Based on the information, we can see from the line plots that Bus 14 tends to have longer travel times than Bus 18 for most of the data points, except for a few outliers.
How to explain the dataIn terms of travel time, Bus 14 and Bus 18 each have a median of 16 minutes. As such, it cannot be inferred from this information alone which mode of transportation tends to arrive more rapidly.
Nevertheless, the line plots reveal that Bus 14's journey takes slightly longer than Bus 18's for most of the data points, except for a few outliers.
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How do i solve for x?
Answer:
78° + 95° + (2x + 115)° + 72° = 360°
(2x + 360)° = 360°, so x = 0.
In a recent year (365 days), a hospital had 5742 births.
a. Find the mean number of births per day.
b. Find the probability that in a single day, there are 18 births.
c. Find the probability that in a single day, there are no births. Would 0 births in a single day be a significantly low number of births?
a. The mean number of births per day is 15.7.
(Round to one decimal place as needed.)
b. The probability that, in a day, there are 18 births is 0.07970.
(Do not round until the final answer. Then round to four decimal places as needed.)
c. The probability that, in a day, there are no births is
(Round to four decimal places as needed.)
a) 15.7
b) 0.07970
c) Having 0 births in a single day would be a significantly low number of births, as the probability is essentially 0.
We have,
a.
To find the mean number of births per day, you need to divide the total number of births (5742) by the number of days in a year (365).
Mean number of births per day = 5742 / 365 = 15.7 births per day (rounded to one decimal place).
b.
To find the probability of having 18 births in a single day, you can use the Poisson probability formula:
P(X = k) = (e^{-λ} x λ^k) / k!
Where λ (lambda) is the mean number of births per day (15.7), k is the number of births we're looking for (18), and e is the base of the natural logarithm (approximately 2.718).
P(X = 18) = (e^(-15.7) x 15.7^18) / 18!
P(X = 18) = (2.718^(-15.7) x 15.7^18) / 18!
P(X = 18) = 0.07970 (rounded to five decimal places)
c.
To find the probability of having no births in a single day, use the same Poisson probability formula with k = 0:
P(X=0) = (e^(-15.7) * 15.7^0) / 0!
P(X=0) = (2.718^(-15.7) * 1) / 1
P(X=0) = 0 (rounded to four decimal places)
Having 0 births in a single day would be a significantly low number of births, as the probability is essentially 0.
Thus,
a) 15.7
b) 0.07970
c) Having 0 births in a single day would be a significantly low number of births, as the probability is essentially 0.
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Determine the roots of each of the following quadratic equations using the factorisation method (b) x^2-10+16=0
(e) 2x^2+3x-9=0
(h) x^-5x=0
Roots of a quadratic equation using the factorisation method, we need to find two numbers that multiply to the constant term of the equation and add up to the coefficient of the linear term. Then, we can use these two numbers to factor the quadratic expression and solve for the roots.
a) For the quadratic equation x^2 - 10x + 16 = 0, we need to find two numbers that multiply to 16 and add up to -10. These numbers are -2 and -8, so we can write the quadratic as (x - 2)(x - 8) = 0. Setting each factor equal to zero, we get x - 2 = 0 and x - 8 = 0, which give us the roots x = 2 and x = 8.
b) For the quadratic equation 2x^2 + 3x - 9 = 0, we need to find two numbers that multiply to -18 (since 2*(-9) = -18) and add up to 3. These numbers are 6 and -3, so we can write the quadratic as 2x^2 + 6x - 9x - 9 = 0. Factoring by grouping, we get 2x(x + 3) - 9(x + 3) = 0, which simplifies to (2x - 9)(x + 3) = 0. Setting each factor equal to zero, we get 2x - 9 = 0 and x + 3 = 0, which give us the roots x = 9/2 and x = -3.
c) For the quadratic equation x^2 - 5x = 0, we can factor out an x to get x(x - 5) = 0. Setting each factor equal to zero, we get x = 0 and x - 5 = 0, which give us the roots x = 0 and x = 5.
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abouth wed of woy and liontin
motaslim Spod
EVED or 1968
If v varies directly with g, and v = 36 when g = 4. Find v when g = 11.
Approximate the following integral using the Composite Simpson Rule with n=4, find a bound for the error using error formula and compare this to the actual error: ∫10.5x4 dx.
