For given data set that consists of first and third quartiles as 9 and 17 respectively outlier comes out to be 41. So, option (d) is correct option.
What are quartiles and outliers?
Three values called quartiles divide sorted data into four equal portions with the same amount of observations in each. Quartiles are a type of quantile.
An outlier is a piece of data that is an exceptional distance from other locations. It is information that is not included in the set's other values, to put it another way.
Outlier is any data point more than 1.5 times interquartile ranges (IQRs) below the first quartile or above the third quartile([tex]Q_{3}[/tex]).
We are given
First quartile, [tex]Q_{1}[/tex] = 9
Third quartile,[tex]Q_{3}[/tex] = 17
IQR = [tex]Q_{3} - Q_{1}[/tex] = 17 – 9 = 8
[tex]1.5*IQR = 1.5*8 = 12[/tex]
[tex]Q_{1} - 1.5*IQR = 1.5*8 = 12[/tex]
[tex]Q_{3} + 1.5*IQR = 17 + 12 = 29[/tex]
So, numbers outside -3 and 29 are considered as outliers.
So, number 41 is outside this interval, therefore it is considered as an outlier.
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evaluate the following expression. express your answer as a fraction or a decimal number rounded to four decimal places. 11C9/11P4
The result of the expression 11C9 / 11P4 is 1 / 144
The given expression is
11C9 / 11P4
The permutation is defined as the method of arranging the numbers or object in order
The combination is defined as the method of selecting the numbers or object from a collection without any order
The given expression is
11C9 / 11P4
Find the value of each term
11C9 = 11! / (11-9)! × 9!
= 55
11P4 = 11! / (11-4)!
= 7920
Substitute the value of each term in the expression
The expression will be
11C9 / 11P4 = 55/7920
= 1/144
Therefore, the result is 1/144
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data were collected on the number of days per week that members visit a certain fitness center. the values varied from 0 to 7, and a distribution of relative frequencies for the values was created. let the random variable x represent the number of days per week that a member visits. the mean of x is 3.12. which of the following statements is the best interpretation of the mean? responses each member visits the fitness center 3 or 4 days per week. each member visits the fitness center 3 or 4 days per week. the average number of days that each member visits the fitness center is 3.12 days per week. the average number of days that each member visits the fitness center is 3.12 days per week. half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more. half the members visit the fitness center 3 days per week or less, and the other half visit 4 days per week or more. the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week. for a random sample of members selected from the population, the average number of visits for the sample will be 3.12 days per week.
The statement that is the best interpretation of the mean is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
The data of the number of days members visited a certain fitness center varied from 0 to 7.
The mean of the random variable x = 3.12
The mean of the random variable is also known as the long-run average value of a random variable.
Hence, we conclude that the best interpretation of the mean in the given question is that the long-run average resulting from repeated sampling of members of the fitness center will approach 3.12 days per week.
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Consider a set of cards that has four cards labeled 1, 3, 5, and 7. Suppose you pick two cards, without replacement, and obtain the mean of the two numbers that are drawn from the set. Which of the following tables shows the sampling distribution? a.) Sample (n = 2) x̄ S1 = {1, 1} 1 S2 = {1,This problem has been solved!You'll get a detailed solution from a subject matter expert that helps you learn core concepts.Consider a set of cards that has four cards labeled 1, 3, 5, and 7.Suppose you pick two cards, without replacement, and obtain the mean of the two numbers that are drawn from the set
Answer:
one 2
one 3
two 4's
one 5
one 6
Step-by-step explanation:
We can use the combination formula to derive how many sets of two can be obtained from this set of 4 numbers. We are using the combination formula instead of the permutation formula because, in this situation, order doesn't matter; the mean of 1 and 3 is the same as the mean of 3 and 1.
