As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3.
what is domain of the function?
The domain of a function is the set of all possible values of the input variable (independent variable) for which the function is defined. It is the set of all x-values for which the function produces a valid output. In order to determine the domain of a function, one needs to consider any restrictions or limitations that the function may have.
The given problem is related to the motion of a soccer ball kicked by Lin. The height of the soccer ball (in feet) is a function of time (in seconds), and it is represented by a graph.
Domain: The domain of the function is the set of all possible values of the input variable (time in seconds). In this case, the soccer ball was in the air for 3 seconds, so the domain is [0, 3], which means that the height function is defined for all values of time between 0 and 3 seconds, including 0 and 3.
Range: The range of the function is the set of all possible values of the output variable (height of the soccer ball in feet). In this case, the soccer ball reached a height of approximately 30 ft while it was in the air. Therefore, the range of the function is [0, 30], which means that the height of the soccer ball is defined for all values between 0 and 30 feet, including 0 and 30.
Line of symmetry: The line of symmetry is a vertical line that passes through the vertex of the parabola (in this case, the highest point that the soccer ball reaches). The parabolic graph of the soccer ball's height function is symmetric with respect to the vertical line passing through the midpoint of the domain. Since the domain is [0, 3], the midpoint is (3/2, 0), so the line of symmetry is x = 3/2.
As the value of x (time in seconds) increases, the height of the soccer ball decreases until it hits the ground at x=3. As the value of x decreases from 3 to 0, the height of the soccer ball increases from 0 to 30 and then decreases again as it hits the ground. The rate of change of the height of the soccer ball is not constant but rather depends on the shape of the parabolic graph of the height function.
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Identify the vertex of the following function f(x)=3(x-1)^2+5
Answer:
Step-by-step explanation:
The answer is (1,5)
Three variants of the gene encoding for the beta-goblin component of hemoglobin occur in the human population of the Kassena-Nankana district of Ghana, West Africa. The most frequent allele, A, occurs at a frequency of 0.83. The other two variants, S (sickle cell) and C, occur at frequency 0.04 and 0.13. Each individual has two alleles, determining the genotype of the beta-globin gene. Assume that the allele occur independently on one another.
a. What is the probability that a randomly sampled individual has two copies of the C allele?
b. What is the probability that a randomly sampled individual is a homozygote (two copies of the same allele)?
c. What is the probability that a randomly sampled individual is AS (one copy of A allele and one copy of S allele)?
d. What is the probability that a randomly sampled individual is AS or AC?
a. The probability that a randomly sampled individual has two copies of the C allele is 0.0169.
b. The probability that a randomly sampled individuTherefore, the answers are:
al is a homozygote is 0.7074.
c. The probability that a randomly sampled individual is AS is 0.0332.
d. The probability that a randomly sampled individual is AS or AC is 0.1411.
The probability of an individual having two copies of the C allele can be calculated using the formula for the probability of independent events: P(CC) = P(C) x P(C) = 0.13 x 0.13 = 0.0169.
The probability of an individual being a homozygote can be calculated by adding the probabilities of having two copies of each allele: P(AA) + P(SS) + P(CC) = (0.83 x 0.83) + (0.04 x 0.04) + (0.13 x 0.13) = 0.6889 + 0.0016 + 0.0169 = 0.7074.
The probability of an individual being AS can be calculated using the formula for the probability of independent events: P(AS) = P(A) x P(S) = 0.83 x 0.04 = 0.0332.
The probability of an individual being AS or AC can be calculated by adding the probabilities of each event: P(AS) + P(AC) = 0.0332 + (0.83 x 0.13) = 0.0332 + 0.1079 = 0.1411.
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3. Consider the matrix \( A \) given by \[ A=\left[\begin{array}{rrr} -3 & -2 & 2 \\ 1 & 3 & 1 \\ 4 & 4 & -1 \end{array}\right] \] (a) Show that the inverse of \( A \) can be written as \( A^{-1}=\lef
The value of A⁻¹ is given by the following matrix:
[[1/5, -2/15, 1/10],
[-1/5, 3/15, -1/10],
[4/5, -4/15, 1/10]]
This can be calculated by solving the equation A x A⁻¹ = I, where I is the identity matrix. In this equation, we can solve for A⁻¹ by multiplying both sides of the equation by the inverse of A, which can be found by solving the system of equations A x X = I.
After solving this system of equations, the inverse of A is the matrix X. The value of A⁻¹ is then found by substituting the values of X into the matrix A⁻¹.
To find the inverse of A, first find the determinant of A, which can be calculated using the formula |A| = (-3)(3)(-1) + (-2)(1)(4) + (2)(4)(1) = -20. Since the determinant is not 0, A is invertible and the inverse can be found.
