Answers
The discounted prices are given as follows:
5) Soccer ball: $7.46.
6) Leather jacket: $202.31.
7) Board game: $15.83.
8) Baseball cap: $11.43.
9) Wooden key: $15.12.
10) Phone charger: $13.30.
How to obtain the discounted prices?The discounted prices are obtained applying the proportions in the context of this problem, multiplying the original price by the decimal equivalent of the discounted price.
Hence the discounted prices are obtained as follows:
5) Soccer ball: 10.65 x (1 - 0.3) = $7.46.
6) Leather jacket: 216.95 x (1 - 0.0675) = $202.31.
7) Board game: 17.69 x (1 - 0.105) = $15.83.
8) Baseball cap: 13.45 x (1 - 0.15) = $11.43.
9) Wooden key: 16.75 x (1 - 0.0975) = $15.12.
10) Phone charger: 15.65 x (1 - 0.15) = $13.30.
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Related Questions
Question 3(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following table represents a linear or nonlinear function?
x −2 −1 0 1 2
y −4 −2 0 2 4
The table represents a nonlinear function because there is not a constant rate of change in the input values.
The table represents a nonlinear function because there is not a constant rate of change in the output values.
The table represents a linear function because there is a constant rate of change in the input and output values.
The table represents a linear function because there is not a constant rate of change in the input and output values.
Question 4(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the following graph represents a linear or nonlinear function?
coordinate plane with a graph that passes through the points negative 3 comma 0 and negative 1 comma 4 and 1 comma 4 and 3 comma 0
The graph represents a nonlinear function because there is a constant rate of change.
The graph represents a nonlinear function because the rate of change is not constant.
The graph represents a linear function because there is a constant rate of change.
The graph represents a linear function because the rate of change is not constant.
Question 5(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the data in the following table represents a linear or nonlinear function?
x y
−4 4
−1 2.5
0 2
4 0
The table represents a nonlinear function because the graph shows a rate of change that is decreasing.
The table represents a linear function because the graph shows a rate of change that is increasing.
The table represents a nonlinear function because the graph does not show a constant rate of change.
The table represents a linear function because the graph shows a constant rate of change.
Question 6(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which statement best explains whether the equation y = 3x2 represents a linear or nonlinear function?
The equation represents a linear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a linear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are on a straight line.
The equation represents a nonlinear function because it has an independent and a dependent variable, each with an exponent of 1.
The equation represents a nonlinear function because its graph contains the points (−1, 3), (0, 0), and (1, 3), which are not on a straight line.
Question 7(Multiple Choice Worth 2 points)
(Linear Functions MC)
Which of the following tables represents a linear function?
x −2 −1 0 1 2
y 5 2 1 2 5
x −2 −1 0 1 2
y 5 3 1 −1 −3
x 3 3 0 3 3
y −2 −1 0 1 2
x 0 1 2 3 4
y 0 −1 2 −3 4
Answers
A graph of linear function is a straight line.
Linear function in a slope-intercept form: y = mx + b: Equation 3: y = 12x + 17.
2)
x|-1 | 0 | 1 | ? |
y| 4 | 7 |10| ? |
a slope: = (Change in y)/ (Change in x)
This means that (7-4)/(0--1) = 3/1 = 3
A slope intercept form is y-y₁ = m(x-x₁)
y-4 = 3[(x-(-1)]
Opening the brackets
y-4=3x+3
Rearrange
y=3x+7
substitute x = 2 to the equation (1):
This implies that y=3(2)+7
y=6+7 = 13
3) The slope is (4-7)/-5+2
S= 3/-3 = 1
If the slope is 1
Then the equation of the line is given as
y-y₁ = m(x-x₁)
y-7 = 1(x+2)
y-7=x+2
Collecting like terms we have
y=x+9
The conclusion: It's a linear function
It is a linear function because there is a constant rate of change in both the input and output values.
