Answer: 124950
Step-by-step explanation:
So, let’s look at this logically. For first place, you can any one of the 51 runners finish there. For 2nd place, you can have any one of the remaining 50 runners finish there. For 3rd place, you can have any one of the 49 runners who haven’t finished finish there. runners who haven’t finished finish doesn’t matter .So, you take all of the possibilities, and times them together, 51*50*40 different possibilities.Now, if you want a generic equation, you can run it through this equation, x being the number of possibilities, and n being the number of ones your choosing:
(51!)/(51-3)!
Out of the numbers 1,5,5,6,8 which is the mad
The mean absolute deviation from the given data set is 1.6
What is a Mean Absolute Deviation?The mean absolute deviation measures how far the data points are on average from a center point. Mean, median, mode, or any other random figure can serve as the center point.
The mean is frequently used as the center point, In this situation, The method for computing mean absolute deviation (MAD) is helpful, which represents the average of the absolute departure of the data points from the mean of the data set.
Mean = (1+5+5+6+8)/5
Mean = 25/5
Mean = 5
The distance of each value from the mean is as follows:
Value distance from the mean 5
1 4
5 0
5 0
6 1
8 3
MAD = (4 + 0 + 0 + 1 + 3)/5
MAD = 8/5
MAD = 1.6
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Writing equations of lines parallel and perpendicular to a given line through a point
Consider the line =−4x-9y=2.
Find the equation of the line that is perpendicular to this line and passes through the point (5 ,−1).
Find the equation of the line that is parallel to this line and passes through the point (5,−1).
The equation of the line that is perpendicular to this line and passes through the point (5, −1) is y = (9/4)x - (49/4) and the equation of the line that is parallel to this line and passes through the point (5,−1) is y = (-4/9)x + (11/9).
An equation of a line is provided: -4x - 9y = 2
-9y = 4x + 2
y = (-4/9)x - 2/9
The slope-intercept form of the line is y = mx + c
So, the Slope of the line is -4/9
The slope of the perpendicular line is -1/(-4/9) = 9/4
Equation of line with slope 9/4 and containing the point (5, -1):
y - (-1) = (9/4)(x - 5)
y = (9/4)x - (49/4)
Parallel lines have the same slope, so the equation of the line with slope -4/9 and which contains the point (5, -1) is:
y - (-1) = (-4/9)(x - 5)
y = (-4/9)x + (11/9)
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Which of the following inequalities would have solutions of -4, 0, 2, 3?
Mark all that apply.
Answer:
Step-by-step explanation:
n
how to calculate hyperboloid of one sheet?
The equation of hyperboloid of one sheet: [tex]\frac{x^{2} }{A^{2} } +\frac{y^{2} }{B^{2} } -\frac{z^{2} }{C^{2} } =1[/tex] which is used to calculate hyperboloid.
The most challenging quadric surface is probably the hyperboloid of a single sheet. For starters, it is puzzling since its equation is quite similar to that of a hyperboloid with two sheets. For information on how to tell them apart, see to the section on the two-sheeted hyperboloid. Its cross portions are also highly intricate equation.
Having said all of that, everyone who has watched The Simpsons, even for the first time, will recognize this form. One-sheet hyperboloids have a striking resemblance to Springfield Nuclear Power Plant cooling towers.
The cross sections of a straightforward one-sheeted hyperboloid with A = B = C = 1.
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Two important ingredients for baking
bread are yeast and flour. To make a loaf of bread
of at most 40 servings, maintain a yeast to flour ratio of
1:200. If you're making a loaf of
more than 40 a servings, use a ratio of 1:180.
If you're making 40 servings of bread and using 0.35 oz of yeast, how
many ounces of
flour do you need?
If you're making 90 servings of bread and using 360 oz of flour. how many ounces of
yeast do you need?
NOTE: Enter only numerals for each of your
answers.
Answer:
14 oz of flour. 2 oz yeast.
