The linear function with the given properties is: f(x) = 8 - 6x.
What is linear function?A linear function is a mathematical equation that describes a straight line when graphed. It is the most basic type of function, where the output is equal to the input multiplied by a constant, known as the slope, and a constant added, known as the y-intercept. Linear functions are used to model relationships between two quantities and can be used to describe a wide range of phenomena, from physical properties to economic trends.
This linear function is used to calculate the value of a variable (x) when given the starting value of the function (f(0)) and the slope of the line (the rate at which the value of the function changes for each unit increase in x). In this case, the starting value of the function (f(0)) is 8, and the slope of the line is -6, meaning that the value of the function decreases by 6 for each unit increase in x. Therefore, the linear function that satisfies these properties is f(x) = 8 - 6x.
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The average yearly salary of a lawyer is $25 thousand less than twice that of an architect. Combined, an architect and a lawyer earn $209 thousand. Find the average yearly salary of an architect and a lawyer
Answer:
Step-by-step explanation:
Let's call the average yearly salary of an architect "A" and the average yearly salary of a lawyer "L".
From the first sentence, we know that:
L = 2A - 25
From the second sentence, we know that:
A + L = 209
We can substitute the first equation into the second equation:
A + (2A - 25) = 209
Simplifying:
3A - 25 = 209
Adding 25 to both sides:
3A = 234
Dividing both sides by 3:
A = 78
Now we can use the first equation to find L:
L = 2A - 25 = 2(78) - 25 = 131
Therefore, the average yearly salary of an architect is $78,000 and the average yearly salary of a lawyer is $131,000.
The Hanwell Company acquired a 30% equity interest in The Northfield Company for CU400,000 on 1 January 20X6. In the year to 31 December 20X6 Northfield earned profits of CU80,000 and paid no dividend. In the year to 31 December 20X7 Northfield incurred losses of CU32,000 and paid a dividend of CU10,000. In Hanwell's consolidated statement of financial position at 31 December 20X7, what should be the carrying amount of its interest in Northfield, according to IAS 28 Investments in associates?
classifying parallelograms
After addressing the issue at hand, we can state that Hence, x = 5.5 and rectangle m El H = 180.
What is rectangle?In Euclidean geometry, a rectangle is a parallelogram with four small angles. Alternately, it might be regarded as a hexagon with a fundamental rule or one with equal angles. Another option for the parallelogram is a straight angle. Four vertices in a square have equal lengths. Four 90° angle vertices and equal parallel sides make up a quadrilateral with a rectangular cross section. Because of this, it is occasionally referred to as a "equirectangular rectangle". A rectangle is occasionally referred to as a parallelogram due to the equal and parallel dimensions of its two sides.
El = 3x + 5, EG = 5x + 16, and m IF G = 270 are all known values. We also understand that a rectangle's diagonals are of equal length. Hence, we can write:
El = HG
EG = IF
From the knowledge provided above, we can formulate two equations in terms of x:
3x + 5 = HG
5x + 16 = IF
90 m HG F and 90 m EFG
Since we know that GH is a straight line because m GHE = 0, m El G must be 180 degrees.
Now that the formulas for HG and IF are equivalent to one another, we may find x:
3x + 5 = 5x + 16
2x = 11\sx = 5.5
Hence, x = 5.5 and m El H = 180.
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A grocery store sells a bag of 3 oranges for $2.43. What is the unit cost?
Answer:
$0.81
Step-by-step explanation:
We know
A grocery store sells a bag of 3 oranges for $2.43.
What is the unit cost?
We take
2.43 / 3 = $0.81
So, the answer is $0.81
Find an equation for the line that passes through the points (4,2) and (-6,4) .
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{2}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{4}}} \implies \cfrac{ 2 }{ -10 } \implies - \cfrac{ 1 }{ 5 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2}=\stackrel{m}{- \cfrac{ 1 }{ 5 }}(x-\stackrel{x_1}{4}) \\\\\\ y-2=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}\implies y=- \cfrac{ 1 }{ 5 }x+\cfrac{4}{5}+2\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 5 }x+\cfrac{14}{5} \end{array}}[/tex]
Find the c and y- intercepts of the parabola y = 3x^2 -9x + 9
The y-intercept is (0, 9), and the parabola has no x-intercepts.
