Answer: 1728 cubic meters
Step-by-step explanation: 12 x 12 x 12 V= LxWxH
You sell 600 shares of AVG Technologies (AVG). You purchased the stock at $2.99 per share and sold it at $0.88 per share. What was the percent decrease in the stock? Round to the nearest whole percent.
71%
29%
42%
24%
Answer:
71%
Step-by-step explanation:
To calculate the percent decrease in the stock, we can use the following formula:
Percent decrease = ((Original value - New value) / Original value) * 100
Given:
Original value (purchase price) = $2.99 per share
New value (selling price) = $0.88 per share
Plugging in the values into the formula:
Percent decrease = ((2.99 - 0.88) / 2.99) * 100
Percent decrease = (2.11 / 2.99) * 100
Percent decrease = 70.57%
Rounding to the nearest whole percent, the correct answer is 71%.
4. Write the equation of the circle tangent to the line y=-4 with center at (5,4)
Answer:
Yo, the equation of the circle that's chillin' and just grazin' against the line y = -4, with its center chillaxin' at (5, 4), is:
(x - 5)^2 + (y - 4)^2 = r^2
where r is the radius of the circle. Keep it cool, bro!
Please help me find the answer
Using trigonometric ratios θ = 26.57°
What is a trigonometric ratio?A trigonometric ratio is the ratio of the sides of a triangle.
To find the value of θ, we notice that in the triangle, we have the hypotenuse side and the adjacent side.
Using the trigonometric ratio cosθ = adjacent/hypotenuse
where
adjacent = 6√5 and hypotenuse = 15So, substituting the values of the variables into the equation, we have that
cosθ = adjacent/hypotenuse
= 6√5/15
= 2√5/5
= 2 × 2.236/5
= 4.472
= 0.8944
cosθ = 0.8944
θ = cos⁻¹(0.8944)
= 26.57°
So, θ = 26.57°
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A police officer invested $5,000 in a treasury bond paying 4.75% interest compounded quarterly. After 25 years, the value of the bond will be $16,280.08. If the police officer's investment was compounded continuously instead of four times per year, what would be the difference in the account balances after 25 years?
Answer:
114.29
Step-by-step explanation:
Select the correct answer from each drop-down menu. Consider the graph of f(x) = (1/2)^x.
Each graph shows the result of a transformation applied to function f.
Complete this statement given that g(x) = -f(x).
This graph of function g is graph __ because the graph of function g is the result of a __ applied to the graph of function f.
Answer:
it (8,0) or (0,8)
Step-by-step explanation:
im not sure but hope this helps.
Complete this statement given that g(x) = -f(x): "This graph of function g is graph (C) because the graph of function g is the result of a reflection applied to the graph of function f."
The graph of function g is a reflection of the graph of function f across the x-axis because of the negative sign in front of f(x) in the definition of g(x) = -f(x). This reflection results in a vertical flip of the graph. When a function is multiplied by a negative value, it gets reflected across the x-axis. The "C" option in the dropdown menu indicates a reflection across the x-axis.
The transformation applied to the graph of function f to get the graph of function g is a reflection, and it occurs due to the negative sign (-) in front of f(x) in the definition of g(x) = -f(x).
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What is 743.2 x 0.045. It was kinda hard for me because of the decimals in it.
Answer:
33.444
Step-by-step explanation:
How many students were in the sample? Math Test Scores 5 0 4 6 5 7 8 7 5 8 8 2 4 5 5 5 6 7 8 9 9 0 0 0 0 4 6 7 9 5 0 = 50 29 5 24 20
It seems that the given data consists of two sets of numbers separated by an equals sign. The first set of numbers appears to be a list of math test scores, while the second set of numbers is unclear.
Assuming that the question is asking about the number of students represented by the first set of numbers (the math test scores), then the answer would be 31. This is because there are 31 numbers in the list, which could represent the scores of 31 individual students.
Answer: 31
Step-by-step explanation:
2. Victoria deposits $1500 into each of two savings accounts. • Account A earns 3.5% annual simple interest. • Account B earns 3.5% interest compounded annually. Victoria does not make any additional deposits or withdrawals into either account. Which amount is closest to the difference between the interest Victoria would earn in Account B and the interest she would earn in Account A at the end of 4 years?
the amount closest to the difference between the interest Victoria would earn in Account B and the interest she would earn in Account A at the end of 4 years is $22.32.
