The diameter of the circle is 40/3 units.
We have,
Let's first recall the formulas for the area of a sector and the length of an arc of a circle:
Area of a sector with central angle θ and radius r: A = (θ/360)πr²
Length of an arc with central angle θ and radius r: L = (θ/360)2πr
We are given that the area of the sector is 5π and the arc measure is 50 degrees.
Let's denote the radius of the circle by r and the central angle of the sector by θ.
We can set up a system of equations using the formulas above:
(θ/360)πr² = 5π (since the area of the sector is 5π)
(θ/360)2πr = L (since the length of the arc is given as 50 degrees)
Simplifying these equations.
(θ/360)r² = 5 (canceling out π on both sides)
(θ/180)r = L/π
Solving for θ in the second equation.
θ = (180/π)(L/r)
Substituting this into the first equation and solving for r.
((180/π)(L/r))/360 r² = 5
(L/r) r = (5π/9)
r = (5π/9) / (L/r)
r = (5πr)/(9L)
Now we can substitute the given values for L and θ into the above expression for r:
L = (50/360)(2πr) = (5/36)πr
θ = 50 degrees = (50/180)π radians
Substituting these into the expression for r.
r = (5πr)/(9L) = (5πr)/(9*(5/36)πr) = (20/3)
Now,
The diameter of the circle is twice the radius.
2r = 2*(20/3) = 40/3
Thus,
The diameter of the circle is 40/3 units.
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How many pounds of a metal containing 20% nickel must be combined with 6 pounds of a metal containing 80% nickel to form an alloy containing 60% nickel
Let's denote the amount of the metal containing 20% nickel that needs to be combined as 'x' pounds.
The amount of nickel in the metal containing 20% nickel is 20% of 'x', which can be expressed as 0.2x pounds.
The amount of nickel in the metal containing 80% nickel is 80% of 6 pounds, which can be expressed as 0.8 * 6 = 4.8 pounds.
To form an alloy containing 60% nickel, the total amount of nickel in the alloy should be the sum of the nickel amounts in each metal. Therefore, we can set up the equation:
0.2x + 4.8 = 0.6(x + 6)
Simplifying and solving for 'x':
0.2x + 4.8 = 0.6x + 3.6
0.2x - 0.6x = 3.6 - 4.8
-0.4x = -1.2
x = -1.2 / -0.4
x = 3
Therefore, 3 pounds of the metal containing 20% nickel must be combined with 6 pounds of the metal containing 80% nickel to form an alloy containing 60% nickel.
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Who’s equation is right for the circle: Pam, Michael, or both?
Answer:
Pam
Step-by-step explanation:
Standard form equation of a circle
(x-h)^2 + (y-k)^2 = r^2 h.k is the center = 3,-2 and r = 2
so the equation is
(x-3)^2 + (y+2)^2 = 2^2 = 4
which is better investment? a. $1200 at 9% simple interest per annum for 2 years. B. $1200 at 8% compound interest per annum for 2 years
Answer: Option B ($1200 at 8% compound interest per annum for 2 years) is a better investment.
Step-by-step explanation:
In option A, the interest is calculated on the principal amount only, which is known as simple interest.
Simple Interest Formula:
Simple Interest = (P × R × T) / 100
Where P is the principal amount, R is the rate of interest and T is the time period.
So, for option A:
P = $1200
R = 9%
T = 2 years
Simple Interest = (1200 × 9 × 2) / 100 = $216
Total Amount = Principal + Simple Interest = $1200 + $216 = $1416
In option B, the interest is calculated on the principal amount as well as the interest earned in previous years, which is known as compound interest.
Compound Interest Formula:
Total Amount = P (1 + R/100) ^n
Where P is the principal amount, R is the rate of interest and n is the number of years.
So, for option B:
P = $1200
R = 8%
n = 2 years
Total Amount = 1200 (1 + 8/100) ^2 = $1369.86
As we can see, option B yields a higher total amount compared to option A, so it is a better investment choice.
A certain bridge arch is in the shape of half an ellipse 114 feet wide and 34.7 feet high. At what horizontal distance from the center of the arch is the height equal to 16.8 feet
Find the probability that the number of people who say auto racing is their favorite sport is more than 37.
The probability of the number of people who say auto racing is their favorite sport being more than 37 can be calculated using statistical methods.