[tex]_nC_r = \dfrac{n!}{r!(n-r)!}[/tex] where [tex]n[/tex] is the number of things to choose from and [tex]r[/tex] is the number of things we are choosing. Hence the equation for this problem is:
[tex]_4C_2 = \dfrac{4!}{2!(4-2)!}[/tex]
[tex]_4C_2=\dfrac{24}{2(2)}[/tex]
[tex]_4C_2 = 6[/tex]
So, there are 6 ways to pick 2 cards from a total of 4. We can lay out these 6 possibilities from the given numbers on each card:
(1, 3) (3, 5) (5, 7)
(1, 5) (3, 7)
(1, 7)
Then, we can calculate the mean, or average, of each.
2 4 6
3 5
4
Finally, we can conclude that the distribution of the means for each possible set of number pairs is:
one 2
one 3
two 4's
one 5
one 6
37. How many solutions does the system of equations have? (1 point)
y=-2x+9
6x+3y=27
O one
Otwo
O infinitely many
O none.
15. A student has a stone. He wants to find its density. (a) He pours 110 cm^3 of water into a measuring cylinder. And then, he places the stone in the water. The water surface in the measuring cylinder moves up. The volume of water and stone is 150 cm^3. What is the volume of stone? (1 mark)
The volume of the stone if, The volume of the water is 110 cm³, and The volume of the water and the stone is 150 cm³, is 40 cm³.
What is volume?The capacity occupied by a three-dimensional solid shape is known as volume. It is difficult to visualize in any shape, yet it may be compared among shapes. For instance, a compass box has a larger volume than an eraser placed inside of it.
Given:
The volume of the water = 110 cm³,
The volume of the water and the stone = 150 cm³,
Calculate the volume of the stone as shown below,
The volume of stone = The volume of the water and the stone - The volume of the water
The volume of stone = 150 - 110
The volume of stone = 40
Thus, the volume of the stone is 40 cm³
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Find the range of the relation
Answer:
1st {-6, -3, 0, 3, 6}
Step-by-step explanation:
range is the output that is "y", so the range is a set of {-6, -3, 0, 3, 6}
If a population of weights is normal with a mean of 75 pounds and a standard deviation of 5.9 pounds, the probability an individual from this population will have a weight greater than 72 pounds is 0.31. O True O False
It is false that the probability of an individual from this population will have a weight greater than 72 pounds is 0.31 instead it is 0.70
According to the question,
Weight of population follows normal distribution
Mean of population : u = 75 pounds
Population Standard deviation : σ = 5.9 pounds
We have to Check if the probability an individual from this population will have a weight greater than 72 pounds is 0.31
Probability that weight is greater than 72 = P( x > 72)
Subtracting by 75 both sides and then dividing by 5.9
=> P( x - 75 / 5.9 > 72 - 75 / 5.9)
Using Z-statistics,
=> P( z > -3/5.9)
=> P( z > -0.508)
=> 1 - P(z < -0.50)
Using Probability distribution table for z,
=> 1 - 0.305
=> 0.70
Which is not equal to 0.31
Hence, It is false that Probability that weight is greater than 72 is 0.31
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Solve the equations :
please help
What is the equation of the circle with center (-3.2, 2.1) and radius 4.3?
A. (x-2.1)^2 - (y + 3.2)^2 = (4.3)^2
B. (x + 3.2)^2 + (y - 2.1)^2 = 4.3^2
C. (x+ 2.1)^2 + (y- 3.2)^2 = 4.3^2
D. (x- 3.2)^2 + (y + 2.1)^2 = (4.3)^2
Thus, (x+3.2)2+(y+2.1)2=18.49 ( x + 3.2 ) 2 + ( y + 2.1 ) 2 = 18.49 is the equation of the circle with the center at (−3.2,−2.1) and a radius of r=4.3 .
When the centre and radius of a circle are known, how do you determine its equation?
Use the formula (x a) 2 + (y b) 2 = r 2 to determine a circle's equation when you are aware of its radius and centre. Here, stands for the circle's centre, and is its radius. This equation is essentially a variant way of writing the general equation for a circle.
