Answers
Answer:
f(x)= - [x] + 3
Step-by-step explanation:
because it describes a negative slope and 3 units up from the origin
Related Questions
A country has 4 states. Their populations are listed below. If the country's legislature has 102 representatives, determine how many representatives should be assigned to each state using Hamilton's, Jefferson's and Webster's methods.
Answers
Here are the populations of the 4 states:
- State A: 10,000,000
- State B: 8,000,000
- State C: 5,000,000
- State D: 3,000,000
Hamilton's method:
- Step 1: Calculate the total population of all 4 states.
Total population = 10,000,000 + 8,000,000 + 5,000,000 + 3,000,000 = 26,000,000
- Step 2: Divide the total number of representatives by the total population.
Priority value = 102 / 26,000,000 = 0.00392307692
- Step 3: Multiply the priority value by each state's population to get its number of representatives.
State A: 10,000,000 * 0.00392307692 = 39.2307692 representatives (rounded to 39)
State B: 8,000,000 * 0.00392307692 = 31.3846154 representatives (rounded to 31)
State C: 5,000,000 * 0.00392307692 = 19.6153846 representatives (rounded to 20)
State D: 3,000,000 * 0.00392307692 = 11.7692308 representatives (rounded to 12)
Jefferson's method:
- Step 1: Divide the total number of representatives by 2.
Half of the representatives = 102 / 2 = 51
- Step 2:
- State A: sqrt(10,000,000) = 3,162.27766
- State B: sqrt(8,000,000) = 2,828.42712
- State C: sqrt(5,000,000) = 2,236.06798
- State D: sqrt(3,000,000) = 1,732.05081
- Step 3: Divide each state's result from step 2 by the sum of all states' results from step 2 and multiply the result by the total number of representatives.
State A: (3,162.27766 / (3,162.27766 + 2,828.42712 + 2,236.06798 + 1,732.05081)) * 102 = 39 representatives (rounded to 39)
State B: (2,828.42712 / (3,162.27766 + 2,828.42712 + 2,236.06798 + 1,732.05081)) * 102 = 35 representatives (rounded to 35)
State C: (2,236.06798 / (3,162.27766 + 2,828.42712 + 2,236.06798 + 1,732.05081)) * 102 = 22 representatives (rounded to 22)
State D: (1,732.05081 / (3,162.27766 + 2,828.42712 + 2,236.06798 + 1,732.05081)) * 102 = 6 representatives (rounded to 6)
Webster's method:
- Step 1: Calculate the average population of the 4 states.
Average population = (10,000,000 + 8,000,000 + 5,000,000 + 3,000,000) / 4 = 6,500,000
- Step 2: Calculate each state's excess population by subtracting the average population from its population.
State A's excess population = 10,000,000 - 6,500,000 = 3,500,000
State B's excess population = 8,000,000 - 6,500,000 = 1,500,000
State C's excess population = 5,000,000 - 6,500,000 = -1,500,000
State D's excess population = 3,000,000 - 6,500,000 = -3,500,000
- Step 3: Calculate each state's modified excess population by taking the square root of its absolute excess population.
State A's modified excess population = sqrt(3,500,000) = 1,870.82869
State B's modified excess population = sqrt(1,500,000) = 1,224.74487
State C's modified excess population = sqrt(1,500,000) = 1,224.74487
State D's modified excess population = sqrt(3,500,000) = 1,870.82869
- Step 4: Calculate each state's priority value by dividing its modified excess population by the sum of all states' modified excess populations and multiplying the result by the total number of representatives.