This would require information on the total number of people surveyed, the number of people who said auto racing is their favorite sport, and other relevant data.
Depending on the specific scenario, the probability could be estimated or calculated exactly.
However, without this information, it is not possible to provide a specific answer to the question.
Therefore, it is important to have all relevant information and data before calculating probabilities or making any conclusions about the likelihood of an event occurring.
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HELP PLEASE I NEED IT
family is building a firepit for their yard that is shaped like a rectangular prism. They would like for the firepit to have a volume of 93.6 ft3. If they already have the length measured at 7.8 feet and the height at 2 feet, what is the width needed to reach the desired volume?
83.8 feet
78 feet
12 feet
6 feet
Answer:
D
Step-by-step explanation:
93.6/2/7.8=6
10. The shape of radishes may be long (SLSL), round (SRSR), or oval (SLSR). If long radishes are crossed to oval radishes and the F1 is then allowed to cross at random among themselves, what phenotypic ratio is expected in the F2
When long radishes (SLSL) are crossed to oval radishes (SLSR), the F1 generation will all have the genotype SLSR because they inherit one allele for long shape from one parent and one allele for oval shape from the other parent. When the F1 generation is allowed to cross at random among themselves, the expected phenotypic ratio in the F2 generation will be 1:2:1 for long:round: oval.
This is because each F1 individual can produce gametes with either the S allele or the L allele, and the S allele is dominant over the L allele for determining shape.
So, when two F1 individuals with the SLSR genotype cross, there are four possible offspring genotypes: SSLR (long), SLSR (long), SRSR (round), and SLSL (oval). The probability of each genotype is 1/4. However, since the S allele is dominant over the L allele, both the SSLR and SLSR genotypes will express the long-shape phenotype. Thus, the phenotypic ratio in the F2 generation will be 1 long: 2 round: 1 oval.
In summary, when long radishes are crossed to oval radishes and the F1 generation is allowed to cross at random among themselves, the expected phenotypic ratio in the F2 generation will be 1 long : 2 round : 1 oval.
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HELP FAST ILL GIVE BRANILYST!!
Answer:
a) Her reasoning is wrong because √50 does not simplify to 2√25, it simplifies to 5√2. With her thinking that √50 simplifies to 2√25, then this leads to her doing 2 * 5 which equals 10.
b) To estimate a square root, you have to find two square numbers that make the number lie in between the two squares. In this case we need to find two square numbers where one square number is smaller than 50 and the other one is bigger. You should have found the two square numbers to be 7 and 8 because 7² = 49 and 8² = 64. Now we divide 50 by either number, either 7 or 8. As we can't use a calculator it is easier to divide 50 by 8 than 7. 50/8 = 6.25 Now we find the average of 6.25 and 8 which is 14.25/2 = 7.125 7.125 rounded to the nearest tenth is 7.1 Therefore the answer for b is 7.1
Answer:
(a) √50 is not equal to 10.
√50 = √25√2 = 5√2
(b) √50 = 5√2 = 5(1.41) = 7.05 = 7.1
PLEASE HELP
The table shows the length, in inches, of fish in a pond.
11 19 9 15
7 13 15 28
Determine if the data contains any outliers. If so, list the outliers.
There is an outlier at 28.
There is an outlier at 7.
There are outliers at 7 and 28.
There are no outliers.
From the given data which shows the length of fish in a pond, there is an outlier at 7.
Hence, the correct option is B.
To determine if the data contains any outliers, we can use the interquartile range (IQR) method. First, we need to find the median and the quartiles of the data set
Arrange the data in order 7, 9, 11, 13, 15, 15, 19, 28.
Median (Q2) = the middle value = 15.
Q1 (the first quartile) = the median of the lower half of the data set = 9.
Q3 (the third quartile) = the median of the upper half of the data set = 19.
Next, we can calculate the IQR as the difference between the third and first quartiles
IQR = Q3 - Q1 = 19 - 9 = 10.
Finally, we can identify any outliers as values that are more than 1.5 times the IQR above the third quartile or below the first quartile.
The upper outlier bound is Q3 + 1.5 x IQR = 19 + 1.5 x 10 = 34.
The lower outlier bound is Q1 - 1.5 x IQR = 9 - 1.5 x 10 = -6.