(x - h)2+ (y - k)2 = r2 is the formula for the equation of a circle, where (h, k) stands for the circle's center's coordinates and r for the radius.
We know that the general equation for a circle is ( x - h )^2 + ( y - k )^2 = r^2, where ( h, k ) is the center and r is the radius.
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Rashaad invested $94,000 in an account paying an interest rate of 3 7/8% compounded
annually. Arianna invested $94,000 in an account paying an interest rate of 4 3/8%
compounded monthly. To the nearest hundredth of a year, how much longer would it
take for Rashaad's money to triple than for Arianna's money to triple?
It would take 3.74 years for for Rashaad's money to triple than for Arianna's money to triple.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which the parameters are given as follows:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.For Rashaad, the parameters are given as follows:
r = 0.03875, n = 1.
Hence the function is given as follows:
[tex]A(t) = A(0)(1.03875)^t[/tex]
The balance triples when A(t) = 3A(0), hence:
[tex]A(t) = A(0)(1.03875)^t[/tex]
[tex]3A(0) = A(0)(1.03875)^t[/tex]
[tex](1.03875)^t = 3[/tex]
[tex]\log{(1.03875)^t} = \log{3}[/tex]
t = log(3)/log(1.03875)
t = 28.9 years.
For Arianna, the parameters are given as follows:
r = 0.04375, n = 12.
Hence the function is given as follows:
[tex]A(t) =A(0)(1.00364583)^{12t}[/tex]
The balance will triple when:
[tex]3A(0) =A(0)(1.00364583)^{12t}[/tex]
[tex](1.00364583)^{12t} = 3[/tex]
tlog((1.00364583)^12) = log(3)
t = log(3)/[log((1.00364583)^12)]
t = 25.16.
Hence the difference in time is given as follows:
28.90 - 25.16 = 3.74 years.
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asap!! :P
given g(x)=5x-5 find g(-6)
The calculation finds that by substituting '-6' for 'x' in the equation g(x)=5x-5, we find the value of g(-6) to be -35.
Explanation:The question asks us to find the value of g(-6) for function g(x)=5x-5. To do this, we substitute '-6' for 'x' in the equation. The calculation is as follows:
g(x)=5x-5 Substituting '-6' for 'x', the equation becomes g(-6)=5*(-6)-5 Multiplying -5 by -6 gives -30, so the equation becomes g(-6)= -30-5 Subtraction gives us g(-6)= -35Learn more about Function Substitution here:https://brainly.com/question/35064274
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Determine the intercepts of the line.
y + 5 = 2(x + 1)
y-intercept:
x-intercept:
The y-intercept of the given linear function y + 5 = 2(x + 1) is (0,-3) and x-intercept is (1.5,0).
What is a linear function?
A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given function,
y + 5 = 2(x + 1)
For y-intercept , x = 0
y + 5 = 2(0 + 1)
y + 5 = 2
y = 2 - 5 = - 3 so (0,-3)
For x-intercept, y = 0
0 + 5 = 2(x + 1)
5/2 = x + 1
x = 2.5 - 1 = 1.5 so (1.5,0)
Hence "The y-intercept of the given linear function y + 5 = 2(x + 1) is (0,-3) and x-intercept is (1.5,0)".
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Sketch the space curve represented by the intersection of the surfaces. Surfaces Parameter x2 + y2 + z2 = 4,x+z=2 x=1+sin t Represent the curve by a vector-valued function r(t) using the given parameter. r(t) = (1+sin t)1+Y2cos(t)1+ (1-sin)k (positive y portion) r(t) =| (1 + sin t)i+(-V2cos t)j+ (1-sin)k 、(negative y portion)
As the point moves along the helix, it traces out a three-dimensional surface in space.The space curve would look like a helix in graph.
1. First, we need to find the vector-valued function r(t) using the given parameter.
2. We can use the parameter x+z=2 to solve for the y-coordinate in terms of t:
y = √(4 − (1+sin t)2 − (1 − sin t)2).
