The greatest positive integer [tex]$n$[/tex] such that [tex]$2^n$[/tex] divides [tex]$k$ is $n = 4$[/tex].
[tex]$k = (2 - 1)(3 - 1)(4 - 1)...(20 - 1)$[/tex]
We can rewrite [tex]$k$[/tex] as [tex]$k = 2^1 \cdot 3^1 \cdot 4^1 \cdot ... \cdot 20^1$[/tex], and then use the formula [tex]$2^n \mid (p_1^{\alpha_1} \cdot p_2^{\alpha_2} \cdot p_3^{\alpha_3} \cdot ... \cdot p_m^{\alpha_m})$ $\iff$ $2^n \mid p_1^{\alpha_1}$[/tex] and [tex]$2^n \mid p_2^{\alpha_2}$[/tex] and[tex]$2^n \mid p_3^{\alpha_3}$ and ... and $2^n \mid p_m^{\alpha_m}$[/tex]
Since all of the exponents [tex]$\alpha_1, \alpha_2, \alpha_3, ..., \alpha_m$[/tex] are equal to 1, we can simplify this to: [tex]$2^n \mid p_1$ and $2^n \mid p_2$ and $2^n \mid p_3$ and ... and $2^n \mid p_m$[/tex]
In this case, [tex]$p_1 = 2$, $p_2 = 3$, $p_3 = 4$[/tex], and so on, so [tex]$2^n$[/tex] must divide all of the prime numbers from 2 to 20 in order for it to divide k. The highest power of 2 that divides all of these prime numbers is [tex]$2^4$[/tex], so the greatest positive integer n such that [tex]$2^n$[/tex] divides [tex]$k$ is $n = 4$[/tex].
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 A town's population has been growing linearly. In 2004 the population was6,200. By 2009 the population had grown to 8,100. Assume this trend
continues
a. Predict the population in 2013.
b. Identify the year in which the population will reach 15,000.
In linear function, 2027 is the year in which the population will reach 15,000.
What is another name for a linear function?
A linear function, also known as a polynomial function of degree zero or one, is a function in calculus and related fields that has a graph that is a straight line.
The phrase "affine function" is frequently used to distinguish such a linear function from the other idea.
Let linear function
Since 2004
In 2004, t=0 ,P=6200
6200=a(0)+b
b=6200
In 2009, t=5 ,P =8100
8100=5a+6200
5a=8100-6200
5a=1900
a=1900/5
a=380
a)Substitute value of a and b in linear function equation .
P = 380t + 6,200
B)In 2013 ,t =2013-2004=9
P=380(9)+6200
P=9620
C) P=15000
15000=380t+6200
380t=15000-6200
t=8800/380
t=23.16
t=23(nearest year)
Year=2004+23=2027
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On your instructors quizzes you expect a score of 100% when you study in a 60% when you don’t suppose the probability that you study is .8 given these facts compute the expected average of all your quizzes 
The expected average of all your quizzes is 92%.
What is Probability?Probability is simply the possibility of getting an event. Or in other words, we are predicting the chance of getting an event.
The value of probability will be always in the range from 0 to 1.
Given that,
Expected score when you study = 100%
Expected score when you don't study = 60%
Probability that you study = 0.8
Probability that you don't study = 1 - 0.8 = 0.2
Expected Value or mean of the random variable X is,
E(X) = Σ(x P(x))
Expected average = (100 × 0.8) + (60 × 0.2)
= 92
Hence the expected value of all your quizzes is 92%.
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Solve for x in the drawing below.
Answer:
x=14
Step-by-step explanation:
Half circle total degree+180
so 180=101-47-(2x-4)
2x-4=180-101-47
2x-4=32
2x=28
x=14
Explain how to eliminate y from the given system of equations.
To eliminate y from the given system of equations, multiply the first equation by 2 and multiply the first equation by 3 and add them.
What is eliminate method to solve an equation?Utilizing the elimination approach is one strategy to resolve a linear system. To create an equation in one variable using the elimination approach, you can either add or subtract the equations.
To eliminate a variable, add the equations when the coefficients of one variable are in opposition, and subtract the equations when the coefficients of one variable are in equality.
