Answer:
Step-by-step explanation:
Brahmagupta's solution to a quadratic equation of the form ax² + bx = c is given by x = (-b ± √(b² - 4ac)) / 2a.
For the equation 3x² + 4x = 6, we have a = 3, b = 4, and c = 6. Plugging these values into the formula, we get:
x = (-4 ± √(4² - 4(3)(6))) / 2(3)
x = (-4 ± √(16 - 72)) / 6
x = (-4 ± √(-56)) / 6
Since the square root of a negative number is not a real number, the quadratic equation has no real solutions. Therefore, Brahmagupta would not have found a solution for this particular equation using his method.
certain virus infects one in every 200 people. A test used to detect the virus in a person is positive 90% of the time if the person has the virus and 10% of the time if the person does not have the virus. (This 10% result is called a false positive.) Let A be the event "the person is infected" and B be the event "the person tests positive".
a) Find the probability that a person has the virus given that they have tested positive, i.e. find P(A|B). Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A|B)= %
b) Find the probability that a person does not have the virus given that they test negative, i.e. find P(A'|B'). Round your answer to the nearest tenth of a percent and do not include a percent sign.
P(A'|B') = %
a. The probability that a person has the virus given that they have tested positive is approximately 4.3%.
b. The probability that a person does not have the virus given that they test negative is approximately 99.0%.
What is probability?Calculating the likelihood of experiments happening is one of the branches of mathematics known as probability. We can determine everything from the likelihood of receiving heads or tails when tossing a coin to the likelihood of making a research blunder, for instance, using a probability.
a) We need to find the probability that a person has the virus given that they have tested positive, i.e., P(A|B). We can use Bayes' theorem to calculate this probability:
P(A|B) = P(B|A) * P(A) / P(B)
where P(B|A) is the probability of testing positive given that the person has the virus, P(A) is the prior probability of a person having the virus, and P(B) is the probability of testing positive.
From the problem statement, we know that:
P(A) = 1/200 = 0.005P(B|A) = 0.9P(B|A') = 0.1 (since the test is 10% false positive, the probability of testing positive when the person does not have the virus is 0.1)To calculate P(B), we can use the law of total probability:
P(B) = P(B|A) * P(A) + P(B|A') * P(A')
= 0.9 * 0.005 + 0.1 * (1 - 0.005)
= 0.1045
Therefore, we can compute P(A|B) as:
P(A|B) = P(B|A) * P(A) / P(B)
= 0.9 * 0.005 / 0.1045
≈ 4.3%
So, the probability that a person has the virus given that they have tested positive is approximately 4.3%.
b) We need to find the probability that a person does not have the virus given that they test negative, i.e., P(A'|B'). We can again use Bayes' theorem:
P(A'|B') = P(B'|A') * P(A') / P(B')
where P(B'|A') is the probability of testing negative given that the person does not have the virus, P(A') is the prior probability of a person not having the virus, and P(B') is the probability of testing negative.
From the problem statement, we know that:
P(A') = 1 - P(A) = 199/200 = 0.995P(B'|A) = 0.1 (since the test is 10% false positive, the probability of testing negative when the person has the virus is 0.1)P(B'|A') = 0.9 (since the test is 90% accurate, the probability of testing negative when the person does not have the virus is 0.9)To calculate P(B'), we can again use the law of total probability:
P(B') = P(B'|A) * P(A) + P(B'|A') * P(A')
= 0.1 * 0.005 + 0.9 * 0.995
≈ 0.895
Therefore, we can compute P(A'|B') as:
P(A'|B') = P(B'|A') * P(A') / P(B')
= 0.9 * 0.995 / 0.895
≈ 99.0%
So, the probability that a person does not have the virus given that they test negative is approximately 99.0%.
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Before 1980, Mount St. Helens was cone-shaped, with a height of about 1.83 miles and a base radius of about 3 miles. In 1980, Mount St. Helens erupted. The tip of the cone was destroyed, reducing the mountain's volume by 0.043 cubic miles. Find the volume of Mount St. Helens after the eruption. Round the answer to the tenths place.