The actual error is:
|4194 - 4787.9476| = 593.9476
Since the bound for the error is 0.371, which is much smaller than the actual error of 593.9476, we can say that the Composite Simpson Rule with n=4 provides a very good approximation to the integral.
Sure! We can approximate the integral ∫10.5x4 dx using the Composite Simpson Rule with n=4.
First, let's split the interval [1,4] into 4 subintervals of equal width:
h = (4-1)/4 = 0.75
x0 = 1, x1 = 1.75, x2 = 2.5, x3 = 3.25, x4 = 4
Next, we need to evaluate the function at the endpoints and midpoints of each subinterval:
f(x0) = f(1) = 10.5(1)^4 = 10.5
f(x1) = f(1.75) = 10.5(1.75)^4 = 100.2842
f(x2) = f(2.5) = 10.5(2.5)^4 = 528.125
f(x3) = f(3.25) = 10.5(3.25)^4 = 1841.7969
f(x4) = f(4) = 10.5(4)^4 = 3360
Now, we can apply the Composite Simpson Rule formula:
∫10.5x4 dx ≈ h/3 [f(x0) + 4f(x1) + 2f(x2) + 4f(x3) + f(x4)]
≈ 0.75/3 [10.5 + 4(100.2842) + 2(528.125) + 4(1841.7969) + 3360]
≈ 4787.9476
To find a bound for the error using the error formula, we can use the following formula:
|E| ≤ K*h^4*(b-a)/180
where K is a constant, h is the width of each subinterval, and (b-a) is the length of the interval.
Since f''''(x) = 840, we can use K = 840.
|E| ≤ 840*(0.75)^4*(4-1)/180
≈ 0.371
To compare this to the actual error, we can find the exact value of the integral using the antiderivative:
∫10.5x4 dx = 10.5(1/5)x^5 + C
evaluated from x=1 to x=4:
= 10.5(1/5)(4^5 - 1^5)
= 4194
The actual error is:
|4194 - 4787.9476| = 593.9476
Since the bound for the error is 0.371, which is much smaller than the actual error of 593.9476, we can say that the Composite Simpson Rule with n=4 provides a very good approximation to the integral.
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Kareem is married with 1 child and files taxes jointly with his wife. Their adjusted gross income is 92,600. Find their taxable income. The standard deduction is 12,600, and the amount of a personal exemption is 4,050.
A: 80,000
B: 67,850
C: 63,800
D: 76,400
Answer:
First, we need to calculate the total exemptions for Kareem, his wife, and their child:
Total exemptions = 3 x 4,050 = 12,150
Next, we subtract the standard deduction and exemptions from their adjusted gross income to find their taxable income:
Taxable income = 92,600 - 12,600 - 12,150 = 67,850
Therefore, the correct answer is (B) 67,850.
Step-by-step explanation:
Branliest please
Write the general form equation for the circle shown.
Check the picture below.
so the circle has a radius of 3 and a center at (-2 , 1)
[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-2}{h}~~,~~\underset{1}{k})}\qquad \stackrel{radius}{\underset{3}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-2) ~~ )^2 ~~ + ~~ ( ~~ y-1 ~~ )^2~~ = ~~3^2\implies (x+2)^2 + (y-1)^2 = 9[/tex]
3. Let C = { v, w, x,y,z }.
a).What is the cardinality of C? What is the
cardinality of P(C)?
b) Draw a tree showing all possible strings of letters
of length 5 or less starting with the letter z. What
is the cardinality of the set M = {all strings of
length 5 or less with letters from C}?
c) Sketch a tree showing all possible strings (of any
length). What is the cardinality of the set K= {all
strings using letters from C}?
a) there are 32 possible subsets of C.
b)The cardinality of set M is the sum of these numbers, which is 781.
C) there are an infinite number of possible strings, the cardinality of set K, which contains all possible strings using letters from C, is also infinite.
a) The cardinality of set C is 5, as there are 5 distinct elements in the set. The cardinality of the power set of C, denoted as P(C), is 2^5 = 32, as there are 32 possible subsets of C.
b) A tree showing all possible strings of letters of length 5 or less starting with the letter z would look like:
z
├── v
│ ├── v
│ ├── w
│ ├── x
│ └── y
├── w
│ ├── v
│ ├── w
│ ├── x
│ └── y
├── x
│ ├── v
│ ├── w
│ ├── x
│ └── y
├── y
│ ├── v
│ ├── w
│ ├── x
│ └── y
└── z
├── v
├── w
├── x
└── y
The cardinality of set M, which contains all possible strings of length 5 or less with letters from C, is equal to the sum of the cardinalities of all sets of strings of each length. Thus,
Set of strings Number of strings
Length 1 1
Length 2 5
Length 3 5^2 = 25
Length 4 5^3 = 125
Length 5 5^4 = 625
The cardinality of set M is the sum of these numbers, which is 1 + 5 + 25 + 125 + 625 = 781.
