Answer: C. The median of 20 is the most accurate to use, since the data is skewed.
The most accurate measure of center to use in this case is the median of 20. This is because the data is skewed, with a few high-value donations (such as the two donations of 55 dollars) that pull the mean up. However, most of the donations are clustered around 10 to 20 dollars. As a result, the median, which is the middle value when the data is sorted in order, is a better representation of the "typical" donation amount.
In this case, the median is 20, which means that half of the donations were less than 20 dollars and half were more. This is a more accurate representation of the central tendency of the data than the mean of 22.7, which is influenced by the high-value donations. Therefore, the charity should use the median of 20 to accurately represent the typical donations received.
Step-by-step explanation:
a restaurant wants to know if its customers like its new menu. in surveys 100 randomly selected customers over one week. what is the population in this study?
In terms of using specific terms in your answer, you should incorporate any keywords or phrases from the student's question that are relevant to your response.
For example, in response to the question "a restaurant wants to know if its customers like its new menu. in surveys 100 randomly selected customers over one week. what is the population in this study?" you might write:"
In this study, the population refers to the entire group of customers who might potentially like or dislike the restaurant's new menu.
While the study only surveyed 100 randomly selected customers over one week, the population could include all customers who visited the restaurant during that time period or even a larger group of potential customers who have not yet visited the restaurant."
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2. Write - (3i) in the form a + bi, where a and b are real numbers.
classify the different measurement systems into one of the four types
of scales. (Exercise)
1. Your checking account number as a name for your account.
2. Your checking account balance as a measure of the amount of money you
have in that account
3. The order in which you were eliminated in a spelling bee as a measure of your
spelling ability.
4. Your score on the first statistics test as a measure of your knowledge of
statistics.
5. Your score on an individual intelligence test as a measure of your
intelligence.
6. The distance around your forehead measured with a tape measure as a
measure of your intelligence.
7. A response to the statement "Abortion is a woman's right" where "Strongly
Disagree" = 1, "Disagree" = 2, "No Opinion" = 3, "Agree" = 4, and "Strongly
Agree" = 5, as a measure of attitude toward abortion.
8. Times for swimmers to complete a 50-meter race
9. Months of the year Meskerm, Tikimit…
10.Socioeconomic status of a family when classified as low, middle and upper
classes.
11. Blood type of individuals, A, B, AB and O.
12.Pollen counts provided as numbers between 1 and 10 where 1 implies there is
almost no pollen and 10 that it is rampant, but for which the values do not
represent an actual counts of grains of pollen.
13.Regions numbers of Ethiopia (1, 2, 3 etc.)
14.The number of students in a college;
15.the net wages of a group of workers;
16.the height of the men in the same town;
I'm begging u PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST
Find the surface area of a square pyramid with side length 6 ft and slant height 7 ft.
Answer: 42
Step-by-step explanation:
6x7=42 ft
SOMEONE PLEASE HELP ME MY GRADE WILL GO DOWN IF I DONT GET THIS TURNED IN
will give brainliest 80 points
Answer: the value of x is 29
Step-by-step explanation:
Answer:
it's in the attachment
Step-by-step explanation:
the one that are the same value as the given value on the transversals are either opposite interior angles or opposite exterior angles
the ones that have different values as the given value on the transversal are subtracted from 180⁰
what is ratio analysis, in your own words? what are the three different categories of ratios? provide examples. why are they important?
a) Ratio analysis is a financial analysis tool that helps to evaluate the financial performance and health of a business by comparing different financial figures
b) There are three categories of ratios in ratio analysis: liquidity ratios, profitability ratios, and solvency ratios.
c) Ratio analysis is important because it helps to provide a quick snapshot of a company's financial health and performance.
Ratio analysis is a financial analysis tool that helps to evaluate the financial performance and health of a business by comparing different financial figures. It involves calculating and interpreting various ratios that provide insight into the financial position, profitability, and liquidity of a company.
There are three categories of ratios in ratio analysis
Liquidity ratios: These ratios help to determine a company's ability to meet its short-term financial obligations. Examples include the current ratio and the quick ratio.
Profitability ratios: These ratios help to evaluate a company's ability to generate profit in relation to its revenue, assets, and equity. Examples include the gross profit margin, net profit margin, and return on assets.
Solvency ratios: These ratios help to assess a company's ability to meet its long-term financial obligations. Examples include the debt-to-equity ratio and the interest coverage ratio.
Ratio analysis is important because it helps to provide a quick snapshot of a company's financial health and performance. It is useful for investors, lenders, and other stakeholders in making informed decisions about investing in or lending to a company.
