14.07.2020

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06.06.2023, solved by verified expert

19) 24 units.
20) 24 cm
21) 14.7 cm

Step-by-step explanation:

19.

GIVEN: AA' = 15 units, BB' = 8 units and AB = 25 units.

To find: A'B'

Draw B'C = AB (ABB'C is a parallelogram)

Therefore, AC  = BB' = 8 units.

CA' = 15 - 8 = 7 units.

A'CB' is a right angle traingle with B'C hypotenuse.

Using the Pythagorean theorem, we can calculate the length of the common external tangent (the side opposite to the right angle):

B'C^2 = A'B'^2 + A'C^2

25^2 = A'B'^2 + 7^2

A'B'^2 = 625 - 49 = 576

A'B' = √576 = 24 units.

Thus, the length of the common tanget = 24 units

20.

GIVEN: AA' = 18 cm, BB' = 8 cm and AB = 18+8 = 26 cm.

To find: A'B'

Draw B'C = AB (ABB'C is a parallelogram)

Therefore, AC  = BB' = 8 cm.

CA' = 18 - 8 = 10 cm.

A'CB' is a right angle traingle with B'C hypotenuse.

Using the Pythagorean theorem, we can calculate the length of the common external tangent (the side opposite to the right angle):

B'C^2 = A'B'^2 + A'C^2

26^2 = A'B'^2 + 10^2

A'B'^2 = 676 - 100 = 576

A'B' = √576 = 24 cm

Thus, the length of the common tanget = 24 cm

21.

GIVEN: AA' = 9 cm, BB' =6 cm and AB = 9+6 = 15 cm.

To find: A'B'

Draw B'C = AB (ABB'C is a parallelogram)

Therefore, AC  = BB' = 6 cm.

CA' = 9 - 6 = 3 cm.

A'CB' is a right angle traingle with B'C hypotenuse.

Using the Pythagorean theorem, we can calculate the length of the common external tangent (the side opposite to the right angle):

B'C^2 = A'B'^2 + A'C^2

15^2 = A'B'^2 + 3^2

A'B'^2 = 225 - 9 = 216

A'B' = √216 = 14.696 cm = 14.7 cm

Thus, the length of the common tanget = 14.7 cm

### Faq

Mathematics

B. 4

Step-by-step explanation:

Interval: 19-21

Scores that are between 19 and 21 are underlined:

Scores in order: 20, 21, 21, 21, 23, 25, 26, 27, 27, 29

Mathematics

Table B is accurate

Step-by-step explanation:

Given

Observations: 21, 22, 20, 29, 25, 21, 21, 27, 26, 25

Required

An accurate frequency table

From both tables in the attachment; both tables use a grouped data to represent the grades.

The grouped data is as follows;

19-21

22-24

25 - 27

28-30

Breaking down these groups into bits:

19-21 :- 19, 20, 21

22-24 :- 22, 23, 24

25 - 27 :- 25, 26, 27

28-30:- 28, 29, 30

Looking up these values in the given data, we have

19-21 :- 21, 20, 21, 21

22-24 :- 22

25 - 27 :- 25, 27, 26, 25

28-30:- 29

Getting their frequencies

19-21 :- 4

22-24 :- 1

25 - 27 :- 4

28-30:- 1

Hence, the second table is accurate

Mathematics

B. 4

Step-by-step explanation:

Interval: 19-21

Scores that are between 19 and 21 are underlined:

Scores in order: 20, 21, 21, 21, 23, 25, 26, 27, 27, 29

Mathematics

Table B is accurate

Step-by-step explanation:

Given

Observations: 21, 22, 20, 29, 25, 21, 21, 27, 26, 25

Required

An accurate frequency table

From both tables in the attachment; both tables use a grouped data to represent the grades.

The grouped data is as follows;

19-21

22-24

25 - 27

28-30

Breaking down these groups into bits:

19-21 :- 19, 20, 21

22-24 :- 22, 23, 24

25 - 27 :- 25, 26, 27

28-30:- 28, 29, 30

Looking up these values in the given data, we have

19-21 :- 21, 20, 21, 21

22-24 :- 22

25 - 27 :- 25, 27, 26, 25

28-30:- 29

Getting their frequencies

19-21 :- 4

22-24 :- 1

25 - 27 :- 4

28-30:- 1

Hence, the second table is accurate

Mathematics

→ Step -1: Factor left side of equation:

→ Step 2: Set factors equal to 0:

______________________________________________________

→ Step -1: Add 13 to both sides:

→ Step 2: Take square root:

+

______________________________________________________

→ Step 1: Factor left side of equation:

→ Step 2: Set factors equal to 0:

Mathematics
19: .26 x 38 = 9.88 so answer is 38.
20: .38 x 26 = 9.88 so answer is 26.
21: apples: .26 x 19 = 4.94 so answer is 19
oranges: .38 x 13 = 4.94 so answer is 13
Mathematics

class        midpoint (m)                     frequency(f)           fm

11-13                 12                                           3                    36

13-15                 14                                          6                    84

15-17                 16                                          9                   144

17-19                  18                                          13                 234

19-21                  20                                          f                   20f

21-23                  22                                          5                 110

23 - 25                 24                                          4                96

∑f= 40 +f       ∑fm= 704+20f

now

mean = ∑fm ÷ ∑f

18= 704 + 20f

40+f

720 + 18f= 704 + 20f

16 = 2f

f = 8

For a moderately skewed distribution it is: If a frequency distribution has a symmetrical frequency curve, the mean, median and mode are equal

Mathematics

Question 19: x=9

Question 20: r<-6

Step-by-step explanation:

For question 19, the answer is nine because if you first add 5to both sides, it would be 18= 2r. If you divide both sides by 2, you would get 9=r.

For question 20, if you subtract 7 on each side, you would get -2r=12 if you divide -2 on each side, r would be -6.

Biology

Explanation:

let B- black fur, A- active behaviour and D-dark eyes

The male mouse is heterozygous for dominant traits of black fur and active behavior but is homozygous recessive for light eyes.

Thus the genotype will be: BbAadd

The female mouse is heterozygous for dark eyes, has white fur, and displays lazy behavior. thus the genotype wil be: bbaaDd

Mathematics

Class Interval             Variate         Frequency

16-18                              16                     1

19-21                               0                     0

22-24                               0                    0

25-27                              26,27              2

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