c) A tree showing all possible strings of any length would have an infinite number of branches. Each node in the tree would represent a different string, and the branches emanating from each node would represent the next letter that could be added to the string. Since there are an infinite number of possible strings, the cardinality of set K, which contains all possible strings using letters from C, is also infinite.
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god filled his gas tanker with 19/5/9 tank of gas if he uses 1 5/6 gallons of gas each day after how many days will he need to refill his tank
It will take God approximately 32 days to use up all the gas in his tanker and need a refill.
If God filled his gas tanker with 19/5/9 tank of gas and uses 1 5/6 gallons of gas each day, we can calculate how many days it will take for him to need a refill.
First, we need to convert the mixed number 19/5/9 to an improper fraction:
19/5/9 = (19 * 9 + 5) / 9 = 176/9
So God has 176/9 tanks of gas in his tanker.
Next, we can calculate how much gas God uses each day:
1 5/6 = (6 * 1 + 5) / 6 = 11/6
So God uses 11/6 gallons of gas each day.
To find out how many days it will take for God to need a refill, we can divide the amount of gas in his tanker by the amount of gas he uses each day:
(176/9) / (11/6) = (176/9) * (6/11) = 32
Therefore, it will take God approximately 32 days to use up all the gas in his tanker and need a refill.
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Find the maximum distance between the point (1, 3) and a point on the circle of radius 4 centered at the origin. Hint: the maximizing distance should be at least 4 and the function has critical points every increment of pi.
To find the maximum distance between the point (1,3) and a point on the circle of radius 4 centered at the origin, we can use the distance formula. Let (x,y) be a point on the circle, then the distance between (1,3) and (x,y) is given by:
d = √((x-1)^2 + (y-3)^2)
Since the point (x,y) lies on the circle of radius 4 centered at the origin, we have:
x^2 + y^2 = 16
We can solve for y in terms of x:
y = ±√(16 - x^2)
Substituting into the distance formula, we get:
d = √((x-1)^2 + (±√(16 - x^2) - 3)^2)
Simplifying and squaring, we get:
d^2 = (x-1)^2 + (±√(16 - x^2) - 3)^2
d^2 = x^2 - 2x + 1 + (16 - x^2 - 6√(16 - x^2) + 9) (or d^2 = x^2 - 2x + 1 + (16 - x^2 + 6√(16 - x^2) + 9))
d^2 = -x^2 - 2x + 26 ± 6√(16 - x^2)
To maximize the distance, we want to maximize d^2. Note that the maximizing distance should be at least 4, which means that we only need to consider the positive root of d^2. The critical points of d^2 occur when the derivative is zero, so we differentiate with respect to x:
d(d^2)/dx = -2x - 2(±3x/√(16 - x^2))
Setting this equal to zero, we get:
x = ±4/√5, ±2√2/√5, 0
Note that x = 0 corresponds to the point (0,4) on the circle, which has distance 5 from (1,3), so it is not a critical point. The other critical points correspond to the points where the circle intersects the x-axis and the y-axis. Evaluating d^2 at these critical points, we get:
d^2 = 18 ± 6√6
The maximum distance is therefore √(18 + 6√6), which occurs when x = ±4/√5.
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A quadratic equation has zeros at -6 and 2. Find standard form
The quadratic equation with zeros at -6 and 2 is y² + 4y - 12 = 0. This is in standard form, which is ax² + bx + c = 0, with a = 1, b = 4, and c = -12.
To find the quadratic equation with zeros at -6 and 2, we can start by using the fact that if a quadratic equation has roots x₁ and x₂, then it can be written in the form
(y - x₁)(y - x₂) = 0
where y is the variable in the quadratic equation.
Substituting the given values of the zeros, we get
(y - (-6))(y - 2) = 0
Simplifying this expression, we get
(y + 6)(y - 2) = 0
Expanding this expression, we get
y² - 2y + 6y - 12 = 0
Simplifying this expression further, we get
y² + 4y - 12 = 0
So the quadratic equation with zeros at -6 and 2 is
y² + 4y - 12 = 0
This is the standard form of a quadratic equation, which is
ax² + bx + c = 0
where a, b, and c are constants. In this case, a = 1, b = 4, and c = -12.