3. We can now substitute this expression into the vector-valued function to obtain:
r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k
4. The space curve represented by the intersection of the surfaces is a helix in a graph.
The space curve represented by the intersection of the surfaces is a helix. It is a three-dimensional curve that can be described by a vector-valued function r(t) with parameter t. The vector-valued function r(t) is given by:
r(t) = (1+sin t)i+ (√(4 − (1+sin t)2 − (1 − sin t)2))j+ (1-sin)k.
The helix can be visualized as a spiral that wraps around a cylinder and is generated by a point travelling around the circumference of the cylinder at a constant speed. This can be observed by noting that the x- and z-coordinates of the vector-valued function are constant and only the y-coordinate changes over time. As the point moves along the helix, it traces out a three-dimensional surface in space.
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show that a vector space over an infinite field cannot be written as a union of finitely many proper subspaces
The proof for the statement given in question is as follows,
By analogy, if V is the set-theoretic union of n proper subspaces Wi (1in), then |F|n1.
Proof:
We can assume that the union of the other subspaces contains no Wi
Then (v + Fu)Wi= and (v + Fu) Wj (ji) ,
can only contain one vector because else Wj would contain u.
Hence
| v + Fu |=|F|≤n−1.
Corollary: Avoidance lemma for vector spaces.
Assume E is a vector space spanning an infinite field. If a subspace is contained in a finite union of subspaces, it is contained in one of them.
It should be noted that there is a similar Avoidance lemma for prime ideals in commutative rings.
A vector space (also known as a linear space) is a set whose members, known as vectors, can be added together and multiplied ("scaled") by integers known as scalars. Scalars are frequently real numbers, but they can also be complex numbers or, more broadly, members of any field.
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Let f:R→S be a surjective homomorphism of rings with identity.
(a) If R is a PID, prove that every ideal in S is principal.
(b) Show by example that S need not be an integral domain.
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
In a homomorphism, corresponding elements of two systems behave very similarly in combination with other corresponding elements. For example, let G and H be groups. The elements of G are denoted g, g′,…, and they are subject to some operation ⊕.
In algebra, a homomorphism is a structure-preserving map between two algebraic structures of the same type (such as two groups, two rings, or two vector spaces). The word homomorphism comes from the Ancient
Let f:R⇒S be a surjective homomorphism of rings with identity.
We have to find if R is a PID, prove that every ideal in S is principal.
We know that,
Let I be the ideal of S
Since f is sufficient homomorphism.
So, f⁻¹(I) is an ideal of R.
Since R is PID so ∈ r ∈ R such that
f⁻¹(I) = <r>
I = <f(r)>
Therefore,
Every ideal of S is principal when f:R⇒S be a surjective homomorphism of rings with identity.
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Advanced Algebra - please help
Answer:
Below
Step-by-step explanation:
Only the middle three are tri -nomials ( three terms)
the third one reduces to (x+ 2)^2
Answer:
3
Step-by-step explanation:
(x+2)^2
find the most general antiderivative or indefinite integral. check your answers by differentiation cos2x-sec^2x
The general anti derivative or indefinite integral of the function
cos2x - sec²x is 1/2 sin2x + tan x + C .
The given function is of the form : cos2x - sec²x
Now we will use the indefinite integral on the above expression:
∫cos2x - sec²x
This can be broken into :
∫cos2x - ∫sec²x
Now we will integrate them separately:
∫cos2x, we will use u-substitution.
Let 2x = u
Differentiation both sides we get:
2 dx = du
or, dx = 1/2 du
Hence we will use this value:
∫cos2x
= ∫cos u · 1/2du
= 1/2 ∫ cos u du
=1/2 sin u + C , where C is a constant.
Again we will do the second part of the integral:
∫sec²x
= tan x + C
Hence the required integral will be:
1/2 sin2x + tan x + C .