Since the minimum value in the data set is 7, which is greater than the lower outlier bound, we have an outlier at 7. The maximum value in the data set is 28, which is less than the upper outlier bound, so it is not an outlier.
Hence, the correct option is B.
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Two different 2-digit numbers are randomly chosen and multiplied together. What is the probability that the resulting product is even
To calculate the probability that the resulting product is even, we need to first determine the total number of possible outcomes. There are 90 two-digit numbers ranging from 10 to 99. If we choose two different numbers, there are a total of 90C2 (90 choose 2) possible combinations, which is equal to 4,005.
To calculate the number of even products, we need to consider the different scenarios. If one of the numbers is even, the product will also be even. There are 45 even numbers in the range from 10 to 99, so the number of even products that can be formed from an even number and an odd number is 45 x 45 = 2025.
If both numbers are odd, then the product will also be odd, and hence not even. There are 45 odd numbers in the range from 10 to 99, so the number of odd products that can be formed from an odd number and an odd number is 45 x 44 = 1980.
Therefore, the total number of even products that can be formed is 2025. The probability that the resulting product is even is then 2025/4005, which simplifies to 9/17, or approximately 0.5294. So, there is a 52.94% chance that the resulting product will be even.
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A rectangular steel bar has a 2.8 inch by 6 inch cross section. What is the moment of inertia, I, about it's weak axis?
The moment of inertia of the rectangular steel bar about its weak axis is 75.6 inches^4. The moment of inertia, I, of a rectangular steel bar about its weak axis can be calculated.
Using the formula
I = (1/12) * b * h^3,
where b is the width of the section and h is the height of the section. In this case, the width is 2.8 inches and the height is 6 inches.
Substituting the values in the formula, we get I = (1/12) * 2.8 * 6^3 = 75.6 inches^4. Therefore, the moment of inertia of the rectangular steel bar about its weak axis is 75.6 inches^4.
The moment of inertia is an important property of a section that determines its resistance to bending. It is commonly used in structural engineering to design beams and columns that can withstand the loads and stresses applied to them. Knowing the moment of inertia of a section helps engineers to calculate the deflection, stress, and strain in a structure under different loading conditions.
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determine the expected score of a person who guesses randomly on a true false quiz with ten questions
Answer:5
Step-by-step explanation: The probability of getting one true or false question correct is 1/2. 10*1/2=5
A ladder 10 feet long is leaning against a wall. If the top of the ladder is sliding down the wall at 4 feet per second, how fast is the foot of the ladder being pulled away from the wall when the foot of the ladder is 8 feet away from the wall
db/dt = 40/12 = 10/3 Feet per second, or approximately 3.33 feet per second. So the foot of the ladder is being pulled away from the wall at a rate of about 3.33 feet per second when it is 8 feet away from the wall and the top of the ladder is sliding down at 4 feet per second.
We can use the Pythagorean theorem to relate the length of the ladder, the distance of its foot from the wall, and the height it reaches on the wall:
[tex]a^2 + b^2 = c^2[/tex]
where c is the length of the ladder, a is the distance of its foot from the wall, and b is the height it reaches on the wall. Differentiating with respect to time, we get:
2a da/dt + 2b db/dt = 2c dc/dt
We are interested in finding db/dt when a = 8 feet and dc/dt = -4 feet per second (negative because the top of the ladder is sliding down). We also know that c = 10 feet, so we can plug in these values and solve for db/dt:
2(8) da/dt + 2b db/dt = 2(10) (-4)
Simplifying:
16 da/dt + b db/dt = -40
We also know that when a = 8 feet and b = 6 feet (from the Pythagorean theorem), the ladder is at a height of 6 feet on the wall. Therefore, we can plug in these values and solve for da/dt:
8 da/dt + 6 db/dt = 0
Simplifying:
da/dt = -(3/4) db/dt
Now we can substitute this expression for da/dt in the first equation, and solve for db/dt:
2(8) (-(3/4) db/dt) + 2(6) db/dt = -40
Simplifying:
-12 db/dt = -40
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In a chemical blending problem, one of the constraints is that the amount of sulfur relative to total output produced of chemical X may not exceed 7%. In a linear programming model, we should express this constraint as
The constraint can then be written as: S ≤ 0.07 × T. This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.
The constraint can then be written as: S ≤ 0.07 × T, This equation represents the constraint for the amount of sulfur in the chemical blend of X and can be incorporated into the linear programming model to ensure that the solution meets the given requirement.