Step-by-step explanation:
If you're making 40 servings of bread and using 0.35 oz of yeast, you need:
0.35 oz yeast / 1 yeast : 200 flour = 0.35 oz yeast / 1 : 200 flour = 0.00175 oz yeast/flour
So, you need 0.00175 oz yeast/flour * 40 servings * 200 flour/serving = 14 oz of flour.
If you're making 90 servings of bread and using 360 oz of flour, you need:
1 yeast : 180 flour = 360 oz flour / 90 servings / 180 flour/serving = 2 oz yeast.
Which statement is true?
The true statement is that the y intercept of function A is less than the y intercept of function B.
What is y Intercept?y intercept is the y coordinate of the point on the line where it touches the Y axis. The x coordinate will be 0 there.
Here we have two functions.
Function A is given in the graph and function B is given in the equation form.
From the graph, the y intercept of function A is the y coordinate of the point touching the Y axis.
Line touches the Y axis at the point (0, -3).
So y intercept of function A = -3.
The equation of function B is the slope intercept form.
In the slope intercept form, y = mx + c, c is the y intercept.
From the equation y = 1/2 x + 4, 4 is the y intercept.
So 4 > -3.
Hence the y intercept of B is greater than that of A.
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A student noticed different gas prices as she drove around town. Find the first quartile. Round your answer to the nearest cent. $3.31 $3.28 $3.42 $3.35 $3.31 $3.26 $3.38 $3.32 $3.34
Answer: $3.32
Step-by-step explanation:
First arrange the given discrete values in ascending order.
$3.26, $3.28, $3.31, $3.31, $3.32, $3.34,$3.35, $3.38, $3.42
we will use the formula 1/2 x (n +1), where n is total number of discrete values which in this case is 9.
This formula doesn't give the answer of the second quartile, it tells which nth term in the arranged set will be the second quartile.
1/2 (9+1) = 5.
Now we will choose the 5th term of the ascending order set.
Second quartile is same as the median, that means you need the mid value.
A group of people were asked if Marilyn Monroe had a thing with John F Kennedy. 110 responded "yes", and 163 responded "no". Find the probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John.
Probability = ______ (Please enter a reduced fraction.)
The probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John is 0.60 or 60%
How to find the probability that if a person is chosen at random, he does NOT believes Marilyn Monroe had an affair with John
We can find the probability that a person does not believe Marilyn Monroe had an affair with John F Kennedy by dividing the number of people who responded "no" by the total number of people who responded to the survey:
Probability of "no" = Number of "no" responses / Total number of responses
Total number of responses = Number of "yes" responses + Number of "no" responses
Total number of responses = 110 + 163 = 273
Probability of "no" = 163 / 273
Simplifying the fraction, we get:
Probability of "no" = 0.5967 or approximately 0.60
So, the probability that if a person is chosen at random, he does not believe Marilyn Monroe had an affair with John F Kennedy is approximately 0.60, or 60%.
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Currently, 2 out of 195
countries celebrate
Groundhog Day. How many
celebrations
could we expect
if there were 950 countries?
If there were 950 countries, we could expect celebrations from 10 countries.
What was the Groundhog Day all about?Groundhog Day is a popular North American tradition celebrated on February 2 in the United States and Canada. It is based on the Pennsylvania Dutch superstition that if a groundhog emerges from its burrows on this day and sees its shadow due to clear weather, it will retreat to its burrow and winter will last six weeks longer.
In our calculation, as 2 out of 195 celebrate the day, we need know how many celebrations we could expect if there were 950 countries.
950 / 195 = 4.87179487179 = 4.87. We will multiply 4.87 by 2 country giving us 9.74, approximately 10 countries.
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What value represents the number of ways in which the expected classes are free to vary in the chi‑square goodness‑of‑fit test?
The value that represents the number of ways in which the expected classes are free to vary in the chi-square goodness-of-fit test is called the degrees of freedom (df).
It is equal to the number of categories minus one. The degrees of freedom provide a measure of the amount of information available in the sample to estimate the parameters of the distribution.