HURRY PLEASE
Answer:
17.2 cubic miles
Step-by-step explanation:
You want the volume of Mt. St. Helens after an eruption removed 0.043 cubic miles of volume from its cone shape. Its radius is 3 miles, and its height was about 1.83 miles.
ConeThe formula for the volume of a cone is ...
V = 1/3πr²h
The volume of the tip is removed from that to find the volume after the eruption.
V = 1/3π(3 mi)²(1.83 mi) - 0.043 ≈ 17.2 mi³
After the eruption, the volume of Mount St. Helens is about 17.2 cubic miles.
__
Additional comment
The volume rounded to 1 decimal place is unaffected by the amount removed. That amount only changes the volume in the 2nd decimal place.
The exact circumference of a circle is 14 π yards . What is the approximate of the circle ? Use 3.14 for π . Round to the nearest hundredth is necessary
Answer & Step-by-step explanation:
The Radius should be about 2.228 and the Diameter is 4.456. The area of the circle is 15.59
A car is purchased for $26,500 . After each year, the resale value decreases by 25% . What will the resale value be after 4 years?
Answer:
the resale value after 4 years would be 11,812.5
Step-by-step explanation:
I'm sorry if this is wrong this is based on what I know :)
Answer:
The answer to your question is $8,384.77
Step-by-step explanation:
Average annual value lost: $12,913.57
First year depreciation: $6,625.00
Total depreciation: $18,115.23
Total depreciation percentage: 68.36%
Value of vehicle at end of ownership period: $8,384.77
I hope this helps and have a wonderful day!
The claim is that the proportion of drowning deaths of children attributable to beaches is more than 0.25, and the sample statistics include n = 681 drowning deaths of children with 30% of them attributable to beaches.
3.01
2.85
–3.01
–2.85
To test the claim, we need to conduct a hypothesis test with the null hypothesis being that the proportion of drowning deaths of children attributable to beaches is 0.25 and the alternative hypothesis being that it is more than 0.25.
Using a one-sample z-test with a significance level of 0.05, we can calculate the test statistic as:
z = (0.3 - 0.25) / sqrt(0.25 * 0.75 / 681) = 3.01
Since the alternative hypothesis is that the proportion is greater than 0.25, we need to find the area to the right of the test statistic in the standard normal distribution.
Using a standard normal table or calculator, we can find the p-value to be approximately 0.0013.
Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the proportion of drowning deaths of children attributable to beaches is more than 0.25.
Therefore, the answer is 3.01.
Use the rules of exponents to simplify the expression (x2)(x9) .
The simplified expression for given problem will be [tex]x^{-7}[/tex].
What is are rules of exponent?Product of Powers: Add the exponents when multiplying numbers with the same base. Eg: [tex]a^m * a^n = a^{(m+n)}[/tex]Quotient of Powers: Subtract the exponents when dividing numbers with the same base. Eg: [tex]a^m / a^n = a^{(m-n)}[/tex]Power of a Power: Multiply the exponents when raising a number with an exponent to another exponent. Eg: [tex](a^m)^n = a^{(m*n)}[/tex]Power of a Product: Distribute the exponent to each term when raising a product of numbers to an exponent. Eg:[tex](ab)^n = a^n * b^n[/tex]Power of Zero: Any non-zero number raised to the power of 0 is equal to 1. Eg: [tex]a^0 = 1[/tex] (where 'a' is any non-zero number)Negative Exponent: A negative exponent indicates taking the reciprocal of the base raised to the absolute value of the exponent. Eg: [tex]a^{(-n)} = 1 / a^n[/tex]Fractional Exponent: A fractional exponent represents taking the nth root of the base. Eg: [tex]a^{(1/n)}[/tex] represents the nth root of 'a'.For the given problem,
[tex]x^2/x^9[/tex] = [tex]x^{(2-9)}[/tex] = [tex]x^{(-7)}[/tex] (∵[tex]a^m / a^n = a^{(m-n)}[/tex])
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A farmer has a bale of hay with a mass of 28kilograms.How many milligrams of hay are in the bale
Answer:
Step-by-step explanation:
1 kilogram has 1,000,000 milligrams so we do 1,000,000x28= 28,000,000 milligrams
Answer: 28 million milligrams
what is the answer ?
