Answer: 500 people
Step-by-step explanation:
Let there are x people in the survey.
According to the question,
People who like football as their favorite sports = 42 % of x = 0.42 x
People who like baseball as their favorite sports = 33 % of x = 0.33 x
People who like soccer as their favorite sports = 25 % of x = 0.25 x
But, 210 people said football was their favorite sport.
⇒ 0.42 x = 210
⇒ 42 x = 21000
⇒ x = 500
Therefore, there are 500 people in the survey.
A) There are a number of ways to compute the determinant of a 3x3 matrix. Since k is on the bottom row, it is convenient to compute the cofactors of the numbers on the bottom row. Then the determinant is ...
1×(2×-1 -3×1) -k×(3×-1 -2×1) +2×(3×3 -2×2) = 5 -5k
bi) Π₁ can be written using r = (x, y, z).
Π₁ ⇒ 3x +2y +z = 4
bii) The cross product of the coefficients of λ and μ will give the normal to the plane. The dot-product of that with the constant vector will give the desired constant.
Π₂ ⇒ ((1, 0, 2)×(1, -1, -1))•(x, y, z) = ((1, 0, 2)×(1, -1, -1))•(1, 2, 3)
Π₂ ⇒ 2x +3y -z = 5
c) If the three planes form a sheath, the ranks of their coefficient matrix and that of the augmented matrix must be 2. That is, the determinant must be zero. The value of k that makes the determinant zero is found in part (a) to be -1.
A common approach to determining the rank of a matrix is to reduce it to row echelon form. Then the number of independent rows becomes obvious. (It is the number of non-zero rows.) This form for k=-1 is shown in the picture.
9514 1404 393
Answer:
$3400
Step-by-step explanation:
The way these tax tables are structured, you pay 3% on the first $10,000, 5% on the next $40,000, and 5.5% on the remaining $20,000 above $50,000.
tax = 0.03·10,000 +0.05·(50,000 -10,000) +0.055·(70,000 -50000)
= 300 + 2000 +1100
= 3400 . . . dollars
The tax owed on $70,000 is $3,400.
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<em>Additional comment</em>
I like to rewrite this sort of table to a different format:
- 3% of income . . . . . . . . . . . . . . . applies for income ≤ 10,000
- (5% of income) -$200 . . . . . . . . applies for 10,000 < income ≤ 50,000
- (5.5% of income) -$450 . . . . . . .applies for 50,000 < income ≤ 100,000
For an income of $70,000, the tax computation using this form is one multiplication and one addition, rather than 3 multiplications and 4 additions as used when navigating the given table.
Answer:
B (8)
Step-by-step explanation:
AB = BC = AC
AB = BC
x+5 = 3x-1
6 = 2x
x = 3
BC = 3x-1 = 3*3 - 1 = 8
