To show that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X, Y), we can start by using the definition of variance, which is var(X) = E[(X - E[X])^2], and the definition of covariance, which is cov(X, Y) = E[(X - E[X])(Y - E[Y])].
Variance is a measure of the spread of a random variable's possible values. It is defined as the expected value of the squared deviation of a random variable from its mean. For a random variable X, the variance is denoted as Var(X) or σ^2(X) and is calculated as:
Var(X) = E[(X - E[X])^2]
Using these definitions, we can write:
var(aX + bY + c) = E[(aX + bY + c - E[aX + bY + c])^2]
Using the properties of expectations and bilinearity, we can simplify this to:
var(aX + bY + c) = E[(a(X - E[X]) + b(Y - E[Y]))^2]
Expanding the square and using bilinearity again, we get:
var(aX + bY + c) = a^2 E[(X - E[X])^2] + b^2 E[(Y - E[Y])^2] + 2ab E[(X - E[X])(Y - E[Y])]
Since the expectations of (X - E[X])^2 and (Y - E[Y])^2 are equal to var(X) and var(Y) respectively, we can substitute these values into the above equation to get:
var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)
Therefore, we have shown that var(aX + bY + c) = a^2 var X + b^2 varY + 2ab cov(X,Y)
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The are and perimeter of a rectangle field arev60m² and 32m respectively .find the length and breadth of the field
The length and breadth of the rectangle are 10m and 6m respectively
What is length and breadth of a rectangle?The shorter side of a rectangle is called its breadth (width) and the longer side is the length.
The area of a rectangle = L×B
and the perimeter = 2(L+B)
where L is the length and B is the breadth
therefore 60 = LB, and B = 60/L
and 32 = 2(L+B)
substitute 60/L for B
32 = 2(L+60/L)
divide both sides by 2
16 = L+60/L
16 =( L²+60)/L
therefore L² +60 = 16L
L² -16L +60= 0
L²-10L-6L +60 = 0
L(L-10)-6(L-10) = 0
L-10 = 0 or L-6 = 0
therefore L = 10 or 6
when L is 10m then B = 60/10 = 6m
when L is 6m then B = 60/6 = 10m
Since the longer side is length then L = 10m and B = 6m
therefore the length and breadth of the rectangle are 10m and 6m respectively.
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What are the rules of absolute value?
Isolate the absolute value on one side of the equation, Then set its contents equal to both the positive and negative value of the number on the other side of the equation and solve both equations.
Piecewise Definition: with respect to a number of discrete intervals, sets, or pieces.
[tex]|a|=\left \{ {{a if a > =0} \atop {-aifa < =0}} \right.[/tex]
Square root definition:
|a|=√a²
There are a few Rules to define absolute value:
1. |–a| = |a|
2. |a| ≥ 0
3. Products: |ab| = |a|*|b|
4. Quotients: |a / b| = |a| / |b|
5. Powers: |an| = |a|n
6. Triangle Inequality: |a + b| ≤ |a| + |b|
7. Alternate Triangle Inequality: |a – b| ≥ |a| – |b|
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how many gallons of water should be packed for two people for three days in the case of an emergency?
According to the Federal Emergency Management Agency (F.E.M.A.) , In case of emergency for two people , three days , number of gallons that should be packed is 6 gallons .
During Emergency Situations as we stock food, we need to take into account the family’s unique needs and tastes.
We try to include foods that require no refrigeration, water, special preparation, or cooking are best in case of emergency .
So , by FEMA , it states that we need to store at least one gallon per person per day .
Since there are two people , so , we need 2 gallons per day ;
and for three days , it would requires [tex]2 \times 3 = 6[/tex] gallons per day .
Therefore , 6 gallons of water should be packed .
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Which is the graph of the cube root function f(x) = ³√√/x?
O
32
-10-8-64-2₁)
2
&&&&
s 4
324
3
6 8 10 x
The required graph has been attached below which represents the cube root function f(x) = ³√x.
The cube root function is given in the question, as follows:
f(x) = ³√x
We have to determine the graph of the given function.
The domain of the square root parent function is x ≥ 0 as the square root of only non-negative values exists and that of negative values does not exist, while the domain of the cube root parent function is the set of all real numbers as the cube root of all numbers exists.
Thus, the required graph has been attached below which illustrates the cube root function f(x) = ³√x.
