Consider the following demographic data for a hypothetical state. Assume everyone votes along party lines. The state has 10 representatives and a population of 7.2 ​million; party affiliations are 70% Democrat and 30​% Republican. Complete parts​(a) and​ (b) below.
a. If districts were drawn​ randomly, what would be the most likely distribution of House​ seats?
​Republicans, =______
Democrats _______
b. If the districts could be drawn without restriction​ (unlimited gerrymandering), what would be the maximum and minimum number of Republican representatives who could be sent to​ Congress?
The maximum number of Republicans representatives could be
_____________
The minimum number of Republicans representatives could be
________________

Answer:

a t-chart to represent you proving a statement. statements are to the left of the t-chart and reasons are to the right.

Step-by-step explanation:

this is used in geometry to prove a given statement.

If the events P(E) and P(F) are independent events and  P(E) = 0.62 and P(F) = 0.60, then the value of P( E or F) is 0.848

If events P(E) and P(F) are independent, then the probability of both events happening can be found by multiplying their individual probabilities:

P(E and F) = P(E) × P(F)

However, since we want to find P(E or F), we need to account for the possibility that both events could happen simultaneously. In order to avoid counting this intersection twice, we can use the following formula:

P(E or F) = P(E) + P(F) - P(E and F)

We already know that P(E) = 0.62 and P(F) = 0.60, but we still need to find P(E and F). Since the events are independent, we can use the multiplication rule to find:

P(E and F) = P(E)  P(F) = 0.62 × 0.60 = 0.372

Now we can substitute these values into the formula for P(E or F):

P(E or F) = P(E) + P(F) - P(E and F) = 0.62 + 0.60 - 0.372 = 0.848

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Answer:

5 is 1 8 is 2 7 is 4 5 is 2 12 is 3

Step-by-step explanation:

The error is when h is some value, the error will be when h/2.

The error of a third-order accurate numerical differentiation method scales with the fourth power of the step size, i.e. if the step size is halved, the error will decrease by a factor of 2⁴=16. So if the error is when h is some value, the error will be when h/2.

The error in numerical differentiation methods can be approximated using Taylor series expansions. For a third-order accurate method, the error term in the Taylor series would be proportional to h⁴. Hence, reducing the step size by a factor of two would reduce the error by a factor of 2⁴ = 16. This relationship between step size and error holds for small step sizes. For larger step sizes, the error may not decrease in such a simple manner and other factors such as the smoothness of the function being differentiated and the presence of singularities or discontinuities may come into play.

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Answer:

We have the length, width, and height of the rectangular prism, so we can calculate V=l×w×h=20cm×10cm×10cm=2,000cm3 V = l × w × h = 20 cm × 10 cm × 10 cm = 2 , 000 cm 3

The surface area of Prism B is approximately 367.25 cm^2.

Since Prisms A and B are similar, their corresponding sides are in proportion, and their volumes are related by the cube of the scale factor between them.

Let the scale factor between Prism A and Prism B be k. Then:

Volume of Prism A / Volume of Prism B = (Side length of Prism A / Side length of Prism B)^3

Given that the volume of Prism A is 375 cm^3 and the volume of Prism B is 648 cm^3, we can set up the equation:

375 / 648 = (Side length of Prism A / Side length of Prism B)^3

Now, let's solve for the scale factor (k):

k^3 = 375 / 648

k^3 = 0.5787037037

k ≈ 0.825 (rounded to three decimal places)

Now, since the surface area of a prism is proportional to the square of its side length, we can find the ratio of the surface areas:

(Surface area of Prism A / Surface area of Prism B) = (Side length of Prism A / Side length of Prism B)^2

Given that the surface area of Prism A is 250 cm^2, we can find the surface area of Prism B:

Surface area of Prism B = Surface area of Prism A / (k^2)

Surface area of Prism B = 250 / (0.825^2)

Surface area of Prism B ≈ 250 / 0.680625

Surface area of Prism B ≈ 367.25 cm^2

Therefore, the surface area of Prism B is approximately 367.25 cm^2.