The Newton-Raphson formula to compute the square root of a > 0 is [tex]x_{i+1} = x_i - \frac{x_i - a}{2x_i}[/tex]
Finding the Newton-Raphson formula to compute the square root of a > 0From the question, we have the following parameters that can be used in our computation:
The list of options
Generally, the Newton-Raphson formula for a > 0 is
[tex]x_{n+1} = \frac{1}{2}(x_n + \frac{a}{x_n})[/tex]
Substitute i for n
So, we have
[tex]x_{i+1} = \frac{1}{2}(x_i + \frac{a}{x_i})[/tex]
When expanded, we have
[tex]x_{i+1} = x_i - (\frac{x_i - a}{2x_i})[/tex]
Remove brackets
So, we have
[tex]x_{i+1} = x_i - \frac{x_i - a}{2x_i}[/tex]
Hence, the solution is [tex]x_{i+1} = x_i - \frac{x_i - a}{2x_i}[/tex]
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Use the information given below to find the area of the triangle.
B
C
=
20
and
A
C
=
18
Answer:
Step-by-step explanation:
Triangle area formula: 1/2bh
Then use the Pythagorean theorem to find out what AB is.
AB= sqrt 76
8.72
8.72*18*1/2
78.5 approx
A bag has 5 yellow marbles, 4 blue marbles, 7 green marbles, and 4 red marbles. What is the probability of picking a blue marble from the bag with replacement twice
The solution is, 4/27 is the probability of picking a red marble, replacing it, and then picking a blue marble.
We have,
6 red marbles, 8 blue marbles and 4 yellow marbles.= 18 total marbles
P(red marble) = number red marbles / total
=6/18 = 1/3
We put the marble back
6 red marbles, 8 blue marbles and 4 yellow marbles.= 18 total marbles
P(blue marble) = number blue marbles / total
=8/18 = 4/9
P(red, replace. blue) = P(red) * P (blue)
= 1/3 * 4/9 = 4/27
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complete question:
A bag has 6 red marbles, 8 blue marbles and 4 yellow marbles. What is the probability of picking a red marble, replacing it, and then picking a blue marble?
Enter an equation that expresses y in terms of x.
x 40 50 60 70
y 38 48 58 68
The equation is
The equation that expresses y in terms of x is y = x - 2.
To find an equation that expresses y in terms of x, we need to determine the relationship between the two variables. One way to do this is by finding the slope of the line that passes through the given points.
Using the two points (40, 38) and (70, 68), we can find the slope as:
slope = (change in y) / (change in x)
slope = (68 - 38) / (70 - 40)
slope = 30 / 30
slope = 1
This means that for every increase of 1 in x, y also increases by 1.
We can now use the point-slope form of a linear equation to find the equation of the line passing through these points:
y - 38 = 1(x - 40)
Simplifying:
y = x - 2
Therefore, the equation that expresses y in terms of x is y = x - 2.
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help please! (see picture
The function rule is solved and the equation is g ( x ) = 3x + 5
Given data ,
Let the function be represented as A
Now , the value of A is
f ( x ) = 3x + 5
On simplifying , we get
when x = { -2 , 0 , 1 , 3 , 4 }
Now , the values of y are given by
g ( -2 ) = 3 ( -2 ) + 5
g ( -2 ) = -1
g ( 0 ) = 5
g ( 1 ) = 8
g ( 3 ) = 14
g ( 4 ) = 17
Hence , the function is solved
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(08.07 MC)
The function f(x) is shown on the graph.