Hence, the correct answer would be an option (B).
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13-45+3+26 = (a) 29 (b) 24 (c)28
answer: none it is -3
What is the difference between the best and worst credit score interest rates?
For a car loan of $25,000, what is the difference in the amount of interest paid the first month between the average and worst score? (I=Prt)
If you (or your parents) want to pay the loan off quicker, which interest rate would allow you to do so while paying the least amount of money, and why?
The difference in the amount of interest paid the first month between the average and worst score is given as follows:
$94.58.
The average interest rate would allow you to do so while paying the least amount of money, due to the lower rate compared to the poor.
How to model the interest?The equation to model the interest accrued after t years is given as follows:
I(t) = Prt
.
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.t is the time, in years.For the average score, the parameters are given as follows:
P = 25000, r = 0.0535, t = 1/12. (as one month = 1/12 of a year).
Hence the interest accrued is of:
I = 25000 x 0.0535 x 1/12
I = 111.46.
For the poor score, the parameters are given as follows:
P = 25000, r = 0,0989, t = 1/12. (as one month = 1/12 of a year).
Hence the interest accrued is of:
I = 25000 x 0.0989 x 1/12
I = 206.04.
Hence the difference is of:
206.04 - 111.46 = $94.58.
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Answer:$
94.58
Step-by-step explanation:
Ratio of boys to girls is 4:5 what fraction of class is boys
Answer:
The ratio of boys to girls is 4:5, which can be simplified to 4/5.
The fraction of the class that is boys is 4/5 (or 0.8), and the fraction of the class that is girls is 5/9 (or 0.5555).
So, 4/9 of the class is boys.
what is 1 2/5 + 1 1/3=??
Answer:
Step-by-step explanation:
2.73 (rounded)
John has four more than twice as many baseball cards as Caleb. If together the boys own 286 baseball cards, how many does Caleb have?
Based on the solution to a system of equations, with John having four more than twice as many baseball cards as Caleb, and altogether the boys owning 286 baseball cards, Caleb alone has 94.
What is a system of equations?A system of equations or simultaneous equations is two or more equations solved simultaneously or concurrently.
Let the number of baseballs Caleb owns = c
Let the number of baseball John has = 2c + 4
The total number of baseball = 286
c + 2c + 4 = 286
3c = 282
c = 94
Thus, Caleb has 94 baseballs while John has 192 baseballs.
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Amira left her house and drove to the store. She stopped and went
inside. From there, she drove in the same direction until she got to the
bank. She stopped and went inside the bank. Then she drove home.
The graph below shows the number of blocks away from home Amira
is a minutes after she left her house, until she got back home.
Distance (Blocks from Home)
INNANG
25
24
23
22
21
20
19
18
17
16
15
755544
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
Time Elapsed (Minutes)
Which of the following statements is true of
Amira at time x = 22?
When x=22 minutes, Amira was 9 blocks away from the house.
What is the graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points. A graph consists of some points and lines between them. The length of the lines and position of the points do not matter.
From the given distance time graph,
At time x=22,
Corresponding y value is 9
Therefore, when x=22 minutes, Amira was 9 blocks away from the house.
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In a Petri dish, there were initially 4 bacteria. Five hours later, there were 972 of them.
Find the exponential function that satisfies the given conditions.
f(t) = 4e^?*t
Answer:
An exponential function has the form y = ab^x, where a and b are constants and x is the independent variable (in this case, time).
Given the initial condition that there were 4 bacteria in the dish, we know that when x = 0, y = 4.
So we can set up the equation: 4 = a(b^0)
Given the condition that 5 hours later there were 972 bacteria in the dish, we know that when x = 5, y = 972.
So we can set up the equation: 972 = ab^5
We can now solve for b by dividing the two equations:
972/4 = ab^5/a(b^0) = b^5
b = (972/4)^(1/5)
With b calculated, we can substitute it into one of the equations to find a:
4 = a(b^0) = ab^0 = a
So the exponential function that satisfies the given conditions is:
y = ab^x = 4(b^x) = 4( (972/4)^(1/5)^x)
This function models the growth of bacteria in the Petri dish
I don't know exactly what the question was, but I'm guessing it's the bacteria growth rate.
