Surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].
How to find the surface area of the cylinder?The surface area of a cylinder can be calculated by adding the area of the two bases (which are circles) and the lateral area (which is the area of the curved surface).
The radius of the cylinder is given as 36m and the height as 46m. Therefore, the diameter of the cylinder is 72m (twice the radius). Using the formula for the area of a circle, we can calculate the area of each base:
[tex]$A_{base} = \pi r^2 = \pi (36m)^2 = 1296\pi m^2$[/tex]
The lateral area of the cylinder can be calculated using the formula:
[tex]$A_{lateral} = 2\pi r h$[/tex]
Substituting the given values, we get:
[tex]$A_{lateral} = 2\pi (36m) (46m) = 3312\pi m^2$[/tex]
Therefore, the total surface area of the cylinder is:
[tex]$A_{total} = A_{base} + A_{lateral} + A_{base} = 2A_{base} + A_{lateral}$[/tex]
Substituting the values we calculated, we get:
[tex]$A_{total} = 2(1296\pi m^2) + 3312\pi m^2 = 5904\pi m^2$[/tex]
So the surface area of the cylinder in terms of [tex]$\pi$[/tex] is [tex]$5904\pi m^2$[/tex].
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Six numbers are shown.
1.25 , -1.5 , -0.75 , -3/4 , 26/8 , 5/4 .
Plot each number on the number line.
According to the information, we can infer that the correct order for these number is -1.5, -0.75, -0.75, 1.25, 3.25.
How to organize the numbers in the numberline?To plot the numbers on a number line, we need to arrange them in increasing order. Here is the organized list of the numbers:
-1.5, -0.75, -0.75, 1.25, 3.25On the number line, we can mark -1.5 first and then move to the right to mark -0.75 twice (since it appears twice in the list), then 1.25, and finally 3.25 . On the number line, we can see that -1.5 is the smallest number and 3.25 is the largest number.
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Suppose f'(x) = 8x³ + 12x + 2 and f(1) = -4. Then f(-1) equals (Enter a number for your answer.)
If f'(x) = 8x³ + 12x + 2 and f(1) = -4, f(-1) is equal to -18.
Given that f'(x) = 8x³ + 12x + 2, we can find the original function f(x) by integrating f'(x) with respect to x:
f(x) = 2x⁴ + 6x² + 2x + C, where C is an arbitrary constant.
We can then use the given initial condition f(1) = -4 to solve for C:
f(1) = 2(1)⁴ + 6(1)² + 2(1) + C = -4
Simplifying, we get:
C = -16
Therefore, the function f(x) is:
f(x) = 2x⁴ + 6x² + 2x - 16
To find f(-1), we substitute x = -1 into the expression for f(x):
f(-1) = 2(-1)⁴ + 6(-1)² + 2(-1) - 16 = -18
Thus, f(-1) equals -18.
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The start of an arithmetic sequence is 29, 17, 21, 25, The rule for the sequence can be written in the form xn=cn+d, where c and d are numbers. a) By first calculating the values of c and d, work out the rule for the sequence. b) What is the value of x11?
Answer:
Step-by-step explanation:
The value of 2s in 43,290 is 2,000, while the value of 2s in 32,865 is 20.
B. 200 is 1/20 the value of 2,000.
This statement is correct, as 200 is 1/10 of 2,000, and there are two 0s in the value of 2s in 43,290 compared to one 0 in the value of 2s in 32,865.
Kurts city took a survey about a plan for a new park. the city surveyed 3000 people. 53% of the people surveyed like the plan for the park. how many people like the plan?
The number of people who like the plan is 1,590 people out of the 3,000 surveyed.
To determine how many people liked the plan, we'll need to use the percentage given and apply it to the total number of people surveyed.
Percentage is a way of expressing a proportion or a fraction as a whole number out of 100. In this case, the percentage we're working with is 53%, which means 53 out of every 100 people surveyed liked the plan. To find the number of people who liked the plan, we can multiply the total number of people surveyed (3,000) by the percentage who liked the plan (53%).
To do this calculation, first convert the percentage to a decimal by dividing 53 by 100, which gives us 0.53. Next, multiply 3,000 by 0.53:
3,000 * 0.53 = 1,590
So, 1,590 people out of the 3,000 surveyed liked the plan for the new park.
