a. At the moment when the batter is halfway to first base, his distance from second base is not changing.
b. His distance from third base increasing at the same moment at rate 6√2 ft/s.
Let A be the starting point of the batter, B be second base and C be third base, and $P$ be the position of the batter when he is halfway to first base.
Note that AP = AB/2 = 45 ft, B = AB - AP = 45 ft, and PC = AC - AP = 45√2 ft.
(a) We want to find [tex]$\frac{d}{dt} PB$[/tex] when AP = 45 ft and [tex]$\frac{dAP}{dt} = 24$[/tex] ft/s.
By the Pythagorean theorem, we have
PB² = AB² - AP² = 90² - 45² = 4050, so PB = √4050 ft.
To find [tex]$\frac{dPB}{dt}$[/tex] , we take the derivative of both sides of the equation PB² = 4050 with respect to time t:
[tex]2PB\frac{dPB}{dt} &= 0 \\\\\\\frac{dPB}{dt} &= 0[/tex]
Therefore, at the moment when the batter is halfway to first base, his distance from second base is not changing.
(b) We want to find [tex]$\frac{d}{dt} PC$[/tex] when AP = 45 ft and [tex]$\frac{dAP}{dt}[/tex] = 24 ft/s.
By the Pythagorean theorem, we have
PC² = AC² - AP² = (90\√2})² - 45² = 5850,
so PC = √5850 ft.
To find [tex]$\frac{dPC}{dt}$[/tex] we take the derivative of both sides of the equation PC² = 5850 with respect to time t:
[tex]2PC\frac{dPC}{dt} &= 2\frac{dAP}{dt}(AC - AP) \\\\\frac{dPC}{dt} &= \frac{dAP}{dt} \frac{AC - AP}{PC} \&= \frac{24(90\sqrt{2} - 45)}{\sqrt{5850}} \&= 16\sqrt{2} \approx 22.63 \text{ ft/s}.\end{align*}[/tex]
Therefore, at the moment when the batter is halfway to first base, his distance from third base is increasing at a rate of 16√2 ft/s.
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need assistance with my homework
Answer:
Step-by-step explana add
6(2x – 1) – 12 = 3(7x + 4)
a.-18
b.9
c.18
Answer:
x = -10/3
Step-by-step explanation:
6(2x – 1) – 12 = 3(7x + 4)
12x - 6 - 12 = 21x + 12
12x - 18 = 21x + 12
-9x - 18 = 12
-9x = 30
x = -30/9
x = -10/3
Answer:
Step-by-step explanation:
[tex]6(2x -1) - 12 = 3(7x + 4)[/tex]
[tex]12x-6-12=21x+12[/tex] (multiplied to remove brackets)
[tex]12x-18=21x+12[/tex]
[tex]12x=21x+30[/tex] (+18 to both sides of the equation)
[tex]-9x=30[/tex] (-21x both sides)
[tex]x=-\frac{30}{9}=-\frac{10}{3}[/tex] (÷-9 both sides and then simplified the
fraction)
None of the answers are correct
Work out the value of f in the following equation:
f sin 42° = 2.5
Give your answer to 2 d.p.
Answer:
f = 3.74
Step-by-step explanation:
f sin 42° = 2.5
f = 2.5 (sin 42° = 0.669)
sin 41°
= 3.736
= 3.74 (2.d.p.)
The value of f in the given equation is 3.74.
What is an Equation?An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.
Given equation is,
f sin 42° = 2.5
Dividing both sides of the equation by sin 42°,
f = 2.5 / sin 42°
f = 3.74
Hence the value of f is 3.74.
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50 PTS!! only right answers pls!!
yesterday there were b junebugs. today there are [tex]b^{2}[/tex]
junebugs. how many where there yesterday?
Answer:
Step-by-step explanationThere are more than 800 species of June bugs known to science and more are discovered every year. Adult beetles are usually blackish or reddish brown in colour, and tend to be very hairy on their fronts:
Garnet has a container with cups of flour in it. She can make one dozen muffins with cups of flour. How many dozens of muffins can Garnet make with the flour she has?