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help asap plsss solve trig problem
Answer:
Set your calculator to degree mode.
cos(48°) = y/35
y = 35cos(48°)
tan(20°) = x / 35cos(48°)
x = 35cos(48°)tan(20°) = 8.5 inches
Answer:
8.5 in
Step-by-step explanation:
Find height, h, of the triangle:
cos48 = h/35
h = cos48(35) = 23.42
tan20 = x/23.42
x = tan20(23.42) = 8.524 ≈ 8.5 in
The balance on a credit card, that charges a 10.5%
APR interest rate, over a 1 month period is given in
the following table:
Days 1-3: $200 (initial balance)
Days 4-20: $300 ($100 purchase)
Days 21-30: $150 ($150 payment)
What is the finance charge, on the average daily
balance, for this card over this 1 month period?
finance charge = $ [?]
Round to the nearest hundredth.
Based on the average daily balance, the finance charge for this credit card that charges 10.5% APR is $2.10.
What is the finance charge?The finance charge consists of the interest and other fees that lenders charge borrowers.
One of the methods for computing the finance charge is the average daily balance, which takes the sum of the daily balances and divides by the number of days in the billing cycle.
APR interest rate = 10.5%
Monthly period days = 30
Days 1-3: $200 (initial balance) 3 days $600 ($200 x 3)
Days 4-20: $300 ($100 purchase) 17 days $5,100 ($300 x 17)
Days 21-30: $150 ($150 payment) 10 days $1,500 ($150 x 10)
Total balances = $7,200
Average daily balance = $240 ($7,200 ÷ 30)
Finance charge = $2.10 ($240 x 10.5% x 30/360)
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Find the surface area of the prism.
5 yd
8 yd
12 yd
13 yd
The surface area of the prism is determined as 300 yd².
What is the surface area of the prism?
The surface area of the prism is calculated as follows;
S.A = bh + (s₁ + s₂ + s₃)L
where;
b is the base of the triangleh is the height of the triangles₁ is the first triangular faces₂ is the second triangular faces₃ is the third triangular faceL is the length of the prismThe surface area of the prism is calculated as;
S.A = 5 (12) + (5 + 12 + 13) x 8
S.A = 60 yd² + 240 yd²
S.A = 300 yd²
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find the center and radius of:
x^2+y^2+2x+6y=26
Answer:
center = -1, -3
radius = 6
Step-by-step explanation:
x² + y² + 2x + 6y = 26
x² + 2x + y² +6y = 26
equation of a circle is,
(x - h)² + (y - k)² = r²
where center of a circle is (h,k)
radius = r
x² + 2x + y² + 6y = 26
finding the middle point for mid term breaking of the equations,
(2/2)² = 1
(6/2)² = 9
x² + 2x + 1 + y² + 6y + 9 = 26 + 1 +9
to balance the equation we have to add the midpoints at both sides,
thus we have equation of a circle,
(x + 1)² + (y + 3)² = 36
so,
centre of a circle = -1, -3
radius = 6
Let f be defined as f(x)= (x-2)(x+3)
1- Expand the expression to make sure that it is a function of the second degree.
2- Complete the table of values with the calculator:
x -4 -3 -2 -1 0 1 2 3
y=x² + x -6
3- At what points does the representative curve of f intersect the axes of the reference frame?
4- Does f have a minimum or a maximum? Give its value using a graphing calculator.
graphing calculator.
5- Draw the parabola on [-4 ;3 ]
The expression to make sure that it is a function of the second degree is x² + x - 6
What is the expression?An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator
When the expression is expanded, it can be represented by f(x) = (x-2)(x+3), which further simplifies to x^2 + x(-2+3) - 2(3) and ultimately results in x^2 + x - 6. Evidently, the highest power of x within the expression is 2, indicating that it's a second-degree function.
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Bilquis decides to estimate the volume of a coffee cup by modeling it as a right cylinder. She measures its height as 8.5 cm and its radius as 3 cm. Find the volume of the cup in cubic centimeters. Round your answer to the nearest tenth if necessary.
The coffee cup has a volume of around 240.3 cubic centimeters.
The volume of a cylinder is given by the formula
V = πr²h, where r is the radius and h is the height.