What is compound interest?
The interest on savings that is computed on both the initial principal and the interest accrued over time is known as compound interest. Compound interest is computed by multiplying the starting principal amount by one and the annual interest rate is raised to the number of compound periods minus one. The final step is to deduct the initial loan principal from the calculated value.
Using the formula for compound interest, we can find the amount at the end of 4 years in Account B:
[tex]A = P * (1 + r/n)^{(nt) = $1500 * (1 + 0.035/1)^{(14) = $1732.32[/tex]
The interest earned in Account B over 4 years is the difference between the amount at the end of the period and the principal:
I = A - P = $1732.32 - $1500 = $232.32
Therefore, the difference between the interest Victoria would earn in Account B and the interest she would earn in Account A at the end of 4 years is approximate:
$232.32 - $210 = $22.32
Therefore, the amount closest to the difference between the interest Victoria would earn in Account B and the interest she would earn in Account A at the end of 4 years is $22.32.
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3. Find the equation of a circle with the endpoints of the diameter at (0, 8) and (0,-2)
Step-by-step explanation:
remember, the general equation for a circle is
(x - h)² + (y - k)² = r²
r is the radius, (h, k) is the center point of the circle.
the line (0, 8) to (0, -2) is a diameter, so, the center of the circle is the midpoint between both points.
remember, the midpoint between 2 points (x1, y1) and (x2, y2) is
((x1+x2)/2, (y1+y2)/2)
in our case :
((0+0)/2, (8-2)/2) = (0, 3)
the distance from the center point to the endpoint is e.g
(0, 3) to (0,8) = 8-3 = 5.
and that is the radius.
the equation of the circle is therefore :
(x - 0)² + (y - 3)² = 5²
x² + (y - 3)² = 25
what is 6 inches but less than 1 foot?
The tree diagram represents the sample space for the repeated experiment of a coin being tossed 4 times.
Determine P(at least 2 talls).
The probability of getting at least 2 tails in 4 coin tosses is 11/16 or approximately 0.6875.
What is probability?Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.
According to given information:To determine P(at least 2 tails), we need to add up the probabilities of all the outcomes in the sample space that have at least 2 tails.
Looking at the tree diagram, we can see that there are 11 outcomes that have at least 2 tails:
TTTT TTTH TTHT TTHH THTT THHT THTH HTTT HTTH HTHT HHTT
The probability of each outcome can be found by multiplying the probabilities along the branches that lead to that outcome. Since the coin is fair, the probability of getting heads or tails on any given toss is 1/2.
So for example, the probability of the outcome TTHH is (1/2) x (1/2) x (1/2) x (1/2) = 1/16.
We can find the probability of getting at least 2 tails by adding up the probabilities of the 11 outcomes listed above:
P(at least 2 tails) = [tex](1/2)^4[/tex] + 4 x [tex](1/2)^3[/tex] x (1/2) + 6 x [tex](1/2)^2[/tex] x [tex](1/2)^2[/tex]
P(at least 2 tails) = 1/16 + 4/16 + 6/16 = 11/16
Therefore, the probability of getting at least 2 tails in 4 coin tosses is 11/16 or approximately 0.6875.
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6. The piece of pizz M
Kinser got forms the
angle KLM that mesure 138, She split the
pizza into 3 pieces that were not equal
in size. What are possible measurements
of the angles of the pieces of pizza if she splits the
pizza into 3 pieces? Please explain your answer.
larl
42
3113
n
18
O
4
L
138⁹
Earl's Biking Company manufactures and sells bikes. The company's profits are P(x)=−2x
2
+260x−5000 where Profits are in hundreds for x hundred bikes. They need to sell at least 300 bikes but not more than 8000 bikes. This means x is between or including 3 to 80 . a) Find the marginal profit function. b) Find the Critical value c) If they need to sell at least 300 bikes but not more than 8000 bikes, find the maximum profit, the number of bikes that must be sold to reach the maximum profit. Be sure to show a table with the values you should check to find the Maximum. (Hint 3≤x≤80 )
According to the given data the maximum profit is $780,000 when 6,500 bikes are sold.
