A zoning board in Pine County is interested in estimating the proportion of its residents in favor of larger school zones in that county. A random sample of Pine County residents was selected. All the selected residents were asked, "Are you in favor of larger school zones in your county?" A 95% confidence interval for the proportion of residents in favor of larger school zones in that county was calculated to be 0.48 ± 0.02. Which of the following statements is correct?

A) At the 95% confidence level, the majority of area residents is in favor of larger school zones in that county.
B) In repeated sampling, 95% of sample proportions will fall in the interval (0.46, 0.50).
C) At the 95% confidence level, the estimate of 0.48 is within 0.02 of the true proportion of county residents in favor of larger school zones in that county.
D)In repeated sampling, the true proportion of county residents in favor of larger school zones in that county will fall in the interval (0.46, 0.50).
E) In repeated sampling, 95% of the time, the true proportion of county residents in favor of larger school zones in that county will be equal to 0.48.

Answer:

The solution is [tex]x = -\frac{5}{6}[/tex]

Step-by-step explanation:

We solve this question using exponential properties.

We have that:

[tex](\frac{25}{4})^{3x} = \frac{32}{3125}[/tex]

Simplifying:

[tex](\frac{5^2}{2^2})^{3x} = \frac{2^5}{5^5}[/tex]

[tex]([\frac{5}{2}]^{2})^{3x} = (\frac{2}{5})^{5}[/tex]

[tex](\frac{5}{2})^{6x} = (\frac{2}{5})^{5}[/tex]

Changing the numerator and denominator in the right side:

[tex](\frac{5}{2})^{6x} = (\frac{5}{2})^{-5}[/tex]

Since both bases are equal:

[tex]6x = -5[/tex]

[tex]x = -\frac{5}{6}[/tex]

The solution is [tex]x = -\frac{5}{6}[/tex]

Answer:

[tex]C)[/tex] [tex]1/32 ~yd^3[/tex]

Step-by-step explanation:

[tex]l*b*h[/tex]

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

hope it helps...

have a great day!!

Answer:

5. m<A = 25.3°; m<B = 64.7°

6. m<A = 40.2°; m<B = 49.8°

Step-by-step explanation:

Recall: SOHCAHTOA

5. Reference angle = <A

Opposite = 9

Adjacent = 19

Apply TOA:

Tan A = Opp/Adj

Tan A = 9/19

A = Tan^{-1}(9/19)

A = 25.3461759° ≈ 25.3° (nearest tenth)

Reference angle = <B

Opposite = 19

Adjacent = 9

Apply TOA:

Tan B = Opp/Adj

Tan B = 19/9

B = Tan^{-1}(19/9)

B = 64.6538241° ≈ 64.7° (nearest tenth)

6. Reference angle = A

Opposite = 20

Hypotenuse = 31

Apply SOH:

Sin A = Opp/Hyp

Sin A = 20/31

A = sin^{-1}(20/31)

A = 40.2° (nearest tenth)

Reference angle = B

Adjacent = 20

Hypotenuse = 31

Apply CAH:

Cos B = Adj/Hyp

Cos B = 20/31

B = cos^{-1}(20/31)

B = 49.8° (nearest tenth)

Answer: 6x+6

Step-by-step explanation:

3*2x=6x

3*2=6

Therefore 3(2x+2) = 6x+6

Answer:

The first answer is right (18).  Second answer is 50= 3.9x+2.8, which is 12.1 so 13 would be the best answer to catch at least 50 fish.

Step-by-step explanation:

Answer: z = 3, -1.5 + 1.5[tex]\sqrt{3}[/tex]i, -1.5 - 1.5[tex]\sqrt{3}[/tex]i

Step-by-step explanation:

      A cubic equation will have three solutions. This equatoin will give us one real solution. We will also have two complex solutions. These are solutions that involve "imaginary numbers" and will utilize the value i. We will write the equation in standard form and factor it.

              z³ - 27 = 0

              (z - 3)(z² + 3z + 9) = 0

      The first factor gives us z = 3, because 3 - 3 = 0. Now, we will look at when the second factor equals 0. Let us complete the square.

              z² + 3z + 9 = 0

              (z² + 3z + 2.25) + 9 - 1.5 = 0

              (z² + 3z + 2.25) + 6.75 = 0

              (z + 1.5)² + 6.75 = 0

      Lastly, we can continue solving. We will subtract 7.5 from both sides of the equation and then take the square root of both sides. Then, we will subtract 1.5 from both sides of the equation and simplify the radical.  [tex]i=\sqrt{-1}[/tex].

              (z + 1.5)² = -6.75

              z + 1.5 = ±[tex]\sqrt{6.75}[/tex]i

              z = -1.5 ±1.5[tex]\sqrt{3}[/tex]i

Answer:

  z = 3, -1.5+1.5√3i, -1.5-1.5√3i

Step-by-step explanation:

You want the solutions to the equation z³ = 27.

A cubic equation has three solutions. This one has one positive real solution and two complex conjugate solutions.

We can rewrite the equation to standard form, then factor the difference of cubes.

  z³ -27 = 0

  (z -3)(z² +3z +9) = 0

The first factor will be zero when z = 3, so that is one solution.

The second factor will be zero when ...

  (z +1.5)² +6.75 = 0 . . . . . . . complete the square

  (z +1.5) = ±√(-6.75) = ±√(-27/4) = ±(3/2)√(-3) . . . subtract 6.75; square root

  z = -1.5 ±1.5√3i

The three solutions to the equation are ...

<95141404393>

Answer:

$20 per week for 10 weeks

Step-by-step explanation:

It's the only one that even mathematically makes sense, and this tactic is also used to make it look better than $200 upfront

Answer:

but where is que

Step-by-step explanation:

i don't see the question

Answer:

(a) 8 balls

(b) 4 balls

Step-by-step explanation:

Let

[tex]N \to[/tex] Number of balls

For a box, the probability that there are N balls in it is:

[tex]Pr = 0.5^N[/tex]

For 2 boxes, it is:

[tex]Pr = 2 * 0.5^N[/tex]

From the question, we have:

[tex]\frac{80}{10000} \to[/tex] Favorable outcome

To solve for N, we have:

[tex]2 * 0.5^N = \frac{80}{10000}[/tex]

[tex]2 * 0.5^N = 0.008[/tex]

Divide both sides by 2

[tex]0.5^N = 0.004[/tex]

Take log of both sides

[tex]\log(0.5^N) = \log(0.004)[/tex]

Apply law of logarithm

[tex]N\log(0.5) = \log(0.004)[/tex]

Make N the subject

[tex]N = \frac{\log(0.004)}{\log(0.5)}[/tex]

[tex]N =7.966[/tex]

Approximate

[tex]N = 8[/tex]

Solving (b): Balls in one of the two boxes.

Here, we assume that each ball will have almost the same number of balls at a given instance;

Hence, we have:

[tex]Balls \approx \frac{N}{2}[/tex]

[tex]Balls \approx \frac{8}{2}[/tex]

[tex]Balls \approx 4[/tex]

4 balls in each box

9514 1404 393

Answer:

  160°

Step-by-step explanation:

The path is a triangle with side lengths 796, 1054, and 411 meters. The turn is opposite the short side. The interior angle of the triangle at that point can be computed using the law of cosines. If we label the sides a, b, c, respectively, then ...

  c² = a² + b² - 2ab·cos(C)

  C = arccos((a² +b² -c²)/(2ab)) = arccos(1575611/1677968) ≈ 20.116°

The external angle at the buoy is 180° -20° = 160°.

The jet skier's turn was about 160°.

829541

Step-by-step explanation:

541,840,829541

I think it is -4 and positive 2

Answer:

0.4

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

Answer:

Length = 5

Width = 21

Step-by-step explanation:

(x)(x + 16) = 105

x^2 + 16x = 105

x^2 + 16x - 105 = 0

(x - 5) x ( x + 21) = 0

x - 10 = 0

x = 5

x + 21 = 0

x = -21

Now that we have the zeroes.

We have to find the most viable one to put in.

Using -21 would not make sense, so we will use 5.

Plug it in:

x = 5

(5) (5 + 16) = 105

5 ( 21) = 105

Answer:

(5, 8)

Step-by-step explanation:

(5. – 5) down 3 units => (5, -8)

reflect x-axis => (5 , 8)

Step-by-step explanation:

-4y+5>-15

-4y>-15-5

-4y>-20

divide both (-)

4y>20

divide through by 4

y>20/4

y>5

Answer:

15.46

Step-by-step explanation:

Answer:

15.46

Step-by-step explanation: if this isnt it im sory

Answer:

n > 4 I think is the answer, I'm not 100% sure

Answer:

n<1/4

Step-by-step explanation:

4<n Sub n on both sides

4n<0 Divide by 4 on both sides

n<1/4

Answer:

0.01

Step-by-step explanation:

The probability of making a Type I error is equal to  \alphaα = 0.01, the significance level of the test

The probability of type 1 error will then be equal to the hypothesis level of significance and this will be 0.01.

Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.

An orange juice manufacturer advertises a new orange juice product that contains 50% less sugar.

An inspector wants to investigate whether the actual percentage of water in the product is within 5% of the intended 50%.

He plans to conduct a significance test at a = 0.01 level to see if there is convincing evidence that the proportion of water added is different from 0.50.

Type I error is referred to as false positives and it means that when a statistically significant difference is validated by the researcher even though the results aren't statistically significant.

Type I error is when one rejects the null hypothesis even though it's true. In this case, the inspector rejects the hypothesis that the proportion of water that is contained in the product is 0.5.

The probability of type 1 error will then be equal to the hypothesis level of significance and this will be 0.01.

Learn more about probability here;

https://brainly.com/question/11234923

#SPJ2

Answer:

c/8=9

Step-by-step explanation:

Answer:

c²+ 3c-40

Step-by-step explanation:

hope that helps

Answer:

50% or 1/2

Step-by-step explanation:

A coin has 2 sides so 100/2 equals 50 so either 50% or 1/2. There is your answer

Answer: y>-2 (The symbol has a underline)

Step-by-step explanation:

Since you want to move -4 to the -6 spot, do the opposite of the negative which is positive. So add +4 to each side. And the -4 will disappear and you will be left with y>-6+4. Solve -6+4= -2 And so the answer is y>-2.

Hope this helps

Answer:

[tex]f(x) = x^3 +5x^2-4x-20[/tex]

Step-by-step explanation:

Given

[tex]Zeros: -5,-2,2[/tex]

Required

The polynomial function

If a function has a, b and c as its zeros, the function is:

[tex]f(x) = (x - a)(x - b)(x - c)[/tex]

So, we have:

[tex]Zeros: -5,-2,2[/tex]

[tex]f(x) = (x - (-5))(x - (-2))(x - 2)[/tex]

Open the inner brackets

[tex]f(x) = (x +5)(x +2)(x - 2)[/tex]

Expand the difference of two squares

[tex]f(x) = (x +5)(x^2 - 4)[/tex]

Expand

[tex]f(x) = x^3 +5x^2-4x-20[/tex]

Answer:

We reject H₀.  We support that the new average credit card debt is bigger than the previous average

Step-by-step explanation:

Five years earlier

μ   = 8189

σ  =  690

Sample size   n  = 32

Recent year debt

x  =  8776

Sample size   n  = 32

a) Hypothesis Test:

Null Hypothesis                        H₀            x  =  μ   = 8189

Alternative Hypothesis           Hₐ             x >  μ

b) z(c)  Alternative Hypothesis establishes that the test is a one tail-test to the right.

z(c)   for significance level  α = 0.05    is  from z-table      z(c) = 1,64

c) z(s)  =  (  x  -   μ ) / σ /√n

z(s)  =  ( 8776  - 8189 ) / 690 /√32

z(s)  =  587 *5,66/ 690

z(s) = 4,81

d) Comparing   z(c)    and z(s)

z(s)  >  z(c)   Then z(c) is in the rejection region and we reject H₀

e) We have evidence that at 95 % of confidence the new value for the debt in credit card is now bigger than the average

Answer:

its c

Step-by-step explanation:

Answer:

If y - 4 = 5 then:

y = 5 + 4

y = 9

Answer:

A

Step-by-step explanation:

where the graph

WHERE THE GRAPH???

Answer:

Hello, it appears you did not provide an image that was supposed to be included in order to help answer your question, so I'm afraid I cannot assist you without seeing it. If you supply the necessary photo, I would be more than happy to help you.

Answer:

No.

Step-by-step explanation:

Explanation below.