Substituting the given values, we have:
V = π(3²)(8.5)
V = 240.331 cubic centimeters (rounded to the nearest tenth)
Therefore, the volume of the coffee cup is approximately 240.3 cubic centimeters.
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12×67=
24×87=
88×88+45=
34+78×23=
66÷4×87=
Answer:
1, 768
2, 2088
3, 7789
4, 1828
5, 1435.
Susan us flying a kite behind her house. She drops her string holder, and the kite get s caught in the top of a tree.
If the string makes 44 degree angle with the ground, and the holder is 90 feet from the base of the tree, how tall is the tree, rounded to the nearest whole foot.
show all work
Answer:
87 feet.
Step-by-step explanation:
To solve the problem, we can use the tangent function, which relates the opposite side of a right triangle (the height of the tree in this case) to the adjacent side (the horizontal distance from the base of the tree to the point directly below the kite) through the angle between them (44 degrees):
tan(44) = height / distance
We know the angle and the distance (90 feet), so we can solve for the height:
height = distance * tan(44)
height = 90 * tan(44)
The value of tan(44) is approximately 0.9656887, which means that if we multiply it by 90, we get:
90 * tan(44) = 90 * 0.9656887
Using a calculator, we get:
90 * 0.9656887 = 86.908983
However, this is not the final answer, because we were asked to round to the nearest whole foot. Since 86.908983 is closer to 87 than to 86, we round up to 87. Therefore, the approximate height of the tree is 87 feet.
In each of the following scenarios, we consider the distribution of a quantity along an axis. a. Suppose that the function c(x) = 200 + 100e0.13 models the density of traffic on a straight road, measured in cars per mile, where x is number of miles east of a major interchange, and consider the definite integral Só (200 + 100e-0.12) dr. i. What are the units on the product c(x) · Ax? ii. What are the units on the definite integral and its Riemann sum approximation given by 1 cle *= c(x) dx = c(x;)Ax? 2=1 iii. Evaluate the definite integral ſ c(x) dx = fó (200 + 100e -0.13) de and write one sentence to explain the meaning of the value you find. b. On a 6 foot long shelf filled with books, the function B models the distribution of the weight of the books, in pounds per inch, where x is the number of inches from the left end of the bookshelf. Let B(x) be given by the rule B(x) = 0.5 + (2+1)2 i. What are the units on the product B(x) · Ax? ii. What are the units on the definite integral and its Riemann sum approximation given by 36 B(x)dt = B(;)Az? 12 21 ii. Evaluate the definite integral f," B(z) dx = fo? (0.5+ (213) de + (x+1) and write one sentence to explain the meaning of the value you find.
In scenario a, the function c(x) represents the density of traffic on a straight road, measured in cars per mile, where x is the number of miles east of a major interchange. The product c(x) · Ax has units of cars, as it represents the number of cars in a certain segment of the road. The definite integral ∫ c(x) dx and its Riemann sum approximation given by 1/n ∑ c(xi) · Δx have units of cars per mile, as they represent the average density of traffic over a certain distance. When evaluating the definite integral ∫ c(x) dx, we get a value that represents the total number of cars on the road between two given points.
In scenario b, the function B(x) represents the distribution of the weight of books on a shelf, in pounds per inch, where x is the number of inches from the left end of the shelf. The product B(x) · Ax has units of pounds, as it represents the weight of books in a certain segment of the shelf. The definite integral ∫ B(x) dx and its Riemann sum approximation given by 1/n ∑ B(xi) · Δx have units of pounds, as they represent the total weight of books on the shelf. When evaluating the definite integral ∫ B(x) dx, we get a value that represents the total weight of books on the shelf.
a. i. The units on the product c(x) · Δx are cars per mile (from c(x)) multiplied by miles (from Δx), resulting in cars.
a. ii. The units on the definite integral and its Riemann sum approximation are the same as the units on the product c(x) · Δx, which are cars.
a. iii. To evaluate the definite integral, we have:
∫(200 + 100e^(-0.12x)) dx
Using the integral rules, we get:
[200x - (100/0.12)e^(-0.12x)] (evaluate this from 0 to a specific value to find the total cars between 0 and that value)
The meaning of the value is the total number of cars on the road between 0 miles and the specified value of x miles east of the major interchange.
b. i. The units on the product B(x) · Δx are pounds per inch (from B(x)) multiplied by inches (from Δx), resulting in pounds.
b. ii. The units on the definite integral and its Riemann sum approximation are the same as the units on the product B(x) · Δx, which are pounds.
b. iii. To evaluate the definite integral, we have:
∫(0.5 + (x+1)^2) dx
Using the integral rules, we get:
[0.5x + (1/3)(x+1)^3] (evaluate this from 0 to 72 to find the total weight of books on the shelf)
The meaning of the value is the total weight of the books on the 6-foot-long shelf.
