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:
<em>when </em><em>x </em><em>=</em><em> </em><em>5</em><em> </em>
<em>then </em><em> </em><em>the </em><em>value </em><em>of</em><em>. </em><em>(</em><em>3</em><em>x</em><em>+</em><em>2</em><em>)</em>
<em>(</em><em>3</em><em>*</em><em>5</em><em>)</em><em> </em><em>+</em><em> </em><em>2</em>
<em> </em><em> </em>
<em>1</em><em>5</em><em> </em><em>+</em><em> </em><em>2</em>
<em>=</em><em>. </em><em>1</em><em>7</em>
<em>her </em><em>mistake </em><em>was </em><em>that </em><em>she </em><em>doesn't</em><em> </em><em>multiplied</em><em> </em><em>5</em><em> </em><em>and </em><em>3</em><em> </em><em> </em>
81.4% ≅ 81%. The probability that a customer ordered a hot drink given that he or she ordered a large is 81%.
The key to solve this problem is using the conditional probablity equation P(A|B) = P(A∩B)/P(B). Conditional probability is the probability of one event occurring with some relationship to one or more other events.
Similarly to the previous exercise, P(A∩B) is the probability that a customer order a large hot drink. So, P(A∩B) = 22/100 = 0.22
For P(B), is the probability that a customer order a large drink whether hot or cold. P(B) = 27/100 = 0.27
P(A|B) = 0.22/0.27 = 0.814
multiplying by 100%, we obtain 81.4%
The interquartile range is A. 15.5
Answer:
.998543
9.92749
sqrt(101)
10 pi
Step-by-step explanation:
10 pi is approximately 10 * 3.14 = 31.4
.998543 is less than 1
9.927
sqrt(101) is a little more than sqrt(100) which is 10
Smallest .998543
9.92749
sqrt(101)
10 pi