What is marginal profit function?The marginal profit function represents the rate at which the profit changes as the number of units sold changes. It is the derivative of the profit function with respect to the number of units sold. The marginal profit function is important in business because it helps companies to determine the optimal level of production that maximizes profit. The critical value of the marginal profit function (when it equals zero) indicates the point where the profit function changes from increasing to decreasing, or vice versa, which can help companies to identify the optimal production level that maximizes profit.
According to the given information:a) To find the marginal profit function, we need to take the derivative of the profit function with respect to x:
P'(x) = -4x + 260
b) To find the critical value, we need to set the marginal profit function equal to zero and solve for x:
-4x + 260 = 0
x = 65
Therefore, the critical value is x = 65.
c) To find the maximum profit, we need to evaluate the profit function at the endpoints of the given interval (3 and 80) as well as at the critical value (65), and then compare the values to see which one is the largest. We can use a table to organize the values:
x P(x)
3 190
65 7800
80 2600
Therefore, the maximum profit is $780,000, which occurs when 6,500 bikes are sold (since each x represents 100 bikes).
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laurel exercises and keeps track of how many minutes she spends participating in different exercise activities
Laurel spent a total of 65 minutes exercising across these activities.
How to solveTo calculate the total minutes Laurel spent exercising, we simply need to add the minutes spent on each activity:
Jogging: 30 minutes
Swimming: 20 minutes
Yoga: 15 minutes
Total minutes = 30 + 20 + 15 = 65 minutes
Laurel spent a total of 65 minutes exercising across these activities.
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How many minutes did Laurel spend exercising in total, if she participated in different activities for the following durations: 30 minutes of jogging, 20 minutes of swimming, and 15 minutes of yoga?
Paul bought a new rug in the shape of a regular decagon. Each side of the decagon is 4.25 feet. Find the area of the rug. Round to the nearest hundredth.
The area of the rug which has the shape of a decagon would be = 178.79ft²
How to find the area of the rug with the shape of a decagon?To calculate the area of the rug that has the shape of a decagon, the formula for the area of a decagon should be used. That is;
Area of decagon = 5/2a²√5+2√5
Where;
a = side length = 4.25 ft
area = 5/2(4.25)²√5+2√5
= 5/2(18.06)√5+2√5
= 45.15× √5+2√5
= 45.15 × √15.65247584
= 45.15× 3.96
= 178.79ft²
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The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt.
The probability of not wearing a seat belt given that the driver survived a car accident is 28%.
What is the probability of not wearing a seat belt?The probability of not wearing a seat belt and that the driver survived a car accident will be calculated using Bayes' theorem.
The Bayes' theorem states that: P(A|B) = P(B|A) * P(A) / P(B) where A is the event of not wearing a seat belt and B is the event of the driver surviving a car accident.
Driver Survived/No seat belt = 168,132
Total Sample = 583,425
Plugging the values, we get:
P(A|B) = 168,132 / 583,425
P(A|B) = 0.288
P(A|B) = 28.8%.
Full question "The table shows the outcome of car accidents in a certain state for a recent year by whether or not the driver wore a seat belt: Wore Seat Belt 415,293 No Seat Belt Total Driver Survived Driver Died Total 168,132 583,425 521 415,814 1643 169,775 2164 585,589 Find the probability of not wearing a seat belt; given that the driver survived a car accident: The probability as a decimal is 0.288 (Round to three decimal places as needed.) The probability as a fraction is (Type an integer or a simplified fraction).
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Carlos needs an average of 90% or greater on his quiz scores to earn an A in science class for the quarter. Each quiz is worth 20 points. The scores of his first four quizzes are shown in the table. There is one more quiz this quarter. Quiz Score 1 2 3 4 18 at least 19 17 20 What is the mininum score Carlos can earn on the final quiz to earn at least a 90% average? points
Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.
We have,
Let's start by finding the total number of points that Carlos can earn in the class:
Total points
= 5 quizzes x 20 points per quiz
= 100 points
If Carlos needs an average of 90% or greater, that means he needs to earn at least 90 points out of 100.
Total points earned.
= 18 + 19 + 17 + 20
= 74 points
To find the minimum score Carlos needs on the final quiz, we can set up an inequality:
(74 + x) / 5 ≥ 0.9
where x is the score on the final quiz.
Simplifying this inequality.
74 + x ≥ 90
x ≥ 16
Therefore,
Carlos needs to earn at least 16 points on the final quiz to earn at least a 90% average.
