The sales price divided by total cost is 123%.
Based on the information provided, I can help you complete the table:
Purchase Price | Load | Total Cost | Sales Price | Sales Price ÷ Total Cost (nearest 1%)
ABC = $425 | 0 | $425 | $850 | 200%
DEF = $600 | $375 | $975 | $1,200 | 123%
For mutual fund ABC, there was no load, so the total cost is equal to the purchase price. The sales price ÷ total cost is 200% (nearest 1%). For mutual fund DEF, the total cost includes the $375 load, resulting in a total cost of $975. The sales price ÷ total cost is 123% (nearest 1%).
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Select two trigonometric functions that are equivalent to the ratio x/y.
Sine and cosine are both equivalent to x/y, depending on the angle of the point on the circle.
To find two trigonometric functions equivalent to the ratio x/y, we can use the unit circle. Let's assume that x and y are the coordinates of a point on the circle, where x represents the horizontal displacement, and y represents the vertical displacement.
From this, we can find that the sine of the angle that x and y make with the x-axis is y, and the cosine of that angle is x. Therefore, the two trigonometric functions equivalent to the ratio x/y are sine and cosine.
We can write this as sin(angle) = y/y and cos(angle) = x/y. It's important to note that the value of the angle depends on the position of the point on the unit circle.
So, sine and cosine are both equivalent to x/y, depending on the angle of the point on the circle.
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show work/steps please
Find the Taylor series for f centered at 6 if f(n) (6) = (-1)"n! 4"(n + 2) Σ n = 0 What is the radius of convergence R of the Taylor series? R = = X
The Taylor series for f centered at 9, given f^(n)(9) = (-1)^n n!/6^n (n + 2), is f(x) = f(9) - (x-9)/2 + (x-9)^2/12 - (x-9)^3/432 + (x-9)^4/10368 - ... .
To find the Taylor series for f centered at 9, we need to use the formula
f(x) = f(a) + f'(a)(x-a)/1! + f''(a)(x-a)^2/2! + f'''(a)(x-a)^3/3! + ...
where f'(x) represents the first derivative of f(x) with respect to x, f''(x) represents the second derivative of f(x) with respect to x, and so on.
In this case, we are given the nth derivative of f(x) evaluated at x = 9, so we can plug in the values and simplify the formula
f(9) = f(9) (since we're centering the series at 9)
f'(9) = (-1)^1 (1!/6^1)(1 + 2) = -1/2
f''(9) = (-1)^2 (2!/6^2)(2 + 2) = 1/6
f'''(9) = (-1)^3 (3!/6^3)(3 + 2) = -1/36
f''''(9) = (-1)^4 (4!/6^4)(4 + 2) = 1/216
and so on. So the Taylor series for f centered at 9 is
f(x) = f(9) - (x-9)/2 + (x-9)^2/2! * 1/6 - (x-9)^3/3! * 1/36 + (x-9)^4/4! * 1/216 - ...
or, simplifying the coefficients
f(x) = f(9) - (x-9)/2 + (x-9)^2/12 - (x-9)^3/432 + (x-9)^4/10368 - ...
This is the Taylor series for f centered at 9, based on the given information.
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The given question is incomplete, the complete question is:
Find the Taylor series for f centered at 9 if f^(n)(9) = (-1)^n n!/6^n (n + 2)
A national forest service wanted to estimate the number of deer in a particular national park. they caught and tagged 55 deer and released them back into the park. later they selected a sample of 319 deer. of the 319 deer, 29 were tagged. assuming that the proportion of tagged deer in the sample holds for all deer in the forest, what is the best estimate of the number of deer in the park?
The best estimate for the number of deer in the park is 1745.
The national forest service caught and tagged 55 deer in order to estimate the number of deer in a particular national park. They then released those deer back into the park and later selected a sample of 319 deer. Of the 319 deer in the sample, 29 were tagged.
Assuming that the proportion of tagged deer in the sample holds for all deer in the forest, we can use a proportion to estimate the number of deer in the park. We know that 29 out of 319 deer in the sample were tagged, so the proportion of tagged deer is 29/319.
