We need to find the base x in the following equation:
First, lets convert 365 from base 7 to base 10. This is given by
where the upperindex denotes the position of eah number. This gives
that is, 365 based 7 is equal to 194 bases 10.
Now, lets do the same for 43 based x. Lets convert 43 based x to base 10:
where again, the superindex 0 and 1 denote the position 0 and 1 in the number 43. This gives
Now, we have all number in base 10. Then, our first equation can be written in base 10 as
For simplicity, we can omit the 10 and get
so, we can solve this equation for x. By combining similar terms. we have
and by moving 197 to the right hand side, we obtain
Finally, we get
Therefore, the solution is x=5
T us assume the two numbers to be "x" and "y".
Then
2x + y = 310
And
x - y = 55
Let us take the second equation and find the value of x in relation to y.
x - y = 55
x = y + 55
Now let us put the value of x in the first equation, we get
2x + y = 310
2(y + 55) + y = 310
2y + 110 + y = 310
3y = 310 - 110
3y = 200
y = 200/3
= 66 2/3
Now putting the value of y in the second equation, we get
x - y = 55
x - (200/3) = 55
3x - 200 = 55 * 3
3x = 165 + 200
x = 365/3
= 121 2/3
So the value of x is 121 2/3 and the value of y is 66 2/3
Answer:
Option A.)−4
Step-by-step explanation:
we have
4x+5y=-12 -----> equation A
-2x+3y=-16 -----> equation B
Solve the system of equations by elimination
Multiply the equation B by 2
2*(-2x+3y)=-16*2
-4x+6y=-32 -----> equation C
Adds equation A and equation C
4x+5y=-12
-4x+6y=-32
-----------------
5y+6y=-12-32
11y=-44
y=-4
Answer:
-The total area of a Rectangular Prism:
Step-by-step explanation:
-To find the total area of a rectangular prism, you need this formula:
Length
Width
Height
-Apply the length, width and height for the formula:
11 in
8 in
5 in
-Then, solve for the area:
So, the total area would be 
.
Answer:
a) The 90% confidence interval is 
b) The margin of error is 0.063.
Step-by-step explanation:
We have to construct a 90% confidence interval for the proportion of students enrolled in college or a trade school within 12 months of graduating from high school in 2013.
We have a sample of 160 students, and a proportion of:
The standard deviation is:
As the sample size is big enough, we use the z-value as statistic. For a 90% CI, the z-value is z=1.645.
Then, the margin of error is:
Then, the 90% confidence interval is:
