Of 43 bank customers depositing a check, 18 received some cash back. (a) Construct a 90% confidence interval for the proportion of all depositors who ask for cash back. (Do not round the intermediate answers. Round your answers to 4 decimal places.)

Answer:

the last one is -4 the first one -2 I think

Step-by-step explanation:

im at this level of math

Answer:

a. True, because they are corresponding angles.

b. False, because angles 1 and 2 are supplementary, meaning that they add up to 180 degrees, but 125 + 65 = 190 degrees.

c. True, because they are corresponding angles.

d. True, becuase they are two angles that add up to 180 degrees.

e. True, because they are both interior angles on opposite sides of the transversal.

Answer:

a. True.

b. False.

c. True.

d. True.

e. True.

Step-by-step explanation:

a. This statement is true because angles 6 and 8 are vertical angles. That means they are congruent.

b. This statement is false because Elm Street is a straight line, which means that angles 1 and 2 are supplementary angles and their measures will add up to be 180 degrees. 65 + 125 = 190, which is not equal to 180.

c. This statement is true because angles 5 and 1 correspond to each other.

d. This statement is true because angles 7 and 8 form a straight line.

e. This statement is true because they are interior angles that are alternate.

Hope this helps!

Answer:

C. 7

Step-by-step explanation:

got em all right on plato

In a crossover trial comparing a new drug to a standard, all statistical tests and confidence intervals support the conclusion that the new drug is better. The required sample size is at least 692.

In a crossover trial comparing a new drug to a standard, π denotes the probability that the new one is judged better. In 20 independent observations, the new drug is better each time. The null and alternative hypotheses are H0: π = 0.5 and Ha: π ≠ 0.5.

a. The likelihood function is given by the formula: \(L(\pi|X=x) = (\pi)^{20} (1 - \pi)^0 = \pi^{20}.\). Thus, the likelihood function is a function of π alone, and we can simply maximize it to obtain the maximum likelihood estimate (MLE) of π as follows: \(\pi^{20} = argmax\pi L(\pi|X=x) = argmax\pi \pi^20\). Since the likelihood function is a monotonically increasing function of π for π in the interval [0, 1], it is maximized at π = 1. Therefore, the MLE of π is\(\pi^ = 1.\)

b. To conduct a Wald test for the null hypothesis H0: π = 0.5, we use the test statistic:z = (π^ - 0.5) / sqrt(0.5 * 0.5 / 20) = (1 - 0.5) / 0.1581 = 3.1623The p-value for the test is P(|Z| > 3.1623) = 0.0016, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the new drug is better than the standard. The 95% Wald confidence interval for π is given by: \(\pi^ \pm z\alpha /2 * \sqrt(\pi^ * (1 - \pi^) / n) = 1 \pm 1.96 * \sqrt(1 * (1 - 1) / 20) = (0.7944, 1.2056)\)

c. To conduct a score test, we first need to calculate the score statistic: U = (d/dπ) log L(π|X=x) |π = \(\pi^ = 20 / \pi^ - 20 / (1 - \pi^) = 20 / 1 - 20 / 0 =  $\infty$.\). The p-value for the test is P(U > ∞) = 0, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the new drug is better than the standard. The 95% score confidence interval for π is given by: \(\pi^ \pm z\alpha /2 * \sqrt(1 / I(\pi^)) = 1 \pm 1.96 * \sqrt(1 / (20 * \pi^ * (1 - \pi^)))\)

d. To conduct a likelihood-ratio test, we first need to calculate the likelihood-ratio statistic:

\(LR = -2 (log L(\pi^|X=x) - log L(\pi0|X=x)) = -2 (20 log \pi^ - 0 log 0.5 - 20 log (1 - \pi^) - 0 log 0.5) = -2 (20 log \pi^ + 20 log (1 - \pi^))\)