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A particle moves along the x-axis with velocity given by v(t) = 3t2 + 6t for time t ≥ 0. If the particle is at position x = 2 at time t = 0, what is the position of the particle at t = 1?
The position of the particle at time t = 1 is x = 4 units.
What is the position of a particle that moves along the x-axis with velocity v(t) = [tex]3t^2[/tex] + 6t at time t = 1 if it is at position x = 2 at time t = 0?To find the position of the particle at time t = 1, we need to integrate the given velocity function v(t) with respect to time from 0 to 1:
x(t) = ∫v(t)dt (from t = 0 to t = 1)
= ∫([tex]3t^2[/tex]+ 6t)dt (from t = 0 to t = 1)
= ([tex]t^3 + 3t^2[/tex]) (from t = 0 to t = 1)
[tex]= (1^3 + 3(1^2)) - (0^3 + 3(0^2))[/tex]
= 4
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please answer, i have 5 mins
Use each of these rules to create 4 ordered pairs using the two sequences.
The first rule is add 12, then divide by 2, starting from 4.
The second rule is multiply by 2, then subtract 2, starting from 3.
Which table shows the 4 ordered pairs created using the two sequences?
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers zero, four, six, and seven. Under column rule 2 are the numbers three, five, nine, and seventeen. Under the column labeled ordered pair are zero and three, four and five, six and nine, and seven and seventeen.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers two, six, eight, and nine. Under column rule 2 are the numbers two, four, ten, and twenty-eight. Under the column labeled ordered pair are two and two, six and four, eight and ten, and nine and twenty-eight.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers four, eight, ten, and eleven. Under column rule 2 are the numbers three, four, six, and ten. Under the column labeled ordered pair are four and three, eight and four, ten and six, and eleven and ten.
A table with three columns. The first column is labeled rule 1, the second column is labeled rule 2, and the third column is labeled ordered pair. There are four rows below the heading row. Under column rule 1 are the numbers six, eight, twelve, and twenty. Under column rule 2 are the numbers one, eight, twenty-two, and fifty. Under the column labeled ordered pair are six and one, eight and eight, twelve and twenty-two, and twenty and fifty.
Ordered pairs must be placed in the following order: (6, 1), (8, 8), (12, 22). (20, 50). The right answer is D.
What is arithmetic?According to the assertions, it deals with a number of operations in mathematics.
For the first series, let the number be x, and for the second, let it be y.
The first rule is to multiply by 2, then, beginning with 6, remove 4.
The sequence can be written as 6 is the first number: = 2x - 4
next number = 2(6) - 4
= 12-4
= 8
The following phrase is thus 8. The following two terms can be written as 12 and 20.
Values of x = 6, 8, 12, 20
The second rule is to add three and then multiply by two, counting backward from one.
= (y + 3)2
First term = 1
Next term = (1 + 3)2
= 8
The next two words can be acquired in a similar manner.
y = 1, 8, 22, 50
Therefore, ordered pairs must be placed in the following order: (6, 1), (8, 8), and (12, 22). (20, 50). The right answer is D.
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Correct question:
The first rule is to multiply by 2, then subtract 4 starting from 6. The second rule is to add 3, then multiply by 2 starting from 1. What are the first four ordered pairs using the two sequences?
A. (0, 0) (6, 1), (8, 2), (12, 22)
B. (6, 1), (10, 8), (14,22), (22, 50)
C. (6, 1), (8, 8), (12, 20), (20, 45)
D. (6, 1), (8, 8), (12, 22), (20, 50)
Help me with homework
Therefore, the perimeter of the rectangle is 38 units that is option C.
What is coordinate?A coordinate is a set of numbers or values that specifies the position or location of a point or object in a space. In mathematics, coordinates are used to describe the position of a point in a plane, a space or a higher-dimensional object. Coordinates can be represented by ordered pairs or tuples, where the first value corresponds to the position on the horizontal axis, and the second value corresponds to the position on the vertical axis.
Here,
First, we need to find the distance between points A and B to determine the length of the rectangle:
Distance AB = |yB - yA|
= |8 - 2|
= 6
Next, we need to find the distance between points B and C to determine the width of the rectangle:
Distance BC = |xC - xB|
= |6 - (-7)|
= 13
Since opposite sides of a rectangle are equal in length, we know that the distance between points A and D is also 13, and the distance between points C and D is also 6.
