The quadratic equation with x-intercepts of x = -3 and x = 2, with an intercept of y = -6, is given as follows:
y = x² + x - 6.
How to define the quadratic equation?A quadratic equation with roots x* and x** is defined as follows:
y = a(x - x*)(x - x**).
In which a is the leading coefficient.
Considering the x-intercepts, the roots of the function are given as follows:
x* = -3, x** = 2.
Hence:
y = a(x + 3)(x - 2)
y = a(x² + x - 6).
The y-intercept is of y = -6, meaning that when x = 0, y = -6, hence the leading coefficient a is given as follows:
-6a = -6
6a = 6
a = 6/6
a = 1.
Hence the function is defined as follows:
y = x² + x - 6.
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what is the solution of the system of equations y=2x+2 y=x
The solution to the two simultaneous linear equations are;
x = -2 and y = -2
How to solve Simultaneous Linear Equations?There are three main ways of solving simultaneous linear equations and they are;
Elimination method
Substitution method
Graphical Method
The two simultaneous equations are;
y = 2x + 2 -----(1)
y = x -----(2)
Plug in eq 2 into eq 1 to get;
x = 2x + 2
x - 2x = 2
-x = 2
x = -2
Thus, y = -2
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A spherical tank with radius 3 m is half full of a liquid that has a density of 900 kg/m3. The tank has a 2 m spout at the top. Find the work W required to pump the liquid out of the spout. (Use 9.8 m/s2 for g.)
Answer:
3.0549 MJ
Step-by-step explanation:
You want to know the work done to empty a half-full spherical tank of radius 3 m containing liquid of density 900 kg/m³ through a 2 m spout at the top of the tank.
MassThe mass of the liquid is the product of its volume and its density. The volume of the hemisphere is ...
V = 2/3πr³ = 2/3π(3³) = 18π . . . . . . cubic meters
Then the mass of the liquid is ...
m = ρV = (900 kg/m³)(18π m³) = 16200π kg
HeightThe centroid of the liquid is 3/8r below the center of the tank. The mass of liquid must be moved from that location to a point 2 m above the top of the tank. The total height the liquid must be moved is ...
3/8(3 m) + 3m + 2m = 6.125 m
WorkThe work done to lift the liquid is ...
W = Fd = (m·g)d = (16200π kg)(9.8 m/s²)(6.125 m) = 972405π J
W ≈ 3,054,900.4 J ≈ 3.0549 MJ
The work required is about 3.0549 megajoules.
__
Additional comment
We could find the incremental work to move a layer of liquid dy thick to the necessary height, then integrate over the depth of liquid. It is much easier to look up the centroid location for a hemisphere, and use that in the calculation.
We have used "m" to represent both mass and meters. We trust you can determine which is which from the context.
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A week before a state election, a random sample of voters from City J and a random sample of voters from City K were taken. Of the 100 voters selected from City J, 65 indicated they were supporting a certain candidate for state senate. Of the 125 voters selected from City K, 75 indicated they were supporting the same candidate. Which of the following is the correct combined proportion, Pc, for the difference in population proportions for the two cities (J minus K) in their support for the candidate?
The proper combined percentage, Pc, for the disparity in population proportions between the two cities' support for the candidate (J minus K) is: 0.65−0.60 / √(0.62) (0.38) (1/100 + 1/125)
What is meant by proportion?An equation in which two ratios are made equal is known as a percentage. As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls). If two ratios or fractions are equivalent, it can be shown using the proportion formula. By dividing the supplied values, we may determine the value that is missing. You may write the percentage formula as a: A and d are the extreme terms, and b and c are the mean terms, according to the formula b::c: d = a/b = c/d.An equation in which two ratios are made equal is known as a percentage.Therefore, the correct answer is 0.65−0.60 / √(0.62) (0.38) (1/100 + 1/125)
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Lucas wants to buy pork to roast cuban sandwhiches. The table below shows how much four local stores charge for different amount of the same type of pork. which store has the lowest price per pound for the pork?
Store A: 2 price dollars: 11.20
Store b: 3 price dollars: 10.95
Store C;4 price dollars : 13.80
Store d : 5 price dollars; 16.25
A line passes through the points ( – 8,9) and ( – 2, – 9). Write its equation in slope-intercept form.