What are intercepts?An intercept in mathematics is a location on the y-axis through which the line's slope passes. It is a place on the y-axis where a straight line or a curve crosses. This is reflected in the equation for a line, which is written as y = mx+c, where m denotes slope and c denotes the y-intercept.
X-intercept and Y-intercept are the two main intercepts. The line's x-intercept and y-intercept are located where the line crosses the x and y axes, respectively.
To find the y-intercept of the parabola, we set x = 0 and solve for y:
y = 3x² - 9x + 9
y = 3(0)² - 9(0) + 9
y = 9
Therefore, the y-intercept is (0, 9).
To find the x-intercepts, we set y = 0 and solve for x:
0 = 3x² - 9x + 9
0 = x² - 3x + 3
Using the quadratic formula, we get:
x = [3 ± √((-3)² - 4(1)(3))]/(2(1))
x = [3 ± √(9 - 12)]/2
x = [3 ± √(-3)]/2
The square root of a negative number is not a real number.
The parabola does not intersect the x-axis, and therefore, there are no x-intercepts.
Therefore, the y-intercept is (0, 9), and the parabola has no x-intercepts.
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An automobile company is running a new television commercial in five cities with approximately the same population. The following table shows the number of times the commercial is run on TV in each city and the number of car sales (in hundreds). Find the Pearson correlation coefficient r for the data given in the table. Round any intermediate calculations to no less than six decimal places, and round your final answer to three decimal places.
Number of TV commercials, x 4
8
12
16
18
Car sales, y (in hundreds) 2
5
9
8
9
The linear regression line is:Y = 0.51X - 14.05
What is number?Number is a mathematical object used to count, measure, and label. It is a fundamental concept in mathematics, and is used in nearly every branch of the discipline. In everyday life, the notion of number is used to count objects, keep track of scores, measure amounts, and label objects.
City TV Commercials Car Sales
A 60 20
B 50 15
C 70 25
D 45 17
E 55 19
Calculating the linear regression line:
m = Slope = (NΣXY - (ΣX)(ΣY)) / (NΣX2 - (ΣX)2)
= (5(1475) - (325)(95)) / (5(5850) - (325)2)
= (7375 - 30875) / (29250 - 105625)
= -38500 / -75375
= 0.51
b = Intercept = (ΣY - m(ΣX)) / N
= (95 - 0.51(325)) / 5
= (95 - 165.25) / 5
= -70.25 / 5
= -14.05
Therefore, the linear regression line is:
Y = 0.51X - 14.05.
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Need help as soon as possible!! Edge 2023
The given quadratic equation is f(x) = x³ - 3x² + 2x-1. The two solutions to the equation are x = (3x + √(9x² + 4))/2x² and x = (3x - √(9x² + 4))/2x².
What is quadratic equation?A quadratic equation is written in the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
To solve this equation, we will use the quadratic formula.
The quadratic formula states that for a quadratic equation of the form ax² + bx + c = 0, the solutions are given by
x = [-b ± √(b² - 4ac)]/2a.
In this equation, a = x², b = -3x, and c = -1. Plugging these values into the formula, we get x = [3x ± √(9x² - 4(x²)(-1))]/2(x²). Simplifying this, we get
x = [3x ± √(9x² + 4)]/2x².
Now, we must solve for the two solutions. The first solution is x = (3x + √(9x² + 4))/2x². The second solution is
x = (3x - √(9x² + 4))/2x².
Therefore, the two solutions to the given equation are
x = (3x + √(9x² + 4))/2x² and
x = (3x - √(9x² + 4))/2x².
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What is the equation in slope-intercept form of the line that passes through the points (0,4) and (2,0)?
Answer:
C: y=2x-4
Step-by-step explanation:
pls mark brainliest
Aaron wraps present in a store. In one hour, he wraps 8 games and one console. How much wrapping paper does Aaron use? How much wrapping paper does Aaron use? Use exercises 1-3 to answer the question.
