Find the polar equation for the ellipse with its focus at the pole, d > 0, and vertices at (1,7) and (5,0). 43

Answer:

(2)(3.141593)v=(6)(3.141593)(120)

Simplify both sides of the equation.

6.283185v=2261.946711

Divide both sides by 6.283185.

6.283185v6.283185=2261.9467116.283185

v=360

Answer:

Step-by-step explanation:

t=0

If you replace t with zero -9=-9(0+1)

0+1=1 and -9(1)=-9

so t=0

Answer:

-2/6 or -1/3

Step-by-step explanation:

2 rise and 6 run

The slope or rise over run of the given line is -1/3.

Slope of the line is defined as the rise over run of the line.

Slope can be calculated by finding the change in the y coordinates to the change in the x coordinates when two points are given.

Slope is usually denoted by m.

From the given line, first we take points.

The point which touches the Y axis is (0, 2)

And we take another point on the line (3, 1)

Slope of the line with two points (x₁, y₁) and (x₂, y₂) is given by,

m = (y₂ - y₁) / (x₂ - x₁)

Substituting the values  (0, 2) and (3, 1) in the equation, we get,

m = (1 - 2) / (3 - 0)

m = -1/3

Hence, the slope of the given line is -1/3

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The two-period moving average model and the two-period weighted moving average model are both common forecasting methods used to predict future demand. and we understand that the model with the lower MAD and MSE values will have the most accurate forecast.

To determine which model is better for this particular data set, we need to compare the accuracy of each model. To do this, we will calculate the Mean Absolute Deviation (MAD) and the Mean Squared Error (MSE) for each model.
For the two-period moving average model, we can calculate the forecast for period 7 by taking the average of p5 and 6:

Period 7 forecast = (Gallons in Period 5 + Gallons in Period 6)/2

For the two-period weighted moving average model, we can calculate the forecast for period 7 by using the weights of 0.6 and 0.4:

Period 7 forecast = (0.6 x Gallons in Period 5) + (0.4 x Gallons in Period 6)

We can then compare the accuracy of each model by calculating the MAD and MSE. To calculate MAD, we need to subtract the actual demand in each period from the forecasted demand and take the absolute value:

MAD = |Actual demand – Forecasted demand|

To calculate MSE, we need to square the differences between the actual demand and the forecasted demand:

MSE = (Actual demand – Forecasted demand)^2

After calculating the MAD and MSE for each model, we can compare the results to determine which model is better for this data set. The model with the lower MAD and MSE values will have the most accurate forecast.

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Answer:

2y=10-5

2y=5

y=5/2

y=2.5

Step-by-step explanation:

you first collect the like terms then you do 5/2 which gives you Y=2.5

Hi

Last repeat the way to find y. Use a scientific calculator to count easier ☺️

Answer:

Exact form: \(\frac{16}{81}\)

Decimal form: 0.1975308

The solution of the equation given as -13x + x = 8x - 20x is infinite many solutions

From the question, the equation is given as

-13x + x = 8x - 20x

To start with, we need to rewrite the expression

So, we have the following representation

x - 13x = 8x - 20x

Solving further, we need to evaluate the like terms

So, we have the following equation

-12x = 8x - 20x

Evaluate the like terms again

So, the equation becomes

-12x = -12x

Both sides of the above equation are the same

i.e. -12x is on both sides of the equation

When we have a solution that all sides of the equation have the same value, then the solution is that the equation has infinite many solutions

Hence, -13x + x = 8x - 20x has infinite solutions

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The value today of $1,400 per year, at a discount rate of 11 percent, with the first payment received 5 years from now and the last payment received 21 years from today, is approximately $6,805.24.

To calculate the value today of future cash flows, we need to discount each cash flow back to its present value using the discount rate. In this case, we have an annuity of $1,400 per year for a total of 17 years (from year 5 to year 21).

Using the formula for the present value of an annuity, which is PV = C * [(1 - (1 + r)^-n) / r], where PV is the present value, C is the cash flow per period, r is the discount rate, and n is the number of periods, we can calculate the present value.

Plugging in the values, we get:

PV = 1400 * [(1 - (1 + 0.11)^-17) / 0.11]

PV ≈ $6,805.24

Therefore, the value today of $1,400 per year, at a discount rate of 11 percent, with the first payment received 5 years from now and the last payment received 21 years from today, is approximately $6,805.24.