In a goodness-of-fit test, the degrees of freedom are calculated as the number of categories minus one, which represents the number of ways in which the expected classes are free to vary.
For example, if you are conducting a chi-square goodness-of-fit test to compare the distribution of a categorical variable with expected frequencies, you would have one degree of freedom for each category or class, with the exception of the last category.
The last category's frequency is determined by subtracting the sum of the observed frequencies for all other categories from the total sample size. This means that the last category is not free to vary independently, so it is not counted in the degrees of freedom calculation.
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Aisha and her children went into a grocery store and will buy apples and bananas. Each apple costs $1.25 and each banana costs $0.60. Aisha has a total of $10 to spend on apples and bananas. Write an inequality that would represent the possible values for the number of apples purchased, a, and the number of bananas purchased, b
The required inequality, which represents the possible values for the number of apples and bananas purchased is 2a + 0.6b ≤10.
What is inequality?
Inequality can be defined as the relation of the expression containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Let, the number of apples purchased, a, and the number of bananas purchased, b.
According to the question, Each apple costs $1.25 and each banana costs $0.60. London has a total of $10 to spend on apples and bananas.
So,
1.25a + 0.6b ≤10
Thus, the required inequality, that represents the possible values for the number of apples and bananas purchased is 1.25a + 0.6b ≤20.
What is the simplified form of x+7/2 subtracted by x+4/2
The simplified form of subtraction is 3/2.
About subtractionThe simplified form of x+7/2 subtracted by x+4/2 is 3/2.
1. Start with the original expression: x+7/2 - (x+4/2)
2. Distribute the negative sign: x+7/2 - x - 4/2
3. Combine like terms: 7/2 - 4/2
4. Simplify by subtracting: 3/2
So the simplified form is 3/2.
Subtraction is an arithmetic operation tat represents the operation of removing an object from a collection. Subtraction is indicated by a minus sign, −. For example, in the image next to it, 5 − 2 peaches—meaning 5 peaches with 2 picked for a total of 3 peaches.
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What does x equal pls my grade is depending on this
What is the value of 6/3 x 2 3
Answer: 16
Step-by-step explanation:
6 ÷ 3 = 2
[tex]2^{3}[/tex] = 2 x 2 x 2
2 x 2 x 2 = 8
2 x 8 = 16
The graph shows the distance, y, in miles, of a bird from its nest over a certain amount of time, x, in minutes.
Based on the graph, what is the initial value of the graph and what does it repr
0.5 mile per minute; it represents the speed of the bird
0.5 mile; it represents the original distance of the bird from its nest
10 miles; it represents the original distance of the bird from its nest
10 miles per minute; it represents the speed of the bird
need it right now fast!!!
Answer:
10 miles; it represents the original distance of the bird from its nes
Step-by-step explanation:
Julian and Nikhil are making paper cones to hold popcorn
to hand out at parent math night. They want the cones to
hold 28.26 (about 9) cubic inches of popcorn. What are
two different possible values for height h and radius r for
the cones?
The possible values for radius r and height h of the cone will be 2 and 2.1485 respectively.
What exactly is a cone?
A cone is a shape formed by connecting a single point known as the apex or vertex to all of the points of a circular base using a series of line segments (which does not contain the apex). The distance from the vertex to the base is the cone's height. The circular base's radius has been measured. The slant height is the length of the cone from the peak to any point along the base's perimeter. The height, radius of base, and slant height of the cone in the figure define it.
Volume of cone=1/3πr²h, where r=base radius and h=cone height
Curved surface area=πrL, where L is the slant height.
Now,
Given Volume of cone to hold popcorn=9 inch³
i.e. 1/3πr²h=9
r²h=9*3*7/22
r²h=8.5943
let r=2
then h=8.5943/4
h=2.1485
Hence,
The possible values for radius r and height h of the cone will be 2 and 2.1485 respectively.
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Which equations support the fact that rational numbers are closed under addition?
Select each correct answer.
