Answer:
Step-by-step explanation:
We need to find the probability that the mechanic will service or more cars.
It's a simpler one given that we have the probabilities of servicing 4 or less cars.
P(at least 5 cars) is given by subtracting the probabilities of servicing both 3 and 4 cars.
Answer:2+x=15-7/8x
We move all terms to the left:
2+x-(15-7/8x)=0
Domain of the equation: 8x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
x-(-7/8x+15)+2=0
We get rid of parentheses
x+7/8x-15+2=0
We multiply all the terms by the denominator
x*8x-15*8x+2*8x+7=0
Wy multiply elements
8x^2-120x+16x+7=0
We add all the numbers together, and all the variables
8x^2-104x+7=0
a = 8; b = -104; c = +7;
Δ = b2-4ac
Δ = -1042-4·8·7
Δ = 10592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
x1=−b−Δ√2ax2=−b+Δ√2a
The end solution:
Δ−−√=10592−−−−−√=16∗662−−−−−−−√=16−−√∗662−−−√=4662−−−√
x1=−b−Δ√2a=−(−104)−4662√2∗8=104−4662√16
x2=−b+Δ√2a=−(−104)+4662√2∗8=104+4662√16
Step-by-step explanation:
There are 78 cookies in box C, 26 cookies in box B and 10 cookies in box A.
let the number of cookies in first box be represented mathematically as B-16
the number of cookies in second box be represented as B
the number of cookies in third box be represented as 3B
Since there are 124 cookies we can make an equation such that it becomes
B-16 +B +3B =124
Solving for B, we have
5B -16 =124
5B =124 +16
5B =130
B=130/5
B=26
Therefore Box A contains B-16 =26-16 =10 cookies
Box C contains 3B =3 X 26=78 cookies
See similar question here: brainly.com/question/23505776
Answer: The number is 75
Lets start by defining the 2-digit number.
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Define the number
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Let x be the digit in the tens place and y be the digit in the ones place.
The number is 10x + y
The reverse of the number is 10y + x
Now we will construct the equations needed
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Construct equations
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When the digits are reversed, the value decreases by 18:
(10x + y) - (10y + x) = 18 . ← Apply distributive property
10x + y - 10y - x = 18 ←Combine like terms
9x - 9y = 18 ←Divide by 9 through
x - y = 2
The sum of the digits is 12:
x + y = 12
Now that we have the two equations, we can solve for x and y.
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Solve for x and y
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x - y = 2 ---------------------- (equation 1)
x + y = 12 ---------------------- (equation 2)
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Make x the subject in equation 1
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x - y = 2 ← Add y from both sides
+ y +y
x = 2 + y
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Substitute x = 2 + y into equation 2
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x + y = 12 ← Substitute x = 2 + y
2 + y + y = 12 ← combine like terms
2 + 2y = 12 ← Subtract 2 from both sides
-2 -2
2y = 10 ← Divide by 2 on both sides
÷2 ÷2
y = 5
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Substitute y = 5 into equation 1
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x - y = 2 ← substitute y = 5
x - 5 = 2 ← add 5 on both sides
+5 +5
x = 7
Now we know the value of x and y. Lets find the 2-digit number.
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Find the 2-digit number
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The number = 10x + y = 10(7) + 5 = 75
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Answer: The number is 75
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Answer:
124
Step-by-step explanation:
Elm St. and Oak St. are parallel lines.
Cedar St. is a transversal to the other two streets.
When parallel lines are cut by a transversal, corresponding angles are congruent.
The angles with measures 9x + 61 and 3x + 103 are corresponding angles, so they are congruent and have the same measure.
9x + 61 = 3x + 103
Subtract 3x from both sides.
6x + 61 = 103
Subtract 61 from both sides.
6x = 42
Divide both sides by 6.
x = 7
9x + 61 = 9(7) + 61 = 63 + 61 = 124
3x + 103 = 3(7) + 103 = 21 + 103 = 124