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What is the value of the expression −204 − 64 − (−3)? 143 137 −265 −271
The value of the expression, which serves as the basis for the response, is 265 for the provided question. answer is option (c).
What is Expression?An expression is a group of numbers, variables, and mathematical operations used to represent a quantity or value in mathematics. Expressions can be straightforward or intricate, and they can contain exponents, coefficients, variables, and constants. Several methods, including factoring, the order of operations, and algebraic manipulation, can be used to evaluate or simplify expressions. The values of an expression's variables and constants determine its value.
The expression −204 − 64 − (−3) can be streamlined by applying the following arithmetic rules:
−204 − 64 − (−3) = −204 − 64 + 3
[the double negative turns positive because]
= −265
Consequently, the expression's value is -265. The correct answer is option (c).
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Question 1 of 10
A computer randomly puts a point inside the rectangle. What is the probability that the point lands in square S?
T2
A. 1/3
B. 5/6
C. 3/8
D. 1/6
The probability that the point land in square S will be 5/6.
What is probability?
Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.
The probability that the point does not land in triangle T is equal to subtract the area of triangle T from the area of rectangle and divided the result by the the area of rectangle
so, Find out the area of rectangle
A = (6)(4)
= 24 unit²
Find out the area of triangle T
A = 1/2(2)(4)
= 4 unit²
The probability is equal to
P = (24-4) / 24
= 20/24
= 5/6
Hence, the probability that the point land in square S will be 5/6.
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If you have ln {A}=.552, how do you take e^x for both sides of the equation? Thanks.
The solution to the equation ln {A} = .552 is A = e[tex]^{0.552}[/tex] = 2.7. In order to calculate eˣ for both sides of the equation ln {A}=.552, one must first understand what the equation signifies.
What is logarithmic equation?A logarithmic equation is an equation involving logarithms of different variables. Logarithmic equations are used to solve various types of problems. It uses the logarithmic properties of multiplication and division to simplify the equation.
This equation is a logarithmic equation, in which ln (natural logarithm) is used to represent a number's exponential value.
This means that the equation is actually stating that A is equal to e raised to the power of 0.552 (e[tex]^{0.552}[/tex] ).
In order to solve for A, one must use the basic rule of logarithms: for any logarithmic equation of the form ln {A} = B, A = e^B.
Therefore, the solution to the equation ln {A} = .552 is
A = e[tex]^{0.552}[/tex] .
This equation can be solved using basic algebra, as e[tex]^{0.552}[/tex] can be replaced with an equivalent expression.
The equation can be rewritten as A = (e[tex]^{0.5}[/tex])(e[tex]^{0.052}[/tex]).
The value of e[tex]^{0.5}[/tex] can be calculated using a calculator, and can be rounded to the nearest tenth.
The value of e[tex]^{0.052}[/tex] can then be calculated, which can also be rounded to the nearest tenth.
Adding the two values together will give the solution to the equation, which is A = 2.7.
Therefore, the solution to the equation ln {A} = .552 is
A = e[tex]^{0.552}[/tex]
= 2.7.
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40 divided by [2=3 (17=15)] evaluate
The inverse operation of division by zero is deemed undefined; therefore, significant analysis for this expression cannot take place.
How to solveIt appears there's some confusion regarding the expression you supplied. To better interpret it, please consider making further explanations visible.
Nonetheless, an attempt to interpret is provided below:
40 divided by [(2=3)(17=15)]
Essentially, the intention is to multiply the results of each step in this expression. Let us begin assessing the individual components:
The first, 2=3 proves false as a statement; thus, we can grant it a value of zero.
Likewise, 17=15 sets out to be incorrect which, rightfully so, can also assume a figure of nothingness.
Let us now multiply the outcomes of both statements:
(0)(0) = 0
Finally, we divide 40 - the stated number - by the result from before:
40 ÷ 0
Conclusively, the inverse operation of division by zero is deemed undefined; therefore, significant analysis for this expression cannot take place.
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Evaluate the following:
40 divided by [2=3 (17=15)]
Solve for v. 2/5v = 10
Find the Fourier transform of (without using Tables). Show details.