Now we will use differentiation to check the integral
d/dx (1/2 sin2x + tan x + C )
= d/dx (1/2 sin2x) + d/dx (tan x) + d/dx (C)
= cos 2x + sec² x
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A checkerboard is 8 squares long and 8 squares wide. The area of each square is 14 square centimeters. Estimate the perimeter of the checkerboard.
The perimeter of the checker board 118.4 cm
Area of each square = 14 sq. cm.
What is the length?
Distance is measured in length. Length has the dimension of distance in the International System of Quantities. The majority of measurement systems choose a base unit for length from which all other units are derived. The meter serves as the foundational unit of length in the International System of Units.
The square root of area is the length of one side
[tex]\text { lengthofeachsquare }=\sqrt{14}=3.7 \mathrm{~cm}[/tex]
[tex]\text { lengthofoneside }=8 * 3.7=29.6 \mathrm{~cm}[/tex]
[tex]P=4 a[/tex]
[tex]=4 * 29.6=118.4 \mathrm{~cm}[/tex]
[tex]\text { Perimeterofthecheckerboard }[/tex]
Therefor we get the perimeter of the checker board 118.4 cm
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What’s 7 1/3 - 5 1/6 ?
Pls hurry !!!
Samuel went to the grocery store and purchased cans of soup and frozen dinners.
Each can of soup has 300 mg of sodium and each frozen dinner has
450 mg
of
sodium. Samuel purchased 5 more frozen dinners than cans of soup and they all
collectively contain 6000 mg of sodium. Write a system of equations that could be
used to determine the number of cans of soup purchased and the number of frozen
dinners purchased. Define the variables that you use to write the system.
A system of equations that could be used to determine the number of cans of soup purchased and the number of frozen dinners purchased is; 300a + 450b = 6000 and a + 5 = b.
The variables x and y respectively represents cans of soup and frozen dinners and a and b represents number of cans of soup and frozen dinners.
Let cans of soup be denoted by x
Let each frozen dinner be denoted by y
Now, we are told that each can of soup has 300 mg of sodium and each frozen dinner has 450 mg. Thus;
x = 300
y = 450
It is said that Samuel purchased 5 more frozen dinners than cans of soup and they all collectively contain 6000 mg of sodium.
Let the no. of cans of soup be 'a' and no. of frozen dinner be 'b'. Thus, we will have the equation as;
ax + by = 6000
a(300) + b(450) = 6000
300a + 450b = 6000 ------(1)
We are told that Samuel purchased 5 more frozen dinners than cans of soup. This can be represented by the equation;
a + 5 = b ------(2)
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A large tank of fish from a hatchery is being delivered to a lake. The hatchery claims that the mean length of fish in the tank is 15 inches, and the standard deviation is 7 inches. A random sample of 51 fish is taken from the tank. Let x be the mean sample length of these fish. What is the probability that x is within 0.5 inch of the claimed population mean? (Round your answer to four decimal places.)
Answer: Since the sample size is large (n > 30) and the population standard deviation is known, we can use the normal distribution to approximate the sampling distribution of the mean.
The standard error of the mean is the standard deviation of the sampling distribution of the mean, and it can be calculated as follows:
standard error of the mean = standard deviation / sqrt(n)
Plugging in the given values, we get:
standard error of the mean = 7 inches / sqrt(51) = 1.17 inches
The probability that x is within 0.5 inches of the claimed population mean (15 inches) is equal to the probability that x is between 14.5 inches and 15.5 inches. We can use the normal distribution to find this probability by standardizing the range 14.5 inches to 15.5 inches and using a z-table or a calculator to find the corresponding probability.
The standardized value for 14.5 inches is (14.5 - 15) / 1.17 = -0.43, and the standardized value for 15.5 inches is (15.5 - 15) / 1.17 = 0.43.
The probability that x is between -0.43 and 0.43 is equal to the area under the standard normal curve between these two values. Using a z-table or a calculator, we can find that this probability is 0.6915.