Therefore, the perimeter of the rectangle is:
Perimeter = 2 * (length + width)
Perimeter = 2 * (13 + 6)
Perimeter = 2 * 19
Perimeter = 38
So the answer is (C) 38.
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PLEASE HELP
What is the probability that
both events will occur?
Two dice are tossed.
Event A: The first die is a 1 or 2
Event B: The second die is 4 or less
P(A and B) = P(A) • P(B)
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
The probability that both events will occur is 0.22.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
Example:
The probability of getting a head in tossing a coin.
P(H) = 1/2
We have,
The probability of Event A is 2/6 or 1/3
(since there are two ways to get a 1 or 2 on a six-sided die).
The probability of Event B is 4/6 or 2/3
(since there are four ways to get a number 4 or less on a six-sided die).
Using the formula for the probability of the intersection of two independent events.
P(A and B)
= P(A) x P(B)
= (1/3) x (2/3)
= 2/9
Rounded to the nearest hundredth,
The probability that both events will occur is 0.22.
Thus,
The probability that both events will occur is 0.22.
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This is part of a city map.
City map with First Street and Second Street as two lines equal distance apart that never meet. Main Street is intersecting Arch, First, Second, and Elm. Elm Street is intersecting Main and First Street.
Which streets are parallel to each other?
A.
First Street and Second Street
B.
First Street and Arch Street
C.
None of the streets are parallel to one another.
D.
Elm Street and Main Street
The data set is 12, 46, 32, 18, 26, 41, 46. the mean is 31.6 and the median is 32. if we add another 12, what affect does this have on the mean and median?
Adding another 12 to the data set would increase the sum of the values by 12, resulting in a new sum of 239. To find the new mean, we divide the new sum by the total number of values in the set, which is now 8. So the new mean would be 29.875, which is slightly lower than the original mean of 31.6.
To find the new median, we first need to rearrange the values in ascending order: 12, 18, 26, 32, 41, 46, 46, 12. Since there are now an even number of values, we take the average of the middle two, which in this case is (26 + 32) / 2 = 29. So the new median would be 29, which is lower than the original median of 32.
In summary, adding another 12 to the data set would slightly decrease the mean and lower the median.
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Which of the pair of linear equations has unique solution, no solution or infinitely many solutions. In case there is unique solution find it by using Substitution Method and Elimination Method
(i) x-3y -3=0, 3x-9y-2=0
(ii) 2x+y=5,3x+2y=8
(iii) 3x-5y=20,6x-10y=40
iv) x-3y-7 =0,3x-3y-15=0
v) 8x+5y=9,3x+2y=4
1. x-3y -3=0, 3x-9y-2=0 has no solution
2. 2x+y=5,3x+2y=8 has a unique solution
3. 3x-5y=20,6x-10y=40 has infinitely many solution
4. x-3y-7 =0,3x-3y-15=0 has No solution
5. 8x+5y=9,3x+2y=4 has a unique solution
How to solve the linear equations(i) To solve using substitution method, we can rearrange the first equation to x=3y+3 and substitute it into the second equation:
3(3y+3) - 9y - 2 = 0
9y + 9 - 9y - 2 = 0
7 = 0
This is a contradiction, so the pair of equations has no solution.
(ii) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:
3x + 2y = 8
(4x + 2y = 10)
-x = -2
So, x = 2. Substituting this value into the first equation, we get:
2x + y = 5
2(2) + y = 5
y = 1
Therefore, the unique solution is (x,y) = (2,1).
(iii) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:
6x - 10y = 40
(6x - 10y = 40)
0 = 0
This equation is true for any value of x and y, so the pair of equations has infinitely many solutions.
(iv) To solve using elimination method, we can subtract the first equation from the second equation:
3x - 3y - 15 - (x - 3y - 7) = 0
2x - 22 = 0
x = 11
Substituting this value into the first equation, we get:
11 - 3y - 7 = 0
-3y = -4
y = 4/3
Therefore, the unique solution is (x,y) = (11,4/3).