The slope-intercept form of the equation of the given line which passes through the points ( – 8,9) and ( – 2, – 9) is:
y = -3x - 15
What is meant by slope-intercept form of the line equation?
The slope (m) and the y-intercept (b) of a line are highlighted in the slope-intercept form of linear equations (y=mx+b). One of the most popular ways to represent a line's equation is in the slope-intercept form of a straight line. When the slope of the straight line and the y-intercept( the y-coordinate of the point where the line intersects the y-axis) are known, the slope-intercept formula can be used to determine the equation of a line. The equation of a line is the equation that each point on the line fulfils.
Given the line passes through the points (– 8,9) and ( – 2, – 9).
When only two points on the line are given, the equation of the line is:
y - y₁ = m ( x - x₁)
m = slope = [tex]\frac{y_2 - y_1}{x_2-x_1}[/tex] = (-9 - 9)/ ( -2 -(-8)) = -18/ 6 = -3
Substituting,
y - 9 = -3 ( x - ( -8))
y - 9 = -3x -24
y = -3x - 15
Therefore the slope-intercept form of the equation of the given line is:
y = -3x - 15
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3. In one pond in the forest, scientists found that a sample of pond water contained 45 minnows for every 27 tadpoles. How many tadpoles would they expect to find in a sample that contained 315 minnows? Show all work and explain how you got your answer
Answer: 189
Step-by-step explanation:
for every 45 minnow there will be 27
315 minnow is 7 times 45 minnow 27*7 is 189
A sidewalk in the shape of two triangles, a rectangle, and a square was built around the edge of a building shown. What’s is the area of the sidewalk in square feet
Answer:144
Step-by-step explanation:
Part C: Charlie designs a square garden. Each side length is 3x + 5.
The perimeter of Charlie's garden is how much larger than the perimeter of Shawn's
garden?i
The requried difference between the perimeters of the two gardens would be, 12x + 20 - 4s.
What is the perimeter?Perimeter is the measure of the figure on its circumference.
Here,
Let's assume that Shawn's garden is also a square with side lengths. Therefore, the perimeter of Shawn's garden would be 4s.
The perimeter of Charlie's garden would be 4(3x + 5), which simplifies to 12x + 20.
The difference between the perimeters of the two gardens would be,
12x + 20 - 4s
We can't simplify this expression any further without knowing the value of s.
Therefore, we can conclude that the difference between the perimeters of the two gardens depends on the side length of Shawn's garden.
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what is 10% of 500000?
Answer:
Step-by-step explanation: the answer is 50000.
The ratio of the number of yellow buttons that Miko had to the number of blue buttons that Miko had was 2: 3. After she had bought 27 more blue buttons, The ratio of the number of yellow buttons to the number of blue buttons became 4:9. How many buttons did Miko have at first?
Answer:
90 buttons
Step-by-step explanation:
the ratio of yellow : blue = 2 : 3 = 2x : 3x ( x is a multiplier )
after buying 27 more blue buttons
2x : 3x + 27 = 4 : 9
expressing the ratios in fractional form
[tex]\frac{2x}{3x+27}[/tex] = [tex]\frac{4}{9}[/tex] ( cross- multiply )
18x = 4(3x + 27)
18x = 12x + 108 ( subtract 12x from both sides )
6x = 108 ( divide both sides by 6 )
x = 18
number of buttons at first = 2x + 3x = 5x = 5 × 18 = 90
You have a job with a gross pay of $68282, what is the partially filled tax bracket?
The partial tax bracket is the 24% tax bracket.
How to get Tax Bracket?To determine your tax bracket, you need to know your taxable income, which is your gross pay minus any applicable deductions and exemptions. Based on the information provided, your taxable income is $68,282.
In the United States, the federal tax brackets for the tax year 2022 (for taxes filed in 2023) are as follows:
10% on taxable income from $0 to $9,950 for individuals12% on taxable income from $9,951 to $40,525 for individuals22% on taxable income from $40,526 to $86,375 for individuals24% on taxable income from $86,376 to $164,925 for individuals32% on taxable income from $164,926 to $209,425 for individuals35% on taxable income from $209,426 to $523,600 for individuals37% on taxable income over $523,600 for individualsBased on these tax brackets, you would be in the 24% tax bracket, since your taxable income is between $86,376 and $164,925.