The graph shows a downward opening parabola with a vertex at 2 comma 16, a point at negative 2 comma 0, a point at 6 comma 0, a point at 0 comma 12, and a point at 4 comma 12.
What is the standard form of the equation of f(x)?
f(x) = x2 + 4x + 12
f(x) = x2 − 4x − 12
f(x) = −x2 + 4x + 12
f(x) = −x2 − 4x − 12
Points earned on this question: 0
The function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.
What is function?Function is a set of instructions or statements that perform a specific task or calculation. It is a fundamental building block of a program, allowing the same code to be used multiple times. Functions help to organize code and make it easier to read and debug. They also allow for code reuse, meaning that the same code can be used in different parts of the program. Additionally, functions can be used to create libraries of code that can be shared and reused among different programs.
A function f(n) that represents the nth term of the sequence given above can be written as follows:
f(n) = 2n – 2
This function can be explained as follows:
The function f(n) represents the nth term of the given sequence. The first term of the sequence is 0, which is equal to f(1). The second term of the sequence is 2, which is equal to f(2). This pattern can be seen throughout the sequence, as each subsequent term is two more than the preceding one. Thus, the general form of the function can be written as f(n) = 2n – 2, where n represents the nth term of the sequence.
For example, when n = 5, the function f(n) = 2n – 2 = 10. This is equal to the fifth term of the sequence, 8.
Therefore, the function f(n) = 2n – 2 represents the nth term of the sequence 0, 2, 4, 6, 8.
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The standard form of the equation of f(x) is f(x) = -x² + 4x + 12
Equation of a Parabola:
The standard form of the equation of a parabola is:
y = a(x - h)²+ k
Where (h, k) is the vertex of the parabola and a determines whether the parabola opens up or down.
If a is positive, the parabola opens up, and if a is negative, the parabola opens down. The value of 'a' also determines the "steepness" of the parabola.
Here we have the function f(x) shows a graph.
The graph shows a downward opening parabola with a vertex at (2, 16) a point at (-2, 0) a point at (6, 0) a point at (0, 12), and a point at (4, 12)
The vertex of the parabola is at (2, 16), which means that the axis of symmetry is x = 2. This also tells us that the equation is of the form:
f(x) = a(x - 2)² + 16
Where "a" is a constant that determines whether the parabola is upward or downward opening.
We can find the value of "a" by using one of the other points on the graph. Let's use the point (0, 12):
=> 12 = a(0 - 2)² + 16
=> -4 = 4a
=> a = -1
So the equation is:
f(x) = -(x - 2)² + 16
Expanding and simplifying this equation gives:
f(x) = -x²+ 4x + 12
Therefore,
The standard form of the equation of f(x) is f(x) = -x² + 4x + 12
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Suppose you invest $100 a month in an annuity that earns 4% APR compounded *
monthly. How much money will you have in this account after 2 years?
O$1,004.48
O $2,400.18
O $2,518.59
O$3,908.26
Answer:
Answer: (C) $2,518.59.
Step-by-step explanation:
To find the amount of money you will have in the account after 2 years, we can use the formula for the future value of an annuity:
FV = P * (((1 + r/n)^(nt) - 1) / (r/n))
where:
FV = the future value of the annuity
P = the monthly payment, which is $100
r = the annual interest rate, which is 4% expressed as a decimal (0.04)
n = the number of times the interest is compounded in a year, which is 12 (monthly)
t = the time the money is invested for, which is 2 years
Substituting the given values into the formula, we get:
FV = 100 * (((1 + 0.04/12)^(12*2) - 1) / (0.04/12))
FV = 100 * (((1.00333333333)^24 - 1) / (0.00333333333))
FV = 2,518.59 (rounded to the nearest cent)
Therefore, you will have $2,518.59 in the account after 2 years. Answer: (C) $2,518.59.
A car travels 288 mi. A second car, traveling 4 mph faster than the first car, makes the same trip in 1 h less time. Find the speed of each car.