If you don't already have equations that allow for the addition or subtraction of a variable, you can start by multiplying one or both equations by a constant to create an analogous linear system that allows for the addition or subtraction of a variable.
Given that, the linear equations are
2x + 3y = 6
3x – 2y = 4
To eliminate y from the given system of equations, multiply the first equation by 2 and multiply the first equation by 3 and add them.
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The complete question is:
Explain how to eliminate y from the given system of equations.
2x + 3y = 6
3x – 2y = 4
the domain of f. f(1)=10, f(2)=-7, f(3)=4
Answer: The domain of the function f refers to the set of all input values (x) for which the function is defined. Based on the information provided, it is not possible to determine the full domain of the function f. The only information provided are the outputs (f(1)=10, f(2)=-7, f(3)=4) for specific input values (1, 2, 3).
Step-by-step explanation:
avg change between x=1 and x=2
The average rate of change of the function from x = 1 to x = 2 is given as follows:
f(2) - f(1).
How to obtain the average rate of change?The average rate of change of a function is given by the change in the output divided by the change in the input.
The change in the output is given as follows:
f(2) - f(1).
The change in the input is given as follows:
2 - 1 = 1.
Hence the rate is given as follows:
[f(2) - f(1)]/1 = f(2) - f(1).
Missing InformationThe problem is incomplete, hence the answer was given in general terms.
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Given the functions f and g below, find g(f(1)).
Select the correct answer below:
O g(f(1)) = 10
O g(f(1)) = 14
O g(f(1)) = -12
Og(f(1)) = 12
O g(f(1)) = -11
f(x)=x-4
g(x) = -5x-3
the value of the function g(f(x)) at x = 1 will be g(f(1)) = 12.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given, Two functions f(x) = x - 4 and g(x) = -5x - 3
So,
g(f(x)) = -5 f(x) -3
g(f(x)) = -5( x -4) -3
g(f(x)) = - 5x +20 -3
g(f(x)) = -5x +17
the value of g(f(x)) at x = 1
g(f(1)) = -5 * 1 + 17
g(f(1)) = 12
therefore, the value of the function g(f(x)) at x = 1 will be g(f(1)) = 12.
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which statement best describes a graph of paired points that form a proportional relationship? responses a straight line can be drawn through all the points, but the line does not pass through the origin. a straight line can be drawn through all the points, but the line does not pass through the origin. a straight line cannot be drawn through all of the the points, but the line passes through the origin. a straight line cannot be drawn through all of the the points, but the line passes through the origin. a straight line cannot be drawn through all of the the points, and the line does not pass through the origin. a straight line cannot be drawn through all of the the points, and the line does not pass through the origin. a straight line can be drawn through all the points, and the line passes through the origin.
A straight line can be drawn through all the points, and the line passes through the origin.
When two variables are proportional, the ratio of their values remains constant. A graph of paired points that form a proportional relationship will show a straight line when plotted on a graph. The position of the line on the graph will depend on the constant of proportionality, which determines the slope of the line. If the constant of proportionality is positive, then the line will slope upwards, and if the constant of proportionality is negative, the line will slope downwards. If the line passes through the origin, it means that when one variable is zero, the other variable is also zero. This is referred to as an "origin-centered proportional relationship." In this case, the line passes through the point (0, 0), which is the origin. If the line does not pass through the origin, it means that there is a non-zero intercept, and that the relationship between the variables is not centered on the origin. In this case, the line will have a non-zero y-intercept, which is the value of the second variable when the first variable is zero.
In conclusion, the statement "a straight line can be drawn through all the points, and the line passes through the origin" best describes a graph of paired points that form a proportional relationship centered on the origin.
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Use this table to answer the question. Read the question carefully!
Infections in Hospital Infections after Release No Infections Total
Hospital 1 350 110 450 910
Hospital 2 175 210 350 735
Hospital 3 210 35 75 320
Hospital 4 437 587 4300 5324
Hospital 5 89 21 356 466
Hospital 6 67 175 298 540
Total 1328 1138 5829 8295
What was the percent of Infections in Hospital for Hospital 6?
The percent of infections for Hospital 6 is given as follows:
44.81%.
How to obtain the percentage?The percentage is obtained applying the proportions in the context of this problem.