State A's priority value = (1,870.82869 / (1,870.82869 + 1,224.74487 + 1,224.74487 + 1,870.82869)) * 102 = 38 representatives (rounded to 38)
State B's priority value = (1,224.74487 / (1,870.82869 + 1,224.74487 + 1,224.74487 + 1,870.82869)) * 102 = 25 representatives (rounded to 25)
State C's priority value = (1,224.74487 / (1,870.82869 + 1,224.74487 + 1,224.74487 + 1,870.82869)) * 102 = 25 representatives (rounded to 25)
State D's priority value = (1,870.82869 / (1,870.82869 + 1,224.74487 + 1,224.74487 + 1,870.82869)) * 102 = 14 representatives (rounded to 14)
Therefore, using Hamilton's method, State A gets 39 representatives, State B gets 31 representatives, State C gets 20 representatives, and State D gets 12 representatives. Using Jefferson's method, State A gets 39 representatives, State B gets 35 representatives, State C gets 22 representatives, and State D gets 6 representatives. Finally, using Webster's method, State A gets 38 representatives, State B gets 25 representatives, State C gets 25 representatives, and State D gets 14 representatives.
A library can seat 48 patrons in the quiet study area. There are 8 tables and each table will need to have the same amount of chairs. Let c represent the number of chairs at the library. Part A Which equation represents the number of chairs at each table in the library? 48 = 8c c = 8 + 48 c = 8 × 48 48 = 8 + c Part B Select the correct value to complete the statement. Each table at the library will have 7 6 8 chairs
Answers
Step-by-step explanation:
Part A
The equation that represents the number of chairs at each table in the library is: 48 = 8c
Part B
To find the correct value, we'll solve the equation from Part A:
48 = 8c
c = 48 ÷ 8
c = 6
So, each table at the library will have 6 chairs.
- Suppose y varies directly as x. If y = -7 when x = -14, find y when x=3
Answers
Answer:1.5
Step-by-step explanation:
Y=1/2 of x
Bitti’s father wants to fence his rectangular farm with sides measuring 100m
and 300m. What is the length of fencing needed?
Answers
Answer:
Step-by-step explanation:
A certain television is advertised as a 85-inch TV (the diagonal length). If the width of the TV is 67 inches, how tall is the TV? Round to the nearest tenth of an inch.
Answers
The height of the TV is approximately 52.3 inches when rounded to the nearest tenth of an inch.Hence, the TV is approximately 52.3 inches tall.
To find the height of the TV, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal) of a right triangle is equal to the sum of the squares of the other two sides.
In this case, the width and height of the TV form the legs of a right triangle, with the diagonal as the hypotenuse.
Let's denote the height of the TV as h. According to the Pythagorean theorem:
h² + 67² = 85²
Simplifying the equation, we have:
h² + 4489 = 7225
Subtracting 4489 from both sides, we get:
h² = 2736
Taking the square root of both sides, we find:
h ≈ 52.3.
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A car travels 37 km in 22 minutes. What is its average speed in km/h? Give your answer rounded to 1 decimal place.
Answers
Answer:
100.9 km/h
Step-by-step explanation:
We use the fraction
37 km = x km
22 min 60min
when we cross multiply, we get
2220=22x, which gives us
x=100.909090...