To estimate the total number of deer in the park, we can use this proportion. We can set up a proportion where x is the total number of deer in the park:
(29/319) = (55/x)
We can then cross-multiply to solve for x:
29x = 319*55
x = 1745
Therefore, the best estimate for the number of deer in the park is 1745. However, it is important to note that this is just an estimate and there may be some error involved.
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The table shows the number of hours that a group of friends been in the first week training to run a marathon. In the second week they each add five hours to their training times what are the mean median mode and range of times for the second week
Jeff - 9
Mark - 5
Karen - 5 Costas - 5
Brett - 7
Nikki - 6
Jack - 7
A. Mean is 10
Median is 11 Mode is 11. 3
Range is 4
B. Mean is 11 Median is 11. 3 Mode is 10
Range is 0. 3
C
Mean is 11. 3
Median is 11 Mode is 10
Range is 4
D
Mean is 11. 3
Median is 11 Mode is 10
Range is 0. 3
Please help this is a test question
The mean, median, mode, and range for the second week of training are: Mean is 11.3, median is 11, mode is 10, and range is 4.
What are the mean, median, mode, and range?To find the mean, median, mode, and range for the second week of training, we first need to calculate the new training times by adding five hours to each person's first week time:
Jeff - 9 + 5 = 14
Mark - 5 + 5 = 10
Karen - 5 + 5 = 10
Costas - 5 + 5 = 10
Brett - 7 + 5 = 12
Nikki - 6 + 5 = 11
Jack - 7 + 5 = 12
The new training times for the second week are:
14, 10, 10, 10, 12, 11, 12
To find the mean, we add up all the training times and divide by the number of people:
Mean = (14 + 10 + 10 + 10 + 12 + 11 + 12) / 7
Mean = 11.3
To find the median, we first need to put the training times in order from smallest to largest:
10, 10, 10, 11, 12, 12, 14
The median is the middle value, which in this case is 11.
To find the mode, we need to find the value that occurs most frequently. In this case, there are two modes, which are 10 and 12.
To find the range, we subtract the smallest value from the largest value:
Range = 14 - 10
Range = 4
Therefore, the answer is option C:
Mean is 11.3
Median is 11
Mode is 10
Range is 4
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Consider a population that grows according to the recursive rule Pn=Pn−1+50
, with initial population P0=30
To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.
We are given a population growth model with a recursive rule and an initial population. Let's break down the information and find the population at any given term n.
Recursive rule: Pₙ = Pₙ₋₁ + 50
Initial population: P₀ = 30
Now let's find the population at any term n, using the recursive rule:
Step 1: Determine the base case, which is the initial population.
P₀ = 30
Step 2: Apply the recursive rule to find the next few terms.
P₁ = P₀ + 50 = 30 + 50 = 80
P₂ = P₁ + 50 = 80 + 50 = 130
P₃ = P₂ + 50 = 130 + 50 = 180
Step 3: To find the population at any given term n, continue to apply the recursive rule.
Pₙ = Pₙ₋₁ + 50
Using this recursive rule and the initial population, you can find the population at any given term n.
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Tim wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 5 3 4 m by 3 1 2 m. Find the area the grass seed needs to cover. Solve on paper. Then check your work on Zearn
The area of the grass seed needs to cover is 38.625 m².
What is the area of the rectangle?
A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel.
Here, we have
Given: Tim wants to buy grass seed to cover his whole lawn, except for the pool. The pool is 5 3/4 m by 3 1/2 m.
We have to find the area the grass seed needs to cover.
Let the area of the grass seed needs to cover be A
Now , the area of the lawn L = ( 11 3/4 ) x 5 m²
The area of the lawn L = 58.75 m²
where the length of the pool l= ( 5 3/4 ) m = 5.75 m
The width of the pool is w = ( 3 1/2 ) m = 3.5 m
Now, Area of Rectangle = Length x Width
On simplifying, we get
Area of the pool P = 5.75 x 3.5 = 20.125m²
Now, the area of the grass seed needs to cover A = L - P
The area of the grass seed needs to cover A = 58.75 m² - 20.125 m²
The area of the grass seed needs to cover A = 38.625 m²
Hence, the area of the grass seed needs to cover is 38.625 m².