A proportion is applied because a percentage is calculated with the division of the number of desired outcomes by the number of total outcomes, a result which is then multiplied by 100%.
Out of 540 patients in Hospital 6, 67 were infected in hospital and 175 after release, hence the percentage is obtained as follows:
P = (67 + 175)/540 = 44.81%.
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Using the region names in the image below, select all regions that represent:
A ∩ B' ∩ C
3 group Venn Diagram with Roman numeral labeled regions
A intersection not B intersection C. Region I: Items only in group A, not in B or C. Region II: Items in A and B, but not C. Region III: Items only in B, not in A or C. Region IV: Items in A and C, but not B. Region V: Items in A, B, and C. Region VI: Items in B and C, but not A. Region VII: Items only in C, not in A or B. Region VIII: Items not in any of the groups.
Items in A and C, but not B is the required region.
What is set?Sets are groups of well-defined objects or components in mathematics. A set is denoted by a capital letter, and the cardinal number of a set is enclosed in a curly bracket to indicate how many members there are in a finite set.
Given:
A ∩ B' ∩ C
That means,
A intersection not B intersection C.
B' is the complement of set B.
So, the region is,
Items in A and C, but not B.
Therefore, the items in A and C but not in B.
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Can you help please
Answer:
the answer will be the second graph
Step-by-step explanation:
in the other graphs, the proportions are not equal
for example, in the top graph, your first and second proportions simplify to 1/5; but your third and fourth simplify to 1/4
in the third graph, your first and second simplify to 1/3 and your third and fourth simplify to 1/4
however, in the second graph, the proportions simplify to 1/3 throughout
Answer:
The answer is Bㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ
circles $\omega$ and $\gamma$, both centered at $o$, have radii $20$ and $17$, respectively. equilateral triangle $abc$, whose interior lies in the interior of $\omega$ but in the exterior of $\gamma$, has vertex $a$ on $\omega$, and the line containing side $\overline{bc}$ is tangent to $\gamma$. segments $\overline{ao}$ and $\overline{bc}$ intersect at $p$, and $\dfrac{bp}{cp}
The ratio of bp to cp in equilateral triangle abc, with a on circle omega(Ω), bc tangent to circle omega(Ω), and p being the intersection of ao and bc, is [tex]\frac{2}{\sqrt{3} }[/tex].
Let's label the center of the larger circle omega(Ω) as O, and the center of the smaller circle gamma(Γ)as G. Draw a perpendicular from O to the line containing side overline{BC}, and label the intersection point as X. By tangency, GX is a radius of gamma(Γ), so GX = 17.
Also, $\overline{OX} = 20. By the Pythagorean Theorem, OP = [tex]\sqrt{OX^{2} -PX^{2} }[/tex] = [tex]\sqrt{20^{2}-17^{2} }[/tex] = [tex]\sqrt{289}[/tex]. Let BP = x. Then CP = [tex]\frac{BC}{2} -x[/tex] = [tex]\frac{BC}{2} -x[/tex] = [tex]\frac{BC-2x}{2}[/tex]. Therefore, [tex]\frac{BP}{CP}[/tex] = [tex]\frac{x}{\frac{BC-2x}{2} }[/tex]= [tex]\frac{2x}{BC-2x}[/tex] = [tex]\frac{2x}{BC}[/tex].
To find BC, we use the fact that ΔABC$ is equilateral. Therefore, AO = BO = CO = 20. Let's apply the Law of Cosines to triangle ABO:
[tex]AB^{2} =AO^{2} +BO^{2} -2.AO.BO.cosA[/tex]
[tex]AB^{2} =20^{2} +20^{2} -2.20.20.cos(60)[/tex]
[tex]AB^{2} =800[/tex]
[tex]AB=\sqrt{800} =20\sqrt{2}[/tex].
Therefore, [tex]BC=AB=20\sqrt{2}[/tex], and [tex]\frac{BP}{CP} =\frac{2x}{BC}=\frac{2x}{20\sqrt{2} }[/tex].
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what is 857+234 estimated???
Answer:
1100
Step-by-step explanation:
I think you just guess the first few digits and put zero?
How do 1/4 and 3/5 compare
Answer:
Is 3/5 greater than 1/4? Is 3/5 bigger than 1/4? Is 3/5 larger than 1/4? These are all the same questions with one answer.
