The total possible outcomes are there if she rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, spins a spinner with 5 equal-sized sections is 20.
<h3>What is permutation and combination?</h3>
A permutation can be defined as the number of ways a set can be arranged, order matters but in combination the order does not matter.
We have:
Total number of outcomes for pyramid = 4
Total number of outcomes for spinner = 5
Total outcomes = 4×5 (multiplication rule of counting)
= 20
Thus, the total possible outcomes are there if she rolls a fair die in the shape of a pyramid that has four sides labeled 1 to 4, spins a spinner with 5 equal-sized sections is 20.
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The expression (-4x + 9)^2 cannot be equal to (-4x)^2 + 9^2 because it is actually equal to the product of two factors (3 + 2sqrt x) (3- 2 sqrt x). One cannot use obviously distributive property. Hence the answer to this problem should be C. as she did not understand both perfect square trinomial and did not determine the product
First convert to feet
3in=3/12=1/4ft
5.5in=5.5/12ft
1:30
multiply scale by 30
1/4ft times 30=30/4=15/2=7.5ft
5.5/12ft times 30=165/12=13.75ft
multiply them
7.5ft times 13.75ft=103.125 ft^2
closest is option D
Answer:
<h3>4.1 x 10^5</h3>
Step-by-step explanation:
10^5 = 100,000 x 4.1 = 410,000
Answer:
(2, 7, 1)
Step-by-step explanation:
We have three equations, and using Gauss-Jordan Elimination, we can solve for x, y, and z
3x + y - 2z = 11
4x - 2y + z = -5
x + 5y - 4z = 33
We can start by taking out the z from all rows except one. To do this, we can work with the second row. I chose the second row because -5 is small and easy to add up with other numbers, and z has no coefficient in this row.
We can add 2 times the second row to the first row and 4 times the second row to the third row to get
11x - 3y = 1
4x - 2y + z = -5
17x -3y = 13
We then have the first and third rows having two variables. Since the y coefficients are the same, we can eliminate the y by adding the negative of the first row to the third row. Our result is then
11x - 3y = 1
4x - 2y + z = -5
6x = 12
From the third row, we can gather that x= 2. We can then plug that into the first row to get
22 -3y = 1
subtract 22 from both sides
-3y = -21
divide both sides by -3
y = 7
We can then plug our x and y values into the second row to get
4(2) - 2(7) + z = -5
8 - 14 + z = -5
-6 + z = -5
add 6 to both sides
z = 1
Our answer is thus (2, 7, 1)