You can use the formula
final amount of bacteria = (initial amount of bacteria)(bacteria growth rate)^number of hours
So,
972 = (4)(x)^5
then simplify this equation to solve for x
x=3
the amount of bacteria increased 3 times more every hour for 5 hours
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Put the following values of 0 (in degree) in order from least to greatest
Answer:
4) is the least with 14.111°
1) is next with 17.9°
2) is next with 30.22°
5) is next with 65.84°
3) is the greatest with 86.82°
Step-by-step explanation:
1) csc θ = 3.2547
1/sinθ = 3.2547
sinθ = 1/3.2547
θ = [tex]sin^{-1}[/tex] 1/3.2547 or 17.9 ° ( I checked using a calculator here)
[tex]sin^{-1}[/tex]x is also known as arcsin.
Now, i will do the rest the same way.
2) θ = arccos(0.8641) = 30.22°
3) θ = arctan(17.9926) = 86.82°
4) θ = arcsin(0.2438) = 14.111°
5) θ = arctan(1/0.4485) = 65.844°
So, now u can tell the orders.
Pls mark as brainliest. This took a while. Cheers.
Complete the statement with >, < or =.
To complete the given statement, we have;
i. SM > DM
ii. <PQS < <RQS
iii. AS > RM
iv. m<1 = m<2
Properties of sides and angles of a triangles.Any given shape which is bounded by straight side is referred to as a plane shape. Examples include: triangles, rectangle, trapezium, parallelogram etc.
It can be observed in the given question that the shapes have different properties regarding their length of sides and measure of internal angles. Each of the statement can be completed as thus;
1. From triangle SJD,
m<SJM > m<DJM
Then, it can be deduced that;
SM > DM
2. From quadrilateral PQRS,
RS > PS
It can be deduced that;
<PQS < <RQS
3. From triangle AMS, it can be deduced that AS > RM.
4. From quadrilateral ABCD,
AD II BC
Then,
m<1 = m<2 (by alternate angle property)
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Why Mean absolute error is always positive?
The reason is that the absolute value of a number discards the sign, so it can't be negative as the absolute value of a number is the distance of the number from zero.
Mean Absolute Error (MAE) is a measure of the difference between the predicted value and the actual value. It is calculated by taking the absolute value of the difference between each predicted value and the actual value, and then averaging the differences.
MAE is always positive because it is calculated using the absolute value of the errors, which always results in a positive value. The absolute value function removes the negative sign from any negative errors, so all errors are treated as positive. Therefore, the sum of all errors will always be positive regardless of whether the predicted values are greater or less than the actual values.
It's used in regression problems to measure how good the model is by comparing the actual value and the predicted value. Since MAE is a positive value, it gives a clear understanding of how far the predicted value is from the actual value, which helps to understand the model's performance.
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if the volume of a cube is increased by a factor of 10, by what factor does the surface area per unit volume change? give your answer to two significant figures.
The surface area per unit volume is increased by a factor of 1000.
1000
The surface area of a cube is 6 times the square of its side length, (A = 6s^2). Since the volume of a cube is the cube of its side length, (V = s^3), the surface area per unit volume is 6/s.
If the volume is increased by a factor of 10, the side length is increased by a factor of 10^(1/3), which is about 3.162. The surface area per unit volume is therefore increased by a factor of 6/3.162, which is about 1,000.
The surface area per unit volume is increased by a factor of 1000.
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The sum of two numbers is 19, and their difference is 55. What are the two numbers?
Answer:
37 and -18
Step-by-step explanation:
Answer:
let x and y be two numbers
Do absolute value of equations always have 2 answers?
No, the absolute value of equations does not always have two answers
Understanding the absolute value is crucial for mathematicians. We place vertical bars on either side of a number to show its absolute value. On a number line, absolute value refers to distance from zero. A negative number's absolute value is a positive number. A positive number has the same absolute value as another positive number.
There are not always two solutions to an equation's absolute value. An equation involving fundamental values may have one or more solutions, depending on the equation's overall structure and the values that are being entered. For example, whereas the equation |x| = 2x has no solutions, but the equation |x| = 1 has two solutions (x = 1 and x = -1).