The p-value for the test is P(LR > 20 log (0.05 / 0.95)) = 0.0016, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the new drug is better than the standard. The likelihood-based 95% confidence interval for π is given by the set of values of π for which: LR ≤ 20 log (0.05 / 0.95)

e. To estimate the probability of preferring the new drug to within 0.05 at a confidence level of 95%, we need to find the sample size n such that: \(z\alpha /2 * \sqrt(\pi^ * (1 - \pi{^}) / n) ≤ 0.05\), where zα/2 = 1.96 is the 97.5th percentile of the standard normal distribution, and π^ = 0.90 is the true probability of preferring the new drug.Solving for n, we get: \(n ≥ (z\alpha /2 / 0.05)^2 * \pi^ * (1 - \pi^) = (1.96 / 0.05)^2 * 0.90 * 0.10 = 691.2\). The required sample size is at least 692.

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Answer:

Question 2: 6x-21

Question 1: -9x+3

Step-by-step explanation:

After d days, the number of lily pads in the pond can be calculated using the formula 2^d. So, if d is the number of days, then the number of lily pads after d days would be 2^d.

Each day, the number of lily pads doubles. So, on the first day, there is 1 lily pad. On the second day, the number doubles to 2. On the third day, it doubles again to 4, and so on. This doubling pattern continues for d days.

To calculate the number of lily pads after d days, we raise 2 to the power of d (2^d). This is because each day, the number of lily pads doubles, which can be represented as 2^1, 2^2, 2^3, and so on. By substituting the value of d into the equation, we can find the number of lily pads after d days.

For example, if d = 5, then the number of lily pads after 5 days would be 2^5 = 32. This means that there would be 32 lily pads in the pond after 5 days.

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Answer:

I think it's 11/6 I think so

Answer:

4-5i

Step-by-step explanation:

Answer:

4-5i

Step-by-step explanation:

(5-2i)-(1+3i)

5-2i-1-3i

5-1-2i-3i

4-5i

The computation shows that the placw on the hill where the cannonball land is 3.75m.

To find where on the hill the cannonball lands

So 0.15x = 2 + 0.12x - 0.002x²

Taking the LHS expression to the right and rearranging we have:

-0.002x² + 0.12x -.0.15x + 2 = 0.

So we have -0.002x²- 0.03x + 2 = 0  

I'll multiply through by -1 so we have

0.002x² + 0.03x -2 = 0.

This is a quadratic equation with two solutions x1 = 25 and x2 = -40 since x cannot be negative x = 25.

The second solution y = 0.15 * 25 = 3.75

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Complete question:

The flight of a cannonball toward a hill is described by the parabola y = 2 + 0.12x - 0.002x 2 . the hill slopes upward along a path given by y = 0.15x. where on the hill does the cannonball land?

it would equl 3.7 kg

Answer:

Exact Form:

x=3/8e^2

Decimal Form:

x=0.05075073…

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

you have to be above ambitious to unlock brainiest answer

Step-by-step explanation:

Answer:

You got wait for 2 people to answer to this then at the bottom right theirs a crown click n that’s how u give brainliest

Step-by-step explanation:

The average rate of change of the function f(x) = √(x-1) over the interval 2≤x≤6 is approximately 0.35.

To find the average rate of change of a function over a given interval, we need to calculate the difference in function values at the endpoints of the interval and divide by the difference in the input values. In this case, we are given the function f(x) = √(x-1) and the interval 2≤x≤6. So, we need to calculate:

[f(6) - f(2)] / [6 - 2]

To do this, we first need to find the function values at the endpoints:

f(6) = √(6-1) = √(5)

f(2) = √(2-1) = 1

Now, we can substitute these values into the formula:

[f(6) - f(2)] / [6 - 2] = [√(5) - 1] / 4

Using a calculator, we can evaluate this expression to the nearest hundredth:

[f(6) - f(2)] / [6 - 2] ≈ 0.35

This means that the function increases at an average rate of 0.35 units for every 1 unit increase in x over this interval.

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The solutions to the equation 8 sin(x) - x = 0 in the interval [0, 2π) are approximately x ≈ 0.860, x ≈ 3.425, and x ≈ 6.065.

