The mean of the thickness of paper is 39 inches, and the standard deviation is 0.1 inches.
To find the mean and standard deviation of the thickness of paper after dividing by 0.0001, you should follow these steps:
1. Divide the mean by 0.0001:
Mean after dividing = 0.0039 inches / 0.0001
Mean after dividing = 39 inches
2. Divide the standard deviation by 0.0001:
Standard deviation after dividing = 0.00001 inches / 0.0001
Standard deviation after dividing = 0.1 inches
The mean of the thickness of paper after dividing by 0.0001 is 39 inches, and the standard deviation is 0.1 inches.
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The Wyler Aerial Tramway in Franklin Mountains State Park begins at the tramway station, which is at an elevation of 4692 feet. It takes 4 minutes to reach Range Peak, which is at an elevation of 5632 feet. What equation is used to estimate the height E of the tramway t seconds after it left the station?
E = 4692-3. 9t
E = 4692 + 3. 9t
E = 5623 + 3. 9t
E = 5623 - 4692t
About the equation used to estimate the height E of the tramway t seconds after it left the station, we first need to calculate the rate of elevation gain per second.
Elevation difference: 5632 feet (Range Peak) - 4692 feet (tramway station) = 940 feet
Time: 4 minutes * 60 seconds/minute = 240 seconds
Rate of elevation gain: 940 feet / 240 seconds = 3.9167 feet/second (approximately 3.9 feet/second)
Now, we can write the equation to estimate the height E of the tramway t seconds after it left the station:
E = initial elevation + (rate of elevation gain * t)
E = 4692 + 3.9t
So, the correct equation is: E = 4692 + 3.9t
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Which expression is equivalent to 1/4 (6x + 10 - 3x)?
Answer:
B
Step-by-step explanation:
3x 5
_ + _
4 2
2. 7.G.1.2 Look at each set of conditions. Do the conditions given describe a unique triangle or many different triangles? Select Unique or Many for each description by placing a check or X in the appropriate box. Conditions Unique Many Side lengths 3 cm, 6 cm, 7 cm Angle measures 30°, 60°, 90° Angle measures 35º, 35°, 110° Side lengths 5 cm, 5 cm, 5 cm Side lengths 3 in and 4 in with an included 95° angle
The Unique or Many for each description by placing a check or X in the appropriate box is given below.
We are given that;
Measurements= 30°, 60°, 90°
Side lengths 5 cm, 5 cm, 5 cm Side lengths 3 in and 4.
Now,
If three angle measures are given, and they add up to 180 degrees, then there are infinitely many similar triangles with those angle measures, but they differ in size. This is called the AAA (angle-angle-angle) similarity criterion.
If two angles and a non-included side are given, then there may be zero, one, or two possible triangles with those measurements, depending on the length of the side and the position of the angles. This is called the AAS (angle-angle-side) or SSA (side-side-angle) criterion.
Using criteria, we can fill in the table as follows:
Conditions | Unique | Many Side lengths 3 cm, 6 cm, 7 cm | ✓ | Angle measures 30°, 60°, 90° | | ✓ Angle measures 35º, 35°, 110° | | ✓ Side lengths 5 cm, 5 cm, 5 cm | ✓ | Side lengths 3 in and 4 in with an included 95° angle | ✓ |
Therefore, by the angle the answer will be given.
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Part e
what is the mean absolute deviation for doctor a's data set on corrective lenses? what is the mean absolute deviation
for doctor b's data set on corrective lenses? write a sentence comparing the variation of the two data sets using their
mean absolute deviations.
The MAD for Doctor A's data set is 0.67 and the MAD for Doctor B's data set is 0.83. Doctor A's data set has less variation than Doctor B's data set, as indicated by their respective MADs.
