8 rational numbers between 3 and 4​

Answer:

a) The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b) The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

Step-by-step explanation:

Question a:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

Sample of 120 registered voters in order to predict the winner of a local election. The Democrat candidate was favored by 62 of the respondents.

So 120 - 62 = 58 favored the Republican candidate, so:

[tex]n = 120, \pi = \frac{58}{120} = 0.4833[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].  

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 - 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.3658[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4833 + 2.575\sqrt{\frac{0.4833*0.5167}{120}} = 0.6001[/tex]

The 99% CI for the true proportion of voters who prefer the Republican candidate is (0.3658, 0.6001). This means that we are 99% sure that the true population proportion of all voters who prefer the Republican candidate is (0.3658, 0.6001).

b. If a candidate needs a simple majority of the votes to win the election, can the Republican candidate be confident of victory? Justify your response with an appropriate statistical argument.

The upper bound of the confidence interval is above 0.5 = 50%, which meas that the candidate can be confidence of victory.

[tex]\boxed{\sf Slope(m)=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{7-4}{10-4}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{3}{6}[/tex]

[tex]\\ \sf\longmapsto m=\dfrac{1}{2}[/tex]

[tex]\\ \sf\longmapsto m\approx0.5[/tex]

Answer:

[tex]m=\frac{1}{2}[/tex]

Step-by-step explanation:

The slope of a line, also known as the change in the line or the ([tex]\frac{rise}{run}[/tex]) can be found using the following formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Where ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]) are points on the line. Substitute the given information into the formula and solve for the slope.

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Points on the line: [tex](4,4)\ \ \ (10, 7)[/tex]

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{7-4}{10-4}[/tex]

[tex]m=\frac{3}{6}[/tex]

[tex]m=\frac{1}{2}[/tex]

[tex]m=0.5[/tex]

Answer:

4/27

Step-by-step explanation:

total number of marbles=9

probability of red=4/9

since you returned the first marble, the total number of marbles remains the same

prob(Blue)=(3/9)=1/3

P(red then blue)=(4/9)*(1/3)

=4/27

Answer:

..... surface area = 16 km^2.

Answer: 0.0228

Step-by-step explanation:

please check photo explanation

The probability that the sample mean will be greater than 22.2 ounces will be equal to 0.0228

Probability is calculated as the proportion of favorable events to all potential scenarios of an event. The proportion of positive results, or x, for an experiment with 'n' outcomes can be expressed.

As per the given values in the question,

[tex]\mu_x[/tex] = 22

σ(x) = σ/√n

= 1/√100

σ(x) = 0.1

P(x>22.2) = 1- P(x<22.2)

= 1- P(x × μ(x))/ σ(x) < (22.2 - 22)/0.1

1 - P (z < 2.00)

1- 0.9772

= 0.0228

To know more about probability:

https://brainly.com/question/11234923

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[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{-12 + (-8) + 30}\\\\\large\textsf{= -12 - 8 + 30}\\\\\large\textsf{-12 - 8 = \bf -20}\\\\\large\textsf{= -20 + 30}\\\\\large\textsf{= \bf 10}\\\\\\\boxed{\boxed{\huge\text{Therefore, your ANSWER is: \textsf{10}}}}\huge\checkmark\\\\\\\\\huge\textsf{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

Kindly check explanation

Step-by-step explanation:

The power of a test simply gives the probability of Rejecting the Null hypothesis, H0 in a statistical analysis given that the the alternative hypothesis, H1 for the study is true. Hence, the power of a test can be referred to as the probability of a true positive outcome in an experiment.

Using this definition, a power of 90% simply means that ; there is a 90% probability that the a Pvalue less Than the α - value of an experiment is obtained if there is truly a significant difference. Hence, a 90% chance of Rejecting the Null hypothesis if truly the alternative hypothesis is true.

Answer:

The volume of the resulting solid is π/2 cubic units.

Step-by-step explanation:

Please refer to the diagram below.

The shell method is given by:

[tex]\displaystyle V = 2\pi \int _a ^b r(x) h(x)\, dx[/tex]

Where the representative rectangle is parallel to the axis of revolution, r(x) is the distance from the axis of revolution to the center of the rectangle, and h(x) is the height of the rectangle.

From the diagram, we can see that r(x) = (2 - x) and that h(x) is simply y. The limits of integration are from a = 0 to b = 1. Therefore:

[tex]\displaystyle V = 2\pi \int_0^1\underbrace{\left(2-x\right)}_{r(x)}\underbrace{\left(x - x^2\right)}_{h(x)}\, dx[/tex]

Evaluate:

[tex]\displaystyle \begin{aligned} V&= 2\pi \int_0 ^1 \left(2x-2x^2-x^2+x^3\right) \, dx\\ \\ &= 2\pi\int _0^1 x^3 -3x^2 + 2x \, dx \\ \\ &= 2\pi\left(\frac{x^4}{4} - x^3 + x^2 \Bigg|_0^1\right) \\ \\ &= 2\pi \left(\frac{1}{4} - 1 + 1 \right) \\ \\ &= \frac{\pi}{2}\end{aligned}[/tex]

The volume of the resulting solid is π/2 cubic units.

Answer:

pi/2

Step-by-step explanation:

I always like to draw an illustration for these problems.

For shells method think volume of cylinder=2pi×r×h

Integrate(2pi(2-x)(x-x^2) ,x=0...1)

Multiply

Integrate(2pi(2x-2x^2-x^2+x^3 ,x=0...1)

Combine like terms

Integrate(2pi(2x-3x^2+x^3) ,x=0...1)

Begin to evaluate

2pi(2x^2/2-3x^3/3+x^4/4) ,x=0...1

2pi(x^2-x^3+x^4/4), x=0...1

2pi(1-1+1/4)

2pi/4

pi/2

9514 1404 393

Answer:

Step-by-step explanation:

Let x represent Atsu's current age. Then Agyappng is 3x. Three years ago the relationship was ...

  (3x -3) = 4(x -3)

  9 = x . . . . . . . . . . . . add 12-3x

Atsu is 9; Agyappng is 27.

Answer:

The sample size must be of 47,059,600.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

Standard deviation:

[tex]\sigma = 3.5[/tex]

If you want the error bound E of a 95% confidence interval to be less than 0.001, how large must the sample size n be?

This is n for which M = 0.001. So

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]0.001 = 1.96\frac{3.5}{\sqrt{n}}[/tex]

[tex]0.001\sqrt{n} = 1.96*3.5[/tex]

[tex]\sqrt{n} = \frac{1.96*3.5}{0.001}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.96*3.5}{0.001})^2[/tex]

[tex]n = 47059600[/tex]

The sample size must be of 47,059,600.

Answer:

A and B must always be congruent

B and D

E and G

F and H

Step-by-step explanation:

I have to be honest. from the picture I cannot see the vertical angles. All I see is a straight blue line and red letters. But based on the vertical theorem

A and B must always be congruent

B and D

E and G

F and H

also if you want to make sure it's right try to include another picture.

Answer:

Step-by-step explanation:

edmentum :)

Answer:

82.8

Step-by-step explanation:

mean = sum of all points, over the total given number of points

84 * 26 = 2184

2184 + 69 + 66 = 2319

Now the total number of tests is 26 + 2 or 28

So divide 2319 by 28

2319/28 = 82.82142

rounded to the nearest tenth is 82.8

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

I believe its  EG and NE but i might be wrong

Step-by-step explanation:

Perimeter = Sum of all sides

Perimeter = 14cm + 8cm + 10cm + 5cm

Perimeter = 22cm + 15cm

Perimeter = 37cm

Step-by-step explanation:

hope it helps you

...

........

9514 1404 393

Answer:

Step-by-step explanation:

For the purpose of selecting the appropriate tile, it is only necessary to figure the real part of the sum or product.