To get the answer, we first convert each fraction into decimal numbers. We do this by dividing the numerator by the denominator for each fraction as illustrated below:
3/5 = 0.6
1/4 = 0.25
Then, we compare the two decimal numbers to get the answer.
0.6 is greater than 0.25.
Therefore, 3/5 is greater than 1/4 and the answer to the question "Is 3/5 greater than 1/4?" is yes.
Which means that this equation is also true: 3/5 > 1/4
Step-by-step explanation:
Note: When comparing fractions such as 3/5 and 1/4, you could also convert the fractions (if necessary) so they have the same denominator and then compare which numerator is larger.
what is the value of x?
x^2-10x+25
Answer:
(x-5)^2
Step-by-step explanation:
The buckingham fountain holds 725 gallons of water. due to the harsh winter, it was discovered that it was cracked and leaking rate of 12.5 gallons per hour. let y represent the amount of water in gallons after x hours of leaking
An equation represent the given scenario is 725=y-12.5x.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, the Buckingham fountain holds 725 gallons of water.
Due to the harsh winter, it was discovered that it was cracked and leaking rate of 12.5 gallons per hour.
Let y represent the amount of water in gallons after x hours of leaking.
Now, equation is 725=y-12.5x
Therefore, an equation is 725=y-12.5x.
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true/false. classify the statement as an example of classical probability, empirical probability, or subjective probability. the probability that a train will be in an accident on a specific route is 1%.
Classification of the statement the probability that a train will be in an accident on a specific route is 1% can be done as Empirical Probability.
In classical probability, the likelihood of an event is determined by the number of possible outcomes and the number of favorable outcomes. Empirical probability, on the other hand, is based on the observed frequency of an event over a large number of trials. In the statement, the probability that a train will be in an accident on a specific route is given as 1%, which suggests that it is an empirical probability, calculated based on past observations of train accidents on that route.
Subjective probability, on the other hand, is based on personal beliefs or opinions, which are not necessarily based on evidence or data. In this case, the probability is given as a specific number, indicating that it is not based on personal beliefs or opinions.
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suppose that a sphere passes through the point and has center . (a) find the distance between the points and
The distance between two points in three-dimensional space is a measure of the separation between the two points. In this case, the two points are the center of a sphere and a point that the sphere passes through.
To find the distance, we can use the distance formula in three dimensions, which is an extension of the distance formula in two dimensions. The distance formula is:
d = √((x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2)
where (x1, y1, z1) is the center of the sphere and (x2, y2, z2) is the point that the sphere passes through. The square root of the sum of the squares of the differences between the corresponding coordinates gives the distance between the two points.
In this problem, the center of the sphere is not given, so it is not possible to calculate the distance between the sphere and the point. The center of the sphere is a crucial piece of information needed to solve this problem.
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write the expression in algebraic form. [hint: sketch a right triangle, as demonstrated in example 3.] tan(arcsec(x/3))
The expression tan(arcsec(x/3)) can be written [tex]1/3 \sqrt{x^2-9}[/tex] in algebraic form.
The inverse secant function, or arcsecant, is defined as the inverse of the secant function, which is the ratio of the length of the hypotenuse of a right triangle to the length of the adjacent side. Given x/3 as the length of the adjacent side, arcsec(x/3) is the measure of the angle that has a secant equal to x/3.
The tangent function is the ratio of the length of the opposite side of a right triangle to the length of the adjacent side. By substituting arcsec(x/3) as the measure of the angle in a right triangle, we can use the tangent function to find the ratio of the lengths of the opposite and adjacent sides, which is equal to [tex]1/3 \sqrt{x^2-9}[/tex].
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let x, y and z be independent and uniformly distributed on the interval [0, 1]. find the joint density function of xy and z2, and show that e(xy < z2)
The joint density function of xy and [tex]z^{2}[/tex] [tex]& f_T(t)=\frac{1}{2 \sqrt{t}} \quad \leqslant t \leq 1 \\&[/tex].
From the given data
x, y, z are independent and uniformly distributed on [0,1] and also Independent.