The wrapping paper used by Aaron is 9 and 2/3 feet of paper
Finding the amount of wrapping paper used:To solve this problem, use the given information about how much wrapping paper is needed for each game and gaming console, and then multiplied by the number of games and consoles that Aaron wraps in one hour. For simple calculation convert mixed fractions into an improper fraction and solve the problem.
Here we have
Aaron wraps present in a store. In one hour, he wraps 8 games and one console.
From the given figure,
Each game takes 2/3 foot of wrapping paper
Each gaming console takes 4 1/3 feet of wrapping paper
From the data
Aaron wraps 8 games in 1 hour
The wrap is used for 8 games = 8 × [ 2/3 foot ] = 16/3 foot
He wraps one console.
The wrap used for 1 console = 4 1/3
Here 4 1/3 = 13/3 [ Converting mixed fraction to improper fraction ]
Hence,
Total amount of wrap used = 16/3 + 13/3
= [ 16 + 13]/3 = 29/3 = 9 2/3
Therefore,
The wrapping paper used by Aaron is 9 and 2/3 feet of paper
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At the base level is the gross income per month of your family. (use $5,000 as an example) 10 percent of the gross income is used for family activities such as eating out, entertainment, ... etc. Your monthly allowance is 10 percent of the family activity money. You give 10 percent of your monthly allowance to support a charity organization in your community. From the energy pyramid, how much money do you give to charity each month?
How much in one year?
give to charity each month?
Based on the given information, you would be giving $5 per month or $60 per year to charity.
How do we calculate the money we give to charity each month?Starting with a monthly gross income of $5,000, we can calculate the amount set aside for family activities as 10% of the gross income, which is:
= $5,000 x 0.10
= $500
Now, we will calculate the monthly allowance as 10% of the family activity money, which is:
= $500 x 0.10
= $50
Since you give 10% of your monthly allowance to support a charity organization, you will be giving:
= $50 x 0.10
= $5 per month
Now, in order to calculate how much you would give to charity in one year, we simply multiply the monthly amount by 12 which gives us:
= $5 x 12
= $60 per year
Therefore, the amount we would be giving to the charity is $5 per month or $60 per year.
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Answer this please!
The homework scores for some students in a health class are shown.
James: 82, 81, 86
Rodney: 78, 82, 61
Traci: 81, 90, 82
Maddi: 67, 66, 69
Which two students have the same median score?
Group of answer choices
James and Rodney
James and Traci
Traci and Maddi
Rodney and Maddi
Answer:
To find out which two students have the same median score, we need to find the median score for each student and compare them.
For James, the median score is 82 (the middle score when the scores are arranged in order).
For Rodney, the median score is 78 (the middle score when the scores are arranged in order).
For Traci, the median score is 82 (the middle score when the scores are arranged in order).
For Maddi, the median score is 67 (the middle score when the scores are arranged in order).
Therefore, the two students who have the same median score are James and Traci, as they both have a median score of 82.
Consider the equation 5 + x = n . What must be true about any value of x if n is a negative number? Explain your answer. Include an example with numbers to support your explanation. Enter your answer, your explanation, and your example in the space provided.
Answer:
x < 5 because any value of x must have a bigger negative number than 5. In this case, formally you say that all x values must be less than 5.
prime and composite numbers hard questions reasoning questions
1-Is the sum of two prime numbers always a prime number?
Solution:
No. Here is an example.
3 + 7 = 10 , 3 and 7 are prime numbers but not their sum 10.
2-Is the product of two prime numbers also a prime number?
Solution:
Never because it will have 1 and itself as factors and also the two numbers involved in the product.
Example: 7 × 11 = 77 ,77 has 1, itself, 7 and 11 as factors.
3-Which is the largest 3 digit prime number?
Solution:
Start with the largest three digit number 999.
4- Which is the smallest 2 digit prime number?
Solution
Start with the smallest 2 digit number 10.
