If y = kx, what is the value of k if y = 20 and x = 0.4? A) 5 B) 8 C) 9.6 D) 50

Mathematics

1 answer:

mariarad [96]2 years ago

7 0

Answer:

D) 50

20/0.4=50

Step-by-step explanation:

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A survey of teenagers found the music preferences listed. If you pick a teenager at random, what is P(rock)?

kherson [118]

We can see from this survey that 7 teenagers prefer rock and roll.
The number of all teenagers in the survey is:
12 + 5 + 7 + 6 + 6 + 4 = 40
P ( rock ) = 7 / 40
Answer: C ) 7 / 40

4 0

2 years ago

Suppose that 1 month before the election a random sample of 500 registered voters are surveyed. From this sample 270 indicate th

Aleonysh [2.5K]

Answer:

[ 0.4964, 0.5836 ]

Step-by-step explanation:

Data provided in the question:

Total sample size = 500

person voting for smith = 270

thus,

P( person voting for smith ), p = $\frac{270}{500}$ = 0.54

Confidence level = 95%

now,

standard error, SE = $\sqrt{\frac{p(1-p)}{n}$

SE = $\sqrt{\frac{0.54(1-0.54)}{500}$

SE = 0.0223

now,

Confidence interval = p ± ( z × SE )

here,

z value for 95% confidence interval is 1.96

Confidence interval = [ 0.54 - ( 1.96 × 0.0223 ), 0.54 + ( 1.96 × 0.0223 ) ]

= [ 0.54 - 0.0436 , 0.54 + 0.0436 ]

= [ 0.4964, 0.5836 ]

8 0

2 years ago

Type the correct answer for each.

xxTIMURxx [149]

If point $\left(x,\ \frac{\sqrt{7}}{3}\right)$ is on the unit ircle, then:

$x^2+\left( \frac{ \sqrt{7} }{3} \right)^2=1 \\ \\ \Rightarrow x^2+ \frac{7}{9} =1 \\ \\ \Rightarrow x^2=1- \frac{7}{9} = \frac{2}{9} \\ \\ \Rightarrow x= \sqrt{ \frac{2}{9} } = \frac{ \sqrt{2} }{3}$

Since, the point is in the second quadrant, x is negative.

Thus, $(x,\ y)=\left(x,\ \frac{\sqrt{7}}{3}\right)=\left(-\frac{ \sqrt{2} }{3},\ \frac{\sqrt{7}}{3}\right)$

Part A:

$3 \sqrt{7} =6\left( \frac{ \sqrt{7} }{2} \right) \\ \\ =6\left( \frac{ \sqrt{7} }{3} \cdot \frac{3}{ \sqrt{2} } \right) \\ \\ =6\left( \frac{ \frac{ \sqrt{7} }{3} }{ \frac{ \sqrt{2} }{3} } \right)=-6\left( \frac{ \frac{ \sqrt{7} }{3} }{ -\frac{ \sqrt{2} }{3} } \right) \\ \\ =-6\left( \frac{y}{x} \right)=-6\tan\theta$

Therefore, $-6\tan\theta=3\sqrt{7}$ .

Part B:

$- \frac{ \sqrt{7} }{2} =- \frac{ \sqrt{7} }{3} \cdot \frac{3}{ \sqrt{2} } \\ \\ =- \frac{ \frac{ \sqrt{7} }{3} }{ \frac{ \sqrt{2} }{3} } = \frac{ \frac{ \sqrt{7} }{3} }{ -\frac{ \sqrt{2} }{3} } = \frac{y}{x} \\ \\ =\tan\theta$

Therefore, $\tan\theta=- \frac{ \sqrt{7} }{2}$