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Write the solution set of the given homogeneous system in parametric vector form. 2X1 + 2X2 + 4x3 = 0 + X1
- 4x4 - 4x2 - 8X3 = 0
- 6x2 - 18X3 = 0 - where the solution set is x = [x1 x2 x3]
Answers
the solution set of the given homogeneous system in parametric vector form. 2X1 + 2X2 + 4x3 = 0 + X1, - 4x4 - 4x2 - 8X3 = 0, - 6x2 - 18X3 = 0 - where the solution set is:
x = x₃ [tex]\left[\begin{array}{ccc}-5\\3\\1\end{array}\right][/tex]
What is the system of equation?Algebra requires the simultaneous solution of two or more equations. There must be an equal number of equations and unknowns for a system to have a singular solution. The several kinds of linear equation systems are as follows:
Dependent: There are an endless number of solutions for the system. The equations' graphs show the identical lines.Independent: There is just one possible outcome for the system. The graphs of the equations come together at this one location.Inconsistent: There is no solution for the system.Given system of equation:
2x₁ + 2x₂ + 4x₃ = 0 + x₁ ................ (1)
- 4x₄ - 4x₂ - 8x₃ = 0 ............. (2)
- 6x₂ - 18x₃ = 0 .............. (3)
- 6x₂ = 18x₃
or, x₂ = 3x₃
From (1) we get:
2x₁ + 2x₂ + 4x₃ = 0
x₁ + x₂ + 2x₃ = 0
x₁ + 3x₃ + 2x₃ = 0
x₁ = -5 x₃
now, take x₃ = k
then, x = [tex]\left[\begin{array}{ccc}-5\\3\\1\end{array}\right][/tex] k
i.e. x = x₃ [tex]\left[\begin{array}{ccc}-5\\3\\1\end{array}\right][/tex]
this is the solution of the system.
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Half of Jonah' clamate are girl, and half of them are boy. What percentage of Jonah' clamate are boy?
Answers
The percentage of boys is 50%.
The concept used in this problem is basic arithmetic, specifically finding percentages. To find the percentage of boys in Jonah's class, we simply take the fraction of boys (1/2) and multiply it by 100 to convert it to a percentage.
Percentages are a way of expressing a fraction as a ratio out of 100. They are commonly used to represent proportions and are often easier to understand and compare than fractions or decimals. In this problem, we use the percentage concept to determine the proportion of boys in Jonah's class and express it as a ratio out of 100. This allows us to easily compare the number of boys in Jonah's class to other values and understand the relationship between the two.
Half of Jonah's classmates are boys, so the percentage of boys is:
(1/2) * 100 = 50%
So, 50% of Jonah's classmates are boys.
Therefore, the percentage of boys is 50%.
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The percentage of boys is 50%.
The concept used in this problem is basic arithmetic, specifically finding percentages. To find the percentage of boys in Jonah's class, we simply take the fraction of boys (1/2) and multiply it by 100 to convert it to a percentage.
Percentages are a way of expressing a fraction as a ratio out of 100. They are commonly used to represent proportions and are often easier to understand and compare than fractions or decimals. In this problem, we use the percentage concept to determine the proportion of boys in Jonah's class and express it as a ratio out of 100. This allows us to easily compare the number of boys in Jonah's class to other values and understand the relationship between the two.
Half of Jonah's classmates are boys, so the percentage of boys is:
(1/2) * 100 = 50%
So, 50% of Jonah's classmates are boys.
Therefore, the percentage of boys is 50%.
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Complete the statement. Round to the nearest hundredth if necessary.
4 ft ≈
m
awenser right give brainlist
Answers
4 ft = 1.22 m (rounded to the nearest hundredth).
A conversion factor is a number that is used to multiply or divide one set of units into another. If a conversion is necessary, it must be carried out with the right conversion factor to produce a value that is identical. For instance, when converting between inches and feet, the right conversion ratio is 12 inches to 1 foot.
It entails the normal conversion of one unit to another one.