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If x = -3, then which inequality is true?
The inequailty y < x + 3 would be true when x = -3 and all values of y are less than 1
If x = -3, then which inequality is true?From the question, we have the following parameters that can be used in our computation:
The statement that x = -3
The above value implies that we substitute -3 for x in an inequality and solve for the variable y
Take for instance, we have
y < x + 4
Substitute the known values in the above equation, so, we have the following representation
y < -3 + 4
Evaluate
y < 1
This means that the inequailty y < x + 3 would be true when x = -3 and all values of y are less than 1
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For a certain company , the cost for producing x items is 50x + 300 and the revenue for selling x items is 90x - 0. 5x^2.
a) set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces (hint: it is a quadratic polynomial)
b) find two values of x that will create a profit of $300
c) is it possible for the company to make a profit of $15,000
Answer:
Step-by-step explanation:
a) Profit = Revenue - Cost = (90x - 0.5x²) - (50x + 300)
= -0.5x² + 90x - 50x - 300
= -0.5x² + 40x - 300
b) -0.5x² + 40x - 300 = 300
-0.5x² + 40x - 600 = 0
use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -600):
x = 20, 60
c) -0.5x² + 40x - 300 = 15000
-0.5x² + 40x - 15300 = 0
use quadratic equation to find the roots of x (a = -0.5, b = 40, c = -15300):
x = 40±10√290i
Not possible to make a profit of $15,000
Describe the clockwise rotation about the origin from the pre-image to the image
The clockwise rotation about the origin from the pre-image to the image include the following: a rotation of 90° clockwise.
What is a rotation?In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Additionally, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
Next, we would apply a rotation of 90° clockwise to the coordinate of triangle ABC as follows;
(x, y) → (y, -x)
Coordinate A = (1, 1) → Coordinate A' = (1, -(1)) = (1, -1)
Coordinate B = (1, 4) → Coordinate B' = (4, -(1)) = (4, -1)
Coordinate C = (5, 1) → Coordinate C' = (1, -(5)) = (1, -5)
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You and a group of friends want to know how many students in your school prefer rap music. There are 440 students in your school. Each person in the group randomly surveys 20 students. The table shows the results.
A. Use each sample to make and estimate for the number of students in your school who prefer rap music
B. Describe the center and variation of the estimates
The survey results show that the estimates for the number of students in the school who prefer rap music range from 110 to 154. The center of the estimates is around 121, with a variation of about 66.
To estimate the number of students who prefer rap music, multiply the proportion who prefer rap in each sample by the total number of students in the school (440)
Sample 1: 0.25 x 440 = 110
Sample 2: 0.20 x 440 = 88
Sample 3: 0.30 x 440 = 132
Sample 4: 0.35 x 440 = 154
The center of the estimates is the average of the four estimates: (110 + 88 + 132 + 154) / 4 = 121. Variability can be described using the range (154 - 88 = 66) or the standard deviation of the estimates, which requires additional calculations.
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Show your work for multiplying the polynomials below and put your answer in standard form in the box below: (No work loses points)
(x+6)(x2−3x−4)
The polynomials are multiplied to give the expression x³ + 3x² - 22x - 24
How to determine the productWe need to know that algebraic expressions are described as expressions that are composed of terms, variables, their coefficients, factors and constants.
Also, these expressions are made up of mathematical operations. They are listed as;
SubtractionMultiplicationDivisionAddition BracketParenthesesFrom the information given, we have the expression;
(x+6)(x2−3x−4)
expand the bracket, we get;
x³ - 3x² - 4x + 6x² - 18x - 24
add the like terms, we get;
x³ + 3x² - 22x - 24
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Three times a week tina walks 3/10 mile from school to library studies for 1 hour and then walks home 4/10 mile home. how much more will she need to walk to win a prize
To calculate how much more Tina needs to walk to win a prize, we first need to determine how much she currently walks in a week.
Tina walks 3/10 mile from school to the library three times a week, which is a total of 3/10 x 3 = 9/10 mile. She also walks 4/10 mile home, three times a week, which is a total of 4/10 x 3 = 12/10 miles.