Answer:
B is correct
Step-by-step explanation:
suppose the time a child spends waiting at for the bus as a school bus stop is exponentially distributed with mean 6 minutes. determine the probability that the child must wait at least 9 minutes on the bus on a given morning.
The probability that the child must wait at least 9 minutes on a given morning is approximately 0.2231.
Let X be the waiting time at the bus stop. We know that X is exponentially distributed with mean 6 minutes. Therefore, the probability density function (PDF) of X is given by:
f(x) = 1/6 * e^(-x/6) for x >= 0
To find the probability that the child must wait at least 9 minutes, we need to calculate the following probability:
P(X >= 9) = integral of f(x) from 9 to infinity
= integral from 9 to infinity of (1/6 * e^(-x/6)) dx
Using integration by substitution, let u = x/6, du = 1/6 dx, so that:
P(X >= 9) = integral from 3/2 to infinity of e^(-u) du
= [e^(-u)] evaluated from 3/2 to infinity
= e^(-3/2)
≈ 0.2231
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Sheila is searching career possibilities. She found that an actuary requires a bachelor's degree in
mathematics or statistics. The median salary is $94,740 a year in some parts of the country. She
also found that a nuras practitioner requires a Bachelor's degree in nursing and a master's or doctorate
in nursing. The median salary is $89.960 a year. In 20 years, how much more would an actuary earn
than a nurse practitioner?
A $1,894,800
8 $95,600
C $4,780
D $1,799,200
Step-by-step explanation:
Based on the information you provided, an actuary earns $94,740 per year while a nurse practitioner earns $89,960 per year. The difference in their annual salaries is $4,780. Over 20 years, an actuary would earn $95,600 more than a nurse practitioner (20 years * $4,780/year = $95,600).
the price of a cup of coffee has risen to $2.75 today. yesterday's price was $2.40. find the percentage increase. round your answer to the nearest tenth of a percent.
To find the percentage increase in price from yesterday's price to today's price, we can use the following formula:
Percentage Increase = ((New Value - Old Value) / Old Value) x 100
Plugging in the given values, we get:
Percentage Increase = ((2.75 - 2.40) / 2.40) x 100
Percentage Increase = (0.35 / 2.40) x 100
Percentage Increase = 0.1458 x 100
Percentage Increase = 14.58%
Therefore, the percentage increase in price from yesterday's price to today's price is 14.58%, rounded to the nearest tenth of a percent.
twenty minutes into the hour, the salesperson has made his first sale. what is the probability that by the end of the hour he will have made no more than 3 sales? g
This means that there is a 25% chance that the salesperson will make no more than 3 sales in an hour.
A salesperson is a professional who works to solicit and close sales with customers. They typically work in retail stores, warehouses, or other businesses where customers come to purchase goods or services. Salespeople focus on providing excellent customer service and developing relationships with potential and existing customers. They must be able to build trust with their customers and understand their needs in order to make successful sales. They must also be able to use different techniques to present products, services, and solutions to customers.
The probability of making no more than 3 sales in an hour is calculated by dividing the total number of possible outcomes with 3 or fewer sales (in this case, 4) by the total number of possible outcomes (16). This gives us a probability of 4/16, or 25%. This means that there is a 25% chance that the salesperson will make no more than 3 sales in an hour.
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By the end of the hour he will have made no more than 3 sales and the probability is 25% or 1/4.
What is probability?
Probability means possibility of something or some incident. In this part of mathematics we deals with the occurrence of a random event. The value is in between zero and one.
The probability of making no more than 3 sales in an hour is calculated by dividing the total number of possible outcomes with 3 or fewer sales.
twenty minutes into the hour, the salesperson has made his first sale.
here the occurrence of 3 or fewer sales is 4
and the total number of possible outcomes is 16
so the probability is 4/16= 1/4
that is 25%.
Hence, there is a 25% chance that the salesperson will make no more than 3 sales in an hour also the probability is 1/4.
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what is the rate of change between 75 and 125 miles driven
The rate of change between 75 and 125 miles is calculated by dividing the difference between the fuel cost at 125 and 75 miles by the distance traveled. The fuel cost at 75 miles is $3.85, while the fuel cost at 125 is $6.35. The rate of change is $0.05 per mile.
