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3 years ago

Find the distance between points P(5,8) and Q(1,7) to the nearest tenth

Mathematics

1 answer:

morpeh [17]3 years ago

3 0

Answer:

$length = \sqrt{ {(x _{1} - x_{2} )}^{2} + {(y _{1} - y_{2} })^{2} } \\ = \sqrt{ {(5 - 1)}^{2} + {(8 - 7)}^{2} } \\ = \sqrt{16 + 1 } \\ = \sqrt{17} \\ length = 4.1 \: units$

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1.44 Make-up exam: In a class of 28 students, 27 of them took an exam in class and 1 student took a make-up exam the following d

Olenka [21]

Answer:

a) Decrease

b) New mean = 78.43

c) Decrease

Step-by-step explanation:

We are given the following in the question:

Total number of students in class = 28

Average of 27 students = 79

Standard Deviation of 27 students = 6.5

New student's score = 63

a) The new student's score will decrease the average.

b) New mean

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean = \dfrac{\displaystyle\sum x_i}{27} = 79\\\\\sum x_i = 27\times 79 = 2133$

New mean =

$\text{ New mean} =\dfrac{ \displaystyle\sum x_i +63}{28}\\\\ =\dfrac{2133+63}{28}= \dfrac{2196}{28} = 78.43$

Thus, the new mean is 78.43

c) Since the new mean decreases, standard deviation for new scores will decrease.

This is because the new value is within the usual values i.e. within two standard deviations of the mean. So, this wont cause a lot of variation as this value will be closer to already available data values. Also number of observations (n) in the denominator is increasing. Based on both these points we can conclude that standard deviation will decrease

Formula for Standard Deviation:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}$

where $x_i$ are data points, $\bar{x}$ is the mean and n is the number of observations.

7 0

3 years ago

Which number line best shows how to solve −4 − (−6)?

lozanna [386]

Answer:

the answer is A

Step-by-step explanation:

because two negatives turn to a positive

3 0

3 years ago

Help me please. I don't understand this.

navik [9.2K]

9514 1404 393

Answer:

see attached

Step-by-step explanation:

Apparently, you're being asked to identify the sequence of steps you would use to compute the volume of the pyramid.

It seems to be a good idea to start with the formula for the volume.

Then, recognize that you need to compute B, so make that computation. The area of the base (B) is the product of the base dimensions (14)(12).

Once you have the value of B, then you can put that, along with the value of h, into the original volume formula.

Evaluating it gives the volume in cubic units.

_____

<em>Additional comment</em>

If you're familiar with the pyramid volume formula, you know that you must compute B before you can make use of the formula. That makes the sequence be B=14(12); B=168; V=1/3Bh; V=1/3(168)(7).

However, if you're starting from scratch, it is probably good to begin with the volume formula. That is what tells you that you need to find B in the first place. This is the sequence we show below.