Therefore, Tina currently walks a total of 9/10 + 12/10 = 21/10 miles in a week.
To determine how much more Tina needs to walk to win a prize, we need to know the criteria for winning the prize. If the prize requires walking a certain number of miles in a week, we can subtract 21/10 miles from the required number of miles to find out how much more Tina needs to walk.
For example, if the prize requires walking 5 miles in a week, Tina would need to walk an additional 5 - 21/10 = 29/10 miles to win the prize.
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Unit 11 volume & surface area homework 4 area of regular figures
The area of the regular figure of side length 24 cm is 1496.45 square centimeter.
The given regular figure is a hexagon.
A hexagon is a polygon with six sides and six angles.
It is a two-dimensional shape formed by connecting six straight line segments.
The side length of hexagon is 24 cm..
The formula for the area of a regular hexagon is 3√3/2 a².
Where a is the side length of hexagon.
Area = 3√3/2 a².
Plug in a value as 24:
Area = 3√3/2 ×24²
= 3√3×576/2
=2992.9/2
=1496.45 square centimeter.
Hence, the area of figure is 1496.45 square centimeter.
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Find the area of the regular figure below:
In March 2020, a newspaper article reported that houses in Nevada are so expensive that many people are unable to
afford the monthly house payments.
This graph shows the average house price and the average monthly payment for all the different counties in Nevada.
House Prices and Payments
1a. What does the pattern of the data indicate
about the connection between house prices and
monthly payments?
Type Here
1b. Find the monthly payment for a house
costing $450,000.
Type Here
1c. Find a formulate connecting the average
monthly payment with the average house price
in slope-intercept form (y = mx + b).
Type Here
Average monthly payment/dollars
5000
4000-
3000
000
100000
Fosfor
200000 300000 400000
Average house price/dollars
500000
The pattern of the data indicates a linear relationship or strong positive correlation between the average house prices and average monthly payments.
The monthly payment for a house costing $450,000 is $3,600.
A formulate connecting the average monthly payment with the average house price in slope-intercept form is y = 0.008x.
What is a proportional relationship?In Mathematics, a proportional relationship can be represented by this equation:
y = kx
Where:
x represents the average house price.y represents the average monthly payment.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) as follows:
Constant of proportionality (k) = y/x
Constant of proportionality (k) = 8/1000
Constant of proportionality (k) = 1/125 or 0.008.
Therefore, a formula that connects the two variables is given by;
y = kx
y = 0.008x
When average house price (x) = $450,000, the average monthly payment (y) is given by:
y = 0.008(450,000)
y = $3,600.
In conclusion, we can logically deduce that the pattern of the data shows a linear relationship or strong positive correlation between the average house prices (x) and average monthly payments (y) because as the average house prices (x) increases, the average monthly payments (y) also increases.
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Please hurry I need it asap
Answer: 2
sqrt 41
Step-by-step explanation:
distance formula is just d=√((x2 – x1)² + (y2 – y1)²)
√(-2+8)^2+(-5-3)^2
√(-10)^2+(-8)^2
√100+64
2√41
Will give brainliest if right
aabc ~ def. what sequence of transformations will move aabc onto adef?
d. a dilation by scale factor of 2, centered at the origin, followed by a reflection over the y-axis
AABC is transformed onto ADEF by a dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis.
The sequence of transformations that will move AABC onto ADEF is a dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis.
Firstly, dilation is a transformation that changes the size of an object but not its shape.
The dilation factor is multiplied by each coordinate, so when the dilation is centered at the origin, the new coordinates will be twice the original coordinates.
Therefore, AABC will be enlarged to A'BC', and DEF will be enlarged to D'E'F, both with double the size.
Then, reflection is a transformation that flips an object over a line of reflection. In this case, the line of reflection is the y-axis.
When we reflect A'BC' over the y-axis, we get A''B''C'', and when we reflect D'E'F over the y-axis, we get D''E''F''.
Therefore, AABC is transformed onto ADEF by a dilation by a scale factor of 2, centered at the origin, followed by a reflection over the y-axis.