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If the coefficient of x4 in the expansion of (2-3px) (4x4+ 5x³-x) is 38, find the value of p.
The answer of the given question based on expression is the value of p that satisfies the given condition is -2.
What is Binomial theorem?The binomial theorem is a fundamental concept in algebra that provides a formula for expanding expressions of the form (a + b)ⁿ, where n is a non-negative integer and a and b are real numbers. The formula is as follows:
(a + b)ⁿ = C(n, 0)aⁿ b⁰ + C(n, 1)a⁽ⁿ⁻¹⁾ b¹ + ... + C(n, r)a⁽ⁿ⁻r⁾ b^r + ... + C(n, n)a⁰bⁿ
The binomial theorem states that the nth power of a binomial can be expanded as the sum of the products of each term in the binomial raised to a power and the corresponding binomial coefficient. The binomial coefficient represents the number of ways of choosing r objects from a set of n objects, and is often denoted by "n choose r" or written as a combination symbol, (nCr).
We can use the binomial theorem to expand the given expression as:
(2-3px) (4x⁴ + 5x₃ - x) = 8x⁴ + 10x³ - 2x - 12px⁵ - 15px⁴ + 3px²
To find the coefficient of x⁴ in this expansion, we need to look at the terms that contain x⁴. There are two such terms: 8x⁴ and -15px⁴. Therefore, the coefficient of x⁴ is 8 - 15p.
We are given that this coefficient is 38, so we can set up the equation:
8 - 15p = 38
Solving for p, we get:
-15p = 30
p = -2
Therefore, the value of p that satisfies the given condition is -2.
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Question 1.
in exploration 5.1.1 question 2, you identified the y-intercept as (0, a) and the
horizontal asymptote as y= b, where
a=
b=
a=b, The curve approaches the line y=a as x approaches infinity or negative infinity.
since the y-intercept is the point where the curve intersects the y-axis, i.e., x=0.
Since we have (0, a) as our y-intercept, then a=b, where a and b are constants.
The y-intercept, as indicated in the question, is (0, a) meaning that for the function f(x), when x=0, then f(x) = a.
The horizontal asymptote of a function is a horizontal line that the graph approaches as x approaches infinity or
negative infinity.
If the horizontal asymptote is y=b, it means that the value of y approaches b as x approaches infinity or negative infinity.
Therefore, since a=b, the curve approaches the line y=a as x approaches infinity or negative infinity.
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Sean is walking around a track that is 440 yards long he Has walked around the track seven times so far if he wants to walk 4 miles how many more Times does he needs to walk around the track?
Answer:
I think the answer is
1760
Which graph shows a system of equations with one unique solution at (0, 5)?
The graph shows two parallel lines.
The graph shows lines, which intersect at 0 comma 5.
The graph shows lines, which intersect at 1 comma 6.
The graph shows two lines, which appear as one line.
The graph which shows a system of linear-equations with one unique solution at (0,5) is option-B which shows lines, intersecting at (0,5).
What is system of linear equations?
The collection of two or more linear equations is called as system of linear equations. The linear equations have the degree of variable as one. Though a single linear equation can have infinite number of solutions, but a pair of linear equation can be classified as consistent or inconsistent. The equations which are consistent have either one solution or infinte solutions. The intersecting pair of consistent equations have unique solution whereas the coinciding pair of consistent equations have infinite number of solutions. The equations which are inconsistent are the parallel lines which do not have any solution.
Here the system must have one unique solution as (0,5)
a)graph as parallel lines: which means they are inconsistent & do not have any solution.
b)The graph shows lines intersecting at (0,5): which means the system is consistent with unique solution (0,5)
c)The graph shows lines intersecting at (1,6): which means the system is consistent with unique solution (1,6)
d)graph shows two lines which appear as one: means the lines are coinciding with infinite solutions.
So the answer is option-B
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Line v has an equation of y=–10/9x–3. Perpendicular to line v is line w, which passes through the point (2,3). What is the equation of line w?
The equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).
What is an equatiοn οf the line?The definitiοn οf an equatiοn οf the line is a linear equatiοn with degree 1. X and Y are twο variables in the equatiοn fοr the line. The slοpe οf the line, which reflects the elevatiοn οf the line, is the third parameter.
The general fοrm οf the equatiοn οf the line:-
y = mx + c
m = slοpe
c = y-intercept
Given that Line, v has an equatiοn οf y=–109x–3. Perpendicular tο line v is line w, which passes thrοugh the pοint (2,3).
