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2 years ago

Given n = 875 and pˆ = 0.45, find the margin of error E that corresponds to a 95% confidence level.

Mathematics

1 answer:

sveticcg [70]2 years ago

4 0

Answer:

The margin of error E that corresponds to a 95% confidence level is: $E=0.03297$

Step-by-step explanation:

The propocion is $p = 0.45$

The sample size $n = 875$

95% confidence level

Level of significance = 1-level of confidence

Level of significance = 1-0.95 = 0.05

The formula for the error is:

$E = Z_{\alpha/2}\sqrt{\frac{p(1-p)}{n}}$

The value for $Z_{0.05/2} =Z_{0.0250}= 1.96$ according to the normal table

So:

$E = 1.96\sqrt{\frac{0.45(1-0.45)}{875}}\\\\SE=0.03297$

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2 years ago

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the wate

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Answer: a. 112 feet, b= 3 seconds, c= 256 feet, d = 6 seconds

Step-by-step explanation:

Here is the complete question:

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the water is modeled by the equation d(t) = −16t2+96t + 112, where t represents time in seconds.

Find the actual value(s) now to each question. Use the solution from the previous question to assist you with what you are actual solving for.

(a) From what height was the quarter tossed?

The quarter was tossed at 112 feet.

(b) How long does it take the quarter to reach its maximum height?

It will take ________ seconds for the quarter to reach its maximum height.

The maximum height of the quarter is ________ feet.

(d) How much time does it take for the quarter to hit the water?

It will take ______ seconds for the quarter to hit the water.

a. Since the function is

d(t) = −16t² + 96t + 112,

The coin is tossed at 112 feet. This is because it is the the initial value of the function. It is the constant term and does not depend on any other variable.

b. To calculate the maximum height, we have to find vertex of the function, that has coordinates of h,k and,

h = -b/2a and k = f(h).

From the question, we are aware that,

a = -16, b = 96, c = 112

Using the values, the vertex will be:

h = -b/2a

= -96/(2 × -16)

= -96/-32

= 3

k = f(3)

= 16t² + 96t + 112

= -16(3)² + 96(3) + 112

= -144 + 288 + 112

= 256

The maximum height is therefore 256 feet, and time needed to reach the height will be 3 seconds.

c. The maximum height has been calculated and it is 256 feet.

d. The time it take for the quarter to hit the water will be:

= 3 seconds × 2 = 6 seconds

Since the maximum height took 3 seconds, it would take another 3 seconds to hit the water. This makes it 6 seconds

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2 years ago

I need the answers thanks :)

bogdanovich [222]

1.) y=3
2.) y=13
2y + y = 3y , 22+17= 39
3y = 39 , divide 3 on each side (which cancels out the 3 with the y which leaves you with y)
3.) y=10
3y - y = 2y , 35-15= 20
2y=20 , do the same as # 2.
4.) y=4
9y - 5y = 4y , 48-32= 16
4y=16, do the same as #2 & #3
5.) (4,5)
x + 3y = 19
2x - 3y = -7
solve for x first ; x + 2x= 3x , 19-7 = 12; 3x = 12 ; divide 3 ; x= 4. You know have to make the x's cancel out. so I will multiply -2 on the first equation. -2(x+3y=19)
-2x - 6y = -38
2x - 3y = -7
Now solve for y ; -6y + -3y = -9y , -38 + -7 = -45; -9y=-45 ; divide by -9 (since they are both negative your answer will be positive) ; y= 5
6.) (6,8)
x + 4y = 38
-x - 3y = -30
solve for y first ; 4y - 3y = y , 38-30 = 8; y=8 (that simple!) Now you need to find a common multiple for 4 & 3 which is 12. So you will have to multiply each equation by either 4 or 3.
(x + 4y = 38)*3 = 3x + 12y = 114
(-x - 3y = -30)*4 = -4x - 12y = -120
solve for x ; 3x - 4x = -x , 114-120= -6 ; -x=-6. Since the x has a negative that means there's still a 1 there so -1x=-6 ; you will need to divide this which makes the 6 a positive; x=6

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