Answers
Answer:
Step-by-step explanation:
[tex]i=2: \frac{3}{2} \times\frac{1}{3^2}=\frac{1}{6}[/tex]
[tex]i=3: \frac{3}{2} \times\frac{1}{3^3}=\frac{1}{18}[/tex]
[tex]i=4: \frac{3}{2} \times\frac{1}{3^4}=\frac{1}{54}[/tex]
[tex]i=5: \frac{3}{2} \times\frac{1}{3^5}=\frac{1}{162}[/tex]
[tex]i=6: \frac{3}{2} \times\frac{1}{3^6}=\frac{1}{486}[/tex]
[tex]sum=\frac{121}{486}[/tex]
Related Questions
Select the correct answer. Which is the correct solution to the expression 3 + 5^2? You can use a calculator to find the answer. A. 10 B. 13 C. 28 D. 64
Answers
The correct solution to the expression 3 + 5^2 is C. 28.
What is an expression?Mathematically, an expression is a combination of variables with numbers, values, or constants.
Mathematical or algebraic expressions use the mathematical operands like addition (+), subtraction (-), division (÷), multiplication (×), exponents (^), etc.
An algebraic expression does not go with the equal symbol (=), unlike an equation.
3 + 5^2
= 3 + 5 x 5
= 3 + 25
= 28
Thus, an evaluation of the algebraic expression 3 + 5^2 gives the solution as Option C.
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5x-4y=3(x+3) slope and y+x intercept
Answers
Answer:
Step-by-step explanation:
To find the slope of the line represented by the equation 5x-4y=3(x+3), we can rearrange the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
5x - 4y = 3(x + 3)
5x - 4y = 3x + 9
5x - 3x = 4y + 9
2x = 4y + 9
y = (2/4)x - 9/4
So, the slope of the line is 2/4, which can be simplified to 1/2.
To find the y-intercept, we can set x = 0 in the equation:
y = (1/2)(0) - 9/4
y = -9/4
Therefore, the y-intercept is -9/4.
To find the x-intercept, we can set y = 0 in the equation:
0 = (1/2)x - 9/4
9/4 = (1/2)x
x = (9/4) / (1/2)
x = 9/2
Therefore, the x-intercept is 9/2.
Answer:
Slope: -1/2 Y-Intercept: -9/4
Step-by-step explanation:
5x - 4y = 3x + 9
Subtract 3x from both sides
2x - 4y = 9
Divide both sides by -4
y = (-1/2)x + (-9/4)
Jerry wants to buy 4 Michelin tires from Sears, calculate his total price, tax rate is 8%.
Answers
Answer:
To calculate Jerry's total price, we need to know the cost of each Michelin tire from Sears. Let's assume that each tire costs $100.
The total cost of the 4 Michelin tires is:
4 tires x $100/tire = $400
Next, we need to calculate the amount of tax that Jerry will need to pay on his purchase. The tax rate is 8%, so we can calculate the amount of tax as:
$400 x 0.08 = $32
Finally, we can calculate Jerry's total cost by adding the cost of the tires to the tax:
$400 + $32 = $432
Therefore, Jerry's total price for 4 Michelin tires from Sears, including tax, is $432
congruent arcs determine ___ central angles
options :
1. complementary
2. congruent
3. infinitely many
4. supplementary
5. three
Answers
Answer:
Congruent arcs determine congruent central angles. This is one of the properties of circles and is true for any two arcs of a circle that have the same measure.
Step-by-step explanation:
The Good’n’Fresh Grocery Store has two checkout lanes and four employees. Employees are equally skilled, and all are able to either operate a register (checkers) or bag groceries (baggers). The store owner assigns one checker and one bagger to each lane. A lane with a checker and a bagger can check out 46 customers per hour. A lane with a checker only can check out 25 customers per hour.
a. In terms of customers checked out per hour, what are total output and average labor productivity for the Good’n’Fresh Grocery Store?
Instructions: Enter your response for total output as a whole number and round your response for average productivity to one decimal place.
Total output:
92
customers per hour.
Average productivity:
24
customers per hour, per worker
b. The owner adds a third checkout lane and register. Assuming that no employees are added, what is the best way to reallocate the workers to tasks?
multiple choice 1
Two lanes with only checkers and one lane with a checker and a bagger.