We are given that the amount of sulfur relative to the total output produced of chemical X may not exceed 7%. To express this constraint in a linear programming model, we can use the following equation:
Sulfur Content ≤ 0.07 × Total Output
Here, the "Sulfur Content" represents the total amount of sulfur present in the chemical blend, while "Total Output" refers to the total amount of chemical X produced. By setting the constraint to be less than or equal to 7% (0.07) of the total output, we are ensuring that the sulfur content does not exceed the given limit.
In a linear programming model, we usually use variables to represent quantities. Let S represent the Sulfur Content and T represent the Total Output. The constraint can then be written as:
S ≤ 0.07 × T
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multiple of 3 but greater than 15 out of 40
Answer:
3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Step-by-step explanation:
Solutions. The first ten multiples of 3 are listed below: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30.
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping diagram does not represent a function, since the element 9 in set A is mapped to two different elements in Set B.
When does a relation represents a function?A relation represents a function if each value of the input is mapped to only one value of the output, that is, one input cannot be mapped to multiple outputs.
From the mapping diagram, we have that the element 9 in Set A is mapped to two different elements of set B, that is, an input is mapped to multiple outputs, hence the mapping diagram does not represent a function.
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At I Love Food restaurant, you can choose from 13 appetizers, 16 entrees and 4 desserts. How many three-course meals can you order
There are 832 different three-course meals that can be ordered at the I Love Food restaurant.
Since there are 13 appetizers to choose from, 16 entrees, and 4 desserts, the number of possible three-course meals is:
13 x 16 x 4 = 832
A food restaurant is a business establishment that specializes in preparing and serving food to customers. These restaurants may offer a variety of cuisines, from traditional and regional dishes to fusion and international flavors. They are typically divided into different categories based on their menus and service styles, such as fast food, casual dining, fine dining, or ethnic restaurants.
Food restaurants are designed to provide a comfortable and enjoyable dining experience for customers, often with attractive decor, seating arrangements, and music. They employ chefs, cooks, servers, and other staff who work together to prepare and serve high-quality food and drinks. Many food restaurants offer takeout or delivery services, allowing customers to enjoy their meals at home or on the go. Some restaurants also provide catering services for events, parties, and other special occasions.
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Find the gradient of the line 2x-3y=5 and convert to the gradient intercept form,y=Mx+c
Answer:
see explanation
Step-by-step explanation:
the equation of a line in gradient- intercept form is
y = mx + c ( m is the gradient and c the y- intercept )
given
2x - 3y = 5 ( subtract 2x from both sides )
- 3y = - 2x + 5 ( divide through by - 3 )
y = [tex]\frac{2}{3}[/tex] x - [tex]\frac{5}{3}[/tex] ← in gradient- intercept form
with gradient m = [tex]\frac{2}{3}[/tex]
The length of one kind of fish is normally distributed. The average length is 2.5 inches, with a standard deviation of 0.4 inches. What is the probability that the average length of 100 randomly selected fishes is less than 2.4 inches
There is only a 0.62% chance that the average length will be less than 2.4 inches. Therefore, we can conclude that it is unlikely for the average length of 100 randomly selected fish to be less than 2.4 inches.
Use the central limit theorem, which states that the distribution of sample means will be approximately normal regardless of the distribution of the population, as long as the sample size is large enough.
In this case, we are given that the length of one kind of fish is normally distributed, with a mean of 2.5 inches and a standard deviation of 0.4 inches. We want to find the probability that the average length of 100 randomly selected fish is less than 2.4 inches.
To apply the central limit theorem, we need to calculate the mean and standard deviation of the sampling distribution of the sample mean. The mean of the sampling distribution will be equal to the population mean, which is 2.5 inches. The standard deviation of the sampling distribution can be calculated using the formula:
standard deviation = population standard deviation / square root of sample size
In this case, the population standard deviation is 0.4 inches, and the sample size is 100, so:
standard deviation = 0.4 / sqrt(100) = 0.04 inches
Now that we have the mean and standard deviation of the sampling distribution, we can use the z-score formula to find the probability of obtaining a sample mean of less than 2.4 inches:
z = (sample mean - population mean) / standard deviation
z = (2.4 - 2.5) / 0.04 = -2.5
Using a standard normal distribution table, we can find that the probability of obtaining a z-score of -2.5 or less is approximately 0.0062. This means that the probability of obtaining a sample mean of less than 2.4 inches is approximately 0.0062.