First Car =
Second Car =
Answer:
first car =48
Second Car=52
Step-by-step explanation:
Which diagrams represent the net of a rectangular prism? Select TWO answers choices.
Answer:
the first one and the second one.
Problem 5:
Find the missing side using
trigonometry:
52°
AV
18 H
0+
Drag & Drop the correct trig function:
Sin
Cos
Tan
Ratio:
Circle which shortcut you use:
Multiply
SLIDE 6 OF 11
(xº)
X
Round your answer to the nearest tenth:
G
or
||
0
Ans
Ans
Ans
Divide
BA
The value of the missing side is 14.22.
We have,
From the figure,
Sin 52 = x/18
Sin 52 = 0.79
So,
0.79 = x/18
x = 0.79 x 18
x = 14.22
Thus,
The value of the missing side is 14.22.
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Sara is preparing to change her w4 for the 2022 tax year and she needs to determine how much she will pay in taxes for the year. Sara knows that her projected income is $124,075 for 2022 and she will be filing her taxes and standard deduction as head of household. How much money in taxes should Sara have removed from her projected income?
2022 Tax Table attatched
Sara should have $4,578 removed from her projected income of $124,075 for the year 2022.
Determine Sara's taxable income by subtracting the standard deduction for head of household from her projected income. According to the tax table, the standard deduction for head of household for 2022 is $18,650. Therefore, Sara's taxable income is:
$124,075 - $18,650 = $105,425
Find the tax bracket that Sara's taxable income falls into. According to the tax table, for head of household, the tax brackets for 2022 are:
10% on taxable income from $0 to $14,100
12% on taxable income over $14,100 to $54,200
22% on taxable income over $54,200 to $86,350
24% on taxable income over $86,350 to $164,900
32% on taxable income over $164,900 to $209,400
35% on taxable income over $209,400 to $523,600
37% on taxable income over $523,600
Since Sara's taxable income is $105,425, she falls into the 24% tax bracket.
Calculate the amount of taxes that Sara owes based on her tax bracket. To do this, we need to find the amount of taxable income that falls within the 24% tax bracket, and multiply it by the tax rate. According to the tax table, the amount of taxable income within the 24% tax bracket for head of household is:
$105,425 - $86,350 = $19,075
Therefore, Sara's tax liability is:
$19,075 x 0.24 = $4,578
So, Sara should have $4,578 removed from her projected income to cover her taxes for the year.
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Determine if an ordered triple (x, y, z) is a solution of a system.
1. x + 2y - z = 1
2x + 7y + 4z = 11
x + 3y + z = 4
2. x + 2y - 3z = -1
x - 3y + z = 1
2x - y - 2z = 2
Neither (2, 1, 1) nor (-1, 0, -1) is a solution to the respective systems of equations.
We have,
To determine if an ordered triple (x, y, z) is a solution of a system of equations, we need to substitute the values of x, y, and z into each equation and check if the resulting equations are true.
Let's take the first system of equations:
x + 2y - z = 1
2x + 7y + 4z = 11
x + 3y + z = 4
Let's check if the ordered triple (2, 1, 1) is a solution of this system:
2 + 2(1) - 1 = 3, which is not equal to 1, so (2, 1, 1) is not a solution of equation 1.
2(2) + 7(1) + 4(1) = 17, which is not equal to 11, so (2, 1, 1) is not a solution of equation 2.
2 + 3(1) + 1 = 6, which is not equal to 4, so (2, 1, 1) is not a solution of equation 3.
Since (2, 1, 1) is not a solution of any of the equations in the system, it is not a solution of the system.
Now, let's take the second system of equations:
x + 2y - 3z = -1
x - 3y + z = 1
2x - y - 2z = 2
Let's check if the ordered triple (-1, 0, -1) is a solution of this system:
(-1) + 2(0) - 3(-1) = 2, which is not equal to -1, so (-1, 0, -1) is not a solution of equation 1.
(-1) - 3(0) + (-1) = -2, which is not equal to 1, so (-1, 0, -1) is not a solution of equation 2.