A. √2+√2=2√2
B. √6+(-√6)=0
C. √9+√9=2√9
D. 1/3+1/3=2/3
Answer:
Step-by-step explanation:
None of the given equations support the fact that rational numbers are closed under addition, because they all involve irrational numbers or fractions, which are not necessarily rational.
Option (A) involves the irrational number √2.
Option (B) involves adding the irrational number √6 with its negative, which results in a rational number, but it doesn't prove that all additions of rational numbers are also rational.
Option (C) involves the perfect square 9, but the square root of a non-square integer is generally an irrational number.
Option (D) involves the addition of two rational numbers, which is a valid example of the closure property of rational numbers under addition.
Therefore, the correct answer is (D) 1/3+1/3=2/3.
Question 13
Peng Peng has $4 in quarters and dimes. She has 34 coins. How many quarters and dimes does Peng Peng have?
Part A
Write a system of equations that represents the situation.
0.25x+
+ y =
Part B
Solve the system of equations. Express the coordinates as decimals if necessary.
Step-by-step explanation:
x = number of quarters
y = number of dimes
x + y = 34
therefore, we can say right away
y = 34 - x
0.25x + 0.1y = 4
because a quarter is worth $0.25, and a dime is worth $0.10.
now we are using the first equation in the second :
0.25x + 0.1(34 - x) = 4
0.25x + 3.4 - 0.1x = 4
0.15x + 3.4 = 4
0.15x = 0.6
x = 0.6/0.15 = 4
y = 34 - x = 34 - 4 = 30
the solution is therefore (4, 30).
she has 4 quarters and 30 dimes.
Peng has 4 quarters and 30 dimes.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, Peng has $4 in quarters and dimes. She has 34 coins.
we need to find the number of quarters and dimes, does Peng have,
Let x = number of quarters and y = number of dimes
Therefore, establishing the equations :-
x + y = 34
y = 34 - x...(i)
Since, a quarter is worth $0.25, and a dime is worth $0.10.
Therefore,
0.25x + 0.1y = 4.....(ii)
Therefore,
0.25x + 0.1(34 - x) = 4
0.25x + 3.4 - 0.1x = 4
0.15x + 3.4 = 4
0.15x = 0.6
x = 0.6/0.15
x = 4
Put x = 4 in the eq(i)
y = 34 - x = 34 - 4 = 30
y = 30
Hence, she has 4 quarters and 30 dimes.
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Casey claims the linear equation for the relationship shown by the graph is c=25j. Use numbers and words to support Casey's claim.
Each points in the graph is satisfying the equation c = 25j, that means the equation is linear.
What is a 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.
Given that, Casey claims the linear equation for the relationship shown by the graph is c=25j.
We have points on it,
(1, 25), (3, 75), (5, 125) and (7, 175)
Put each point in the equation,
c = 25j
Put j = 1, 3, 5, and 7
We get the corresponding value, 25, 75, 125, 175
That means, the points are satisfying the equation,
Hence, Each points in the graph is satisfying the equation c = 25j, that means the equation is linear.
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The given graph is :-
8)
Determine the measure
of angle 8.
G.8.B
Answer:
140 ° , because it is vertically opp to angle 4 and angle 4 is corresponding 8 .
Solve the equation AB=BCAB=BC for AA, assuming that A,BA,B and CC are square matrices and BB is invertible.
The equation AB=BC for [tex]A=BCB^{-1}[/tex].
The solution of AB = BC for A, assuming that A,B and C are square matrices and B is invertible is
We have to solve the equation
AB = BC given that these all are square matrices and B is invertible.
Write the required Equation:
AB = BCMultiply both sides by inverse of B
The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.
Since the outcome of multiplying a matrix by an identity matrix is always the same original non-identity (non-unit) matrix, as was previously stated, the identity matrix is also known as a "unit matrix."⇒[tex]ABB^{-1} =BCB^{-1}[/tex]
⇒[tex]AI=BCB^{-1}[/tex]
⇒[tex]A=BCB^{-1}[/tex]
Therefore, the solution of AB = BC is [tex]A=BCB^{-1}[/tex].