To approximate the solutions of the equation, we can use a graphing utility to plot the equation and identify the x-values where the graph intersects the x-axis. In this case, we are looking for the x-values that satisfy the equation 8 sin(x) - x = 0.

By using a graphing utility and restricting the x-values to the interval [0, 2π), we can see that the graph intersects the x-axis at approximately x ≈ 0.860, x ≈ 3.425, and x ≈ 6.065.

These are the approximate solutions to the equation 8 sin(x) - x = 0 in the interval [0, 2π), rounded to three decimal places.

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Answer:

Negative 12

Step-by-step explanation:

-10 ≥ 2x + 14

-24 ≥ 2x [subtract 14 from both sides]

2x ≤ -24 [read right to left]

x ≤ -12  [divide both sides by 2]

Answer:

Step-by-step explanation:

because is not equal

To educate a patient on how to judge the appropriate size of a serving of chicken or lean beef, a good estimate of a 3-ounce serving size is a typical deck of cards or the palm of their hand. This will help them make healthy choices and keep track of their portions. So, a good estimate of a 3-ounce serving size is a typical deck of cards or the palm of your hand.

A serving size is a standardized amount of food or drink that is intended to make it easier for people to compare the nutritional content of different products and understand how much they are consuming. A serving size might be listed on a food label or recommended as part of a healthy eating plan or diet.

The recommended serving size for different foods and beverages can vary depending on several factors, including a person's age, sex, and physical activity level, as well as the nutrient content of the food or drink.

For example, a serving of fresh vegetables might be 1 cup, while a serving of meat, poultry, or fish might be 3 ounces. A good estimate of a 3-ounce serving size is a typical deck of cards or the palm of your hand. This can help you make healthy choices and keep track of your portions.

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Answer:

y = 36

Step-by-step explanation:

4(9) = 4 x 9 = 36

The given sequence is `an = 4n / (1 + 5n)`.

To determine whether the sequence converges or diverges, we need to find the limit of the sequence.Here,lim n→[infinity] an = lim n→[infinity] 4n / (1 + 5n)

On simplifying the above expression,lim n→[infinity] an = lim n→[infinity] 4 / (5/n + 1)

The limit is of the form `k / ∞`, where k is a finite number.

Therefore,lim n→[infinity] an = 0

Thus, the given sequence converges, and its limit is 0.

Hence, the correct option is A.

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The given system with two coupled subsystems has an undamped natural frequency of 6.714 rad/s and a damping ratio of 0.3001.

The given system consists of two coupled subsystems: a rotational system and a field-controlled motor system. The rotational system is described by the equation of motion 30 dtdt​ + 10w = T(t), where T(t) is the torque applied by an electric motor. The motor system is modeled by the equation 0.001 dtdi​ + 5i = v(t), where i is the field current in amperes and v(t) is the voltage applied to the motor.

The damping ratio of the combined system can be determined by dividing the sum of the two time constants by the undamped natural frequency, i.e. ζ = (τ1 + τ2)ωn​. Given the time constants of the rotational and motor systems as 3 seconds and 0.001 seconds respectively, and the undamped natural frequency as ωn​ = 10 rad/s, we can calculate the damping ratio as ζ = (3 + 0.001) x 10 / 10 = 0.3001.

The combined system's undamped natural frequency is determined by solving the characteristic equation of the system, which is given by (30I + 10ωs)(0.001s + 5) = 0, where I is the identity matrix. This yields the roots s = -0.1667 ± 6.714i. The undamped natural frequency is therefore ωn​ = 6.714 rad/s.

In summary, the given system with two coupled subsystems has an undamped natural frequency of 6.714 rad/s and a damping ratio of 0.3001.

