x=Money after withdrawals.
x=450-200(3)
x=450-600
x=-250
After making 3 $200 withdrawals from his account after initially starting with $450 he has a balance of negative $250 in his account.
Answer:
<u>The correct answer is that the number of different ways that the letters of the word "millennium" can be arranged is 226,800</u>
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Number of letters of the word "millennium" = 10
Letters repeated:
m = 2 times
i = 2 times
l = 2 times
n = 2 times
2. The number of different ways that the letters of millennium can be arranged is:
We will use the n! or factorial formula, this way:
10!/2! * 2! * 2! * 2!
(10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)/(2 * 1) * (2 * 1) * (2 * 1) * (2 *1)
3'628,800/2*2*2*2 = 3'628,800/16 = 226,800
<u>The correct answer is that the number of different ways that the letters of the word "millennium" can be arranged is 226,800</u>
Answer:
The dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
Step-by-step explanation:
Given
Rectangle Pyramid
Base Length = 3x + 1
Base Width = x
Height = 12
Volume = 96
Required
Dimension of the base of the pyramid
Given that the volume of the pyramid is ⅓ of the base area * the height.
This is represented mathematical as
Volume = ⅓ * base area * height.
Where
Base area = width * length
Base area = (3x + 1) * x
Base area = 3x² + x.
So,
Volume becomes
Volume = ⅓ * (3x² + x) * 12.
Volume = (3x² + x) * 4
Substitute 96 for volume
96 = (3x² + x) * 4
Divide both sides by 4
96/4 = (3x² + x) * 4/4
24 = 3x² + x
Subtract 24 fr both sides
24 - 24 = 3x² + x - 24
0 = 3x² + x - 24
3x² + x - 24 = 0
Expand
3x² + 9x - 8x - 24 = 0
Factorize
3x(x + 3) - 8(x + 3) = 0
(3x - 8)(x + 3) = 0
3x - 8 = 0 or x + 3 = 0
3x = 8 or x = -3
x = 8/3 or x = -3
Recall that
Length = 3x + 1
Width = x
For any of the above expression, x can't be less than 0; so, x = -3 can't be considered.
Substitute x = 8/3
Length = 3x + 1
Length = 3(8/3) + 1
Length = 8 + 1
Length = 9
Width = x
Width = 8/3
Hence, the dimension of the base of the Rectangle Pyramid is Length = 10 and Width = 8/3
The linear model is the best fit for the relationship.
According to the statement
we have given that the relationship between gross box office sales and home video units significant and the linear model is the best fit for the relationship.
And we explain all the given statements.
So, For this purpose, we know that the
Since the p-value of the independent variable, 0.0000, is less than 0.05, we can be 95% confident that there is a significant linear relationship between gross box office and home video units.
And the
linear model is used in different ways according to the context. The most common occurrence is in connection with regression models.
So, the linear model is appropriate for the comparisons.
So, The linear model is the best fit for the relationship.
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