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raketka [301]
3 years ago
15

In the figure below, O is between M and P, and N is the midpoint of MO. IF NO=3 and MP = 10, find OP.

Mathematics
1 answer:
abruzzese [7]3 years ago
7 0

Answer:

OP = 4

Step-by-step explanation:

N is the midpoint of MO.

Since NO = 3, then MN = 3, and MO = 3 + 3 = 6

MO + OP = MP

6 + OP = 10

OP = 4

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Y is inversely proportional to x.
Inessa [10]

Answer:

1. xy = 63

2. y = 3

Step-by-step explanation:

Given

Variation: inverse Proportion

y = 7, x = 9

Required

- Write an equation connecting y and x

- Find y when x = 21

Given that thee variation is inversely proportional;

This implies that

y\ \alpha\ \frac{1}{x}

Convert variation to equation

y\ = \frac{k}{x} ----------- Equation 1

Where k is the constant of variation

Substitute 7 for y and 9 for x in equation 1

7 = \frac{k}{9}

Multiply both sides by 9

9 * 7 = 9 * \frac{k}{9}

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Substitute 63 for k in equation 1

y = \frac{63}{x}

Multiply both sides by x

x * y = \frac{63}{x} * x

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Hence, the equation connecting x and y is xy = 63

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4 0
3 years ago
What is the standard deviation of this data set? Use a calculator to help you.
ale4655 [162]

Answer:

Standard deviation = 14.064

Step-by-step explanation:

We are given the following data;

        X                          X - Xbar                  (X-Xbar)^{2}

       20                     20 - 46 = -26                    676

       23                     23 - 46 = - 23                    529

       32                     32 - 46 = -14                      196

       36                     36 - 46 = -10                      100

       41                      41 - 46 = -5                         25

       43                     43 - 46 = -3                          9

       44                     44 - 46 = -2                          4

       45                     45 - 46 = -1                           1

       47                      47 - 46 = 1                            1

       54                      54 - 46 = 8                        64

       55                      55 - 46 = 9                        81

      59                       59 - 46 = 13                      169

       61                       61 - 46 = 15                       225

       63                       63 - 46 = 17                      289

       66                       66 - 46 = 20                <u>     400    </u>    

                                                    \sum(X-Xbar)^{2} <u>= 2769 </u>

Firstly we will calculate Mean, Xbar = \frac{\sum X}{n}

  Xbar = \frac{20+ 23+ 32+ 36+ 41+ 43+ 44+ 45+ 47+ 54+ 55+ 59+ 61+ 63+ 66}{15} = 45.93 ≈ 46

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3 years ago
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