The joint probability density function (joint pdf) is a function used to characterize the probability distribution of several continuous random variables, which together form a continuous random vector.The joint probability density function (joint pdf) is a function used to characterize the probability distribution of several continuous random variables, which together form a continuous random vector.⇒[tex]& f(x, y)=f_x(x) \quad f y(y) \\[/tex]
⇒[tex]& \omega=x y \\[/tex]
⇒[tex]& f_\omega(\omega)=P(\omega \leq \omega) \\[/tex]
The probability density function (pdf) f(x) of a continuous random variable X is defined as the derivative of the cdf F(x): f(x)=[tex]\frac{d}{dx}[/tex]F(x).[tex]& =\int_A \int_1 1 d x d y \\[/tex]
⇒[tex]& A \rightarrow\left\{(x, y): \quad \begin{array}{ll} & 0 \leq x \leq 1 \\0 \leq y \leq 1\end{array} \quad x y \leq \omega\right\} \\[/tex]
⇒[tex]& f_\omega(w)=\omega+\int_z^1 \int_0^x(y) d y d x \\[/tex]
[tex]& =\omega+\int_z^1[y]_0^{w / x} d x \\[/tex]
[tex]& =\omega+y / w(\omega / x) d x \\[/tex]
[tex]& =\omega+\omega[\ln x]_\omega^{\prime} \omega \\[/tex]
[tex]& =\omega+\omega(0-\ln \omega) \\[/tex]
⇒[tex]& f_\omega(\omega)=\omega-\omega \ln . \\[/tex]
⇒[tex]& f_\omega(\omega)=\frac{\partial}{\partial \omega}(f \omega(\omega)) \\[/tex]
[tex]& =1-[\omega / \omega+\ln \omega] \\[/tex]
⇒[tex]& f_\omega(\omega)=-\ln \omega \quad \quad 0 \leq \omega \leq 1 \\[/tex]
⇒[tex]& \text { Pdf of } z^2 \\[/tex]
⇒[tex]& T=z^2 \\[/tex]
⇒[tex]& f_T(t)=P(T \leq t) \\[/tex]
[tex]& =p\left(z^2 \leq t\right) \\[/tex]
[tex]& =p(r \leqslant \sqrt{t}) \\[/tex]
[tex]& =\int_0^{\sqrt{t}} 1 d z \\[/tex]
[tex]& =[z]_0^{\sqrt{t}} \\[/tex]
[tex]& =\sqrt{t} \\[/tex]
⇒[tex]& 0 \leq t \leq 1 \\[/tex]
⇒[tex]& F_T(t)=\sqrt{t} \\[/tex]
⇒[tex]& F_T(t)=F_T^{\prime}(t) \\[/tex]
⇒[tex]& f_T(t)=\frac{1}{2 \sqrt{t}} \quad \leqslant t \leq 1 \\&[/tex]
Therefore, the joint density function of xy and [tex]z^{2}[/tex] [tex]& f_T(t)=\frac{1}{2 \sqrt{t}} \quad \leqslant t \leq 1 \\&[/tex]
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andre and priya are tracking the number of steps they walk. andre records that he can walk 6000 steps in 50 minutes. priya writes the equation y
Andre walks more steps than Priya
What is an equation?An equation is the equality between two algebraic expressions, which have at least one unknown or variable.
To solve this problem, we have to state the equation using the information of the problem:
Calculating Andre's steps we have:
y(Andre) = 6000 steps/50 minutes
y(Andre) = 120 steps/ minute
If the total of hours is 5 hours we convert hours to minutes and we have:
5 hours * (60 minutes/ 1 hours) = 300 minutes
Andre's steps in 300 minutes are:
y(Andre) = 120 steps/ minute * 300 minutes
y(Andre) = 36000 steps
Now we calculate the steps of Pria with the equation given:
y=118x
y(Pria) = 118*300
y(Pria) = 35400 steps
36000 steps > 35400 steps
y(Andre) > y(Pria)
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Correctly written question:
Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walk for a total of 5 hours. Who walks more steps?
knowing that the tension in cable ac is 2140 n, determine the components of the force exerted on the plate at c.
The components of the force exerted on the plate at C are 1080N in the x direction and 1060N in the y direction.