The slοpe οf the required line will be inverse and the οppοsite οf the given line,
m = 1/109
The intercept will be calculated as,
y = mx + b
3 = (1/109)2 + b
3 = 2/109 + b
327/109 = 2/109 + b
325/109 = b
The equatiοn οf the line is written as,
y = (1/109)x + (325/109)
Therefοre, the equatiοn οf the line w will be equal tο y = (1/109)x + (325/109).
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The first quadrant is lava. the rest of the plane (including the x and y axes) is safe. to traverse the lava, you can place a board, which is a line segment of length at most 1, between two safe endpoints. once a board is placed, the line segment becomes safe, and points on it may be used as endpoints of a subsequent board. your goal is to reach the point (2023, 2023).
a. prove that one million boards aren't enough.
b. give a specific number of boards with which you can reach (2023, 2023).
c. prove that one billion boards aren't enough
Proof that one million boards aren't enough. .Therefore, one million boards are not enough to reach (2023, 2023).
A total of 2023 boards are needed to reach (2023, 2023).
How to explain the problemThis problem is a mathematical puzzle that involves traversing a hazardous area to reach a specific point using a limited number of resources.
The problem is set in the Cartesian plane, where the first quadrant (i.e., the region where both x and y coordinates are positive) is covered with lava, making it impossible to traverse.
Let's assume that we can reach (2023, 2023) with one million boards. We know that each board can cover a distance of at most 1. Therefore, the total distance we can cover with one million boards is at most one million. However, the distance between the origin (0, 0) and (2023, 2023) is ✓2023² + ✓2023² = 2855.9
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What is the volume, in cubic inches, of a basketball with
a diameter of 9 inches?
Answer:
381.7 cubic inches.
4. Nicolas has $650 to deposit into two separate accounts.
Nicolas will deposit $350 into Account I, which earns 3.5% simple annual interest
He will deposit $300 into Account II, which earns 3.25%
interest compounded annually
Nicolas will not make any additional deposits or withdrawals for
5 years.
a. Which account had a better return on investment?
b. What is the total amount of money Nicolas will have in both
accounts?
c. What is the difference between the interest earned on the
two accounts?
Account I.
What is the total amount of money Nicolas will have in bothaccounts?$822.12
What is the difference between the interest earned on thetwo accounts?$17.88
a hospital receives 1/5 of its flu vaccine shipments from company x and the remainder of its shipments from other companies. each shipment contains a very large number of vaccine vials. for company x's shipments, 8% of the vials are ineffective. for every other company, 3% of the vials are ineffective. the hospital tests 30 randomly selected vials from a shipment and finds that one vial is ineffective. what is the probability the shipment came from company x?
The probability that the shipment came from company X, given one ineffective vial was found, is 0.4 or 40%.
To find the probability ,we will use the Bayes' theorem.
Determine the prior probabilities.
P(X) = Probability that the shipment is from company X = 1/5
P(Y) = Probability that the shipment is from other companies = 1 - 1/5 = 4/5
Determine the likelihood probabilities.
P(I|X) = Probability of finding an ineffective vial given the shipment is from company X = 8%
P(I|Y) = Probability of finding an ineffective vial given the shipment is from other companies = 3%
Determine the probability of finding an ineffective vial.
P(I) = P(I|X) × P(X) + P(I|Y) × P(Y) = (8% × 1/5) + (3% × 4/5)
= 0.08 × 0.2 + 0.03 × 0.8 = 0.016 + 0.024
= 0.04
Use Bayes' theorem to find the probability that the shipment is from company X given an ineffective vial.
P(X|I) = (P(I|X) × P(X)) / P(I)
= (0.08 × 0.2) / 0.04 = 0.016 / 0.04
= 0.4
The probability that the shipment came from company X, given one ineffective vial was found, is 0.4 or 40%.
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6.1 true or false: points that minimize a nonlinear function are inherently less accu- rately determined than points for which a non- linear function has a zero value.
The given statement, points that minimize a nonlinear function are inherently less accurately determined than points for which a nonlinear function has a zero value is FALSE.
What is a nonlinear function?In mathematics, a nonlinear function is a function that is not linear, i.e. a function whose graph is not a straight line. Simplest non-linear functions are quadratic function, exponential function and logarithmic functions. Nonlinear functions do not follow the superposition principle, which is fundamental to linear systems, which states that if the input is scaled by any factor, then the output will also be scaled by that factor.
