The amount of time it would take Element X to decay to a mass of 230 grams is 9.5 minutes.
How to determine the amount of time to decay?Mathematically, the mass of a radioactive element that is remaining after time (t-hours) is given by this exponential function:
A(t) = A₀·e^{t/τ}
Where:
A(t) represents the mass remaining or current mass measured in grams.A₀ represents the initial mass measured in grams.τ is the time constant measured in minutes.t represents the half-life or time to decay measured in minutes.Next, we would determine the time constant by using this mathematical expression:
Time constant, τ = t/ln2
Time constant, τ = 5/0.6932
Time constant, τ = 7.2130 minutes.
Now, we can determine the amount of time to decay by making half-life (t) the subject of formula as follows:
A(t) = A₀·e^{t/τ}
Half-life, t = -τ·ln(A(t)/A₀)
Substituting the parameters into the formula, we have;
Half-life, t = -7.2130·ln(230/860)
Half-life, t = -7.2130 × ln(0.2674)
Half-life, t = -7.2130 × -1.3190
Half-life, t = 9.51 ≈ 9.5 minutes.
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this is a 45-45-90 triangle, what is the measure of x? rationalize the denominator
The value of x in the right triangle is 15√2.
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
The sides of a right triangle can be named base on the angle position. This includes hypotenuse side, opposite side and adjacent side.
Therefore, the side x of the right triangle can be found using trigonometric ratios as follows:
cos 45 = adjacent / hypotenuse
cos 45° = x / 30
cross multiply
30 cos 45° = x
Therefore,
x = 30 × 1 / √2
x = 30 / √2 × √2 / √2
x = 30√2 / 2
x = 15√2
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You have $1200 for your trip to the beach. You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare. Write an inequality that can be used to determine the maximum number of days you can stay at the beach. Clearly indicate what the variable represents. Then Solve the inequality, and interpret your answer in a complete sentence.
Explanation
Step 1
let x represents the numbers of days you can stay at the beach
then,
You estimate that it will cost $160 a day for food, entertainment and hotel, plus $230 round trip airfare.
so
[tex]\text{total}=230+160x[/tex]but, you have only $1200, so the total needs to be smaller or equal than 1200
[tex]230+160x\leq1200\rightarrow Inequality[/tex]Step 2
solve the inequality
[tex]\begin{gathered} 230+160x\leq1200\rightarrow Inequality \\ subtract\text{ 230 in both sides} \\ 230+160x-230\leq1200-230 \\ 160x\leq970 \\ \text{divide both sides by 160} \\ \frac{160x}{160}\leq\frac{970}{160} \\ x\leq6.0625 \\ \text{rounded} \\ x\leq6 \end{gathered}[/tex]it means you can stay maximum 6 days
I hope this helps you
Solve using substitution.
X = 7
-2x 9y = 13
(__ , __)?
Submit
Answer:
(7,-3)
Step-by-step explanation:
x = 7
-2x - 9y = 13
* Substituition is the easieat way to solve such a function.
- Firstly, put "7" instead of "x" in the equation.
- multiply "7" by "-2"
- Solve for "y"
* -2x-9y = 13
* -2×7-9y = 13
* -14-9y = 13
* -9y = 27
* -9y/-9 = 27/-9
* y = -3
# Since x = 7, the output/"y" will be -3
(7,-3)
Can someone help me please with this !!!!!
Answer:
A. [tex]9n - 190 = 5n[/tex]
Step-by-step explanation:
Dora earning 5 dollars per song is represented by [tex]5n[/tex].
Gary earning 9 dollars a song but paying the $190 fee is represented by [tex]9n - 190[/tex] because the fee from the coffee shop is subtracted from his total earnings.
For the function Rx) = +2, which of these could be a value of Ax) when x isclose to 2? A. 0.01B. 2C. -0.01D. 10,000
The given function F(x) is,
[tex]F(x)=\frac{1}{x-2}[/tex]Take the limit of the function when x ix close to 2.
