Answer:
The test statistic Z = 3.125
Step-by-step explanation:
<em>Given Population proportion P = 0.25</em>
<em>Given sample size 'n' = 696</em>
<em>Sample proportion 'p⁻' = 0.30</em>
Test statistic


<u><em>Final answer</em></u>:-
The test statistic Z = 3.125
Answer:
1.56%
Step-by-step explanation:
A standard deck of cards has 52 cards, and 13 of these are hearts, as there are 4 suits, and 52/4=13. This means the probability of choosing a heart card from a deck of cards is 1/4, or 25%. Now to find the probability of doing this from 3 decks in a row, we simply cube 1/4 to get 1/64, and in percentage this is ~1.56%.
Answer:
- $5000 at 10%, $10000 at 12% and 10000 at 16%
Step-by-step explanation:
- <em>One part of $ 25,000 is invested at 10% interest, another part at 12%, and the rest at 16%. The total annual income from the three investments is $ 3,200. Also, the income from the investment at 16% is equal to the income from the other two investments combined. How much was invested at each interest rate?</em>
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Let the parts be x, y and z
<u>As per given we get below system of equations:</u>
- x + y + z = 25000
- 0.1x + 0.12y + 0.16z = 3200
- 0.1x + 0.2y = 0.16z
<u>Substitute 0.1x + 0.2y in the second equation:</u>
- 0.16z + 0.16z = 3200
- 0.32z = 3200
- z = 3200/0.32
- z = 10000
<u>Now we have:</u>
- x + y + 10000 = 25000 ⇒ x + y = 15000
and
- 0.1x + 0.12y + 0.16*10000 = 3200 ⇒ 0.1x + 0.12y = 1600
<u>Multiply the second equation and then subtract the first one:</u>
- 10(0.1x + 0.12y) = 10(1600) ⇒ x + 1.2y = 16000
- x + 1.2y - (x + y) = 16000 - 15000
- 0.2y = 1000
- y = 10000
Then
<u>So the parts are:</u>
- $5000 at 10%, $10000 at 12% and 10000 at 16%
Answer:
y=4x+7
Step-by-step explanation:
Line M is parallel to line L, so the equation for line M is y=4x+b
Plug in the coordinates of point (2,15), you get:
15=4*2+b
Solve that to get b=7
Therefore the equation of Line M is y=4x+7
V = S*h
h = V/S = 250*pi / 50*pi = 5 m