However, it's important to note that the marginal tax rate, which is the rate applied to your last dollar of income, does not reflect the average tax rate you will pay on your entire taxable income. Your actual tax liability will depend on the total amount of your taxable income and any other applicable tax credits or deductions.
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Leo replaces the strings on some guitars. He puts 6 new strings on Each guitar. He uses 18 strings. How many guitars does leo put Strings on?
Using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.
What is division?One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.
The other operations are multiplication, addition, and subtraction.
On a fundamental level, counting the instances in which one number is included within another is one interpretation of the division of two natural numbers.
When no more full chunks of the size of the second number can be allocated during the computation of the quotient, the division with a remainder or Euclidean division of two natural numbers yields an integer quotient, which is the number of times the second number is entirely contained in the first number, and a remainder, which is the portion of the first number that remains.
So, we know that:
6 new strings are put on each guitar.
He uses 18 strings.
Then, the number of guitars:
⇒ 18/6 = 3
Therefore, using division, we know that Leo replaces 6 new strings from 3 guitars which are a total of 18 strings.
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Which one of the following best defines the notion of the P-value of a hypothesis test? a. The probability of rejecting H_o, whether it's true or not b. The probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true c. The probability of the type I error d. The probability of the type II error
P-value of a hypothesis test is an important measure of the strength of evidence against the null hypothesis and helps us make informed decisions about rejecting or failing to reject the null hypothesis.
A hypothesis test is a statistical method used to test the validity of an assumption or a hypothesis about a population based on a sample data.
The correct answer is b. The P-value of a hypothesis test is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true.
In hypothesis testing, we start with a null hypothesis, which is usually denoted as H_0, that represents the status quo or the default assumption. The alternative hypothesis, denoted as H_a, represents the opposite of the null hypothesis.
The P-value is the probability of observing a sample statistic more extreme than the one actually obtained, assuming the null hypothesis is true. A low P-value indicates that the sample data provides strong evidence against the null hypothesis, and we reject the null hypothesis.
A high P-value indicates that the sample data does not provide strong evidence against the null hypothesis, and we fail to reject the null hypothesis.
In mathematical terms, the P-value is calculated as the probability of observing a test statistic Z that is more extreme than the one actually obtained, assuming the null hypothesis is true.
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Which events are mutually exclusive?
please help!!!! i need help pls
The volumes of the objects are;
1) 252 in^3
2) 850 cm^3
3) 90 cm^3
4) 936 feet^3
5) 168 cm^3
6) 125 m^3
How do we find volume of a cube?The volume of a cube can be found by using the formula:
V = s^3
where V is the volume and s is the length of one side of the cube. In other words, the volume of a cube is equal to the length of one side of the cube raised to the power of 3.
1) Volume = 7 * 9 * 4 = 252 in^3
2) Volume = 50 * 17 = 850 cm^3
3) Volume = 30 * 3 = 90 cm^3
4) Volume = 6 * 12 * 13 = 936 feet^3
5) Volume = 56 * 3 = 168 cm^3
6) Volume = 5^3 = 125 m^3
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If 0° ≤ Θ≤ 360°, then find angle(s) Θ.
1) csc Θ = undefined
Answer:
that these angles are inclusive of 0° and 360° because the question states that 0° ≤ Θ ≤ 360°.
Step-by-step explanation:
If csc Θ is undefined, that means that the sine of the angle is zero, because csc Θ is the reciprocal of the sine function, and division by zero is undefined.
So we need to find all the angles where sin Θ = 0.
The sine function is equal to zero at multiples of 180 degrees, so the solutions to sin Θ = 0 are:
Θ = 0°, 180°, 360°
Note that these angles are inclusive of 0° and 360° because the question states that 0° ≤ Θ ≤ 360°.
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8 Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
For the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.
What is variability?
The extent to which data points in a statistical distribution or data collection diverge or vary from the average value, as well as the extent to which these data points differ from one another, is practically by definition the concept of variability.
The given stem and leaf plot is:
stem leaf
0 5
1 0, 3,7
2 4,6,8
3 2
5 8
The value in the stem is the ten's place and the value in the leaf is the one's place.
So the scores are 05, 10, 13, 17, 24, 26, 28, 32 and 58.
