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Aleks04 [339]
3 years ago
8

Sydney is playing a game on a map with a marked grid. To start, she places a game piece at (1, 4). She moves 3 units east and 2

units north and places a second game piece at (4, 6). She continues playing game pieces so that each piece is 3 units east and 2 units north in relation to the previous piece. What is the location of the third game piece she places?
Mathematics
1 answer:
Anastasy [175]3 years ago
6 0

Answer:

(7, 8)

Step-by-step explanation:

If Sidney places each piece 3 units east and 2 units north of the last one, we can figure out which coordinate comes first by subtracting the position of the second piece (S) by the position of the first piece (F):

S - F = (4,6) - (1,4) = (3,2)

We can conclude that coordinates are in the (East, North) format.

Therefore, the location of the third piece (T) is:

T = S(E,N) +(3,2)= (4,6)+(3,2)\\T = (7,8)

You might be interested in
V = u + at <br> u = 2 and a= -5 and t= 1/2<br> work out the value of v
Darina [25.2K]

Step-by-step explanation:

v=u+at

v=2+(-5)<u>1</u>

<u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u><u> </u>2

v=2-2.5

v=-0.5m/s²

hope it helps.

8 0
3 years ago
Read 2 more answers
"A manufacturer of automobile batteries claims that the average length of life for its grade A battery is 55 months. Suppose the
STALIN [3.7K]

Answer:

\\ P(z>-2) = 0.97725 or P(x>49) is about 97.725% (or being less precise 97.5% using the <em>empirical rule</em>).

Step-by-step explanation:

We solve this question using the following information:

  1. We are dealing here with <em>normally distributed data</em>, that is "<em>the frequency distribution of the life length data is known to be mound-shaped</em>".
  2. The normal distribution is defined by two parameters: the population mean (\\ \mu) and the population standard deviation (\\ \sigma). In this case, we have that \\ \mu = 55 months, and \\ \sigma = 3 months.
  3. To find the probabilities, we have to use the <em>standard normal distribution</em>, which has \\ \mu = 0 and \\ \sigma = 1. The probabilities for this distribution are collected in the <em>standard normal table</em>, available in Statistics books or on the Internet. We can also use statistics programs to find these probabilities.
  4. For most cases, we need to use the <em>cumulative standard normal table, </em>and for this we have to previously "transform" a raw score (x) into a z-score using the next formula: \\ z = \frac{x - \mu}{\sigma} [1]. A z-score tells us the distance from the mean that a raw score is from it in <em>standard deviations units</em>. If this value is <em>negative</em>, the raw score is <em>below</em> the mean. Conversely, a <em>positive</em> value indicates that it is <em>above</em> the mean.
  5. The <em>cumulative standard normal table </em>is made for positive values of z. Since the normal distribution is <em>symmetrical</em> around the mean, we can find the negative values of z using this formula: \\ P(z [2].

Having all this information, we can solve the question.

<h3>The percentage of the manufacturer's grade A batteries that will last more than 49 months</h3>

<em>First Step: Use formula [1] to find the z-score of the raw score x = 49 months</em>.

\\ z = \frac{49 - 55}{3}

\\ z = \frac{-6}{3}

\\ z = -2

This means that the raw score is represented by a z-score of \\ z = -2, which tells us that it is<em> two standard deviations below</em> the population mean.

<em>Second Step: Consult this value in the cumulative standard normal table for z = 2 and apply the formula [2] to find the corresponding probability.</em>

For a z = 2, the probability is 0.97725.  

Then

\\ P(z

\\ P(z2)

\\ P(z2)

But we <em>are not asked</em> for P(z<-2) but for P(z>-2) = P(x>49). This probability is the <em>complement</em> of the previous result, that is

\\ P(z>-2) = 1 - P(z

\\ P(z>-2) = 1 - 0.02275

\\ P(z>-2) = 0.97725

That is, the "<em>percentage of the manufacturer's grade A batteries will last more than 49 months</em>" is

\\ P(z>-2) = 0.97725 or about 97.725%

A graph below shows this result.

Notice that if we had used the <em>68-95-99.7 rule</em> (also known as the <em>empirical rule</em>), that is, in a normal distribution, the interval between <em>one standard deviation below and above the mean</em> contains, approximately, 68% of the observations; the interval between <em>two standard deviations below and above the mean</em> contains, approximately, 95% of the observations; and the interval between <em>three standard deviations</em> below and above the mean contains, approximately, 99.7% of the observations, we could have concluded that 2.5 % of the manufacturer's grade A batteries will last <em>less</em> than 49 months, and, as a result, 1 - 0.025 = 0.975 or 97.5% will last more than 49 months.

We can conclude that with a less precise answer (but faster) because of the <em>symmetry of the normal distribution</em>, that is, 1 - 0.95 = 0.05. At both extremes we have 0.05/2 = 0.025 or 2.5% and we were asked for P(x>49) = P(z>-2) (see the graph below).

6 0
3 years ago
Ms rodriguez planted 24 tulips in her flowerbed. of the tulips 1/3 are red how many tulips are red
xeze [42]


You would do 1/3 * 24

Which would give you 8

So 8 are red

4 0
3 years ago
Read 2 more answers
2. Hanna made 5 hit out of 13 during her first baseball game. What percentage of hits did she make?
MrRa [10]

Answer:

B. 38%

Explanation:

Given parameters:

Number of hits = 5hit

Total hits = 13

Unknown:

Percentage of hits shed made = ?

Solution;

The percentage of hit made = \frac{number of hits }{Total hits} x 100

input the parameters and solve;

        Percentage of hit made = \frac{5}{13} x 100

       Percentage of hit = 38%

Percentage of hit = 38%

4 0
3 years ago
I only need number 1 i don’t understand.
valentinak56 [21]

Answer:

12

Step-by-step explanation:

in this problem there is A+b=15

A=9

B=12

5 0
3 years ago
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