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2 years ago

PLZ HELP ASAP USE SIMMILAR AND CONGRUENT TRIANGLES

Mathematics

1 answer:

masya89 [10]2 years ago

4 0

Area of triangle DUO: A=?
Formula of the area of a triangle: A=(1/2)bh
Base of the triangle: b
Height of the triangle: h

In this case:
b=OD=OM+MD=4+10→b=14
h=MU=?

Since DR is perpendicular to OP:
Angle RDO = 90° = Angle RDP

Like angle RDU is congruent with angle RDA, the angle UDM must be congruent with angle ADP.

If angle UMO is 90°, the angle UMD is 90° too.

The triangles ADP and UDM have two congruent angles:
Angle UMD = 90° = Angle APD
Angle UDM = Angle ADP
Then the triangles UDM and ADP are similars, and theirs sides must be proportionals:
MU/MD=AP/DP
Replacing the known values:
MU/10=4.5/3.75
MU/10=1.2
Solving for MU. Multiplying both sides of the equation by 10:
10(MU/10)=10(1.2)
MU=12

A=(1/2)OD*MU
A=(1/2)(14)(12)
A=84

Answer: The area of triangle DUO is 84.00 square units.

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95% confidence interval for the mean number of months is between a lower limit of 6.67 months and an upper limit of 25.73 months.

Step-by-step explanation:

Confidence interval is given as mean +/- margin of error (E)

Data: 5, 15, 12, 22, 27

mean = (5+15+12+22+27)/5 = 81/5 = 16.2 months

sd = sqrt[((5-16.2)^2 + (15-16.2)^2 + (12-16.2)^2 + (22-16.2)^2 + (27-16.2)^2) ÷ 5] = sqrt(58.96) = 7.68 months

n = 5

degree of freedom = n-1 = 5-1 = 4

confidence level (C) = 95% = 0.95

significance level = 1 - C = 1 - 0.95 = 0.05 = 5%

critical value (t) corresponding to 4 degrees of freedom and 5% significance level is 2.776

E = t×sd/√n = 2.776×7.68/√5 = 9.53 months

Lower limit of mean = mean - E = 16.2 - 9.53 = 6.67 months

Upper limit of mean = mean + E = 16.2 + 9.53 = 25.73 months

95% confidence interval is (6.67, 25.73)

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