1.)PPF
2.)FFP
hope it helps
He can use three bookshelves. there will be 3 math books on each of the three shelves and 2 reading books on each of the shelves. 3 is the greatest common factor of 9 and 6.
Answer:
30%
Step-by-step explanation:
Initial area is 40 square feet
Final area is 28 square feet
Difference between the initial and final areas will be 40-28=12 square feet
Taking the initial area as the base area and expressing the area change in percentage then the percentage decrease will be equivalent to
Therefore, the decrease in area expressed as a percentage is equal to 30%
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work
EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same
For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y
For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4
Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.
Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the
x²y = -4 ... (I)
Condition 2: Real parts are the same
x² + y = -3 ... (II)
We have a system of equations since both conditions must be satisfied
x²y = -4 ... (I)
x² + y = -3 ... (II)
We can rearrange equation (II) so that we have
y = -3 - x² ... (II)
Substituting into equation (I)
x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0
Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.
Solve for y:
y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4
So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:
-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i
x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i
They result in conjugates
Answer:
b. You would conclude that the differences in the average scores can be traced to differences in the working memory of the two groups.
Step-by-step explanation:
Though the average scores of the two sets could have lead to various conditions, but retentive ability deminishes with respect to an increase in age. With respect to the age of the elderly people involved, it is expected that some of them would not be able to retain information for a long period of time. Thus, their average score is 72%.
The college students' are younger, so it is expected that they should be able to retain more information. That ability is one of the reasons why their average score is 85%.
It can be concluded from the research that the differences in the average scores is probably due to the working memory of the two groups.
