A length of a cable 26.48 long is cut into 4 equal part.what is the length of each piece
what is 26.48/4?
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26.48/4=
A length of a cable 14.48m long is cut into 4 equal pieces. What is the length of each piece
The expression can be simplified as:
10x^7 y^3 / (2x^3 y^2)
To simplify further, we can divide the numerator and denominator by the greatest common factor, which is 2x^3 y^2:
10x^7 y^3 / (2x^3 y^2) = (10/2) (x^7 / x^3) (y^3 / y^2)
Simplifying the exponents:
= 5x^(7-3) y^(3-2)
= 5x^4 y
Therefore, the simplified expression is 5x^4y.
2³x=2exponent5x-9.find x
10exponentx=10000.find x
2^(3x) = 2^(5x-9)
3x = 5x-9
2x = 9
x = 9/2
10^x = 10000 = 10^4
x = 4
To find the length of each piece of the cable, we can divide the total length of the cable by the number of pieces it is divided into.
Length of each piece = Total length of cable / Number of pieces
Length of each piece = 14.48 m / 4
Length of each piece = 3.62 m
Therefore, each piece of the cable is 3.62 meters long.
10x to the power7 y to the power3 over 2x to the power3 and y to the power2
Ages(19,24,29,34,39,44)
Number of works(3,7,8,4,5,3)
Calculate the mean age of the workers?Correct to the one decimal place
To find the mean age of the workers, we need to calculate the sum of the ages and divide by the total number of workers.
First, we can find the sum of the ages by multiplying each age by the number of workers and adding up the products:
Sum of ages = (19 x 3) + (24 x 7) + (29 x 8) + (34 x 4) + (39 x 5) + (44 x 3)
Sum of ages = 57 + 168 + 232 + 136 + 195 + 132
Sum of ages = 920
Next, we can find the total number of workers by adding up the number of workers:
Total number of workers = 3 + 7 + 8 + 4 + 5 + 3
Total number of workers = 30
Finally, we can find the mean age by dividing the sum of the ages by the total number of workers:
Mean age = Sum of ages / Total number of workers
Mean age = 920 / 30
Mean age = 30.67
Therefore, the mean age of the workers is 30.7 (correct to one decimal place).
A man borrows GHC560 on condition that he will repay GHC700at the end of the 4 years. What is the rate of interest percent per annum?
If16^x=64, what is the value of x?
To find the rate of interest percent per annum, we can use the formula:
Simple interest = (Principal x Rate x Time) / 100
where Principal is GHC560, Simple interest is GHC700 - GHC560 = GHC140, and Time is 4 years. We can rearrange the formula to solve for the rate:
Rate = (Simple interest x 100) / (Principal x Time)
Putting in the values:
Rate = (140 x 100) / (560 x 4)
Rate = 25%
Therefore, the rate of interest percent per annum is 25%.
To find the value of x in the equation 16^x = 64, we can take the logarithm of both sides with base 2:
log2 (16^x) = log2 64
Using the rule of logarithms that loga (b^c) = cloga (b), we can simplify the left side:
x log2 16 = log2 64
Since 16 = 2^4, we can substitute:
x log2 2^4 = log2 64
Using the rule of logarithms that loga (b^c) = cloga (b), we can simplify the left side again:
4x log2 2 = log2 64
Since log2 2 = 1, we get:
4x = log2 64
Since 64 = 2^6:
4x = 6
x = 6/4
x = 1.5
Therefore, the value of x is 1.5.
In an examination, 80%of the student passed. If 400 students passed the examination, how many students failed?
Let the total number of students be "x". We know that 80% of the students passed, which means 20% failed. We can express this as an equation:
20% of x = number of students who failed
We are given that 400 students passed, so:
80% of x = number of students who passed
We can solve for "x" by dividing both sides by 80%, or 0.8:
x = (number of students who passed + number of students who failed) / 0.8
x = (400 + number of students who failed) / 0.8
Multiplying both sides by 0.8:
0.8x = 400 + number of students who failed
Subtracting 400 from both sides:
0.8x - 400 = number of students who failed
Therefore, the number of students who failed is:
number of students who failed = 0.8x - 400
We know that 400 students passed, so:
number of students who failed = 0.8x - 400
number of students who failed = 0.2x (since 80% passed, we know that 20% failed)
Now we can substitute this expression into the equation for x:
0.2x = number of students who failed
x = total number of students
x = (number of students who passed + number of students who failed)
Substituting the first expression:
x = (400 + 0.2x)
Solving for x:
0.8x = 400
x = 500
Therefore, the total number of students is 500, and the number who failed is:
number of students who failed = 0.2x
number of students who failed = 0.2(500)
number of students who failed = 100
So, 100 students failed the examination.