[tex]Lt_{x\rightarrow2}\frac{1}{x-2}=\infty[/tex]Hence, the function diverges.
The figure is not drawn to scale. m
For the given function
The sum of all angles = 360°
So,
[tex]\begin{gathered} y+x+125+90=360 \\ m\angle x=27 \\ So,\text{ } \\ y+27+125+90=360 \\ y+242=360 \\ y=360-242=118 \end{gathered}[/tex]So, the difference between x and y will be:
[tex]y-x=118-27=91[/tex]So, the answer will be:
∠x is 91° smaller than ∠y
There is a daily fee for renting a moving truck, plus a charge of $0. 50 per mile driven. If driven 48 miles, it cost $64 to rent a truck. Write and solve an equation to find the daily fee
Using concept of Linear equations, we find $40 is the daily fee for renting a moving truck.
Linear equations are generally equations of the first order. The linear equations are defined for the lines in the coordinate system. When the equation having a homogeneous variable of degree 1 (i.e. only one variable), then it is called as a linear equation in one variable. A linear equation can have more than one variables. If the linear equation has two variables, then it is known as linear equations in two variables and so on. Some of the examples of linear equations which are listed here 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.
So, lets suppose daily fee for renting a movie a truck is $x
Then according to question,
Daily fee+ total distance travelled × charge per mile=total cost
=>x+48×0.50=64
On solving x, we get x=40
Hence, daily fee cost is $40 which is required for renting a moving truck.
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there are 100 coins and someone flips them and doesn't tell us the results. i can ask one yes/no question. after the answer i will start guessing the coin flip results. for each correct guess i get 1 dollar and for each wrong guess i lose 1 dollar. what is the best strategy to play this game and what is the maximum expected value of the return.
The answer is not 1 so it is not that simple that you can divide it into 2 equal size subsets and ask whether the final sequence is in there. From what I got through his hints, it should be related to Central Limit theorem.
Given that,
One hundred coins are flipped, but the outcome is kept a secret. I am able to pose one yes/no query. I'll begin speculating on the outcomes of the coin toss following the response. I receive $1 for each accurate guess, and I lose $1 for each unreliable guess.
To find:
What is the most effective gaming approach and what is the highest possible return on investment
By Central Limit Theorem,
It is not straightforward to divide the response into two subsets of equal size and then check to see if the final sequence is present because the answer is not 1. His indications led me to believe that it should be connected to the Central Limit theorem.
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Write the equation of the line that passes through the given points.
1,2.5) and (0,-1.5)
Answer:
y = 4x - 1.5
Step-by-step explanation:
We need to find the slope (m) and the y-intercept (b), if we are writing this in the slop intercept form of a line.
y =mx + b
The slope is the change in y over the change in x.
The two points give us the y's ad x's
The y's are: -1.5 and 2.5
The x's are: 0 and 1
[tex]\frac{-1.5 - 2.5}{0-1}[/tex] = [tex]\frac{-4}{-1}[/tex] = 4 A negative divided by a negative is a positive.
We have the slope. The slope is the point (0,b). We are given that point.
(o, -1.5) The y-intercept is -1.5
y =mx + b
y = 4x - 1.5
Please answer the 3 questions in the photo! ( 30 points + brainliest )
The required measures of the angle A, L, and J is 40.8°, 83°, and 95° respectively.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
1.
The sum of the vertical angle is 180°. So,
∠A + ∠B = 180
Substitute value in the above equation,
x + 4x - 24 = 180
5x - 24 = 180
5x = 204
x = 204 / 5
x = 40.8°
∠A = 40.8°
Similarly,
2. ∠L = 83°
3. ∠J = 95°
Thus, the required measures of the angle A, L, and J is 40.8°, 83°, and 95° respectively.
