The slope of the line is 6.
What is a point on a line?
In geometry, a point is a place. It is completely empty, meaning it has no width, length, or depth. A dot indicates a point. A line is described as a collection of points that stretches in both directions indefinitely.
Given table is
x 12 13 14 15
y -4 2 8 14
The points on the lines are (12,-4), (13,2), (14,8), (15,14).
The formula of slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).
Now consider two points (12,-4), (13,2) to find the slope:
m = (2 - (-4))/(13 - 12)
m = (2 + 4)/1
m = 6/1
m = 6
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A news agent conducted a survey of business magazine subscribers in a town and found that there was
circulation of only three business magazines. He made the Venn diagram below to show the number of
subscribers to each of the three magazines: Board Review, Strategy and Finance, and Investor Journal
394 subscribers are represented in the venn diagram.
What is venn diagram?Venn diagrams are charts that are used to visually represent relationships between sets, operations on those relationships, and set relationships. The Venn diagram, which uses circles that are overlapped, intersected, and not intersected to depict the relationship between sets, was created by John Venn. A set diagram or a logic diagram is another name for a Venn diagram, which shows a variety of set operations such the intersection, union, and difference of sets.
Additionally, it can be used to set items. a depiction of each relationship between several sets. Any closed figure, such as a circle or a polygon (square, hexagon, etc.), can be used to represent a Venn diagram. However, each group is typically represented as a circle.
according to the venn diagram
196+41+21+52+84 = 394
There are 394 subscribers
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Given the two functions, which statement is true? f(x) = 3x, g(x) = 3x + 5 Question 12 options: g(x) is translated up 5 units compared to f(x) g(x) is translated left 5 units compared to f(x) g(x) is translated down 5 units compared to f(x) g(x) is translated right 5 units compared to f(x)
The correct statement is: g(x) is translated up 5 units compared to f(x).
The correct answer is A.
To determine the translation between the two functions, we can observe that the only difference between them is the constant term.In f(x) = 3x, there is no constant term, so the graph of f(x) passes through the origin (0, 0).In g(x) = 3x + 5, there is a constant term of 5 added to the function. This means that the graph of g(x) is shifted vertically upward by 5 units compared to the graph of f(x).Therefore, g(x) is translated up 5 units compared to f(x).The correct answer is A.
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greatest common divisor of 66 and 90
Answer:
6
Step-by-step explanation:
66 / 6 =11
90/6 =15
11 & 15 prime to each other, so 6 is the answer.
6 units to the right of 0
A survey found that 20% of the people in Fiji drive the car without seatbelt. If 3 people are randomly selected, find the probability that at least 2 drive without seat.
Answer:
0.104 = 10.4% probability that at least 2 drive without a seatbelt.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they drive without a seatbelt, or they do not. The probability of a person driving without a seatbelt is independent of any other person. This means that we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.
\(C_{n,x} = \frac{n!}{x!(n-x)!}\)
And p is the probability of X happening.
20% of the people in Fiji drive the car without seatbelt.
This means that \(p = 0.2\)
3 people are randomly selected
This means that \(n = 3\)
Find the probability that at least 2 drive without a seatbelt?
This is:
\(P(X \geq 2) = P(X = 2) + P(X = 3)\)
In which
\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)
\(P(X = 2) = C_{3,2}.(0.2)^{2}.(0.8)^{1} = 0.096\)
\(P(X = 3) = C_{3,3}.(0.2)^{3}.(0.8)^{0} = 0.008\)
\(P(X \geq 2) = P(X = 2) + P(X = 3) = 0.096 + 0.008 = 0.104\)
0.104 = 10.4% probability that at least 2 drive without a seatbelt.
Find the distance between the point (5,12) and the line y = 5x + 12 (rounded to the nearest hundredth).
A. 1.36 units
B. 2.19 units
C. 4.81 units
D. 4.90 units
The distance between the point (5,12) and the line y = 5x + 12 is 4.90 units
How to find the distance between a point and a line?