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1. why do financiers need hypothesis testing? data sets do not cover every instance of an event or measurement. so they can predict within a degree of certainty where stock prices will go in the future. stock and bond pricing data is difficult to obtain and impossible to predict. the normal distribution does not give them enough information to make sound decisions. 2. what method would you use to gather a data set on voter preferences? hypothesizing sampling distributing engineering 3. the null hypothesis represents . no idea at all, a placeholder the new idea that you wish to prove the old idea that you wish to disprove a third idea that is completely neutral 4. the alternative hypothesis represents . no idea at all, a placeholder the new idea that you wish to prove the old idea that you wish to disprove a third idea that is completely neutral 5. the result of any hypothesis test is . we reject or fail to reject the null hypothesis we accept or fail to accept the alternative hypothesis we accept or fail to accept the null hypothesis
Hypothesis testing is an act in statistics whereby an analyst tests an assumption regarding a population parameter.
The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis.
Hypothesis testing is used to assess the plausibility of a hypothesis by using sample data.
Such data may come from a larger population, or from a data-generating process.
1 The correct option is B.
As the hypothesis testing helps to predict when certain certainty within which range the stock value will fluctuate.
The sampling is used to gather data from the population.
The sampling can be either random or systematic. The correct option is B.
2 The correct option is C
as the null hypothesis represents the current and present claim or knowledge.
The Alternate hypothesis is the assumption about the parameter need to be checked against the null hypothesis that is it is a new assumption to be proven. So the correct option is B.
3 The correct option is A.
As either there can be sufficient evidence to reject the null hypothesis or insufficient evidence to reject the null hypothesis.
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Samuel is remodeling his basement. One part of the planning involved the flooring. He knows that he would like both carpet and hardwood, but isn’t sure how of each he will use. The most amount of flooring area he can cover is 2000 square feet. The carpet is $4. 50 per square foot and the hardwood is $8. 25 per square foot. Both prices include labor costs. Samuel has budgeted $10,000 for the flooring.
Write a system of inequalities to represent the maximum amount of flooring needed and the maximum amount of money Samuel wants to spend
The system of inequalities to represent the maximum amount of flooring needed and the maximum amount of money Samuel wants to spend is x + y <= 2000 and 4.50x + 8.25y <= 10000.
Let x be the number of square feet of carpet and y be the number of square feet of hardwood.
The most amount of flooring area he can cover is 2000 square feet. So the first inequality represents the maximum amount of flooring area that Samuel can cover:
x + y <= 2000
The carpet is $4. 50 per square foot and the hardwood is $8. 25 per square foot and Samuel has a budget of $10,000. So the second inequality represents the maximum amount of money that Samuel wants to spend:
4.50x + 8.25y <= 10000
So the system of inequalities is:
x + y <= 2000
4.50x + 8.25y <= 10000
This system represents the possible combinations of carpet and hardwood that Samuel can use while staying within his budget and the maximum amount of flooring area he can cover.
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Which expression is equivalent to −3(2x − 8) + 4x?
A -2x - 8
B -2x + 24
C -10x - 8
D -10x + 24
Answer:
The answer is B -2x +24
Step-by-step explanation:
I will show you how I got this answer step by step
-3(2x-8) + 4x
step 1
distribute the -3 through the parentheses
-6x + 24 + 4xstep 2
collect like terms
so -6x+4x = -2x
ANSWER: -2x+24
The expression is equivalent to the given expression is -2x +24
What is an expression?An expression in math is a statement having minimum of two numbers, or variables, or both and an operator connecting them.
Given that, is an expression -3(2x-8)+4x, we need to find an expression equal to the given,
Simplifying the expression,
= -3(2x-8) + 4x
= -6x + 24 + 4x
= -6x+4x = -2x
Hence, the expression is equivalent to the given expression is -2x +24
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1) Form a polynomial whose real zeros and degree are given.
Zeros: -1, 0, 6 Degree: 3
2) Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f.
Degree 4; zeros: 7i, 2, -2
The polynomial whose real zeros and degree are given will be x(x + 1)(x - 6). And the remaining zeroes of f(x) will be - 7i.
How to get polynomials with zeroes?Let a, b, c, and d are the zeroes of the polynomial.
Then the polynomial is given as,
⇒ (x - a)(x - b)(x - c)(x - d)
The degree of the polynomial will be greater than or equal to the number of zeroes.
Form a polynomial whose real zeros and degree are given.
Zeros: -1, 0, 6 and Degree: 3
Then the polynomial is given as,
⇒ (x + 1)(x + 0)(x - 6)
⇒ x(x + 1)(x - 6)
Information is given about a polynomial f(x) whose coefficients are real numbers.