We notice that the second product (-xy) is -1/2 times the first product (2xy). This can let you find the answers on that basis alone. The only tiles with a (-1) : (2) relationship are (-29 -53i) : (58 +106i).

__

The sum -5x +y has a real part of -5(3) +7 = -8.

The sum 2x -3y has a real part of 2(3) -3(7) = 6 -21 = -15.

Hence the sequence of answers needed on the right side is as shown above.

_____

Additional comment

You know that arithmetic operations with complex numbers (multiplication and addition) are identical to those operations performed on any polynomials. That is, "i" can be treated as a variable. The simplification comes at the end, where any instances of i² can be replaced by -1.

  xy = (3 +8i)(7 -i) = 3·7 -3·i +8·7·i -8·i·i = 21 +53i -8i²

  = (21 +8) +53i . . . . replaced i² with -1, so -8i² = +8

  = 29 +53i

Answer:

B

Step-by-step explanation:

I took a test in school and this was the answer...at least for my class.

Answer:

(1,-2)

Step-by-step explanation:

P(-1,2) and (x, y) -> (x + 2, y - 4). Plugging in x and y in the transformation, the transformed points are (-1+2, 2-4) = (1,-2)

Answer:

40

Step-by-step explanation:

2x² - 5y + 7 when x = 2 and y = -5

2(2)² - 5(-5) + 7

= 2(4) -5(-5) + 7

= 8 + 25 + 7

= 40

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

Explanation:

Let's isolate the variable 'a' in the given inequality.

4a + 2 > 12

4a + 2-2 > 12-2

4a > 10

4a/4 > 10/4

a > 2.5

In the second step, I subtracted 2 from both sides to undo the "plus 2". In the second to last step, I divided both sides by 4 to undo the multiplication.

The solution is a > 2.5, meaning that anything larger than 2.5 will work in the original inequality.

For example, we could try a = 3 to get

4a + 2 > 12

4*3 + 2 > 12

12 + 2 > 12

14 > 12

which is true. This makes a = 3 a solution. The value a = 3.5 is a similar story, so it's also a solution.

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

As an example of a non-solution, let's try a = 1

4a + 2 > 12

4*1 + 2 > 12

4 + 2 > 12

6 > 12

which is false. So we can see why a = 1 is not part of the solution set. You should find that a= 0.5 and a = 2.5 won't work as well for similar reasoning.

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

Just a correction, the characteristic roots of the equation are [tex]y = 7[/tex] and [tex]y = -\frac{1}{2}[/tex], thus, we should test for:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

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

Question a:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime\prime} = 49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}[/tex]

[tex]2y^{\prime\prime} - 13y^{\prime} - 7y = 0[/tex]

[tex]2(49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}) - 13(7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}) - 7(Ae^{7x} + Be^{-\frac{x}{2}}) = 0[/tex]

[tex]98Ae^{-7x} + \frac{1}{2}Be^{\frac{x}{2}} - 91Ae^{-7x} + \frac{13}{2}e^{-\frac{x}{2}} - 7Ae^{7x} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]98Ae^{-7x} - 91Ae^{-7x} - 7Be^{-\frac{x}{2}} + \frac{1}{2}Be^{\frac{x}{2}}  + \frac{13}{2}e^{-\frac{x}{2}} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]0A + 0B = 0[/tex]

[tex]0 = 0[/tex], thus, we found the identity, and for each constant A and B, the following is a solution.