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Answer:

{5, 15, 19}

Step-by-step explanation:

According to the triangle inequality theorem, the sum of the lengths of any two sides of a ∆ must be greater than the length of the third side.

Thus, any of the given sets of numbers will represent the 3 sides of a ∆, if the following condition is satisfied:

a + b > c

b + c > a

a + c > b

Where a and b are the smaller side lengths, and c is the length of the longest side.

Let's check each set of numbers given to see if any satisfies this condition.

✍️Option 1: {6, 20, 28}

6 + 20 is not greater than 28

20 + 28 > 6

6 + 28 > 20

❌This set of numbers does not represent the sides of a ∆.

✍️Option 2: {4, 11, 15}

4 + 11 = 15

11 + 15 > 4

4 + 15 > 11

❌This set of numbers does not represent the sides of a ∆.

Option 3: {9, 19, 30}

9 + 19 is not greater than 30

19 + 30 > 9

9 + 30 > 19

❌This set of numbers does not represent the sides of a ∆

Option 4: {5, 15, 19}

5 + 15 > 19

15 + 19 > 5

5 + 19 > 15

✅This set of numbers does not represent the sides of a ∆

Only option 4, satisfied the condition stated earlier, therefore, based on the triangle inequality theorem, {5, 15, 19}, is the set of numbers that represents the 3 sides of a triangle.

The resulting p-value would decrease in both scenarios if we sampled twice as many students but found the same sample proportion as before.

The p-value is the probability of observing a sample proportion as extreme or more extreme than the one calculated from the sample data, assuming the null hypothesis is true. When we increase the sample size, the standard error of the sample proportion decreases, which means that the sample proportion becomes more representative of the population proportion.

In other words, the larger the sample size, the more accurate the estimate of the population parameter (in this case, the proportion of students who support the change). As a result, the difference between the sample proportion and the hypothesized population proportion (under the null hypothesis) is likely to be smaller, leading to a smaller p-value.

To compute the p-value, we use the test statistic, which is a measure of how many standard errors the sample proportion is from the hypothesized population proportion under the null hypothesis. When we increase the sample size, the test statistic becomes larger, which means that the p-value becomes smaller. Therefore, the p-value would decrease if we sample twice as many students but find the same sample proportion as in exercise 6.

In summary, increasing the sample size while keeping the sample proportion constant would result in a smaller p-value, indicating stronger evidence against the null hypothesis.

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Answer: The answer is 3

Step-by-step explanation:

we need to visit 31 households to reach the 6th household with an adult over 65. A. 42 households.

To determine how many households would need to be visited to get to 6 households with an adult over 65, we need to simulate the process using the given list of random numbers.

Starting from the beginning of the list, we count the number of households visited until we reach the 6th household with an adult over 65.

Using the list of random numbers provided:

78 61 83 18 43 27 91 46 50 68 24 37 11 28 92 42 50 94 76 35 78 75 60 70 62 71 54 37 02 28 75 20 18 00 99 84 45 25 80 80 37 91 91 03

The first household with an adult over 65 appears at the 31st position (number 02).

Therefore, we need to visit 31 households to reach the 6th household with an adult over 65.

The correct answer is A. 42 households.

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A congruent polygon refers to two or more polygons that have the same shape and size. There must be an equal number of sides between two polygons for them to be congruent.

Congruent polygons have parallel sides of equal length and parallel angles of similar magnitude. When two polygons are congruent, they can be superimposed on one another using translations, rotations, and reflections without affecting their appearance or dimensions. Concluding about the matching sides, shapes, angles, and other geometric properties of congruent polygons allows us to draw conclusions about them.

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The time of motion of the frog after it jumped into air is determined as 0.8 second.

The time of motion of the frog is determined by solving the quadratic equation as follows;

60t - 75t² = 0

60t = 75t²

divide both sides by t

60 = 75t

divide both sides by 75

60/75 = t

0.8 s = t

Thus, the time of motion of the frog after it jumped into air is determined as 0.8 second.

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(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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The coin is flipped at least 52 times in order to obtain a 99% confidence interval of width of at most . 18 for the probability of flipping a head.

Hence, Option F is correct answer.

In a sample with a number n of people surveyed with a probability of a success of π , and a confidence level of (1-α), we have the following confidence interval of proportions.

\(\pi\) ± z\(\sqrt{\frac{\pi \p(1-\pi )}{n} }\)

z is the z-score that has a pvalue of \(1-\frac{\alpha }{2}\)

Since, the coin is fair, so \(\pi =0.5\).

The margin of error is:

\(M=z\sqrt{(\frac{\pi (1-\pi )}{n} )}\)

99% confidence level:

So \(\alpha =0.01\) ,z is the value of Z that has a p value of 1-\(\frac{0.01}{2}\)=0.995,

so Z= 2.575

We have to flip the coin in order to obtain a 99% confidence interval of width of at most 18 for the probability of flipping a head at least n times.

n is found when M=0.18 .

So

M=\(z\sqrt{\frac{\pi (1-\pi )}{n} }\)

\(0.18=2.575\sqrt{\frac{0.5*0.5}{n} }\)

\(0.18\sqrt{n} =2.575*0.5\)

\(\sqrt{n}=\frac{2.575*0.5}{0.18}\)

\(\sqrt{n} ^{2} =(\frac{2.575*0.5}{0.18} )^{2}\)

n = 51.16

Thus, we have to flip the coin at least 52 times.

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Answer:

138 because if u add 60+78 it equals 138

Answer:

zero or 0 ..

because.. . None of the people watched both types.

138 people ( 60 & 78 ) only watched one type ...... while the remaining 5 people dont watch programmes.

i hope this is correct

The term for the value that occurs most often in a series of numbers is called the mode.

The mode is one of the three main measures of central tendency, along with the mean and the median. It is a useful descriptive statistic that can provide insights into the characteristics of a dataset.

To find the mode of a set of data, you first need to arrange the data in order, either in increasing or decreasing order. Then, you simply identify the most frequent data point, which is the mode. In some cases, there may be more than one mode if multiple data points occur with the same maximum frequency.

The mode is particularly useful when dealing with categorical or nominal data, where there are distinct categories or values that cannot be ordered in a meaningful way. For example, the mode can help identify the most popular color among a group of people or the most common type of car on a given street. It can also be used for continuous data, although it may be less useful in this case than the mean or median.

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\( {x}^{8} + {x}^{4} + 1 - (24)(7) - 45\)

the simplest form.

\( {x}^{8} + {x}^{4} + 1 - (24)(7) - 45\)

\( = {x}^{8} + {x}^{4} + 1 - 168 + - 45\)

\( = ( {x}^{8} ) + ( {x}^{4} ) + (1 + - 168 + - 45)\)

\( = {x}^{8} + {x}^{4} - 212\)

Answer:

1

Step-by-step explanation:

1 is answer.it may help you to understand.

Answer:

(a) The standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

Step-by-step explanation:

We are given that the average annual amount American households spend on daily transportation is $6312 (Money, August 2001). Assume that the amount spent is normally distributed.

(a) It is stated that 5% of American households spend less than $1000 for daily transportation.

Let X = the amount spent on daily transportation

The z-score probability distribution for the normal distribution is given by;

                          Z  =  \(\frac{X-\mu}{\sigma}\)  ~ N(0,1)

where, \(\mu\) = average annual amount American households spend on daily transportation = $6,312

           \(\sigma\) = standard deviation

Now, 5% of American households spend less than $1000 on daily transportation means that;

                      P(X < $1,000) = 0.05

                      P( \(\frac{X-\mu}{\sigma}\) < \(\frac{\$1000-\$6312}{\sigma}\) ) = 0.05

                      P(Z < \(\frac{\$1000-\$6312}{\sigma}\) ) = 0.05

In the z-table, the critical value of z which represents the area of below 5% is given as -1.645, this means;

                           \(\frac{\$1000-\$6312}{\sigma}=-1.645\)                

                            \(\sigma=\frac{-\$5312}{-1.645}\)  = 3229.18

So, the standard deviation of the amount spent is $3229.18.

(b) The probability that a household spends between $4000 and $6000 is given by = P($4000 < X < $6000)

      P($4000 < X < $6000) = P(X < $6000) - P(X \(\leq\) $4000)

 P(X < $6000) = P( \(\frac{X-\mu}{\sigma}\) < \(\frac{\$6000-\$6312}{\$3229.18}\) ) = P(Z < -0.09) = 1 - P(Z \(\leq\) 0.09)

                                                            = 1 - 0.5359 = 0.4641

 P(X \(\leq\) $4000) = P( \(\frac{X-\mu}{\sigma}\) \(\leq\) \(\frac{\$4000-\$6312}{\$3229.18}\) ) = P(Z \(\leq\) -0.72) = 1 - P(Z < 0.72)

                                                            = 1 - 0.7642 = 0.2358  

Therefore, P($4000 < X < $6000) = 0.4641 - 0.2358 = 0.2283.

(c) The range of spending for 3% of households with the highest daily transportation cost is given by;

                    P(X > x) = 0.03   {where x is the required range}

                    P( \(\frac{X-\mu}{\sigma}\) > \(\frac{x-\$6312}{3229.18}\) ) = 0.03

                    P(Z > \(\frac{x-\$6312}{3229.18}\) ) = 0.03

In the z-table, the critical value of z which represents the area of top 3% is given as 1.88, this means;

                           \(\frac{x-\$6312}{3229.18}=1.88\)                

                         \({x-\$6312}=1.88\times 3229.18\)  

                          x = $6312 + 6070.86 = $12382.86

So, the range of spending for 3% of households with the highest daily transportation cost is $12382.86 or more.

If a two-factor analysis of variance produces a statistically significant interaction, it means that the effect of one independent variable on the dependent variable changes depending on the level of the other independent variable.

In other words, the effect of one independent variable on the dependent variable is not the same across all levels of the other independent variable. Therefore, the interaction term is necessary to properly model the relationship between the independent variables and the dependent variable. It is important to interpret the interaction carefully to fully understand the relationship between the variables being studied.

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Step-by-step explanation:

we have two lines you have to draw.

one is all in the bottom left quadrant (for x<=0) and one in the upper right quadrant (for x>5).

the easiest is for x>5. the line function is only

f(x) = y = 3

so, this is a horizontal line on the grid line for y = 3. it starts above x=5 and then goes all the way to the right ("to infinity and beyond !"). just, if possible, mark the starting point at x=5 as a little empty "circle" instead of a full dot, as x=5 is explicitly excluded (due to x>5).

and for x<=0 the line

f(x) = y = 4x - 3

goes sharp down but goes a little bit to the left the further down it goes. it starts with x=0, which gives y=-3 per the function.

so, the starting point (with a full dot, as x=0 is included) is (0,-3).

from there it goes sharp down and a little bit to the left.

for example the next point is for x=-1, which gives y=-7, so it is the point (-1,-7). x=-2 gives y=-11 and the point (-2,-11).

the line has to go through so these points and further down (again, "to infinity and beyond !"), as to move further left on the negative x-axis.

The value of the algebraic expression 11.5x + 10.9y  at x = 6 and y = 7 is 145.3

What is an algebraic expression?

Algebraic expression consists of variables and numbers connected with addition, subtraction, multiplication and division

The given algebraic expression is 11.5x + 10.9y

We have to find the value of the algebraic expression at x = 6 and y = 7

Putting x = 6 and y = 7 in the algebraic expression,

\(11.5 \times 6 + 10.9 \times 7\)

69 + 76.3

145.3

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Answer:

  50.8°

Step-by-step explanation:

The mnemonic SOH CAH TOA is intended to remind you of the relationship between side lengths and trig functions for a right triangle. Here, you are given the short side and the hypotenuse, and asked for the largest acute angle.

__

The short side is adjacent to the largest acute angle, so the relevant relation is ...

  Cos = Adjacent/Hypotenuse

  cos(β) = (2√6)/(2√15) = √0.4

The angle measure is found using the inverse cosine function:

  β = arccos(√0.4) ≈ 50.8°

The larger acute angle is about 50.8°.

15 + 2x = Price

The price of a medium-sized pizza at Desminos Pizza's online menu is $15 plus $2 per topping. The equation for this is 15 + 2x = Price, where x represents the number of toppings.

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Answer:

\({ \rm{ - 2x + 4 = 15x}}\)

-2 & 15

Coefficients (in -2x+4=15x):

What are coefficients?

Coefficients are the constants in an equation.