Because extreme values and outliers have a smaller impact on the interquartile range than the complete data range, statisticians prefer using them to measure variability. To understand the centre and spread of your data, utilise the IQR along with a measure of central tendency, like the median.
Range for this data = 58 - 5 = 53.
To find the Inter Quartile Range (IQR), we first find the median.
Median = 24
So Q1 is the first quartile.
This is the median of the first half of the scores(5,10,13,17).
Q1 = 10+13 / 2 = 11.5
Q3 is the third quartile.
This is the median of the second half of the scores (26, 28, 32 58).
Q3 = 28+32 / 2 = 30
Now,
IQR = Q3 - Q1 = 30 - 11.5 = 18.5
Therefore for the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.
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Answer:
Step-by-step explanation:
For the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.
What is variability?
The extent to which data points in a statistical distribution or data collection diverge or vary from the average value, as well as the extent to which these data points differ from one another, is practically by definition the concept of variability.
The given stem and leaf plot is:
stem leaf
0 5
1 0, 3,7
2 4,6,8
3 2
5 8
The value in the stem is the ten's place and the value in the leaf is the one's place.
So the scores are 05, 10, 13, 17, 24, 26, 28, 32 and 58.
Because extreme values and outliers have a smaller impact on the interquartile range than the complete data range, statisticians prefer using them to measure variability. To understand the centre and spread of your data, utilise the IQR along with a measure of central tendency, like the median.
Range for this data = 58 - 5 = 53.
To find the Inter Quartile Range (IQR), we first find the median.
Median = 24
So Q1 is the first quartile.
This is the median of the first half of the scores(5,10,13,17).
Q1 = 10+13 / 2 = 11.5
Q3 is the third quartile.
This is the median of the second half of the scores (26, 28, 32 58).
Q3 = 28+32 / 2 = 30
Now,
IQR = Q3 - Q1 = 30 - 11.5 = 18.5
Therefore for the given data, the best measure of variability is the interquartile range (IQR) and its value is 18.5.
I totally didnt copy - 0
What is a 2 sample z-test?
Answer:
Two-Sample Z-Test. The Two-Sample Z-test is used to compare the means of two samples to see if it is feasible that they come from the same population. The null hypothesis is: the population means are equal.
Step-by-step explanation:
have a nice day.
Graph the line that has a slope of 1/4 and includes the point (0,4).
.
Answer: y = mx+b
y = -1x+1/4
Step-by-step explanation:
7:31 PM Wed Feb 8
S÷
7
9
for s=4.
ixl.com
Write your answer as a fraction or as a whole or mixed number.
Submit
The expression S÷7 when s = 4 is simplified to 4/7
What is a fraction?
A fraction can be described as the part of a whole variable, number or element
There are several types of fractions which includes;
Mixed fractionsSimple fractionsProper fractionsImproper fractionsComplex fractionsFrom the information given, we have that;
S÷7 is the given expression as a quotient.
For s = 4, we have to substitute the value of s as 4 in the expression, we have;
4/7
Hence, it is an example of a proper fraction where the denominator is greater than the numerator.
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What are four solutions of this equation that are ordered pairs? y=2x+4
Answer: (0,4), (1,6), (2,8), (3,10)
Step-by-step explanation:
you can plug this equation into a graphing calculator (if you don't have a physical one, you can use desmos online graphing calculator) or just graph it on paper.
If you graph it on paper, start at (0,4) because that is the y-intercept. Then go up 2 and right 1 and plot a point there. Up 2 and right 1 and plot a point, etc.
Some points on this line are (0,4), (1,6), (2,8), (3,10)
can anyone please help me do this? I need it done asap but nothing makes sense
Answer:
Skip it bro this fin be hard and i can do the next one i tryed to do this and it hard
Step-by-step explanation:
Help me find the measurements please.
Please help! 100 POINTS!!!!
Answer:
Answer is B.
[9 9]
[-3 2]
example: 3+6=9 9+0=9
5+ -8= -3 -2+4= 2
Branly please
What is the cost of 0. 85 pound of imported cheese at $7. 90 per pound
Answer:
Step-by-step explanation:
Cost = 0.85 x $7.90
Cost = $6.72
the scale of a map is 1:50000 find the area in square km of a square field 4cm² on the map.
The area in square km of a square field 4 cm² is given as follows:
1 km².