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A taxi company charges a base fee of $3.00 plus $0.75 per mile. Write an equation to represent the cost of a taxi ride Y for the distance of X miles.
0.75 times the amount of miles+the base fee
Answer:
Y=0.75X+3
A gym teacher has a large canvas bag that contains 8 tennis balls, 2 volleyballs, 1 basketball, 3 baseballs, and 5 footballs. If you reach into the bag at random, what is the probability that you select a tennis ball?
8/19 or 42.1%
add all values up to a total, then find the percentage from that total.
8 + 2 + 1 + 3 + 5 = 19 balls total
8 tennis valls to 19 total.
8/19 or 42.1%
help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
25%
Step-by-step explanation:
x + 0.25x = y
y - 0.25x = x
If the size of a circle increases by 25% and then decreases back down to it's original size it's going to be the same percentage 25%.
Brandon is a California CPA who is renewing his license in active status. During the two years prior to his renewal date, Brandon's highest level of service provided was a compilation engagement. How many hours, out of the total of 80 continuing education hours required, must Brandon complete pursuant to the Accounting and Auditing Education Requirement? - 8 hours, -16 hours, -24 hours, -40 hours
According to the California Board of Accountancy's requirements for CPA license renewal, if the highest level of service provided during the two years prior to the renewal date was a compilation engagement, the CPA must complete 24 hours of continuing education in accounting and auditing subjects.
Here is the breakdown of the requirements for the Accounting and Auditing Education Requirement:
- If the highest level of service provided was an audit, review, or attestation engagement, the CPA must complete 40 hours of continuing education in accounting and auditing subjects.
- If the highest level of service provided was a compilation engagement, the CPA must complete 24 hours of continuing education in accounting and auditing subjects.
- If the highest level of service provided was preparation of financial statements, the CPA must complete 8 hours of continuing education in accounting and auditing subjects.
- If the CPA did not provide any of the above services, they are not required to complete any continuing education in accounting and auditing subjects.
In Brandon's case, since his highest level of service provided was a compilation engagement, he must complete 24 hours of continuing education in accounting and auditing subjects out of the total of 80 continuing education hours required.
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What is PPM and How do I calculate it?
PPM stands for "parts per million" and is a way of expressing small concentrations of substances in a larger mixture. To calculate PPM, divide the mass or volume of the substance by the total mass or volume of the mixture and multiply by one million.
To calculate PPM, you need to know the mass of the substance in question and the total mass of the mixture. Here are the steps to calculate PPM:
1. Determine the mass of the substance in question. For example, let's say you have a mixture that contains 0.5 grams of salt.
2. Determine the total mass of the mixture. For example, let's say the total mass of the mixture is 1000 grams.
3. Divide the mass of the substance by the total mass of the mixture. In this example, 0.5 grams / 1000 grams = 0.0005.
4. Multiply the result by 1,000,000 to get the PPM. In this example, 0.0005 x 1,000,000 = 500 PPM.
So, the concentration of salt in the mixture is 500 PPM. Remember to always use the same units of measurement for both the substance and the mixture when calculating PPM.
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The ratio of Sarah's age to her father's age now is 1:3. In 6 years' time, the ratio becomes 2:5. What is Sarah's age now?
Sarah's age now is 18.
What is meant by Ratio?Ratio is defined as the relationship between two quantities for which it tells how much one quantity is contained in the other.
Normally, the ratio of two quantities a and b is denoted as a : b.
Given in the question that,
The ratio of Sarah's age to her father's age now is 1:3.
Suppose that x is the age of Sarah now.
Then, from the information given, father's age now = 3x
After 6 years,
Sarah's age = x + 6
Father's age = 3x + 6.
Given that, In 6 years' time, the ratio becomes 2:5.
So, numerically,
(x + 6) / (3x + 6) = 2 / 5
Doing the cross multiplication, we get,
5 (x + 6) = 2 (3x + 6)
5x + 30 = 6x + 12
5x - 6x = 12 - 30
-x = -18 or x = 18
Hence now, age of Sarah is x = 18.