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Answer:

7.8

Step-by-step explanation:

Polynomial function of least degree with integral coefficients that has the given zeros imaginary \(\\f(x) & =x^4+5 x^2-6\)

As per the given data:

\(\sqrt{6} i$\) is a zero.

Therefore \($-\sqrt{6} i$\) is also a zero.

\($(x+1),(x-1),(x-\sqrt{6} i)$\) and \($(x+\sqrt{6} i)$\) are factors

\($$\begin{aligned}f(x) & =(x+1)(x-1)(x-\sqrt{6} i)(x+\sqrt{6} i) \\& =\left(x^2-1\right)\left(x^2-(\sqrt{6} i)^2\right) \\& =\left(x^2-1\right)\left(x^2-6 i^2\right) \\& =\left(x^2-1\right)\left(x^2+6\right) \\& =x^4+6 x^2-x^2-6 \\f(x) & =x^4+5 x^2-6\end{aligned}$$\)

Therefore the polynomial function is \(\\f(x) & =x^4+5 x^2-6\)

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Write a polynomial function of least degree with integral coefficients that have the given zeros of-1, 1, and i times square root of 6.

Answer:

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

No, the mean and mode are not equal.

Mean of the series is 10

Mode of the series is 12

Averages can only be computed for numeric variables, regardless of whether the variables are discrete or continuous. This is obtained by simply dividing the sum of all values ​​in the dataset by the number of values. Calculations can be performed from raw data or data aggregated into frequency tables.

The calculation for mode is fairly straightforward. Arrange all numbers in a specific set. This is lowest to highest or highest to lowest, counting the number of times each number appears in the set. The mode that comes up most often is mode.

For the given data:

Mean = \(\frac{12+9+13+4+12}{5}\)

= 10

For mode lets arrange the data in series:

4, 9, 12, 12, 13

The most occurring value is 12 so it is considered as mode.

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The value of x in the similar triangles is 40.

Those triangles that looks the same but different in sizes.

And in the similar triangle,

the corresponding sides in proportion to each other and corresponding angles are equal to each other.

Given:

Triangles are similar.

That means,

the corresponding sides are in the proportion to each other.

That means,

(x + 8)/x = 12/10

10x + 80 = 12x

2x = 80

x = 40

Therefore, the value of x is 40.

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Answer: \(9x+4y=-20\)

Step-by-step explanation:

Standard form is ax+by=c. What we can do is put the given point and slope into slope-intercept point, and then manipulate it to standard form.

\(y=-\frac{9}{4} x-5\)                  [add both sides by \(\frac{9}{4} x\)]

\(\frac{9}{4} x+y=-5\)                   [multiply both sides by 4]

\(9x+4y=-20\)

Therefore the standard form is \(9x+4y=-20\).

Developing 95% confidence intervals for the mean age and the rate of having children of subscribers will provide insight into whether the magazine is a good place to advertise for companies selling educational software and computer games for young children. The mean household income of subscribers can also be estimated and compared with the Texas median income $70,316 using an appropriate hypothesis test with the 0.05 and 0.01 level of significance to make conclusions, and comment on whether there is any difference in the results.

The 95% confidence interval for the mean age of subscribers indicates that it ranges from 31.28 years to 38.72 years, and the 95% confidence interval for the rate of having children of subscribers is 0.455 ± 0.059. It can be concluded that the magazine is a good place to advertise for companies selling educational software and computer games for young children as the subscribers are relatively young with nearly 46% having children.

An estimate of the mean household income of subscribers can be obtained using the available data, and an appropriate hypothesis test can be developed to compare the average household income of the subscribers with the Texas median income $70,316. The null hypothesis is that the mean household income of subscribers is equal to $70,316, while the alternative hypothesis is that it is not equal to $70,316. Using a two-tailed t-test with a significance level of 0.05, the calculated t-value is 2.05, which is less than the critical value of 2.262. Therefore, the null hypothesis cannot be rejected at the 0.05 level of significance. However, at the 0.01 level of significance, the calculated t-value is 2.05, which is greater than the critical value of 2.896. Therefore, the null hypothesis can be rejected at the 0.01 level of significance. It can be concluded that there is no significant difference between the mean household income of subscribers and the Texas median income $70,316 at the 0.05 level of significance, but there is a significant difference at the 0.01 level of significance.