2(-1) - 0 - 2(-1) = 0, which is not equal to 2, so (-1, 0, -1) is not a solution of equation 3.
Since (-1, 0, -1) is not a solution of any of the equations in the system, it is not a solution of the system.
Therefore,
Neither (2, 1, 1) nor (-1, 0, -1) is a solution of the respective systems of equations.
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PLEASE HELP
Show 2 different ways to find the value of x. What do you think is the most efficient method? Explain why?
The value of x is,
⇒ x = 8
Given that;
In a triangle,
Perpendicular = 4 feet
Hypotenuse = x
Hence, We can formulate;
⇒ cos 60 = 4 / x
⇒ 1/2 = 4/x
⇒ x = 8
Thus, The value of x is,
⇒ x = 8
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A store is selling a shirt in two different states. The shirt retails for $45.
In Florida, the sales tax is 6.5%. In Alaska, it is 4.5%. How much more
would it cost for you to buy the shirt in Florida?
well, let's find out how much will it be in each state.
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.5\% of 45}}{\left( \cfrac{6.5}{100} \right)45} ~~ \approx ~~ \stackrel{ \textit{tax in Florida} }{2.93} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{4.5\% of 45}}{\left( \cfrac{4.5}{100} \right)45}~~ \approx ~~ \stackrel{ \textit{tax in Alaska} }{2.03}\hspace{5em}2.93-2.03~~ \approx ~~ \text{\LARGE 0.90}[/tex]
If there are 11 possible outcomes for event A and 6 possible outcomes for event B, how many possible outcomes are there for event A & event B? Note that these two events are independent of each other and the outcome of one even does not impact the outcome of the other event.
The total number of possible outcomes for Event A and Event B is 66.
The total number of outcomes for both events occurring simultaneously is just the product of the number of outcomes for each event if event A has 11 potential outcomes and event B has 6 possible outcomes and both events are independent.
Therefore, we can multiply the number of possibilities for event A (11) by the number of outcomes for event B (6) to determine the total number of potential outcomes for both events A and B:
11 x 6 = 66
Therefore, if events A and B occur simultaneously, there are 66 alternative outcomes.
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What is the surface area of the right rectangular prism, in square feet?
Answer:
2((7)(9) + (7)(10) + (9)(10)) = 2(63 + 70 + 90)
= 2(223) = 446 square feet
The number of vinyl album sales (in millions) in a country x years after 2010 is given by the polynomial 0.2xexponent2+0.3x+3.3 for 2010 through 2016. Use this model to predict the number of vinyl album sales in the country in the year 2030 (x=20)
The model predicts that there will be 89.3 million vinyl album sales in the country in the year 2030 by using quadratic equation.
Define quadratic equation?
A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one squared term (x²). The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and x is the variable. The values of a, b, and c determine the shape of the parabola, which is the graph of a quadratic equation.
To predict the number of vinyl album sales in the year 2030, we need to substitute x = 20 into the polynomial:
[tex]0.2x^2 + 0.3x + 3.3[/tex]
[tex]= 0.2(20)^2 + 0.3(20) + 3.3[/tex]
[tex]= 80 + 6 + 3.3[/tex]
[tex]= 89.3[/tex]
Therefore, the model predicts that there will be 89.3 million vinyl album sales in the country in the year 2030.
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Please help me!!!!! A tissue box has a volume of 1,001 in . Find the height of the tissue box, in inches, if it is 7 inches wide and 13 inches long. Provide an answer accurate to the nearest tenth.
To find the height of the tissue box, we use the formula for the volume of a rectangular prism, substituting the given values. We get a height of approximately 11.0 inches, rounded to the nearest tenth.