To solve for A⁻¹, first calculate the cofactor matrix C for A by taking the transpose of the matrix of minors for A, which can be found by calculating the determinants of each submatrix of A.
Then, take the determinant of A and divide each element in C by it, giving the matrix C⁻¹. Finally, multiply A and C⁻¹ to get the inverse of A, which is the matrix A⁻¹.
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Consider the matrix A given by
A = [[-3,-2,2],[1,3,1],[4,4,-1]]
Find the value of A⁻¹.
if f(x)=2x+1 and g(x)=x^2 find g(f(3))
i need answers quick please
g(f(-1)) = g(2(-1)-1) = g(-3)
g(-3) = (-3)^2 + 3 = 9+3 = 12
So g(f(-1)) = 12
Hope this helps.
Identify the numbers of Solutions.
9t6-14+³ +4+- 1 = 0
There are ___ Solutions.
Answer:
"t3" was replaced by "t^3".
1 more similar replacement(s).Step by step solution :
STEP 1:Equation at the end of step 1 (((9 • (t6)) - (2•7t3)) + 4t) - 1 = 0
STEP 2 :Equation at the end of step 2: ((32t6 - (2•7t3)) + 4t) - 1 = 0
STEP 3:Checking for a perfect cube 3.1 9t6-14t3+4t-1 is not a perfect cube
Trying to factor by pulling out : 3.2 Factoring: 9t6-14t3+4t-1
Thoughtfully split the expression at hand into groups, each group having two terms:
Group 1: 4t-1
Group 2: -14t3+9t6
Pull out from each group separately:
Group 1: (4t-1)
(1)Group 2: (9t3-14) • (t3)
Factoring by pulling out fails : The groups have no common factor and can not be added up to form a multiplication.Polynomial Roots Calculator : 3.3
Find roots (zeroes) of : F(t) = 9t6-14t3+4t-1
Polynomial Roots Calculator is a set of methods aimed at finding values of t for which F(t)=0 Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers t which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 9 and the Trailing Constant is -1. The factor(s) are: of the Leading Coefficient : 1,3 ,9 of the Trailing Constant : 1 Let us test .... P Q P/Q F(P/Q) Divisor -1 1 -1.00 18.00 -1 3 -0.33 -1.80 -1 9 -0.11 -1.43 1 1 1.00 -2.00 1 3 0.33 -0.17 1 9 0.11 -0.57 Polynomial Roots Calculator found no rational roots Equation at the end of step 3: 9t6 - 14t3 + 4t - 1 = 0
STEP 4:Equations of order 5 or higher: 4.1 Solve 9t6-14t3+4t-1 = 0In search of an interavl at which the above polynomial changes sign, from negative to positive or the other wayaround.Method of search: Calculate polynomial values for all integer points between t=-20 and t=+20 Found change of sign between t= -1.00 and t= 0.00 Approximating a root using the Bisection Method :We now use the Bisection Method to approximate one of the solutions. The Bisection Method is an iterative procedure to approximate a root (Root is another name for a solution of an equation).The function is F(t) = 9t6 - 14t3 + 4t - 1At t= 0.00 F(t) is equal to -1.00 At t= -1.00 F(t) is equal to 18.00 Intuitively we feel, and justly so, that since F(t) is negative on one side of the interval, andpositive on the other side then, somewhere inside this interval, F(t) is zero Procedure :(1) Find a point "Left" where F(Left) < 0(2) Find a point 'Right' where F(Right) > 0(3) Compute 'Middle' the middle point of the interval [Left,Right](4) Calculate Value = F(Middle)(5) If Value is close enough to zero goto Step (7)Else : If Value < 0 then : Left <- MiddleIf Value > 0 then : Right <- Middle(6) Loop back to Step (3)(7) Done!! The approximation found is MiddleFollow Middle movements to understand how it works : Left Value(Left) Right Value(Right)
0.000000000 -1.000000000 -1.000000000 18.000000000
0.000000000 -1.000000000 -1.000000000 18.000000000
-0.500000000 -1.109375000 -1.000000000 18.000000000
-0.500000000 -1.109375000 -0.750000000 3.508056641
-0.500000000 -1.109375000 -0.625000000 0.454410553
-0.562500000 -0.473213613 -0.625000000 0.454410553
-0.593750000 -0.050185024 -0.625000000 0.454410553
-0.593750000 -0.050185024 -0.609375000 0.191316528
-0.593750000 -0.050185024 -0.601562500 0.067944440
-0.593750000 -0.050185024 -0.597656250 0.008233857
-0.595703125 -0.021135877 -0.597656250 0.008233857
-0.596679688 -0.006491229 -0.597656250 0.008233857
-0.596679688 -0.006491229 -0.597167969 0.000861241
-0.596923828 -0.002817510 -0.597167969 0.000861241
-0.597045898 -0.000978764 -0.597167969 0.000861241
-0.597106934 -0.000058919 -0.597167969 0.000861241
-0.597106934 -0.000058919 -0.597137451 0.000401122
-0.597106934 -0.000058919 -0.597122192 0.000171092
-0.597106934 -0.000058919 -0.597114563 0.000056084
-0.597110748 -0.000001418 -0.597114563 0.000056084
-0.597110748 -0.000001418 -0.597112656 0.000027333
-0.597110748 -0.000001418 -0.597111702 0.000012957
-0.597110748 -0.000001418 -0.597111225 0.000005770 Next Middle will get us close enough to zero: F( -0.597110868 ) is 0.000000379 The desired approximation of the solution is: t ≓ -0.597110868
Note, ≓ is the approximation symbol One solution was found : t ≓ -0.597110868
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There is 1 solution to this equation.