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Answer:

8.69>8.6

Step-by-step explanation:

Because 8.69 has .09 more than 8.6

Answer:

8.69 > 8.60

Step-by-step explanation:

You need to add a zero to the end to 8.6 so it's easier to compare. Since all the digits in the two numbers are the same except 9 and zero, those are what you need to compare. 9>0, so 8.69 > 8.6

hope this helped! :)

The amount of Chemical  B needed is 1.6 g.

This refers to a diagram that shows a series of one or more points, lines, line segments, curves, or areas that represents the variation of a variable when compared with that of one or more other variables.

The quantity of Chemical B is plotted against the quantity of  Chemical A.

Chemical B  is plotted on the vertical axis using the scale of 1 cm to represent 2 units. Chemical A is plotted on the horizontal axis using the scale of 1 cm to represent 1 unit.

Therefore, on the graph, the line passing through the origin of the graph shows that when  1.4 g of Chemical A is used  1.6 g of Chemical B is needed.

Chemical B  is plotted on the vertical axis using the scale of 1  cm to represent 2 units.

To get the amount of Chemical B is  on vertical axis =  2 grams

                                                                                             5 boxes

                                                                                       =0.4 g

Tracing the mass of Chemical A used 1.4 g it meets the line passing through the center at 4th line (4th box).

To get the amount of Chemical B is  on vertical axis = amount of Chemical B per box * the number of line (boxes).

To get the amount of Chemical B is  on vertical axis = 0.4 g * 4 lines (boxes)

                                                                                        = 1.6 g

Hence The amount of Chemical  B needed is 1.6 g.

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Answer:

6885.1 yd^3

Step-by-step explanation:

the shape in the attached image is a sphere.

thus, we are to find the volume of a sphere

Volume = 4/3 nr^3

n = 22/7

r = radius

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

radius = 23.6/2 = 11.8 ft

4/3 x 22/7 x 11,8^3 = 6885.1 yd^3

the tenth is the first number after the decimal place. To convert to the nearest tenth, look at the number after the tenth (the hundredth). If the number is greater or equal to 5, add 1 to the tenth figure. If this is not the case, add zero

To find the probability that Catherine's number is at least 4.5, we need to consider the probability that each of the four individuals selects a number less than 4.5, since Catherine's number will be the maximum of these four numbers.

1. Katelynn selects a number from an exponentially distributed random variable with mean 4. The probability that she selects a number less than 4.5 is given by the cumulative distribution function of the exponential distribution: P(Katelynn < 4.5) = 1 - e^(-4/4.5) ≈ 0.602.

2.Catelyn selects a number at random by rolling a fair six-sided die and counting the number of dots on the top surface. The probability that she selects a number less than 4.5 is given by: P(Catelyn < 4.5) = 0, since the maximum value she can roll is 6.

3. Katelin selects a number from a normally distributed random variable with mean 3.5 and standard deviation 1. The probability that she selects a number less than 4.5 is given by the standard normal distribution: P(Z < (4.5 - 3.5)/1) ≈ 0.841, where Z is the standard normal variable.

4. Caytlin selects a number at random from a binomial distribution with 5 attempts and probability of success 0.9. The probability that she selects a number less than 4.5 is given by the cumulative distribution function of the binomial distribution: P(Caytlin < 4.5) = Σ(i=0 to 4) (5 choose i) (0.9)^i (0.1)^(5-i) ≈ 0.033.

So, the probability that Catherine's number is at least 4.5 is: P(Catherine ≥ 4.5) = 1 - P(Katelynn < 4.5) * P(Catelyn < 4.5) * P(Katelin < 4.5) * P(Caytlin < 4.5), ≈ 1 - 0.602 * 0 * 0.841 * 0.033, ≈ 0.386, Therefore, the answer is option 2: Less than 0.50.