Two lanes with a checker and bagger and one lane left empty.
Instructions: Enter your response for total output as a whole number and round your response for average productivity to one decimal place.
What are total output and average labor productivity (in terms of customers checked out per hour) now?
Total output:
customers per hour
Average productivity:
customers per hour, per worker
c. The owner adds a fourth checkout lane and register. Assuming that no employees are added, what is the best way to reallocate the workers to tasks?
multiple choice 2
Four lanes with checkers only.
Do not use the fourth lane.
Two lanes with one checker and one bagger each.
Instructions: Enter your response for total output as a whole number and round your response for average productivity to one decimal place.
Total output:
customers per hour
Average productivity:
customers per hour
The owner adds a fifth checkout lane and register. Assuming that no employees are added, what is the best way to reallocate the workers to tasks?
multiple choice 3
Two lanes with only checkers and one lane with a checker and a bagger.
Do not use the fifth lane.
Two lanes with one checker and one bagger at each.
Do you observe diminishing returns to capital in this example?.
multiple choice 4
Yes, adding a third lane will not increase output
Yes, adding a fifth lane will not increase output.
Yes, adding a fourth lane will not increase output
No, adding all five lanes will increase output.
Answers
41 clients can be checked out in an hour on a lane with a checker and a bagger. Only 25 people can be checked out per hour at a checker-only line.
a. The Good'n'Fresh Grocery Store's total production and average labor productivity are 92 customers per hour and 23.5 customers per hour per worker, respectively.
b. Two lanes with a checker and a bagger, and one lane with a checker only, are the ideal configurations for reassigning the workers to duties.
a. The total output of the Good’n’Fresh Grocery Store is:
Total output = 2 lanes x 46 customers/lane/hour + 2 lanes x 25 customers/lane/hour
= 92 customers/hour
The average labor productivity is:
Average productivity = Total output / Total number of workers
= 92 customers/hour / 4 workers
= 23 customers/hour/worker
≈ 23.0 customers/hour/worker
Therefore, the total output is 92 customers per hour, and the average labor productivity is 23.0 customers per hour, per worker.
b. With three lanes, the best way to reallocate the workers to tasks is to have:
Two lanes with a checker and a bagger, and one lane with a checker only.
This way, each lane will have one checker and one bagger, which is the most efficient way to operate a lane. The total output will be:
Total output = 3 lanes x 46 customers/lane/hour
= 138 customers/hour
The average labour productivity is:
Average productivity = Total output / Total number of workers
= 138 customers/hour / 4 workers
= 34.5 customers/hour/worker
≈ 34.5 customers/hour/worker
Therefore, the total output is 138 customers per hour, and the average labour productivity is 34.5 customers per hour, per worker.
c. With four lanes, the best way to reallocate the workers to tasks is to have:
Two lanes with a checker and a bagger, and two lanes with a checker only.
This way, each lane will have either one checker and one bagger or one checker only, which is the most efficient way to operate a lane. The total output will be:
Total output = 4 lanes x 46 customers/lane/hour
= 184 customers/hour
The average labour productivity is:
Average productivity = Total output / Total number of workers
= 184 customers/hour / 4 workers
= 46 customers/hour/worker
≈ 46.0 customers/hour/worker
Therefore, the total output is 184 customers per hour, and the average labour productivity is 46.0 customers per hour, per worker.
d. With five lanes, the best way to reallocate the workers to tasks is to have:
Two lanes with a checker and a bagger, and three lanes with a checker only.
This way, each lane will have either one checker and one bagger or one checker only, which is the most efficient way to operate a lane. The total output will be:
Total output = 5 lanes x 46 customers/lane/hour
= 230 customers/hour
The average labour productivity is:
Average productivity = Total output / Total number of workers
= 230 customers/hour / 4 workers
= 57.5 customers/hour/worker
≈ 57.5 customers/hour/worker
Therefore, the total output is 230 customers per hour, and the average labour productivity is 57.5 customers per hour, per worker.
e. Yes, we observe diminishing returns to capital in this example because adding more lanes does not increase output proportionally. Adding a third lane increases output by 46 customers/hour, adding a fourth lane increases output by 46 customers/hour, and adding a fifth lane increases output by 46 customers/hour. Therefore, the marginal output of adding each additional lane is decreasing. The correct multiple-choice answer is:
Certainly, adding a fifth lane won't boost productivity.