Points that minimize a nonlinear function are inherently less accurately determined than points for which a nonlinear function has a zero value. The above statement is false because the points that minimize a nonlinear function can be determined more accurately than the points where the nonlinear function has zero value.
Also, there is no such rule that the points that minimize a nonlinear function are less accurate than points for which a nonlinear function has a zero value.
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Ayish used the quadratic formula to solve a quadratic equation in y to get y=7+-sqrt of 160/10
The solutions for y are:
y = (7 + 4sqrt(10))/10y = (7 - 4sqrt(10))/10To solve this problemWe can simplify the expression sqrt(160) by factoring 160 into its prime factors:
160 = 2^5 * 5
Taking the square root of each factor, we get:
sqrt(160) = sqrt(2^5 * 5) = sqrt(2^4 * 2 * 5) = 2^2 * sqrt(2 * 5) = 4 * sqrt(10)
Therefore, we can simplify the expression for y as follows:
y = (7 +- sqrt(160))/10 = (7 +- 4sqrt(10))/10
So the solutions for y are:
y = (7 + 4sqrt(10))/10
y = (7 - 4sqrt(10))/10
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What key features do the functions f(x) = 12x and g of x equals the square root of x minus 12 end root have in common? both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions have an x-intercept in common. both f(x) and g(x) include domain values of [12, ∞) and range values of [0, ∞), and both functions have a y-intercept in common. both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions increase over the interval (-6, 0). both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).
f(x) = 12x and [tex]g(x)= \sqrt{x-12}[/tex] both include domain values of [12, ∞), and both functions increase over the interval (12, ∞).
The set containing all input values is known as a function's domain while a function's range is the collection of all possible output values.
Function f(x) is defined by: f(x) = 12x.
It has a positive slope, hence it is increasing all over it's domainRange is all real values.No restriction, hence the domain is also all real values.Function g(x) is defined by: [tex]g(x)= \sqrt{x-12}[/tex]
This function increases over all it's domain.The range of this function is (0,∞)(x-12) cannot be negative, hence the domain is [12, ∞), which is contained into the domain of f(x).Therefore, the correct option is (d) Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).
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Please help! 30 points promised! please also show work as I am confuzzled
The solution to the equation is 3[tex]z^{2}[/tex] - [tex]z^{3}[/tex] = 5z + 1 and it has been obtained by using the arithmetic operations.
What are arithmetic operations?
All real numbers can be described by the four fundamental operations, sometimes known as "arithmetic operations." Operations like quotient, product, sum, and difference come before operations like division, multiplication, addition, and subtraction in mathematics.
We are given an equation as:
[tex]\frac{z+1}{z-1}[/tex] - [tex]\frac{z}{3}[/tex] = [tex]\frac{2}{z-1}[/tex]
Now, we will simplify the equation first.
⇒ [tex]\frac{z+1}{z-1}[/tex] - [tex]\frac{z}{3}[/tex] = [tex]\frac{2}{z-1}[/tex]
⇒ [tex]\frac{3(z+1) - z(z-1)}{3 (z-1)}[/tex] = [tex]\frac{2}{z-1}[/tex]
Now, on cross multiplying we get,
⇒[3 (z + 1) - z (z - 1)] * (z - 1) = 2 (3z - 1)
⇒[3z + 3 - [tex]z^{2}[/tex] - z] * (z - 1) = 6z - 2
⇒3[tex]z^{2}[/tex] + 3z - [tex]z^{3}[/tex] - [tex]z^{2}[/tex] - 3z - 3 + [tex]z^{2}[/tex] + z = 6z - 2
⇒3[tex]z^{2}[/tex] - [tex]z^{3}[/tex] - 3 + z = 6z - 2
⇒3[tex]z^{2}[/tex] - [tex]z^{3}[/tex] = 5z + 1
Hence, the required solution has been obtained.
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When you dilate by a scale factor greater than 1 the figure shrinks.
True
False
Answer:
true
Step-by-step explanation:
The equation of a circle is given below. ( � + 9 ) 2 + ( � − 46 ) 2 = 123 (x+9) 2 +(y−46) 2 =123left parenthesis, x, plus, 9, right parenthesis, squared, plus, left parenthesis, y, minus, 46, right parenthesis, squared, equals, 123 What is its center? ( (left parenthesis , ,comma ) )right parenthesis What is its radius? If necessary, round your answer to two decimal places.The equation of a circle is given below. ( � + 9 ) 2 + ( � − 46 ) 2 = 123 (x+9) 2 +(y−46) 2 =123left parenthesis, x, plus, 9, right parenthesis, squared, plus, left parenthesis, y, minus, 46, right parenthesis, squared, equals, 123 What is its center? ( (left parenthesis , ,comma ) )right parenthesis What is its radius? If necessary, round your answer to two decimal places.
