If y varies directly as x and y =3 when x=7,find y when x =63
Answers
Answer: y = - 3
-
Step-by-step e
xplanation:
Answer:
27
Step-by-step explanation:
we have to do Unitary method.
x=7 when y=3
x=1 when y=3/7
x=63 when y=(3*63)/7
y=27
Related Questions
Find the gradients of lines A and B
Answers
Step-by-step explanation:
\(the \: gradient \: of \: line \: a \: is\)
\(m = \frac{4}{1 } \\ m = 4\)
\(the \: gradient \: of \: line \: b \: is\)
\(m = \frac{ - 2}{1} \\ m = - 2\)
Gradients of line A is equals to \(4\) and gradients of line B is equals to \(-2\).
What is gradients?" Gradients is defined as the ratio of difference of y-coordinates to the difference of x-coordinates."
Formula used
Gradients \(= \frac{y_{2}- y_{1}}{x_{2}- x_{1}}\)
According to the question,
Given from the graph,
Coordinates of Line A
\((x_{1} ,y_{1} ) = ( 3,3)\\\\(x_{2} ,y_{2} ) = ( 4,7)\)
Substitute the value in the formula we get,
Gradient of line A \(= \frac{7-3}{4-3}\)
\(= 4\)
Coordinates of Line B
\((x_{1} ,y_{1} ) = ( -1,3)\\\\(x_{2} ,y_{2} ) = ( -2,5)\)
Gradient of line B \(= \frac{5-3}{-2-(-1)}\)
\(= -2\)
Hence, gradients of line A is equals to \(4\) and gradients of line B is equals to \(-2\).
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: Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it fo graph the function and verify the real zeros and the given function value n3 3 and 2 i are zeros, f(1)-10 f(x)=0 (Type an expression using x as the variable. Simplify your answer.) Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value n3 - 3 and 8+4i are zeros: f(1) = 260 (Type an expression using x as the variable. Simplify your answer.)
Answers
First scenario: The polynomial function that satisfies the given conditions is f(x) = (x - 3)(x^2 + 4). The real zeros are x = 3, and the complex zeros are x = 2i and x = -2i. The function value f(1) = -10 is also satisfied.
Second scenario: The specific polynomial function is not provided, but it will have real coefficients and the zeros x = -3, x = 8 + 4i, and x = 8 - 4i. The function value f(1) = 260 can be confirmed using a graphing utility.
To find an nth-degree polynomial function with real coefficients that satisfies the given conditions, we can use the fact that complex zeros occur in conjugate pairs.
In the first scenario, we are given that n = 3, and the zeros are 3 and 2i. Since complex zeros occur in conjugate pairs, we know that the third zero must be -2i. We are also given that f(1) = -10.
Using this information, we can construct the polynomial function. Since the zeros are 3, 2i, and -2i, the polynomial must have factors of (x - 3), (x - 2i), and (x + 2i). Multiplying these factors, we get:
f(x) = (x - 3)(x - 2i)(x + 2i)
Expanding and simplifying this expression, we find:
f(x) = (x - 3)(x^2 + 4)
To verify the real zeros and the given function value, we can graph this function using a graphing utility. The graph will show the x-intercepts at x = 3, x = 2i, and x = -2i. Additionally, substituting x = 1 into the function will yield f(1) = -10, as required.
In the second scenario, we are given that n = 3 and the zeros are -3 and 8 + 4i. Again, since complex zeros occur in conjugate pairs, we know that the third zero must be 8 - 4i. We are also given that f(1) = 260.
Using this information, we can construct the polynomial function. The factors will be (x + 3), (x - (8 + 4i)), and (x - (8 - 4i)). Multiplying these factors, we get:
f(x) = (x + 3)(x - (8 + 4i))(x - (8 - 4i))
Expanding and simplifying this expression may be more cumbersome due to the complex numbers involved, but the resulting polynomial will have real coefficients.
To verify the real zeros and the given function value, we can graph this function using a graphing utility. The graph will show the x-intercepts at x = -3, x = 8 + 4i, and x = 8 - 4i. Substituting x = 1 into the function should yield f(1) = 260, as required.
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PLZ HELP
Which rule describes the relationship between x and y coordinates on the following graph?
Choose 1 answer
A y=2x
B y=x+2
Answers
Solve for x, where M is molar and s is seconds. x=(6.4×10
3
M
−2
s
−1
)(0.46M)
3
Enter the answer. Include units. Use the exponent key above the answer box to indicate any exponent on your units.
