Answer:
10 days
Step-by-step explanation:
Mogaka and Ondiso working together can do a piece of job in 6 days. Mogaka working alone takes 5 days longer than Ondiso. How many days does it take Ondiso to do the work alone?
Let us represent :
The number of days
Mogaka worked alone = x
Ondiso worked alone = y
Total days worked together = T
Mogaka and Ondiso working together can do a piece of job in 6 days.
Hence,
1/x + 1/y = 1/T
Mogaka working alone takes 5 days longer than Ondiso.
x = y + 5
Therefore:
1/y + 5 + 1/y = 1/6
Multiply all through by (y+5)(y)
= y + y + 5 = (y+5)(y)/6
= 2y + 5/1 = (y+5)(y)/6
Cross Multiply
6( 2y + 5) = (y+5)(y)
12y + 30 = y² + 5y
= y² + 5y - 12y - 30 = 0
= y² - 7y - 30 = 0
Factorise
= y² +3y - 10y - 30 = 0
y(y + 3) - 10(y + 3) = 0
(y + 3)(y -10)= 0
y + 3 = 0, y = -3
y - 10 = 0
y = 10 days
Note that
The number of days Ondiso worked alone = y
Hence, it takes 10 days for Ondiso to work alone
Answer: 1) 13 2) 11, 144°, 36° 3) 18, 54°, 126°
Step-by-step explanation:
For the first one to find x make the equations equivalent to each other
to make an equation.
7x - 16 = 5x + 10 // Now solve for x
add 16 to both sides
7x = 5x + 26
subract 5 from both x
2x = 26
Now divide by 2
x = 13
For the 2nd one do the same thing as last time because the equations are across from each other in parallel lines meaning they are equivalent.
12y + 12 = 15y - 21
add 21 to both sides
12y + 33 = 15y
subtract 12 from both y
33 = 3y
Now divide by 3
y = 11
Angle A is 144°
Angle B is 36°
Now solve for A ( replace y by 11 in the equation a to get an output )
12(11) +12
132 + 12 = 144°
Now to find b subtract 144 from 180
180 - 144 = 36°
For the 3rd one same thing since they are parallel.
5z - 36 = 3z
add 36 to both sides
5z = 3z + 36
now subtract 3 from both z
2z = 36
divide by 2
z = 18
Solve for C
5(18) - 36
90 - 36 = 54°
Z is 18
angle C is 54°
angle D is 126°
Answer:
80
Explanation:
The mean of the distribution of sample means always target the population mean. What this line tells is that whatever the population mean will be, the mean of the distribution of sample means will be same. Since the population mean is 80, the mean of distribution of sample means will also be 80.
However, the standard deviation of the sample distributions is different and is equal to the population standard deviation divided by square root of sample size. So in this case the standard deviation of distribution of sample means will be 6 .
The answer to this question is y=28
Check the first picture. Our goal is to map <span>EFHG to E′F′H′G′.
</span>
All choices involve a rotation by 90° or 270°<span> counterclockwise about the origin.
consider a rotation </span>by 90° counterclockwise. Each point P(a, b) can be rotated 90° cwise about the origin to form P"(a",b") :
by drawing the right angle POP", such that |PO|=|OP"|.
or by plotting each P"(a",b") so that (a",b")=(-b, a)
for example if G(3, 1) is mapped to G(-1, 3) by either of the procedures described.
check picture 2.
EFHG is mapped to E′'F'′H'′G′'.
In order to map E′'F'′H'′G′' to E'F′H'G′, we need to translate the figure 1 unit right.
Answer:
"<span>A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right</span>"