According to the given question, the center of the circle is (-9, 46) and its radius is approximately 11.09.
What is equation of circle?The equation of a circle is a formula that describes the relationship between the x and y coordinates of any point on the circle.
The standard equation of circle is:
(x - h)²+(y - k)²=r²
This equation states that the sum of the squares of the differences between the x-coordinate and the center, and the y-coordinate and the center, is equal to the square of the radius.
The equation of the circle is given by (x+9)² + (y-46)² = 123.
Comparing this to the standard equation of a circle, (x-h)² + (y-k)² = r², we can see that the center of the circle is (-9, 46) and the radius is √(123) = 11.09.
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A sportscaster predicted that the local high school baseball team has a 75% chance of winning tonight. Select all of the values that represent the probability of the team not winning.
the values that represent the probability of the team not winning.
b) 0.25
d) 25%
e) 3/4
f) 1/4
These values represent the probability of the team not winning, which is the complement of the probability of winning (75%).
b) 0.25 is the decimal representation of the probability of not winning, which is 1-0.75.
d) 25% is the percentage representation of the probability of not winning, which is also 100%-75%.
e) 3/4 is the fraction representation of the probability of winning, so 1-3/4 gives the probability of not winning.
f) 1/4 is the fraction representation of the probability of not winning, which is the complement of the probability of winning (3/4).
These are the options that represent the probability of the team not winning.
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A sportscaster predicted that the local high school baseball team has a 75% chance of winning tonight. Select all of the values that represent the probability of the team not winning.
a)0.75 b)25% c)0.25d) 75%e)3/4f)1/4
25 points to whoever solves
Answer:
[tex] \frac{25}{121} [/tex]
Step-by-step explanation:
Given:
r (dartboard) = 11 m
r (shaded area) = 5 m
π = 3,14
First, let's find the area of the dartboard:
A (dartboard) = πr^2 = 3,14 × 121 = 379,94 m^2
A (shaded area) = 3,14 × 25 = 78,5 m^2
Let's call this event A:
A - "A dart must hit the shaded area":
All outcomes:
n = 379,94
Favorable outcomes:
m(A) = 78,5
[tex]p(a) = \frac{78.5}{379.94} = \frac{25}{121} [/tex]
I assume, this is the right answer
If Oscar the ostrich travels 215 miles in 5 hours on land, how fast does he travel?
How long must the brace be on a closet rod holder if the vertical side is 15 cm and the horizontal side must be attached 35 cm from the wall?
The brace must be approximately 38.1 cm long.
To find the length of the brace for the closet rod holder,
we can use the Pythagorean theorem,
which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the vertical side is 15 cm and the horizontal side is 35 cm.
Let's call the length of the brace (the hypotenuse) "c".
According to the Pythagorean theorem:
[tex]c^2 = (15 cm)^2 + (35 cm)^2[/tex]
[tex]c^2 = 225 cm^2 + 1225 cm^2[/tex]
[tex]c^2 = 1450 cm^2[/tex]
Now, to find the length of the brace, we need to take the square root of both sides:
[tex]c = \sqrt{(1450 cm^2)}[/tex]
c ≈ 38.1 cm.
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If a square has an area that is 49 square feet or less, what are the possible lengths x for the side of the square. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ft A. The possible lengths x for the side of the square is the interval, (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The possible lengths x for the side of the square is the list of values, x = ft. (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) C. There are no possible lengths x for the side of the square.
The possible lengths x for the side of square A. The possible lengths x for the side of the square is the interval [-7,7].
Since the area of a square is given by the formula A = x^2, where x is the length of the side, we can solve for x to find the possible lengths of a square with area 49 square feet or less.
A ≤ 49
x^2 ≤ 49
|x| ≤ 7
So the possible lengths for the side of the square are any values of x between -7 and 7, inclusive.
Therefore, the answer is: A. The possible lengths x for the side of the square is the interval [-7,7].
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Please Help! No Silly Answers Please! I would appreciate correct answers. Thank you all! Please try and include Scratch Work, Thank you.
