an antique has a price of 269. the sales tax rate for the country is 8.8%.how much sales tax will be due

Your friend claims that it is possible to draw a right triangle where the cosine of either angle (theta) is exactly the same val

avanturin [10]

Answer:

B. No

$Cos \ \theta\neq Cos (90-\theta)\textdegree$

Step-by-step explanation:

-A right angle triangle has two complimentary acute angles and one right angle.

- $\theta$ is usually one of the acute angles and is equivalent to 90º minus it's complimentary acute angle.

-Complimentary angles add up to 90º.

#For complimentary angles:

$Sin \ \theta=Cos \ (90-\theta)\textdegree\\\\Cos \ \theta=Sin(90-\theta)\textdegree\\\\\therefore Cos \ \theta\neq Cos (90-\theta)\textdegree$

The two acute angles cannot have the same Cosine value.

Hence, she's not correct.

5 0

3 years ago

Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 13. Use the empirical rule

Yuri [45]

Answer:

(a) 68% of people has an IQ score between 87 and 113.

(b) 5% of people has an IQ score less than 74 or greater than 126.

(c) 0.15% of people has an IQ score greater than 139.

Step-by-step explanation:

Given information:Scores of an IQ test have a bell-shaped distribution,

mean = 100

standard deviation = 13

According to the empirical rule

68% data lies between $\overline{x}-\sigma$ and $\overline{x}+\sigma$ .

95% data lies between $\overline{x}-2\sigma$ and $\overline{x}+2\sigma$ .

99.7% data lies between $\overline{x}-3\sigma$ and $\overline{x}+3\sigma$ .

(a)

$\overline{x}-\sigma=100-13=87$

$\overline{x}+\sigma=100+13=113$

$[\overline{x}-\sigma,\overline{x}+\sigma]=[87,113]$

Using empirical rule we can say that 68% of people has an IQ score between 87 and 113.

(b)

$\overline{x}-2\sigma=100-2(13)=74$

$\overline{x}+2\sigma=100+2(13)=126$

$[\overline{x}-2\sigma,\overline{x}+2\sigma]=[74,126]$

Using empirical rule we can say that 95% of people has an IQ score between 74 and 126.

The percentage of people has an IQ score less than 74 or greater than 126 is

P = 1- percent of people has an IQ score between 74 and 126.

P = 1- 95%

P = 5%

Therefore 5% of people has an IQ score less than 74 or greater than 126.

(c)

$\overline{x}-3\sigma=100-3(13)=61$

$\overline{x}+3\sigma=100+3(13)=139$

$[\overline{x}-3\sigma,\overline{x}+3\sigma]=[61,139]$

Using empirical rule we can say that 99.7% of people has an IQ score between 61 and 139.

The percentage of people has an IQ score less than 61 or greater than 139 is

P = 1- percent of people has an IQ score between 61 and 139.

P = 1- 99.7%

P = 0.3%

The percentage of people has an IQ score greater than 139 is

$P=\frac{1}{2}(0.3\%)=0.15\%$

Therefore 0.15% of people has an IQ score greater than 139.

5 0

3 years ago

Please help giving brainless to the first person to help me. Thank you

kotykmax [81]

Answer:

Step-by-step explanation:

To find the population density of any state:

We must divide the population number by the area

Thus Washington state's population density equals 7,705,281 / 71297.95

Which equals 108.1

Hope that helps!

4 0

2 years ago

Read 2 more answers

Segments DF, DH, and GF are tangent to the circle. Andrew was asked to find DF. Explain andrew's error.

ANEK [815]

Answer:

DF = 14

Step-by-step explanation:

Andrew was wrong in the assumption that DE = EF

Segments of tangents to a circle from the same external point are congruent

That is

EF = FG = 8

Then

DF = DE + EF = 6 + 8 = 14

5 0

3 years ago

Which smallest number must be assigned to # to make the number 378#96 divisible by 8?

skelet666 [1.2K]

Answer:

2

Step-by-step explanation:

378296/8=47287

5 0

3 years ago