All categories

3 years ago

Solve 11 2/5 = q - 4 2/7 + 2 1/7

1 answer:

6 0

I turn the mixed numbers into decimals before doing anything else.
11 2/5----> 57/5----> 11.4
4 2/7----> 30/7----> 4.29
2 1/7----> 15/7----> 2.14

11.4=q-4.29+2.14
11.4=q-2.15
13.55= q

13.55 converted to a fraction is 13 11⁄20
q=13 11⁄20

You might be interested in

Solve with interval notation Solve: 5 | x − 2 | + 4 > 8

Gnesinka [82]

Answer:

x<6/5, x>14/5

Step-by-step explanation:

Steps

$5\left|x-2\right|+4>8$

$\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}$

$5\left|x-2\right|+4-4>8-4$

$\mathrm{Simplify}$

$5\left|x-2\right|>4$

$\mathrm{Divide\:both\:sides\:by\:}5$

$\frac{5\left|x-2\right|}{5}>\frac{4}{5}$

$\mathrm{Simplify}$

$\left|x-2\right|>\frac{4}{5}$

$\mathrm{Apply\:absolute\:rule}:\quad\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad\mathrm{or}\quad\:u\:>\:a$

$x-2<-\frac{4}{5}\quad\mathrm{or}\quad\:x-2>\frac{4}{5}$

Show Steps

$x-2<-\frac{4}{5}\quad:\quad x<\frac{6}{5}$

Show Steps

$x-2>\frac{4}{5}\quad:\quad x>\frac{14}{5}$

$\mathrm{Combine\:the\:intervals}$

$x<\frac{6}{5}\quad\mathrm{or}\quad\:x>\frac{14}{5}$

5 0

3 years ago

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:

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.

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.

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

Mr. Walker, a runner, asked students to find the unit rate of the winner of the first Boston Marathon in 1897. John J. McDermott

EleoNora [17]

Answer: 8.4 miles per hour

Step-by-step explanation:

Since, total distance = 24.5 miles,

Time taken = $175 \text{ minutes} = \frac{175}{60} \text{ hours} =\frac{35}{12} \text{ hours}$