Answers
The solution for x is 621.5424 M \(s^{-1}\), with units of molar per second (M \(s^{-1}\)).
To solve for x in the equation x = (6.4×10^3 M^(-2) s^(-1))(0.46M)^3, we can simplify the expression and calculate the result. Let's break it down step by step: x = (6.4×10^3 M^(-2) s^(-1))(0.46M)^3
First, let's simplify (0.46M)^3: (0.46M)^3 = (0.46^3)(M^3) = 0.097336M^3
Now, substitute this back into the equation:
x = (6.4×10^3 M^(-2) s^(-1))(0.097336M^3)
Next, multiply the terms: x = 6.4×10^3 × 0.097336 M^(-2) s^(-1) M^3
When multiplying the terms with the same base, we add the exponents:
x = 6.4×10^3 × 0.097336 M^(-2 + 3) s^(-1)
Simplifying the exponent: x = 6.4×10^3 × 0.097336 M^(1) s^(-1)
Now, multiply the numerical values: x = 621.5424 M s^(-1)
Therefore, the solution for x is 621.5424 M s^(-1), with units of molar per second (M s^(-1)).
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Use the drawing tool(s) to form the correct answers on the provided number line.
Yeast, a key ingredient in bread, thrives within the temperature range of 90°F to 95°FWrite and graph an inequality that represents the temperatures where yeast will NOT thrive.
Answers
The inequality of the temperatures where yeast will NOT thrive is T < 90°F or T > 95°F
Writing an inequality of the temperatures where yeast will NOT thrive.from the question, we have the following parameters that can be used in our computation:
Yeast thrives between 90°F to 95°F
For the temperatures where yeast will not thrive, we have the temperatures to be out of the given range
Using the above as a guide, we have the following:
T < 90°F or T > 95°F.
Where
T = Temperature
Hence, the inequality is T < 90°F or T > 95°F.
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Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
Suppose annual salaries for sales associates from a particular store have a bell-shaped distribution with a mean of $32,500 and a standard deviation of $2,500. Refer to Exhibit 3-3. The z-score for a sales associate from this store who earns $37,500 is
Answers
To find the z-score for a sales associate who earns $37,500, we can use the formula:
z = (x - μ) / σ
Where:
x is the value we want to convert to a z-score (in this case, $37,500),
μ is the mean of the distribution (in this case, $32,500), and
σ is the standard deviation of the distribution (in this case, $2,500).
Substituting the given values into the formula, we have:
z = (37,500 - 32,500) / 2,500
z = 5,000 / 2,500
z = 2
Therefore, the z-score for a sales associate who earns $37,500 is 2.
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The z-score for a sales associate earning $37,500 in a system where the mean salary is $32,500 and the standard deviation is $2,500 has a z-score of 2. This score indicates that the associate's salary is two standard deviations above the mean.
Explanation:The z-score represents how many standard deviations a value is from the mean. In this case, the value is the salary of a sales associate, the mean is the average salary, and the standard deviation is the average variation in salaries.
We calculate the z-score by subtracting the mean from the value and dividing by the standard deviation, like so:
Z = (Value - Mean) / Standard Deviation
So, the z-score for an associate earning $37,500 would be:
Z = ($37,500 - $32,500) / $2,500
This gives us a z-score of +2, indicating that a salary of $37,500 is two standard deviations above mean.
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(a) how many 4-permutations are there of a set of six objects? (b) how many 2-permutations are there of a set of nine objects?
Answers
There will be a total of 720 4- permutations of a set of six objects. And there will be a total of 72 2- permutations of a set of nine objects.
The calculation for 4-permutations of a set containing six objects
P(6,4)! = 6! / (6-4)1
P(6,4)! = 6×5×4×3x2
P(6,4)! = 720
Therefore, there will be a total of 720 permutations.
The calculation for 2- permutation of a set containing 9 objects
P(9,2)! = (9,7)! = (9-2) = 9! / 7!
P(9,2)! = 9×8x7! / 7!
P(9,2)! = 72
Therefore, there will be a total of 72 permutations.
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Express in the form 1 : n . Give n as a decimal. 20 : 15
Answers
Answer:
1 : 0.75
Step-by-step explanation:
Given the ratio
20 : 15 ← divide both parts by 20
\(\frac{20}{20}\) : \(\frac{15}{20}\)
= 1 : 0.75
Answer:
n=0.75
Step-by-step explanation:
w+5r use w=4 and r=6
Answers
4 + 5(6)
4 + 30
answer = 34
hope this helps!