() = { 2
, − 1 < < 1
0 , ℎ
As a result, the following is the given function's Fourier transform:
F(ω) = (1/π) * (sin(ω) / ω)
What is the Fourier transform?The Fourier transform is a mathematical operation that separates the frequencies that make up a waveform, which is a function of time. The Fourier transform's output is a complex valued function of frequency.
We must assess the integral in order to determine the given function's Fourier transform, f(x):
F() is equal to 1/(2) * [from - to -] F(x) E(-i) X Dx
where the frequency parameter is and i is the fictitious unit.
We can simplify the integral bounds as follows since the function f(x) is non-zero only in the range -1 x 1.
F() is equal to 1/(2)*[from -1 to 1] F(x) E(-i) X Dx
Let's analyse this integral in stages.
The value of the function f(x) is zero for x -1 or x > 1. As a result, we can increase the integral limits to - and + without changing the integral's value:
F(ω) = 1/(2π) * ∫(from - to -) F(x) = E(-ix) dx = 1/(2*) * the range [- to -1] from -1 to 1 + 0 dx 2dxe(-ix)+[from 1 to ] 0 dx = 1/(2π) * 2 * ∫E(-ix) dx [from -1 to 1]
Let's concentrate on the central integral:
∫[in the range of -1 to 1] e(-ix) dx = (-1/i)* [e^(-iωx)](-1/i)* _[from -1 to 1] (e^(-iω) - e^(iω))
Adding this back into the formula for the Fourier transform results in:
F(ω) = 1/(2π) * 2 * (-1/iω) * (e^(-iω) - e^(iω)) = (1/π) * (sin(ω) / ω)
As a result, the following is the given function's Fourier transform:
F(ω) = (1/π) * (sin(ω) / ω).
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The Fourier transform of the given function f(x) is:
F(ω) = 2 [ - sin(ω) / ω ]
What is Fourier Analysis?
Fourier analysis is a branch of mathematics that deals with the study of the decomposition of a complex signal into simpler components, known as harmonics, using a mathematical tool called the Fourier transform.
To find the Fourier transform of the given function f(x), we need to use the following formula:
F(ω) = ∫ f(x) e^(-iωx) dx
where F(ω) denotes the Fourier transform of f(x) and ω is the frequency variable.
Let's apply this formula to the given function f(x):
F(ω) = ∫ f(x) [tex]e^{(-iωx)}[/tex] dx
= ∫[tex]-1^{1}[/tex] 2 [tex]e^{(-iωx)}[/tex] dx + ∫{-∞}^{∞} 0 [tex]e^{(-iωx)}[/tex] dx
= 2 ∫_[tex]{1}^{{1}}[/tex] [tex]e^{(-iωx)}[/tex] dx + 0
= 2 [ (1/iω) [tex]e^{(-iωx)}[/tex] ]_[tex]-1^{1}[/tex]
= 2 [ [tex]e^{(-iωx)}[/tex] - [tex]e^{(iω)}[/tex] / iω ]
Simplifying this expression, we get:
F(ω) = 2 [ (cos(ω) - i sin(ω)) / iω - (cos(-ω) - i sin(-ω)) / iω ]
= 2 [ (cos(ω) - i sin(ω)) / iω - (cos(ω) + i sin(ω)) / iω ]
= 2 [ -2i sin(ω) / (2iω) ]
= 2 [ - sin(ω) / ω ]
Therefore, the Fourier transform of the given function f(x) is:
F(ω) = 2 [ - sin(ω) / ω ]
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The median monthly rent in 2000 we $602 and $651 in 2003. What was the percent increase in the median monthly rent prices from 2000 to 2003?
$8.11 was the percent increase in the median monthly rent prices from 2000 to 2003.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
2000 = $602
2003 = $651
= 651 - 602/602 * 100
= $8.11
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please help me answer this
Sequence 1: 13, 16, 19, 22, 25, Sequence 2: 15, 13, 11, 9, 7 and Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7).
what is sequence?
An ordered list of numbers is a sequence. The three dots indicate that the established pattern should move forward.
A. Sequence 1: 13, 16, 19, 22, 25
Sequence 2: 15, 13, 11, 9, 7
Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)
B. Sequence 1: 1, 5, 17, 53, 161
Sequence 2: 6, 15, 33, 69, 141
Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (161, 141)
C. Input (x) | Output
1 | 17, 2 | 19, 3 | 21, 4 | 23
D. Input (x) | Output
1 | 30, 2 | 15, 3 | 7.5
To find the outputs, we use the formula: output = 60 ÷ 2x.