What is the rate of change of the cost of fuel when the car travels from 75 miles to 125 miles?To calculate the rate of change between 75 and 125 miles, subtract the fuel cost at 125 miles from the fuel cost at 75 miles and divide the difference by the distance travelled:
Rate of change = (fuel cost at 125 miles - fuel cost at 75 miles) / (125 - 75)
First, we need to find the fuel cost at 75 miles:
() = 0.1 + 0.05x
() = 0.1 + 0.05(75)
() = 3.85
The fuel cost at 75 miles is $3.85.
Next, we need to find the fuel cost at 125 miles:
() = 0.1 + 0.05x
() = 0.1 + 0.05(125)
() = 6.35
The fuel cost at 125 miles is $6.35.
Now we can substitute these values into the rate of change formula:
Rate of change = (6.35 - 3.85) / (125 - 75)
Rate of change = 2.5 / 50
Rate of change = 0.05
The rate of change of the cost of fuel when the car travels from 75 miles to 125 miles is $0.05 per mile.
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The complete question is: If a car travels x miles, the cost of fuel used is given by the function () = 0.1 + 0.05x dollars. What is the rate of change of the cost of fuel when the car travels from 75 miles to 125 miles?
Consider the following 7 natural numbers: 6,8,11, 16, 19, 22, 23. a) Three of these numbers can be decomposed in the form 2. A + 1, where A is another natural number. Which three numbers can be written in this form? Show your work. b) In one sentence, identify what the numbers in part a) have in common.
I need help with this! Someone explain please
a) The numbers that can be decomposed in the form 2A + 1 are the ones that are odd when subtracted by 1 and then divided by 2. So, we can check each number to see if it satisfies this condition:
6: (6 - 1)/2 = 2.5 (not a natural number)
8: (8 - 1)/2 = 3.5 (not a natural number)
11: (11 - 1)/2 = 5
16: (16 - 1)/2 = 7.5 (not a natural number)
19: (19 - 1)/2 = 9
22: (22 - 1)/2 = 10.5 (not a natural number)
23: (23 - 1)/2 = 11
So, the three numbers that can be decomposed in the form 2A + 1 are 11, 19, and 23.
b) The numbers in part a) have in common that they are odd.
Adriana opened a savings account 3 years ago. The account earns 7% interest, compounded quarterly. If the current balance is $300.00, how much did she deposit initially?
Answer: 243.617
Step-by-step explanation:
300 = [tex]x[/tex] x (1 + 7/100/4)^(4 x 3)
300 = [tex]x[/tex] x (1.0175)^12
300 = [tex]x[/tex] x 1.231
[tex]x[/tex] = 300/1.231
[tex]x[/tex] = 243.617
consider the sample of 1,400 past negligence cases. suppose you are willing to let the 67% estimate be within .025 (2.5%) of the true proportion. you are willing to assume a 95% confidence. a. is 1,400 an adequate sample size for the estimate of 67%? show why or why not\
We can be reasonably confident that our estimate adequate sample size of 67% is within 2.5% of the true proportion.
To determine if a sample size of 1,400 is adequate for estimating a proportion of 67%, we need to calculate the margin of error and compare it to the given tolerance level of 0.025.
We can use the following formula to calculate the margin of error:
[tex]E = z \sqrt{\frac{(p (1-p)}{n} )[/tex]
where:
E is the margin of errorz is the z-score corresponding to the desired confidence level (95% corresponds to a z-score of 1.96)p is the estimated proportion (67% or 0.67 as a decimal)n is the sample size (1,400)Plugging in the values, we get:
[tex]E = 1.96 \sqrt{(0.67 (1-0.67)/1400)[/tex]
≈ 0.025
Thus, the error margin is around 0.025. This indicates that there is a 95% chance that the real percentage will be within 0.025 of the estimated proportion.
We may infer that a sample size of 1,400 is sufficient for predicting a proportion of 67% with the provided degree of confidence and tolerance as the computed margin of error is equal to the required tolerance level. As a result, we can say with some degree of assurance that our estimate of 67% is within 2.5% of the actual proportion.