10 is not a prime number
Answer: 11 is a prime number
The table below shows the cost of downloading songs from a website. Number of Songs Number of Songs Total Cost Total Cost 6 6 $ 1.80 $1.80 12 12 $ 3.60 $3.60 20 20 $ 6 $6 What is the constant of proportionality between the total cost and the number of songs?
Answer:
Step-by-step explanation:
To find the constant of proportionality, we can use the formula for a proportional relationship: y = kx, where y is the total cost, x is the number of songs, and k is the constant of proportionality.
Using the table, we can find two pairs of values for y and x:
When x = 6, y = $1.80
When x = 12, y = $3.60
We can set up a proportion:
y1 / x1 = y2 / x2
$1.80 / 6 = $3.60 / 12
Simplifying, we get:
$0.30 = $0.30
This tells us that the constant of proportionality is $0.30.
We can check this by using another pair of values:
When x = 20, y = $6
Using the formula y = kx, we get:
$6 = ($0.30)(20)
Simplifying, we get:
$6 = $6
This checks out, so we can be confident that the constant of proportionality is $0.30.
PLEASE HELP IM TIMED
Write equivalent fractions for 3/10 and 1/7 using the least common denominator. Type the fractions, using a slash ( / ) to separate the numerator and denominator.
3/10=
1/7=
Answer: Your welcome!
Step-by-step explanation:
The equivalent fractions for 3/10 and 1/7 using the least common denominator are 6/20 and 3/20. The least common denominator of 3/10 and 1/7 is 20, so the fractions must be multiplied by the same number to reach the denominator of 20. 3/10 multiplied by 2/2 is 6/20, and 1/7 multiplied by 3/3 is 3/20.
Three men took part in a business. They put in N2 000, N4 000 and N1 500 as capital. The profit made was divided among them in the same proportion as the amounts put in. If the profit was N300, how much did each man get?
Answer:
The total amount of capital invested is:
N2,000 + N4,000 + N1,500 = N7,500
The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:
N2,000 / N7,500 * N300 = N80
The second man gets:
N4,000 / N7,500 * N300 = N160
The third man gets:
N1,500 / N7,500 * N300 = N60
Therefore, each man gets N80, N160, and N60, respectively.
Step-by-step explanation:
Answer:
N80, N160, and N60
Step-by-step explanation:
The total amount of capital invested is:
N2,000 + N4,000 + N1,500 = N7,500
The proportion of the profit that each man gets is equal to the proportion of the capital that he invested. Therefore, the first man gets:
N2,000 / N7,500 * N300 = N80
The second man gets:
N4,000 / N7,500 * N300 = N160
The third man gets:
N1,500 / N7,500 * N300 = N60
Therefore, each man gets N80, N160, and N60, respectively.
What is 6 equations that are equivalent to 6m=48?
Answer:
3m=24
m=8
12m=96
24m=192
48m=384
96m=768
A group of collage students are going to a lake house for the weekend and plan on renting small cars(s) and large(l) cars to make the trip. Each car can hold 5 people and each large car 8 people. A total of 15 cars were rented which can hold 90 people altogether. Determine the number of large car and rental cars.
Answer:
10 small, 5 large
Step-by-step explanation:
if they were all small cars, 5x15 would be 75. there need to be 15 more spots, and each large can hold an extra 3. 15/3 is 5. so there are 10s and 5l
students would need to rent 5 small cars and 8 large cars
Nakia is an architect designing a house with a peaked roof. She is trying to decide what the limitations are on her design. If AB is 8 feet and triangle ABC will be isosceles, describe the possible lengths for AC.
The possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).
How did we get the value?If triangle ABC is isosceles, then AC must be equal to BC. Let's call the length of AC "x".
Using the Pythagorean theorem, we can find the length of the diagonal line segment BD (which is also the height of the peaked roof):
BD^2 = AB^2 - (AC/2)^2
BD^2 = 8^2 - (x/2)^2
BD^2 = 64 - x^2/4
To ensure that the roof is peaked, we need BD to be less than x (otherwise, the roof would be flat). So we can set up an inequality:
BD < x
√(64 - x^2/4) < x
64 - x^2/4 < x^2
256 - x^2 < 4x^2
5x^2 > 256
x^2 > 51.2
x > √(51.2)
Therefore, the possible lengths for AC are any values greater than the square root of 51.2 (approximately 7.15 feet).