We've got
1.m. equals 3.28 ft.
1 ft = 0.3048 m
multiply both sides by 4.
4 ft = 4 x 0.3048 m
4 ft = 1.2192 m
To the closest hundredth, round.
4 ft = 1.22 m
Thus,
1.22 meters are equal to 4 feet.
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Kit is baking cakes. She has 5 cups of sugar and each cake needs 3/4 cup of sugar. Determine the number of cakes Kit can make
Find 5÷3/4
Express your answer in simplest fraction form.
Answers
Answer:
Step-by-step explanation:
Im sorry I think it might be 2/4
Answer:
Step-by-step explanation:
To find the number of cakes Kit can make, we need to divide the total amount of sugar (5 cups) by the amount of sugar required for each cake (3/4 cup).
5 ÷ 3/4 = (5 × 4/3) ÷ (3/4) = 20/3 ÷ 3/4 = 20/3 × 4/3 ÷ 3/4 = 20/3 ÷ 3/3 ÷ 4/4 = 20/3 ÷ 1 ÷ 4/4 = 20/3 ÷ 1 ÷ 1 = 20/3 ÷ 1 = 20/3= 6 2/3 cakes
So Kit can make 6 2/3 cakes. This fraction cannot be reduced further, so it is the final answer.
In the
figure a cylindrical can with a hemi-
spherical lid is given.
20cm
27cm and find the CSA of the can
Answers
The lateral surface area of the can is approximately 2962.76 cm².
The lateral surface area (CSA) of a cylindrical can with a hemispherical lid can be calculated as follows:
CSA = 2πrh + πr²
Where:
r is the radius of the cylindrical part of the can
h is the height of the cylindrical part of the can
We know the height of the cylindrical part is 27 cm and the diameter of the hemispherical lid is 20 cm, so the radius is half the diameter or 10 cm.
So, the lateral surface area of the cylindrical part is:
CSA = 2πr × h = 2 × π × 10 ×:27 = 540 π cm²
And the surface area of the hemispherical lid is:
CSA = 4π × r² = 4 × π × 10² = 400π cm²
Therefore, the total lateral surface area of the can is:
CSA = 540π + 400π = 940π cm²
So the answer is approximately 2962.76 cm².
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The market value of Julie’s home is $180,000 of which she still owes $100,000. If she wanted to take out a home equity loan, what is the maximum amount that she can borrow? (Assume that she can borrow up to 80 percent of the market value of the home. )
Answers
The amount which she can borrow from the home equity loan is $44,000.
According to the question
According to the following equation:
maximum loan amount = market value of the home * borrowing limit
Julie is able to borrow a maximum amount for a home equity loan.
The maximum loan amount is
$180,000 * 80% = $144,000,
In Julie's situation because the home's market value is $180,000 and the borrowing ceiling is 80%.
Julie can only borrow the $44,000
difference between the maximum loan amount and the remaining debt because she still owes $100,000 on her house.
The difference is calculated as follows: $144,000 - $100,000 = $44,000.
Julie is therefore qualified for a home equity loan of up to $44,000.
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The amount which she can borrow from the home equity loan is $44,000.
According to the question
According to the following equation:
maximum loan amount = market value of the home * borrowing limit
Julie is able to borrow a maximum amount for a home equity loan.
The maximum loan amount is
$180,000 * 80% = $144,000,
In Julie's situation because the home's market value is $180,000 and the borrowing ceiling is 80%.
Julie can only borrow the $44,000
difference between the maximum loan amount and the remaining debt because she still owes $100,000 on her house.
The difference is calculated as follows: $144,000 - $100,000 = $44,000.
Julie is therefore qualified for a home equity loan of up to $44,000.
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if the confidence coefficient is 0.77, what is the implied probability of error α?
A) 0.15
B) 0.85
C) 1
D) 0.05
Answers
if the confidence coefficient is 0.77, implied probability of error α is 0.23.
