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Vsevolod [243]
1 year ago
11

3. What is the converse of the following statement?If M is the midpoint of line segment PQ, then line segment PM is congruent to

line segment QM
Mathematics
1 answer:
Len [333]1 year ago
6 0

Solution

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Define the converse of a statement

The converse of a statement is formed by switching the hypothesis and the conclusion.

STEP 2: break down the given statements

Hypothesis: If M is the midpoint of line segment PQ,

Conclusion: line segment PM is congruent to line segment QM

STEP 3: Switch the two statements

Hence, the answer is given as:

If line segment PM is congruent to line segment QM, then M is the midpoint of line segment PQ,

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Kendrick takes a sheet of paper and makes a cut from corner to corner the cut he makes is 9 inches long the length of the paper
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765

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3 years ago
Marvin invested 65% of his retirement account in stocks and 35% in gold. Marvin believes that the return to stocks over the next
ser-zykov [4K]

Answer:

1)

the mean rate of return is 17 %

the standard deviation of return is 17.06055

2)

the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325

Step-by-step explanation:

Given the data in the question;

1)

For the portfolio, the mean return and standard deviation are computed as follows;

Mean = Return = 0.65 × 10 + 0.35 × 30

= 6.5 + 10.5

= 17 %

Therefore, the mean rate of return is 17 %

Standard deviation will be;

σp = √( 0.65² × 15² + 0.35² × 40² )

= √( 0.4225 × 225 + 0.1225 × 1600 )

= √( 95.0625 + 196 )  

= √291.0625

= 17.06055  

Therefore, the standard deviation of return is 17.06055

2)  

probability that Marvin's portfolio will make at least 20% over the next 12 months.

P( X > 20 )

we convert to a standard normal variable;

Z = \frac{20-17}{17.06055} )

Z = 0.17

from z table, p-value is;

p( X < 20 ) = 0.5675

P( X > 20 ) 1 - 0.5675  = 0.4325

Therefore, the probability that Marvin's portfolio will make at least 20% over the next 12 months is 0.4325

5 0
3 years ago
The height of the Empire State Building is 1250 feet tall. Your friend, who is 75 inches tall, is standing nearby and casts a sh
Lyrx [107]
Answer:

The length of the building's shadow = 550.66 ft

Explanations:

The height of the Empie State Building = 1250 feet

The friend's height = 75 inches

The length of the friend's shadow = 33 inches

\frac{Actual\text{ height of the friend}}{\text{Length of the friend's shadow}}=\text{ }\frac{Height\text{ of the building}}{\text{Length of the building's shadow}}\begin{gathered} \frac{75}{33}=\text{ }\frac{1250}{\text{Length of the building's shadow}} \\ 2.27\text{ =  }\frac{1250}{\text{Length of the building's shadow}} \\ \text{Length of the building's shadow = }\frac{1250}{2.27} \\ \text{Length of the building's shadow = }550.66\text{ f}et \end{gathered}

6 0
1 year ago
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