What is equation?An equation is a mathematical statement that two expressions are equal. It consists of two expressions separated by an equals sign (=), and expresses a relationship between the two expressions. Equations can be used to represent a variety of problems and can help solve real-world problems. For example, an equation can be used to calculate the amount of money someone will have after a certain period of time, or to calculate the distance between two points.
In order to answer this question, we must first solve the equation. 9t6-14+³ +4+- 1 = 0 can be written as 9t6 - 11 + 4 - 1 = 0. After simplifying, this equation becomes 9t6 - 7 = 0, which can be further simplified to t6 = 7. Taking the sixth root of both sides, we can determine that t = √7. Therefore, there is 1 solution to this equation.
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29. What is the truth value of (~p V q) Arif p is true, q is false, and r is true?
Answer:
Step-by-step explanation:
~P is true
q is true
~p v q is true
the hypothesis (or antecedent) is true
the conclusion (or consequent) is false
R is false and ~q is false
the conditional says if true then false
so the conditional is false
Use the given conditions to write an equation for the line in point-slope form and in slope-intercept form. Passing through (8. – 6) and perpendicular to the line whose equation is y= 4x+1 Write an equation for the line in point-slope form
_________
The equation of the line in point-slope form is y - (-6) = (-1/4)(x - 8), and the equation of the line in slope-intercept form is y = (-1/4)x - 4.
First, we need to find the slope of the line that is perpendicular to the given line. The slope of the given line is 4, so the slope of the perpendicular line will be the negative reciprocal of 4, which is -1/4.
Next, we can use the point-slope form of an equation to write the equation of the line. The point-slope form of an equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. Plugging in the slope and the given point, we get:
y - (-6) = (-1/4)(x - 8)
Simplifying, we get:
y + 6 = (-1/4)x + 2
Finally, we can rearrange the equation to get it in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. Subtracting 6 from both sides of the equation gives us:
y = (-1/4)x - 4
So the equation of the line in slope-intercept form is y = (-1/4)x - 4.
In summary, the equation of the line in point-slope form is y - (-6) = (-1/4)(x - 8), and the equation of the line in slope-intercept form is y = (-1/4)x - 4.
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5. The FBI Standard Survey of Crimes shows that for about 84% of all property crimes (burglary, larceny, car theft, etc.
the criminals are never found, and the case is never solved. Suppose
a neighborhood district in
a large city sumers
repeated property crimes, not always perpetrated by the same criminals. The police are investigating seven properti
crime cases in this district. What is the expected number (u) that will arrive on time? What is the standard deviation
of this distribution?
The expected number (μ) of property crimes that will be solved in this district can be found by multiplying the total number of property crimes by the probability that a property crime will be solved. Since the probability that a property crime will be solved is 1 - 0.84 = 0.16, the expected number of property crimes that will be solved is:
μ = 7 × 0.16 = 1.12
The standard deviation (σ) of this distribution can be found by taking the square root of the product of the total number of property crimes, the probability that a property crime will be solved, and the probability that a property crime will not be solved:
σ = √(7 × 0.16 × 0.84) = 1.01
Therefore, the expected number of property crimes that will be solved in this district is 1.12, and the standard deviation of this distribution is 1.01.
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As a salesperson, Ken is paid $55 per week, plus $4 per sale. This week Ken wants to make more than $115. Write the inequality for the number of sales Ken needs to make this week, in dollars. Use x to represent the number of sales and do not include any $ symbols in the inequality
The inequality for the number of sales Ken needs to make this week in dollars is: 4x + 55 > 115. Where x is the number of sales.
Inequalities are the mathematical term for the relationship between two values that are not equal. Not all people are created equal. We typically use the "not equal symbol ()" when two values are not equal. However, various inequalities are utilized to compare the values, whether they are less than or greater than.