Choose the expression that is equivalent to the one shown.
- 25 + - 30
- 25 + 30
25 - 30
- 25 - 30
Answers
Answer:
I'm pretty sure it's the last one
Step-by-step explanation:
both equal -55 when I use my calculator
Jonczyk Company is considering two different, mutually exclusive capital expenditure proposals. Project A will cost $454,000, has an expected useful life of 13 years and a salvage value of zero, and is expected to increase net annual cash flows by $68,000. Project B will cost $300,000, has an expected useful life of 13 years and a salvage value of zero, and is expected to increase net annual cash flows by $47,000. A discount rate of 9% is appropriate for both projects. Click here to view PV table.
Calculate the net present value and profitability index of each project. (If the net present value is negative, use either a negative sign preceding the number e.g. -45 or parentheses e.g. (45). Round present value answers to 0 decimal places, e.g. 125 and profitability index answers to 2 decimal places, e.g. 15.52. For calculation purposes, use 5 decimal places as displayed in the factor table provided, e.g. 1.25124.)
Answers
Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.
A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.
Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14
Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96
The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.
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Sal was asked by his teacher to
compare the numbers 153.098 and
153.408. Which is the correct way to
compare these two numbers?
A. 153.098 > 153.408
B. 153.098 = 153.408
C. 153.408 < 153.098
D. 153.408 > 153.098
Answers
Answer:
153.098
153.408
When we look at these numbers, we want to see which one has the greatest digit.
Shown below, I'm going to compare both numbers and start from the hundreds place and gradually go further into the other digits until we've seen which number is the greatest.
153.098:
1
153.408:
1
153.098:
15
153.408:
15
153.098:
153
153.408
153
153.098:
153.0
153.408
153.4
Now, we can automatically know that 153.408 is the greatest because the 4 in the tenths place is bigger than 0 in the tenths place in the other number.
So 153.408 > 153.098, D is your answer.
(a)
Part A
Is 64 = (-8) positive or negative?
A positive
B negative
(b)
Part B
What is the value of the expression - 48 : (-4)?
Thanks!!
Answers
Which graph best represents the solution to the system of equations shown below?
y = -2x + 14
y = 2x + 2
Answers
Answer:
1st
Step-by-step explanation:
Persevere the ratio of the volume of cylinder a to the volume of cylinder b is 5:1. Cylinder a is similar to cylinder c with a scale factor of 2:1, and cylinder b is similar to cylinder d with a scale factor of 3:1. What is the ratio of the volume of cylinder c to the volume of cylinder d? explain your reasoning
Answers
The ratio of the volume of cylinder C to the volume of cylinder D is ∛6:1.
To determine the ratio of the volume of cylinder C to the volume of cylinder D, we need to consider the relationship between the scale factors of the cylinders.
Given that the ratio of the volume of cylinder A to the volume of cylinder B is 5:1, we can infer that the scale factor between A and B is the cubic root of the volume ratio, which is ∛(5/1) = ∛5.
Similarly, the scale factor between cylinder B and cylinder D is 3:1, which implies that the cubic root of the volume ratio is ∛(3/1) = ∛3.
Now, we know that cylinder A is similar to cylinder C with a scale factor of 2:1. This means that the scale factor between A and C is 2:1, and the cubic root of the volume ratio is ∛(2/1) = ∛2.
By combining the scale factors, we can find the ratio of the volume of cylinder C to the volume of cylinder D:
Ratio of C to D = (Ratio of A to C) * (Ratio of B to D)
= ∛2 * ∛3
= ∛(2*3)
= ∛6
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What is the probability that a random chosen male voter is a registered Democrat? Round your answer to the nearest tenth of a percent.
Answers
If G is the midpoint of FH, FG = 14x + 25, and GH = 73 – 2x, find
FH.
Answers
The total length of line segment FH = 140
We have a line segment FH and G is its midpoint such that - FG = 14x + 25 and GH = 73 – 2x.
We have to find FH.
What is Line Segment?A line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
According to question, we have -
FG = 14x + 25.
GH = 73 – 2x.
Since, G is the midpoint of line FH, therefore -
FG = GH
Now -
FG = GH
14x + 25 = 73 – 2x
14x + 2x = 73 - 25
16x = 48
x = 3
Therefore, the total length of the Line segment is -
FG + GH = 14x + 25 + 73 – 2x
Substitute x = 3, we get -
FH = 14 x 3 + 25 + 73 - 2 x 3 = 73 + 67 = 140
Hence. the total length of line segment FH = 140
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expand this question
(a+3)(a+5)
Answers
Answer:
Work shown below!