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what is answer of this answer
hope you understood the answer
1/6 + 1/4
will it be less than 1/2 or greater than 1/2
The sum of 1/6 and 1/4 is greater than 1/2.
The sum of 1/6 and 1/4 is greater than 1/2. This can be demonstrated with a simple formula and calculation.
To begin, the fraction 1/6 can be written as the decimal 0.1667, and the fraction 1/4 can be written as the decimal 0.25. When these two decimals are added together, the sum is 0.4167. This number can then be converted back into a fraction. 0.4167 can be written as 41/99. When simplified, this fraction is 41/99, which is greater than 1/2 when written as a fraction.
This can be demonstrated with a formula as well. The sum of 1/6 and 1/4 can be written as the equation 1/6 + 1/4 = x. When this equation is solved, the sum is x = 5/12. This fraction can be simplified to 41/99, which is greater than 1/2.
In conclusion, the sum of 1/6 and 1/4 is greater than 1/2. This can be shown with a simple calculation and formula.
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The table shows information about the masses of some dogs.
ork out the minimum number of dogs that could have a mass of more than
26 kg.
ork out the maximum number of dogs that could have a mass of more than
26 kg.
a. The minimum number of dogs which could have a mass of more than 26 kg is of: 5.
b. The maximum number of dogs that could have a mass of more than 26 kg is of: 16.
What is observed on the frequency table?The frequency table shows the number of times that each value, or values in each range, appears in the data-set.
A number of 11 weights are between 20 and 30, hence:
The minimum number of dogs that could have a mass of more than 26 kg is of 5, when all the dogs in the interval 20 ≤ x < 30 have weights that are less than 26 kg, hence only the dogs on the interval 30 ≤ x < 40 will have a mass of more than 26 kg.The maximum number of dogs that could have a mass of more than 26 kg is of 16, when when all the dogs in the interval 20 ≤ x < 30 have weights that are more than 26 kg, along with all the dogs on the interval 30 ≤ x < 40.Full words "The table shows information about the masses of some dogs.
a) Work out the minimum number of dogs that could have a mass of more than 26 kg
b) Work out the maximum number of dogs that could have a mass of more than 26 kg
Mass, x (kg) Frequency
0≤x≤10 4
10≤x≤20 8
20≤x≤30 11
30≤x≤40 5
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solve the inequality 4x-7<5
Answer:
x < 3
Step-by-step explanation:
4x -7 < 5
4x < 12
x < 3
Answer:x < 3
Step-by-step explanation:4x -7 < 5
4x < 12
x < 3
I NEED HELP ON THIS ASAP!!
The coordinates of Point V, given the base of the triangle and the coordinates of the triangle is (4, 3).
How to find the coordinates ?To find the coordinates of point V, which is the intersection of the height YV and the base XZ, we first need to find the equation of the line XZ and then the equation of the perpendicular line YV.
First, find the slope of XZ:
m_XZ = (y2 - y1) / (x2 - x1) = (1 - 5) / (6 - 2) = (-4) / (4) = -1
We can plug in the coordinates of point X (2, 5) to find b:
5 = -1 x 2 + b
5 = -2 + b
b = 7
So the equation of line XZ is:
y = -x + 7
The equation of line YV is:
y = x - 1
To find the intersection point V, we need to solve the system of equations:
y = -x + 7
y = x - 1
-x + 7 = x - 1
7 = 2x - 1
x = 4
Now plug x back into either equation to find y. We'll use the second equation:
y = 4 - 1
y = 3
So the coordinates of point V are (4, 3).
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Hey can you please help me
Answer:
Step-by-step explanation:
Mason subtracted 5 from each side instead of adding 5.
x - 5 < 11
x - 5 + 5 < 11 + 5
x < 16
The number line will have an open circle at 16 since it does not include
16. It will be shaded to the left from that open circle as it includes
all values less than 16.
driving at a constant speed, sharon usually takes minutes to drive from her house to her mother's house. one day sharon begins the drive at her usual speed, but after driving of the way, she hits a bad snowstorm and reduces her speed by miles per hour. this time the trip takes her a total of minutes. how many miles is the drive from sharon's house to her mother's house?