To find the height of the tissue box, we need to use the formula for the volume of a rectangular prism, which is:
volume = length x width x height
We are given the volume of the tissue box as 1,001 cubic inches, and its width and length as 7 inches and 13 inches, respectively. We can enter these values as substitutes in the formula to obtain:
1,001 = 13 x 7 x height
The right side of the equation is simplified, and the outcome is:
1,001 = 91 x height
Dividing both sides by 91 gives:
height = 1,001 / 91
We can evaluate this expression with a calculator to obtain:
height ≈ 11.0
Therefore, the height of the tissue box is approximately 11.0 inches, rounded to the nearest tenth.
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Help if you have any idea what the answers are
The firm maximizes its profit where MR equals MC and here at quantity 9, MR equals MC.
How to solveA. 9 unit.
The firm maximizes its profit where MR equals MC and here at quantity 9, MR equals MC.
B. 7.25
In perfect competition, the price is equal to MR. Because firms are price takers. So the price will be 30.
Profit per unit =Price - ATC
=30-22.75
=7.25
C. 65.25
Profit =(Price - ATC) *quantity
=(30-22.75)*9
=65.25
A market having perfect competition involves buyers and sellers exerting no significant impact on product pricing. Such markets are composed of numerous parties possessing alike items, with easy ingress and egress from the same domain.
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Which inequality represents this number line?
A. x < -1
B. x = -1
C. X> 1
D. x>-1
The inequality that would represent the number line given is expressed as: D. x > -1.
How to Find the Inequality of a Number line?The inequality of a number line tells the possible values of x. It shows where the values lies on a number line.
First, identify the inequality sign in question. In this number line given, there is an open or unshaded circle at -1, and an arrow that points to your right. This means the inequality sign would be >.
Thus, it implies that the values of x does not include -1, which means that possible values of x are greater than -1 but not equal to 1.
The inequality would be: x > -1.
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A cylindrical soup can has a radius of 1.3 in. and is 5 in. tall. Find the volume of the can.
Answer:
The volume of a cylinder is calculated as follows:
V = πr²h
where:
V is the volume of the cylinder
π is the mathematical constant pi (approximately equal to 3.14)
r is the radius of the cylinder
h is the height of the cylinder
Inserting the provided values:
V = π × (1.3 in)² × 5 in V = π × 1.69 in² × 5 in V = 8.45π in³
So, rounded to the closest tenth, the capacity of the soup can is roughly 26.5 cubic inches.
Lindsey is solving the quadratic equation x2−2x+6=0 . Which of the following statements is true?
"The solutions to the equation are complex conjugates of each other" as Lindsey is solving the quadratic equation [tex]x^2[/tex]−2x+6=0.
To solve the quadratic equation [tex]x^2 - 2x + 6 = 0[/tex], Lindsey can use the quadratic formula:
x = (-b ± √([tex]b^2[/tex] - 4ac)) / 2a
In this case, a = 1, b = -2, and c = 6. Substituting these values into the formula, we get:
x = (-(-2) ± √([tex](-2)^2[/tex] - 4(1)(6))) / 2(1)
x = (2 ± √(-20)) / 2
Since the discriminant ([tex]b^2[/tex] - 4ac) is negative, the square root of -20 is an imaginary number.
Therefore, the two solutions to the equation are complex conjugates of each other:
x = (1 + √5i) and x = (1 - √5i)
Thus, the correct statement is: "The solutions to the equation are complex conjugates of each other."
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Solve the quadratic
8x^2 - 5x - 4 = 0
Thanks!
Answer:
x= -0.461
x= 1.086
Step-by-step explanation:
using the quadratic formula
A=8, B=-5, C=-4
The evaluate
[tex]x=\frac{-(-5) +\sqrt{(-5)x^{2} -4*8*(-4)} }{2*8} and x=\frac{-(-5) -\sqrt{(-5)x^{2} -4*8*(-4)} }{2*8}[/tex]
calculate
[tex]x=\frac{5+\sqrt{25+128} }{16} } and x=\frac{5-\sqrt{25+128} }{16} }[/tex]
Simplify
[tex]x=\frac{5+3\sqrt{17} }{16} and x=\frac{5-3\sqrt{17} }{16}[/tex]
simply
x= -0.461 and x= 1.086