but since we're rounding, we simply give the answer
100.9 km/h
please help with this
Answers
The complete polynomial is f(x) = 2x⁴ - 3x² - 6 and the values are n = 4 and a = -3
Calculating the values of a and nFrom the question, we have the following parameters that can be used in our computation:
f(x) = 2xⁿ + ax² - 6 is divided by (x - 1), the remainder is -7f(x) = 2xⁿ + ax² - 6 is divided by (x + 3), the remainder is 129This means that
f(1) = 7
f(-3) = 129
So, we have
f(1) = 2(1)ⁿ + a(1)² - 6
f(-3) = 2(-3)ⁿ + a(-3)² - 6
Evaluate
f(1) = 2 + a - 6
f(-3) = 2(-3)ⁿ + a(-3)² - 6
Recall that
f(1) = -7 and f(-3) = 129
So, we have
2 + a - 6 = -7
2(-3)ⁿ + 9a - 6 = 129
This gives
a = -3
Recall that
2(-3)ⁿ + 9a - 6 = 129
So, we have
2(-3)ⁿ + 9(-3) - 6 = 129
2(-3)ⁿ = 162
Divide by 2
(-3)ⁿ = 81
Solve for n
n = 4
So, the complete polynomial is f(x) = 2x⁴ - 3x² - 6
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Rewrite the integrand in terms of u so that the integral
f(u)
Answers
a. In the integrand ∫[x/(6x² + 5)²]dx, we make the substitution u = (6x² + 5)
b. Writing the integrand ∫[x/(6x² + 5)²]dx in the form ∫f(u)du, f(u) = u²/12
What is integration?Integration is the reverse of differentiation
a. Since we want to find the substitution in order to evaluate the following integrand ∫[x/(6x² + 5)²]dx, we proceed as follows
In the integrand ∫[x/(6x² + 5)²]dx, we see that the other function is the polynomial in the denominator which is (6x² + 5). So, we make the substitution u = (6x² + 5)
b. To rewrite the integrand in terms of u so that ∫[x/(6x² + 5)²]dx is int he form ∫f(u)du, we proceed as follows
Since integrand ∫[x/(6x² + 5)²]dx and u = 6x² + 5. Differentiation u with respect to x, we have that
du/dx = d(6x² + 5)/dx
= d(6x²)/dx + d5/dx
= 12x + 0
= 12x
So, du/dx = 12x
xdx = du/12
So, substituting this into the integrand, we have that
∫[x/(6x² + 5)²]dx = ∫[x/u²]dx
= ∫[xdx/u²]
= ∫[du/12/u²]
= ∫[du/12u²]
So, comparing ∫[f(u)du] = ∫[du/12u²]
So, f(u) = u²/12
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Answer:
[tex]f(u)=\dfrac{1}{12u^5}[/tex]
Step-by-step explanation:
Integration by substitution is a technique used to simplify the integration of complex functions. It involves writing part of the function in terms of a new variable u, where u is some function of x.
Given integral:
[tex]\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x[/tex]
Substitute u for 6x² + 5.
Differentiate u with respect to x and rearrange the equation to isolate dx:
[tex]\dfrac{\text{d}u}{\text{d}x}=12x \implies \text{d}x=\dfrac{1}{12x}\; \text{d}u[/tex]
Substitute the expressions for u and dx into the original expression to rewrite the original integral in terms of u and du:
[tex]\begin{aligned}\displaystyle \int \dfrac{x}{(6x^2+5)^5}\; \text{d}x &= \int \dfrac{x}{u^5} \cdot \dfrac{1}{12x}\; \text{d}u\\\\&= \int \dfrac{1}{12u^5}\; \text{d}u\\\\\end{aligned}[/tex]
Therefore:
[tex]f(u)=\dfrac{1}{12u^5}[/tex]
Make a table for the function f(x) = 3 * (3/4) ^ x using the input values x = - 3, - 1, 0, 1, 3 Then graph the function using the ordered pairs from the table as a guide. Describe the function you graphed . The function is an exponential growth function. The function is a linear function with negative slope . The function is a linear function with a positive slope . The function is an exponential decay function
Answers
Here is the table for the function f(x) = 3 * (3/4) ˣ:
x f(x)
-3 16.000
-1 4.000
0 3.000
1 2.250
3 1.688
The function is an exponential decay function
How to know the value type of functionf(x) = 3 * (3/4) ˣ, in the given exponential function the starting function is
3. The base is 3/4.
The base is what determines exponential decay or growth. The condition for determining exponential growth or exponential decay is
exponential growth, has a factor greater than 1exponential decay, has a factor less than 1The base function here is a factor which is 3/4 = 0.75 and less than one and hence a decay function
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An examiner marks 70 papers. The mean mark is 68 per paper. What is the total number of marks awarded by the examiner?
Answers
Step-by-step explanation:
70 x 68 = 4760 marks
# mrks / 70 papers = 68 marks/paper
# marks = 70 papers * 68 marks/paper
India’s population has increased steadily from 439 million in 1961 to 1028 million in 2001. Find the total increase in population of India from 1961 to 2001.