The distance between her house and her mother's house =135 miles
Let the entire distance be 3x
Normally that takes 180 minutes
speed would be (3x)/180 = x/60 miles per minute
It would take 60 minutes to go the first distance of x and 276-60 = 216 minutes to the next 2x miles
She hits a bad snowstorm and reduces her speed by 20 miles per hour.
So her speed would be, (x - 20)/60 miles
for given situation we formulate an equation,
(x - 20)/60 = 2x/216
(x - 20)/10 = x/18
18x - 360 = 10x
8x = 360
x = 45 miles
So, the total distance would be:
3x = 3 × 45
= 135 miles
Therefore, the required distance is 135 miles
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Find x and y . I don’t understand. Math help plsssss
Answer:
x = y = 5
Step-by-step explanation:
This triangle and its markings show that the acute angles are equal. Given that it is a right triangle, this is a 45-45-90 triangle. This also means that the values of x and y are equal. Note that for any triangle, if two angles are equal, then their corresponding side lengths are also equal. The side lengths for this type of triangle follow the pattern s - s - s√2 where the first two are side lengths and last value is the length of the hypotenuse. (s represents the length of a side)
We want to find x and y, so we need the value of s.
s√2 = 5√2
s = 5
Therefore, x = 5, y = 5.
Which inequality is not true?
- 7/8 < -0. 60
- 7/8 > -0. 50
-7/8 > - 15/16
- 7/8 < - 1/4
7/8 is greater than -0.50, greater than -15/16, and less than -1/4. All of these inequalities are true except for 7/8 being less than -0.60.
To solve the inequality 7/8 < -0.60, we need to manipulate it to get it in the form of an equation. First, we can multiply both sides of the inequality by 8, to get 7 < -8(0.60). Next, we can distribute the negative sign on the right side to get 7 < -4.80. Finally, we can subtract 7 from both sides of the equation to get 0 < -4.80 - 7, which equals 0 < -11.80. This means that 7/8 is not less than -0.60, which is the answer to the inequality.
To confirm this answer, we can also solve the inequality 7/8 > -0.50. Again, we can multiply both sides of the inequality by 8 to get 7 > -8(0.50). We can then distribute the negative sign to get 7 > -4. Now, if we subtract 7 from both sides of the equation, we get 0 > -4 - 7, which equals 0 > -11. This means that 7/8 is indeed greater than -0.50.
To further confirm our answer, we can solve the inequality 7/8 > -15/16.
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FH bisects ZEFG. Find the indicated
angle measures.
m/GFH=71°. Find m/EFH and
m/EFG.
m/EFH=
m/EFG =
m/EFH = 109° and m/EFG = 18°. Angles in a straight line sum to 180°. Since m/GFH is 71°, the remaining angle measures must add up to the remaining 109°. Therefore, m/EFH must be 109° and m/EFG must be 18°.
To find m/EFH and m/EFG, we need to use the fact that angles in a straight line sum to 180°. We can use this fact to work out the missing angle measures.
First, we note that m/GFH is 71°. This means that the remaining angles must add up to the remaining 109°.
We can then calculate m/EFH by subtracting m/GFH from 180°. m/EFH is therefore 180° - 71° = 109°.
Next, we can calculate m/EFG by subtracting m/EFH from 180°. m/EFG is therefore 180° - 109° = 18°.
Therefore, m/EFH = 109° and m/EFG = 18°.
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The triangle ABC id mapped onto triangle A' B'C' with vertices A'(3,1) , B'(1,-2) , C'(1,2)
Under the translation T= (2/3)Find the vertices of triangle ABC. (No need to draw).
Step-by-step explanation:
To find the vertices of triangle ABC after the translation T = (2/3), we can use the following formula:
(x', y') = (x + 2/3, y + 2/3)
where (x, y) are the coordinates of the original point and (x', y') are the coordinates of the translated point.
Using this formula, we can translate each vertex of triangle A'B'C' back to its original position:
Vertex A:
x = 3 - 2/3 = 7/3
y = 1 - 2/3 = 1/3
Therefore, the coordinates of vertex A in triangle ABC are (7/3, 1/3).
