Marcus has created a budget for his upcoming trip to the theme park. Admission is 40% of the budget. He plans to spend 32% of his money on food, 23% on souvenirs, and save 5% for emergencies. He knows the admission will be $6 less than he will spend on food and souvenirs. How much money will Marcus need to take to the park?
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Interval notation is used to write a set of real numbers from one value to another value.
On the left, you start with left parenthesis or left bracket.
Then you follow by two numbers separated by a comma.
You then finish with a right parenthesis or right bracket.
To include a number, use a square bracket.
To exclude a number use parenthesis.
To write the set of numbers, you need to list the smallest number in the set followed by the largest number in the set. An interval is always stated with two numbers, from the smallest in the set to the largest in the set. The numbers are always separated by a comma.
Examples:
1) All numbers from 6 to 10, including 6 and 10.
Algebra: 6 <= x <= 10
Interval: [6, 10]
Notice brackets since both 6 and 10 are included in this interval.
2) All number from 5 to 20, including 5 but not including 20.
Algebra 5 <= x < 20
Interval: [5, 20)
Bracket with 5 means include 5. Parenthesis with 20 means 20 is not included.
3) All numbers greater than or equal to 7.
Algebra: x >= 7
Interval: [7, ∞)
The 7 has a bracket because it is included. Infinity always has parenthesis.
With the infinity symbol, always use parenthesis, not square bracket.
4) All numbers less than -5.
Algebra: x < - 5
Interval: (-∞, 5)
Now for your problems.
10.
This is a line. Both the domain and range all all real numbers.
That means the interval is from negative infinity to positive infinity.
(-∞, ∞)
Both the domain and range are that same interval, all real numbers, from negative infinity to positive infinity.
13.
The domain is all real numbers as you can see the x-coordinates extend left forever and right forever. The domain is the same interval as the domain and range of problem 10.
The range is zero and all positive numbers.
You can think of it a all values of y such that y is greater than or equal to zero. Notice that zero is included in the interval.
[0, ∞)
Since zero is included, we use a left bracket, not left parenthesis.
With infinity, we alyways use parentheses, not brackets.
Answer:
H(s)=(∫_(t=o)^∞▒〖x(t)e^(-st) dt〗)/(∫_(t=o)^∞▒〖y(t) e^(-st) dt〗)
Step-by-step explanation:
L{f(t)}=F(s)=∫_(t=0)^∞▒〖f(t)e^(-st) dt〗
Answer:
Whre is the question I don't get it
Answer: " y = 30° " .
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<u>Note</u>: The sum total of the measure of all angles lying on a straight
line is 180°.
So; x + y + z = 180 .
Given: x = 2y ;
z = 3y ;
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Find the value of: " y " ;
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Since: x + y + z = 180 ;
Substitute: "2y" for "x" ;
and: "3y" for "z" ;
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2y + y + 3y = 180 ;
6y = 180 ;
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Divide EACH SIDE of the equation by "6" ; to isolate "y" on one side of the equation; and to solve for "y" ;
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6y/ 6 = 180 / 6 ;
y = 30 ;
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Let us check our work;
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2y + y + 3y = 180 ;
Substitute our solved value: "30" ; for "y" ; in the equation; to see if the equation holds true:
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2(30) + 30 + 3(30) =? 180 ?
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60 + 30 + 90 = ? 180 ?
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90 + 90 = ? 180 ? Yes!
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