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We have

\(\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} \vec f(\vec r(t)) \cdot \dfrac{d\vec r}{dt} \, dt\)

and

\(\vec f(\vec r(t)) = 5\sin(t) \, \vec\imath - \cos(t) \, \vec\jmath + t \, \vec k\)

\(\vec r(t) = \sin(t)\,\vec\imath + \cos(t)\,\vec\jmath + t\,\vec k \implies \dfrac{d\vec r}{dt} = \cos(t) \, \vec\imath - \sin(t) \, \vec\jmath + \vec k\)

so the line integral is equilvalent to

\(\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (5\sin(t) \cos(t) + \sin(t)\cos(t) + t) \, dt\)

\(\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (6\sin(t) \cos(t) + t) \, dt\)

\(\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (3\sin(2t) + t) \, dt\)

\(\displaystyle \int_C \vec f \cdot d\vec r = \left(-\frac32 \cos(2t) + \frac12 t^2\right) \bigg_0^{\frac{3\pi}2}\)

\(\displaystyle \int_C \vec f \cdot d\vec r = \left(\frac32 + \frac{9\pi^2}8\right) - \left(-\frac32\right) = \boxed{3 + \frac{9\pi^2}8}\)

Answer:6

Step-by-step explanation:

factor the quadratic

(x-6)(x-6)=0

x=6

Step-by-step explanation:

I have explained everything in the picture, I hope you can see it and if any questions please do ask.

The task involves modifying the given code to implement binary search on an array in descending order. The logic of the code needs to be adjusted accordingly.

The task requires modifying the existing code to perform binary search on an array sorted in descending order. In the original code, the logic for the ascending order was based on comparing the key with the middle element of the list. However, in the descending order case, we need to adjust the logic.

To implement binary search on a descending array, we need to swap the order of the conditions in the code. Instead of checking if the key is less than the middle element, we need to check if the key is greater than the middle element. Similarly, the condition for equality also needs to be adjusted.

The modified code for binary search in descending order would look like this:

public static int binarysearch2(int[] list, int key) {

   int low = 0;

   int high = list.length - 1;

   while (high >= low) {

       int mid = (low + high) / 2;

       if (key > list[mid])

           high = mid - 1;

       else if (key < list[mid])

           low = mid + 1;

       else

           return mid;

   }

   return -1; // Not found

}

By swapping the conditions, we ensure that the algorithm correctly searches for the key in a descending ordered array.

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All rational functions can be expressed as f(x)=p(x)/q(x), where p and q are polynomial functions and q(x) cannot be equal to 0.

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are polynomial functions and q(x) ≠ 0.

Rational function is the ratio of two polynomial functions where the denominator polynomial is not equal to zero. It is usually represented as R(x) = P(x)/Q(x), where P(x) and Q(x) are polynomial functions. In past grades, we learnt the concept of the rational number. It is the quotient or ratio of two integers, where the denominator is not equal to zero. Hence, the name rational is derived from the word ratio

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Answer:

y2=3

Step-by-step explanation:

4y2+7=19

Subtract 7 from both sides.

4y  2 =19−7

Subtract 7 from 19 to get 12.

4y2=12

Divide both sides by 4.

y2= 12/4

Divide 12 by 4 to get 3.

y2=3

​  

Answer:

4y2 + 7 = 19

Step-by-step explanation:

4y2 =19-7

4y2=12

4yx2=12

8y=12

dbs by 8

y=1.5 or 2

Answer:

D

Step-by-step explanation:

V40+8V10+V90

= V4×V10+ 8V10+ V9×V10

= 2V10+8V10+3V10

=13V10

Answer:

image is unclear

Step-by-step explanation:

Answer:

The correct expression to solve for z is z = 8 tan 22°. This expression uses the tangent function and the angle measure in degrees to find the value of z. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle, and the angle measure must be in degrees in order to use the tangent function. The other answer choices do not use the tangent function or the angle measure in degrees, so they are not correct.

Step-by-step explanation:

Answer:

Step-by-step explanation:

\(a_1=8\\a_2=48\\a_3=288\\\\288:48=6\\48:8=6\\\\ \dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}= 6\)

Therefore it's geometric sequence with common ratio of 6

\(a_n=a_1\cdot r^{n-1}\\\\a_1=8\\r=6\\\\a_n=8\cdot6^{n-1}\)