To solve for x, we first need to isolate it on one side of the inequality. We can start by subtracting 55 from both sides:
4x > 60
Then, we can divide both sides by 4:
x > 15
Therefore, Ken needs to make more than 15 sales this week to earn more than $115.
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1. Solve ARST (find all missing sides and angles). SHOW ALL WORK, Express angles to the nearest degree and side lengths to one decimal place.
ST = 7.5m
S ∟
angle RS = 32°
A = 32°, R = 9.09m, S = 6.89m, T = 7.06m, and angle ASR = 114.90°.
To solve ARST, we must first use the given information (ST = 7.5m and S ∟ angle RS = 32°). Using the law of sines, we can calculate the following:
A = 32°R = (7.5m/sin32°) = 9.09mT = (7.5m/sin180°-32°) = 7.06mThen, using the law of cosines, we can calculate the following:
S = (9.09^2 + 7.06^2 - 2(9.09)(7.06)cos32°)^0.5 = 6.89mAngle ASR = (180° - 32° - arcsin((7.06sin32°)/6.89)) = 114.90°Therefore, the missing sides and angles of ARST are A = 32°, R = 9.09m, S = 6.89m, T = 7.06m, and angle ASR = 114.90°.
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010, Vikki paid $1.66 for a dozen eggs. In 2022, Vikki paid $2.52 for a dozen eggs. If the rise in the cost of eggs is linear, what was the cost of egg $1.87 $2.01 $2.09 $2.71
Therefore, the cost of eggs in the given years are as follows:
2015: $1.87
2016: $1.94
2017: $2.01
2018: $2.09
2019: $2.16
2020: $2.24
2021: $2.31
2022: $2.39
The cost of eggs is increasing in a linear fashion, meaning that it is increasing at a constant rate. To find the cost of eggs in a specific year, we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope of the line and b is the y-intercept.
First, we need to find the slope of the line. The slope is the change in y divided by the change in x. In this case, y is the cost of eggs and x is the year.
Slope = (y2 - y1)/(x2 - x1) = ($2.52 - $1.66)/(2022 - 2010) = $0.86/12 = $0.0717
Next, we need to find the y-intercept. We can use one of the points and the slope to solve for b in the equation y = mx + b.
$1.66 = ($0.0717)(2010) + b
b = $1.66 - ($0.0717)(2010) = -$141.44
Now we have the equation for the cost of eggs in a given year:
y = $0.0717x - $141.44
To find the cost of eggs in a specific year, we can plug in the value of x and solve for y.
For example, to find the cost of eggs in 2015:
y = ($0.0717)(2015) - $141.44 = $1.87
Therefore, the cost of eggs in 2015 was $1.87.
Similarly, we can find the cost of eggs in other years:
In 2016: y = ($0.0717)(2016) - $141.44 = $1.94
In 2017: y = ($0.0717)(2017) - $141.44 = $2.01
In 2018: y = ($0.0717)(2018) - $141.44 = $2.09
In 2019: y = ($0.0717)(2019) - $141.44 = $2.16
In 2020: y = ($0.0717)(2020) - $141.44 = $2.24
In 2021: y = ($0.0717)(2021) - $141.44 = $2.31
In 2022: y = ($0.0717)(2022) - $141.44 = $2.39
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Find the real zeros (if any ) of the rational function. Use a gra g(x)=(x^(2)-13x+42)/(x^(2)+9) x= NONE Submit Answer
The real zeros of the rational function [tex]g(x)=(x^2-13x+42)/(x^2+9)[/tex] are x=7 and x=6, and there are no vertical asymptotes
The real zeros of a rational function are the values of x that make the numerator equal to zero. In this case, we need to
find the values of x that satisfy the equation [tex]x^2-13x+42[/tex]=0.
We can use the quadratic formula to find the real zeros:
x = (-b ± √(b^(2)-4ac))/(2a)
where a=1, b=-13, and c=42.
Plugging these values into the formula,
we get: [tex]x = (-(-13) ± √((-13)^2-4(1)(42)))/(2(1))[/tex]
Simplifying the expression, we get:
x = (13 ± √(169-168))/2
x = (13 ± √1)/2
x = (13 ± 1)/2
The two real zeros are:
x = (13 + 1)/2 = 14/2 = 7
x = (13 - 1)/2 = 12/2 = 6
Therefore, the real zeros of the rational function are x=7 and x=6.
As for the denominator, since [tex]x^2+9[/tex]=0 has no real solutions, there are no values of x that make the denominator equal to zero. Therefore, the rational function has no vertical asymptotes.
In conclusion, the real zeros of the rational function [tex]g(x)=(x^2-13x+42)/(x^2+9)[/tex] are x=7 and x=6, and there are no vertical asymptotes.
