The base of an isosceles triangle is 7 cm longer than the legs. Find the legs if the perimeter of the triangle is 43 cm.
2 answers:
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Answer:
Step-by-step explanation:
Hello!
The variable of interest in this case is:
X: length of time before a major repair is required on a new car. (months)
This variable has a normal distribution with mean μ= 36 months and a standard deviation σ= 9 months.
If he wants to set a guarantee period in which only 5% of the sold cars fell, the objective is to find the value of X that has below 5% of the cars that need major repairs before the end of the guarantee period.
Check the attachment, the curve represents the distribution of the population of the time it takes before a new car needs major repairs, I've marked approximately where this value of X should be.
Symbolically:
P(X≤a)=0.05
To reach the proper value of "a" you have to work using the standard normal distribution because is a tabulated distribution and you can extrapolate it to any normal distribution.
So the first step is to look in the table of the Z distribution for the value that accumulates 0.05 of probability since it is such a low probability, you have to look for the value in the left side of the table (negative values of Z). You look for 0.05 in the body of the table and then the margins for the corresponding value (see second attachment)
Then the value that accumulates 0.05 of probability is -1.64, now you have to reverse the standardization to reach the asked value of X
Z= (a- μ)/σ
(Z*σ)= a - μ
a=(Z*σ)+ μ
a=(-1.64*9)+36
a= 21.24 months.
The guarantee period should be 21.24 months so that only 5% of the sold cars will need major repairs before it wears of.
I hope it helps!
i ) 3(2x - 3) = 4(2x + 4)
ii )2(x + 2) + 5(x + 5) = 4(x-8) + 2(x - 2)
2. 3x /4 - 7 /4 = 5x + 12
cancel 4 from both sides
3. x +7 - 8x/3 = 17/6 - 5x/8
put x = 4
L.H.S. = R.H.S.
<h2>--------------------</h2>4. Let 3 consecutive integers : x , x+1 , x+2
As per the question : 2x + 3(x+1) + 4(x+2) = 56
9x + 11 = 56
Transpose 11 to RHS
9x = 45
Divide both sides by 9
x = 5 ,
x + 1 = 5 + 1 = 6
x + 2 = 5 + 2 = 7
Numbers are 5 , 6 and 7 .
<h2>-----------------------</h2>5. Let the age of Jane’s younger sister is x.
Age of Jane will be x + 6
As per the question, after 10 years the sum of their ages will be 50.
After 10 years,
age of Jane = x + 16
age of her younger sister = x + 10
Therefore,
x + 16 + x +10 = 50
2x + 26 = 50
2x = 24
x = 12
Thus, the present age of Jane’s younger sister is 12 years.
And of Jane’s is 12 + 6 = 18 years.
<h2>---------------------</h2>6. Let the breadth of rectangular swimming pool be x metres.
Then, its length = (2x + 2) metres.
We know that the Perimeter of a rectangle
= 2(Length + Breadth)
= 2(2x + 2 + x) = 6x + 4
According to the given condition, we have
6x + 4 = 154
6x = 154 − 4
6x = 150
[Dividing both sides by 6]
x = 25
Thus, breadth = 25 m and
length = 25 × 2 + 2 = 52 m .
<h2>---------------------</h2>7. Let the digit in ten's .
Place be x and the digit in the one's place be y.
x − y = 5 ⟶ (i)
Two digit number = 10x + y
Two digit after reversing the digits = 10y + x
According to question ,
10x + y + 10y + x = 99
11x + 11y = 99
x + y = 9 ⟶ (ii)
On adding (i) and (ii),
2x = 14
x = 7
Putting the value of x in equation (i)
x − y = 5
y = 2
Number = 10x + y
=72 .
<h2>-----------------------</h2>8. Let the speed of the steamer in still water be x km/h.
Then , the speed downstream = (x+2) km/h
and the speed upstream = (x−2) km/h
Given , distance covered in 4 hours downstream = distance covered in 5 hours upstream
4(x + 2) = 5(x − 2)
4x + 8 = 5x − 10
4x − 5x = − 10 − 8
[Transposing 5x to LHS and 8 to RHS]
−x = −18 or x = 18 km/h .
<h2>-----------------------</h2>9. Let the number of notes of different denomination be x.
∴ Numbers of Rs 100 notes , 50 notes and Rs 10 notes will be 2x , 3x and 5x respectively.
Amount of 100 Rs notes ⇒Rs 100 × 2x = 200x
Amount of 50 Rs notes ⇒Rs 50 × 3x = 150x
Amount of 10 Rs notes ⇒Rs 10 × 5x = 50x
As per the question
Total amount = 400000
200x + 150x + 50x = 400000
400x = 400000 , x = 1000
No of Rs 100 notes = 2x = 2 × 1000 = 2000
No of Rs 50 notes = 3x = 3 × 1000 = 3000
No of Rs 10 notes = 5x = 5 × 1000 = 5000 .
<h2>------------------------</h2>10. Let the age of the man be x
Then age of his son becomes (x − 24)
2 years later from now,
Age of man will be = x + 2
and age of his son will be = (x − 24 + 2) = x − 22
According to question,
2(x − 22) = x + 2
i.e., 2x − 44 = x + 2
i.e., x = 46
Therefore ,
Present age of man = 46 years
And present age of his son = 46 − 24 = 22 years .