Answers
Answer:
Total Increase in Population of India from 1961 to 2001 = 1028-439 million = 659 million
please help with this
Answers
The range of the equation y = |x| is
∞ > x ≥ 0
How to determine the rangeThe absolute value function x returns the distance between x and 0 on the number line regardless of the sign of x
Plotting a graph of y = | x| also have it that the smallest possible value of |x| is 0 which occurs when x = 0
for any other value of x, the unction y = |x | will be positive
hence we can say that the range of |x| is [0, ∞).
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Solve the following inequality, indicate the number of solutions and plot the solutions on a number line.
d. 3(x + 3) + 12 ≤ 3x + 28
Answers
Let's start by simplifying the left side of the inequality:
3(x+3) + 12 <= 3x + 28
3x + 9 + 12 <= 3x + 28
3x + 21 <= 3x + 28
Subtracting 3x from both sides, we get:
21 <= 28
This is a true statement, which means that the inequality is true for all values of x. In other words, there are infinitely many solutions.
To represent this graphically, we can draw a number line and shade in all values of x for which the inequality is true. Since it's true for all values of x, we shade in the entire number line:
<=======()------------------->
In this number line, the open circle () indicates that the inequality is not true for that particular value (in this case, there is no specific value for x that makes the inequality false). The arrow indicates that the inequality is true for all values of x to the left and right of the open circle.
In summary, the inequality 3(x+3)+12 <= 3x+28 is true for all values of x, and there are infinitely many solutions.
I'm 15 BTW
tudent Progress Examination (SPE) MATHEMATICS Year 5. (a) A piece of steel wire, measuring 240 cm long, is used up completely to form 4 identical squares as shown below. Find the length of each side of the square. NOT TO SCALE Ans: cm (2)
Answers
Since there are 4 squares, the total number of sides is 4 x 4 = 16.
Therefore, the length of each side of the square is:
240 cm ÷ 16 = 15 cm
Hence, the length of each side of the square is 15 cm.
What number lies exactly halfway between 1/5 and 1/9?
Answers
Answer:
7/45
Step-by-step explanation:
What number lies exactly halfway between 1/5 and 1/9?
you have to find the mean of the two fractions, adding and then dividing by two
(1/5 + 1/9) : 2 =
14/45 : 2 =
7/45
Given an isosceles triangle with a base length of 30 and a median (drawn from the vertex
angle) length of 21, what is the length of a leg?
Answers
The length of each leg is 14.69 in the triangle
In an isosceles triangle, the median drawn from the vertex angle also acts as an altitude, dividing the triangle into two congruent right triangles.
Let the length of one of the legs of the triangle "x".
Using the Pythagorean theorem, we can write:
x²+ (15)² = (21)²
x² + 225 = 441
x² = 441 - 225
x² = 216
Taking the square root of both sides, we find:
x = √216
x =14.69
Therefore, the length of each leg is 14.69 in the triangle
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Solve the right triangle. Round decimal answers to the nearest tenth. Find m/_C. Can you help me guys with this question please?
Answers
The measure of angle C is 13. 94 degrees
How to determine the valueTo determine the value of the angle, we need to know the six different trigonometric identities.
These identities are;
tangentcotangentsecantcosecantsinecosineFrom the information given, we have that;
The Hypotenuse side of the triangle ABC = 34
the adjacent side of the triangle = 33
Using the cosine identity, we have that;
cos C= adjacent/hypotenuse
cos C = 33/34
Divide the values
cos C = 0. 9706
Find the inverse
C = 13. 94 degrees
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Out of 400 people sampled, 48 said they want to live in a big city. With 95% confidence, what is the approximate percentage of people in the population who want to live in a big city?
Answers
Answer:
Step-by-step explanation:
Divide 400 by 48 people who wants to live in a city.
400 / 48 = .12 is 12%
More than two-thirds of undergraduate students who graduated with a bachelor's degree had student loan debt. The average student loan debt among these graduating seniors was $28,654. The average interest rate on student loans was 6.1%. How much interest did a student with $28,654 in student loan debt pay in the first year? Round to the nearest cent.