Step-by-step explanation:
(a + 3)(a + 5) = \(a^{2} +5a+3a+15=a^{2}+8a+15\)
a(a+5)+3(a+5)
a^2+5a+3a+15
a^2+8a+15
Next Londell needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week delivering newspapers. How many weeks will Londell have to deliver papers to have enough money to buy the bicycle?
Answers
Londell needs to deliver newspapers for 24 weeks to have enough money to buy the bicycle.
Londell currently has $40 saved, and he needs a total of $400 to buy the bicycle. Each week, he earns $15 delivering newspapers.
To calculate the number of weeks Londell needs to work, we can set up an equation:
$40 (current savings) + $15 (weekly earnings) × (number of weeks) = $400 (total cost of the bicycle)
Simplifying the equation:
$40 + $15 = $400
Subtracting $40 from both sides of the equation:
$15 = $400 - $40
$15 = $360
Dividing both sides of the equation by $15:
= $360 / $15
≈ 24
Therefore, Londell will have to deliver newspapers for approximately 24 weeks to have enough money to buy the bicycle.
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Last week, Mel ate 3 apples, 2 bananas, and 4 oranges. Find the ratio of bananas to the total of fruit.
Answers
Answer:
2:9
Step-by-step explanation:
there are 2 bananas.
the total amount of fruit is 9 because 2+4+3= 9.
the ratio is 2:9 because there are 2 bananas and 9 fruits in total.
2:9 cannot be simplified any smaller.
Answer:
2:9
Step-by-step explanation:
3 apples, 2 bananas and 4 oranges
bananas: total number of fruits
3 : 3 + 2 + 4
2:9
help solve this equation
Answers
Answer:
If you're supposed to use elimination to find (x, y) the answer is (6, 1)
Step-by-step explanation:
Add:
2x+3y=15
x-3y= 3
y cancels out and left with...
2x=15
x=3
that becomes
3x=18
find x
18/3= 6
x=6
Then plug in x (which is 6) to one of the equations to solve for y
6- 3y= 3
-3y= 3-6
-3y= -3
y= 1
(x, y) equals (6, 1)
formulate but do not solve the following exercise as a linear programming problem. national business machines manufactures two models of portable printers: a and b. each model a costs $90 to make, and each model b costs $160. the profits are $25 for each model a and $40 for each model b portable printer. if the total number of portable printers demanded per month does not exceed 2,400 and the company has earmarked not more than $600,000/month for manufacturing costs, how many units of each model should national make each month to maximize its monthly profits p in dollars? (let x represent the number of units of model a and y represent the number of units of model b.)
Answers
The linear programming problem can be formulated as follows:
Maximize: P = 25x + 40y (profit function)
Subject to:
90x + 160y ≤ 600,000 (manufacturing cost constraint)
x + y ≤ 2,400 (demand constraint)
x, y ≥ 0 (non-negativity constraint)
Maximize: P = 25x + 40y (profit function) - This objective function represents the total profit, which is the sum of the profits from selling model A (25x) and model B (40y).
Subject to: 90x + 160y ≤ 600,000 (manufacturing cost constraint) - This constraint ensures that the total cost of manufacturing model A and model B does not exceed $600,000.
Subject to: x + y ≤ 2,400 (demand constraint) - This constraint ensures that the total number of portable printers produced (model A + model B) does not exceed 2,400 units, which represents the total demand.
Subject to: x, y ≥ 0 (non-negativity constraint) - This constraint ensures that the number of units produced for each model cannot be negative; they must be non-negative values.
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this summer, Gina rode in a 20,00-meter bicycle race. How many kilometers did Gina race?
A. 2 km
B. 20 km
C. 200 km
D. 2,000 km
Answers
Answer:
2,000
Step-by-step explanation:
I don't know what to say
Answer:
2,000 km
Step-by-step explanation:
this summer Gina road in a 20,00-meter bicycle race. 1000 kilometers gina race. 2,000—1000
Six farmers each have 6 barrels. In
each barrel are 6 cats who each have 6
kittens. How many legs are there? (Don't
forget the farmers' legs.)
Answers
Answer:
There would be 876 legs.
Step-by-step explanation:
To do it you could first find how many legs there are on one farm. SO you would take the 6 cats in one barrel. Then times it by the 6 kittens each of them have. That's the number of cats. Then times than number by 4 to get the total number of legs in one barrel. Then you add in the two legs of the farmer. Then times that total number by 6 to get all the legs on all six farms.
