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vlada-n [284]
3 years ago
13

Twice the difference of a number and seven is equal to three times the sum of the number and seven

Mathematics
1 answer:
Nana76 [90]3 years ago
5 0
2(n-7) = 3(n+7)
2n-14 = 3n + 21
   -35  = n  (answer)
You might be interested in
In a chess tournament, each player plays every other player exactly once. If it is known that 105 games were played, how many pl
diamong [38]

Answer:

15 players played in the chess tournament.

Step-by-step explanation:

When there are 15 players, the first player plays 14 games and step aside.

remaining 14 player

next player plays 13 games. steps aside

remaining 13 players

next player plays 12 games. steps aside

remaining 12 players

next player plays 11 games. steps aside

remaining 11 players

.

.

.

.

Last player plays 1 game and steps aside

remaining 1 player who will not play against himself.

∴ Sum of all games played

= 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105 games played

3 0
3 years ago
Number like 10 10 1000 and so on are called
DochEvi [55]
These number r called patterns
7 0
3 years ago
An equilateral triangle has three congruent sides. If sides are congruent, the opposite angles are congruent.
VladimirAG [237]

Answer:

B)law of detachment

Step-by-step explanation:

5u56i566i56

4 0
2 years ago
The volume of the triangular prism is 12.5 m³. The length is 2.5 m and the base is 2 m. What is the width?
Fantom [35]

Answer:

  (4)  5 m

Step-by-step explanation:

You want the length of side x of a right triangular prism with base edge lengths of 2.5 m and 2 m, and a volume of 12.5 m³.

<h3>Volume</h3>

The volume of the prism is given by the formula ...

  V = Bh

where B is the area of the base:

  B = 1/2bh . . . . where b and h are the leg dimensions of the right triangle

Using these formulas together, we have ...

  V = 1/2(2.5 m)(2 m)x

  12.5 m³ = 2.5x m²

Dividing by 2.5 m², we find x to be ...

  (12.5 m³)/(2.5 m²) = x = 5 m

The dimension labeled x has length 5 meters.

6 0
11 months ago
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of
jarptica [38.1K]

Answer:

The "probability that a given score is less than negative 0.84" is  \\ P(z.

Step-by-step explanation:

From the question, we have:

  • The random variable is <em>normally distributed</em> according to a <em>standard normal distribution</em>, that is, a normal distribution with \\ \mu = 0 and \\ \sigma = 1.
  • We are provided with a <em>z-score</em> of -0.84 or \\ z = -0.84.

Preliminaries

A z-score is a standardized value, i.e., one that we can obtain using the next formula:

\\ z = \frac{x - \mu}{\sigma} [1]

Where

  • <em>x</em> is the <em>raw value</em> coming from a normal distribution that we want to standardize.
  • And we already know that \\ \mu and \\ \sigma are the mean and the standard deviation, respectively, of the <em>normal distribution</em>.

A <em>z-score</em> represents the <em>distance</em> from \\ \mu in <em>standard deviations</em> units. When the value for z is <em>negative</em>, it "tells us" that the raw score is <em>below</em> \\ \mu. Conversely, when the z-score is <em>positive</em>, the standardized raw score, <em>x</em>, is <em>above</em> the mean, \\ \mu.

Solving the question

We already know that \\ z = -0.84 or that the standardized value for a raw score, <em>x</em>, is <em>below</em> \\ \mu in <em>0.84 standard deviations</em>.

The values for probabilities of the <em>standard normal distribution</em> are tabulated in the <em>standard normal table, </em>which is available in Statistics books or on the Internet and is generally in <em>cumulative probabilities</em> from <em>negative infinity</em>, - \\ \infty, to the z-score of interest.

Well, to solve the question, we need to consult the <em>standard normal table </em>for \\ z = -0.84. For this:

  • Find the <em>cumulative standard normal table.</em>
  • In the first column of the table, use -0.8 as an entry.
  • Then, using the first row of the table, find -0.04 (which determines the second decimal place for the z-score.)
  • The intersection of these two numbers "gives us" the cumulative probability for z or \\ P(z.

Therefore, we obtain \\ P(z for this z-score, or a slightly more than 20% (20.045%) for the "probability that a given score is less than negative 0.84".

This represent the area under the <em>standard normal distribution</em>, \\ N(0,1), at the <em>left</em> of <em>z = -0.84</em>.

To "draw a sketch of the region", we need to draw a normal distribution <em>(symmetrical bell-shaped distribution)</em>, with mean that equals 0 at the middle of the distribution, \\ \mu = 0, and a standard deviation that equals 1, \\ \sigma = 1.

Then, divide the abscissas axis (horizontal axis) into <em>equal parts</em> of <em>one standard deviation</em> from the mean to the left (negative z-scores), and from the mean to the right (positive z-scores).  

Find the place where z = -0.84 (i.e, below the mean and near to negative one standard deviation, \\ -\sigma, from it). All the area to the left of this value must be shaded because it represents \\ P(z and that is it.

The below graph shows the shaded area (in blue) for \\ P(z for \\ N(0,1).

7 0
3 years ago
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