To calculate the mean absolute deviation (MAD) for a data set, we first find the mean of the data set, and then find the absolute deviation of each value from the mean. We then find the mean of these absolute deviations.
a) For Doctor A's data set on corrective lenses, the mean is:
Mean = (15+18+17+16+14)/5 = 16
The absolute deviations from the mean are:
|15-16| = 1
|18-16| = 2
|17-16| = 1
|16-16| = 0
|14-16| = 2
The mean of these absolute deviations is:
MAD = (1+2+1+0+2)/5 = 1.2
Therefore, the MAD for Doctor A's data set is 1.2.
b) For Doctor B's data set on corrective lenses, the mean is:
Mean = (17+19+20+16+18)/5 = 18
The absolute deviations from the mean are:
|17-18| = 1
|19-18| = 1
|20-18| = 2
|16-18| = 2
|18-18| = 0
The mean of these absolute deviations is:
MAD = (1+1+2+2+0)/5 = 1.2
Therefore, the MAD for Doctor B's data set is also 1.2.
Comparing the two data sets using their MAD, we can see that they have the same amount of variation or dispersion from the mean. Both sets have a MAD of 1.2, indicating that the average absolute deviation of each value from the mean is the same for both sets.
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Answer:
Doctor A MAD: 11.8
Doctor B MAD: 9.32
Step-by-step explanation:
This is what I got on the assignment.
The amount of time spent practicing shooting free throws and the percentage made in a game
The relationship between the amount of time spent practicing shooting free throws and the percentage made in a game can be described as a positive correlation.
As a basketball player dedicates more time to practicing free throws, their skill and accuracy in making these shots during a game typically improve.
Consistent practice is crucial for developing muscle memory and fine-tuning shooting techniques, which contribute to a higher success rate in making free throws during games. This increased success rate is reflected in the percentage of free throws made in a game, an essential factor that can influence the outcome of the match.
However, it is important to note that the correlation is not always linear. For example, a player who practices for hours on end may experience diminishing returns due to fatigue or lack of focus. Additionally, other factors such as pressure, game context, and individual differences in learning abilities can affect the percentage of free throws made in a game.
In conclusion, investing time in practicing free throws generally leads to an improvement in a player's in-game performance. While there are external factors that may influence the success rate, the positive correlation between practice time and the percentage of free throws made in a game emphasizes the importance of consistent and focused training for basketball players.
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4) a certain compound has a half-life of four
days. write and use an exponential decay
function to find the amount of compound
remaining from a 75-ounce sample after
three weeks.
a) 1.97 oz b) 1.58 oz
c) 0.52 oz d) 2.14 oz
The amount of compound remaining from a 75-ounce sample after three weeks is 0.52 oz. The correct option is c) 0.52 oz.
To find the amount of compound remaining after three weeks, we need to first convert three weeks into days. Since one week is equal to seven days, three weeks is equal to 21 days. The exponential decay function is given by: N = [tex]N0e^(-kt)[/tex]
Where N is the amount of compound remaining after time t, N0 is the initial amount of compound, k is the decay constant, and t is time. The half-life of the compound is given as four days, which means that k = ln(2)/4 = [tex]0.1733 day^-1.[/tex]
Substituting the values, we get: N =[tex]75e^(-0.1733*21[/tex]. N = 0.52 oz to find the amount of compound remaining after a certain amount of time, we can use the exponential decay function N =[tex]N0e^(-kt)[/tex]. We first need to convert the given time into the appropriate units and calculate the decay constant using the half-life. We can substitute the values to find the answer.
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Barak is going to buy 550 nails from one of these companies.
Nail Company
50 nails
£4. 15 plus VAT at 20%
Hammer Company
25 nails
£2. 95
Special offer
Buy 100 get 25 free
He wants to buy the nails at the cheaper cost.
Where should he buy the nails, from the Nail Company or the Hammer Company?
Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.
Let's first calculate the cost of buying 550 nails from each company:
Nail Company:
Cost of 1 nail = £4.15 + (20% of £4.15) = £4.15 + £0.83 = £4.98 (rounded to 2 decimal places)
Cost of 50 nails = £4.98 x 50 = £249
Cost of 550 nails = £249 x 11 = £2739
Hammer Company:
Cost of 1 nail = £2.95/25 = £0.118 (rounded to 3 decimal places)
Cost of 75 nails (buy 100 get 25 free) = 100 x £0.118 x 3 = £35.40
Cost of 550 nails = 550 x £0.118 = £64.90
Therefore, Barak should buy the nails from the Hammer Company as it is cheaper than buying from the Nail Company.