In other words, if we were to randomly select 100 fish from this population and calculate the average length, there is only a 0.62% chance that the average length would be less than 2.4 inches. Therefore, we can conclude that it is unlikely for the average length of 100 randomly selected fish to be less than 2.4 inches.
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Suppose that the scores of golfers on the PGA tour have a mean of 67.15 and a standard deviation of 3.084. A random sample of 30 is taken from the population. What is the distribution of the sample mean
The distribution of the sample mean can be represented as: X ~ N(67.15, 3.084/√30)
The distribution of the sample mean is a normal distribution with a mean equal to the population mean µ and a standard deviation equal to the population standard deviation σ divided by the square root of the sample size n.
Therefore, for this problem, the distribution of the sample mean can be represented as:
X ~ N(67.15, 3.084/√30)
where X is the sample mean, N represents a normal distribution, 67.15 is the population mean, 3.084 is the population standard deviation, and √30 is the square root of the sample size.
This distribution assumes that the sample is randomly selected from the population and the sample size is large enough to satisfy the central limit theorem.
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Determine whether the infinite geometric series is convergent or divergent. If it is convergent, find its sum. (If the series is divergent, enter DIVERGENT.) 1 1 5 1 25 1 125
The sum of the convergent geometric series is 5/4, or 1.25. The given infinite geometric series is 1, 1/5, 1/25, 1/125, ...
To determine if this series is convergent or divergent, we need to examine the common ratio (r) between each term. The common ratio can be calculated by dividing a term by its previous term. For example, (1/5) / 1 = 1/5, (1/25) / (1/5) = 1/5, and so on. Thus, the common ratio (r) is 1/5.
A geometric series converges if the absolute value of its common ratio is less than 1 (i.e., |r| < 1). In this case, since |1/5| < 1, the series is convergent.
To find the sum of the convergent geometric series, we use the formula:
S = a / (1 - r)
where S is the sum of the series, a is the first term, and r is the common ratio.
Here, a = 1 and r = 1/5. Plugging these values into the formula, we get:
S = 1 / (1 - (1/5))
S = 1 / (4/5)
S = 5/4
Thus, the sum of the convergent geometric series is 5/4, or 1.25.
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Help pleaseeee
Aspapppp
Answer:
the awnser to the question is: 40°
how to solve decimal and fraction problems on number line where the first number is a whole number than the other two numbers are decimal numbers
We label the fractions on the number line as 3 1/5 and 4 7/10. To find the distance between the two fractions, we subtract 16/5 from 47/10, which equals 9/10. Therefore, the distance between 3.2 and 4.7 is 0.9.
To solve decimal and fraction problems on a number line where the first number is a whole number and the other two numbers are decimal numbers, follow these steps:
1. Draw a number line and label the whole number as the starting point.
2. Convert the decimals to fractions, if needed.
3. Place the fractions on the number line, starting from the whole number and moving to the right.
4. If the decimal is less than 0.5, place the fraction closer to the whole number. If the decimal is greater than 0.5, place the fraction closer to the next whole number.
5. Label the fractions on the number line.
6. To find the distance between the two fractions, subtract the smaller fraction from the larger fraction.
7. If needed, convert the resulting fraction to a decimal.
For example, let's say we want to plot 3.2 and 4.7 on a number line starting from 2. We convert the decimals to fractions: 3.2 is 16/5 and 4.7 is 47/10. We place 16/5 closer to 3 and 47/10 closer to 5. We label the fractions on the number line as 3 1/5 and 4 7/10. To find the distance between the two fractions, we subtract 16/5 from 47/10, which equals 9/10. Therefore, the distance between 3.2 and 4.7 is 0.9.
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Which would it be more accurate, calculating the energy converted every two minutes and adding these values or calculating the energy converted from the average power and total time
The more accurate method for calculating the total energy converted would be calculating the energy converted from the average power and total time.
To do this, follow these steps:
1. Determine the average power (in watts) during the given time period.
2. Calculate the total time (in seconds) of the conversion process.
3. Use the formula: Energy (in joules) = Average Power (in watts) x Total Time (in seconds).
This method provides a more accurate representation of the energy conversion as it takes into account the overall average power and time, rather than making multiple separate calculations and adding them together, which could result in potential discrepancies due to varying power levels throughout the process.