If a point P with the coordinates (x₁, y₁), and we need to know its distance from the line represented by ax + by + c = 0
Then the distance of a point from the line is given by the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
Given: the point (5,12) and the line y = 5x + 12. The line can be written as
5x-y+12 = 0. Thus:
x₁ = 5, y₁ = 12, a = 5, b = -1, c = 12. Substitute these into the formula:
d = (ax₁ + by₁ + c) / √(a² + b²)
d = (5×5 + (-1×12) + 12) / √(5² + (-1)²)
d = 25/√26 = 4.90 units
Therefore, the distance between the point and the line is 4.90 units. Option D is the answer
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Use implicit differentiation to find dy/dx and d^2y/dx^2.
Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.
Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.
Given the equation x² + xy + y² = 5,
we can differentiate both sides with respect to x using the chain rule as follows:
2x + (x(dy/dx) + y) + 2y(dy/dx) = 0
Simplifying this equation yields:
(x + 2y)dy/dx = -(2x + y)
Hence, dy/dx = -(2x + y)/(x + 2y)
Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.
That is:
d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))
= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))
Simplifying this equation yields:
d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³
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Pahelpppp po pang grade 6 po yan na math
A golf ball rolls at a speed of 8 m/s for 12 seconds. Mandy hits the golf ball and it rolls
for 16 seconds at a speed of 12 m/s. What is the total distance travelled by the golf ball?
Using the given information, the total distance travelled by the golf ball is 288 m
Calculating the total distance travelled by the golf ballFrom the question, we are to calculate the total distance travelled by the golf ball
The distance travelled by the golf ball can be calculated by using the formula,
Distance = Speed × Time
From the given information,
The golf ball rolls at a speed of 8 m/s for 12 seconds
Thus,
The distance travelled at this time is
Distance = 8 m/s × 12 s
Distance = 96 m
Also,
Mandy hits the golf ball and it rolls for 16 seconds at a speed of 12 m/s
The distance travelled at this time is
Distance = 12 m/s × 16 s
Distance = 192 m
The total distance travelled by the golf ball is 96 m + 192 m
=
Hence, the total distance travelled by the golf ball is 288 m
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Given the following function, find and simplify (f⋅g)(1/3)
The simplification of the composite function expression (f • g)(1.3) when
f(x) = -x + 3 and g(x) = -x - 1 is; 3²/₃
How to simply products of composite functions?
Composite functions are defined as when the output of one function is used as the input of another. If we have a function f and another function g, the function f ⋅ g ( x ), said as “ f of g of x is the composition of the two functions.
What the composite function expression (f • g)(x) denotes is;
f(g(x))
Now, we are given that the functions are;
f(x) = -x + 3
g(x) = -x - 1
Thus;
f(g(x)) = f(-x - 1) = -(-x + 3) - 1 = x - 3 - 1 = x - 4
Therefore since we want to find (f⋅g)(1/3), we will plug in 1/3 for x to get;
f(g(x)) = (1/3) - 4 = 3²/₃
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Complete function is;
Given the following functions, find and simplify (f • g)(1.3).
f(x) = -x + 3
g(x) = -x - 1
• 10%
5) An experiment consists of spinning the spinner shown below 200 times and recording the
results in a frequency table. Based on theoretical probability, how many times would you
expect the color blue or green to be spun?
BLUE
GREEN
YELLOW
REd
Based on their given probabilities, e would expect the color blue or green to be spun approximately 75 times in this experiment.
How many times can the blue or green color be obtained?To find the expected number of times the color blue or green will be spun, we first need to add their probabilities:
0.25 + 0.125 = 0.375
This means that, on average, we would expect to see blue or green spun 0.375 times for every spin. To find the expected number of times this will happen over 200 spins, we can multiply the probability by the number of spins:
0.375 x 200 = 75
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solve the file please
Answer:
z + 4 × 9
Sorry if this is wrong.
What fraction is equal to 15/18
(x + 1) (x+8) multiply binomials and put in standard form.
Answer:
x² + 9x + 8
Step-by-step explanation:
Step 1: FOIL
x² + 8x + x + 8
Step 2: Combine like terms
x² + 9x + 8
Answer:
x^2 + 9x + 8
Step-by-step explanation:
(x + 1)(x + 8)
x(x + 1) +8(x + 1)
x^2 + x + 8x +8
x^2 + 9x + 8
. (a) What is demographics?
Demographics are data that describe populations and their characteristics. Demographic analysis is the study of a population's characteristics such as age, race, and gender.
What is demography?Demography is the statistical study of populations, particularly human populations. Demographic analysis investigates and quantifies population dimensions and dynamics; it can apply to entire societies or groups defined by criteria such as education, nationality, religion, and ethnicity.