Answers
The interest paid for the loan is $1748
Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,
We need to find the interest paid for the same.
So,
Simple Interest = principal × time × rate / 100
= 28654 × 1 × 6.1 / 100
= 28654 × 0.061
= 1747.894
= 1748
Hence the interest paid for the loan is $1748
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Fill in the blanks !! Please
Answers
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From the origin, move 3 units to the right, and then move 9 units up is the intersection of the graphs of the two equations be located on a coordinate grid
What is Equation?
Two or more expressions with an Equal sign is called as Equation.
Given that solution to a system of two linear equations is x = 3: y = 9.
We need to find how the intersection of the graphs of the two equations be located on a coordinate grid
As we know that the numbers on right side of zero are positive and number of upside of zero on y axis are positive.
As x=3 which is positive
y=9 which is positive.
So From the origin, move 3 units to the right, and then move 9 units up is the intersection of two equations
Hence, From the origin, move 3 units to the right, and then move 9 units up is the intersection of the graphs of the two equations be located on a coordinate grid
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The table below shows the amount of time Varghese, Youfang, Waverley, and Kimora spent running during their first of training for a half marathon. For which runner is there a proportional relationship between the of training and the amount of time spent running?
A. Wlaverey
B. Youfang
C. Varghese
D. Kimora
Answers
The runner for which there is a proportional relationship between the of training and the amount of time spent running is given as follows:
D. Waverley.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
Waverley is the only runner for which the situation is modeled by a proportional relationship, as for each input, the output is 30 times the input.
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1 A circle has a radius of 6 cm. Write down the circumference of the circle in terms of pi [1 mark]
Answers
Answer:
The circumference of the circle is 12pi cm.
Answer:
The circumference of the circle is 12π cm.
that's the answer
3/4 of students in a certain school credited Igbo language in 2013 WAEC result,5/9 credited Agriculture. Every student in the school credited at least one of the two subjects. If 22 students credited both Igbo and Agriculture, how many students are in the school.represent in a Venn diagram
Answers
There are 72 students in the school.
The number for Igbo language = 54
The number for Igbo language = 40
The Venn diagram is attached
how to find the number of students in the schoolAssuming that the total number of students in the school is x.
Information from the problem
3/4 of students credited Igbo language and
5/9 credited Agriculture.
every student in the school credited at least one of the two subjects. hence we have that
3/4x + 5/9x - 22 = x
Simplifying this equation gives
3/4x + 5/9x - x = 22
11x / 36 = 22
11x = 36 * 22
x = (36 * 22) / 11
x = 72
The number for Igbo language
= 3/4 * 72 = 54
The number for Igbo language
= 5/9* 72 = 40
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select the correct button in the table to show wether each pair of angles is alternate interior,corresponding or same-side exterior angles
Answers
The correct relationship between the angles are:
(1) Corresponding angles(2) Alternate interior angles(3) Corresponding angles(4) Corresponding angles(5) Alternate exterior angles(6) Alternate exterior anglesSelecting the correct relationship between the anglesFrom the question, we have the following parameters that can be used in our computation:
The figures (see attachment)
Using the figures and the definition of angle relationships, we have the relationships of the angles to be:
(1) Corresponding angles(2) Alternate interior angles(3) Corresponding angles(4) Corresponding angles(5) Alternate exterior angles(6) Alternate exterior anglesRead more about angles at
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You're filling prescriptions in a pharmacy. Your work surface tray gives you an area of 240 square inches to work. If the length is 24 inches, what is the width of the tray?
Answers
The masses in kilograms of 20 bags of maize were;90,94,96,98,99,102,105,91,102,99,105,94,99,90,94,99,98,96,102,and 105.i state the mode ii calculate the mean mass per bag
Answers
The mean mass per bag is 99 kilograms.