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Four drivers recorded the distance they drove each day for a week. Which driver's data set has a mode that is greater than the mean or median AND a median with the lowest value of the three measures?
a
Kadisha: 8, 17, 23, 16, 17, 18, 125
b
Cole: 14, 26, 34, 22, 47, 22, 45
c
Fabian: 7, 12, 11, 23, 13, 23, 30
d
Ling: 52, 36, 41, 31, 31, 37, 59
Driver's data set that has a mode that is greater than the mean or median is Fabian and a median with the lowest value of the three measures is Kadisha.
Data of Fabian: 7, 12, 11, 23, 13, 23, 30
Mean = sum of all observation / total no. of observation
Mean = (7+ 12+ 11+ 23+ 13+ 23+ 30) / 7
Mean = 17
Mode = most repeating observation
Mode = 23
For median we have to write observation in ascending order
7,11,12,13,23,23,30
Median = (N+1)/2
Where N = No. of observation
Median = (7+1)/2
Median = 4th observation
Median = 13
Here mode that is greater than the mean or median.
similarly for,
Kadisha: 8, 17, 23, 16, 17, 18, 125
Mean = 32
Median = 17
Mode = 17
Here median with the lowest value of the three measures.
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Triangle A′B′C′ is a dilation of triangle ABC about point P with a scale factor of 1/2. Is the dilation a reduction or an enlargement? reduction enlargement
Triangle A′B′C′ is a dilation of triangle ABC about point P with a scale factor of 1/2. The dilation is a reduction.
A dilation is a transformation that changes the size of a figure, but not its shape. It can be either an enlargement or a reduction depending on the value of the scale factor.
If the scale factor is greater than 1, then the image will be larger than the original figure. This is called an enlargement.
If the scale factor is between 0 and 1, then the image will be smaller than the original figure. This is called a reduction.
In this case, the scale factor is 1/2, which is less than 1. Therefore, the image of triangle ABC is smaller than the original triangle, and the dilation is a reduction.
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Use the given odds to determine the probability of the underlined event.
Odds against getting injured by falling off a ladder: 8,988 to 1
The probability of getting injured by falling off a ladder is approximately 0.0001113.
The odds against getting injured by falling off a ladder are 8,988 to 1. This means that for every 8,988 people who do not get injured by falling off a ladder, only one person does get injured by falling off a ladder.
To determine the probability of the underlined event, we can use the formula:
Probability = 1 / (odds + 1)
Plugging in the given odds, we get:
Probability = 1 / (8,988 + 1)
Probability = 1 / 8,989
Probability ≈ 0.0001113
Therefore, the probability of getting injured by falling off a ladder is approximately 0.0001113, or about 0.01113%. This is a very low probability, which highlights the importance of taking safety precautions when using a ladder.
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Alex can stack exactly 16 cookies, each with a diameter of 5 cm inside a cylindrical container with the same diameter and a volume of 100% cm³. What is
the surface area of the container? Round your answer to the nearest square centimeter.
Answer:
Read
Step-by-step explanation:
If Alex can stack exactly 16 cookies with a diameter of 5 cm inside a cylindrical container with the same diameter, then the height of the cylinder will be equal to the height of 16 cookies stacked on top of each other, which is 16 multiplied by the height of one cookie.
The diameter of each cookie is 5 cm, so the radius is 2.5 cm. The volume of each cookie is πr²h, where r is the radius and h is the height, so the volume of one cookie is:
V1 = π(2.5 cm)²h
The volume of 16 cookies will be:
V16 = 16π(2.5 cm)²h
Since the volume of the cylindrical container is 100% cm³, we have:
V16 = Vcyl
where Vcyl is the volume of the cylindrical container. Therefore:
16π(2.5 cm)²h = Vcyl
The height of 16 cookies stacked on top of each other is 16 times the height of one cookie, so:
h = 16(1 cm) = 16 cm
Substituting this value into the equation above and solving for the radius, we get:
r = √(Vcyl / (16πh)) = √(100 cm³ / (16π(16 cm))) ≈ 1.03 cm
The surface area of the cylindrical container is given by the formula:
A = 2πr² + 2πrh
Substituting the values we found for r and h, we get:
A = 2π(1.03 cm)² + 2π(1.03 cm)(16 cm) ≈ 142 cm²
Therefore, the surface area of the container is approximately 142 square centimeters. Rounded to the nearest square centimeter, the answer is 142 square centimeters.
The surface area of the given cylindrical container is 290 cm².
What is the volume of a cylinder?The volume of a cylinder is given by the formula:
V = πr²h
where r is the radius of the cylinder and h is its height.
We know that the volume of the cylindrical container is 100π cm³ and that it has the same diameter as the cookies, which is 5 cm.
Since the diameter of the container is 5 cm, its radius is 2.5 cm.
We can rearrange the formula for volume to solve for
h = V/πr²
h = 100π/π(2.5)²
h = 16
So, the height of the container is 16 cm.
To find the surface area of the container, we can use the formula:
A = 2πrh + 2πr²
where r is the radius of the container and h is its height.
Substituting the values we have, we get:
A = 2π(2.5)(16)+2π(2.5)²
A = 92.5π
A ≈ 290.45
Rounding to the nearest square centimeter,
A = 290
Thus, the surface area of the container is 290 cm².
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A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
Answer:The answer is B
Step-by-step explanation:
A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.
Jack, Martina, and Napier are racing their bikes. Each has an equal chance of winning the race
What is the probability that Jack wins the race, and Martina finishes last?
Therefore, the probability that Jack wins the race and Martina finishes last is 1/6 or approximately 0.167.
What is the probability that Jack wins the race, and Martina finishes last?There are 3 people racing, so there are 3! = 6 possible ways the race can end (assuming no ties).
These are:
Jack, Martina, Napier
Jack, Napier, Martina
Martina, Jack, Napier
Martina, Napier, Jack
Napier, Jack, Martina
Napier, Martina, Jack
Of these 6 outcomes, there is only 1 where Jack wins the race and Martina finishes last: outcome 2.
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N
the accurate scale drawing shows
the positions of port p and a lighthouse l.
n
lindsey sails her boat from port p
on a bearing of 050°
she sails for 12 hours at an average
speed of 5km/h to a port q.
l*
p*
scale: 1 cm represents 3 km.
a) indicate the position of port q on the drawing (use the x tool).
(2)
b) find the distance, in km, of port q from lighthouse l.
(2)
c) find the bearing of port q from lighthouse l.
total marks:
A line segment of length 15 cm at a bearing of 50° from P to locate the position of Q on the drawing. Use the Law of Cosines the distance d between Q and L, which is approximately 71.2 km. Use the Law of Sines the angle x opposite d, which is approximately 29.5°, giving the bearing of Q from L.
Using the given scale of 1 cm represents 3 km, we can draw a line segment of length 15 cm (since 5 km/h x 12 h = 60 km) on a bearing of 50° from P to locate the position of Q. The point Q can be marked on the drawing using the x tool.
We can use the Law of Cosines to find the distance d between Q and L. Let a = 60 km (distance from P to Q), b = 36 km (distance from P to L), and C = 130° (the angle between a and b, which is equal to the sum of the angles at Q and L). Then
d² = a² + b² - 2ab cos(C)
d² = (60)² + (36)² - 2(60)(36)cos(130°)
d ≈ 71.2 km
Therefore, the distance of port Q from lighthouse L is approximately 71.2 km.
We can use the Law of Sines to find the angle x opposite the distance d between Q and L. Let a = 60 km (distance from P to Q), b = 36 km (distance from P to L), and sin(A) = sin(130°)/d. Then
sin(x)/60 = sin(130°)/d
sin(x) = (60/d)sin(130°)
x ≈ 29.5°
Therefore, the bearing of port Q from lighthouse L is approximately 29.5°.
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You pick a card at random.
What is P(even or prime)?
Write your answer as a percentage
Probability of picking an even or prime card at random is approximately 88.89%.
To find the probability of picking an even or prime card at random, we first need to identify the possible cards that meet these conditions.
In a standard deck of cards, there are 52 cards, but we only consider the numerical values, which are 2-10 for each of the four suits (hearts, clubs, spades, and diamonds).