(v) To solve using elimination method, we can multiply the first equation by 2 and subtract it from the second equation:
3x + 2y = 4
(16x + 10y = 18)
-29x - 18y = -14
Solving for y, we get:
y = (29/18)x + (7/9)
Substituting this expression for y into the first equation, we get:
8x + 5((29/18)x + (7/9)) = 9
(143/18)x = 2/9
x = 2/13
Substituting this value into the expression for y, we get:
y = (29/18)(2/13) + (7/9) = 41/117
Therefore, the unique solution is (x,y) = (2/13,41/117).
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The spinner has 8 congurent sections it is spun 24 times what is a reasonable prediction for the number of times the spinner will land on the number 3.
A reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.
Since the spinner has 8 congruent sections and is spun 24 times, we can use probability to make a reasonable prediction for the number of times it will land on the number 3.
1. Calculate the probability of landing on the number 3 for a single spin:
Since there are 8 congruent sections, the probability of landing on the number 3 is 1/8.
2. Determine the expected number of times the spinner will land on the number 3:
To do this, multiply the probability of landing on the number 3 (1/8) by the total number of spins (24).
Expected number of times = (1/8) * 24
3. Simplify the expression:
Expected number of times = 3
So, a reasonable prediction for the number of times the spinner will land on the number 3 is 3 times.
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π × 4 to the second power × 3 ( with steps !! )
in a class, 12 students finished early. this represents 40% of the students. model this situation by evenly distributing the 12 students in the 4 shaded sections
Answer:Each of the shaded sections represents 25% of the total number of students in the class, and since we have evenly distributed the 12 students among them, each shaded section now represents 30% of the students (i.e., 25% + 5% = 30%).
Step-by-step explanation: To model this situation, we need to determine the total number of students in the class. We can use the given percentage to set up a proportion:
40% = 12 students / x total students
To solve for x, we can cross-multiply and simplify:
0.4x = 12
x = 12 / 0.4
x = 30
Therefore, there are 30 students in the class.
To evenly distribute the 12 students in the 4 shaded sections, we can divide 12 by 4 to get the number of students for each section:
12 students / 4 sections = 3 students per section
Consider the variable coefficient linear second order non-homogeneous ODE
x^2y^n - 2xy' + (x^2 +2)y =. 3x^3, for x > 0
Write down the associated homogeneous equation.
x²y' - 2xy' + (x² + 2)y = 0 is the associated homogeneous equation with non-homogeneous ODE x²yⁿ - 2xy' + (x² +2)y = 3x³.
It should be noted that the equation is same as the variable coefficient linear second order non-homogeneous ODE but just the right side zero.
The complementary solutions or homogeneous solutions to this homogeneous equation serve as the foundation for the space of all solutions to the non-homogeneous equation.
By assuming that y has the form y(x) = xr and substituting this into the homogeneous equation to create a characteristic equation, we can determine the complementary solutions. We may find the values of r that correspond to solutions of the type y(x) = xr by looking at the characteristic equation's roots.
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Assume base is 2.a b c
a = 5
b = 4
c= 0
Therefore, the equation for graph C is Y = a ^b + c
Y = 5 ^4 + 0
What is a graph?A graph is described as a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Graphs are a popular tool for graphically illuminating data relationships. A graph serves the purpose of presenting data that are either too numerous or complex to be properly described in the text while taking up less room.
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Noel borrows $800
and is charged compound interest at 60%
per year. How much will he have to pay back in total after 8
years?
Answer:
Step-by-step explanation:
Find the perimeter of a rectangle whose vertices are (3,2), (13,2), (13,9), and (3,9).
The perimeter of a rectangle is 34 units.
To find the perimeter of the rectangle with vertices (3,2), (13,2), (13,9), and (3,9), you need to determine the lengths of its sides.
The distance between (3,2) and (13,2) is the length of the base: 13 - 3 = 10 units.
The distance between (3,2) and (3,9) is the height: 9 - 2 = 7 units.
The perimeter of a rectangle is given by the formula P = 2*(length + width). In this case, P = 2*(10 + 7) = 2*17 = 34 units.
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1ST ONE TO ANSWER MY QUESTION WILL BE MARKED BRAINLIESTT! ANSWER 1 QUESTION!
2x²t + 7xy
Step-by-step explanation:To simplify, we will combine like terms.