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SOMEONE PLEASE HELP WITH THESE 3 Questions! You will get TONS of points
zma = a + b Solve for A
x + m = p - n + yx Solve for X
z = am + an + ap Solve for A
Answer:
1. [tex]a=\frac{b}{zm-1}[/tex] 2. [tex]x=\frac{p-n-m}{1-y}[/tex] 3. [tex]a=\frac{z}{m+n+p}[/tex]
Step-by-step explanation:
1. zma = a+b : [tex]z=\frac{a+b}{ma} ;[/tex] [tex]m\neq 0[/tex]
zma = a + b Divide both sides by ma: [tex]m\neq 0[/tex]
[tex]\frac{zma}{ma} =\frac{a}{ma} +\frac{b}{ma} ;[/tex] [tex]m\neq 0[/tex]
2. Subtract m from both sides
x + m - m = p - n + yx - m
Simplify
x = p - n + yx - m
Subtract yx from both sides
x - yx = p - n + yx - m - yx
simplify
x - yx = p - n - m
Factor x - yx: x(1 - y)
x(1 - y) = p - n - m
simplify x = [tex]\frac{p -n-m}{1-y} ;y\neq 1[/tex]
3.Apply the sum /Different Rule : (f + g)' = f ' + g'
= [tex]\frac{d}{dp} (am)+\frac{d}{dp} (an)+\frac{d}{dp} (ap)[/tex]
[tex]\frac{d}{dp} (am)=0[/tex]
[tex]\frac{d}{dp} (an)=0[/tex]
[tex]\frac{d}{dp} (ap)=a[/tex]
= 0 + 0 + [tex]a[/tex]
simplify
= a
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what is i (5+5) vey (5-5) u
The sentence that represents the expression (5 + 5)ve y(5-5) u is:
love you.
How to translate the expression to a sentence?The expression is given as follows:
(5 + 5)ve y(5-5)u
There are two operations in the expression, as follows:
5 + 5 = 10. (addition of 5 and 5 = multiplication of 5 by 2).5 - 5 = 0. (subtraction of 5 and 5).Then the expression, with the numbers, is given as follows:
10ve y0o.
The number 10 can be interpreted as the two letters lo, as l and 1 are very similar symbols, as are 0 and o, then the updated expression is:
love y0u.
The same is applied to the final zero, as 0 and o are very similar symbols, hence the sentence that represents the expression is:
love you.
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a student has taken 6 tests and received scores of 88, 73, 81, 80, 79, and 94. the seventh test is coming up and the student wants to know what score is needed on the seventh test to have a mean score of 83. determine the score the student needs. show your work.
Solution:
Let the score for the seventh test be represented below as
[tex]=x[/tex]The mean score t be attained after the sevent tests is
[tex]mean=83[/tex]The scores from the 6 tests are given below as
[tex]88,73,81,80,79,94[/tex]To figure out the seventh score, we will do the calculation below
[tex]\begin{gathered} mean=\frac{additionofthescores}{number\text{ of tests}} \\ 83=\frac{88+73+81+80+79+94+x}{7} \\ 83=\frac{495+x}{7} \\ cross\text{ multpily} \\ 83\times7=495+x \\ 495+x=581 \\ x=581-495 \\ x=86 \end{gathered}[/tex]Hence,
The final asnwer is
[tex]\Rightarrow86[/tex]8. Kyle went out to eat. His meal was
$18, not including tip. Once tip was
added he paid $21. What was the
percent of increase in the price he paid?
$3
the amount paid after adding tip is $21
the amount for the meal is $18
$21-$18=$3
Max and his friends picked apples at an apple orchard. The weight in pounds, each person's bag of apples are listed below.what is the interquartile range, in pounds, of the wait?
Answer:
Choice A. 1.1
Explanation:
When an integer is subtracted from 2 times the next consecutive odd integer, the
difference is 9. Find the value of the greater integer.
Answer:
7
Step-by-step explanation:
Let x be the "integer." We'll assume it is odd.
The next consecutive odd integer would be x+2.
(2(x+2) - x) =9 [When an integer is subtracted from 2 times the next consecutive odd integer the difference is 9]
(2(x+2) - x) =9
(2x+4) - x) =9
x+4 =9
x = 5
The greater integer is x+2 or 7
Check:
If 5 is subtracted from 2 times the next consecutive odd integer, 7, is the difference 9?