PLEASE HELP!!!!!
If n/8 has a remainder of 5, then which of the following has a remainder of 7?
A) n+1/8
B) n+2/8
C) n+5/8
D) n+7/8
Answers
Answer:
\(\frac{n+2}{8}\) has a remainder of 7 ⇒ B
Step-by-step explanation:
In m ÷ n = c + \(\frac{r}{n}\) ,
m is the dividendn is the divisorc is the quotientr is the remainderm = (n × c) + rLet us use the facts above to solve the question
∵ \(\frac{n}{8}\) has a remainder of 5
→ Let us find the first number divided by 8 and give a reminder of 5
that means let the quotient = 1
∵ n = (8 × 1) + 5 = 8 + 5
∴ n = 13
∵ \(\frac{n+x}{8}\) has a remainder of 7
→ Let us find the first number divided by 8 and give a reminder of 7
that means let the quotient = 1
∵ n + x = (8 × 1) + 7 = 8 + 7
∴ n + x = 15
∵ n = 13
∴ 13 + x = 15
→ Subtract 13 from both sides
∴ 13 -13 + x = 15 - 13
∴ x = 2
∴ \(\frac{n+2}{8}\) has a remainder of 7
Volume of a cube (cm') = width (cm) x height (cm) x length (cm). 1.1) Using the equation above, determine the volume of a cube that measures 3 cm wide, 3 cm tall, and 3 cm long. 1.2) Let's say this cube is made out of ice and has a mass of 24.76 grams (g). What is this ice cube's density? 1.3) The density of liquid water is slightly higher than that of frozen water ice. Liquid water's density at standard pressures and temperatures is 1.00 grams per cubic centimeter (g/cm'). Given that density, what is the mass of a cube of water measuring 3 cm wide, 3 cm tall, and 3 cm long? 1.4) Compare the weight of the water you calculated in question 1.3 with the weight of the ice of the same volume given in question 1.2. Which is heavier, the liquid water or the ice? Notice that the cube of water is the same size (or volume) as the cube of ice. 1.5) You know that ice floats on water. Explain why.
Answers
1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).
1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.
1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:
Volume = 3 cm x 3 cm x 3 cm = 27 cm³.
Therefore, the volume of the cube is 27 cubic centimeters.
1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:
Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.
Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).
1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:
Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.
Therefore, the mass of the water cube is 27 grams.
1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.
Therefore, the weight of the water and the ice would be the same under the same conditions.
1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.
When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.
In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.
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the number of hits on the campus ready website follows a poisson process with a rate of 3 per minute. what is the probability that more than a minute foes by without a hit
Answers
The probability that more than a minute foes by without a hit is 0.0498.
Let X denote the waiting time in minutes until the next hit.
From the question, we have
The probability density function of exponential distribution is,
f(x)=λe^(-λ*) λ>0
Probability =
P(X>1) =∫_1^∞ 3e^(-3x) dx
=3(e^(-3z)/(-3))_1^∞
=e^(-3)
=0.0498
Probability = 0.0498
Probability:
Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.
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A. Function A is linear and Function B is exponential.
B. Function A is exponential and Function B is linear.
C. Both functions are linear.
D. Both functions are exponential.
Answers
Solve the following linear programming problem using the simplex method: Minimize: Z = X1 + 2X2 subject to
A. X1+3X2 ≥90
B. 8X1 +2X2 ≥ 160
C. 3X1 +2X2 ≥ 120
D. X2 ≤70
E. X1, X2 ≥ 0
Answers
The answer to the given linear programming problem, which is solved using the simplex method, is as follows:
The optimal solution to minimize the objective function Z = X1 + 2X2 is X1 = 20 and X2 = 0, with the objective function value Z = -100.
To solve the problem, we'll first convert the inequalities to equations by introducing slack and surplus variables. Then we'll set up the initial simplex tableau and iterate through the simplex algorithm until we reach an optimal solution.
