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3 years ago

10

Mrs.fan wrote 5 tenths minus 3 hundredths on the board. Michael said the answer is 2 tenths because 5 minus 3 is 2. Is he correc

t? Explain.

1 answer:

yKpoI14uk [10]3 years ago

3 0

0.5 - 0.03 = 0.47
2 tenths= 0.2
5 tenths and 3 hundredths are not similar units so you can't simply subtract 5 and 3. The correct answer is 0.47.

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3. Decide whether each equation is true or false, and explain how you know.

BARSIC [14]

Answer:

a.false

b.true

c.false

d.I really can't get about it.

e.false

Step-by-step explanation:

So,here;

a.9.9.3=35 is given

or,243=35 (which is false)

b.7+7+7=3+3+3+3+3+3+3

or,21=21 (which is true)

c.2/3/2=2/3

or,2*2/3=2/3

or,4/3=2/3(which is false)

e.6+6+6=63

or,18=63 (which is false)

5 0

2 years ago

The scores on the GMAT entrance exam at an MBA program in the Central Valley of California are normally distributed with a mean

Kaylis [27]

Answer:

58.32% probability that a randomly selected application will report a GMAT score of less than 600

93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\mu = 591, \sigma = 42$

What is the probability that a randomly selected application will report a GMAT score of less than 600?

This is the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{600 - 591}{42}$

$Z = 0.21$

$Z = 0.21$ has a pvalue of 0.5832

58.32% probability that a randomly selected application will report a GMAT score of less than 600

What is the probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600?

Now we have $n = 50, s = \frac{42}{\sqrt{50}} = 5.94$

This is the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{600 - 591}{5.94}$

$Z = 1.515$

$Z = 1.515$ has a pvalue of 0.9351

93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

What is the probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600?

Now we have $n = 50, s = \frac{42}{\sqrt{100}} = 4.2$

$Z = \frac{X - \mu}{s}$

$Z = \frac{600 - 591}{4.2}$

$Z = 2.14$

$Z = 2.14$ has a pvalue of 0.9838

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

8 0

3 years ago

Find the sum and express it in simplest form <br> (6y-2c+2)+(-3y+4c)

Taya2010 [7]

Well, kid all you have to do is add like terms and place the subjected terms in alphabetical order.
1. (6y-2c+2)+(-3y+4c)
2. 6y + - 3y = 3y
3. -2c+4c =2c
4. the positive in the first set of parenthesis has to term other than its number by itself. (so it remains alone and only positive 2)
5. take all the separate term answers and add them into a complete expression- 3y + 2c + 2: and that is all

3 0

3 years ago

Eddi Din [679]

Answer:

a) $y=\dfrac{5}{2}x$

b) yes the two lines are perpendicular

c) $y=\dfrac{5}{4}x+6$

Step-by-step explanation:

a) All this is asking if to find a line that is perpendicular to 2x + 5y = 7 AND passes through the origin.

so first we'll find the gradient(or slope) of 2x + 5y = 7, this can be done by simply rearranging this equation to the form $y = mx + c$

$5y = 7 - 2x$

$y = \dfrac{7 - 2x}{5}$

$y = \dfrac{7}{5} - \dfrac{2}{5}x$

$y = -\dfrac{2}{5}x+\dfrac{7}{5}$

this is changed into the $y = mx + c$ , and we easily see that -2/5 is in the place of m, hence $m = \frac{-2}{5}$ is the slope of the line 2x + 5y = 7.

Now, we need to find the slope of its perpendicular. We'll use:

$m_1m_2=-1$ .

here both slopes $m_1$ and $m_2$ are slopes that are perpendicular to each other, so by plugging the value -2/5 we'll find its perpendicular!

$\dfrac{-2}{5}m_2=-1$ .

$m_2=\dfrac{5}{2}$ .

Finally, we can find the equation of the line of the perpendicular using:

$(y-y_1)=m(x-x_1)$

we know that the line passes through origin(0,0) and its slope is 5/2

$(y-0)=\dfrac{5}{2}(x-0)$

$y=\dfrac{5}{2}x$ is the equation of the the line!

b) For this we need to find the slopes of both lines and see whether their product equals -1?

mathematically, we need to see whether $m_1m_2=-1$ ?

the slopes can be easily found through rearranging both equations to $y=mx+c$

Line:1

$2x + 3y =6$

$y =\dfrac{-2x+6}{3}$

$y =\dfrac{-2}{3}x+2$

Line:2

$y = \dfrac{3}{2}x + 4$

this equation is already in the form we need.

the slopes of both equations are

$m_1 = \dfrac{-2}{3}$ and $m_2 = \dfrac{3}{2}$

using

$m_1m_2=-1$

$\dfrac{-2}{3} \times \dfrac{3}{2}=-1$

$-1=-1$

since the product does equal -1, the two lines are indeed perpendicular!

c)if two perpendicular lines have the same intercept, that also means that the two lines meet at that intercept.

we can easily find the slope of the given line, y = − 4 / 5 x + 6 to be $m=\dfrac{-4}{5}$ and the y-intercept is $c=6$ the coordinate at the y-intercept will be (0,6) since this point only lies in the y-axis.

we'll first find the slope of the perpendicular using:

$m_1m_2=-1$

$\dfrac{-4}{5}m_2=-1$

$m_2=\dfrac{5}{4}$

we have all the ingredients to find the equation of the line now. i.e (0,6) and m

$(y-y_1)=m(x-x_1)$

$(y-6)=\dfrac{5}{4}(x-0)$

$y=\dfrac{5}{4}x+6$

this is the equation of the second line.

side note:

this could also have been done by simply replacing the slope(m1) of the y = − 4 / 5 x + 6 by the slope of the perpendicular(m2): y = 5 / 4 x + 6

8 0

3 years ago

Write the inequality represented by the graph below.

Nikolay [14]

I believe this is an inequality because this doesn’t pass the origin point 0

Does not pass 0,0

If I’m wrong so sorry

4 0

2 years ago