2*7 - 5 = 9?
14 - 5 = 9?
14 - 5 = 9? YES
a number m is randomly selected from the set {11, 13, 15, 17, 19}, and a number n is randomly selected from {1999, 2000, 2001, . . . , 2018}. what is the probability that mn has a units digit of 1?
According to Euler's Theorem, if gcd(a,n) = 1, then a(n) 1. (mod n). The number of relatively prime integers in the range of 1, 2,..., n-1 is represented by the Euler totient function.
The probability that mn has a units digit of 1 = 2/5
What is Euler's theorem ?According to Euler's Theorem, if gcd(a,n) = 1, then a(n) 1. (mod n). The number of relatively prime integers in the range of 1, 2,..., n-1 is represented by the Euler totient function, or (n). This theorem is simply Fermat's little theorem when n is a prime.The remainder of a(m), when divided by a positive integer m that is relatively prime to a, is 1, according to Euler's Theorem. Because Fermat's Theorem is merely a special case of Euler's Theorem, this is the only way we can demonstrate Euler's Theorem. This is because (p)=p1 holds for a prime number p.By Euler's Theorem, we have that [tex]$a^{4} \equiv 1 \pmod {10}$[/tex] if [tex]$\gcd(a,10)=1$[/tex] Hence[tex]$m=11,13,17,19$,[/tex][tex]$n=2000,2004,2008,2012,2016$[/tex] work.
Also note that [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex] because [tex]$11^b=(10+1)^b=10^b+10^{b-1}1+...+10(1)+1$[/tex], and the latter[tex]$\pmod {10}$[/tex]is clearly [tex]$m=11$[/tex], [tex]$n=1999,2001,2002,2003,2005,...,2018$[/tex] work (not counting multiples of 4 as we would be double counting if we did).
We can also note that [tex]$19^{2a}\equiv 1 \pmod {10}$[/tex] because[tex]$19^{2a}=361^{a}$[/tex], and by the same logic as why [tex]$11^{\text{any positive integer}}\equiv 1 \pmod {10}$[/tex]we are done. Hence [tex]$n=2002, 2006, 2010, 2014, 2018$[/tex] and [tex]$m=19$[/tex] work (not counting any of the aforementioned cases as that would be double counting).
We cannot make any more observations that add more[tex]$m^n$[/tex] with unit digit [tex]$1$[/tex], hence the number of [tex]$m^n$[/tex] that have units digit one is [tex]$4\cdot 5+1\cdot 15+1\cdot 5=40$.[/tex] And the total number of combinations of an element of the set of all [tex]$m$[/tex]and an element of the set of all n is [tex]$5\cdot 20=100$[/tex]. Hence the desired probability is [tex]$\frac{40}{100}=\frac{2}{5}$[/tex].
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I need help!
Use the given information to select the factors of f(x). f(4)=0 f(-1)=0 f(3/2)=0. Make sure to select all correct answers for full credit.
Using the information of the factors f ( x ) are
( x + 1 ) ⇒ f ( -1 )( x - 4 ) ⇒ f ( 4 )( 2x - 3 ) ⇒ f ( 3/2 )What is a function in math?The term function as used n math refers to a relation consisting of variables. the variables are of two major types which include
The dependent variableThe independent variableThe given function is substituted in the several equations given but the equations that yielded the desirable result of f ( x ) = 0 are:
option 4option 5option 6Therefore they are the correct choice
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a weighted die has probability 0.102 of landing on a 6. if you roll the die until you get a 6 for the first time, what is the expected number of rolls it will take?
This is an example of a geometric distribution with success probability p=0.102
The expected number of rolls is 10.
