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3 years ago

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A student used his place value chart to show a number. After the teacher instructed him to divide his number by 100,the chart sh

owed 28.003. Draw a picture of what the place value chart looked like at first.

2 answers:

NeX [460]3 years ago

5 0

When you divide by 100 you are essentially moving the decimal of the number two places to the left. In undoing this you would have to move the decimal of the number two places to the right.

28.003 would then turn into 2,800.3

Unfortunately I cannot draw a chart on here but that is the best I can do.

My name is Ann [436]3 years ago

4 0

When you divide by a decimal your moving the decimal over to the left and rounding to the nearest hundredth

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The volume of a cube depends on the length of its sides. This can be written in function notation as v(s). V(4)=64

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The probability that a student has a Visa card (event V) is .73. The probability that a student has a MasterCard (event M) is .1

snow_lady [41]

We assumed in this answer that the question b is, Are the events V and M independent?

Answer:

(a). The probability that a student has either a Visa card or a MasterCard is<em> </em> $\\ P(V \cup M) = 0.88$ . (b). The events V and M are not independent.

Step-by-step explanation:

The key factor to solve these questions is to know that:

$\\ P(V \cup M) = P(V) + P(M) - P(V \cap M)$

We already know from the question the following probabilities:

$\\ P(V) = 0.73$

$\\ P(M) = 0.18$

The probability that a student has both cards is 0.03. It means that the events V AND M occur at the same time. So

$\\ P(V \cap M) = 0.03$

The probability that a student has either a Visa card or a MasterCard

We can interpret this probability as $\\ P(V \cup M)$ or the sum of both events; that is, the probability that one event occurs OR the other.

Thus, having all this information, we can conclude that

$\\ P(V \cup M) = P(V) + P(M) - P(V \cap M)$

$\\ P(V \cup M) = 0.73 + 0.18 - 0.03$

$\\ P(V \cup M) = 0.88$

Then, <em>the probability that a student has either a Visa card </em><em>or</em><em> a MasterCard is </em> $\\ P(V \cup M) = 0.88$ .<em> </em>

Are the events V and M independent?

A way to solve this question is by using the concept of <em>conditional probabilities</em>.

In Probability, two events are <em>independent</em> when we conclude that

$\\ P(A|B) = P(A)$ [1]

The general formula for a <em>conditional probability</em> or the probability that event A given (or assuming) the event B is as follows:

$\\ P(A|B) = \frac{P(A \cap B)}{P(B)}$

If we use the previous formula to find conditional probabilities of event M given event V or vice-versa, we can conclude that

$\\ P(M|V) = \frac{P(M \cap V)}{P(V)}$

$\\ P(M|V) = \frac{0.03}{0.73}$

$\\ P(M|V) \approx 0.041$

If M were independent from V (according to [1]), we have

$\\ P(M|V) = P(M) = 0.18$

Which is different from we obtained previously;

That is,

$\\ P(M|V) \approx 0.041$

So, the events V and M are not independent.

We can conclude the same if we calculate the probability

$\\ P(V|M)$ , as follows:

$\\ P(V|M) = \frac{P(V \cap M)}{P(M)}$

$\\ P(V|M) = \frac{0.03}{0.18}$

$\\ P(V|M) = 0.1666.....\approx 0.17$

Which is different from

$\\ P(V|M) = P(V) = 0.73$

In the case that both events <em>were independent</em>.

Notice that

$\\ P(V|M)*P(M) = P(M|V)*P(V) = P(V \cap M) = P(M \cap V)$

$\\ \frac{0.03}{0.18}*0.18 = \frac{0.03}{0.73}*0.73 = 0.03 = 0.03$

$\\ 0.03 = 0.03 = 0.03 = 0.03$

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3 years ago

Find the slope of each line 8x-3y=9

Anna71 [15]

first isolate y so it is in slope intercept formula:

8x-3y=9

Subtract 8x from both sides

8x - 8x - 3y= 9 - 8x

-3y = 9 - 8x

Now divide both sides by -3 to isolate y

-3/-3y = 9/(-3) - 8x/(-3)

y = -3 + 8/3x

y = 8/3x - 3

Slope: 8/3

Hope it helps :)

branliest would be appreciated

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