The mode is the value that appears most frequently in a dataset. In the given dataset of bag masses, the mode would be the mass value that occurs most often. Let's find the mode.
The masses of the bags are:
90, 94, 96, 98, 99, 102, 105, 91, 102, 99, 105, 94, 99, 90, 94, 99, 98, 96, 102, and 105.
To find the mode, we can simply count the frequency of each mass value and identify the one that appears most often:
90 appears twice
94 appears three times
96 appears two times
98 appears two times
99 appears four times
102 appears three times
105 appears three times
91 appears once
Therefore, the mode in this dataset is 99, as it appears most frequently.
To calculate the mean mass per bag, we need to sum up all the masses and divide by the number of bags. Let's calculate it:
Sum of masses = 90 + 94 + 96 + 98 + 99 + 102 + 105 + 91 + 102 + 99 + 105 + 94 + 99 + 90 + 94 + 99 + 98 + 96 + 102 + 105
Sum of masses = 1980
Number of bags = 20
Mean mass per bag = Sum of masses / Number of bags
Mean mass per bag = 1980 / 20
Mean mass per bag = 99 kilograms
Therefore, the mean mass per bag is 99 kilograms.
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find the value of a + b if
Answers
The value of the given fraction is 18.
Given is fraction, [tex]\frac{2+\sqrt{5} }{2-\sqrt{5}} +\frac{2-\sqrt{5} }{2+\sqrt{5}}[/tex], we need to show it in a+b√5 form,
So,
[tex]\frac{2+\sqrt{5} }{2-\sqrt{5}} +\frac{2-\sqrt{5} }{2+\sqrt{5}}\\\\\\= \frac{(2+\sqrt{5})^2+(2-\sqrt{5} )^2 }{(2+\sqrt{5})(2+\sqrt{5} ) } \\\\\\= \frac{4+5+4\sqrt{5}+4+5-4\sqrt{5} }{2^2-\sqrt{5}^2 } \\\\\\= 18[/tex]
Hence the value of the given fraction is 18.
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The rectangular prism below has a base area of 24.1 units² and a height of 7 units. Find its volume.
Answers
The volume of the rectangular prism is 168.7 cubic units.
The volume of a rectangular prism can be calculated using the following formula:
V = base area x height
A prism is a polyhedron in three dimensions with two identical ends.
In this case, the base area is 24.1 units² and the height is 7 units.
Let the base area can be represented as B and the height be described as H,
then volume can be rearranged as,
V = BH
Here:
B = 24.1 units²
H = 7 units
When these values are entered into the formula, we get:
V = 24.1 x 7
V = 168.7
Therefore, the volume of the rectangular prism is 168.7 cubic units.
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Simplify-15(y^2)^4/ -5y^3y^2
•3y^2
•3y^3
•3y
•-3y^3
Answers
Answer:
It is 3y^3.
Step-by-step explanation:
We can simplify the expression as follows:
-15(y^2)^4/(-5y^3y^2)
= -15y^8/(-5y^5)
= 3y^3
So, the simplified expression is 3y^3.
you local gym wants to estimate the mean amount of time (in hours) that their members spend each week at their center. They would like a 95% confidence interval with a margin of error of 30 minutes. based on previous data, they know that the population standard deviation is 2.2 hours. What is the smallest size that will allow this confidence interval to be built?
Answers
The smallest size that will allow this confidence interval to be built is given as follows:
n = 75.
What is a z-distribution confidence interval?The bounds of the confidence interval are given by the rule presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is calculated as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
The desired margin of error is of M = 0.5, as we have the time in hours, with [tex]\sigma = 2.2[/tex], hence the sample size is obtained as follows:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.5 = 1.96\frac{2.2}{\sqrt{n}}[/tex]
[tex]0.5\sqrt{n} = 1.96 \times 2.2[/tex]
[tex]\sqrt{n} = \frac{1.96 \times 2.2}{0.5}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{1.96 \times 2.2}{0.5}\right)^2[/tex]
n = 75 -> rounded up.
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