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A random variable X has a normal distribution with mean 50 and variance of 10. Find the range of scores that lies
a. within two standard deviations from the mean
b. the lowest score which lies two standard deviations above the mean
c. the highest score which lies three standard
deviations below the mean.
handwritten pls, asap. will thumbs up if handwritten and correct
The range of scores that lies within two standard deviations from the mean is (43.68, 56.32), the lowest score which lies two standard deviations above the mean is 56.32, and the highest score which lies three standard deviations below the mean is 40.52.
The random variable X has a normal distribution with mean 50 and variance of 10. The standard deviation of X is the square root of the variance, which is √10 ≈ 3.16.
a. The range of scores that lies within two standard deviations from the mean is (50 - 2*3.16, 50 + 2*3.16) = (43.68, 56.32).
b. The lowest score which lies two standard deviations above the mean is 50 + 2*3.16 = 56.32.
c. The highest score which lies three standard deviations below the mean is 50 - 3*3.16 = 40.52.
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The bar graph shows the results of spinning a spinner 100 times. Use the bar graph to find the experimental probability of spinning an even number.
The probability of spinning an even number is 39/10
How to determine the probability of spinning an even number.The missing barchart is added as an attachment
The bar chart (see attachment) represents the graph that would be used to calculate the required probability
On the bar chart, we have the sample size of the even number
Even number = 18 + 21
Even number = 39
So, we have
P(Even) = Even/Total
By substitution. we have
P(Even) = 39/100
Hence, the probability is 39/100
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The speed of sound is approximately 1,2251, kilometers per hour. When an object travels faster than the speed of sound, it creates a sonic boom.
The speed of sound is about 343 meters per second (or approximately 1,225 kilometers per hour).
The assertion you made appears to be incorrect. At sea level, the actual speed of sound is roughly 1,225 kilometres per hour, or 767 miles per hour.
The distance that sound travels through a medium, such air, in a predetermined length of time is known as the speed of sound. It is impacted by the medium's temperature, pressure, and humidity. The speed of sound is roughly 343 metres per second in dry air at 20 degrees Celsius (or approximately 1,225 kilometres per hour).
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Chandra is building a 5,280 foot fence around her property. Her property is the shape of a rectangle. The length of the property is three times the width of the property.
a. Write an equation that can be used to find the length and width of the property. Explain how you came up with your equation,
b. Find the length and width of the property. Justify your answer, using the conditions given in the problem.
Answer:
a. Let's denote the width of the property as "w". According to the problem, the length of the property is three times the width, so we can represent the length as "3w".
To find the equation that can be used to solve for the length and width, we can use the formula for the perimeter of a rectangle:
Perimeter = 2(length + width)
Since we know the perimeter (5,280 feet), and we have expressions for the length and width, we can substitute these values into the formula and solve for the variables:
2(3w + w) = 5,280
2(4w) = 5,280
8w = 5,280
w = 660
Therefore, the width of the property is 660 feet, and the length is 3 times the width, or 1,980 feet.
b. To check that these values are correct, we can substitute them back into the formula for perimeter and make sure it equals 5,280:
2(1,980 + 660) = 5,280
This is true, so we can be confident that the width of the property is 660 feet and the length is 1,980 feet.
Whelp the teacher said to solve them and something abt shading HELP
Shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
First, we graph the lines y = -x-2 and y = -5x+2 using their y-intercepts and slopes.
The line y = -x-2 has a y-intercept of -2 and a slope of -1, which means that for every increase of 1 in x, y decreases by 1.
The line y = -5x+2 has a y-intercept of 2 and a slope of -5, which means that for every increase of 1 in x, y decreases by 5.
The shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.
Hence, shaded region represents the set of all points (x, y) that satisfy both inequalities y > -x-2 and y < -5x+2.
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Change 42 kilograms into stones
42 kilograms are equal to 6.6 stones.
What is Unit?A unit is a common element used to quantify similar physical quantities.
As per the given data:
1 kilogram = 2.2 pounds
1 stone = 14 pounds
For converting 42 kilogram to stones:
42 kilogram = 2.2 × 42 pounds
= 92.4 pounds
1 pound = (1/14) stone
= 92.4 × (1/14) stones
= 6.6 stones
Hence, 42 kilograms are equal to 6.6 stones.