The confidence coefficient is a measure of the reliability of a statistical estimate, often used in hypothesis testing. In hypothesis testing, we aim to estimate the probability of error, denoted as alpha (α). Given a confidence coefficient of 0.77, we can find the implied probability of error α by using the formula:
α = 1 - confidence coefficient
So, in this case:
α = 1 - 0.77 = 0.23
Therefore, the answer is 0.23, and option (A) 0.15 is not correct.
It is important to note that the confidence coefficient is often expressed as a percentage, for example, a confidence coefficient of 0.77 would be expressed as 77%.
This can lead to confusion when trying to determine the probability of error α, as it is often expressed as a decimal.
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Let ff be the function given by f(x)=17x7−76x6+3x5−54x4−163x3+6x2f(x)=17x7−76x6+3x5−54x4−163x3+6x2. Which of the following statements is true?f′(−1.1)Answer A: f prime of negative 1.1, is less than f prime of 0.5, which is less than f prime of 1.4Af′(−1.1)Answer B: f prime of negative 1.1, is less than f prime of 1.4, which is less than f prime of 0.5Bf′(0.5)Answer C: f prime of 0.5, is less than f prime of 1.4, which is less than f prime of negative 1.1Cf′(1.4)
Answers
The correct statement is that f′(−1.1) is less than f′(0.5) which is less than f′(1.4).
The derivative of a function, denoted by f′(x), is the rate at which the function value changes with respect to a change in the independent variable. In this case, the function is given by f(x) = 17x7 − 76x6 + 3x5 − 54x4 − 163x3 + 6x2. So, the derivative of this function can be computed as follows:
f′(x) = 119x6 − 456x5 + 15x4 − 216x3 − 489x2 + 12x
Now, let's evaluate the derivative for x = −1.1, 0.5, and 1.4. Firstly, for x = −1.1,
f′(−1.1) = 119(−1.1)6 − 456(−1.1)5 + 15(−1.1)4 − 216(−1.1)3 − 489(−1.1)2 + 12(−1.1)
= −1709.085
Next, for x = 0.5,
f′(0.5) = 119(0.5)6 − 456(0.5)5 + 15(0.5)4 − 216(0.5)3 − 489(0.5)2 + 12(0.5)
= 112.75
Finally, for x = 1.4,
f′(1.4) = 119(1.4)6 − 456(1.4)5 + 15(1.4)4 − 216(1.4)3 − 489(1.4)2 + 12(1.4)
= −914.56
Therefore, the correct statement is that f′(−1.1) is less than f′(0.5) which is less than f′(1.4).
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use the equation for specific heat capacity to determine the function needed to solve for the variables associated with temperature change.
Answers
C = Q/mT, where C is the specific heat capacity, Q is the heat energy, m is the mass, and T is the temperature change, is the equation for specific heat capacity. C = Q/mT is the function that must be used to solve for the variables related to temperature change.
C = Q/mT, where C is the specific heat capacity, Q is the heat energy, m is the mass, and T is the temperature change, is the equation for specific heat capacity. This equation can be used to determine how much energy is required to alter the temperature of a given mass by a certain amount. The formula C = Q/mT must be used to find the variables related to temperature change. According to this equation, the specific heat capacity (C) is multiplied by the temperature change (T) to determine the amount of heat energy (Q) required to create a temperature change (T) in a given mass (m). The specific heat capacity (C) and mass can be multiplied to find the heat energy (Q) by rearranging the equation (m).
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A school is constructing a rectangular play area against an exterior wall of the
school building. It uses 120 feet of fencing material to enclose three sides of the
play area. Write an equation to represent A, the area in square feet, as a function
of w, the width in feet. *
Answers
An equation to represent A, the area in square feet, as a function of w, the width in feet is A = 120W -2W²
According to the question, the school uses 120 feet of fencing material to enclose three sides of the play area. This means there are 3 sides.