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What is the y- coordinate for the solution to the system of equations? {8x−4y=−32, 2x+2y=4
The y- coordinate for the solution to the system of equations is 4
How to determine the y-coordinateFrom the question, we have the following parameters that can be used in our computation:
8x−4y=−32,
2x+2y=4
Multiply the second equation by 4
So, we have the following representation
8x − 4y = −32
8x + 8y = 16
Subtract the equations
So, we have the following representation
12y = 48
Divide by 12
y = 4
Hence, the solution is y = 4
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The y-coordinate for the solution to the system of equations is equal to 4.
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by this ordered pair (-2, 4).
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Two rectangles each with dimensions
c cm ⇥ b cm are used to form a cross as shown. The arms of the cross are all of equal length.
a) The perimeter of the cross is: P = 4a = 4(c - b) = 4c - 4b
b) The area of the cross is:[tex]A= 2cb - 2b^2 \ cm^2[/tex]
c) b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]
What is area and perimeter?
The perimeter of a shape is the distance around its outside. The space inside a shape is measured by area.
a) The perimeter, P, of the cross is equal to the sum of the lengths of its four arms.
The length of one arm of the cross can be found by subtracting the length of one rectangle from the length of the other rectangle. Since each rectangle has dimensions c cm × b cm, the length of one arm is:
a = c - b
Therefore, the perimeter of the cross is:
P = 4a = 4(c - b) = 4c - 4b
b) The area, A, of the cross is equal to the area of the two rectangles minus the area of the four triangles formed by the arms of the cross.
The area of each rectangle is:
[tex]Area_{rect} = c * b[/tex]
The area of each triangle is:
[tex]Area_{tri} = (a * b) / 2 \\\\= \frac{[(c - b) * b]}{2} \\\\= \frac{ (c * b - b^{2} )}{2}[/tex]
Since there are four triangles, the total area of the triangles is:
[tex]4A_{tri} = 2cb - 2b^2\ cm^2[/tex]
Therefore, the area of the cross is:
[tex]A = 2A_{rect} - 4A_{rect} \\\\ = 2cb - 2b^2[/tex]
c) c) To find b in terms of A and C, we can use the formula for the area of the cross that we found in part b:
[tex]A = 2cb - 2b^2[/tex]
We can rearrange this equation to put it in the form of a quadratic equation:
[tex]2b^2 - 2cb + A = 0[/tex]
This is a quadratic equation in standard form, with a = 2, b = -2c, and c = A. We can use the quadratic formula to solve for b:
b = (-b ± sqrt(b^2 - 4ac)) / 2a
b = (2c ± sqrt((2c)^2 - 4(2)(A))) / (2 × 2)
[tex]b=\frac{-b ± \sqrt{(b^2 - 4ac)} }{2a} \\\\b= \frac{2c ± \sqrt{(2c^2 - 4(2)c)}}{4} \\\\b= \frac{2c ± \sqrt{(4c^2 - 16A)}}{4} \\\\b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]
Therefore, b in terms of A and C is: [tex]b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}[/tex]
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PLEASE HELP!!!! Which of the following statements are equivalent to the statement the price decreased by 1/2%. Choose all the correct answers
A) The price doubled
B) The price is 150% of the price before
C) The price was reduced by a quarter of what it was before
D) The price is half of what it was before
E) The price is now 1.5 times greater than what it was before
F) The price now is 66 2/3% of what it was before
G) The price now is 200% of what it was before
H) The price is 75% of what it was before
The equivalent to the statement the price decreased by 1/2% will be 0.995x. Thus, all options are incorrect.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
Let the price be 'x'. Then the equivalent to the statement the price decreased by 1/2% is given as,
⇒ (1 - 0.5 / 100) x
⇒ 0.995x
The equivalent to the statement the price decreased by 1/2% will be 0.995x. Thus, all options are incorrect.
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