MATHEMATICS COLLEGE

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What is the geometric mean of the measures of the line segments A Dand DC? Show your work.

Answers

Answer 1

Answer:

Answer:

AC2 = AB2 + BC2 ---> AC2 = 122 + 52 ---> AC = 13

AD / AB = AB / AC ---> AD / 12 = 12 / 13 ---> AD = 144/13

DC = AC - AD ---> DC = 13 - 144/13 ---> DC = 25/13

AD / DB = DB / DC ---> DB2 = AD · DC ---> DB2 = (144/13) · (25/13) ---> DB = 60/13

DB is the geometric mean of AD and DC.

Step-by-step explanation:

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10 ) Which Property of Multiplication is shown? (5 + 3) x 2 = 5 x 2 + 3 x 2A. Identity Property
C. Associative Property
B. Distributive Property
D. Commutative Property

Answers

Property of Multiplication that is shown on the expression (5 + 3) x 2 = 5 x 2 + 3 x 2 is Distributive Property (option b)

The property of multiplication that is shown in the given equation is the Distributive Property. The Distributive Property states that multiplication distributes over addition. In other words, when we multiply a number by the sum of two other numbers, it is the same as multiplying the number by each of the individual addends and then adding the results together.

In the given equation, we have "(5 + 3) x 2 = 5 x 2 + 3 x 2." Let's break down the left-hand side first. "(5 + 3)" represents the sum of 5 and 3, which is 8. So, we have "8 x 2." By applying the Distributive Property, we can rewrite this as "5 x 2 + 3 x 2."

Now, on the right-hand side, we have "5 x 2 + 3 x 2." Here, we are multiplying 5 by 2 and 3 by 2 individually and then adding the products together. This aligns with the Distributive Property, which states that the result will be the same as on the left-hand side.

So, the Main Answer is option B. Distributive Property

To know more about multiplication here

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Answer:

B. Distributive Property of Multiplication

Step-by-step explanation:

The given equation shows that two similar expressions are equal to each other.

How? Well, they both equal 16 to start. These are the same expressions - one is just distributed out!

$2 \cdot (5 + 3) \n2 \cdot 5 + 2 \cdot3 \n10 + 6 = 16$

and...

$5 \cdot 2 + 3 \cdot 2\n10 + 6\n16$

In the equations, the only difference is that we distributive 2 and multiplied in by 5 and 3!

I hope I was of assistance! #SpreadTheLove <3

. Emma is making bracelets for her friends. She noticed that 12 out of 20 of her beads are red. What decimal is equivalent to the fraction of Emma's beads that are red?

Answers

Answer:

0.6

Step-by-step explanation:

12/20 = 6/10 = 0.6

Whats y=1/4x-12, solve for x

Answers

Answer:

x=48

Step-by-step explanation:

Suppose human weights are normally distributed with mean 175 and standard deviation 36 pounds. A helicopter is evacuating people from a building surrounded by zombies, and this helicopter can fit 9 people and with a maximum weight of 1800 pounds, i.e., an average of 200 pounds per person. If 9 people are randomly chosen to be loaded on this helicopter, what is the probability that it can safely lift off (i.e., the average weight of a person in the helicopter is less than 200)?

Answers

Answer:

$P(\bar X <200)=P(Z<(200-175)/((36)/(√(9)))=2.083)$

And using a calculator, excel or the normal standard table we have that:

$P(Z<2.083)=0.981$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Solution to the problem

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(175,36)$