The forces exerted on the plate at C can be determined using the equations of equilibrium. According to the equation of equilibrium, the sum of the forces in the x and y direction must be equal to zero. Therefore, we can calculate the x and y components of the force as follows:
Fx = 0 = Tcos(theta) – Fc
Fy = 0 = Tsin(theta) – Fb
Where T is the tension in the cable AC, theta is the angle of the cable AC, Fc is the force in the x direction, and Fb is the force in the y direction.
Using the given information, we can solve for Fc and Fb as follows:
Fc = Tcos(theta) = 2140N * cos(60°) = 1080N
Fb = Tsin(theta) = 2140N * sin(60°) = 1060N
Therefore, the components of the force exerted on the plate at C are 1080N in the x direction and 1060N in the y direction.
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PLEASE ANSWER QUICK U WIL, GET BRANLIEST The diameter of a hat is 5.3 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
Answer:
the answer is 16.63 inches
Answer: Hi! The answer would be 16.63 inches.
If you want steps, dm me! <3 Good luck!!
yeah i don't know this answer so help pleez
The measure of side BC is 2√3 units and AB is 2√13 units.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In triangle BCD,
tan60°=BC/DC
√3=BC/2
BC=2√3
By Pythagoras theorem,
BD²=BC²-DC²
BD²=(2√3)²-2²
BD²=12-4
BD²=8
BD=2√2
By Pythagoras theorem,
AC²=BC²+AB²
8²=(2√3)²+AB²
64=12+AB²
AB²=52
AB=√52
AB=2√13
Therefore, the measure of side BC is 2√3 units and AB is 2√13 units.
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Use the table of values to evaluate the expressions below.
By using the given table of values, the solution to the expressions include the following:
f(g(8)) = 3.
g(f(3)) = 5.
f(f(7)) = 0.
g(g(1)) = 3.
How to evaluate the expressions by using the given table of values?In Mathematics, a function is typically used to uniquely map an independent value (input variable or domain) to a dependent value (range or output variable).
This ultimately implies that, an independent value (domain) represents the value on the x-axis of a cartesian coordinate while a dependent value (range) represents the value on the y-axis of a cartesian coordinate.
By using the given table of values, each of the independent value (domain) and output value would be used to evaluate the expressions as follows;
f(g(8)) = f(7) = 3.
g(f(3)) = g(0) = 5.
f(f(7)) = f(3) = 0.
g(g(1)) = g(5) = 3.
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examine the two figures above. which illustrates a society that produces more capital goods than consumer goods?
The figure on the left illustrates a society that produces more capital goods than consumer goods, as indicated by a Total Value of Goods difference of $200.
The figure on the left illustrates a society that produces more capital goods than consumer goods. This is because the total value of the capital goods is greater than the total value of the consumer goods. This can be calculated using the formula Total Value of Goods (TVG) = Price of Goods x Quantity of Goods. By using this formula we can calculate that the TVG of the capital goods is $400 (20 x 20) and the TVG of the consumer goods is $200 (10 x 20). The difference between the two is $200, indicating that the society is producing more capital goods than consumer goods.
The figure on the left illustrates a society that produces more capital goods than consumer goods, as indicated by a Total Value of Goods difference of $200.
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the following times were recorded by the quarter-mile and mile runners of a university track team (times are in minutes). quarter-mile times: 0.92 0.96 1.04 0.93 1.00 mile times: 4.52 4.35 4.60 4.71 4.51 after viewing this sample of running times, one of the coaches commented that the quarter-milers turned in the more consistent times. use the standard deviation and the coefficient of variation to summarize the variability in the data. quarter-milers standard deviation (to decimals) coefficient of variation (to decimal) % milers standard deviation (to decimals) coefficient of variation (to decimal) % does the use of the coefficient of variation indicate that the coach's statement should be qualified? (i) yes; the coefficient shows that as a percentage of the mean, the quarter-milers' times show less variability. (ii) no; the coefficient shows that as a percentage of the mean, the quarter-milers' times show more variability. choose the correct answer. - select your answer -
No; the coefficient shows that as a percentage of the mean, the quarter-milers' times show more variability.
How did we arrive at this assertion?To summarize the variability in the data, we can calculate the standard deviation and the coefficient of variation for both the quarter-mile and mile runners.