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A secretary listed the frequency of calls by a patient to a doctor's office during a year, and the data is displayed in the histogram.
A histogram titled Calls To A Doctor. The x-axis is labeled Number of Calls and has intervals listed for 1 to 25, 26 to 50, 51 to 75, and 76 to 100. The y-axis is labeled Frequency and begins at 0, with tick marks every five units up to 60. There is a shaded bar for 1 to 25 that stops at 58, for 26 to 50 that stops at 34, for 51 to 75 that stops at 17, and for 76 to 100 that stops at 12.
Which of the following best describes the spread and distribution of the data?
The data is skewed to the higher values because many patients call the doctor several times a day when they are sick.
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
The data is bimodal with a narrow spread because many patients call the doctor several times a day when they are sick.
The data is normal and has a wide spread because many patients only call the doctor once or twice a year when they are sick.
Answers
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
Define the terms spread and distribution?Spread and distribution of data are statistical concepts that describe how a set of data is spread out or distributed.
Distribution refers to how the data is distributed or arranged. It is typically described in terms of its shape, center, and spread. Common types of distributions include normal distribution, skewed distribution, and uniform distribution. The distribution can be visualized using various graphs such as histograms, box plots, and scatter plots.
Based on the histogram description, the best answer is:
The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
The histogram shows that the frequency of calls is highest for the 1 to 25 interval, with decreasing frequency for each subsequent interval. The fact that the shaded bars stop at relatively low frequencies for each interval suggests that there are very few patients who call the doctor frequently, skewing the data towards the lower values. The histogram also shows a wide range of values, or spread, with the highest interval going up to 100, but the low frequencies in each interval suggest that the data is not normally distributed.
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Answer:its b
Step-by-step explanation:
At the hardware store, a zinc washer has an inner radius of r inches and a width of 1 inch from inner edge to outer edge. Write a polynomial equation for the area A of one side of the zinc washer.
Answers
A polynomial equation for the area of one side of the zinc washer is given by A = pi*(r+1)² - pi*r².
What is polynomial?Polynomial is a mathematical expression containing one or more terms, each of which is composed of a constant coefficient and one or more variables raised to a power. It can be used to represent a variety of functions, such as linear, quadratic, and cubic functions.
This equation is derived from the area formula for a circle, which states that the area of a circle is equal to pi multiplied by the square of the radius. In this case, the inner radius of the zinc washer is r and the outer radius is r + 1, so the area of one side of the zinc washer is equal to the area of a circle with a radius of r + 1 minus the area of a circle with a radius of r. This can be expressed mathematically as pi*(r+1)² - pi*r², which is a polynomial equation for the area of one side of the zinc washer.
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A cuboid has faces with areas 24, 32, and 48 square centimeters. what are the lengths of its sides?
Answers
Answer:
Let's denote the length, width, and
height of the cuboid as "l", "w", and
"h, respectively. Then, we have:
lw= 24 (Area of one face)
Ih 32 (Area of another face)
wh 48 (Area of the third face)
To solve for the dimensions of the
cuboid, we can use a system of
equations. We can start by solving
for one of the variables in terms of
the other two. For example, from the
first equation, we have:
W 24/
Substituting this into the second
equation, we get:
Ih 32
I(24/)h = 32
24h 32
h 32/24
h 4/3
Next, we can substitute the values of
h and w into the third equation to
solve for:
wh = 48
I(24/)(4/3) = 48
I2 72
= sqrt(72)
I= 6sqrt(2)
Finally, we can use the values of I
and w to solve for the remaining
dimension:
lw 24
(6sqrt(2))(24/(6sqrt(2))) = 24
W = 4sqrt(2)
Therefore, the lengths of the sides of
the cuboid are:
Length () = 6v2 cm
Width (w) = 4/2 cm
Height (h) = 4/3 cm
The quotient of a number and negative eight is seven-eighths. Find the number.
Answers
The value of the numer is negative seven ( -7 ).
What is the unknown number?Given the statement in the question; the quotient of a number and negative eight is seven-eighths.
Let's translate the given statement into an algebraic equation to solve for the unknown number.
"The quotient of a number and negative eight" means that we are dividing the number by -8.