Age, gender, occupation, cultural background, and family status are the five major demographic segments. Demographic analysis is the study of a population's characteristics such as age, race, and gender. Demographic data is a statistical representation of socioeconomic information such as employment, education, income, marriage rates, birth and death rates, and so on.
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4.Think about the expression (x-8)(x+4).
(a) For what values of x will this expression be
equal to zero? Show how you arrived at your
Answer
Answer:
x-8 to get the zero for the 8 you have to add it. And for the second part you have to subtract four from itself.
Step-by-step explanation:
From the expression (x - 8) (x + 4), the values of x need to be 8 or -4, for x to be equal to zero.
Given that:
(x - 8) (x + 4) = 0
The expression from above is the expanded form of a given quadratic equation.
To find the quadratic equation, we will use the values of one enclosed bracket to multiply the values of the other.
i.e.
(x -8) (x + 4) = 0
x² + 4x - 8x - 32 = 0
x² - 4x - 32 = 0
(So, this above expression shows the quadratic equation from which the roots of (x-8) (x-4) is being derived from)From the roots;
(x - 8) (x + 4) = 0
Let;
(x - 8) = 0 or (x +4) = 0
x - 8 = 0 or x + 4 = 0
x = 8 or x = -4
Therefore, we can conclude that the value of x needs to be 8 or -4 for x to be equal to zero.
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What’s the x intercept of -2x+5y=-30
Answer:(15,0)
Step-by-step explanation:
A junior high athletic club is making blankets and plans to sell them as a fundraiser.They are able to make 10 blankets and want to sell them for $35 each.The total amount raised can be represented by y = 35x. A: Is this function discrete or continuous?B: Determine the domain.C: Determine the range.
Functions can either be discrete or continuous.
The function is discreteThe domain and the range are \(\mathbf{[0,\infty)}\).The function is given as:
\(\mathbf{y = 35x}\)
Where x represents the number of blankets
x can only take whole numbers (i.e 0, 1, 2....)
A discrete function is such that can only non-decimal values.
Hence, the function is discrete
(b) The domain
In (a), we listed the values of x to be: (0,1,2...)
This means that, the domain is: \(\mathbf{[0,\infty)}\)
(c) The range
When x = 0, we have:
\(\mathbf{y = 35x}\)
\(\mathbf{y = 35 \times 0 = 0}\)
This means that, the range is: \(\mathbf{[0,\infty)}\)
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Perform the indicated operation:
(4 + 2i) (1 + 5i)
-6 +22i
6-221
-14 + 18i
6+22i
Answer:
-235+84i
Step-by-step explanation:
I hope this is what you were looking for.
Sean baked 18 dozen chocolate cupcakes and 13 dozen vanilla cupcakes. About how many cupcakes did sean bake
2
Let g(x) = x + 4x-7.
What is g(x) in graphing form?
(x + 2) - 7 = 4
O g(x) = (x + 2)²-7
Onone of the answer choices
x² + 4x-7=0
O g(x) = (x + 2)² - 11
The graphing form of the function g(x) is: C) none of the answer choices.
The function g(x) = \(x^2 + 4x - 7\)is already in the standard form of a quadratic equation. In graphing form, a quadratic equation can be represented as y =\(ax^2 + bx + c,\) where a, b, and c are constants.
Comparing the given function g(x) =\(x^2 + 4x - 7\)with the standard form, we can identify the coefficients:
a = 1 (coefficient of x^2)
b = 4 (coefficient of x)
c = -7 (constant term)
Therefore, the graphing form of the function g(x) is:
C) none of the answer choices
None of the given answer choices (A, B, D, or E) accurately represents the graphing form of the function g(x) =\(x^2 + 4x - 7\). The function is already in the correct form, and there is no equivalent transformation provided in the answer choices. The given options either represent different equations or incorrect transformations of the original function.
In graphing form, the equation y = \(x^2 + 4x - 7\) represents a parabolic curve. The coefficient a determines the concavity of the curve, where a positive value (in this case, 1) indicates an upward-opening parabola.
