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g100num [7]
3 years ago
5

K is between P and Q. Suppose PQ- 10x - 16, PK - 6x + 8, and KQ-8. What is PQ?

Mathematics
1 answer:
Alex17521 [72]3 years ago
8 0

Answer:

PQ = 64

Step-by-step explanation:

PQ = PK + KQ

10x - 16 = 6x + 8 + 8

10x - 16 = 6x + 16

4x = 32

x = 8

PQ = 10(8) - 16

     = 80 - 16

     = 64

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Are the marks one receives in a course related to the amount of time spent studying the subject? To analyze this mysterious poss
sertanlavr [38]

Answer:

a) 98.522

b) 0.881

c) The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time.

Step-by-step explanation:

a.

As the mentioned in the given instruction the co-variance is first computed in excel by using only add/Sum, subtract, multiply, divide functions.

Marks y Time spent x y-ybar x-xbar (y-ybar)(x-xbar)

77                    40 5.1         1.3 6.63

63                     42 -8.9            3.3 -29.37

79                     37 7.1            -1.7 -12.07

86                     47 14.1            8.3 117.03

51                    25 -20.9  -13.7 286.33

78                     44 6.1            5.3 32.33

83                      41 11.1            2.3 25.53

90                     48 18.1            9.3 168.33

65                     35 -6.9           -3.7 25.53

47                    28 -24.9 -10.7 266.43

Covariance=\frac{sum[(y-ybar)(x-xbar)]}{n-1}

Co-variance=886.7/(10-1)

Co-variance=886.7/9

Co-variance=98.5222

The co-variance computed using excel function COVARIANCE.S(B1:B11,A1:A11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted co-variance is 98.52222.

b)

The correlation coefficient is computed as

Correlation coefficient=r=\frac{sum[(y-ybar)(x-xbar)]}{\sqrt{sum[(x-xbar)]^2sum[(y-ybar)]^2} }

(y-ybar)^2 (x-xbar)^2

26.01        1.69

79.21       10.89

50.41             2.89

198.81       68.89

436.81       187.69

37.21       28.09

123.21        5.29

327.61        86.49

47.61         13.69

620.01         114.49

sum(y-ybar)^2=1946.9

sum(x-xbar)^2=520.1

Correlation coefficient=r=\frac{886.7}{\sqrt{520.1(1946.9)} }

Correlation coefficient=r=\frac{886.7}{\sqrt{1012582.69} }

Correlation coefficient=r=\frac{886.7}{1006.2717 }

Correlation coefficient=r=0.881

The correlation coefficient computed using excel function CORREL(A1:A11,B1:B11) where B1:B11 contains Time x column and A1:A11 contains Marks y column. The resulted correlation coefficient is 0.881.

c)

The correlation coefficient and co-variance shows that there is positive association between marks and study time. The correlation coefficient suggest that there is strong positive association between marks and study time. It means that as the study time increases the marks of student also increases and if the study time decreases the marks of student also decreases.

The excel file is attached on which all the related work is done.

Download xlsx
7 0
3 years ago
A customer tells you that they will call at 3PM Eastern Standard Time. If you are located in the Pacific Standard Time Zone (whi
posledela
You should expect the call at 12:00pm
8 0
3 years ago
Read 2 more answers
144 flowers in a vase the ratio of yellow to pink flowers is 5 to 6 how many yellow flowers are in the vase
azamat

\frac{5}{11}  \times 144 \: is \: the \: amount \: of \: yellow \: flowers \\  \\  \frac{5}{11}  \times 144 = 65.45 = 65
therfore there is 65 yellow flowers
4 0
3 years ago
What is the asymptote for the graph of this logarithmic function?<br><br> f(x) = log3(x – 1)
Pepsi [2]

Answer:

Vertical Asymptote:

x=1

Horizontal asymptote:

it does not exist

Step-by-step explanation:

we are given

f(x)=log_3(x-1)

Vertical asymptote:

we know that vertical asymptotes are values of x where f(x) becomes +inf or -inf

we know that any log becomes -inf when value inside log is zero

so, we can set value inside log to zero

and then we can solve for x

x-1=0

we get

x=1

Horizontal asymptote:

we know that

horizontal asymptote is a value of y when x is +inf or -inf

For finding horizontal asymptote , we find lim x-->inf or -inf

\lim_{x \to \infty}  f(x)= \lim_{x \to \infty}log_3(x-1)

\lim_{x \to \infty}  f(x)=log_3(\infty-1)

\lim_{x \to \infty}  f(x)=undefined

so, it does not exist

7 0
3 years ago
Read 2 more answers
1. Bob tried to answer the following question by finding the missing angle and rounding the answer to the nearest degree.
iren2701 [21]

Answer:

Part 1)

Bob's mistake was to have used the cosine instead of the sine

The measure of the missing angle is 53.13\°

Part 2) The surface area of the pyramid is 288\ cm^{2}

Step-by-step explanation:

Part 1)

Let

x----> the missing angle

we know that

In the right triangle o the figure

The sine of angle x is equal to divide the opposite side angle x to the hypotenuse of the right triangle

sin(x)=\frac{16}{20}

x=arcsin(\frac{16}{20})=53.13\°

Bob's mistake was to have used the cosine instead of the sine

Part 2) we know that

The surface area of the square pyramid is equal to the area of the square base plus the area of its four lateral triangular faces

so

SA=b^{2}+4[\frac{1}{2}(b)(h)]

where

b is the length side of the square

h is the height of the triangular lateral face

In this problem

h=b/2 -------> by an 45° angle

so

b=2h

sin(45\°)=\frac{h}{6\sqrt{2}}

h=6\sqrt{2}(sin(45\°))=6\ cm

Find the value of b

b=2(6)=12\ cm

Find the surface area

SA=12^{2}+4[\frac{1}{2}(12)(6)]=288\ cm^{2}

3 0
3 years ago
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