We can represent this using the division symbol " / ":
Let the number be represented by x.
x / (-8)
"Is" means "equals" " = "
"Seven-eighths" can be written as a fraction:
7/8
Nowm putting it all together, we get:
x / (-8) = 7/8
To solve for x, we can multiply both sides by -8:
x = (-8) × (7/8)
Simplifying the right side, we get:
x = -7
Therefore, the value of x is -7.
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Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 2 more
than 2 times the number of marbles Mark has, how many does each boy have to sell if the total number
of marbles is 71?
Answers
Mark has 23 marbles and Don has 48 marbles.
What is equation?
An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.
Mark and Don, are selling their marbles at a garage sale. Don has more marbles than Mark and his number of marbles is equal to "2 more than 2 times the number of marbles Mark has."
Let x be the number of marbles that Mark has. Then, we can represent the number of marbles that Don has as 2x + 2.
Since the total number of marbles is 71, we can set up the equation:
x + (2x + 2) = 71
Simplifying the left side of the equation, we get:
3x + 2 = 71
Subtracting 2 from both sides, we get:
3x = 69
Dividing both sides by 3, we get:
x = 23
So Mark has 23 marbles. To find out how many marbles Don has, we can substitute x = 23 into the expression we derived earlier:
2x + 2 = 2(23) + 2 = 48
Therefore, Don has 48 marbles.
In total, they have 23 + 48 = 71 marbles, as given in the problem statement.
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Consider the following function.
g(x)=3−1/2x
Step 2 of 2 : Find two points on the line to graph the function.
Answers
Answer:(0,3) (2,2)
Step-by-step explanation:
You can afford a $350 per month car payment. You've found a 5 year loan at 6% interest. How big of a loan can you afford?
Answers
Roberto bought a $400,000 house, paying 24% down, and financing the rest at 6.2% interest for 30 years. Her
monthly payments are $1861.91. How much will he really pay for her $400,000 house?
Roberto will pay a total of $
for the house.
Answers
Answer:
24% of $400,000 = 0.24 x $400,000 = $96,000
The amount he financed is:
$400,000 - $96,000 = $304,000
To calculate the total amount Roberto will pay for the house, we need to add up the principal (the amount he borrowed), the interest, and any fees or charges. We can use the formula for the monthly payment of a mortgage to find the total amount:
M = P [ i(1 + i)^n ] / [ (1 + i)^n - 1]
where M is the monthly payment, P is the principal, i is the monthly interest rate (6.2% divided by 12), and n is the total number of payments (30 years times 12 months per year).
Plugging in the values, we get:
$1861.91 = $304,000 [ 0.00516667(1 + 0.00516667)^360 ] / [ (1 + 0.00516667)^360 - 1]
Solving for P, we get:
P = $304,000
So the total amount Roberto will pay for the house is:
$96,000 (down payment) + $1861.91 x 360 (monthly payments for 30 years) = $96,000 + $670,287.60 = $766,287.60
Therefore, Roberto will pay a total of $766,287.60 for the $400,000 house.
Bridge B is 186 feet shorter than Bridge A. The combined length of the two bridges is 9456 feet. Find the length of each bridge.
Answers
Answer:
Length of Bridge A = 4821
Length of Bridge B = 4635
Step-by-step explanation:
Let's call the length of Bridge A "x" which is measured in feet. According to the problem, the length of Bridge B is "186 feet shorter than Bridge A." This can be written as the following:
Length of Bridge B = x - 186
The problem also tells us that the "combined length of the two bridges is 9456 feet," which we can write as:
Length of Bridge A + Length of Bridge B = 9456
Now we can substitute the expression we found for the length of Bridge B into this equation. This can be shown as the following:
x + (x - 186) = 9456
Simplifying this equation, we can combine the two x terms and get the following:
2x - 186 = 9456
Now, we can solve for x
2x - 186 + 186 = 9456 + 186
2x = 9642
x = 4821
So the length of Bridge A is 4821 feet. To find the length of Bridge B, we can use the expression we found earlier:
Length of Bridge B = x - 186 = 4821 - 186 = 4635
Therefore, the length of Bridge A is 4821 feet, and the length of Bridge B is 4635 feet.
Find the linear function with the following properties.
f(0)=6
Slope of f=−9
Answers
Answer: y=-9x+6
Step-by-step explanation: The common form of a line is the Slope-Intercept form which is y=Mx+B. M represents the slope of the line, B represents the y-intercept, and x and y represent a point on the xy plane such as (1,2). The y-intercept is the point at which x = 0. The slope of a line is given by the equation (y2-y1)/(x2-x1) where (y1,x1) and (y2,x2) are points on a coordinate plane.
In this problem, we are already given M or the slope which is -9. We are also given the y-intercept but it's not as clear. f(x)=y represents a general function where you input an x-coordinate x into f(x) and the function produces a y-coordinate y. If we had a function f(x)=2x+1 and we input 3 as x we replace all the x's with 3 which gives us f(x)=2(3)+1=7. f(3)=7 which can be written as (3,7) being a point on the function. Lines in the coordinate plane represent linear functions because they have a constant slope due to no exponents.
Here, we are told f(0)=6 which can be rewritten as (0,6) being a point on the linear function. I said earlier that the y-intercept is when x=0 and this point has x=0. y=6 when x=0 so 6 is our y-intercept. Now we plug into the slope-intercept form y=mx+b giving us y=-9x+6 which is our answer.
Hope this helps! For practice, find the linear function that has the two points (1,2) and (3,6) on it.
0 is greater than or equal to 0
A.) No solution
B.) all real numbers
Answers
The answer of the given question based on the inequality is option B) all real numbers.
What are Real numbers?A real numbers are set of numbers that include all rational and irrational numbers, which can be expressed as decimal expansions that go on forever without repeating. The set of real numbers is denoted by symbol ℝ and includes numbers such as 1, 2, 3, -4, -5/6, π, √2, and e.
B.) all real numbers
A statement "0 is greater than or equal to 0" is always true, regardless of value of variable or any other conditions. This is because any number is always equal to the itself, and 0 is no exception. Therefore, solution to this inequality is all the real numbers.
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The circle below has center o, and its radius is 4 yd. Given that m
Answers
Answer:
length = 0.89π yd
area = 14.22π yd^2
Step-by-step explanation:
Given r = 4, θ = 40
Length of an arc = 2πr(θ/360º)
l = 2π(4)(40/360) = π(320/360) = π(8/9) = 0.89π
Given r = 4, θ = 360 - 40 = 320
Area of a sector of circle = πr^2(θ/360º)
A = π(4^2)(320/360) = π(16)(8/9) = 14.22π
When a specific variety of radish is grown without
fertilizer, the weights of the radishes produced are
, normally distributed with mean 40 g and standard
deviation 10 g.
Determine the proportion of radishes grown:
a) Without fertilizer with weights less than 50 grams
C
b) Without fertilizer with weights between 20 and 60 g
c) Without fertilizer with weights greater than 60 g
0
Submit
When the same variety of radish is grown in the same
way but with fertilizer added, the weights of the
radishes produced are also normally distributed, but
with mean 140 g and standard deviation 40g.
Determine the proportion of radishes grown:
d) With fertilizer with weights less than 60 grams
e) With fertilizer with weights between 20 and 60 g
f) With fertilizer with weights greater than 60 g
Answers
Answer:
Step-by-step explanation:
a) Without fertilizer with weights less than 50 grams:
Let X be the weight of radishes produced without fertilizer. Then, X ~ N(40, 10^2).
We need to find P(X < 50).
Using the standard normal distribution, we have:
Z = (X - 40)/10
P(X < 50) = P(Z < (50-40)/10) = P(Z < 1) = 0.8413 (using a standard normal table or calculator)
Therefore, the proportion of radishes grown without fertilizer with weights less than 50 grams is 0.8413.
b) Without fertilizer with weights between 20 and 60 g:
We need to find P(20 < X < 60).
Using the standard normal distribution, we have:
Z1 = (20 - 40)/10 = -2
Z2 = (60 - 40)/10 = 2
P(20 < X < 60) = P(-2 < Z < 2) = 0.9544 (using a standard normal table or calculator)
Therefore, the proportion of radishes grown without fertilizer with weights between 20 and 60 grams is 0.9544.
c) Without fertilizer with weights greater than 60 g:
We need to find P(X > 60).
Using the standard normal distribution, we have:
Z = (60 - 40)/10 = 2
P(X > 60) = P(Z > 2) = 0.0228 (using a standard normal table or calculator)
Therefore, the proportion of radishes grown without fertilizer with weights greater than 60 grams is 0.0228.
d) With fertilizer with weights less than 60 grams:
Let Y be the weight of radishes produced with fertilizer. Then, Y ~ N(140, 40^2).
We need to find P(Y < 60).
Using the standard normal distribution, we have:
Z = (60 - 140)/40 = -2
P(Y < 60) = P(Z < -2) = 0.0228 (using a standard normal table or calculator)
Therefore, the proportion of radishes grown with fertilizer with weights less than 60 grams is 0.0228.
e) With fertilizer with weights between 20 and 60 g:
We need to find P(20 < Y < 60).
Using the standard normal distribution, we have:
Z1 = (20 - 140)/40 = -3
Z2 = (60 - 140)/40 = -2
P(20 < Y < 60) = P(-3 < Z < -2) = 0.0668 (using a standard normal table or calculator)
Therefore, the proportion of radishes grown with fertilizer with weights between 20 and 60 grams is 0.0668.
f) With fertilizer with weights greater than 60 g:
We need to find P(Y > 60).
Using the standard normal distribution, we have:
Z = (60 - 140)/40 = -2
P(Y > 60) = P(Z > -2) = 0.9772 (using a standard normal table or calculator)
Therefore, the proportion of radishes grown with fertilizer with weights greater than 60 grams is 0.9772.
In the figure, XYZ and MNL
Find m
Answers
Answer:
∠ Y = 124°
Step-by-step explanation:
given the triangles are congruent , then corresponding angles are congruent, that is
∠ Y = ∠ N = 124°
The length of tile B is about 3.16228 inches. Which mark on the tape measure is closest to 3.16228 inches? Remember, the tape measure is marked in sixteenths of an inch.
Answers
The closest mark on the tape measure to 3.16228 inches in eighths of an inch is the mark for 25 eighths of an inch.
What is the mark on the tape?
To find the closest mark on the tape measure to 3.16228 inches, we need to convert 3.16228 inches to sixteenths of an inch, which is the unit used on the tape measure.
We can start by multiplying 3.16228 by 16 to convert it to sixteenths of an inch:
3.16228 * 16 = 50.59648
Next, we can round 50.59648 to the nearest whole number, which is 51. This means that the closest mark on the tape measure to 3.16228 inches is the mark for 51 sixteenths of an inch.
Note that we can also convert 3.16228 inches to eighths of an inch by multiplying by 8, which gives us:
3.16228 * 8 = 25.29824
Rounding 25.29824 to the nearest whole number gives us 25. This means that the closest mark on the tape measure to 3.16228 inches in eighths of an inch is the mark for 25 eighths of an inch.
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1. An airplane flies in the path shown by the vector CD on the graph below. What is the magnitude and direction of CD? (1 unit represents 1 mile)
Answers
The magnitude of CD is 5 miles and its direction is approximately 53.13°.
option D.
What is the magnitude and direction of the vector?To find the magnitude and direction of CD, we first need to calculate the distance between points C and D, which will give us the magnitude of the vector CD.
The distance formula between two points (x1, y1) and (x2, y2) is:
d = √((x2 - x1)² + (y2 - y1)²)
Plugging in the values for points C and D, we get:
d = √((0 - (-4))² + (1 - 4)²)
= √(16 + 9)
= √(25)
= 5 miles
To find the direction of CD, we can use the arctan function to find the angle that CD makes with the x-axis.
tan(θ) = (y2 - y1) / (x2 - x1)
Plugging in the values for points C and D, we get:
tan(θ) = (1 - 4) / (0 - (-4))
= -3/4
Taking the arctan of both sides, we get:
θ = arctan(-3/4)
≈ -36.87°
However, since CD points in the negative x-direction, we need to add 90 degrees to get the correct direction.