Vertex B:
x = 1 - 2/3 = 1/3
y = -2 - 2/3 = -8/3
Therefore, the coordinates of vertex B in triangle ABC are (1/3, -8/3).
Vertex C:
x = 1 - 2/3 = 1/3
y = 2 - 2/3 = 4/3
Therefore, the coordinates of vertex C in triangle ABC are (1/3, 4/3).
Therefore, the vertices of triangle ABC are (7/3, 1/3), (1/3, -8/3), and (1/3, 4/3).
Answer:
Let A(x1, y1), B(x2, y2), and C(x3, y3) be the vertices of triangle ABC.
Under the translation T, each point (x, y) is mapped to the point (x + 2/3, y), which means that the new coordinates of A, B, and C will be:
A' = (x1 + 2/3, y1)
B' = (x2 + 2/3, y2)
C' = (x3 + 2/3, y3)
We are given the coordinates of A' (3, 1), B' (1, -2), and C' (1, 2), so we can set up a system of equations to solve for the coordinates of A, B, and C:
x1 + 2/3 = 3 => x1 = 2 1/3
y1 = 1
x2 + 2/3 = 1 => x2 = 1/3
y2 = -2
x3 + 2/3 = 1 => x3 = 1/3
y3 = 2
Therefore, the vertices of triangle ABC are A(2 1/3, 1), B(1/3, -2), and C(1/3, 2).
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A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 40 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 12 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 14 yards.
What is the area of the playground?
1,728 square yards
1,264 square yards
864 square yards
800 square yards
The area οf the playgrοund is 1264 square yards. Hence, οptiοn B is cοrrect.
What is the geοmetry?Geοmetry is a branch οf mathematics that deals with the study οf shapes, sizes, pοsitiοns, angles, and dimensiοns οf οbjects in space.
Tο find the area οf the playgrοund, we need tο divide it intο twο triangles and οne rectangle, and then find the area οf each and add them tοgether.
The rectangle has a length οf 12 yards and a width οf 20 yards, sο its area is:
40 x 20 = 800 square yards.
Area of Triangle 1 with base 40 yd and height 12 yd:
= 1/2 × 40 × 12
= 240 square yards.
Area of Triangle 2 with base (12 + 20) yd and height 14 yd:
= 1/2 × 32 × 14
= 224 square yards.
Adding all the areas:
= 800 + 240 + 224
= 1264 square yards.
Thus, the area of the playground is 1264 square yards. Hence, option B is correct.
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Complete question:
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
What is the area of the playground?
1,728 square yards
1,264 square yards
864 square yards
800 square yards
The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate.T/F
The given statement " The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate " is false because the allowable range for an objective function coefficient assumes that the original estimates for other coefficients are approximately correct
The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are approximately correct, but not necessarily completely accurate. The allowable range takes into account the potential variability or uncertainty in the estimated values of the other coefficients, as well as the impact of any errors or discrepancies in the data used to estimate the model.
Therefore, the allowable range provides a range of values within which the objective function coefficient can vary while still producing a valid and useful model. It does not assume that the other coefficients are completely accurate or that this is the only coefficient whose true value may differ from its original estimate.
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Determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form. 45 , 15 , 5 , . . . 45,15,5,...
Answer: Geometric and common difference is 1/3
Step-by-step explanation:
i’m stuck between A and D
Answer:
A
Step-by-step explanation:
Proofs attached to answer
56x^2 = 252x Solve using the quadratic formula
Answer:
x=0,[tex]\frac{9}{2}[/tex] Decimal Form: 0, 4.5
Step-by-step explanation:
1 )Move all terms to one side.
56[tex]x^{2}[/tex]-252x=0
2 )Factor out the common term 28x.
28x(2x−9)=0
3 )Solve for x
x=0,[tex]\frac{9}{2}[/tex] Decimal Form: 0, 4.5
f(x)=3 squared root x + 11. Find the inverse of f(x)
Answer:
[tex] \frac{x {}^{2} }{9} - 11[/tex]