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

Question b:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]A + B = 3 \rightarrow B = 3 - A[/tex]

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

[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]7A - \frac{1}{2}B = -5[/tex]

Using [tex]B = 3 - A[/tex]

[tex]7A - \frac{3}{2} + \frac{A}{2} = -5[/tex]

[tex]\frac{14A}{2} + \frac{A}{2} = -\frac{10}{2} + \frac{3}{2}[/tex]

[tex]\frac{15A}{2} = -\frac{7}{2}[/tex]

[tex]15A = -7[/tex]

[tex]A = -\frac{7}{15}[/tex]

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

Then, B is given by:

[tex]B = 3 - A = 3 - (-\frac{7}{15}) = \frac{45}{15} + \frac{7}{15} = \frac{52}{15}[/tex]

Thus, the values are: [tex]A = -\frac{7}{15}, B = \frac{52}{15}[/tex]

A similar problem is given at https://brainly.com/question/2456414

Answer:

~~314.16

Step-by-step explanation:

lol i dont have 100000000 points. anyways

you can find the area of a sphere with the formula 4πr^2 with r being the radius

this sphere's radius is 5 as shown in the image

so

4π*r^2

4π*(5)^2

=4π*25

=100π

put into calculator

~~314.16cm^3

hope this helps

Answer:

46

Step-by-step explanation:

200/2 = 100, and the x coordinate that line up with the y-coordinate of 100 is 46.

50 - (16 + 19)

= 50 - 35

= 15m

Answer:

.......................

Answer:

g

Step-by-step explanation:

f

Answer:

11 meters

Step-by-step explanation:

First, we can say that the square has a side length of x. The perimeter of the square is 4x, and that is how much wire goes into the square. To maximize the area, we should use all the wire possible, so the remaining wire goes into the triangle, or (11-4x).

The area of the square is x², and the area of an equilateral triangle with side length a is (√3/4)a². Next, 11-4x is equal to the perimeter of the triangle, and since it is equilateral, each side has (11-4x)/3 length. Plugging that in for a, we get the area of the equilateral triangle is

(√3/4)((11-4x)/3)²

= (√3/4)(11/3 - 4x/3)²

= (√3/4)(121/9  - 88x/9 + 16x²/9)

= (16√3/36)x² - (88√3/36)x + (121√3/36)

The total area is then

(16√3/36)x² - (88√3/36)x + (121√3/36) + x²

= (16√3/36 + 1)x² -  (88√3/36)x + (121√3/36)

Because the coefficient for x² is positive, the parabola would open up and the derivative of the parabola would be the local minimum. Therefore, to find the maximum area, we need to go to the absolute minimum/maximum points of x (x=0 or x=2.75)

When x=0, each side of the triangle is 11/3 meters long and its area is

(√3/4)a² ≈ 5.82

When x=2.75, each side of the square is 2.75 meters long and its area is

2.75² = 7.5625

Therefore, a maximum is reached when x=2.75, or the wire used for the square is 2.75 * 4 = 11 meters

The length of the square must be 4 m in order to maximize the total area.

When we put the differentiation of the given function as zero and find the value of the variable we get maxima and minima.

We have,

Length of the wire = 11 m

Let the length of the wire bent into a square = x.

The length of the wire bent into an equilateral triangle = (11 - x)

Now,

The perimeter of a square = 4 side

4 side = x

side = x/4

The perimeter of an equilateral triangle = 3 side

11 - x = 3 side

side = (11 - x)/3

Area of square = side²

Area of equilateral triangle = (√3/4) side²

Total area:

T = (x/4)² + √3/4 {(11 -x)/3}² _____(1)

Now,

To find the maximum we will differentiate (1)

dT/dx = 0

2x/4 + (√3/4) x 2(11 - x)/3 x -1 = 0

2x / 4 - (√3/4) x 2(11 - x)/3 = 0

2x/4 - (√3/6)(11 - x) = 0

2x / 4 = (√3/6)(11 - x)

√3x = 11 - x

√3x + x = 11

x (√3 + 1) = 11

x = 11 / (1.732 + 1)

x = 11/2.732

x = 4

Thus,

The length of the square must be 4 m in order to maximize the total area.

Learn more about maxima and minima here:

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Answer:

Step-by-step explanation:

(x-2)(x+4)=x^2+4x-2x-8=0=> x =2, x=0

Answer:

A

Step-by-step explanation: