Help plz i kind of get it but i want clarification

As discussed in Exercise 6.10, the General Social Survey reported a sample where about 61% of US residents thought marijuana sho

Maslowich

Answer: 2285

Step-by-step explanation:

Formula to find the sample size is given by :-

$n=p(1-p)(\dfrac{z_c}{E})^2$

, where p = prior estimate of population proportion.

E= Margin of error.

$z_c$ = z-value for confidence interval of c.

Given : Confidence interval : 95%

From the z-value table , the z-value for 95% confidence interval = $z_c=1.96$

The General Social Survey reported a sample where about 61% of US residents thought marijuana should be made legal.

i.e. the prior estimate of population proportion of US residents thought marijuana should be made legal : p=0.61

[∵ sample proportion is the best estimate for population proportion.]

Margin of error : E= 2%=0.02

Now, the required minimum sample size would be :-

$n=0.61(1-0.61)(\dfrac{1.96}{0.02})^2$

Simplify ,

$n=0.2379\times9604=2284.7916\approx2285$

Thus , we need to survey 2285 Americans .

4 0

3 years ago

4) The path of a satellite orbiting the earth causes it to pass directly over two

Naily [24]

Answers:

Satellite is approximately 2446.43 km from station A.
Satellite is approximately 2441.61 km above the ground.

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

Explanation:

I'm assuming tracking stations A and B are at the same elevation and are on flat ground. In reality, this is likely not the case; however, for the sake of simplicity, we'll assume this is the case.

The diagram is shown below. Points A and B describe the two stations, while point C is the satellite's location. Point D is on the ground directly below the satellite. We have these lengths

AB = 60 km
AD = x
CD = h

Focusing on triangle ACD, we can apply the tangent rule to isolate h.

tan(angle) = opposite/adjacent

tan(A) = CD/AD

tan(86.4) = h/x

x*tan(86.4) = h

h = x*tan(86.4)

We'll use this later in the substitution below.

--------------------

Now move onto triangle BCD. For the reference angle B = 85, we can use the tangent rule to say

tan(angle) = opposite/adjacent

tan(B) = CD/DB

tan(B) = CD/(DA+AB)

tan(85) = h/(x+60)

tan(85)*(x+60) = h

tan(85)*(x+60) = x*tan(86.4) ............. apply substitution; isolate x

x*tan(85)+60*tan(85) = x*tan(86.4)

60*tan(85) = x*tan(86.4)-x*tan(85)

60*tan(85) = x*(tan(86.4)-tan(85))

x*(tan(86.4)-tan(85)) = 60*tan(85)

x = 60*tan(85)/(tan(86.4)-tan(85))

x = 153.612786190499

--------------------

We'll use this approximate x value to find h

h = x*tan(86.4)

h = 153.612786190499*tan(86.4)

h = 2441.60531869599

h = 2441.61 km is how high the satellite is above the ground.

Return to triangle ACD. We'll use the cosine rule to determine the length of the hypotenuse AC

cos(angle) = adjacent/hypotenuse

cos(A) = AD/AC

cos(86.4) = x/AC

cos(86.4) = 153.612786190499/AC

AC*cos(86.4) = 153.612786190499

AC = 153.612786190499/cos(86.4)

AC = 2446.43279498247

AC = 2446.43 km is the distance from the satellite to station A.

6 0

3 years ago

2,5, 25/2, ... find the 10th term

notka56 [123]

Answer:

The $10^{th}$ term of the given sequence

$t_{10} = \frac{5^{9} }{2^{8} }$

Step-by-step explanation:

Step(i):-

Given sequence 2 , 5, $\frac{25}{2}$

First term a = 2

The difference of given geometric sequence

$d = \frac{r_{2} }{r_{1} } = \frac{5}{2}$

Step(ii):-

The $n^{th}$ term of the given sequence

$t_{n} = ar^{n-1}$

The $10^{th}$ term of the given sequence

$t_{10} = (2)(\frac{5}{2} )^{10-1}$

$t_{10} = (2)(\frac{5}{2} )^{9}= \frac{5^{9} }{2^{8} }$

8 0

3 years ago

Can someone please help me?

Katyanochek1 [597]

The matrix represents the system:

-3x+5y=15

2x+3y=-10, which is choice c.

We can see it more clearly from the way we multiply matrices, as follows:

$
 \left[ {\begin{array}{cc}
 -3 & 5 \\
 \ 2 & 3 \\
 \end{array} } \right]
\] \cdot \[
 \left[ {\begin{array}{c}
 x \\
 y \\
 \end{array} } \right]
\]= \left[ {\begin{array}{c}
 -3\cdot x+5\cdot y \\
 2\cdot x+3\cdot y \\
 \end{array} } \right]
\]= \[ \left[ {\begin{array}{c} 15 \\ -10 \\ \end{array} } \right]$

Answer: C

7 0

3 years ago

Suppose the graph of a cubic polynomial function has the same zeroes and passes through the coordinate (0, –5). Describe the ste

olga_2 [115]

1. "the graph has the same zeros" : so let a be the "triple" root of the cubic polynomial function.

2. So f(x)= $(x-a)^{3}$

3. Don't forget that the expression might have a coefficient b as well, and still maintain the conditions:

$f(x)=b(x-a)^{3}$

4. Now, f(0)=-5 so $-5=f(0)=b(0-a)^{3}=b(-a) ^{3}=-ba ^{3}$

$-5=-ba ^{3}$

$5=ba ^{3}$

$b= \frac{5}{ a^{3} }$

5. the function is $f(x)=\frac{5}{ a^{3} }(x-a)^{3}$ where a can be any real number except 0

7 0

3 years ago

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