Answer:
Total number of required ways = 12 × 51!
Step-by-step explanation:
Number of total cards in the deck = 52
Number of face cards in the deck = 12
Now, we need to find the number of ways such that the first card is always a face card
Now, first card is face card so number of cards left to be arranged = 52 - 1 = 51
Number of ways to arrange 51 cards = 51!
Also, Number of face cards = 12
So, Total number of required ways = 12 × 51!
Answer:
The order of the start of the proof seems fine; we're to choose the next steps I guess.
segment UV is parallel to segment WZ Given
Points S, Q, R, and T all lie on the same line. Given
m∠SQT = 180° Definition of a Straight Angle
m∠SQV + m∠VQT = m∠SQT Angle Addition Postulate
m∠SQV + m∠VQT = 180° Substitution Property of Equality
That's all valid up to here. It seems to me sort of the hard way to get to linear supplements but here we are.
ZRS is mentioned in the rest of the lines; let's find the one that comes first.
III m∠VQT + m∠ZRS = 180° Same-Side Interior Angles Theorem
Now we have two things equal to 180 degrees, so they're equal to each other.
II m∠SQV + m∠VQT = m∠VQT + m∠ZRS Substitution Property of Equality
Now comes
I m∠SQV + m∠VQT − m∠VQT = m∠VQT + m∠ZRS − m∠VQT
m∠SQV = m∠ZRS Subtraction Property of Equality
And we conclude,
∠SQV ≅ ∠ZRS Definition of Congruency
Complete Question
If $12000 is invested in an account in which the interest earned is continuously compounded at a rate of 2.5% for 3 years
Answer:
$ 12,934.61
Step-by-step explanation:
The formula for Compound Interest Compounded continuously is given as:
A = Pe^rt
A = Amount after t years
r = Interest rate = 2.5%
t = Time after t years = 3
P = Principal = Initial amount invested = $12,000
First, convert R percent to r a decimal
r = R/100
r = 2.5%/100
r = 0.025 per year,
Then, solve our equation for A
A = Pe^rt
A = 12,000 × e^(0.025 × 3)
A = $ 12,934.61
The total amount from compound interest on an original principal of $12,000.00 at a rate of 2.5% per year compounded continuously over 3 years is $ 12,934.61.
*see attachment for the possible choice answers showing the boxes and dimensions
Answer:
Box D = 27 ft³
Step-by-step explanation:
To find out which has the greatest volume, we need to calculate the volume of each box given in the option using the formula of the volume of a rectangular prism = w × h × l.
Where w = width; h = height; and l = length.
Thus, the volume for the boxes are as follows:
=>Box A:
V = w × h × l
V = 3 × 1 × 5
V = 15 ft³
=>Box B:
V = w × h × l
V = 2 × 3 × 4
V = 24 ft³
=>Box C:
V = w × h × l
V = 1 × 2 × 7
V = 14 ft³
=>Box D:
V = w × h × l
V = 3 × 3× 3
V = 27 ft³
The shipping box with the largest volume is box D with a volume of 27 ft³
The answer is D just keep subtracting 6