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#4 Which series of transformations correctly show that △CAT≅△DOG?
Select all that apply.
The series of transformations correctly show that △CAT≅△DOG is rotate ACAT 180° about the origin, the correct option is A.
We are given that;
△CAT≅△DOG
Now,
To show that ACAT and ADOG are congruent, we need to find a sequence of rigid transformations that maps one onto the other.
One possible sequence is:
This will map A to D, C to O, A to G, and T to O.
Translate the image 2 units left. This will align the image with ADOG.
Therefore, by transformation the answer will be rotate ACAT 180° about the origin.
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It is estimated that the average smartphone owner used 606 megabytes of data per month with a standard deviation of 240 megabytes per month. A random sample of 64 smartphone users was selected a. What is the mean of the sample mean, my? b. What is the standard deviation (standard error) of the sample mean? C. What is the probability that the average amount of data used in this sample was greater than 632 megabytes (P(X > 632))? Show your work! >
Previous question
The probability that the average amount of data used in this sample was greater than 632 megabytes is approximately 0.1922 or 19.22%.
a. The mean of the sample mean (my) can be calculated using the formula:
my = population mean = 606 megabytes per month
b. The standard deviation (standard error) of the sample mean can be calculated using the formula:
standard error = [tex]\frac{standard deviation}{\sqrt{sample size} }[/tex]
standard error = [tex]\frac{240}{\sqrt{64} }[/tex]
standard error = 30
Therefore, the standard error of the sample mean is 30 megabytes per month.
c. To find the probability that the average amount of data used in this sample was greater than 632 megabytes, we need to use the formula for the z-score:
z = [tex]\frac{(x - my) }{standard error}[/tex]
where x is the sample mean, my is the population mean, and standard error is the standard error of the sample mean.
z = [tex]\frac{(632 - 606) }{30}[/tex]
z = 0.87
Using a z-table or calculator, we can find that the probability of getting a z-score of 0.87 or higher is 0.1922. Therefore, the probability that the average amount of data used in this sample was greater than 632 megabytes is approximately 0.1922 or 19.22%.
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Imagine you bought 100 shares of stock three years ago and are selling it today. Select a company and research its stock prices. You can start with websites like Nasdaq and Fidelity. Determine the stock's price three years ago, or the purchase price, and its price today, or the selling price.
Part Two–Determine the Real Return
Calculate the real return of your stock investment using the following information:
Purchase price of 100 shares of stock
Selling price of 100 shares of stock
10% tax rate
3% inflation rate
2% administrative fee on the selling price of the stock
Part Three–Evaluate
Analyze your research and calculations, and answer the following questions:
What company did you select to buy stock in? Why did you select the company?
Consider the real return of the stock investment. Do you consider it a wise investment? Why or why not?
1. I imagine buying 100 shares of Amazon.com Inc. on January 3, 2020, when the stock price was $93.75, investing $9,375.
Today, October 31, 2022, the stock price of Amazon.com Inc. is $102.44.
2. The real return on my investment in Amazon.com Inc was a net loss of 7.12% or $667.60.
3. The company I selected to buy its stock three years ago was Amazon.com Inc.
4. I decided on Amazon.com Inc., hoping to earn spectacular returns since it is a multinational technology company.
5. When I consider the actual return on the stock investment in Amazon.com Inc., I think it was an unwise investment.
6. The investment returned a negative real value because I realized less than I initially invested; I actually lost about $667.60 overall.
What is the stock investment?Stock investment is the purchase of shares for an ownership interest in a publicly-listed company.
The investor makes the investment with the hope that the investee will grow and perform well over some period, enabling the investor to earn some real returns (in the form of dividends and capital appreciation).