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7 women and 7 men are on the faculty in the mathematics department at a school. how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
In 1981 number of ways a committee of five members of the department if at least one woman must be on the committee.
By choosing some items from a set and creating subsets, permutation and combination are two approaches to express a collection of things. It outlines the numerous configurations for a certain set of data. Permutations are the selection of data or objects from a set, whereas combinations are the order in which they are represented. Both ideas are critical to mathematics.
The number of ways of picking 5 from 14 is what the question is actualy asking minus combinations of 5 from 7 , because there must be 1 woman
so 5 from 14 is given by :
= [tex]\frac{14*13*12*11*10}{5*4*3*2*1}[/tex]
which is :
14 x 13 x 11 = 2002
combinations of 5 from 7 is :
(9x8x7x6x5) / (5x4x3x2x1)
[tex]\frac{7*6*5*4*3}{5*4*3*2*1}[/tex]
which is :
7 x 3= 21
so the final answer is 2002 - 21 = 1981.
Therefore, in 1981 ways a committee of five members of the department if at least one woman must be on the committee.
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Help with the question in photo please!
Answer:
3x
Step-by-step explanation
HELP FAST PLEASEEE
Question down below ⬇️
Answer:
That's the correct order.
Step-by-step explanation:
2x+20+5=55
2x+25=55
2x=30
x=15
atlantic auditorium has 850 seats . tickets were sold for 816 of the seats. for what percent of the seats were tickets sold
Answer:
96 percent
Step-by-step explanation:
If you divide 816 by 850 you get 0.96. If you multiply 0.96 by 100% you get 96%.
A store sells cashews for $6. 00 per pound and peanuts for $3. 00 per pound. The manager decides to mix 20
pounds of peanuts with some cashews and sell the mixture for $4. 00 per pound. How many pounds of cashews
should be mixed with the peanuts so that the mixture will produce the same revenue as would selling the nuts
separately?
The amount of cashews needed to be mixed with the peanuts so that the mixture will produce the same revenue as selling the nuts separately is 10 pounds.
To solve this problem, we need to use the equation:
$3(20) + 6x = 4(20 + x)$
where x is the number of pounds of cashews needed.
First, we simplify the equation by multiplying:
$60 + 6x = 80 + 4x$
Then we isolate x by subtracting 4x from both sides and subtracting 60 from both sides:
$2x = 20$
Finally, we solve for x by dividing both sides by 2:
$x = 10$
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The function R = 73. 3*/M3, known as Kielber's law, relates the basal metabolic rate R In Calories per day
burned and the body mass M of a mammal In kilograms.
a. Find the basal metabolic rate for a 180 kilogram lion. Then find the formula's prediction for a 80
kilogram human. If necessary round down to the nearest 50 Calories.
b. Use your metabolic rate result for the lion to find what the basal metabolic rate for a 80 kllogram
human would be if metabolic rate and mass were directly proportional. Compare the result to the result
from part a.
a. Kleiber's law for lion
Calories
Kleiber's law for humans
Calories
b. If metabolic rate and mass were directly proportional
Calories
If the metabolic rate were directly proportional to mass, then the rate for a human would be
(select)
than the actual prediction from Kleiber's law. Kleiber's law Indicates that smaller
organisms have a (select) v metabolic rate per kilogram of mass than do larger organisms.
The estimate from direct proportionality is higher than the prediction from KLEIBER's law.
a. For a 180 kilogram lion, we can use KLEIBER's law: R = 73.3*(180^0.75) = 6136.5 Calories per day. For an 80 kilogram human, we can use the same formula: R = 73.3*(80^0.75) = 1537.6 Calories per day.
b. If metabolic rate and mass were directly proportional, we could use the ratio of the masses to find the basal metabolic rate for an 80 kilogram human.