Substitute into the perimeter of the rectangle will give:
120 = L + 2W
Area = LW
We know that the area of a rectangle is l × w
When w =10, length = 120 - 20 = 100, area = 100 x 10 = 1000
When w = 20, length = 120 - 40 = 80, area = 80 x 20 = 1600
When w = 40, length = 120 - 80 = 40. area = 40 x 40 = 1600.
So, the completed table will be
Width Length Area
10 100 1000
20 80 1600
40 40 1600
w 120 - 2w (120 - 2w) w
In order to maximize the area with the given fencing, from the equation written above, then w = 30 feet and l = 60
On substituting, we have;
A = LW = (120 - 2W) W
L = 120 - 2W,
On simplification, we have
A = 120W -2W²
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determine the probability of the couple having five children with no children being affected by the disorder.
Answers
The probability of a couple having five children with no children being affected by the disorder is given by the formula (1 - 0.0025)⁵.
This formula calculates the probability of a certain event (in this case, having no children affected by the disorder) happening five times in a row. However, this does not give the probability of all five children being unaffected by the disorder.
To find the probability of all five children being unaffected, you would need to multiply the probability of each child being unaffected, which is (1 - 0.0025), five times:
(1 - 0.0025) * (1 - 0.0025) * (1 - 0.0025) * (1 - 0.0025) * (1 - 0.0025) = 0.99609This result is the correct probability of a couple having five children with no children being affected by the disorder.
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the region bounded by the graphs of y = in x, y = 0, and x = e is revolved about the y-axis. find the volume of the resulting solid.
Answers
The volume of the resulting solid as V = 2π(0)(in e)e = 2πe^2in. can be found by using the method of cylindrical shells.
This method involves calculating the volume of a series of infinitesimally thin cylindrical shells that, when added together, form the solid of interest. The formula for the volume of a single cylindrical shell is V = 2πrhΔx, where r is the radius, h is the height, and Δx is the change in x.
To find the volume of the solid, we must first find the integral of the area of the region bounded by the graphs of y = in x, y = 0, and x = e. This integral can be found by integrating the equation y = in x from 0 to e, which gives us the area of the region. Then, we can use the formula V = 2πrhΔx to find the volume of the solid by substituting the radius of the shell (the radius of the y-axis) for r, the area of the region for h, and the change in x (e - 0) for Δx. This gives us the final volume of the solid as V = 2π(0)(in e)e = 2πe^2in.
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Liam made a deposit of $31,050 into an account with a rate of 20%. How long should he leave the money into the account if he wants to earn $93,150 in interest?
Answers
Answer 15 years
Step-by-step explanation: 93,150/31,050=3
if you want the number to be multiplied by three you need it to increase by 300%.
300/20=15
31050x(20%x15)=93,150
solve the system linaer equations by elimlnation x-2y=7 3x+2y=3
Answers
Answer:
x-2y=7
Step-by-step explanation:
How are diagonals and angle measures related in kites and trapezoids?
Answers
Answer: The diagonals of a kite are perpendicular to each other. Exactly one diagonal bisects the other.
Step-by-step explanation:
the line.
Distance (miles)
УГ
150
100
50
0
Bus Trip
(2, 120)
(1, 60)
1 2
Time (hours)
3 x
The slope of the line is. T
Answers
As a result, when the graph's slope and speed are 60 and 60 mph, respectively, the slope is 60 and the speed is 60 mph.
what is slope ?The steepness of a line determines its slopes. "Gradient overflows" is the name of a contour mathematical equation (the change in y divided by the change in x). The inclination is the ratio of such vertical (rise) to the horizontal (run) change in level between any two places. The gradient form of an answer is used to illustrate a straight line when its equation is represented as y = mx + b. The y-intercept is situated where the slope of the line is m, b is b, and (0, b). For instance, considering como and slope of the eqs y = 3x - 7 (0, 7). The line has a slope of m, a b quantity at the y-intercept, and (0, b). As
given
The graph's slope and speed are as follows:
Slope = 60
Speed is 60 mph.