What is a geometric distribution?A discrete probability distribution of a random variable "x" that meets some requirements is referred to as a geometric distribution. The conditions for the geometric distribution are. a phenomenon that has undergone a number of tests. There are only two outcomes that can occur in a trial: success or failure.Geometric distribution: If a discrete random variable X has a probability density function (p.d.f.) of the form P(X = x) = q(x-1)p, where q = 1 - p, it is said to have a geometric distribution.Given a finite number of trials, the geometric distribution can be used to estimate the likelihood of success. This is extremely useful in the real world, where it is uncommon to conduct unlimited (and unrestricted) trials.This is an example of a geometric distribution with success probability p=0.102 The expected value of the random variable of a geometric distribution is 1/p=1/0.102=9.80
Therefore, the expected number of rolls is 10.
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Zack plans to attend the Carroll County Fair and is trying to decide what would be a better deal. He can pay $40 for unlimited rides, or he can pay $15 for admission plus $1 per ride. If Zack goes on a certain number of rides, the two options wind up costing him the same amount. How many rides is that?
Let
x -----> number of rides
y ----> the total cost
so
The linear equation that represents both situations are
y=40 -----> equation A
y=x+15 ----> equation B
equate both equations
40=x+15
solve for x
x=40-15
x=25
therefore
the number of rides is 25an envelope contains eight bills: 22 ones, 22 fives, 22 tens, and 22 twenties. two bills are drawn at random without replacement. what is the probability that their sum is \$20$20 or more?
When two bills are drawn randomly without replacement, the probability that their sum is $20 or more is 1/2.
Given,
An envelope contains 8 bills;
Two of $1 bills, Two of $5 bills, Two of $10 bills, Two of $20 bills.
When two bills are drawn randomly without replacement, we have to find the probability that their sum is $20 or more.
Total outcomes = 2 x 2 x 2 x 2 = 16
Total possible outcomes, more than 20;
(1, 20), (20, 1), (5, 20), (20, 5), (10, 10), (20, 10), (10, 20), (20, 20) = 8 cases
That is,
The total possible outcomes is 8.
Now,
The probability of bill to be $20 or more = Possible outcome / Total outcome
Probability = 8/16 = 1/2
That is,
When two bills are drawn randomly without replacement, the probability that their sum is $20 or more is 1/2.
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What is the solution for the equation 2/5 x - 4 = 26 ?
The given expression is,
[tex]\frac{2}{5}x-4=26[/tex]Multiplying all the terms with 5, we get
[tex]\begin{gathered} 5\times\frac{2}{5}x-(5\times4)=(26\times5) \\ 2x-20=130 \\ 2x=130+20 \\ 2x=150 \\ x=\frac{150}{2}=75 \end{gathered}[/tex]Thus, the solution is, x = 75.
If ax-3=bx+5 then the solution for x in terms of a and b is
In this equation the solution for x in terms of a and b is 8.
What is equation?
There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign. Mathematical algebraic equations typically have one or more variables.
Sol- As per the question given that- ax-3= bx+5------(equation 1)
Let ax=3-----(equation 2)
And bx =5------(equation 3)
On adding equation(1)and (2) we get
(ax)+(bx)= 3+5
(ax)+(bx)=8
x(a+b)+y(a+b)=8
(x+y)+(a+b)=8
1×(a+b)=8
Thus
a+b=8
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A and B are complementary angles. If mA = (2x +27)° and mB =
(2x-21), then find the measure of A.
Answer:
mA = 69 degrees
Step-by-step explanation:
A complementary angle has a measure of 90 degrees.
(2x + 27) + (2x - 21) = 90
Simplify
4x + 6 = 90
-6
4x = 84
/4
x = 21
mA: 2(21) + 27 = 69
Answer:
A = 69°
Step-by-step explanation:
Complementary angles sum 90°
A + B = 90°
(2x + 27) + (2x-21) = 90°
4x + 27 - 21 = 90°
4x + 6 = 90°
4x = 90 - 6
4x = 84°
x = 84°/4
x = 21
Then A:
A = 2x + 27
A = 2*21 + 27
A = 42 + 27
A = 69°
B = 2x - 21
B = 2(21) + 27
B = 42 - 21
B = 21°
Check:
69 + 21 = 90
if 6x-1=29, what is the value of x2+x
We are given
[tex]6x-1=29[/tex]Therefore the value of x can be gotten by simplifying the above equation
[tex]\begin{gathered} 6x=29+1 \\ 6x=30 \\ x=\frac{30}{6} \\ x=5 \end{gathered}[/tex]Given that x is 5, we can proceed to find the value of the expression.