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7 1/2 divied by 3/4 what is it?
Answer:
7/9
Step-by-step explanation:
Find the reciprocal of the divisor
Reciprocal of 3/4 : 4/3
Now multiply it with the dividend..
so, 7/12 ÷ 3/4 = 7/12 × 4/3
=7/12×4/3 = 28/36
And after reducing the fraction, the answer is 7/9
Q14: In the store, Lean Statks up eight cans each weighing 1 1/3 kg. What is the total weight of the cans
Answer:
10 2/3 kg
8 X 1 1/3 kg = 10 2/3 kg
In a triangle if y equals 940 inches Y equals 100 degrees W equals 38 degrees what length is w
Answer: W = 357.2
Step-by-step explanation:
x/38 * 940/100
100x * 35,720
x=357.2
6 friends share 3 apples.
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Curriculum which addresses learning goals across multiple subjects areas at the same time known as
A curriculum is said to as "integrated" when it simultaneously targets learning objectives across different topic areas.
Explain about the integrated curriculum?Children can pursue learning holistically with an integrated curriculum, free from the limitations frequently imposed by topic boundaries.
Early childhood programs have a strong emphasis on how all subject areas relate to one another and how they all work together to give kids fundamental learning skills. It acknowledges that reading, writing, thinking, speaking, literature, drama, world history, integrated maths ,science, health, sport science, music, and creative arts are all part of the primary school curriculum.Moreover, technology and investigative techniques are included in the curriculum. Integration recognizes and strengthens the connections that exist among the things. A curriculum that is integrated involves learning that is synthesised across conventional topic areas and learning experiences that are intended to reinforce one another.Know more about the curriculum
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Fill in the blank to complete the comparison. 21 is 7 times as many as
Answer:
3
Step-by-step explanation:
21 is 7 times the number three. You can get this answer by dividing 21 by 7 (answer is 3). You can check your work by multiplying 7 x 3 (you would get 21)
Let W be the event that a randomly chosen person drinks sixty-four ounces of water per day. Let V be the event that a randomly chosen person has varicose veins. Place the correct event in each response box below to show:
Given that the person drinks sixty-four ounces of water per day, the probability that a randomly chosen person has varicose veins.
For the given situation the probability event can be denoted mathematically as P(V|W).
What is probability?
Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
The event we are interested in is "a randomly chosen person has varicose veins" (V), given that "the person drinks sixty-four ounces of water per day" (W).
So, we can write this as -
P(V|W)
which is the conditional probability of event V given event W.
Therefore, the event can be denoted as P(V|W).
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What is the volume of this hemisphere?
Therefore , the solution of the given problem of volume comes out to be a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.
What is volume, exactly?The volume of a three-dimensional item, which is measured in cubic units, describes how much room it occupies. Liter and in3 are these marks for cubic measurements. To compute an object's measurements, you must, however, comprehend its volume. Converting an object's weight into mass units including grams and kilograms is a common procedure.
Here,
The formula: can be used to determine the capacity of a hemisphere with a radius of 2 inches.
=> V = (2/3) * π * r³
where "π" is a mathematical constant that is roughly equivalent to 3.14159 and "r" is the hemisphere's radius.
When we substitute the radius's value, we obtain:
=> V = (2/3) * π * 2³
=> (2/3) * π* 8
=> V = 16.755 cubic inches. (approx)
Therefore, a hemisphere with a 2 inch radius has a capacity of roughly 16.755 cubic inches.
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help me please i got 5849.82 but thats not on there
Answer: 1863[tex]\pi[/tex] cm^3 (option C)
Step-by-step explanation:
The volume is given by the equation
[tex]V=\pi r^2h[/tex]
Just placing the values:
[tex]V=\pi (9)^2(23)[/tex]
Notice the pi is left over, so just get the 9^2*23=1863
So the answer for the volume is 1863[tex]\pi[/tex] in cm^3
So your answer is just fine, 5849. Just notice the pi is not in it.