The ratio of the ascent to the run is the line's slope.
Rise is equal to y2 - y1 = (120 - 60) = 60.
Run = x2 - x1 = (2 - 1) = 1
The incline is equal to (Rise / Run) = (60 / 1) = 60.
The slope indicates that the bus will travel 60 miles per hour throughout the journey.
The distance traveled per hour is the speed.
You can compute the speed as follows:
(120 ÷ 2) = 60 mph
As a result, when the graph's slope and speed are 60 and 60 mph, respectively, the slope is 60 and the speed is 60 mph.
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The area of the quare i 1 quare unit. The area of the one triangle i labeled. Determine a many other area a you can
Answers
2 fully filled squares and 4 partially filled squares make up the figure. As a result, this figure will have a 4 square unit area.
What is meant by unit area?The quantity of unit squares that completely encircle the surface of a closed figure is its area. Square measurements for area include cm² and m². A shape's area can only be measured in two dimensions. A two-dimensional shape's area, which is expressed in square units, is the total surface area it can occupy. The square meter (m²), a derived measure, serves as the area unit in the SI system.Every length unit has a corresponding area unit, which is the area of a square with the specified side length. As a result, areas can be expressed in square metres (m²), square centimeters (cm²), square millimetres (mm²), square kilometers (km²), square feet (ft²), square yards (yd²), square miles (mi²), and so on.The complete question is:
If the area of one square is 1 square unit then find the areas of the following figure by counting the squares.
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Which event will have a sample space of S = {h, t}?
Flipping a fair, two-sided coin
Rolling a six-sided die
Spinning a spinner with three sections
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
Answers
Flipping a fair, two-sided coin will have a sample space of S = {h, t}.
What is sample space?The sample space S of a random experiment is defined as the set of all possible outcomes of an experiment. In a random experiment, the outcomes, also known as sample points, are mutually exclusive
All we have to do is multiply the events together to get the total number of outcomes. Using our example above,
notice that flipping a coin has two possible results, and rolling a die has six possible outcomes.
If we multiply them together, we get the total number of outcomes for the sample space: 2 x 6 = 12!
Spinning a spinner with three sections will give 3 outcomes.
Choosing a tile from a pair of tiles, one with the letter A and one with the letter B will give multiple outcomes depending on the Total number of tiles.
Therefore, Flipping a fair, two-sided coin will have a sample space of S = {h, t}.
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PLEASE HELP ASAP THANK YOU, I'LL GIVE BRAINLIEST
Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars. Represent the number of cupcakes that the customer can buy as an inequality.
Write the solution to the inequality in interval notation below.
Answers
Answer: The amount of cupcakes Rebecca can buy can be represented as: x < 45
Step-by-step explanation:
1. A recipe requires 1 cup of milk for every 4 cups of flour. Write a linear equation that describes the relationship.
Answers
Linear equation for the relationship between flour and milk cups
y = 4x,
where x is number of milk cups
y is number of flour cups
What is linear equation?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation.
A recipe requires 1 cup of milk for every 4 cups of flour.
Ratio between milk(x) and flour(y)
x/y = 1/4
y = 4x
where x number of cups of milk
y is number of cups of flour
Hence, y = 4x is the linear equation that defines the relationship.
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What is the best approximation of the solution to the system to the nearest integer values?.
Answers
The best approximation of the solution to the system to the nearest integer values is ( -5, 1).
We have a system of linear equations, such that
x- y = -6 --(1)
5x + 2y = 23 --(2)
and we have to determine the approximate solution point for this system.
The intersection point of the two graphs ( lines, curves, etc.) is act as the solution to an equation.So, we determine the intersection point between two equations in system . Using the substitution method, substitute the value of x, x = y -6 from (1) to equation(2) ,
=> 5x + 2y = 23
=> 5( y - 6) = 23
=> 5y - 30 = 23
=> 5y = 23 + 30 = 53
=> y = 54/5 = 1.07 ~ 1 ( nearest integer value)
Now, from equation (1), x = y - 6
=> x = 1 - 6 = -5
Thus, the required solution point of system of equations is (-5 , 1).