Purchase of 100 shares Jan. 3, 2020 = $9,375 (100 x $93.75)
Sales of 100 shares Oct. 31, 2022 = $10,244 (100 x $102.44)
Tax (10%) = $1,024.40 ($10,244 x 10%)
Inflation (3%) = $307.32 ($10,244 x 3%)
Administration fee on sales (2%) = $204.88 ($10,244 x 2%)
Real Returns in dollars = $8,707.40 ($10,244 - $1,024.40 - $307.32 - $204.88)
Loss on returns = $667.60 ($8,707.40 - $9,375)
Loss percentage = 7.12% ($667.60/$9,375 x 100)
Unfortunately, Amazon.com Inc. did not pay any dividends during the period of my investment, and I really lost funds to taxes, inflation, and administration fees when I sold it.
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Suppose y=f(x) is continuous for all real numbers. Use the sign chart for the first derivative to answer the question that follows: f'() 0 +++ 0 1 Determine which of the following best describes what must be true about absolute extrema on the interval [0,00) There is an absolute maximum at x-1 There is an absolute minimum at x--1 There is an absolute maximum at x=-1 There is an absolute minimum at x 1
Based on the provided information, f'(x) changes from positive to negative at x=1, indicating that the function has a local maximum at this point.
Since y=f(x) is continuous for all real numbers and the interval is [0, ∞), there is an absolute maximum at x=1. The best description of the absolute extrema is: "There is an absolute maximum at x=1." Based on the sign chart for the first derivative, we know that the function is increasing from negative infinity to x=-1, and then decreasing from x=-1 to positive infinity. This means that there is an absolute maximum at x=-1 since the function is increasing to that point and decreasing after it. Therefore, the correct statement is: "There is an absolute maximum at x=-1."
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"Evaluate the following continuous-time convolution integrals
(k) y(t)=e-yt u (t) x (u(t+2)-u(t))
This question is in the Signals and Sysytems 2nd edition."
The continuous-time convolution integral of y(t) is [tex]$y(t) = k e^{-yt} u(t) * (u(t+2)-u(t))$[/tex].
To evaluate this convolution integral, we first need to express the integrand as a piecewise function. Since u(t) is 1 for t >= 0 and 0 for t < 0, we can rewrite u(t+2)-u(t) as a piecewise function:
u(t+2)-u(t) =
1, 0 <= t < 2
0, t >= 2
0, t < 0
Now we can evaluate the convolution integral using the definition:
y(t) = ∫[tex]_0^t[/tex] x(τ)h(t-τ)dτ
Substituting the given functions for x(t) and h(t) and simplifying using the piecewise function for u(t+2)-u(t), we get:
y(t) = k ∫[tex]_0^t[/tex] [tex]e^}(-yt)}[/tex]dτ = [tex]k[-(1/y)e^{(-yt)}]_0^t = k(1 - e^{(-yt)})/y[/tex], t >= 0
Therefore, the continuous-time convolution integral of y(t) is [tex]$y(t) = k e^{-yt} u(t) * (u(t+2)-u(t))$[/tex] for t >= 0.
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find vertices of:
(x-2)^2/16-(y-1)^2/4=1
show work pls!!
We can see here that the vertices will be:
(6, 1)(-2, 1)What is vertex?The vertex, in geometry, is the intersection of two or more lines, curves, or edges. It can also refer to the vertex of a parabola, which is where a function reaches its highest or lowest value.
We can see here that the equation of the hyperbola is seen in standard form. It is known that the center of the hyperbola is at (h, k) is (2, 1).
The distance between the center and vertices = a
where a² = coefficient of the positive term
So we see that a² = 16
a = 4.
Also, the distance between the center and co-vertices = b
where b² = 4
b = 2.
Thus,
Vertex 1 = (2 + 4, 1) = (6, 1)
Vertex 2 = (2 - 4, 1) = (-2, 1).
Therefore, the vertices are:
(6, 1) and (-2, 1).
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Express the function graphed on the axes below as a piecewise function
please help
The function graphed on the axes above should be expressed as a piecewise function as follows;
f(x) = -3x - 8 {x ≤ -2}
= 6x - 17 {x > 3}
How to determine the piecewise function?In order to determine the piecewise function, we would determine an equation that represent each of line shown on the graph. Therefore, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (4 + 2)/(-4 + 2)
Slope (m) = 6/-2
Slope (m) = -3.
At data point (-2, -2) and a slope of -3, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 2 = -3(x + 2)
y = -3x - 8
For the second line, we have:
Slope (m) = (7 - 1)/(4 - 3)
Slope (m) = 6/1
Slope (m) = 6.