Given:
5xy - x²t + 2xy + 3x²t
Reorder like terms:
5xy + 2xy + 3x²t - x²t
Combine like terms:
➜ 5 + 2 = 7
➜ 3 - 1 = 2
7xy + 2x²t
Reorder by degree:
2x²t + 7xy
What is the osmotic pressure for a 4. 50% by a mass aqueous solution of glucose (C6H12O6) at 300 K?
The osmotic pressure for a 4.50% by mass aqueous solution of glucose (C6H12O6) at 300 K is 0.616 atm.
To calculate the osmotic pressure of a solutionWe can use the equation:
π = MRT
where:
π = osmotic pressure
M = molarity of the solution
R = gas constant
T = temperature in Kelvin
We must translate the proportion by mass to molarity in order to determine the molarity of the glucose solution. Glucose (C6H12O6) has a molecular weight of 180 g/mol.
So, for a 4.50% by mass solution of glucose, we have:
4.50 g glucose / 100 g solution = (4.50 g glucose / 180 g/mol) / (Molarity of solution)
Solving for molarity, we get:
Molarity of solution = 0.025 mol/L
Now we can plug in the values into the equation for osmotic pressure:
π = (0.025 mol/L) * (0.0821 L atm / mol K) * (300 K)
π = 0.616 atm
Therefore, the osmotic pressure for a 4.50% by mass aqueous solution of glucose (C6H12O6) at 300 K is 0.616 atm.
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Question below, please help! this is part of my grade.. (30 points)
Answer:
y = 1 + 2√7 or y = 1 - 2√7
Step-by-step explanation:
To complete the square, you need to add and subtract the square of half of the coefficient of the y term.
First, you can factor out a 1 from the y^2 - 2y term:
y^2 - 2y - 27 = 0
y^2 - 2y = 27
Next, take half of the coefficient of the y term (-2/2 = -1) and square it (1):
y^2 - 2y + 1 - 1 = 27
The "+1 -1" doesn't change the value of the equation, it's just a way to add 0 to the equation so we can complete the square.
Now you can rewrite the left side as a perfect square:
(y - 1)^2 - 28 = 0
Add 28 to both sides:
(y - 1)^2 = 28
Take the square root of both sides (remembering to include both positive and negative square roots):
y - 1 = ±√28
y = 1 ± 2√7
So the solutions are:
y = 1 + 2√7
y = 1 - 2√7
Answer: y=± 2√7+1
6.29
Step-by-step explanation: Use the formula
(b/2)^2 in order to create a new term. Solve for y by using this term to complete the square.
100 POINTS IF HELP
what is the average rate of change for the function g(x) for the interval [4,9]?
SHOW ALL WORK
g(x)=4x^2+3x-2
Answer:
Step-by-step explanation:
Find the Riemann sum S₅ for the following information. Round your answer to the nearest hundredth. f(x) = 64 - x²; [a, b] = (-8, -3]; n = 5.c₁ = -7.5.c² = -6.5.c₃ = -5.5.c₄ = - 4.5.c₅ = -3.5
The Rounding to nearest hundredth, we get S₅ ≈ -12.25
How to find the Riemann sum S₅?The formula for a Riemann sum with n subintervals is:
[tex]S_n[/tex]= ∑ᵢ₌₁ⁿ f(cᵢ) Δx,
where Δx = (b - a)/n is the width of each subinterval and cᵢ is a point in the i-th subinterval. The value of cᵢ can be chosen arbitrarily, but here we are given specific values for c₁, c₂, c₃, c₄, and c₅.
In this problem, we have:
f(x) = 64 - x²
[a, b] = (-8, -3]
n = 5
Δx = (b - a)/n = (-3 - (-8))/5 = 1
Therefore, the width of each subinterval is 1.
The Riemann sum S₅ is:
S₅ = f(c₁) Δx + f(c₂) Δx + f(c₃) Δx + f(c₄) Δx + f(c₅) Δx
Substituting the given values for c₁, c₂, c₃, c₄, and c₅, we get:
S₅ = f(-7.5) + f(-6.5) + f(-5.5) + f(-4.5) + f(-3.5)
where f(x) = 64 - x².
Evaluating each term, we get:
f(-7.5) = 64 - (-7.5)² = 17.75
f(-6.5) = 64 - (-6.5)² = 5.75
f(-5.5) = 64 - (-5.5)² = -2.75
f(-4.5) = 64 - (-4.5)² = -12.25
f(-3.5) = 64 - (-3.5)² = -20.75
Therefore,
S₅ = 17.75(1) + 5.75(1) - 2.75(1) - 12.25(1) - 20.75(1) = -12.25.