The coefficients b and c affect the position of the vertex and the intercepts of the curve. To graph the function, one can plot points or use techniques such as completing the square or the quadratic formula to find the vertex and intercepts. Option C
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Solve the inequality 6x^2 + 5x < 4
Answer: -4/3 < x< 1/2
Step-by-step explanation: inequality form
Select one number from each column to make the equation true,
4
32
234 = 5 x 36
33
Answer:
6 x 39 = 234
Step-by-step explanation:
9 x 6 is 54. 30 x 6 is 180. 180+54 is 234.
Determine if the correlation between the two given variables is likely to be positive or negative, or if they are not likely to display a linear relationship. The retail price of a particular smartphone and the number of units sold at that price
Answer:
no correlation
Step-by-step explanation:
The price of the smartphone is fixed beforehand, therefore price does not depend upon the number of units sold.
Hence, there is no correlation between the two given variables.
Hence, no correlation would be the answer.
Select all the correct answers
A. Reflection across the x-axis followed by reflection across the y-axis and then a dial action by scale factor 0.5
B. A 90 counterclockwise rotation about the origin and then dialation by scale factor
C. A 180 clockwise rotation about the origin and then a dialation by scale factor of 0.5
D. A transition 2 units down and 5 units left and then a dialation by scale factor
Find the difference between the sum and product of 2 1/4 and 1 4/5
Answer: 0 is the answer
if my answer is correct mark as brainliest
Rewrite the fractions as improper fractions:
2 1/4 = 9/4
1 4/5 = 9/5
Rewrite the fractions to have a common denominator:
9/4 = 45/20
9/5 = 36/20
The sum is adding the two together:
45/20 + 36/20 = 81/20
Rewrite as a mixed number:
81/20 = 4 1/20
Product is multiplication:
For multiplying you can use different denominators so you can use the first improper fractions:
9/4 x 9/5 = (9x9)/(4x5) 81/20
Rewrite as a mixed number: 4 1/20
Now subtract to find the difference: 4 1/20 - 4 1/20 = 0
The difference = 0
Two and three fifths of a number equals −26 . What is the number?
Answer:
-10
Step-by-step explanation
-26 x 2 3/5 = -10
-10 x 2 = -20
3/5 of -10 is -6
-20 - 6 = -26
The number is 10.
What is an Equation?An equation is a mathematical statement that is formed when two algebraic expressions are equated using an equal sign.
Let the number is n,
The equation formed from the statement is
(2 3/5 ) * n = -26
(13/5 ) * n =26
n = 26 * 5 / 13
n = 10
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The mayor of a town has proposed a plan for the annexation of a new bridge. A political study took a sample of 900 voters in the town and found that 42% of the residents favored annexation. Using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 38%. State the null and alternative hypotheses.
Answer:
H0 : p ≤ 0.38
H1 : p > 0.38
Step-by-step explanation:
Given :
Claim : percentage of residents who favor annexation is above 38%
The claim in the context here is the alternative hypothesis ; since the null and the alternative are always the opposite, then the ;
The null hypothesis : percentage is less than equal to 38%
The alternative hypothesis ; percentage is greater than 38%
Null hypothesis H0 : p ≤ 0.38
Alternative hypothesis H1 : p > 0.38
-8/9 + (-2)/57
find the absolute value of the following rational number
The absolute value of the Rational number -474/513 is 474/513.
To find the sum of the rational numbers -8/9 and -2/57, you need to have a common denominator. The least common multiple (LCM) of 9 and 57 is 513. So, you can rewrite the fractions with a common denominator:
-8/9 = (-8/9) * (57/57) = -456/513
-2/57 = (-2/57) * (9/9) = -18/513
Now, you can add the fractions:
-456/513 + (-18/513) = (-456 - 18)/513 = -474/513
To find the absolute value of the rational number -474/513, you simply ignore the negative sign and take the value as positive:
| -474/513 | = 474/513
Therefore, the absolute value of the rational number -474/513 is 474/513.
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It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end. How long will it take you to read 6.25 pages and also take the test?
The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
It takes you 0.8 of a minute to read each page of your health book. It takes you 5.5 minutes to take the test at the end.
The number of minutes to read 6.25 pages will be given as,
⇒ 6.25 x 0.8
⇒ 5 minutes
The number of minutes to take the test will be given as,
⇒ 5.5 - 5
⇒ 0.50 minute
⇒ 0.50 x 60
⇒ 30 seconds
The number of minutes to read is 6.25 pages and taking the test will be 5 minutes and 0.50 minutes, respectively.
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