At data point (3, 1) and a slope of 6, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 1 = 6(x - 3)
y = 6x - 17
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What is 8. 19 divided by 4. 2 and show your work
8.19 divided by 4.2 is approximately equal to 1.94047624, which can be rounded to 1.94 (to two decimal places).
In mathematics, division is a basic arithmetic operation that involves separating a quantity or a number into equal parts or groups. The division operation is denoted by the symbol "/", or in some cases, the symbol "÷"
When we divide one number by another, we are essentially finding out how many times the second number "fits into" the first number
To divide 8.19 by 4.2, we can use long division as follows:
1.9 4 0 4 7 6 2 4 3 3 3...
--------------------------
4.2| 8.1 9 0 0 0 0 0 0 0 0 0
8 4
----
2 6 0
2 5 2
-----
8 0 0
7 1 4
-----
8 5 0
8 4 8
-----
2 0 0
1 6 8
-----
3 1 0
2 5 2
-----
5 8
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3. Isaac paid $119. 70 for a racket, a bag and a pair of shoes. A pair of shoes cost three times as much as a bag. The racket cost twice as much as the bag. How much did Isaac pay for the racket?
Isaac pay for the cost of racket is 39.9.
The cost of a pair of shoes is three times the cost of a bag, so we can write:
Cost of shoes = 3b
Similarly, the cost of the racket is twice the cost of the bag, so we can write:
Cost of racket = 2b
Now we can use the given information to set up an equation:
Cost of racket + Cost of bag + Cost of shoes = $119.70
Substituting the expressions we found above, we get:
2b + b + 3b = $119.70
Simplifying the equation:
6b = $119.70
Dividing both sides by 6:
b = $19.95
So the cost of the bag is $19.95.
We can use this to find the costs of the shoes and racket:
Cost of shoes = 3b = 3($19.95) = $59.85
Cost of racket = 2b = 2($19.95) = $39.90
Therefore, Isaac paid $39.90 for the racket.
A cost is an expenditure required to produce or sell a product or get an asset ready for normal use. In other words, it's the amount paid to manufacture a product, purchase inventory, sell merchandise, or get equipment ready to use in a business process.
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2. Show that the following limits do not exist: (i) lim x→0(1/x²); (x> 0) (ii) lim x→0 (1/√x²) ;(x>0)
(iii) lim x→0(x+(x)) (iv) lim x→0 sin (1/x)
The left-hand limit and the right-hand limit both do not exist, the limit of sin(1/x) as x approaches 0 does not exist.
(i) To show that the limit of (1/x^2) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or they both go to infinity. Let's consider the right-hand limit:
lim x→0+ (1/x^2) = +∞ (the limit goes to infinity)
Now let's consider the left-hand limit:
lim x→0- (1/x^2) = +∞ (the limit goes to infinity)
Since the left-hand limit and the right-hand limit are both infinite and not equal, the limit does not exist.
(ii) To show that the limit of (1/√x^2) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or one or both of them goes to infinity. Let's consider the right-hand limit:
lim x→0+ (1/√x^2) = lim x→0+ (1/|x|) = +∞ (the limit goes to infinity)
Now let's consider the left-hand limit:
lim x→0- (1/√x^2) = lim x→0- (1/|x|) = -∞ (the limit goes to negative infinity)
Since the left-hand limit and the right-hand limit are not equal, the limit does not exist.
(iii) To show that the limit of (x+(x)) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or one or both of them goes to infinity. Let's consider the right-hand limit:
lim x→0+ (x+(x)) = 0+0 = 0
Now let's consider the left-hand limit:
lim x→0- (x+(x)) = 0+0 = 0
Since the left-hand limit and the right-hand limit are equal, the limit exists and equals 0.
(iv) To show that the limit of sin(1/x) as x approaches 0 does not exist, we need to show that the limit from the left-hand side and the right-hand side are not equal or one or both of them goes to infinity. Let's consider the right-hand limit:
lim x→0+ sin(1/x) does not exist
This is because sin(1/x) oscillates infinitely many times between -1 and 1 as x approaches 0 from the right-hand side, and the limit does not approach any single value.
Now let's consider the left-hand limit:
lim x→0- sin(1/x) does not exist
This is because sin(1/x) oscillates infinitely many times between -1 and 1 as x approaches 0 from the left-hand side, and the limit does not approach any single value.
Since the left-hand limit and the right-hand limit both do not exist, the limit of sin(1/x) as x approaches 0 does not exist.
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