Rounding to the nearest hundredth, we get S₅ ≈ -12.25.
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you purchase a computer for 875 plus 5% sales tax. you decide to finance it through the stores 0% program for 12 months. the terms state that you must pay
The amount of interest paid for missing the payment in the eight month would be C. $87.28
How to find the interest ?First, find the total cost of the computer including the sales price :
= 875 x ( 1 + 0. 05 )
= 875 x 1. 05
= $ 918. 75
Then, find the monthly rate of interest :
= 14. 25 / 12
= 1. 1875 %
This leads to an eight month interest rate of :
= 8 x 1. 1875 %
= 9. 5 %
The interest to be paid:
= 9. 5 % x 918. 75
= $ 87. 28
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Full question is:
You purchase a computer for $875.00 plus 5% sales tax. You decide to finance it through the store's 0% program for 12 months. The terms state that you must pay $100.00/month and that if you miss a payment, you will be assessed a late fee of $39.00 plus the interest accrued to that point at a 14.25% APR. If you miss a payment in the eighth month, how much interest will you be charged?. A. $83.13. B. $16.63. C. $87.28. D. 58.19
Apple Inc. Stock closes at $109. 99 per share. The next day the stock goes up $1. 49. What is the new price per share? (Just type the amount of money. Do not type the words "per share". )
The new price per share is $111.48.
Stock price is the current market value of a share of a publicly traded company's stock. It represents the price at which buyers and sellers agree to trade shares in the open market. Stock prices are determined by a variety of factors, including the company's financial performance, industry trends, and overall market conditions. The stock price is often used as an indicator of investor sentiment about the company and its future prospects.
To find the new price per share, follow these steps:
1. Note the initial stock price: $109.99
2. Note the increase in stock price: $1.49
3. Add the increase to the initial stock price: $109.99 + $1.49 = $111.48
The new price per share is $111.48.
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Describe the specific sequence of transformations that would map triangle abc to triangle a'b'c'.
Translation, rotation, and reflection, By following these transformations in sequence, you can map triangle ABC to triangle A'B'C'.
To map triangle ABC to triangle A'B'C', you would need to follow a specific sequence of transformations, which may include translation, rotation, and reflection. Here's a step-by-step explanation:
Step 1: Translation
Translate triangle ABC by a specific vector (x, y) so that point A moves to point A'. The same vector will also move points B and C to their corresponding new positions.
Step 2: Rotation
If triangle A'B'C' is rotated compared to the translated triangle, rotate the translated triangle around point A' by a specific angle, either clockwise or counterclockwise, until point B aligns with point B'.
Step 3: Reflection
If triangle A'B'C' is a mirror image of the rotated triangle, reflect the rotated triangle across a line of symmetry (usually a line passing through A'). This will change the orientation of the triangle and align point C with point C'.
By following these transformations in sequence, you can map triangle ABC to triangle A'B'C'. Keep in mind that the specific details of translation, rotation, and reflection will depend on the coordinates and orientation of the given triangles.
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The Royal Fruit Company produces two types of fruit drinks. The first type is 30% pure fruit juice, and the second type is 55% pure fruit juice. The company is attempting to produce a fruit drink that contains 40% pure fruit juice. How many pints of each of the two existing types of drink must be used to make 60 pints of a mixture that is 40% pure fruit juice?
Let's use the method of setting up a system of equations to solve this problem.
Let x be the number of pints of the first type of fruit drink (30% pure), and y be the number of pints of the second type of fruit drink (55% pure). We want to find the values of x and y that will produce 60 pints of a mixture that is 40% pure.
We can start by setting up two equations based on the information given:
Equation 1: x + y = 60 (since we want to produce 60 pints of the mixture)
Equation 2: 0.3x + 0.55y = 0.4(60) (since we want the mixture to be 40% pure)
Simplifying Equation 2, we get:
0.3x + 0.55y = 24
Now we have a system of two equations with two unknowns:
x + y = 60
0.3x + 0.55y = 24
We can solve this system using substitution or elimination. Here, we'll use substitution:
Solving Equation 1 for x, we get x = 60 - y. Substituting this expression for x in Equation 2, we get:
0.3(60 - y) + 0.55y = 24
Expanding and simplifying, we get:
18 - 0.3y + 0.55y = 24
Combining like terms, we get:
0.25y = 6
Dividing by 0.25, we get:
y = 24
Substituting this value of y back into x + y = 60, we get:
x + 24 = 60
Solving for x, we get:
x = 36
Therefore, we need 36 pints of the 30% pure fruit drink and 24 pints of the 55% pure fruit drink to make 60 pints of a mixture that is 40% pure.