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Regular hexagon ABCDEFG in inscribed into circle O and AB=8cm. Calculate each of the following:
(a)What is the radius of circle O
(b)What is the area of circle O
(c)What is m
(d)What is m
(e)What is the measure of arc AB
(f)What is the measure of arc ACE
(g)What is the length of arc AB
(h)What is the area of sector AOB
a. The radius of the circle O is 8 cm.
c. The circle has an area of 213.66 square centimeters.
e. AB's arc length equals 60 degrees
f. ACE has arc measure of 240 degree.
g. the arc length is 8.38 cm
h. area of the sector AOB is 33.51 cm²
How to find the radius of the circlea. The radius of the circle is solved using the properties of a regular hexagon
It has equal sides and angles on all six sides.There is a 120° inside angle and a 60° outside angle.There are six equilateral triangles in it.The radius is 8 cm since the base of one of the equilateral triangles is the radius.
b. Area of circle O
= 3.142 * 8^2
= 213.66 squared cm
e. measure of arc AB
The center angle that creates the intercepted arc is what is known as the arc measure, which is measured in degrees.
= 60 degrees
f. measure of arc ACE
= arc AB + arc BC + arc CD + arc DE
= 60 + 60 + 60 + 60
= 240 degrees
g. length of arc AB
= 60/360 * 2 * 3.142 * 8
= 8.38 cm
h. area of the sector AOB
= 60/360 * 3.142 * 8²
= 33.51 cm²
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25)
Suppose a flare is shot from the top of a 120 foot building at a speed of 160 feet per second. The equation h = −16t + 160t + 120 models the h height at t seconds of the flare. How long will it take for the flare to hit the ground? (to the nearest tenth of a second
The flare takes 10.7 seconds to hit the ground if a flare is shot from the top of a 120-foot building at a speed of 160 feet per second.
The given data is as follows:
Height of building = 120 feets
Speed = 160 feet per second
The given equation is h = −16t + 160t + 120
Time required to hit the ground =?
The flare hits the ground when h=0.
Substitute in the given equation we get,
-16t^2 + 160t + 120 = 0
By applying the Quadratic equation formula to find out the value of t,
Quadratic equation formula = ( -b± [tex]\sqrt{b^{2} - 4ac }[/tex] ) / 2a
x = (-160 ± [tex]\sqrt{160^{2} - 4(-16)(120) }[/tex] ) / 2(-16)
x = (-160 ± [tex]\sqrt{33280}[/tex] ) / -32
x = (-160 +[tex]\sqrt{33280}[/tex] ) / -32, (-160 -[tex]\sqrt{33280}[/tex] ) / -32
x = -10.70, 10.70
Neglecting the time in Negative values, x = 10.70 seconds
Therefore, we can conclude that the flare takes 10.7 seconds to hit the ground.
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for what values of k both the quadratic equations 6x² -17x+12=0 and 3x²-2x+k=0 will have a common root
The value of k for which both 6x² - 17x + 12 = 0 and 3x² - 2x + k = 0 have a common root is k = 1/3.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The discriminant of the first quadratic equation, 6x² - 17x + 12 = 0, is:
b² - 4ac = (-17)² - 4(6)(12) = 1
Since the discriminant is not zero, this quadratic equation does not share a common root with any other equation.
For the second quadratic equation, 3x² - 2x + k = 0, to have a common root with 6x² - 17x + 12 = 0, its discriminant must be zero.
The discriminant of the second quadratic equation is:
b² - 4ac = (-2)² - 4(3)(k) = 4 - 12k
To find the values of k that make the discriminant equal to zero, we solve the equation:
4 - 12k = 0
Simplifying, we get:
12k = 4
k = 4/12
k = 1/3
Therefore, the value of k for which both 6x² - 17x + 12 = 0 and 3x² - 2x + k = 0 have a common root is k = 1/3.
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96n^3 - 84n^2 + 112n - 98
Answer:
2(8n-7)(6n^2+7)
CL 7-123. Without using a calculator, rewrite each expression without parentheses and using only positive exponents.
The final expressiοns fοr a, b, c and d will be 3x(3y)(1/2) / (y¹/3), 1/x, 5²/3, 8z³/2 / x².
Define the term expressiοn?An expressiοn is a mathematical phrase that cοmbines numbers, variables, and οperatοrs tο represent a value οr a quantity. It can include cοnstants, variables, cοefficients, and mathematical οperatiοns.
a. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can simplify the radicals and rewrite the expοnents as fractiοns.
(9¹/2x²y) (27¹/3y-¹) = 3xy¹/2) * 3*(3/3) * y⁻¹/3 = 3x(3y)(1/2) / (y¹/3)
b. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can apply the negative expοnent rule and simplify the radical.
(x¹/2)⁻² = (1/x¹/2)² = 1/x
c. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can simplify the radical and rewrite the expοnent as a fractiοn.
(25)²/3 = (5²)¹/3 = 5²/3
d. Tο rewrite the expressiοn withοut parentheses and using οnly pοsitive expοnents, we can simplify the radical and mοve the negative expοnent tο the denοminatοr.