Degree 4; zeros: 7i, 2, -2
The last root will be opposite to the 7i and will be - 7i.
The polynomial whose real zeros and degree are given will be x(x + 1)(x - 6). And the remaining zeroes of f(x) will be - 7i.
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Evaluate the iterated integral by converting to polar coordinates. 20 sqrt(2x − x2) 0 6 sqrt(x2 + y2) dy dx
The supplied statement states that the iterated integral after being converted to interpolation is 32/3.
What is the definition of an integral?In mathematics, an integral is either a number representing the region beneath a function's graph over a certain interval or just a new function, the reverse of which contains the original mechanism (indefinite integral). To complete the whole, an essential component is required. The term "essential" is almost a synonym in this context. Trigonometric functions of functional and equations are a concept in mathematics. Integral is a derivative of Middle English, Latin integer, and Medieval Latin integralis, each of which mean "making up a whole."
Therefore, the area is,
[tex]R=\left\{(x, y) \mid 0 \leq x \leq 2,0 \leq y \leq \sqrt{2 x-x^2}\right\}[/tex]
So,
[tex]y=\sqrt{2 x-x^2}[/tex]
y² = 2x - x²
x² - 2x + y² = 0
x² - 2x + 1 + y² = 1
(x-1)² + y² = 1
In other words, the area is the middle section of the disk with a radius of 1 and a center at (0,1).
Region R's polar coordinates are
x = r cos∅, y = r sin∅
So,
[tex]y=\sqrt{2 x-x^2}[/tex]
y² = 2x - x²
x² + y² = 2x
r² = 2r cos∅
r = 2 cos∅
The polar coordinates of the sphere of integration as,
[tex]R=\left\{(r, \theta) \mid 0 \leq \theta \leq \frac{\pi}{2}, 0 \leq r \leq 2 \cos \theta\right\}[/tex]
The provided integral then becomes,
[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r \cdot r d r d \theta \\= & \int_0^{\frac{\pi}{2}} \int_0^{2 \cos \theta} 6 r^2 d r d \theta \\= & \int_0^{\frac{\pi}{2}} 6\left(\frac{r^3}{3}\right)_0^{2 \cos \theta} d \theta\end{aligned}[/tex]
[tex]\begin{aligned}& =\int_0^{\frac{\pi}{2}} 2\left(8 \cos ^3 \theta-0\right) d \theta \\& =16 \int_0^{\frac{\pi}{2}} \cos ^2 \theta \cdot \cos \theta d \theta \\& =16 \int_0^{\frac{\pi}{2}}\left(1-\sin ^2 \theta\right) \cdot \cos \theta d \theta\end{aligned}[/tex]
Let u = sin∅ then du = cos ∅ d∅
If ∅ = 0 then u = 0 and if ∅ = π/2 then u = 1.
The above integral thus becomes,
[tex]\begin{aligned}& \int_0^2 \int_0^{\sqrt{2 x-x^2}} 6 \sqrt{x^2+y^2} d y d x \\= & 16 \int_0^1\left(1-u^2\right) d u \\= & 16\left(u-\frac{u^3}{3}\right)_0^1 \\= & 16\left(1-\frac{1}{3}\right)\end{aligned}[/tex]
= 32/3
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So far this week, Sara has run 3.5 miles. Her goal is to run a total of 8.75 miles. If Sara runs
1.75 miles per day, how many more days must she run to reach her goal? Write and solve
an equation. Check your solution.
Answer: 3 more days
Step-by-step explanation:
8.75mi(has to run)-3.5mi(already ran)=5.25mi(left to run)
5.25mi(left to run)/1.75mi(how many she runs in a day)=3 more days (until she runs 8.75 mi)
Ai Mi has a part-time job at an ice skating rink selling hot cocoa. She decided to plot the number of hot cocoas she sold relative to the day's high temperature and then draw the line of best fit. Based on the line of best fit, how many hot cocoas would you predict Ai Mi to sell if the day’s high temperature were 64
∘
∘
F?
The number of hot cocoas the Ai Mi would be expected to sell with a high temperature of 64 ºF is given as follows:
60.
How to define the linear function?As the graph of the linear function is given, the most practical way to define the function is using the slope-intercept format, as follows:
y = mx + b.
