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sattari [20]
3 years ago
12

Angle ABD and Angle CBD are supplementary angles and Angle CBD and Angle DBE are complementary. If the measure of angle ABD is 1

44 degrees what is the measure of angle DBE
Mathematics
1 answer:
gizmo_the_mogwai [7]3 years ago
3 0

Answer:

54°

Step-by-step explanation:

ABD = 144°

ABD + CBD = 180°......(i)

CBD + DBE = 90°........(ii)

From (i)

144° + CBD = 180°

CBD = 180° - 144°

= 36°

From (ii)

CBD + DBE = 90°

36° + DBE = 90°

DBE = 90 - 36

= 54°

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The lifespan of a lion in a particular zoo are normally distributed. The average lion lives 12.5 years the. Standard deviation i
Anika [276]

Answer:

0.1585

Step-by-step explanation:

Solution:-

The lifespan of a lion in a particular zoo is normally distributed with average lion lives:

                    Mean u = 12.5 years

                    Standard deviation s = 2.4 years

We are to use the empirical rule ( 68-95-99.7% ) to estimate the probability of a lion living between 5.3 and 10.1.

- The empirical rule ( 68-95-99.7% ) states:

                     P ( u - s < X < u + s ) = 68%

                     P ( u - 2s < X < u + 2s ) = 95%

                     P ( u - 3s < X < u + 3s ) = 99.7%

- The test have the following number of standard deviations (s):

                 

                    u - s < X < u + s  = 12.5 - 2.4 < X < 12.5 + 2.4  = 10.1 < X < 14.9

                    u - 2s < X < u + 2s = 12.5 - 4.8 < X < 12.5 + 4.8  = 7.7 < X < 17.3

                    u - 3s < X < u + 3s = 12.5 - 7.2 < X < 12.5 + 7.2  = 5.3 < X < 19.7

Hence,

                   P ( 10.1 < X < 14.9 ) = 0.68

                   P ( 7.7 < X < 17.3 ) = 0.95

                   P ( 5.3 < X < 19.7 ) = 0.997

-  We need P ( X < 10.1 ) and P ( X < 5.3 ):

                  P ( X < 10.1 ) = [ 1 - P ( 10.1 < X < 14.9 ) ] / 2

                                      = [ 1 - 0.68 ] / 2

                                      = 0.16

                  P ( X < 5.3 ) = [ 1 - P ( 5.3 < X < 19.7 ) ] / 2

                                      = [ 1 - 0.997 ] / 2

                                      = 0.0015

Hence,

                 P ( 5.3 < X < 10.1 ) = P ( X < 10.1 ) - P ( X < 5.3 )

                                               = 0.16 - 0.0015

                                               = 0.1585

5 0
3 years ago
The perimeter of a rectangle is 50 inches the length of the rectangle is 17 inches He cuts out another rectangle that is the sam
Brums [2.3K]

Step-by-step explanation:

A rectangle: P=2l+2w or P=2(l+w) (same formula written differently)

50=2x17+2w

50=34+2w

2w=50-34

2w=16

w=16÷2=8

Since it says twice as wide then we will multiply w with 2

2xW

2x8=16 which is the width of the 2nd rectangle

Hope this helps :)

6 0
2 years ago
How is 60 divided by 9 = 6.66666667?
saveliy_v [14]
60/9=6 remainder 4
Some division problems that require decimals
can be repeated 
To simplify 6.6666667 also means 6.666666666...and so on
To simplify 6.6666...
u put a bar over the 6 in the tens place.


7 0
3 years ago
The equation of the line that passes through and how did you solve it?
luda_lava [24]

Answer:

3

Step-by-step explanation:

to find the slope you do the formula

y2-y1 divided by x2-x1. (keep it in fraction form). it doesnt really matter what order you put the points as but keep it consistent

8 0
2 years ago
Read 2 more answers
The biggest among three numbers is 2.4 larger than the smallest one. If 15 times the smallest one is equal to 12 times the secon
g100num [7]

Answer:

18

Step-by-step explanation:

Let x represent smallest number and y represent second number.

We have been given that the biggest among three numbers is 2.4 larger than the smallest one. So biggest number would be x+2.4.

We are also told that 15 times the smallest one is equal to 12 times the second and 10 times the third. We can represent this information in equations as:

15x=12y...(1)

15x=10(x+2.4)...(2)

Upon solving 2nd equation, we will get:

15x=10x+24

15x-10x=10x-10x+24

5x=24

x=\frac{24}{5}

x=4.8

Therefore, the smallest number is 4.8.

The biggest number would be x+2.4\Rightarrow 4.8+2.4=7.2.

Upon substituting x=4.8 in equation (1), we will get:

15(4.8)=12y

72=12y

y=\frac{72}{12}

y=6

Therefore, 2nd number would be 6.

Let us find sum of all numbers as:

4.8+6+7.2=18

Therefore, the sum of all 3 numbers would be 18.

5 0
2 years ago
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