⇒ Convert the inequalities to equations:
A. X1 + 3X2 + S1 = 90 (where S1 is the slack variable)
B. 8X1 + 2X2 + S2 = 160 (where S2 is the slack variable)
C. 3X1 + 2X2 + S3 = 120 (where S3 is the slack variable)
D. X2 + S4 = 70 (where S4 is the surplus variable)
⇒ Set up the initial simplex tableau:
| X1 | X2 | S1 | S2 | S3 | S4 | RHS |
----------------------------------------------
Z | -1 | -2 | 0 | 0 | 0 | 0 | 0 |
----------------------------------------------
S1 | 1 | 3 | 1 | 0 | 0 | 0 | 90 |
S2 | 8 | 2 | 0 | 1 | 0 | 0 | 160 |
S3 | 3 | 2 | 0 | 0 | 1 | 0 | 120 |
S4 | 0 | 1 | 0 | 0 | 0 | -1 | 70 |
⇒ a) Select the most negative coefficient in the Z row, which is -2. Choose the corresponding column as the pivot column (X2 column).
b) Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 70/1 = 70. Thus, the pivot row is S4.
c) Perform row operations to make the pivot element (1 in S4 row) equal to 1 and eliminate other elements in the pivot column:
- Divide the pivot row by the pivot element (1/1 = 1).
- Replace other elements in the pivot column using row operations:
- S1 row: S1 = S1 - (1 * S4) = 90 - 70 = 20
- Z row: Z = Z - (2 * S4) = 0 - 2 * 70 = -140
- S2 row: S2 = S2 - (0 * S4) = 160
- S3 row: S3 = S3 - (0 * S4) = 120
d) Update the tableau with the new values:
| X1 | X2 | S1 | S2 | S3 | S4 | RHS |
----------------------------------------------
Z | -1 | 0 | 0 | 0 | 2 | -2 | -140|
----------------------------------------------
S1 | 1 | 3 | 1 | 0 |
0 | 0 | 20 |
S2 | 8 | 2 | 0 | 1 | 0 | 0 | 160 |
S3 | 3 | 2 | 0 | 0 | 1 | 0 | 120 |
S4 | 0 | 1 | 0 | 0 | 0 | -1 | 70 |
e) Repeat steps a to d until all coefficients in the Z row are non-negative.
- Select the most negative coefficient in the Z row, which is -1. Choose the corresponding column as the pivot column (X1 column).
- Find the pivot row by selecting the minimum ratio of the RHS value to the positive values in the pivot column. The minimum ratio is 20/1 = 20. Thus, the pivot row is S1.
- Perform row operations to make the pivot element (1 in S1 row) equal to 1 and eliminate other elements in the pivot column.
- Update the tableau with the new values.
f) The final simplex tableau is:
| X1 | X2 | S1 | S2 | S3 | S4 | RHS |
----------------------------------------------
Z | 0 | 0 | 0 | 0 | 1 | -3 | -100|
----------------------------------------------
X1 | 1 | 3 | 1 | 0 | 0 | 0 | 20 |
S2 | 0 | -22 | -8 | 1 | 0 | 0 | 140 |
S3 | 0 | -7 | -3 | 0 | 1 | 0 | 60 |
S4 | 0 | 1 | 0 | 0 | 0 | -1 | 70 |
⇒ Read the solution from the final tableau:
The optimal solution is X1 = 20 and X2 = 0, with the objective function value Z = -100.
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You work in Social Media as a consultant. You are working on a new report to examine trends in Social Media usage and age. You conducted a survey of 1072 people randomly selected in the United States (you limited minimum age to 12). The file "Usagef.xlsx" has results of the survey. For each Social Media platform you have a 0/1 variable indicating whether or not the person said they used the platform in the last 6 months. For each of those variables, 1 means the person did use the platform in the last 6 months and 0 means they did not. You also have the age of each respondent calculated based on birth date (so 43.56 means the individual is 43.56 years old). There are two additional variables:
Young adult: 1=respondent is under 35; 0=respondent is 35 or over.
Platforms Used: The total number of Social Media platforms used in the last 6 months.
Please use this information and the data in the excel spreadsheet "Usagef.xlsx" to answer the following questions:
Assuming the sample is a random sample of the U.S. population, what is the upper bound of the 95% confidence interval for the average age in the U.S?
Answers
The upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.
To determine the upper bound of the 95% confidence interval for the average age in the U.S., we can use the sample data from the survey. The sample size is 1072 people, randomly selected from the U.S. population, with a minimum age of 12. By calculating the average age of the respondents, we can estimate the average age of the entire U.S. population.
Using the given information that the average age of the respondents is 43.56 years, and assuming that the sample is representative of the population, we can calculate the standard error. The standard error measures the variability of the sample mean and indicates how much the sample mean might deviate from the population mean.
Using statistical methods, we can calculate the standard error and construct a confidence interval around the sample mean. The upper bound of the 95% confidence interval represents the highest plausible value for the population average age based on the sample data.
Therefore, based on the provided information and calculations, the upper bound of the 95% confidence interval for the average age in the U.S. is 48.29 years.
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