In which the coefficients are given as follows:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.From the graph, when x = 0, y = 111, hence the intercept b is given as follows:
b = 111.
When x increases by 5, from 0 to 5, y decays by four, from 111 to 107, hence the slope m is obtained as follows:
m = -4/5
m = -0.8.
Hence the function that predicts the amount of hot cocoa sold for a high temperature of x ºF is given as follows:
y = -0.8x + 111.
The prediction for a high temperature of x = 64 is given as follows:
y = -0.8(64) + 111
y = 60 hot cocoas, rounded.
Missing InformationThe graph is given by the image presented at the end of the answer.
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Help me please I don’t know just tell me the answer
Step-by-step explanation:
(e) = number of erasers she had originally.
now she has 38.
so,
A
38 = (e) + 10
B
38 - 10 = (e) + 10 - 10
28 = (e)
she had originally 28 erasers.
Which relation is a function?
The required, relation shown in graphs A and D is functions.
What are functions?Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
The curves shown in graphs B and C are not functional, as both graphs consist of only one variable.
While curve shown in graph A and D are function because it shows the relationship between two variables x and y.
Graph A shows, Absolute value function,
Graph D shows the quadratic function.
Thus, the Relation shown in graphs A and D is functions.
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. On a sunny summer day, you are taking the scenic boat ride from Stein am Rhein, Switzerland, to Schaffhausen, down the Rhein River. This nonstop trip takes 40 minutes, but the return trip to Stein, upstream, will take a full hour. Back in Stein, you decide to stay on the boat and continue on to Constance, Germany, now traveling on the still waters of Lake Constance. How long will this nonstop trip from Stein to Constance take
The nonstop trip from Stein to Constance will take 48 minutes.
What is distance?Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Let us suppose the distance between Stein to Constance as d:
Then according to the distance formula, we have:
Distance = Speed * Time
Now, let the velocity of boat be v, and the velocity of water be x.
To go from Stein to Schaffhausen it takes 40 minutes. This is represented as:
d = (v + x) (40) equation 1
To go from Schaffhausen to Stein it takes 60 minutes, this is represeted as:
d = (v - x)(60) equation 2.
Divide the equation 1 and equation 2 wegwt thw following:
3v - 3x = 2v + 2x
v = 5x
Substitute this value in the distance formula:
d = (5x + x) (40)
d = 240x
d/ x = 240
X can be written as v/5, substitute this value in the above equation we have:
d/ v = 48 minutes.
Hence, nonstop trip from Stein to Constance will take 48 minutes.
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PLEASE HELPPPP
2(y+a)/a(x-3)
find the restriction
Answer:
a ≠ 0
Step-by-step explanation:
You want to know the restriction applicable to 2(y+a)/a(x-3).
UndefinedA rational expression is undefined when its denominator is zero. The restrictions are applied so that no denominator is zero.
Here, the expression is ...
[tex]\dfrac{2(y+a)}{a}(x-3)[/tex]
The only denominator is 'a'. It cannot be zero.
The restriction is a ≠ 0.
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Additional comment
If we assume this is a relation in which x- and y- are the only variables, there is no restriction on the relation as written.
Perhaps you intend that (x-3) be a denominator factor. Then the relation would have the restriction x≠3. Such an expression would need to be written as ...
2(y+a)/(a(x-3)) . . . . . . using parentheses around the denominator
<95141404393>
Which transformations could be performed to show that △ABC is similar to △A"B"C"?
Answer:
A [tex]180^{\circ}[/tex] rotation about the origin, then a dilation by a scale factor of [tex]\frac{1}{3}[/tex]
Step-by-step explanation:
The preimage is larger than the image.
Eliminate options 1 and 3.Also, the orientiation of the triangle didn't change.
Eliminate option 2.16. if you change your lights to high beam when the driver of an approaching vehicle fails to dim his lights, the probability of an accident increases because:
If blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle which is denoted as option C.
What is a Vehicle?This refers to something which is used to transport people and goods from one place to another and examples include car, lorry etc. The lights are used at night for proper vision of the road so as to reduce the risk of accidents on the road.
here,
In a situation whereby an individual is blinded by an approaching motor vehicle at night, it is best to slow down and avoid looking directly into the lights of the approaching vehicle so as to prevent temporary vision impairment.
This helps to prevent accidents on the road and for the safety of the driver thereby making it the correct choice.
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