Answer:
y in (7,y) = 14
Step-by-step explanation:
A General Linear function is as the following:
y = mx + c, Where: m: slope of the line, c: y-intercept
Given that:
Point 1 (P1) = (1,5)
Point 2 (P2) = (3, 11)
Point 3 (P3) = (7,y)
By substituting in the linear function with P1:
5 = m + c ---> (1)
By substituting in the linear function with P2:
11 = 3m + c ---> (2)
By multiplying equation (1) times 3 and subtracting eq. (2) from it:
(15 = 3m + 3c) - (11 = 3m + c) =
4 = 2c
Then, c = 2
By substituting with "c" in eq. (1):
5 = m + 2
Then, m = 3
Hence,
the function of this line is:
y = 3x + 2
So,
to get "y" in P3, we are going to substitute with 7:
y = 3(7) + 2
then "y" in P3 = 23
Another Solution:
by getting the slope of the line:
[tex]Slope = \frac{\triangle y}{\triangle x}[/tex] Where: Δy: change in y points, Δx: change in x points
by utilizing P1 & P2 in slope formula:
[tex]slope = \frac{11 - 5}{3 - 1} = \frac{6}{2} = 3[/tex]
By substituting with P1 in the linear function:
5 = 3 + c
Then, c = 2
the function of the line is:
y = 3x + 2
So,
to get "y" in P3, we are going to substitute with 7:
y = 3(7) + 2
then "y" in P3 = 23
hope you find this easy to understand....
Have any questions? Write in the comments.
give me brainliest if you found this answer useful
Y=x-2
5x+4y=28
Solve for substitution
Answer:
x = 4
y = 2
Step-by-step explanation:
{y = x - 2,
{5x + 4y = 28;
Replace y in the second equation with the 1st equation's value:
5x + 4(x - 2) = 28
5x + 4x - 8 = 28
9x = 28 + 8
9x = 36 / : 9
x = 4
y = 4 - 2 = 2
Q5
The graph represents a relation where x represents the independent variable and y represents the dependent variable.
a graph with points plotted at negative 5 comma 1, at negative 2 comma 0, at negative 1 comma negative 1, at 0 comma 2, at 1 comma 3, and at 5 comma 1 Is the relation a function? Explain.
No, because for each input there is not exactly one output.
No, because for each output there is not exactly one input.
Yes, because for each input there is exactly one output.
Yes, because for each output there is exactly one input.
The relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."
Why is the given relatiοn nοt a functiοn?Lοοking at the given pοints, we can see that the input x = -5 has an οutput y = 1, and the input x = 5 alsο has an οutput y = 1.
This means that there are twο different inputs (x-values) that cοrrespοnd tο the same οutput (y-value), viοlating the definitiοn οf a functiοn.
Tο determine if the relatiοn is a functiοn, we need tο check if fοr each input (x-value), there is exactly οne οutput (y-value).
Therefοre, the relatiοn is nοt a functiοn. The cοrrect answer is "Nο, because fοr each input there is nοt exactly οne οutput."
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In a math class with 28 students, a test was given the same day that an assignment was due. There were 18 students who passed the test and 19 students who completed the assignment. There were 7 students who failed the test and also did not complete the assignment. What is the probability that a student who did not complete the homework passed the test?
Therefore, the probability that a student who did not complete the homework passed the test is 2/5 or 0.4 (or 40%).
What is Probability?Probability is a measure of the likelihood of an event occurring. It is a numerical value between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
To calculate the probability of an event, we divide the number of favorable outcomes by the total number of possible outcomes. For example, if we toss a fair coin, the probability of getting heads is 1/2 because there is one favorable outcome (getting heads) out of two possible outcomes (getting heads or tails).
Let's define the following events:
A: passing the test
B: completing the assignment
We know that:
[tex]P(A) = 18/28 = 9/14[/tex] (since 18 students out of 28 passed the test)
[tex]P(B) = 19/28[/tex] (since 19 students out of 28 completed the assignment)
P (A ∩ B) = P(B) = 19/28 (since every student who completed the assignment also took the test)
We want to find P (A | not B), which represents the probability of passing the test given that the student did not complete the assignment.
Using Bayes' theorem, we have:
P (A | not B) = P (not B | A) * P (A) / P (not B)
We know that:
P (not B | A) = P (A' ∩ B') / P(A') = 7/28 / 10/28 = 7/10 (since 7 students failed the test and did not complete the assignment)
P (not B) = 1 - P(B) = 9/28 (since not completing the assignment is the complement of completing the assignment)
Plugging in these values, we get:
[tex]P(A | not B) = (7/10) * (9/14) / (9/28)[/tex]
[tex]P(A | not B) = 2/5[/tex]
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