Answer and Step-by-step explanation:
When trying to figure this out, we know that the numbers have to be one after the other, like 1, 2, 3, 4, or 55. 56, 57, 58. The last digit in the numbers also have to add to 6.
<u>The answer is:</u>
100 + 101 + 102 + 103
It adds up to 406, and the integers are consecutive.
<u><em>#teamtrees #PAW (Plant And Water)</em></u>
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<u><em>I hope this helps!</em></u>
Answer:
486 mm
Step-by-step explanation:
solve each side on it's own first
First 2 rectangles: 288 mm all together
2 rectangle: 144 mm
Triangles: 54 mm
Then add rectangles and triangles:
288 mm + 144 mm + 54 mm = 486 mm
4 products are being purchased.
Step-by-step explanation:
Given,
Time taken to select each product = 5 seconds
Time taken to complete check out process = 60 seconds
Total time taken for a transaction = 80 seconds
Let,
x be the number of products purchased.
Time taken for each product*Number of product + Time for check out process = total process
Dividing both sides by 5
4 products are being purchased.
Keywords: variable, division
Learn more about division at:
#LearnwithBrainly
Answer:
(a) E(X) = -2p² + 2p + 2; d²/dp² E(X) at p = 1/2 is less than 0
(b) 6p⁴ - 12p³ + 3p² + 3p + 3; d²/dp² E(X) at p = 1/2 is less than 0
Step-by-step explanation:
(a) when i = 2, the expected number of played games will be:
E(X) = 2[p² + (1-p)²] + 3[2p² (1-p) + 2p(1-p)²] = 2[p²+1-2p+p²] + 3[2p²-2p³+2p(1-2p+p²)] = 2[2p²-2p+1] + 3[2p² - 2p³+2p-4p²+2p³] = 4p²-4p+2-6p²+6p = -2p²+2p+2.
If p = 1/2, then:
d²/dp² E(X) = d/dp (-4p + 2) = -4 which is less than 0. Therefore, the E(X) is maximized.
(b) when i = 3;
E(X) = 3[p³ + (1-p)³] + 4[3p³(1-p) + 3p(1-p)³] + 5[6p³(1-p)² + 6p²(1-p)³]
Simplification and rearrangement lead to:
E(X) = 6p⁴-12p³+3p²+3p+3
if p = 1/2, then:
d²/dp² E(X) at p = 1/2 = d/dp (24p³-36p²+6p+3) = 72p²-72p+6 = 72(1/2)² - 72(1/2) +6 = 18 - 36 +8 = -10
Therefore, E(X) is maximized.