8z³/2x⁻² = 8(z¹/2)³ / x² = 8z³/2 / x²
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Choose a positive integer N from the infinite set of positive integers N= {1,2,3,....n-1, n, n+1,...,[infinity]} with probability PN = 1/2^n For example P(N = 1) = P1 = 1/2, P(N = 2) = P2 = 1/4, P(N = 3) = P3 = 1/8, and so on. Consider the three events A = {1,2,3,4}, B = {n ∈ N is even} and C = {n ∈ N is odd} (a) Determine P(A) (b) Determine P(B) (c) Determine P(BIA) (d) Determine P(CAB).
The probability of P(A) = 15/16, P(B) = 1/3, P(BIA) = 1/3, and P(CAB) = 0.
The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.
(a) P(A) = P(1) + P(2) + P(3) + P(4) = 1/2 + 1/4 + 1/8 + 1/16 = 15/16
(b) P(B) = P(2) + P(4) + P(6) + ... = 1/4 + 1/16 + 1/64 + ... = 1/3
(c) P(BIA) = P(B ∩ A) / P(A) = (P(2) + P(4)) / P(A) = (1/4 + 1/16) / (15/16) = 5/15 = 1/3
(d) P(CAB) = P(C ∩ A ∩ B) / P(A ∩ B) = 0 / P(A ∩ B) = 0
Therefore, the probabilities of the events are: P(A) = 15/16, P(B) = 1/3, P(BIA) = 1/3, and P(CAB) = 0.
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In an upper tail test about the population mean, where the population standard deviation is known, a sample of size 30 was taken. Use 5% significance. Find the critical value(s).
Select one:
a. Both -1.96 and 1.96
b. Only 1.699
c. Only -1.699
d. Only -1.645
e. Both -2.045 and 2.045
f. Only 1.645
In an upper tail test about the population mean, where the population standard deviation is known, a sample of size 30 was taken. Use 5% significance the critical value is 1.645. The correct answer is option f. Only 1.645.
In an upper tail test about the population mean, where the population standard deviation is known, we need to find the critical value(s) for a 5% significance level.
To find the critical value(s), we need to use the z-table. The z-table shows the probability of a z-score being less than or equal to a certain value.
Since this is an upper tail test, we need to find the z-score that corresponds to a probability of 0.95 (1 - 0.05).
Looking at the z-table, we can see that the z-score that corresponds to a probability of 0.95 is 1.645.
Therefore, the critical value for this upper tail test is 1.645. The correct answer is f. Only 1.645
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1. Find the domain of the equation (
a) √(x + 2) - √2 = 2x b) sin^3 x = sin x + 1 c) tan x + cot x = sin x d) x+1 / x^2 -1 + cos x = csc x 2. Simplify each expression using the fundamental ident (a) (sin^2 θ) / (sec^2 θ -1)
(b) (1 / (1 + tan^2 x) + (1 / (1 + cot^2 x)
(c) 1 – (cos^2 x / 1 + sin x)
(d) sin θ / cos θ tan θ
1. Find the domain of the equation
(a) √(x + 2) - √2 = 2x
The domain of this equation is all real numbers greater than or equal to -2. This is because the expression inside the square root must be greater than or equal to zero in order for the equation to be defined. Therefore, x + 2 ≥ 0, which simplifies to x ≥ -2.
(b) sin^3 x = sin x + 1
The domain of this equation is all real numbers. This is because the sine function is defined for all real numbers.
(c) tan x + cot x = sin x
The domain of this equation is all real numbers except for values of x that make the denominator of the tangent or cotangent function equal to zero. These values are x = nπ, where n is any integer. Therefore, the domain is all real numbers except for multiples of π.
(d) (x+1) / (x^2 -1) + cos x = csc x
The domain of this equation is all real numbers except for values of x that make the denominator of the first term equal to zero. These values are x = 1 and x = -1. Therefore, the domain is all real numbers except for 1 and -1.