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Complete question :
What is the best approximation of the solution to the system to the nearest integer values?
x- y = -6
5x + 2y = 23
A) (7, −2)
B) (6, −2)
C) (−2, 7)
D)(−2, 6)
Z= 12. 1+29i
What is the real part of z ?
What is the imaginary part of z ?
Answers
The real part of z is 12.1, and the imaginary part of z is 29 i.
Thi equation used for this is a+ bi.
where the imaginary part is bi and the real part (a)
I does not act as a multiplier in the real component. It is 12.1
The coefficient of I or 29 i., is the imaginary portion.
Whether or whether I is included in the imaginary section is a matter of some debate. According to one source, the portion that uses I as a factor is the imaginary portion (29i). According to a different source, the real number that multiplies I is the imaginary half (29). We utilized the later term up above. Please refer to your course materials for the appropriate term.
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the periodic function f (t) is defined on its period –2 ≤ t ≤ 2 by the formula: , when 2 0. ( ) , when 0 2..(a) Plot the function f(t) on the interval -8≤1≤8.b) Determine the period of the function.c) Determine, whether the function is odd or even?d) Find the mean value of the function on its period.e) Find the Fourier coefficients of the given function.f) Present the function by the Fourier series using the symbol Σ.[5 marks][1 mark][1 mark][1 mark]17 marks]15 marksg) Present first four terms of the Fourier series together with the mean value in the explicitfor
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The solution of the periodic function is explained below.
A periodic function is a function that repeats its values after a certain interval of time, called its period.
The periodic function f(t) is defined on its period –2 ≤ t ≤ 2 and is described by the formula:
f(t) = t^2, when -2 ≤ t < 0
f(t) = -t^2, when 0 ≤ t ≤ 2
a) Plotting the function on the interval -8 ≤ t ≤ 8 would show us the repeating pattern of the function. To plot the function, we need to evaluate it for different values of t and plot the corresponding points on the coordinate plane.
b) The period of the function can be found by determining the smallest interval in which the function repeats. In this case, the period of the function is 2.
c) To determine whether the function is odd or even, we need to check if f(-t) = f(t) or f(-t) = -f(t). In this case, the function is an even function as f(-t) = f(t).
d) The mean value of the function on its period can be found by finding the average value of the function over one period. This is given by the formula:
(1/period) * ∫_0^period f(t) dt
e) The Fourier coefficients of the function can be found by using the formula:
ak = (2/period) * ∫f(t) cos(kπt/period) dt
bk = (2/period) * ∫f(t) sin(kπt/period) dt
f) The Fourier series of the function can be found by using the Fourier coefficients. This is given by the formula:
=> f(t) = a0/2 + ∑_(n=1)^∞
g) The first four terms of the Fourier series can be found by finding the first four values of the sum in the Fourier series formula. To find the explicit form, we need to evaluate the integrals and the sums.
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Find the volume of the solid obtained by rotating the region bounded by the curves y2 = x and x = 2y about the line y = -1. Volume =
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The solid volume obtained by rotating the region enclosed by the curves y2=x and x=2y about the line y=-1 is 5.024 units.
What is volume?Every three-dimensional item requires some amount of space. The volume of this space is measured. Volume is defined as the space occupied by an item inside the confines of three-dimensional space. It is also known as the object's capacity. A 3D object's volume is the amount of actual space it occupies. It is the 3D counterpart of a 2D shape's area. It is measured in cubic units, such as cm3. This may be calculated by multiplying its length, height, and breadth. Volume is the measurement in cubic units of the three-dimensional space filled by matter or contained by a surface. The cubic meter (m3), a derived unit, is the SI unit of volume.
