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3 years ago

Find m∠DEC (the picture is not drawn to scale).

Mathematics

1 answer:

pochemuha3 years ago

8 0

Answer:

M∠DEC equals 123º.

Step-by-step explanation:

The sum of a triangle's three angles always equal 180º. The exterior angle, x, equals the two non-adjacent interior angles.

180 - {(x - 45)+(x - 12)} = m∠DEC

m∠DEC + x = 180

(x - 45) + (x - 12) = x

Solving for x:

(x - 45) + (x - 12) = x

x - 45 + x - 12 = x Remove parenthesis

2x - 57 = x Combine like terms

2x = x + 57 Add 57 to both sides

x = 57 Subtract x from both sides

Finding m∠D:

x - 45 = ?

57 - 45 = 12º

Finding m∠C:

x - 12 = ?

57 - 12 = 45º

** (Checking x: 12 + 45 = 57) **

Finding m∠DEC:

AC is a straight line, and because straight lines are equivalent to 180º, we subtract 57 from 180:

180 - 57 = 123º

Hope this helps,

❤A.W.E.S.W.A.N.❤

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Multiply both sides of the equation by 6. {(4a + 1) = 2a ? (4a + 1) = ? a

solniwko [45]

Answer:

24a+6=12a

Step-by-step explanation:

6(4a+1)

24a+6

2a X 6= 12a

24a+6=12a

6 0

3 years ago

High-power experimental engines are being developed by the Stevens Motor Company for use in its new sports coupe. The engineers

Maurinko [17]

Answer:

The 99% of a confidence interval for the average maximum HP for the experimental engine.

(536.46, 603.54)

Step-by-step explanation:

Step:-1

Given that the mean of the Population = 540HP

Given that the size of the sample 'n' = 9

Given that the mean of the sample = 570HP

Given that the sample standard deviation = 30HP

Step(ii):-

Degrees of freedom = n-1 =9-1 =8

t₀.₀₀₅ = 3.3554

The 99% of a confidence interval for the average maximum HP for the experimental engine.

$(x^{-} - t_{\frac{0.01}{2} ,8} \frac{S.D}{\sqrt{n} } ,x^{2} + t_{\frac{0.01}{2},8 } \frac{S.D}{\sqrt{n} } )$

$(570-3.354\frac{30}{\sqrt{9} } , 570+3.354\frac{30}{\sqrt{9} } )$

(570 - 33.54 , 570+33.54)

(536.46 , 603.54)

Final answer :-

The 99% of a confidence interval for the average maximum HP for the experimental engine.

(536.46, 603.54)

4 0

3 years ago

Need help fast!! pleaseeeeeeeeeeeeeeeeeeeeeeee

bekas [8.4K]

What am I supposed to help with. You didn't put anything.

8 0

2 years ago

Can someone please help me with this question.

Ber [7]

Answer:

square root of 2

Step-by-step explanation:

Sides are 1 and 1 and the hypotenuse is the longest side (opposite the right angle)

We can use pythagerouses theorem : a^2+b^2=c^2

this means that 1^2+1^2=c^2

1+1=c^2

2=c^2

c=2/sqrt

c is the square root of 2

the hypotenuse is the square root of 2

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3 years ago

A certain genetic condition affects 8% of the population in a city of 10,000. Suppose there is a test for the condition that has

enot [183]

Solution:

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As genetic condition affects 8% of the population.

8 % of 10,000

$=\frac{8}{100}\times 10,000=800$

As, it is also given that, there is an error rate of 1% for condition (i.e., 1% false negatives and 1% false positives).

So, 1% false negatives means out of 800 tested who are found affected , means there are chances that 1% who was found affected are not affected at all.

So, 1% of 800 $=\frac{1}{100}\times 800=8$

Also, 1% false positives means out of 10,000 tested,[10,000-800= 9200] who are found not affected , means there are chances that 1% who was found not affected can be affected also.

So, 1% of 9200 $=\frac{1}{100}\times 9200=92$

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2. Test positive =92

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4. Total =800 +92 +8=900

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that is Probability equal to 0.01 or 1%.

7 0

3 years ago