The ratio of the masses is 80/180 = 0.44. We can multiply this by the basal metabolic rate for the lion to get an estimate for the human: 0.44*6136.5 = 2701.26 Calories per day.
This estimate is higher than the prediction from Kleiber's law for an 80 kilogram human (1537.6 Calories per day). KLEIBER's law indicates that smaller organisms have a higher metabolic rate per kilogram of mass than do larger organisms.
Therefore, the estimate from direct proportionality is higher than the prediction from KLEIBER's law.
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Patrick buys a tissue box in the shape of a cube. how many cubic centimeters of space do the tissues occupy if the box it half full
The total cubic centimeters of space the tissue box requires is 500 cubic centimeters, under the condition that the box is half full.
The volume of a cube is evaluated by multiplying its length by its width by its height. If all sides of a cube are equal,
we can use the formula
V = s³
here
s = length of one side of the cube.
If we let s be the length of one side of the cube and V be its volume,
V = s³
If we know that the tissue box is half full, then let us consider that half of its volume is occupied by tissues. Then
V' = 0.5 × V
Staging V = s³ in the equation
V' = 0.5 × s³
s = 10 cm (given)
V' = 0.5 × 1000 = 500 cubic centimeters
Hence, if Patrick's tissue box has a volume of 1000 cubic centimeters and it is half full, then the tissues occupy 500 cubic centimeters of space.
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The complete question is
Patrick buys a tissue box in the shape of a cube of side 10 centimeters. How many cubic centimeters of space do the tissues occupy if the box is half full? Show all work
4. What are the possible values for b, if x2 + bx - 9 is factorable?
(List factor pairs and add them to show your work. )
If x² + bx - 9 is factorable, then the possible values for b are -6 and 6.
To factor x² + bx - 9, we need to find two numbers that multiply to -9 and add up to b. We can write this as (x + a)(x + b) = x² + bx - 9. Since the coefficient of x² is 1, the two numbers that multiply to -9 must add up to the coefficient of x, which is b. We can find the factor pairs of -9 to see which ones add up to b:
-1 and 9 add up to 8
-3 and 3 add up to 0
-9 and 1 add up to -8
3 and -3 add up to 0
1 and -9 add up to -8
9 and -1 add up to 8
Only -6 and 6 add up to b, so the possible values for b are -6 and 6. Therefore, x² - 6x - 9 and x² + 6x - 9 are both factorable.
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Alex throws a ball straight upward, releasing the ball 4 feet above the ground. At 1.5 seconds the ball reaches its maximum height, then the ball begins falling toward the ground. The graph represents the height of the ball over time. Use the graph to write the function in the form f(t) = a(t - h)^2 + k, where f(t) is the height of the ball (in feet) and t is time (in seconds). Alex catches the ball 3 feet above the ground. How long is the ball in the air before it is caught?
The quadratic function for the graph and the duration the ball is in the air are;
Function; f(t) = -16·(t - h)² + k
Duration the ball is in the air is about 3.02 seconds
What is a quadratic function?A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.
The height at which the ball Alex releases the ball = 4 feet above the ground
The time it takes the ball to reach maximum height = 1.5 seconds
The required form of the function to be obtained based on the graph is f(t) = a·(t - h)² + k
f(t) = The height of the ball at time t
The required form of the function is the vertex form of a quadratic equation, where;
(h, k) = The coordinates of the vertex = (1.5, 40)
The points on the graph are; (0, 4), (3, 3)
Therefore; f(0) = a·(0 - 1.5)² + 40 = 4
a·(0 - 1.5)² = 4 - 40 = -36
a = -36/(1.5²) = -16
The equation is; f(t) = -16·(t - 1.5)² + 40
The time the ball is in the air can be obtained from the function f(t) = -16·(t - 1.5)² + 40 as follows;
f(t) = -16·(t - 1.5)² + 40 = 3
-16·(t - 1.5)² = 3 - 40 = -37
(t - 1.5)² = -37/(-16)
(t - 1.5) = (√(37))/4
t = (√(37))/4 + 1.5 ≈ 3.02
The time the ball is in the air about 3.02 seconds
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Find the time taken for $400 to amount to $650 at 6% compound interest annually
The time taken for $400 to amount to $650 at 6% compound interest annually is 8.33 years.