Therefore, the probability that x is within 0.5 inches of the claimed population mean is approximately 0.6915, which is the final answer.
Average Bloxyy
Which is not an equation of the line going through (3, -6) and (1, 2)?
A. y=-4x+6
B. y+ 6 = -4(x- 3)
C. y- 1=-4(x-2)
D. y - 2 = -4(x-1)
An equation of the line going through two points (x1, y1) and (x2, y2) can be written in the form y - y1 = m(x - x1), where m is the slope of the line. The slope of the line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Plugging in the values for (x1, y1) and (x2, y2) from the problem, we get:
m = (2 - (-6)) / (1 - 3) = 8/ -2 = -4
Therefore, an equation of the line going through (3, -6) and (1, 2) is of the form y - (-6) = -4(x - 3).
Option B is of this form, so it is an equation of the line going through (3, -6) and (1, 2). The other options are not of this form, so they are not equations of the line going through (3, -6) and
PLEASE ANSWER QUICK!!
Consider the functions and f(x)=|x|-2 and g(x)=2f(x).
a. Complete the table.
b. Describe the graph of f. How does each point on the graph of f map to the corresponding point on g?
The function f(x) is an absolute function and the function g(x) will be twice the function f(x). The table is completed below.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The functions are given below.
f(x) = |x| - 2 and g(x) = 2 f(x)
The function g(x) is rewritten as,
g(x) = 2 (|x| - 2)
g(x) = 2|x| - 4
The function f(x) is an absolute function and the function g(x) will be twice the function f(x).
x f(x) = |x| - 2 g(x) = 2f(x)
-2 0 0
-1 -1 -2
0 -2 -4
1 -1 -2
2 0 0
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A table of values of a linear function is shown below.
X
y
y-intercept:
slope:
-1
-5
equation:
0
-2
1
1
Find the y-intercept and slope of the function's graph, and find the equation for the function.
11
2
4
3
7
DO
X
0/0
08
0=0
The y intercept of the graph is 1/2, slope is 1/2 and the equation is 2y = x+1
What is y intercept?The y intercept of a graph is a point where the line intersects the y-axis.
Given is the table of the values of a linear function,
Considering two coordinates, (-1, -5) and (0, -2)
We know that, the slope of a line is given by = (y₂-y₁)/(x₂-x₁)
Slope = (-2-0)/(-5+1) = 2/4 = 1/2
slope = 1/2
The equation of a line passing through two points is given by,
y-y₁ = (y₂-y₁)/(x₂-x₁)(x-x₁)
y-0 = 1/2(x+1)
y = x/2+1/2 or, 2y = x+1
For y intercept, put x = 0
y = 0/2+1/2
y = 1/2
Hence. the equation is 2y = x+1, slope = 1/2 and y intercept = 1/2
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I need help with this please help me
Two different meal combinations at a chicken restaurant have the same number of total calories.
- The first meal has 8 chicken nuggets and a large order of fries.
- The second meal has 12 chicken nuggets and a small order of fries.
- The larger order of fries contains 288.5 calories.
- The small order of fries contains 193.5 calories.
Which equation and solution can be used to determine n, the number of calories in each chicken nugget?
A 12 n-288.5=8 n-193.5 ; n=24.1
B 8 n+193.5=12 n+288.5 ; n=23.75
C 193.5+12 n=288.5+8 n ; n=24.1
D 8 n+288.5=12 n+193.5 ; n=23.75
The equation which can be used to determine n, the number of calories in each chicken nugget would be 193.5+12 n=288.5+8n
And n = 24.1
Option (C) is correct.
What is a linear equation?
A linear equation is an equation that describes a straight line. Linear equations have the form y = mx + b, where x and y are variables and m and b are constants. The constant m is the slope of the line, and the constant b is the y-intercept, which is the point where the line crosses the y-axis.
