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Andreyy89
3 years ago
8

One angle is twice its supplement increased by 54 degrees. Find the measures of the two supplementary angles.

Mathematics
1 answer:
AnnyKZ [126]3 years ago
6 0

Answer: The two angles are 24 degrees and 156 degrees

======================================================

Explanation:

Let x and y be the two supplementary angles

"one angle is twice its supplement increased by 54 degrees"

means that

y = 2(x+54)

Whatever angle x is, we add on 54, then double it to get angle y.

x+y = 180 since they are supplementary angles

x+2(x+54) = 180 plug in y = 2(x+54)

x+2x+108 = 180

3x = 180-108

3x = 72

x = 72/3

x = 24

y = 2(x+54)

y = 2(24+54)

y = 156

as a check

x+y = 24+156 = 180

so x and y are confirmed to be supplementary angles.

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Can some one please help me !!
irina1246 [14]
Should be 55 I believe
3 0
3 years ago
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A survey of 700 adults from a certain region​ asked, "What do you buy from your mobile​ device?" The results indicated that 59​%
Kryger [21]

Answer:

a) the test statistic z = 1.891

the null hypothesis accepted at 95% level of significance

b) the critical values of 95% level of significance is zα =1.96

c) 95% of confidence intervals are  (0.523 ,0.596)

Step-by-step explanation:

A survey of 700 adults from a certain region

Given sample sizes n_{1} = 400 and n_{2} = 300

Proportion of mean p_{1} = \frac{236}{400} = 0.59 and p_{2} = \frac{156}{300} = 0.52

<u>Null hypothesis H0</u> : assume that there is no significant difference between males and women reported they buy clothing from their mobile device

p1 = p2

<u>Alternative hypothesis H1:</u>- p1 ≠ p2

a) The test statistic is

Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} }+\frac{1}{n_{2} )}  } }

where p = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1}+n_{2}}= \frac{400X0.59+300X0.52}{700}  

on calculation we get   p = 0.56    

now q =1-p = 1-0.56=0.44

Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} }+\frac{1}{n_{2} )}  } }\\   =\frac{0.56-0.52}{\sqrt{0.56X0.44}(\frac{1}{400}+\frac{1}{300}   }

after calculation we get z = 1.891

b) The critical value at 95% confidence interval zα = 1.96 (from z-table)

The calculated z- value < the tabulated value

therefore the null hypothesis accepted

<u>conclusion</u>:-

assume that there is no significant difference between males and women reported they buy clothing from their mobile device

p1 = p2

c) <u>95% confidence intervals</u>

The confidence intervals are P± 1.96(√PQ/n)

we know that = p = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1}+n_{2}}= \frac{400X0.59+300X0.52}{700}

after calculation we get P = 0.56 and Q =1-P =0.44

Confidence intervals are ( P- 1.96(√PQ/n), P+ 1.96(√PQ/n))

now substitute values , we get

( 0.56- 1.96(√0.56X0.44/700), 0.56+ 1.96(0.56X0.44/700))

on simplification we get (0.523 ,0.596)

Therefore the population proportion (0.56) lies in between the 95% of <u>confidence intervals  (0.523 ,0.596)</u>

<u></u>

3 0
3 years ago
The sum of two numbers is 33.the larger number is 3 more than two times the smaller number.what are the numbers?
e-lub [12.9K]

Answer: The numbers are 10 and 23

Step-by-step explanation:

Let the smaller number be x

And the larger number be y

Ist sentence;

1. The sum of two numbers is 33.

X + y= 33 .........eqn 1

2. second sentence

the larger number is 3 more than two times the smaller number.

Y = 3 +2x

Put y into eqn 1

X+ 3 +2x = 33

3x= 33- 3

3x= 30

X = 30/3

X= 10 and y= 3+ 2x

Y= 3+ 2(10)

Y = 3+ 20

Y= 23

Therefore the two numbers are 10 and 23

8 0
3 years ago
PRE ALGEBRA / PLEASE HELP!!||| How many kilometers is it from the main gate to the Manatee Springs? (Hint: to convert from yards
mars1129 [50]

Answer:

  • 6.04 km (per angle marks)
  • 5.36 km (per side hash marks)

Step-by-step explanation:

Going by the angle indicators, the ratios of corresponding sides of the similar triangles are ...

  x/2000 = 4200/3500

  x = 2000·6/5 = 2400 . . . . yards

Then the distance of interest is ...

  (2400 yd + 4200 yd)×(0.0009144 km/yd) = 6.6×.9144 km

  = 6.03504 km ≈ 6.04 km

_____

Going by the red hash marks, the ratios of corresponding sides of the similar triangles are ...

  x/2000 = 3500/4200

  x = 2000·(5/6) = 5000/3 . . . . yards

Then the distance of interest is ...

  (5000/3 + 4200) yd × 0.0009144 km/yd ≈ 5.36 km

_____

<em>Comment on the figure</em>

The usual geometry here is that the outside legs (opposite the vertical angles) are parallel, meaning that the angle indicators are the correct marks. It is possible, but unusual, for the red hash marks to be correct and the angle indicators to be mismarked. The red hash marks seem tentatively drawn, so seem like they're more likely to be the incorrect marks.

7 0
3 years ago
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Find the measure of VYX.
loris [4]

Step-by-step explanation:

follow the above attachment, hope this helps you.

4 0
2 years ago
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