θ = arctan(-3/4) + 90°
≈ 53.13°
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Find the two linearly independent solutions of the LODE following for x>0, and determine at least the first four leading terms in the second solution y(2). 9x²y" - 6xy' + 2y = 0
Please, I need the solution
Answers
Using Cauchy-Euler equation, the solution of the second-order homogeneous differential equation is y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x
What is the solution to the equationThe given LODE is a second-order homogeneous differential equation with constant coefficients. The characteristic equation is given by:
9r^2 - 6r + 2 = 0
Using the quadratic formula, we find the roots to be:
r = (1/3) ± i/sqrt(3)
Thus, the general solution to the differential equation is:
y(x) = c1 * x^(1/3) * cos((1/3)*arccos(sqrt(3)*r)) + c2 * x^(1/3) * sin((1/3)*arccos(sqrt(3)*r))
To find the first solution, we can choose either the cosine or sine term. Let's choose the cosine term for simplicity:
y1(x) = x^(1/3) * cos((1/3)*arccos(sqrt(3)*r))
To find the second solution, we can use the method of reduction of order. Assume that the second solution has the form:
y2(x) = v(x) * y1(x)
Substituting this into the differential equation, we obtain:
9x^2(v''(x)*y1(x) + 2v'(x)*y1'(x) + v(x)*y1''(x)) - 6x(v'(x)*y1(x) + v(x)*y1'(x)) + 2v(x)*y1(x) = 0
Simplifying this equation by dividing by x^2*y1(x), we get:
9v''(x) + (18/r)x*v'(x) + ((2/r^2) - 1)v(x) = 0
where r = sqrt(3)
This is a Cauchy-Euler equation, which can be solved by assuming a solution of the form:
v(x) = x^m
Substituting this into the equation, we obtain:
9m(m-1) + (18/r)m + ((2/r^2) - 1) = 0
Simplifying this equation, we get:
9m^2 + 6m + 1 = 0
Using the quadratic formula, we find the roots to be:
m = (-1/3) or (-1/3)
Thus, the second solution is given by:
y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * ln(x)
To determine the first four leading terms in the second solution, we can use the Taylor series expansion of the natural logarithm:
ln(x) = (x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...
Substituting this into the second solution, we obtain:
y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * [(x-1) - (1/2)(x-1)^2 + (1/3)(x-1)^3 - ...]
Simplifying this expression, we get:
y2(x) = c3 * x^(1/3) + c4 * x^(1/3) * (x-1) - c4 * x^(1/6) * (1/2)(x-1)^2 + c4 * x^(1/3) * (1/3)(x-1)^3 - ...
Thus, the first four leading terms in the second solution are:
y2(x) = c3 * x^(1/3) + c4 * x^(4/3) - (1/2) * c4 * x
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You survey customers at a restaurant who have contracts with three different wireless telecommunication providers. The survey asks whether they have cell phone service at the restaurant. The results, given as joint relative frequencies, are shown in the two-way table. Find the probability that a randomly selected customer has a contract with provider B. Then find the probability that a randomly selected customer who does not have cell phone service has a contract with provider B. Write your answers as decimals rounded to the nearest hundredth. Use your answers to determine whether having a contract with provider B and not having cell phone service are independent events.
Provider A Provider B Provider C
Yes 0.31 0.43 .12
No 0.04 0.07 .03
Answers
Having a contract with provider B and not having cell phone are independent events.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.
If two events are independent, the multiplication of the probabilities of each event is equals to the probability of both events happening.
The probabilities for this problem are given from the table as follows:
Provider B: 0.43 + 0.07 = 0.5.No cell phone: 0.04 + 0.07 + 0.3 = 0.14.Provider B and no cell phone: 0.07.The multiplication of the probabilities of each event is:
0.5 x 0.14 = 0.07 -> independent events = Provider B and no cell phone: 0.07.
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which of the following is a point of tangency on the circle below
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The correct option is C. Point B as only the line BC touching the circle at point B is tangent to the circle.
Tangent to a circle theoremThe tangent to a circle theorem states that a line is tangent to a circle if and only if the line is perpendicular to the radius drawn to the point of tangency
We can observe that the line BC touches the circle at point B and the radius of the circle will be perpendicular to the line BC
Therefore, since the radius of the circle is perpendicular to the line BC at point B, then it is tangent to the circle
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The residual plot shows the residuals for a person's age and their vertical jump (in inches). Which statement best
assesses the linearity of the relationship between age and vertical jump if it is known that the scatterplot appears to
be approximately linear?
Although it is given that the scatterplot is approximately linear, because the residual plot has no obvious pattern,
it is appropriate to use the line of best fit to predict vertical jump based on age.