Here,
It turns out
(R(y)outer) → x = 2y [Equation 1]
(R(y)inner) → y^2 = x [Equation 2]
Set equations equal by substituting Equation 1 into Equation 2 for x:
y^2=(2y)
Solve for y to determine your lower and upper bounds:
y^2 – 2y = 0 → y(y - 4) = 0
y = 0 and y = 2 {We now have our lower & upper bound}
Now we have our equation: V = ∫ π [ (2y)^2 – (y^2)^2] dy {Integral bounded from 0 to 2}
Lower bound = 0 so it'll make entire expression 0
After plugging in 2 into y and simplifying:
V=π(y³-1/5*y^5)
V=π(8-1/5*32)
V=3.14*(8-6.4)
V=3.14*1.6
=5.024 units
The volume of the solid obtained by rotating the region bounded by the curves y2=x and x=2y about the line y=-1 is 5.024 units.
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? what quantitative rule may be used to determine univariate outliers, and are there situations in which deleting a case/participant may be justified?
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The Interquartile Range (IQR) rule is a commonly used quantitative rule to determine univariate outliers and deleting a case may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.
The Interquartile Range (IQR) rule is a commonly used method for identifying outliers in a univariate data set. It is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1). Outliers are considered to be any values that fall outside of the range Q1 - 1.5 * IQR to Q3 + 1.5 * IQR. This range encompasses approximately 75% of the data, with outliers being any values that fall outside of this range.
In some cases, deleting a case or participant may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.
This decision should be made carefully and only after careful consideration of the implications, as removing data can affect the validity of the results and the conclusions that can be drawn from the analysis. In some cases, it may be better to keep the outlier and consider it a potential error or to conduct further analysis to determine if there is a valid reason for the outlier.
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75 POINTS WILL GIVE BRAINLIEST
A zoologist recorded the speed of two cheetahs. Cheetah A ran 18 miles in 16 minutes. Cheetah B ran 54 miles in 50 minutes. Which statement is correct?
Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is greater than 54 over 50.
Cheetah A has a higher ratio of miles per minute than Cheetah B because 18 over 16 is less than 54 over 50.
Cheetah B has a higher ratio of miles per minute than Cheetah A because 18 over 16 is greater than 54 over 50.
Both cheetahs have the same ratio of miles per minute.
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Answer: C. Cheetah B has a higher ratio of miles per minute than Cheetah A because 18 over 16 is greater than 54 over 50.
Step-by-step explanation:
Answer:
Step-by-step explanation:
C. Cheetah B has a higher ratio of miles per minute than Cheetah A because 18 over 16 is greater than 54 over 50.
How do you solve this?
(3^{x-1}*27^x*9^2)/(3^{2x-4)*81^x}
Answers
Answer: The expression can be simplified as follows:
(3^{x-1} * 27^x * 9^2) = 3^{x-1 + 2} * 27^x
(3^{2x-4) * 81^x} = 3^{2x-4 + 2x} * 3^{-2x}
Replace in the expression: (3^{x-1 + 2} * 27^x) / (3^{2x-4 + 2x} * 3^{-2x}) = 3^{x-1 + 2 - 2x + 4} * 27^x / 3^4 = 3^3 * 27^x / 81
So the simplified expression is 3^3 * 27^x / 81.
Step-by-step explanation:
F=35g-12
what is the dependent variable and what is the independent variable.
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course 3 chapter 5 triangles and the pythagorean theorem answer key
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In the given right triangle, the perimeter is 12 in.
According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the length of the two legs (a and b). Hence,
c^2 = a^2 + b^2
In the given triangle,
c = x in
a = 3 in
b = 4 in
Hence,
x^2 = 3^2 + 4^2
x^2 = 9 + 16
x^2 = 25
x = √25
x = 5
The perimeter of a geometric shape is the sum of all its side. Hence,
Perimeter = 3 + 4 + 5 = 12 in
Note: The question is incomplete. The complete question probability is: Using the Pythagorean theorem, find the perimeter of the triangle.
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