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Ganezh [65]
3 years ago
10

Find the distance between the points given. (2, 2) and (5, 5)

Mathematics
1 answer:
mario62 [17]3 years ago
7 0
Distance between two points, d, is given by
d= \sqrt{ ( x_{2} - x_{1}) ^{2} + (y_{2} - y_{1}) ^{2} }

where: (x1, y1) = (2, 2) and (x2, y2) = (5, 5)
d= 
\sqrt{ ( 5 - 2) ^{2} + (5 - 2) ^{2} } \\ d= \sqrt{ (3)^{2} + 3^{2} }  
\\ d= \sqrt{9+9}  \\ d= \sqrt{18}  \\ d=3\sqrt{2} \ units


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A normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97. What percentage of values lies between
lana [24]

Answer:

63% of the values lies between 70 and 85.

Step-by-step explanation:

We are given that a normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97.

<em>Let X = Set of numbers</em>

The z-score probability distribution for is given by;

                Z = \frac{  X -\mu}{\sigma}  ~ N(0,1)

where, \mu = mean value = 75

            \sigma = standard deviation = 7.97

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.

So, percentage of values that lies between 70 and 85 is given by = P(70 < X < 85) = P(X < 85) - P(X \leq 70)

   P(X < 85) = P( \frac{  X -\mu}{\sigma} < \frac{  85-75}{7.97} ) = P(Z < 1.25) = 0.89435  {using z table}

   P(X \leq 70) = P( \frac{  X -\mu}{\sigma} \leq \frac{  70-75}{7.97} ) = P(Z \leq -0.63) = 1 - P(Z < 0.63)

                                                 = 1 - 0.73565 = 0.26435

<em>Now, in the z table the P(Z </em>\leq<em> x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.25 and x = 0.63 in the z table which has an area of 0.89435 and 0.73565 respectively.</em>

Therefore, P(70 < X < 85) = 0.89435 - 0.26435 = 0.63 or 63%

<em>Hence, 63% of the values lies between 70 and 85.</em>

6 0
3 years ago
Half of the students in Max's class volunteer at the local community center.Fifteen students do not volunteer.If there are 12 bo
yulyashka [42]
18 girls
Half of the students volunteer
15 don't -- so the other half must be 15 as well making there 30 students in the class.
If 12 are boys, then 30(students in class) - 12 (boys) = 18 girls
7 0
3 years ago
Can somebody give me an answer to this it would be really helpful thanks!
kvv77 [185]

Answer:

.625 for decimal, and 62.5 percent.

Step-by-step explanation:

1/8 is 1.25 and that times 5 is .625. .625 * 100 = 62.5

Please give me brainliest

7 0
3 years ago
Read 2 more answers
What number must you add to complete the square?<br> X2+8x=-3<br> A. 8<br> B. 16<br> C. 4<br> D. 64
GREYUIT [131]

Answer:

I think it is 16

4 0
3 years ago
Read 2 more answers
Is the following number irrational or rational? Explain
sashaice [31]

Answer:

Rational

Step-by-step explanation:

It can be expressed as the ratio of two integers.

i.e. 0.01011011101111 = 1 011 011 101 111 / 100 000 000 000 000

6 0
2 years ago
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