Compound interest is expressed as below:
[tex]A = P(1+\frac{r}{n})^{nt[/tex]
where A is the amount
P is principal
r is the rate of interest
n is the frequency with which interest is compounded per year
t is the time
A = $650
P = $400
r = 0.06
n = 1 because the interest is compounded annually. Thus the frequency of interest compounded per year is 1
650 = 400 [tex](1+0.06)^t[/tex]
1.625 = [tex]1.06^t[/tex]
t = 8.33 years
Thus, it takes 8.33 years for $400 to convert to $650 at 6% compound interest annually.
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652 10(3) trying to determine platelet count from a test result.
The platelet count is 652 x 10^3.
How to determine platelet count?Based on the information provided, it seems that the platelet count from a test result is 652, and the normal range for platelet count is 150,000 to 450,000 platelets per microliter of blood. The value "10(3)" likely refers to the measurement being in thousands.
To convert the measurement to the standard unit of platelet count, we need to multiply the given value by 1,000. Thus, 652 * 1,000 = 652,000 platelets per microliter.
It's important to note that platelet counts can vary depending on various factors, and medical professionals typically interpret the results in conjunction with other clinical information. If the obtained value of 652,000 platelets per microliter is accurate, it would be significantly higher than the upper limit of the normal range.
It's crucial to consult a healthcare professional or a qualified medical practitioner for an accurate interpretation of test results and any necessary medical advice or treatment.
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#SPJ11Describe the transformations f(x)= square root 4x
The transformation of f(x) = √(4x) from the parent function g(x) = √(x) includes a horizontal stretch by a factor of 1/4, with no horizontal or vertical shifts.
The function f(x) = √(4x) is a transformation of the parent function, g(x) = √(x). The transformations include a horizontal stretch, a horizontal shift, and a vertical shift. Let's break down each transformation step-by-step:
1. Horizontal Stretch: The factor 4 inside the square root function multiplies the input (x) by 4. This results in a horizontal stretch by a factor of 1/4, meaning the graph is compressed horizontally towards the y-axis.
2. Horizontal Shift: There is no additional value added or subtracted from the input (x), so there is no horizontal shift in this function. The graph remains in its position along the x-axis.
3. Vertical Shift: Similarly, there is no additional value added or subtracted from the output (the entire function), so there is no vertical shift in this function. The graph remains in its position along the y-axis.
This results in the graph of f(x) being compressed towards the y-axis compared to the graph of g(x).
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Eva signs up for dance classes. She pays a onetime registration fee and then the same monthly tuition. Eva pays $110 the first month and at the end of 9 months has paid $670 in all. Which equation can be used to model the tuition and registration fees?
Answer: (670 -110)/8
Step-by-step explanation:
Months: 110 the first month
*Now since she paid 670 in total she subtracts the 110 from the first month which is 560, and now there is an event amound paid in the other months so you divide 560 by 8 since 8 months are left over resulting in $70 each month.
January,
February,
March,
April,
May,
June,
July,
August,
please help with this photo problem
and describe the resulting transformation
The option that represents the resulting transformation is: Option C
How to find the reflection over a line?A reflection over line is defined as a transformation in which each point of the original figure which is also called the pre-image possesses an image that is the essentially the same distance from the reflection line as the original point, but then is on the opposite side of the line. In a reflection, the image is the same size and shape as the pre-image.
Now, looking at the letter Q, when we reflect it once, it should be the mirror image but when reflect it the second time about same line, it becomes exactly the original copy.
Thus, we can conclude that Option C represents the resulting transformation.
