they sell. Write an equation that shows how their total earnings, y, depend on the number of cups sold, x.
Answer:
y = 2x
Step-by-step explanation:
We know
They earn $2 for each cup of lemonade they sell. So, the equation is
y = 2x
can you halep me for this quastion too lease
The equation of a line that has a slope of -1/3 and y-intercept at (0, 1) is y = -x/3 + 1.
What is the slope-intercept form?In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:
y = mx + c
Where:
x and y represents the data points.m represents the slope of a line.c represents the y-intercept of a line.From the information provided above, we have the following slope and y-intercept on the line:
y-intercept = 1Slope, m = -1/3Therefore, the required equation of line is given by:
y = mx + c
y = (-1/3)x + 1
y = -x/3 + 1
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This set of ordered pairs defines a function.
{(-49,7), (-56,8), (-63,9), (-70,10)}
Which table represents the inverse of the function defined by the ordered pairs?
The inverse of the function defined by the ordered pairs are (7, -49), (8, -56), (9,-63), (10, 70)
What is an inverse function?An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of the function produces the output x. x. A function that has an inverse is called invertible, and the inverse is denoted by f⁻¹.
Given that, a set of ordered pairs defines a function.
{(-49,7), (-56,8), (-63,9), (-70,10)}
We need to find its inverse function,
Since, we know that,
The inverse of a function means that the input becomes the output of the function and the output becomes input.
When the function is given in the form of ordered pairs, the first element of each ordered pair represents the input and the second element represents the output.
Therefore,
The inverse will be:
{(7, -49), (8,-56), (9,-63), (10, -70)}
Hence, the inverse of the function defined by the ordered pairs are (7, -49), (8, -56), (9,-63), (10, 70)
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1. Make a conjecture about the relationship between tan(0) and tan(90 – 0).
2. Prove your conjecture.
Conjecture about the relationship between tan(0) and tan(90 – 0) is tan(90-θ) is equal to cot θ.}. Tan(-) is equal to -tan, as is known. Therefore, eqn1 can be expressed as follows: -tan(90-), which results in -cot.
The equivalent of the given angle (90 degrees) in radians can also be used to indicate a tan angle of 90 degrees (1.57079 . . .) 90 degrees = 90° (180°/90°) rad = /2 or 1.5707... Given that the tangent function is periodic, we can write tan 90° as tan(90° + n 180°), where n Z.
tan(90-θ) is equal to cot θ.}
Tan(-θ) = -tanθ
-tan(90-θ) = -cotθ.
-cotθ.
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Binomial Distribution Algebra 2B
Roughly 75% of students take the bus to school. If you were to ask 9 students in your class, what is the probability that at most 8 of them take the bus to school?
The probability that at most 8 of 9 students take the bus to school is approximately 0.9538.
To find the probability of at most 8 students taking the bus, we can use the cumulative distribution function (CDF) of the binomial distribution.
The CDF gives the probability of getting a certain number or fewer of successes in a fixed number of trials, where each trial has a fixed probability of success.
The CDF of a binomial distribution with parameters n (number of trials) = 9 and p (probability of success) = 0.75 is given by:
F(k) = Σ(i = 0 to k) (9 choose i) * (0.75)^i * (0.25)^(9-i)
where (9 choose i) is the binomial coefficient, which gives the number of ways to choose i successes from n trials.
Thus, to find the probability of at most 8 students taking the bus, we compute the CDF at k = 8:
F(8) = Σ(i = 0 to 8) (9 choose i) * (0.75)^i * (0.25)^(9-i)
Using a binomial calculator or programming language, we can find the value of F(8) which is approximately 0.9538.
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Aaron's car gets an average of 15 miles to the gallon in the city, and he pays an average
of $1.09 per gallon of gas. What is his monthly commuting cost if he drives 10.5 miles
round-trip 22 days a month for work?
Select one:
O a. $26.09
O b. $18.28
O C. $16.79
Answer:
C
Step-by-step explanation:
15mpg
$1.09/gallon
10.5 per day * 22 days = 231 miles
will need 231/15 gallons of gas = 15.4gallons
cost = 15.4*1.09 = $16.79
Hanz and Franz are in a shooting competition. The object of the match is to be the first to hit the bull's eye of a target 100 feet away. The two opponents alternate turns shooting, and each opponent has a 40% chance of hitting the bull's-eye on a given shot. If Hans graciously allows Franz to shoot first, what is the probability that Hans will win the competition and take no more than three shots?
Answer: The probability of Hans winning and taking no more than three shots can be calculated using the principle of total probability and the law of total probability.
Let's call the event of Hans winning and taking no more than three shots "A". Then, the probability of event A can be broken down into several cases:
Case 1: Hans wins in one shot: P(A|Hans wins in one shot) = P(Hans wins in one shot) = 0.4.
Case 2: Hans wins in two shots: P(A|Hans wins in two shots) = P(Franz misses in the first shot) * P(Hans wins in the second shot) = (1 - 0.4) * 0.4 = 0.24.
Case 3: Hans wins in three shots: P(A|Hans wins in three shots) = P(Franz misses in the first two shots) * P(Hans wins in the third shot) = (1 - 0.4)^2 * 0.4 = 0.144.
Finally, the probability of event A can be calculated using the law of total probability as follows:
P(A) = P(A|Hans wins in one shot) + P(A|Hans wins in two shots) + P(A|Hans wins in three shots) = 0.4 + 0.24 + 0.144 = 0.784.
So, the probability of Hans winning the competition and taking no more than three shots is 0.784.
Step-by-step explanation: