Gallup conducted a poll in September 2021 of parents with children under the age of 12 about whether or not they plan to get their children vaccinated. The poll compared several demographic of the parents, including political party indentification. There were 305 parents who identified as democrat, with 253 of them saying they plan to get their children vaccinated. Test the null hypothesis of no difference between the population proportions of Democrat and republican parents who plan to get their children under the age of 12 vaccinated.
What is the researrch hypothesis?

To find the price at which the designer will sell the maximum number of shirts, we need to determine the vertex of the quadratic function representing the number of shirts sold.

The equation for the number of shirts sold is given by:

S = -4x^2 + 80x - 76

This is a quadratic function in the form of:

S = ax^2 + bx + c

To find the price at which the maximum number of shirts is sold, we need to locate the vertex of the quadratic function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

In this case, a = -4 and b = 80. Plugging in these values, we can calculate the x-coordinate:

x = -80 / (2*(-4))

x = -80 / (-8)

x = 10

Therefore, the designer will sell the maximum number of shirts at a price of $10. Hence, the correct option is c) $10.

It takes approximately 417 seconds, or about 7 minutes, to flush the tank until there is only 2 micrograms of the contaminant left. To estimate the time it takes to flush the tank, we can use the concept of exponential decay.

The rate of decrease of the contaminant concentration in the tank is proportional to the current concentration. Mathematically, we can express this relationship as:

dC/dt = -kC

where C is the concentration of the contaminant in the tank at time t, and k is the decay constant.

Given that the initial concentration is 2 grams and the final concentration is 2 micrograms (10^-6 grams), we can find the value of k:

2 grams = 2 x 10^6 micrograms

k * 200 litres = -ln(10^-6 / 2) = ln(2 x 10^6)

k = ln(2 x 10^6) / 200

Now, let's estimate the time it takes to reach the final concentration using the exponential decay formula:

C(t) = C0 * e^(-kt)

where C0 is the initial concentration, C(t) is the concentration at time t, and e is the base of the natural logarithm.

To simplify the estimation, we'll use the fact that ln(2) is approximately 0.7. Therefore, ln(2 x 10^6) is approximately 0.7 + 6 = 6.7.

Using this approximation, we can find the decay constant:

k = 6.7 / 200 = 0.0335 (approximately)

To estimate the time, we need to solve for t in the equation:

10^-6 = 2 * e^(-0.0335t)

Taking the natural logarithm of both sides:

ln(10^-6 / 2) = -0.0335t

Using the approximation ln(10^-6 / 2) ≈ -14, we have:

-14 = -0.0335t

Solving for t:

t ≈ 14 / 0.0335 ≈ 417 (approximately)

Therefore, it takes approximately 417 seconds, or about 7 minutes, to flush the tank until there is only 2 micrograms of the contaminant left.

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The equation of the perpendicular bisector of the line segment with endpoints (1,6) and (-9,-2) is y = (-5/4)x - 3.

Any location on the perpendicular bisector is equally spaced from the line segment's terminal points, according to the perpendicular bisector theorem.

These procedures must be taken in order to determine the equation of a line segment's perpendicular bisector:

Determine the line segment's midway.

Determine the line segment's slope.

In order to determine the slope of the perpendicular bisector, calculate the negative reciprocal of the slope.

To determine the equation of the perpendicular bisector, use a line's point-slope form.

These procedures allow us to determine the equation for the perpendicular bisector of the line segment with ends (1, 6) and (-9, -2), which is as follows:

Midpoint: The midpoint of the line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates:

Midpoint = ((1 + (-9))/2, (6 + (-2))/2)

= (-4, 2)

Slope: The slope of the line segment can be found using the formula:

slope = (change in y) / (change in x)

slope = (6 - (-2)) / (1 - (-9))

= 8/10

= 4/5

Negative reciprocal: The slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment:

slope of perpendicular bisector = -1 / slope

= -1 / (4/5)

= -5/4

Equation: We can now use the point-slope form of a line to find the equation of the perpendicular bisector. We will use the midpoint of the line segment as the point on the line:

y - y1 = m(x - x1)

where m is the slope of the perpendicular bisector, and (x1, y1) is the midpoint of the line segment. Substituting the values we found, we get:

y - 2 = (-5/4)(x + 4)

Simplifying, we can write the equation in slope-intercept form:

y = (-5/4)x - 3

Hence, the equation of the perpendicular bisector of the line segment with endpoints (1,6) and (-9,-2) is y = (-5/4)x - 3.

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Answer:

The equation is x = -5

The slope is 0

Step-by-step explanation:

If the line is perpendicular to the x axis, that means it is a vertical line.

Vertical lines only reach one x value, which is -5 in this case.

So, the equation will simply be x = -5.

The slope is 0.

Weight of a 24 square foot, 2 inch thick aluminum plate will be: 720 lbs.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: weight of a 24 square foot, 2 inch thick aluminum plate

Finding:

By unitary method, we get:

Weight of 1 square foot aluminum plate = 15 lbs.

Weight of 24 square foot aluminum plate = 15(24) lbs = 360 lbs.

Again, by unitary method, we get:

Weight of 1 square foot, 1 inch thick aluminum plate = 15 lbs.

Weight of 24 square foot, 1 inch thick aluminum plate = 15(24) lbs = 360 lbs.

Weight of 24 square foot, 2 inch thick aluminum plate = 360(2) lbs = 720 lbs.

Hence, Weight of 24 square foot, 2 inch thick aluminum plate = 720 lbs.

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Answer:

7598.8 \(cm^{2}\)

Step-by-step explanation:

v (volume) = π\(r^{2}\)h

v = 3.14 x \(11^{2}\) x 20

v = 3.14 x 121 x 20

v = 7598.8

Answer:

7598.8 cm³

Step-by-step explanation:

Given :-

height = 20 cm

radius = 11 cm

value of π = 3.14

Formula to be used :-

Volume of cylinder = πr²h

Inputting the values :-

V = 3.14 x 11 x 11 x 20

= 3.14 x 121 x 20

= 3.14 x 2420

= 7598.8 cm³

Answer:

12 i think im not exactly shore

Step-by-step explanation:

The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Answer:7

Step-by-step explanation:

100/20 = 5

35/5 = 7

Answer:

Harry has a loan of $9000 in total. Harry obtained a loan from the bank. Explanation Harry's remaining debt, expressed in dollars, is modeled as a function of time t, expressed in months, by the function D(t). The role is played by, This function can be used to determine that $200 is being subtracted each month from the function, meaning Harry is paying $200 toward his loan. Harry has not yet made any payments, therefore we may set t=0 to obtain the total amount of his solo. Therefore, the value of D(t) will reveal the loan's net amount. Harry's borrowing, therefore, equals to $9000.

Step-by-step explanation:

As,

x + 14 + 3x = 90 [Complementary Angles]

=> 4x = 90 - 14

=> 4x = 76

\( = > x = \frac{76}{4} \)

=> x = 19

Hence,

<1 = x + 14°

= 19 + 14 = 33°

<2 = 3x

= 3 × 19° = 57°

The optimal solution, obtained through graphical method, is: x₁ = 4, x₂ = 2, with the maximum value of Z = 80.

To solve the given linear programming problem graphically, we start by plotting the feasible region defined by the constraints:

Constraint 1: 10x₁ + 20x₂ ≤ 120

Constraint 2: 8x₁ + 8x₂ ≤ 80

Non-negativity constraint: x₁ ≥ 0, x₂ ≥ 0

The feasible region is the area of the graph that satisfies all the constraints.

Next, we calculate the objective function Z = 12x₁ + 16x₂. We plot the objective function as a line on the graph.

The optimal solution, which maximizes Z, is the point where the objective function line intersects the boundary of the feasible region.

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Answer:

x=15

Step-by-step explanation:

Well we start with the fundamentals of a triangle we know that all the angles of a triangle add up to 180*, so you can start by adding 55* and 65* and end up with 120* then you can add 30* and get 150* then you can take the total of 150* and subtract it from 180* to get 30 now you take that 30 and divide it by 2 and get 15* for the final angle of the triangle.

Line a & b are parallel

Line c is perpendicular to both lines a & b

Step-by-step explanation:

Let's solve for y in all the lines, starting with line a

-3x - 12y = 36

Add 3x to both sides

-3x - 12y = 36

+ 3x          + 3x

-12y = 3x + 36

Divide both sides by -12

-12y/-12 = (3x + 36)/-12

y = -x/4 - 3

Now for line b

x + 4y = 2

- x      - x

4y = -x + 2

4y/4 = (-x + 2)/4

y = -x/4 + .5

Since line a and b have the same slop, they are parallel

Notice how their slops are opposite and flipped of line c, 4x, making them perpendicular to line c.

Green = line a

Blue = line b

Purple = line c

Answer:

The answer would be

Step-by-step explanation:

A. develop a point estimate of the population mean number of units sold per month.

I must say, I do hope this helps so good luck dude

Answer:

4 times

Step-by-step explanation:

1. 16 cups in a gallon

2. 16 total cups divided by 4 available cups in water bottle equals 4 times

A residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.

The residual plot is a graphical tool used to assess the appropriateness of the line of best fit or the regression model for the data. It helps to examine the distribution and patterns of the residuals, which are the differences between the observed data points and the predicted values from the regression model.

In a residual plot, the horizontal axis typically represents the independent variable or the predicted values, while the vertical axis represents the residuals. The residuals are plotted as points or dots, and their pattern can provide insights into the line of best fit.

To determine if the line of best fit is appropriate, you would generally look for the following characteristics in the residual plot:

Randomness: The residuals should appear randomly scattered around the horizontal axis. If there is a clear pattern or structure in the residuals, it suggests that the line of best fit is not capturing all the important information in the data.

Constant variance: The spread of the residuals should remain relatively constant across the range of predicted values. If the spread of the residuals systematically increases or decreases as the predicted values change, it indicates heteroscedasticity, which means the variability of the errors is not constant. This suggests that the line of best fit may not be appropriate for the data.

Zero mean: The residuals should have a mean value close to zero. If the residuals consistently deviate above or below zero, it suggests a systematic bias in the line of best fit.

It's important to note that a residual plot alone does not provide a definitive answer about the appropriateness of the line of best fit. It should be used in conjunction with other diagnostic tools, such as examining the regression coefficients, goodness-of-fit measures (e.g., R-squared), and conducting hypothesis tests.

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Answer:

Step-by-step explanation:

(3x+8)(x+4), distribute 3x over the second parenthesis first and then the 8

3x² + 12x + 8x + 32 , combine like terms

3x² + 20x + 32

Answer:

3x^2 + 20x + 32

Step-by-step explanation:

Distribute 3x over the second parenthesis first and then the 8.

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Answer:

y=5x

Step-by-step explanation:

If y is 25 and x is 5

25 = 5 (5)

25=25

(a) The real discrete Fourier transform (DFT) is calculated for the given data set to analyze the helicopter's acoustic signature.

(b) To obtain the ck values and illustrate the relative size of each term in the Fourier series, we calculate the magnitude of each coefficient and plot their amplitudes on a bar graph against the corresponding frequency component, k.

To analyze the helicopter's acoustic signature, the real DFT is computed for the provided data set. The DFT transforms the time-domain measurements of acoustic pressure into the frequency domain, revealing the different frequencies present and their corresponding amplitudes. This analysis helps in understanding the spectral characteristics of the helicopter's acoustic signature and identifying prominent frequency components.

Using the Fourier series representation, the amplitudes (ck's) of the different frequency components in the Fourier series are determined. These amplitudes represent the relative sizes of each term in the series, indicating the contribution of each frequency component to the overall acoustic signature. By plotting the amplitudes on a bar graph, the relative strengths of different frequency components become visually apparent, enabling a clear comparison of their importance in characterizing the helicopter's acoustic signature.

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Answer:4 1/4

Step-by-step explanation:

1 3/4 + 2 1/4 + 1/4= 4 1/4

Answer: it’s the second one

Step-by-step explanation:

The standard deviation of the costs is 37 Dhs

The given mean is 173 and 3% of costs exceed 243. We have to calculate the standard deviation of the cost. Therefore, let's first start by calculating the z-score as follows;z-score formula = `(x - μ) / σ`z-score = `243 - 173 / σ`z-score = `70 / σ`We need to find the standard deviation of the costs. Since the z-score formula includes standard deviation, we can first calculate the z-score and then use it to calculate the standard deviation.Using the z-table, we can find the z-score for 3% = -1.88-1.88 = (243 - 173) / σσ = (243 - 173) / -1.88σ = -70 / -1.88σ = 37.23≈ 37The standard deviation of the costs is 37 Dhs. Hence, the correct option is as follows.Option D is the correct option.

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In the given scenario, angle DBC is 51 degrees, and line segment BD is a diameter of circle E. Circle E is inscribed within triangle BCD, where BD is also a diameter.

Line segments DC and CB are secants. We need to determine the measure of arc BC.

Since line segment BD is a diameter, angle BDC is a right angle, measuring 90 degrees. We are given that angle DBC is 51 degrees. In a circle, an inscribed angle is equal to half the measure of its intercepted arc.

Therefore, the measure of arc BC can be calculated as follows:

Arc BC = 2 * angle DBC = 2 * 51 degrees = 102 degrees.

Hence, the measure of arc BC is 102 degrees.

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Answer:

The common difference is 2.

Answer:

The common difference of the arithmetic sequence 14, 16, 18 is **2**.

In any arithmetic sequence, each term is equal to the previous term plus the common difference. So, the second term is equal to the first term plus the common difference. In this case, the second term, 16, is 2 more than the first term, 14. Therefore, the common difference is 2.

We can also find the common difference by subtracting any two consecutive terms in the sequence. For example, we can subtract the second term from the third term to get 18 - 16 = 2.

The common difference of an arithmetic sequence is always constant. This means that the difference between any two consecutive terms in the sequence will always be the same. In this case, the difference between any two consecutive terms is 2.

Step-by-step explanation:

Answer:

8%

Step-by-step explanation:

If he earned $120 out of $1500, just do 120/1500 which will give you 0.08 which is 8 percent.

hi

here is  the  method :

you take  Value 1  and Value 2

And you do :   ( Value 2 - Value 1)  / (Value 1 )    * 100

Here we have :    Value 1 = 352 000

                            Value 2 =  337 920

So now we apply :

( 337 920 - 352 000 )  /  ( 352 000)   * 100 =  -4  

Population decreased by by  4 %

You can also make :  

352 000 * X = 337 920

                 X =  337 920 / 352 000

                 X = 0.96

if  the multiplier is  0.96 ,  it's mean that we lost  1 -0.96 = 0.04  

which mean  - 4%

The solution is,  the percent decrease is 4%.

A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

here, we have,

One year, the population of a city was 352,000.

Several years later it was 337,920.

now,

the  method :

you take  Value 1  and Value 2

And you do :   ( Value 2 - Value 1)  / (Value 1 )    * 100

Here we have :    Value 1 = 352 000

                           Value 2 =  337 920

So now we apply :

( 337 920 - 352 000 )  /  ( 352 000)   * 100 =  -4  

Population decreased by by  4 %

You can also make :  

352 000 * X = 337 920

                X =  337 920 / 352 000

                X = 0.96

if  the multiplier is  0.96 ,  it's mean that we lost 1 -0.96 = 0.04  

which mean is  4%

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