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Of the 90 people who attended BayBridge Middle School Winter formal, 18 are not students at baybridge
Fill in the grid
________________________________
Students Who Don't Attend: = 18 ÷ 90 × 100= 20% Students Who Do Attend: = 100 - 20= 80%80% of The Students Will Attend The Baybridge Academy Winter Formal & 20% Will Not Be Attending.________________________________
1. Find the first derivative of x2/3 + y2/3 = k1 2. Find the first derivative of x cos(k1 x + k2 y) = y sen x.
We get:
[tex]y' = [x k_1 sin(k_1 x + k_2 y) - cos(k_1 x + k_2 y)] / [cos x - y sin x][/tex]
How to find the first derivative?To find the first derivative of [tex]x^{(2/3)} + y^{(2/3)} = k_1^2[/tex], we can use implicit differentiation with respect to x. Taking the derivative of both sides, we get:
[tex](2/3)x^{(-1/3)} dx/dx + (2/3)y^{(-1/3)} dy/dx = 0[/tex]
Simplifying and solving for [tex]dy/dx[/tex], we get:
[tex]dy/dx = - (x/y)(y/x)^{(-2/3)} = - (x/y) (y/x)^{(2/3)}[/tex]
which can also be written as:
[tex]dy/dx = - (y/x)^{(1/3)}[/tex]
To find the first derivative of [tex]x cos(k_1 x + k_2 y) = y sin x[/tex], we can also use implicit differentiation with respect to x. Taking the derivative of both sides, we get:
[tex]cos(k_1 x + k_2 y) - x k_1 sin(k_1 x + k_2 y) = y \cos x[/tex]
Solving for y' (i.e., [tex]dy/dx[/tex]), we get:
[tex]y' = [x k_1 sin(k_1 x + k_2 y) - cos(k_1 x + k_2 y)] / [cos x - y sin x][/tex]
Note that we could have also solved for x' (i.e., [tex]dx/dy[/tex]) if we had chosen to differentiate with respect to y instead of x
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Alexandra likes to skate at a game store that is due south of her school and due west of her
favorite skate park. If the game store is 7.3 kilometers from her school and the straight-line
distance between the school and the skate park is 8.7 kilometers, how far is the game store
from the skate park? If necessary, round to the nearest tenth.
We can use the Pythagorean theorem to find the distance between the game store and the skate park.
Let's call the distance between the game store and the skate park "d". Then we have:
d^2 = (distance between school and game store)^2 + (distance between school and skate park)^2
d^2 = 7.3^2 + 8.7^2
d^2 = 106.18
d ≈ 10.3
Therefore, the game store is approximately 10.3 kilometers from the skate park.
These ranges are called continuous ranges. Explain why these ranges are expressed in inequality notation.
The explanation of the continuous range is added below
Explaining the continuous rangeContinuous ranges are expressed in inequality notation because they represent a set of infinitely many numbers between two endpoints.
Inequality notation allows us to describe this range using mathematical symbols to show that the values can be any number between the two endpoints, including the endpoints themselves.
For example, a continuous range might be described as "all real numbers between 0 and 1, including 0 and 1".
This can be expressed in inequality notation as 0 ≤ x ≤ 1, where x is a real number.
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A baker puts 4 cups of fruit into each pie he bakes. He pays $0.75 for 1 cup of fruit and $2.50 for the pie crust. He sells each pie for $10.25. After subtracting the cost of the fruit and pie crust, how much does he earn if he sells 10 pies?
PLEEEEES HELPMEEEEE
Step 1: Find the cost of 1 pie
1 pie = 4 cups of fruit + 1 pie crust
1 pie = 4(0.75) + 1(2.50)
1 pie = 3 + 2.50
1 pie = 5.50
Step 2: Find the amount of money a baker makes by selling 1 pie
1 pie cost = 5.50
1 pie revenue = 10.25
1 pie profit = 4.75
Step 3: Find the amount of money a baker makes by selling 10 pies
1 pie profit = 4.75
10 pies profit = 47.5
Answer: $47.50
Hope this helps!
"Evaluate the integral using the indicated trigonometric
substitution. Sketch and label the associated right triangle."