Standard deviation:
Quarter-mile times:
mean = (0.92 + 0.96 + 1.04 + 0.93 + 1.00) / 5 = 0.97
differences from mean = [0.92 - 0.97, 0.96 - 0.97, 1.04 - 0.97, 0.93 - 0.97, 1.00 - 0.97] = [-0.05, -0.01, 0.07, -0.04, 0.03]
squared differences = [0.0025, 0.0001, 0.0049, 0.0016, 0.0009]
sum of squared differences = 0.01
standard deviation = √(sum of squared differences / (number of data points - 1)) = sqrt(0.01 / 4) = 0.049
Mile times:
mean = (4.52 + 4.35 + 4.60 + 4.71 + 4.51) / 5 = 4.56
differences from mean = [4.52 - 4.56, 4.35 - 4.56, 4.60 - 4.56, 4.71 - 4.56, 4.51 - 4.56] = [-0.04, -0.21, 0.04, 0.15, -0.05]
squared differences = [0.0016, 0.0441, 0.0016, 0.0225, 0.0025]
sum of squared differences = 0.0727
standard deviation = √(sum of squared differences / (number of data points - 1)) = sqrt(0.0727 / 4) = 0.139
Coefficient of variation:
Quarter-mile times: coefficient of variation = standard deviation / mean = 0.049 / 0.97 = 0.051 (to 2 decimal places)
Mile times: coefficient of variation = standard deviation / mean = 0.139 / 4.56 = 0.0305 (to 4 decimal places)
The use of the coefficient of variation indicates that the coach's statement should be qualified. The coefficient shows that as a percentage of the mean, the mile runners' times have less variability (3.05%) compared to the quarter-mile runners' times (5.1%). So, the answer is (ii) no; the coefficient shows that as a percentage of the mean, the quarter-milers' times show more variability.
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Write the equation of a line that has a slope of 3 and passes through the point (5,7).
Explanation please
Answer:
y = 3x - 8
Step-by-step explanation:
[tex]y=mx+b\\y=3x+b\\7=3(5)+b\\7=15+b\\-8=b\\\\y=3x-8[/tex]
Here, we used slope-intercept form to solve for the unknown y-intercept so the graph of the line will pass through (5,7) initially given our slope of 3.
find the numerical value of each expression. (round your answers to five decimal places.) (a) cosh(7)
The numerical value of cosh(7) is 25.78543.
The hyperbolic cosine function, cosh(x), is the inverse of the hyperbolic sine function, sinh(x). It is defined as the sum of the series cosh(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + …, where x is any real number and n! is the factorial of n.
To find the numerical value of cosh(7), we need to evaluate the series at x = 7. To do this, we start by calculating the first two terms of the series, 1 and 7²/2!. The first term is 1, and the second term is 7²/2! = 49/2 = 24.5. Then we add them together to get the result cosh(7) = 25.5.
To get a more accurate result, we can add more terms to the series. For instance, by adding the third term, 7⁴/4!, we get cosh(7) = 25.5 + 585/24 = 25.70833. We can continue this process to get an even more accurate result.
After adding the sixth term, 7⁶/6!, we get cosh(7) = 25.70833 + 90090/720 = 25.78542.
Finally, we round the result to five decimal places to get cosh(7) = 25.78542 ≈ 25.78543.
The numerical value of cosh(7) is 25.78543.
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A ∩ B = ∅, P(A) = 0.4, P(A ∪ B) = 0.9. Find P(B)
Find P(B).
If intersection of A & B null set and P(A) = 0.4, P(A ∪ B) = 0.9 then P(B) = 0.5
What are sets ?In mathematics, a set is a collection of distinct objects, called elements, which can be anything from numbers, to letters, to functions, or even other sets. The objects in a set are unordered, meaning their position or arrangement doesn't matter. Sets are often denoted using curly braces {} and the elements within the set are separated by commas.
For example, the set of positive even numbers less than 10 can be written as {2, 4, 6, 8}.
Given that,
A ∩ B = ∅,
P(A) = 0.4,
P(A ∪ B) = 0.9,
P(B) = ?
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
0.9 = 0.4 + P(B) - 0
P(B) = 0.9 - 0.4
= 0.5
Hence, the probability of event B is 0.5
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