11-(11-4)+13
To simplify this expression, we work from left to right, following the order of operations:
11 - (11 - 4) + 13
First, we need to evaluate the parentheses:
11 - (11 - 4) + 13
= 11 - 7 + 13
Next, we perform the subtraction and addition:
11 - (11 - 4) + 13
= 17
Therefore, the expression simplifies to 17.
What is the property of addition is defined by (a+b)+C=a+(b+c)
The property of addition that is defined by the equation (a + b) + c = a + (b + c) is called the associative property of addition.
This property states that, regardless of the grouping of the numbers being added, the sum will always be the same. In other words, if we are adding three or more numbers, we can group them in any way we want, and the sum will remain the same.
For example, if we have four numbers:
(a + b) + (c + d)
We can group them as (a + d) + (b + c) or (c + b) + (a + d), and we will get the same answer. This property is very useful when adding long strings of numbers, as we can group them for easier evaluation.
Find the sum of all even numbers between 70 and80
There are three even numbers between 70 and 80: 72, 74, and 76.
To find the sum of these numbers, we can simply add them up:
72 + 74 + 76 = 222
Therefore, the sum of all even numbers between 70 and 80 is 222.
5(3t+1)-6(t-1)
To simplify the expression 5(3t+1)-6(t-1), we can use the distributive property of multiplication over addition and subtraction:
5(3t+1) - 6(t-1) = 15t + 5 - 6t + 6
Simplifying by combining like terms:
15t + 5 - 6t + 6 = 9t + 11
Therefore, the simplified form of the expression is 9t + 11.
The value of an obtuse angle lies between
The value of an obtuse angle lies between 90 degrees and 180 degrees.
An obtuse angle is any angle that measures greater than 90 degrees, but less than 180 degrees. So, any angle greater than 90 degrees and up to 180 degrees is considered an obtuse angle.
Express 2/5 as a percentage
To express 2/5 as a percentage, we can multiply the fraction by 100:
2/5 * 100 = 40
Therefore, 2/5 is equivalent to 40%.
-2<x<2
The inequality -2 < x < 2 represents all real numbers that are greater than -2 and less than 2.
In interval notation, we can write this as (-2, 2).
We use parentheses because the endpoints (-2 and 2) are not included in the interval. If the inequality included the endpoints, we would use brackets. For example, the inequality -2 ≤ x ≤ 2 would be written as [-2, 2].
A set of furniture was sold for GHC300,000.00 at a profit of 20%.find the cost price
Let the cost price of the furniture be "C". We know that the furniture was sold for GHC300,000.00 at a profit of 20%, which means the selling price was 120% of the cost price. We can express this as an equation:
120% of C = GHC300,000.00
We can convert 120% to a decimal by dividing by 100:
1.2C = GHC300,000.00
Dividing both sides by 1.2:
C = GHC300,000.00 / 1.2
C = GHC250,000.00
Therefore, the cost price of the furniture was GHC250,000.00.
HCF of 2^3times3^2 and 2^3 times3^4
The prime factorization of 2^3 × 3^2 is:
2^3 × 3^2 = 8 × 9 = 2^3 × 3^2
The prime factorization of 2^3 × 3^4 is:
2^3 × 3^4 = 8 × 81 = 2^3 × 3^4
To find the highest common factor (HCF) of these two numbers, we need to find the highest power of each common prime factor. The only common prime factor is 2 raised to the power of 3. The highest power of 2 that divides both numbers is 2^3. The highest power of 3 that divides both numbers is 3^2.
Therefore, the HCF of 2^3 × 3^2 and 2^3 × 3^4 is:
2^3 × 3^2 = 72
(Note that we don't need to multiply by any other prime factors that are not common to both numbers.)