Even numbers: 2, 4, 6, 8, 10
Prime numbers: 2, 3, 5, 7
Combining the even and prime numbers, we have: 2, 3, 4, 5, 6, 7, 8, 10. Note that 2 appears only once in the combined list.
Now we find the probability by dividing the number of favorable outcomes (even or prime numbers) by the total number of possible outcomes (cards numbered 2-10).
P(even or prime) = (Number of even or prime cards) / (Total number of cards from 2-10)
P(even or prime) = 8 / 9
To express the probability as a percentage, multiply by 100:
P(even or prime) = (8 / 9) × 100 ≈ 88.89%
So, the probability of picking an even or prime card at random is approximately 88.89%.
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Juanita keeps 25% of the monthly sales from her ice cream shop as a profit. If the shop makes an average of $750 in sales this month, how much money will Juanita keep as profit this month?
Juanita will keep $187.50 as profit from her ice cream shop's sales this month.
Juanita will keep 25% of the monthly sales as profit, which is equivalent to $750 x 0.25 = $187.50. This means that out of the total monthly sales of $750, Juanita will keep $187.50 as her profit, while the remaining $562.50 will go towards the expenses of running the ice cream shop.
Profit is the amount of money that a business earns after deducting all its expenses. It is the excess revenue that remains after all the costs of doing business have been taken into account. Profit is essential for businesses as it helps them to sustain their operations, invest in growth opportunities, and generate returns for their owners or shareholders.
In Juanita's case, her profit is 25% of the monthly sales, which is a significant amount that can help her to keep her ice cream shop running smoothly. By keeping a portion of the sales as profit, Juanita can use the money to pay for her expenses, such as rent, utilities, and supplies, while still having enough left over to reinvest in her business or save for her personal use.
Overall, understanding the concept of profit is crucial for entrepreneurs and business owners to ensure that they can generate enough revenue to cover their expenses and make a profit that will help them to grow and succeed in the long run.
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Two weeks ago i bought 20 cupcakes last week I bought 13 help me continue the pattern
Answer:
If the pattern is to continue, the next value would be a decrease of 7 from the previous value because 20-13=7. Therefore, the value for this week would be:
13 - 7 = 6
So, if you were to continue the pattern, you would have bought 6 cupcakes this week.
3x + 5y = -59 complete the solution of the equation
The solutions of the equation are y = (-3/5)x - 59/5 and x = (-5/3)y - 59/3
Completing the solution of the equationTo solve for one variable in terms of the other, we can rearrange the equation to isolate one of the variables. For example, solving for y in terms of x:
3x + 5y = -59
5y = -3x - 59
y = (-3/5)x - 59/5
So the solution of the equation is:
y = (-3/5)x - 59/5
Alternatively, we could solve for x in terms of y:
3x + 5y = -59
3x = -5y - 59
x = (-5/3)y - 59/3
So another possible solution of the equation is:
x = (-5/3)y - 59/3
Note that both solutions represent the same line in the xy-plane, since they are equivalent equations.
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find the equation of the line that has a gradient of 2 and passes through the point (-3,3)
Answer:
[tex]y = 2x + 9[/tex]
Step-by-step explanation:
It is given that the slope of the line is 2, and it passes through (-3 , 3). The equation of straight lines is y = mx + b, in which:
y = (x , y) = 3
m = slope (gradient) = 2
x = (x , y) = -3
b = y-intercept
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Plug in the corresponding numbers to the corresponding variables:
y = mx + b
3 = (2)(-3) + b
First, multiply -3 with 2:
[tex]3 = (2)(-3) + b\\3 = (2 * -3) + b\\3 = -6 + b[/tex]
Next, isolate the variable, b. Note the equal sign, what you do to one side, you do to the other. Add 6 to both sides of the equation:
[tex]3 = b - 6\\3 (+6) = b - 6 (+6)\\b = 3 + 6\\b = 9[/tex]
Plug in 2 for slope, and 9 for y-intercept, in the given equation:
[tex]y = mx + b\\m = 2\\b = 9\\[/tex]
[tex]y = 2x + 9[/tex] is your answer.