6. (2.5 pts) at the beginning of week 5, they broke up. jack wanted to run off to the city with
diane, but diane said he was crazy. unfortunately, their relationship ended. both were
angry with each other. suppose we could somehow quantify and measure anger. let's
call the units "anger units". on the day of the break-up, jack had 100 anger units. every
week he lost 5% of his anger. recall that the growth factor needs to be the amount that
"stays on" jack (not the 5% that "comes off" jack). for example, after 1 week, he had 95
anger units. after 2 weeks he had 90.25 anger units, and so on. write an equation that
models jack's anger (let that be )) after t weeks.
We'll model Jack's anger in anger units after t weeks using an exponential decay equation, as he loses 5% of his anger every week.
To write an equation that models Jack's anger (let that be A(t)) after t weeks, we need to follow these steps:
1. Identify the initial amount of anger units (A0): Jack had 100 anger units at the beginning (t=0).
2. Determine the growth factor (1 - decay rate): Since Jack loses 5% of his anger every week, the growth factor is 1 - 0.05 = 0.95.
3. Set up the exponential decay equation: A(t) = A0 * (growth factor)^t.
By following these steps, the equation modeling Jack's anger after t weeks is:
A(t) = 100 * (0.95)^t
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USA Today reported that Parkfield, California is dubbed the world's earthquake capital because it sits on top of the notorious San Andreas fault. Since 1857, Parkfield has had a major earthquake on an average of 2. 0 times every 22 years.
(d) Compute the probability of at least one major earthquake in the next 49 years. Round
λ
to the nearest hundredth, and use a calculator. (Use 4 decimal places. )
(e) Compute the probability of no major earthquakes in the next 49 years. Round
λ
to the nearest hundredth, and use a calculator. (Use 4 decimal places. )
(d) Probability of at least one major earthquake in the next 49 years is 0.9884, and (e) the probability of no major earthquakes in the next 49 years is 0.0116.
We will use the Poisson distribution to compute the probabilities. First, we need to find the value of λ (average number of earthquakes in a given time period).
(d) Compute the probability of at least one major earthquake in the next 49 years:
1. Calculate λ for 49 years:
(2.0 earthquakes / 22 years) * 49 years = 4.45 (rounded to the nearest hundredth)
2. Compute the probability of no major earthquakes (P(0)) in the next 49 years using Poisson distribution formula:
P(0) = (e^(-λ) * (λ^0)) / 0! = (e^(-4.45) * (4.45^0)) / 1 = 0.0116 (rounded to 4 decimal places)
3. Compute the probability of at least one major earthquake:
P(at least 1) = 1 - P(0) = 1 - 0.0116 = 0.9884
So, the probability of at least one major earthquake in the next 49 years is 0.9884 (rounded to 4 decimal places).
(e) Compute the probability of no major earthquakes in the next 49 years:
As calculated in step (d), the probability of no major earthquakes in the next 49 years is 0.0116 (rounded to 4 decimal places).
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Can someone help me I'm stuck.
Alexandria rolled a number cube 60 times and recorded her results in the table.
What is the theoretical probability of rolling a one or two? Leave as a fraction in simplest from
The theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.
The theoretical probability of an event happening is the number of favorable outcomes divided by the total number of possible outcomes.
In this case, Alexandria rolled the number cube 60 times and recorded her results in the table.
Looking at the table, we can see that the number 1 came up 16 times and the number 2 came up 20 times.
So the number of favorable outcomes is 16 + 20 = 36.
And the total number of possible outcomes is 60.
Therefore, the theoretical probability of rolling a one or two is:
P(1 or 2) = favorable outcomes/total outcomes = 36/60
Simplifying the fraction, we get:
P(1 or 2) = 3/5
So the theoretical probability of rolling a one or two is 3/5 or 0.6 as a decimal.
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