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Answer:

(1,-4)

Step-by-step explanation:

Answer:

x=7

Step-by-step explanation:

Since these angles are complementary, they will add up to 90 degrees, so you can set up the equation like so:

8x+5+3x+8=90

First, combine like terms:

(8x+3x)+(5+8)=90

11x+13=90

Then, subtract 13 from both sides:

11x+13(-13)=90(-13)

11x=77

Then divide both sides by 11:

11x(/11)=77(/11)

x=7

7 is your answer

hope this helps!

Answer:

x=7

Step-by-step explanation:

Said it in the last question you had.

Answer:

To convert 2 Bigha into Kattha:

If 1 Bigha = 20 Kattha:

2 Bigha = 2 * 20 Kattha = 40 Kattha

If 1 Bigha = 16 Kattha:

2 Bigha = 2 * 16 Kattha = 32 Kattha

Answer and Step-by-step explanation:

1.

c(1) = -0.6

c(n) = c(n - 1) × -5

Those are the answers.

#teamtrees #PAW (Plant And Water)

We can argue that the volume of square prism is greater than the volume of the cylinder.

To find the volume of a prism, we need to multiply the of area of base by the height. Since the height is the same for both the square prism and the cylinder, we can focus on comparing the areas of their respective cross-sections.

The area of the cross-section of the square prism is given as 157 square units. Since the cross-section is a square, we can find the side length by taking the square root of the area. So, the side length of the square is √157 units.

The area of the cross-section of the cylinder is given as 50π square units. Since the cross-section is a circle, we can find the radius by taking the square root of the area divided by π. So, the radius of the cylinder is √(50π/π) = √50 units.

Now, to compare the volumes, we need to calculate the volume of each shape. The volume of the square prism is equal to the area of the base multiplied by the height, which is (√157)^2 * height. The volume of the cylinder is equal to the area of the base (π * (√50)^2) multiplied by the height. Since the heights are the same, we can compare the volumes by comparing the areas of the bases.

Since (√157)^2 is greater than (√50)^2, we can conclude that the area of the base of the square prism is greater than the area of the base of the cylinder. Therefore, the volume of the square prism is greater than the volume of the cylinder.

In summary, based on the given information, we can argue that the volume of the square prism is greater than the volume of the cylinder.

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The probability for the third woman to have a girl is 50%, not influenced by the outcome of the previous two pregnancies.

The probability for a woman to have a girl is 50%. So, the probability for two women to have girls is (0.5 x 0.5 = 0.25 or 25%).

However, this does not mean that the third woman will also have a girl. Each pregnancy is independent and the outcome of one pregnancy does not affect the outcome of another.

So, the probability for the third woman to have a girl is still 50%, regardless of the outcome of the other two pregnancies. The probability of having three girls in a row is 0.25 x 0.5 = 0.125 or 12.5%.

Therefore, the probability for the third woman to have a girl is 50%, not influenced by the outcome of the previous two pregnancies.

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Explanatory variable: The type of pill the men took each day.

Response variable: Whether a subject had a heart attack.

We have been given that :

Participated candidates are 400

Men are divided randomly so we find out explanatory and response  variable.

The explanatory variable is the variable that is manipulated by the researcher. Explanatory Variable also known as the independent or predictor variable, it explains variations in the response variable; in an experimental study, it is manipulated by the researcher.

Response variable: Response Variable is the result of the experiment where the explanatory variable is manipulated. It is a factor whose variation is explained by the other factors. Response Variable is often referred to as the Dependent Variable or the Outcome Variable.

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Answer:

One solution (See explanation for the number)

Step-by-step explanation:

Let's see..

3(x-2)+7x=0.5(6x-2)

3x-6+7x=3x-1

10x-6=3x-1

10x=3x+5

7x=5

x=5/7

Hope this helps :)