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Alguém que entende de curva abc? eu tenho um exercício pra fazer sobre, em que o enunciado diz: "4. construir a curva abc com os seguintes dados da tabela abaixo:" e só me dá a tabela mesmo, ele não me dá nenhuma proporção do tipo: a classe a são os produtos que somam 70% sabe? queria saber como vou fazer a divisão abc se não sei a porcentagem de cada um?
ABC curve: order, calculate percentages, and classify items accordingly.
How to construct ABC curve analysis?A Curva ABC é uma ferramenta de gestão de estoques que classifica os itens de acordo com sua importância em termos de valor monetário. Para construir a curva ABC, é necessário primeiro ordenar os itens por ordem decrescente de valor monetário (ou de outro critério relevante, como o volume de vendas). Em seguida, deve-se calcular a porcentagem acumulada do valor total de todos os itens, começando pelo mais valioso.
Assim, a classe A será composta pelos itens que representam os primeiros 20% a 30% do valor total (ou outro percentual definido pela empresa), a classe B pelos itens seguintes que representam cerca de 30% a 50% do valor total, e a classe C pelos itens restantes que representam cerca de 20% a 50% do valor total.
Se o enunciado do seu exercício não especificou a proporção de cada classe, você pode assumir as proporções padrão que são amplamente utilizadas na prática empresarial. Assim, a classe A é composta pelos itens mais importantes, que representam cerca de 20% a 30% do valor total, a classe B pelos itens seguintes que representam cerca de 30% a 50% do valor total, e a classe C pelos itens menos importantes que representam cerca de 20% a 50% do valor total.
Para construir a curva ABC, você pode seguir os seguintes passos:
1. Ordene os itens da tabela em ordem decrescente de valor monetário (ou do critério relevante) e calcule o valor total de todos os itens.
2. Calcule a porcentagem acumulada do valor total de cada item, começando pelo mais valioso. Por exemplo, se o item mais valioso representa 10% do valor total, e o segundo item mais valioso representa 15% do valor total, então a porcentagem acumulada dos dois primeiros itens seria de 25%
3. Classifique os itens de acordo com as proporções padrão da curva ABC (20-30% para a classe A, 30-50% para a classe B e 20-50% para a classe C).
4. Desenhe a curva ABC, representando no eixo X o percentual acumulado dos itens e no eixo Y o percentual do valor total.
5. Identifique os itens que pertencem a cada classe (A, B ou C) na curva ABC.
Espero que isso ajude! Se você tiver mais alguma dúvida, não hesite em perguntar.
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Four levels, coded as −3, −1, 1, and 3 were chosen for each of two variables X1 and X2, to provide a total of sixteen experimental conditions when all possible combinations (X1,X2) were taken. It was decided to use the resulting sixteen observations to fit a regression equation including a constant term, all possible first-order, second-order, third-order and fourth-order terms in X1 and X2. The data were fed into a computer routine which ususlly obtains a vector estimate b = (X X) −1X Y The computer refused to obtain the estimates. Why? The experimenter, who had meanwhile examined the data, decided at this stage to ignore the levels of variable X2 and fit a fourth-order model in
"The computer refused to obtain the estimates because of perfect multicollinearity caused by including all possible fourth-order terms in the regression model."
Perfect multicollinearity occurs when there is an exact linear relationship between predictor variables in a regression model. In this case, including all possible fourth-order terms in X1 and X2 resulted in perfect multicollinearity.
When there is perfect multicollinearity, it becomes impossible to calculate the regression estimates using the standard formula, as the matrix (X'X)^-1 does not exist. The presence of perfect multicollinearity creates redundancy and ambiguity in the model, making it impossible for the computer routine to obtain valid estimates.
To address this issue, the experimenter decided to ignore the levels of variable X2 and fit a fourth-order model solely in X1. By focusing on one variable and excluding the other, the problem of perfect multicollinearity was resolved, and the regression model could be estimated successfully.
In conclusion, the computer refused to obtain the estimates due to perfect multicollinearity caused by including all possible fourth-order terms in the regression model. Ignoring one variable helped overcome the issue and allowed the experimenter to fit the desired fourth-order model.
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