2. Simplify each expression using the fundamental identities
(a) (sin^2 θ) / (sec^2 θ -1)
Using the fundamental identity sec^2 θ = 1 + tan^2 θ, we can simplify the denominator to get:
(sin^2 θ) / (tan^2 θ)
Using the fundamental identity tan^2 θ = (sin^2 θ) / (cos^2 θ), we can simplify the expression further to get:
(cos^2 θ)
(b) (1 / (1 + tan^2 x) + (1 / (1 + cot^2 x)
Using the fundamental identities tan^2 x = (sin^2 x) / (cos^2 x) and cot^2 x = (cos^2 x) / (sin^2 x), we can simplify the expression to get:
(cos^2 x) + (sin^2 x)
Using the fundamental identity cos^2 x + sin^2 x = 1, we can simplify the expression further to get:
1
(c) 1 – (cos^2 x / 1 + sin x)
Using the fundamental identity cos^2 x = 1 - sin^2 x, we can simplify the expression to get:
1 - ((1 - sin^2 x) / (1 + sin x))
Distributing the negative sign and combining like terms gives us:
(sin^2 x) / (1 + sin x)
(d) sin θ / cos θ tan θ
Using the fundamental identity tan θ = (sin θ) / (cos θ), we can simplify the expression to get:
(sin θ) / ((cos θ) * ((sin θ) / (cos θ)))
Simplifying the denominator gives us:
(cos^2 θ) / (sin θ)
Using the fundamental identity cos^2 θ = 1 - sin^2 θ, we can simplify the expression further to get:
(1 - sin^2 θ) / (sin θ)
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Se graficó la ganancia semanal (en dólares) como una función de la cantidad de pimentón que vendió esa semana (en kilogramos) (la ganancia negativa significa que los gastos de Jada superaron las ganancias)
By considering the graph, Jade's rate will be 8 dollars profit per kilogram sold.
How do we calculate Jade's rate?Since profit is a function of kilograms sold, x is the kilograms sold and y is the profit.
Two points of the line are (35, 0) and (60, 200).
The Rate or slope is given by:
m = y2 - y1/x2 - x1
m = 200 - 0 / 60 -35
m = 200 / 25
m = 8
Therefore, Jade's rate is 8 dollars profit per kilogram sold.
The translated question is "Jada sells ground paprika. Her weekly profit (in dollars) as a function of the amount of paprika she sold that week (in kilograms) is graphed. What is Jade's rate? "
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TIME REMAINING 17:48 The graph of f(x) = x2 is translated to form g(x) = (x – 2)2 – 3. On a coordinate plane, a parabola, labeled f of x, opens up. It goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). Which graph represents g(x)? On a coordinate plane, a parabola opens up. It goes through (0, 1), has a vertex at (2, negative 3), and goes through (4, 1).
The graph of g(x) is a parabola that opens up, goes through (0, 1), has a vertex at (2, -3), and goes through (4, 1).
What is parabola ?
A parabola is a U-shaped curve that is formed by graphing a quadratic function. In other words, a parabola is the set of all points in a plane that are equidistant from a fixed point (called the focus) and a fixed line (called the directrix).
The graph of g(x) can be obtained by translating the graph of f(x) = x^2 to the left by 2 units and down by 3 units.
The vertex of g(x) is obtained by subtracting 2 from the x-coordinate and subtracting 3 from the y-coordinate of the vertex of f(x). Thus, the vertex of g(x) is (2, -3).
The point (-2, 4) on f(x) is translated left by 2 units to (−4, 4) on g(x) and then down by 3 units to (−4, 1). The point (2, 4) on f(x) is translated left by 2 units to (0, 4) on g(x) and then down by 3 units to (0, 1).
Therefore, the graph of g(x) is a parabola that opens up, goes through (0, 1), has a vertex at (2, -3), and goes through (4, 1).
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Answer:
A
Step-by-step explanation:
The equation 4x+5y=35 represents the total cost, in dollars, of a customer’s purchase at a home improvement store, where x is the price of an extension cord, and y is the price of a lightbulb. Which represents the equation when solved for the price of a lightbulb, y?
The equation when solved for the price of a lightbulb, y, is: [tex]y=7 - \frac{4}{5} x[/tex]
What is linear equation?A statement that shows the equality of the two expressions is known as an equation. Mathematical operations including addition, subtraction, multiplication, division, and exponentiation are included, along with one or more variables, constants, and other operations.
To solve the equation 4x + 5y = 35 for the price of a lightbulb, y, we need to isolate y on one side of the equation. Here are the steps:
Subtract 4x from both sides of the equation:
4x + 5y - 4x = 35 - 4x
Simplifying, we get:
5y = 35 - 4x
both sides divided by 5 in the equation:
(5y)/5 = (35 - 4x)/5
Simplifying, we get:
y = (35/5) - (4/5)x
y = 7 - (4/5)x
Therefore, the equation when solved for the price of a lightbulb, y, is: [tex]y=7 - \frac{4}{5} x[/tex]
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A right triangle has side lengths 5, 12, and 13 as shown below. Use these lengths to find sinY, tanY, and cosY.
The value of
1 sinY = 12/13
2. cos Y = 5/13
3. tanY = 12/5
What is trigonometry?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.
sin Y = opp/hyp
cos Y = adj/hyp
tan Y = opp/adj
if opp = 12
adj = 5
hyp = 13
then,
sinY = 12/13
cos Y = 5/13
tanY = 12/5
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