[tex]\begin{gathered} x^2+x \\ \Rightarrow(5)^2+5 \\ \Rightarrow25+5 \\ \Rightarrow30 \end{gathered}[/tex]This implies that
[tex]x^2+2\Rightarrow30[/tex]Pls help me. I'm struggling so bad
The formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
in the question ,
it is given that the
formula to find , "gravitational force" between two objects is
[tex]F_{g}[/tex] = (G*M₁*M₂)/r²
to express the formula in terms of M₁ ,
we first multiply both the sides by r² ,
on multiplying , we get
[tex]F_{g}[/tex]*r² = G * M₁ * M₂
On dividing both sides by G ,
we get
( [tex]F_{g}[/tex]*r² ) /G = M₁ * M₂
we have to find the formula for M₁ ,
we divide both sides by M₂,
So , on dividing both sides by M₂ , we get
( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) = M₁
hence M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ )
Therefore , the formula for M₁ in terms of [tex]F_{g}[/tex] , G , M₂ , r is M₁ = ( [tex]F_{g}[/tex]*r² ) /(G*M₂ ) .
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how to graph y=2x+2 please help
The graph of the equation is attached to the solution.
We can graph the equation of the line by finding the x and y intercept of the line.
We know that the equation is in the slope intercept form.
Hence, we can write the y-intercept of the line as 2.
The coordinates of the point will be (0,2).
To find the x - intercept, we can put y = 0
0 = 2x + 2
-2 = 2x
x = -2/2 = -1
x = -1
The coordinates of the point will be (-1,0).
We can find another point on the line.
Let x = 1
y = 2(1) + 2
y = 2 + 2
y = 4
The coordinates of the point will be (1,4).
We can plot these points on the graph and get our graph.
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Simplify the expression. Assume that x is nonzero. Your answer should have only positive exponents. x to the power of negative 10 multiplied by x to the power of 6
The answer after simplifying the expression, [tex]x^{-10} *x^{6}[/tex], will be [tex]1/x^{4}[/tex].
According to the question,
We have the following expression:
[tex]x^{-10} *x^{6}[/tex]
Now, we know that if two numbers are being multiplied with the same base but different powers then their powers are added.
(More to know: if the numbers are in division with the same base but different powers then their powers are subtracted.)
So, we have:
[tex]x^{-10+6}[/tex]
[tex]x^{-4}[/tex]
Now, we know that if powers are in negative then the number can be inverted to make the power positive (because it is given that the answer should have only positive exponents).
[tex]1/x^{4}[/tex]
Hence, the value after solving the expression is [tex]1/x^{4}[/tex].
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Safiya travels at an average speed of 40 mph for 30 miles.
Without stopping, Safiya then travels 50 miles in 1.5 hours.
Find her average speed for the entire journey to 2 dp.
Pls help
Average speed is 35.56 mph.
Calculating average speed involves dividing the whole distance travelled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time. Average speed refers to the average speed during the course of a journey.
We have to find the average speed of the whole journey.
First we have to find total distance for whole journey and then total time for whole journey.
Total distance for whole journey = 30 miles + 50 miles = 80 miles
Time for 30 miles = distance/speed = 30/40 = 3/4 hrs = 0.75 hrs
Total time = 1.5 + 0.75 hrs = 2.25 hrs
Average speed = total distance/ total time
= 80/2.25
= 35.56 mph.
The average speed is 35.56 mph.
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15 points for thiz one.
Answer:
(I) y=10-6x. (ii) y=x/-2 - 3