How to obtain the area?The area is obtained applying the proportions in the context of the problem.
The scale is of:
1 cm : 50000 cm -> 1 cm = 0.5 km, as 1 cm = 10^-5 km.
Hence, for the areas, in square units, the scale is obtained squaring both sides, as follows:
(1 cm)² = (0.5 km)²
1 cm² = 0.25 km².
Meaning that the area of the square field is of:
4 x 0.25 = 1 km².
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Please solve this math problem and give an explanation for more points and brainliest
Correct numerical expression is G. 6(18)2 – 27(6)(12).
What is expression?In mathematics, an expression is a combination of numbers, symbols and operations such as addition, subtraction, multiplication and division that may be evaluated to produce a single number, a variable or a set of numbers.
This expression calculates the number of cubic inches of the box filled with packing material by subtracting the volume of the cylinder from the volume of the cube. The volume of the cube is 6(18)2, and the volume of the cylinder is 27(6)(12). Thus, the number of cubic inches of the box filled with packing material is 6(18)2 – 27(6)(12).
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Fill the blank! if a residual is negative, then that data point lies _____________ the regression line.
If a residual is negative, then that data point lies below the regression line. In a regression analysis, the goal is to find the line that best describes the relationship between two variables.
The line is determined by finding the values of the slope and intercept that minimize the sum of the squared errors between the observed data points and the predicted values on the line.
The difference between the actual value of the dependent variable and the predicted value on the line is known as the residual. A residual represents the vertical distance between the observed data point and the regression line.
If the residual is positive, it means that the observed value is above the regression line, and if the residual is negative, it means that the observed value is below the regression line.
When a residual is negative, it means that the predicted value on the regression line is higher than the actual value of the dependent variable for that particular data point. In other words, the observed data point is lower than what we would expect based on the relationship described by the regression line.
This situation indicates that the regression line may not fit the data very well at that point, and it may be worth investigating further to see if there are other factors that may be affecting the relationship between the two variables.
In summary, a negative residual means that the observed data point lies below the regression line, and it indicates that the regression line may not be the best fit for that particular data point.
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A double ferris wheel is pictured below. A large rotating arm with diameter 20 is centered 14 meters off the ground, and completes one rotation every 11 minutes. At the end of each side of the large arm is a smaller wheel with diameter 6 meters, which completes one rotation about its center every 6 minutes.
If you board the ferris wheel at point P at time t = 0, and each wheel rotates in the direction shown by the arrows, find an equation for your height, H above ground after t minutes.
This equation reflects the passenger's height above the ground after t minutes: H = 14 + 3 + (10)sin(2πt/11) + (3)sin(2πt/6).
What is equation?An equation in mathematics is a statement that two mathematical expressions are equal. Equations are used to represent mathematical relationships and to describe the behavior of systems or processes. An equation typically consists of two sides, separated by an equal sign (=). On one side of the equal sign is the expression representing what is known or given, and on the other side is the expression representing what is being found or sought. Equations can be used to model real-world situations, to describe the behavior of mathematical functions, to solve problems, and to make predictions. They are an important tool in many areas of mathematics and science, including algebra, calculus, physics, and engineering.
Here,
The height of a passenger on a double Ferris wheel can be calculated by considering the combined effect of two rotations: the rotation of the large arm and the rotation of the smaller wheel.
Let's call the length of the small arm as x, which is equal to half of the diameter of the small wheel, i.e. x = 3.
At time t = 0, the passenger is at point P, which is x meters above the ground. As the large arm rotates, the height of the passenger will change according to the formula:
H = 14 + x + (20/2)sin(2πt/11)
Where H is the height above the ground after t minutes, and (20/2) is half of the diameter of the large arm.
Additionally, as the small wheel rotates, the height of the passenger will change according to the formula:
H = H + (3)sin(2πt/6)
So, combining both the effects, the height of the passenger on the Ferris wheel can be expressed as:
H = 14 + 3 + (10)sin(2πt/11) + (3)sin(2πt/6)
This equation represents the height of the passenger above the ground after t minutes: H = 14 + 3 + (10)sin(2πt/11) + (3)sin(2πt/6).
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What is the equation of this graph
Answer:
[tex]7y {}^{2} = 0[/tex]
Answer:
the correct answer is y = -1/2x + 6
Step-by-step explanation: