find the value of x in the figure

The given data is as follows: Hostogram of the collected dataHere, we can see that the data shows how many hours people read per day.  The Chi-Square goodness-of-fit test is a test that determines if an observed distribution of data is a good fit for the proposed or expected theoretical distribution.

The given data shows the frequency of reading hours of people. Hence, the number of degrees of freedom (df) = (number of classes – 1) – k
Here, the number of classes = 6, and the number of parameters = 1 (exponential distribution has one parameter i.e λ)Therefore, the degrees of freedom (df) = 6-1-1 = 4.
The null hypothesis H0: The data follows an exponential distribution.The alternate hypothesis H1: The data does not follow an exponential distribution. The expected frequencies are as follows:
Number of hours (x) Frequency (f)   Midpoint of class (m)Expected frequency (fe)
Observed – Expected (O - E)O – E (O - E)2(O - E)2 / E00.50.25 0.43750.230.33 1.1020.11 0.012 0.04540.70.21 0.57270.651.35 1.8200.42 0.045 0.05471.00.34 0.81360.962.18 4.7370.99 0.129 0.15811.51.02 1.26750.941.73 2.9910.67 0.112 0.13232.01.24 1.5920.310.08 0.00640.004 0.00363.00.78 2.56250.232.22 4.9280.92 0.287 0.186
The test statistic is obtained by calculating the chi-square statistic. To calculate the chi-square statistic, we use the formula:χ2 = Σ(O - E)2 / ESo, χ2 = 0.012 + 0.045 + 0.054 + 0.129 + 0.112 + 0.287 + 0.186= 0.825The p-value is obtained using the chi-square distribution table for the calculated value of chi-square, 0.825, with degrees of freedom of 4. Using the table, the p-value is found to be 0.934.Since the p-value (0.934) is greater than the level of significance α=0.05, we fail to reject the null hypothesis that the data follows an exponential distribution.Thus, we can conclude that the given data follows an exponential distribution.

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We are given a histogram of the collected data to answer the question. If the p-value is less than the significance level, we reject the null hypothesis and conclude that the data does not follow an exponential distribution with the given parameters.

We can see that the data follow an exponential distribution with the given parameters. The chi-square goodness of fit test gives us a test statistic of 19.6. The p-value is less than 0.01. Therefore, we reject the null hypothesis and conclude that the data do not follow an exponential distribution with the given parameters.

To determine whether the given data follows an exponential distribution, we need to use the Chi-Square goodness-of-fit test. The first step is to determine the expected frequencies of the data, assuming that the data follows an exponential distribution with given parameters. Here, the parameters are given as a rate of 2 hours per day. Using the formula for the expected frequencies, we can compute the expected frequencies for each bin in the histogram. The formula is given as:

Expected frequency = N × P

Where N is the total number of observations and P is the probability of the event occurring in the specified bin. The probability of an event occurring in the specified bin is given by the cumulative distribution function of the exponential distribution. For this, we can use the formula:

F(x) = 1 − e^(-λx)

Where λ is the rate parameter and x is the upper limit of the bin. We can use this formula to compute the probabilities for each bin in the histogram. Once we have the expected frequencies, we can compute the test statistic as:

χ² = ∑(O - E)² / E

where O is the observed frequency and E is the expected frequency. Finally, we can use the chi-square distribution table to compute the p-value for the test statistic. If the p-value is less than the significance level, we reject the null hypothesis and conclude that the data does not follow an exponential distribution with the given parameters.

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Answer: 68 seconds

Step-by-step explanation:

Answer: 68sec

Step-by-step explanation:

Answer:

18

Step-by-step explanation:

Answer:

The (population) standard deviation is 26 miles or \( \\ \sigma = 26\) miles.

Step-by-step explanation:

We can solve this question using the concept of z-score or standardized value, which is given by the formula:

\( \\ z = \frac{x - \mu}{\sigma}\) [1]

Where

\( \\ z\) is the z-score.

\( \\ x\) is the raw score.

\( \\ \mu\) is the population's mean.

\( \\ \sigma\) is the population standard deviation.

Analyzing the question, we have the following data to solve this question:

Therefore, using all this information, we can determine the (population) standard deviation using formula [1].

Then, substituting each value in this formula:

\( \\ z = \frac{x - \mu}{\sigma}\)

Solving it for \( \\ \sigma\)

Multiplying each side of the formula by \( \\ \sigma\)

\( \\ \sigma*z = (x - \mu) * \frac{\sigma}{\sigma}\)

\( \\ \sigma*z = (x - \mu) * 1\)

\( \\ \sigma*z = x - \mu\)

Multiplying each side of the formula by \( \\ \frac{1}{z}\)

\( \\ \frac{1}{z}*\sigma*z = \frac{1}{z}*(x - \mu)\)

\( \\ \frac{z}{z}*\sigma = \frac{x - \mu}{z}\)

\( \\ 1*\sigma = \frac{x - \mu}{z}\)

\( \\ \sigma = \frac{x - \mu}{z}\)

Then, this formula, solved for \( \\ \sigma\), will permit us to find the value for the population standard deviation asked in the question.

\( \\ \sigma = \frac{431.8 - 450}{-0.7}\)

\( \\ \sigma = \frac{-18.2}{-0.7}\)

\( \\ \sigma = 26\)

Thus, the (population) standard deviation is 26 miles or \( \\ \sigma = 26\) miles.

Answer:

I am pretty sure its D

Step-by-step explanation:

If u want to be sure tho search up the dilation scale factor on Google:)

The correct statement is C.) The proportion of the variation in height that is explained by a regression on age is 0.64.

The coefficient of determination (R2), which ranges from 0 to 1, expresses how accurately a statistical model forecasts a result.

The correlation Coefficient R = 0.8,  which demonstrates the strong correlation between children's age and height. With the correlation coefficient value, we can calculate the coefficient of determination (R2), which indicates the proportion of variation that the regression model can account for.

Coefficient of determination \((R^{2} ) = 0.8^{2}\)

= 0.64.

0.64 of the variation in children's height that can be attributed to age and 0.36 to other factors.

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missing Options :

A.) On average, the height of a child is 80% of the age of the child.

B.) The least-squares regression line of height versus age will have a slope of 0.8.

C.) The proportion of the variation in height that is explained by a regression on age is 0.64.

D.) The least-squares regression line will correctly predict height based on age 80% of the time.

E.) The least-squares regression line will correctly predict height based on age 64% of the time.

Answer:

60

Step-by-step explanation:

30% of 200 is 60

The division of the polynomials x² - 9x + 6 ÷ x + 1  is (c) x - 10 + 16/(x + 1)

From the question, we have the following parameters that can be used in our computation:

x² - 9x + 6 ÷ x + 1

Using the synthetic division, the set up is

-1  |   1  -9  6

   |__________

Bring down the first coefficient, which is 1 and repeat the process

-1  |   1  -9  6

   |___-1__10_____

        1  -10 16

This means that the quotient is x - 10 and the remainder is 16

So, we have

x² - 9x + 6 ÷ x + 1 = x - 10 + 16/(x + 1)

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The solution of the differential equation is  U=x+2y. (A)

To solve the differential equation (x + 2y)dx + ydy = 0 using substitution, you can use the substitution U = x + 2y.


1. Substitute U for x+2y: dU = (dx + 2dy)

2. Replace (x + 2y)dx + ydy with dU - 2ydy + ydy: dU - ydy = 0

3. Factor out dy: dU - ydy = dy(U - y) = 0

4. Separate variables: (1/dU) dU = dy/y

5. Integrate both sides: ∫(1/dU) dU = ∫(dy/y)

6. Obtain the solution: ln|U| = ln|y| + C

7. Replace U with x+2y: ln|x+2y| = ln|y| + C

8. Exponentiate both sides: x+2y = k*y, where k = e^C

Thus, the differential equation (x + 2y)dx + ydy = 0 can be solved using the substitution U = x + 2y.(A)

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Answer:

Step-by-step explanation:

Please see the 2 attachments

Let's assume the amount invested at the higher interest rate (16%) is x dollars.

The amount invested at the lower interest rate (6%) would then be ($80,000 - x) dollars, as the total investment is $80,000.

The interest earned from the investment at 16% is calculated as (x * 16%) = 0.16x dollars.

The interest earned from the investment at 6% is calculated as (($80,000 - x) * 6%) = 0.06(80,000 - x) dollars.

According to the given information, the retiree receives a total interest of $8,900 per year. So we can set up the equation:

0.16x + 0.06(80,000 - x) = 8,900

Now, let's solve the equation to find the value of x:

0.16x + 0.06(80,000 - x) = 8,900

0.16x + 4,800 - 0.06x = 8,900

0.1x + 4,800 = 8,900

0.1x = 8,900 - 4,800

0.1x = 4,100

x = 4,100 / 0.1

x = 41,000

Therefore, $41,000 is being invested at the higher interest rate (16%).

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To maximize his earnings, John should install 5 Secure alarms and 5 Maximum Secure alarms, and then demonstrate 5 Secure alarms and 2 Maximum Secure alarms.

Let's first consider the time constraints. Since John cannot work more than 40 hours per week, we have the following inequality:

1h(install Secure) x + 2.2h(install Maximum Secure) y + 0.25h(demo Secure) x + 0.4h(demo Maximum Secure) y <= 40

where x and y are the number of Secure and Maximum Secure alarms John installs, respectively.

John is required to work a minimum of 20 hours per week as an installer and a maximum of 20 hours as a demonstrator. So we have the following constraints:

1h(install Secure) x + 2.2h(install Maximum Secure) y >= 20 (minimum hours as installer)

0.25h(demo Secure) x + 0.4h(demo Maximum Secure) y <= 20 (maximum hours as demonstrator)

Now, we can set up the objective function to maximize John's earnings:

E(x,y) = 3(install Secure) x + 3(install Maximum Secure) y + 2(demo Secure) x + 2(demo Maximum Secure) y

= 5x + 5.6y

Using linear programming techniques, we can solve for the optimal values of x and y that maximize the objective function and satisfy the constraints. The optimal values turn out to be x=5 and y=5 for installing alarms, and x=5 and y=2 for demonstrating alarms. Therefore, John should install 5 Secure alarms and 5 Maximum Secure alarms, and then demonstrate 5 Secure alarms and 2 Maximum Secure alarms, to maximize his earnings.

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Answer:

The answer is A

Step-by-step explanation:

Well, there is an actual way of doing it but I forgot how to do it, my calculator got A so yeah, hope that helps

A minimum sample size of 1069 is required to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle such that the margin of error is no more than 0.03 for a 95 percent confidence interval.

In order to estimate the proportion of elementary, middle, and high school teachers who contributed to a candidate during a recent election cycle, a researcher in campaign finance law wants to determine the minimum sample size such that the margin of error is no more than 0.03 for a 95 percent confidence interval.

Assuming that the researcher wants to establish a 95% confidence interval, the level of significance (α) is 1 - 0.95 = 0.05. Furthermore, we can assume that there is no prior knowledge of the population proportion, which is the proportion of elementary, middle, and high school teachers who contributed to a candidate during the election cycle. The standard deviation of a proportion is calculated using the following formula:

\(σ_p=√(p(1−p)/n)\)

Here, n is the sample size and p is the proportion of elementary, middle, and high school teachers who contributed to a candidate during the election cycle. Because there is no prior knowledge of p, it is assumed that the sample proportion, p-hat, is equal to 0.5.

Using these values, we can calculate the minimum sample size required for a margin of error of 0.03 for a 95 percent confidence interval.

α/2=0.025 can be determined by dividing the level of significance (α) by two. This will allow us to calculate the appropriate critical value. To calculate the critical value, we can look up the value of 0.025 in a standard normal distribution table.

Z_α/2=1.96 is the corresponding z-value for a 95% confidence interval.With the critical value, we can now calculate the minimum sample size using the formula below:

\(n = (Z^2) (p) (1 - p) / (E^2)\)

where, Z = critical valueα = level of significance (0.05)

E = margin of error (0.03)

p-hat = 0.5

The minimum sample size for a 95% confidence interval with a margin of error of 0.03 and no prior knowledge of the population proportion is as follows:

\(n = (1.96)^2 (0.5) (0.5) / (0.03)^2n = 1068.44444 ≈ 1069\)

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Answer:

trailing zeros can be ommited and have use in the real value, unless you are separating digits in a number

Step-by-step explanation:

trailing zeros can be ommited and have use in the real value, unless you are separating digits in a number

To find the points where the height of the Gateway Arch is 100 meters, we need to solve the equation y = 100 for x.

Substituting y = 100 into the equation for the central curve of the arch, we get:

100 = 211.49 - 20.96 cosh (0.03291765x)

Rearranging the equation, we get:

cosh (0.03291765x) = (211.49 - 100) / 20.96

cosh (0.03291765x) = 5.21

Taking the inverse hyperbolic cosine of both sides, we get:

0.03291765x = acosh(5.21)

x = (1/0.03291765) acosh(5.21)

Solving for x using a calculator, we get:

x = ± 64.975

Therefore, the height of the Gateway Arch is 100 meters at the points (64.975, 100) and (-64.975, 100).

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The graph of the inequality y ≥ (1/2)x - 1 and x - y > 1 is attached. Shannon's graph is correct.

An equation is an expression that shows the relationship between two or more numbers and variables. Equations can either be linear, quadratic, cubic and so on depending on the degree.

Inequalities are used for the non equal comparison of numbers and variables.

Given the inequalities:

y ≥ (1/2)x - 1     (1)

and

x - y > 1     (2)

The graph of the inequality is attached. Shannon's graph is correct.

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Answer:

$1,461.60

Step-by-step explanation:

Value of the stock in the first year if value increased by 16% = 1500 x (1.16) = $1740

1.16 = 100% + 16% = 116%

Value of the stock in the second year if value decreased by 16% = $1740 x 0.84 = $1,461.60

0.84 = 100% - 16% = 84%

The expression for the mass of the bacteria is m(t) = \(7*2^t\)

to verify the expression we have to evalaute the value of m(t) at different values of t

so m(0) = 7 * 2^0 =7

 m(1) = 7* 2^1 =2* 7 =14

m(2)= 7 * 2^2 =28

m(3) = 7*2 ^3 = 56

we can observe here that every next hour the population of bacteria increases than that of its previous hour

so m(t) = 7 * 2^t is correct expression of the equation

since we have verify the expression for certain value of t i.e 0 ,1 ,2, 3

now we need to find it for any value of t

so the population at t  hours  = 7 * 2^t

population at t-1 hours  is = 7 * 2^(t-1)

so growth rate = \(\frac{m(t)}{m(t-1)} = \frac{ 7* 2^t}{ 7 * 2^(t-1)} = 2\)

so growth rate = 2 which is given in the question , so the above equation satisfies the question conditon

so , m(t) = \(7*2^t\)

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Answer:

3 50/100 or 3 1/2

Step-by-step explanation:

Each 100% is one, so that would equal 3. There would be 50% left, and that would be 50/100 or 1/2.

The roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x=-7 and x=1.

Any equation in algebra that can be written in the standard form where x stands for an unknown value and a, b, and c stand for known values is said to be a quadratic equation.

In general, it is assumed that a > 0; equations with a = 0 are regarded as degenerate since they become linear or even simpler.

So, the roots of 0 = 2x² + 12x-14 are:

2x² + 12x-14  = 0

2x² + 14x - 2x -14

2x(x + 7) - 2(x + 7)

(2x - 2) (x + 7)

Now, use the zero product property as follows:

2x - 2 = 0

2x = 2

x = 2/2

x = 1

And

x + 7 = 0

x = -7

Therefore, the roots of the quadratic equation 0 = 2x² + 12x-14 is (C) x = -7 and x = 1.

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Correct question:

What are the roots of the quadratic equation 0 = 2x² + 12x-14?

a. 1,6, -7

b. 2,12,-14

c. -7,1

d. -1,7

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

We know that Betrys is cooking for 8 people, and we know that a recipe for 2 people needs 10 ounces.

8 people is 4 times 2 people, then for 8 people you need 4 times 10 ounces, this is 4*10 oz = 40 ounces.

Now we can apply a change of units, remember that:

1 oz = 28 grams

Then the total amount she needs is:

40 oz = 40*28 g = 1,120 g

So she needs in total 1,120 grams, and in the balance, she already has 720 grams, so the amount that she needs is given by the subtraction:

1,120 g - 720g = 400

Betrys needs another 400 grams of diced potatoes to make her vegetable stew for 8 people.

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Answer:

Step-by-step explanation:

we call one side x and the other side 4x-7. Because in a rectangle opposite sides are equal we can now set up an equation.

x + x + 4x-7 +4x-7 = 180

              10x - 14 = 180

                   10x = 194

                    x = 19.4

the lenght of the other side is 4(19.4)-7 = 70.6

The system has exactly one solution, which is (p, q) = (-0.2118, -8.0).

We are given the system of equations:

1.7p - 0.34q = 0

0.17(q+1) - 0.85(p-1) = 0

We can simplify the second equation by distributing the 0.17 and 0.85 terms:

0.17q + 0.17 - 0.85p + 0.85 = 0

0.17q - 0.85p = -0.72

Now we have two equations in two variables, which we can solve using substitution or elimination. We will use elimination here.

Multiplying the first equation by 5, we get:

8.5p - 1.7q = 0

Multiplying the second equation by 2, we get:

0.34q - 1.7p = -1.44

Adding these two equations, we get:

6.8p = -1.44

p = -0.2118

Substituting this value of p into either of the original equations, we get:

1.7(-0.2118) - 0.34q = 0

q = -8.0

So the system has exactly one solution, which is (p, q) = (-0.2118, -8.0).

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Answer:

51

Step-by-step explanation:

The coordinate of point P1 (Northing) is 312.84m, and the coordinate of point P1 (Easting) is 276.99m.

To determine the coordinates of point P1, we can use the observed bearing and distance from point A. The observed bearing is N 50°34' W, which means that the angle between the line connecting point A to point P1 and the north direction is 50 degrees and 34 minutes towards the west.

First, let's convert the observed bearing into decimal degrees. To do this, we add the degrees and the minutes:

50° + 34' = 50.57°

Next, we need to calculate the change in coordinates (northing and easting) from point A to point P1 using the observed distance of 78.67m.

To calculate the change in northing, we multiply the distance by the cosine of the observed bearing angle:

Change in northing = 78.67m * cos(50.57°)

To calculate the change in easting, we multiply the distance by the sine of the observed bearing angle:

Change in easting = 78.67m * sin(50.57°)

Now, let's calculate the coordinates of point P1 by adding the change in northing and easting to the coordinates of point A:

Northing of P1 = Northing of A + Change in northing
Easting of P1 = Easting of A + Change in easting

Using the given coordinates of point A:
Northings = 257.78m
Eastings = 345.25m

We can substitute the values into the equations:

Northing of P1 = 257.78m + Change in northing
Easting of P1 = 345.25m + Change in easting

Calculating the changes in northing and easting using a calculator, we get:

Change in northing = 55.06m
Change in easting = -68.26m

Substituting the values back into the equations, we can calculate the coordinates of point P1:

Northing of P1 = 257.78m + 55.06m = 312.84m
Easting of P1 = 345.25m - 68.26m = 276.99m

Therefore, Point P1's Northing coordinate is 312.84 metres, while its Easting coordinate is 276.99 metres.

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