For x = 1, output = 60 ÷ 2(1) = 30
For x = 2, output = 60 ÷ 2(2) = 15
For x = 3, output = 60 ÷ 2(3) = 7.5
E. Input (x) | Output
1 | 23, 2 | 30, 3 | 37, 14 | 102, 15 | 109, 16 | 116, 27 | 205, 70 | 498
To find the outputs, we use the formula: output = 16 + 7x.
For x = 1, output = 16 + 7(1) = 23
For x = 2, output = 16 + 7(2) = 30
For x = 3, output = 16 + 7(3) = 37
For x = 14, output = 16 + 7(14) = 102
For x = 15, output = 16 + 7(15) = 109
For x = 16, output = 16 + 7(16) = 116
For x = 27, output = 16 + 7(27) = 205
For x = 70, output = 16 + 7(70) = 498
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You deposit $200 in an account earning 6% interest compounded annually. How much will you have in the
account in 10 years?
find the zeros of the function. State the multiplicity of multiple zeros.
y=7x^3-7x select the correct choice below and if necessary fill in the boxes within your choice.
1. The numbers _ are zeros of multiplicity 3
2. The numbers _ are zeros of multiplicity 2
3. The numbers _ are zeros of multiplicity 1
4. The numbers _ are zeros of multiplicity 1 and the numbers _ are zeros of multiplicity 2.
(picture added if needed :))
The numbers 0, 1, and -1 are zeros of multiplicity 1.
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
To find the zeros of the function [tex]y=7x^3-7x[/tex], we can set y equal to zero and solve for x:
[tex]7x^3 - 7x = 0[/tex]
Factor out 7x:
[tex]7x(x^2 - 1) = 0[/tex]
Factor the quadratic expression:
7x(x - 1)(x + 1) = 0
The zeros of the function are the values of x that make y equal to zero. From the factored expression, we see that the zeros are:
x = 0 (with multiplicity 1)
x = 1 (with multiplicity 1)
x = -1 (with multiplicity 1)
Therefore, the correct choice is: The numbers 0, 1, and -1 are zeros of multiplicity 1.
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Find the LCM of 6(x – 1)2(x + 2)(x – 3) and 9(x – 1)(x + 2)2(x – 3).
Answer:
To find the LCM of the two expressions, we need to factor each expression completely and then take the product of the highest powers of each factor.
So, let's factor each expression:
6(x – 1)2(x + 2)(x – 3) = 2 × 3 × (x – 1) × (x – 1) × (x + 2) × (x – 3)
9(x – 1)(x + 2)2(x – 3) = 3 × 3 × (x – 1) × (x + 2) × (x + 2) × (x – 3)
Now, we can identify the highest powers of each factor.
The LCM will be the product of those highest powers:
LCM = 2 × 3 × 3 × (x – 1)2 × (x + 2)2 × (x – 3)
Therefore, the LCM of 6(x – 1)2(x + 2)(x – 3) and 9(x – 1)(x + 2)2(x – 3) is 54(x – 1)2(x + 2)2(x – 3).
If n=22, ¯x (x-bar)=45, and s=10, find the margin of error at a 95% confidence level (use at least two decimal places)
Write an exponential growth equation for the following graph (i’ll give brainliest)
The exponential growth equation that passes through the given points is [tex]y = 6 \times 1.5^x[/tex]
How to find an exponential growth equation ?
An exponential growth equation that passes through the given points. We aretaking the equation takes the form [tex]y = a×b^x [/tex] where a is the initial value and b is the growth factor. We can use the three given points to form a system of equations.
It is clear that the equation passes through points ( -1,4), (0,6), (1,9)
So,
[tex]4 = ab^{-1} \\ 6 = ab^0 \\ 9 = a \times b^1[/tex]
We are dividing the second equation by the first equation,
[tex] \frac{6}{4} = \frac{(ab^0)}{(ab^{-1})}[/tex]
1.5 = b
Next, we can use this value of b in the third equation to find a,
9 = a×1.5¹
a = 6
Therefore, the exponential growth equation that passes through the given points is [tex]y = 6 \times 1.5^x[/tex]
Learn more about exponential growth equation here,
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