Answer:
d = 6.997 or 7
Step-by-step explanation:
Use Pythagorean Theorem to find the diagonal of the end of the prism
2^2 + 3^2 = C^2 Simplify
4 + 9 = C^2 Add
13 = C^2 Take the square root of both sides
3.6 = C
Now plug this into the Pythagorean Theorem equation for the diagonal of the whole prism.
3.6^2 + 6^2 = d^2 Simplify
12.96 + 36 = d^2 Add
48.96 = d^2 Take the square root of both sides
6.997 = d This can be rounded up to 7, if needed
Answer:
Option B, Area of pentagon = 58.5 Square feet
Step-by-step explanation:
The remaining part of the question is attached as image
Solution
Area of pentagon has a triangle and a trapezoid
Area of triangle = 0.5 *base *height = 0.5*9 *3 = 13.5 square feet
Area of trapezoid = Area of rectangle – 2* area of smaller triangles
= 9 ft * 6ft – ( 2 * 0.5 * 6 ft * (9 ft – 6ft) /2
= 54 – (1*6*1.5)
Area of pentagon = 13.5 + 45 = 58.5 Square feet
Hence, option B is correct
Answer:
See the explanation
Step-by-step explanation:
We know that
f(x) = 2x⁶ + 3x⁴ - 4x³ + (1/x) - sin2x
Lets calculate the derivatives:
f'(x) = 6(2x⁵) + 4(3x³) - 3(4x²) -( 1/x²) - 2(cos2x)
f'(x) = 12x⁵ + 12x³ - 12x² - (1/x²) - 2cos2x
Similarly:
f''(x) = 60x⁴ + 36x² - 24x + (2/x³) + 4sin2x
f'''(x) = 240x³ + 72x - 24 - (6/x⁴) + 8cos2x
Rearrange:
f'''(x) - 240x³ +72x - (6/x⁴) + 8cos2x - 24
f''''(x) = 720x² + 72 + (24/x⁵) - 16sin2x
Rearrange:
f''''(x) = 720x² + (24/x⁵) - 16sin2x +72
7/438.... just solve it like thus.....EVERY FRACTION IS A DIVITION PROBLEM
Answer:
a. 7/22
b. 28/33
c. 7/22
d. dependent events
Step-by-step explanation:
The total number of cards is given as 7 + 5 = 12.
The probability if a card being green on the first pick, P(G) = 7/12
The probability of a card being yellow on the first pick, P(Y) = 5/12
Because there is no replacement, the card are going to be short by one card. Therefore, the second pick will be like this:
P(GG) = ( 7/12×6/11)
P(GY) = ( 7/12 × 5/11)
P(YG) = ( 5/12×7/11)
P(RR) = ( 5/12 ×4/11)
a. P (G1 and G2) = ( 7/12×6/11)
= 7/22
b. P( At least one is green) = ( 7/12×6/11) + ( 7/12 × 5/11) + ( 5/12×7/11)
= 28/33
c. P(G2G1) = 7/22
d. the events are dependent. They do not give the same result.