To derive this equation, we can start with the fact that the two meals have the same number of total calories. This means that the number of calories in the first meal is equal to the number of calories in the second meal. We can represent this relationship with the equation:
8 nuggets * calories/nugget + 193.5 calories = 12 nuggets * calories/nugget + 288.5 calories
We can then rearrange the terms on the left and right sides of the equation to get the equation in the form given in option C:
193.5 + 12 n = 288.5 + 8 n
Finally, we can solve this equation for n by subtracting 8n from both sides and then dividing both sides by 4:
n = (193.5 - 288.5) / 4 = (-95) / 4 = -23.75
Therefore, the number of calories in each chicken nugget is 24.1 calories.
Hence, option (C) is correct.
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12) Name three points collinear with point A.
Answer:
c, e, f
Step-by-step explanation:
Collibear means lying on or passing through the same straight line.
The sum of an infinite geometric series with first term a and common ratio r < 1 is given by The sum of a given a/1-r infinite geometric series is 300, and the common
ratio is 0.1. What is the second term of this series?
The second term of the series will be 27.
What is a Geometric progression?Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio. This progression is also known as a geometric sequence of numbers that follow a pattern.
Sum to infinity = a/1-r
where s = 300
r = 0.1
a = 300 (1 - 0.1)
a = 300 (0.9)
a = 270
The second term of the progression will be = ar
Second term = 270 x 0.1
Second term = 27
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1. Solve the following for the variable indicated:
a. x²=36
b. x²=√50
c. x²=√100
Consider the function f (same as in the previous problem) defined on the interval [0, 4) as follows, F(x) = { 2/2 x. x € [0,2]. 2, x € [2, 4]Find the coefficients Cn of the eigenfunction expansion of function ff(x) = Σ[infinity], n=1 cnyn(x), where y... for n = 1,2,3,... are the unit eigenfunctions of the Regular Sturm-Liouville system - y^n = ꟾλy, y’(O) = 0, y(4) = 0Note: Label your eigenfunctions so the eigenfunction for the lowest eigenvalue corresponds ton = 1. Therefore, use 2n – 1 instead of 2n +1.C= ___
Coefficient Cn is determined by Cn = 1/2 ∫[0,2] (x+2)yn(x) dx
To find the coefficients Cn of the eigenfunction expansion of a function f(x), f(x) must be expanded with the eigenfunction yn(x). The expansion of f(x) with respect to the eigenfunction yn(x) is given by
f(x) = Σ[∞], n=1 cnyn(x)
To find the coefficient cn, we need to compute the dot product of f(x) and yn(x).
cn = (f,yn) = ∫[0,4]f(x)yn(x)dx
Since the eigenfunctions yn(x) are orthonormal, the scalar product is given by
cn = ∫[0,4]f(x)yn(x)dx = ∫[0,2]f(x)yn(x)dx + ∫[2,4]f(x)yn(x)dx
Since f(x) = 2/2 x for x in [0,2] and f(x) = 2 for x in [2,4], compute the coefficient cn as I can do it.
cn = ∫[0,2](2/2x)yn(x)dx + ∫[2,4](2)yn(x)dx
= ∫[0,2]xyn(x)dx + ∫[2,4]2yn(x)dx
= 1/2 ∫[0,2] (xyn(x) + 2yn(x)) dx
= 1/2 ∫[0,2] (x+2)yn(x) dx
Therefore, the coefficient Cn is given by
Cn = 1/2 ∫[0,2] (x+2)yn(x) dx
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If >p and >Q are complementary angles m>p = 7x +3, and m>q= 16x -5, find m>p
Answer:
m<P = 31°
Step-by-step explanation:
Use this symbol < for angle, not <.
<P and <Q are complementary.
That means that their measures add to 90°.
m<P + m<Q = 90°
Now we substitute 7x + 3 for m<P and 16x - 5 for m<Q.
7x + 3 + 16x - 5 = 90
Solve for x.
23x - 2 = 90
23x = 92
x = 4
m<P = 7x + 3 = 7 × 4 + 3 = 31
Answer: 31°