∫dx / x^2√4-x^2
So, the final answer is:
(1/2)(-√(4 - x^2) / x) + C. To evaluate the integral ∫dx / (x^2√(4-x^2)), we will use the trigonometric substitution x = 2sin(θ). This substitution is chosen because it simplifies the expression under the square root, as 4 - x^2 becomes 4 - 4sin^2(θ) which can be factored into 4cos^2(θ).
Now, we need to find dx in terms of dθ. Differentiating x with respect to θ, we get:
dx/dθ = 2cos(θ) => dx = 2cos(θ)dθ
Substituting x = 2sin(θ) and dx = 2cos(θ)dθ into the integral:
∫(2cos(θ)dθ) / ((2sin(θ))^2√(4(1-sin^2(θ))))
= ∫(2cos(θ)dθ) / (4sin^2(θ)√(4cos^2(θ)))
Simplifying the integral, we get:
= (1/2) ∫(cos(θ)dθ) / (sin^2(θ)cos(θ))
= (1/2) ∫dθ / sin^2(θ)
Now, use the identity csc^2(θ) = 1/sin^2(θ) and integrate:
= (1/2) ∫csc^2(θ) dθ
= (1/2)(-cot(θ)) + C
To find cot(θ), we draw a right triangle with the opposite side x, the adjacent side √(4 - x^2), and the hypotenuse 2:
cot(θ) = adjacent / opposite = √(4 - x^2) / x
So, the final answer is:
(1/2)(-√(4 - x^2) / x) + C
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Jorge and his two brothers each water the plants.
Jorge's watering can holds half as much water as
his older brother's watering can. His younger
brother's watering can holds 8 cups. Altogether, the
watering cans hold 2 gallons. How many cups does
Jorge's watering can hold?
Jorge's older brother's watering can holds approximately 165.33 cups of water. And since Jorge's watering can holds half as much water as his older brother's watering can, Jorge's watering can holds approximately (1/2) × 165.33 = 82.67 cups of water, which we can round to 4 cups.
Let's represent the amount of water that Jorge's older brother's watering can holds by x. According to the problem, Jorge's watering can holds half as much water as his older brother's watering can. Therefore, Jorge's watering can holds (1/2)x cups of water.
We also know that Jorge's younger brother's watering can holds 8 cups of water. Altogether, the watering cans hold 2 gallons, which is equal to 2 × 128 = 256 fluid ounces (since there are 128 fluid ounces in a gallon).
We can write an equation based on the given information:
x + (1/2)x + 8 = 256
Simplifying the equation, we get:
(3/2)x = 248
x = 248 × 2/3 = 165.33
Therefore, jorge's watering can holds 4 cups of water.
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Selika give her garden a makeover. She spends money on plant,materials, and labour in the ratio of 1:5:12. She spends £848. 75. How much money does she spend on labour costs
Selika spends £565.85 on labour costs.
Given, Selika spends money on plants, materials, and labor in the ratio of 1:5:12 and spends a total of £848.75. We have to find how much money she spends on labor costs.
Let the amount of money Selika spends on plants be x. Then, the amount of money she spends on materials is 5x, and the amount of money she spends on labor is 12x.
The total amount of money she spends is £848. 75
x + 5x + 12x = 848.75
18x = 848.75
x = 848.75/18
x = 47.15
She spend on labour 12x = 12 × 47.15
= 565.85
Therefore, Selika spends £565.85 on labour costs.
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Which situation describes a proportional relationship? A:Eddy begins with 15 cans and collects 30 cans from each classroom to donate to the food bank B: Justin saves $5:50 every month to contribute to his college fund C: Sonia has painted 18 square feet of fence and plants to paint 42 square feet of fence every untl she's finished D: Ana bakes 3 dozen cookies every hour to add to the one dozen cookies she has already baked
The situation that can be represented by a proportional relationship is given as follows:
B: Justin saves $5:50 every month to contribute to his college fund.
What is a proportional relationship?A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other.
The equation that defines the proportional relationship is given as follows:
y = kx.
In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.
A proportional relationship is a linear function with an intercept of zero, meaning that the initial amount should be of zero, meaning that option B is the correct option for this problem.
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