The total number of bills and coins is 14.
Step-by-step explanation:
To minimize the count of bills and coins, start with the largest denominations that fit within the amount.
The change due is $39.49.
Start with:
-$20 bill (largest under $39.49)
Remaining: $19.49
-$10 bill (largest under $19.49)
Remaining: $9.49
-$5 bill (largest under $9.49)
Remaining: $4.49
Then:
4 × $1 bills (to cover $4.49)
Remaining: $0.49
-$0.25 coin (quarter)
Remaining: $0.24
2 × $0.10 coins (dimes)
Remaining: $0.04
4 × $0.01 coins (pennies)
The final composition includes:
1 twenty-dollar bill
1 ten-dollar bill
1 five-dollar bill
4 one-dollar bills
1 quarter
2 dimes
4 pennies
Totaling 14 pieces.
The cubic equation formed is L^3 - 52L +144 = 0. Dimensions: Length = 4 inches, Width = 2 inches, Height = 3 inches. To determine this, let L be the length, W the width, and H the height. The box volume is 24 cubic inches, and its total surface area is 52 sq. inches. Setting W = L/2 leads to Volume = L * W * H, thus substituting W gives us the equation 0.5L^2 * H = 24 resulting in H = 48/L^2. The surface area equation simplifies to (L*W) + (L+H) + (W+H) = 26. Introducing W = 0.5L yields 0.5L^2 + 1.5LH = 26. Substituting H into this gives 0.5L^2 + 72/L = 26. Multiplying throughout by L to eliminate denominators yields 0.5L^3 - 26L + 72 = 0. After multiplying through by 2: L^3 - 52L +144 = 0. Testing L=4 confirms a factor, thus Length (L) = 4 inches, and subsequently, W and H calculate to 2 inches and 3 inches respectively.
The highest 5% of scores corresponds to the 95th percentile, meaning the cutoff score
is defined as
When transformed into the standard normal distribution,
A cumulative probability of 95% corresponds to a z-score of approximately
, indicating that the cutoff score is likely around
Answer:
Step-by-step explanation:
1) True. This stems from the fact that the divergence of F is 1, indicating that F is a linear function. The orientation is outward from the surface. Integrating a linear function over a surface with outward orientation leads to the volume enclosed by that surface.
2) True. This is fundamentally what the Divergence theorem states.
3) False. Had F been specified as 3/pi instead of div(F), this claim would have held true.
4) False. The gradient of divergence can vary. The curl of the divergence of a vector function is 0, contradicting the notion of the gradient of divergence being 0.
5) False. While calculating divergence, derivatives are computed for different variables. Since the derivative of constants is 0, both vector functions F and G can contain distinct constant components even when their divergences are equal.