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The management of First American Bank was concerned about the potential loss that might occur in the event of a physical catastrophe such as a power failure or a fire. The bank estimated that the loss from one of these incidents could be as much as $100 million, including losses due to interrupted service and customer relations. One project the bank is considering is the installation of an emergency power generator at its operations headquarters. The cost of the emergency generator is $800,000, and if it is installed, no losses from this type of incident will be incurred. However, if the generator is not installed, there is a 10% chance that a power outage will occur during the next year. If there is an outage, there is a .05 probability that the resulting losses will be very large, or approximately $80 million in lost earnings. Alternatively, it is estimated that there is a .95 probability of only slight losses of around $1 million. Using decision tree analysis, determine whether the bank should install the new power generator.
The expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.
The management of First American Bank faces a decision regarding the installation of an emergency power generator to mitigate potential losses from physical catastrophes such as power failures or fires.
To evaluate this decision, we can use decision tree analysis.
Without the generator, there is a 10% chance of a power outage. In the event of an outage, there is a 0.05 probability of very large losses ($80 million) and a 0.95 probability of slight losses ($1 million). To calculate the expected loss from not installing the generator, we can use the following formula:
Expected loss = (probability of outage) x [(probability of large loss x large loss amount) + (probability of slight loss x slight loss amount)]
Expected loss = 0.1 x [(0.05 x $80 million) + (0.95 x $1 million)]
Expected loss = 0.1 x [$4 million + $950,000]
Expected loss = 0.1 x $4.95 million
Expected loss = $495,000
Now let's compare this expected loss to the cost of installing the emergency power generator, which is $800,000. Since the expected loss without the generator ($495,000) is less than the cost of installing the generator ($800,000), it would not be economically justifiable for the bank to install the new power generator based on this decision tree analysis.
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Hi! I am confused about this question…. Can someone explain it to me please?
30 points
Answer:
20 tins
Step-by-step explanation:
Since EACH dog eats 3/5 of a tin each day, that means that 3/5 + 3/5 or 6/5 of a tin is eaten everyday. Now that we know the daily amount, multiply it by 16 to find the number of tins for 16 days:
16* 6/5 = 19.2. Since we have to find the number of least entire tins, we round up to 20 tins.
This is a linear algebra question.Let V be the vector space of polynomials of degree < 2 with real coefficients, endowed with the structure of an inner product space by setting (f,g) := scoglodt f(t)g(t)dt. Produce an orthonormal basi
The orthonormal basis for V is: {v1 = 1/√(2), v2 = (t - √(2)/2)/√(2), v3 = (√(3)/2)t^2 - (√(6)/2)t}. To produce an orthonormal basis for V, we need to find a set of vectors that are linearly independent and can span the space V. Since we are working with polynomials of degree less than 2, we can write them in the form:
p(t) = at^2 + bt + c
where a, b, and c are real coefficients.
To find the basis, we can start with the standard basis for V, which is {1, t, t^2}. We can then use the Gram-Schmidt process to produce an orthonormal basis.
Here are the steps:
1. Normalize the first vector in the basis, which is 1, to obtain:
v1 = 1/√(2)
2. Calculate the projection of t onto v1 and subtract it from t to obtain the second vector in the basis:
v2 = (t - (t, v1)v1)/∥(t - (t, v1)v1)∥
where (t, v1) is the inner product of t and v1.
Simplifying, we get:
v2 = (t - √(2)/2)/√(2)
3. Finally, calculate the projection of t^2 onto v1 and v2, and subtract these projections from t^2 to obtain the third vector in the basis:
v3 = (t^2 - (t^2, v1)v1 - (t^2, v2)v2)/∥(t^2 - (t^2, v1)v1 - (t^2, v2)v2)∥
where (t^2, v1) and (t^2, v2) are the inner products of t^2 with v1 and v2, respectively.
Simplifying, we get:
v3 = (√(3)/2)t^2 - (√(6)/2)t
Therefore, the orthonormal basis for V is:
{v1 = 1/√(2), v2 = (t - √(2)/2)/√(2), v3 = (√(3)/2)t^2 - (√(6)/2)t}
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An angle measures 120° less than the measure of its supplementary angle. What is the measure of each angle?