O Although it is given that the scatterplot is reasonably linear, because the residual plot has no obvious pattern, it is
not appropriate to use the line of best fit to predict vertical jump based on age.
O Although it is given that the scatterplot is reasonably linear, because the residual plot has a clear curved pattern,
it is appropriate to use the line of best fit to predict vertical jump based on age.
Although it is given that the scatterplot is reasonably linear, because the residual plot has a clear curved pattern,
it is not appropriate to use the line of best fit to predict vertical jump based on age.
Answers
The statement that best assesses the linearity of the relationship between age and vertical jump, given that the scatterplot appears to be approximately linear, is:
Although it is given that the scatterplot is reasonably linear, because the residual plot has no obvious pattern, it is appropriate to use the line of best fit to predict vertical jump based on age.
The second option is correct.
What is a residual plot ?
A residual plot is described as a graphical technique that attempts to show the relationship between a given independent variable and the response variable given that other independent variables are also in the model.
If the residual plot has no obvious pattern, it suggests that the relationship between the variables is linear and that the line of best fit is appropriate for predicting the vertical jump based on age.
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Answer:
thx to the comments
Step-by-step explanation:
e) What is the expected number of 6's if you roll 9 dice?
Expected number is
Round answer to two decimal places
Answers
Answer:
approximately 1.5 times but round up to 2
Answer
if you were to roll a dice 9 times you would have the chance to roll 6, 1.5 times.
1/6 and 0.5/3
Step-by-step explanation:
for every number on a dice there is a chance that you'll get that number 1.5 times
Find the values of a and b. Write your answers in simplest form.
Answers
The answer of the given question based on finding the values of a and b are 12 and 9, respectively.
What are Triangle?A triangle is geometric shape that consists of the three straight sides and three angles. Triangles are one of basic shapes in geometry and often used in the various mathematical applications.
Since triangles are similar, their corresponding sides are in the proportion. That is:
AB/DE = BC/EF = AC/DF
We can use this proportion to find the values of a and b.
From the diagram, we can see that:
AB = 12 + a
BC = 9 + b
AC = 15
DE = 8
EF = 6
Using the proportion, we get:
AB/DE = BC/EF
(12 + a)/8 = (9 + b)/6
Cross-multiplying, we get:
6(12 + a) = 8(9 + b)
72 + 6a = 72 + 8b
6a = 8b
a/b = 4/3
Similarly, using the other part of the proportion, we get:
AC/DF = 15/DF = (AB + BC)/(DE + EF) = (12 + a + 9 + b)/(8 + 6)
15DF = 21 + a + b
Substituting the value of a/b = 4/3, we get:
15DF = 21 + (4/3)b + b
15DF = 21 + (7/3)b
45DF = 63 + 7b
45DF = 7(b + 9)
Dividing both sides by 7, we get:
DF = (b + 9)
Substituting this value in the previous equation, we get:
45(b + 9) = 63 + 7b
45b + 405 = 63 + 7b
38b = 342
b = 9
Substituting the value of b in the equation a/b = 4/3, we get:
a/9 = 4/3
a = 12
Therefore, the values of a and b are 12 and 9, respectively.
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Siobhan rotates a right triangle 90° counterclockwise about the origin.
Is the image of the triangle congruent to the preimage?
Answers
Answer:
yes
Step-by-step explanation:
congruent means similar
A triangular prism and its net are shown below. Please answer the questions EASY 20 points
Answers
Answer: SEND ME THE PIC
Step-by-step explanation:
What is the solution to 4^x = 5^x +^2
Answers
The solution to 4^x = 5^x +^2 is
x = -2log 5/( log 5 - log 4)
Option C is correct.
How do we calculate?We will rewrite the equation as:
4^x = 5^x * 5^2
applying the logarithm function to both sides of the equation.
log(4^x) = log(5^x * 5^2)
simplifying the right side of the equation, using the properties of logarithms,
log(4^x) = log(5^x) + log(5^2)
log(4^x) = xlog(4) = x2log(2)
log(5^x) + log(5^2) = xlog(5) + log(25)
Substituting these results back into the original equation, we have:
x2log(2) = x*log(5) + log(25)
x*(2*log(2) - log(5)) = log(25)
Divide both sides by (2*log(2) - log(5)), we get:
x = x = -2log 5/( log 5 - log 4)
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