This is IXL
1.155 How much vitamin C do you need? The U.S. Food and Nutrition Board of the Institute of Medicine, working in cooperation with scientists from Canada, have used scientific data to answer this question for a variety of vitamins and minerals. 42 Their methodology assumes that needs, or requirements, follow a distribution. They have produced guidelines called dietary reference intakes for different gender-by-age combinations. For vitamin C, there are three dietary reference intakes: the estimated average requirement (EAR), which is the mean of the requirement distribution; the recommended dietary allowance (RDA), which is the intake that would be sufficient for 97% to 98% of the population; and the tolerable upper level (UL), the intake that is unlikely to pose health risks. For women aged 19 to 30 years, the EAR is 60 milligrams per day (mg/d), the RDA is 75 mg/d, and the UL is 142 2000 mg/d. 43 (a) The researchers assumed that the distribution of requirements for vitamin C is Normal. The EAR gives the mean. From the definition of the RDA, let’s assume that its value is the 97.72 percentile. Use this information to determine the standard deviation of the requirement distribution. (b) Sketch the distribution of vitamin C requirements for 19- to 30-year-old women. Mark the EAR, the RDA, and the UL on your plot.
(a) The standard deviation of the required distribution for vitamin C is approximately 7.98 mg/d.
(B) The plot should show a bell-shaped curve centered at 60 mg/d, with the RDA located slightly to the right of the center.
(a) To determine the standard deviation of the required distribution for vitamin C, we can use the information provided about the estimated average requirement (EAR) and the recommended dietary allowance (RDA). The EAR is the mean of the distribution (60 mg/d), and the RDA (75 mg/d) is assumed to be the 97.72 percentile.
We can use the Z-score formula to find the standard deviation:
Z = (X - μ) / σ
Where Z is the Z-score, X is the value of the RDA, μ is the mean (EAR), and σ is the standard deviation.
First, find the Z-score corresponding to the 97.72 percentile. Using a standard normal table or calculator, we find that Z ≈ 2.0.
Now, plug in the values into the Z-score formula:
2.0 = (75 - 60) / σ
σ = (75 - 60) / 2.0
σ = 15 / 2.0
σ = 7.5 mg/d
Plugging in the values, we get:
1.88 = (75 - 60) / σ
Solving for σ, we get:
σ = (75 - 60) / 1.88 = 7.98
The standard deviation of the required distribution is 7.5 mg/d.
(b) To sketch the distribution of vitamin C requirements for 19- to 30-year-old women, follow these steps:
1. Draw a normal distribution curve.
2. Mark the mean (EAR) at 60 mg/d on the horizontal axis.
3. Mark the RDA at 75 mg/d and the UL at 2000 mg/d on the horizontal axis.
4. Indicate that the standard deviation is 7.5 mg/d.
The distribution of vitamin C requirements for 19- to 30-year-old women is Normal, with a mean of 60 mg/d and a standard deviation of 7.98 mg/d. The EAR, RDA, and UL can be marked on the plot as follows:
- EAR: 60 mg/d, located at the center of the distribution
- RDA: 75 mg/d, located at the 97.72 percentile of the distribution
- UL: 2000 mg/d, located at the far right end of the distribution (beyond the range of the plot)
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Dr. Tremble sends out surveys to faculty at 57 randomly selected colleges to assess their perceptions of faculty harassment. This is an example of _____ research.
Dr. Tremble's study is an example of quantitative research. This type of research involves the use of numerical data and statistical analysis to draw conclusions about a population.
In Dr. Tremble's study, he used surveys to collect data on the perceptions of faculty harassment from a sample of 57 colleges. By randomly selecting these colleges, he aimed to obtain a representative sample of the population of all colleges in the United States.
Quantitative research is useful for testing hypotheses and identifying patterns or trends in large sets of data. In Dr. Tremble's study, he can use statistical techniques to analyze the survey results and draw conclusions about the prevalence and nature of faculty harassment in colleges. He can also use the data to identify any patterns or trends in the types of colleges or faculty members that experience harassment.
Overall, quantitative research allows researchers like Dr. Tremble to draw generalizable conclusions about a population based on a sample. This makes it a valuable tool for studying large groups and identifying patterns that may not be apparent from individual cases or small-scale studies.
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