Plz help me!!!!!!!!!!!!!

The sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.

The power of a test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. In this case, we wish to find the power of the z-test to detect a difference of δ1 - δ2 = 0.1 when the sample size is 100 and the significance level is 0.05.

a) First, we need to find the critical value for the z-test at a significance level of 0.05. This can be found using a z-table or a calculator. The critical value is 1.645.

Next, we need to find the standardized difference between the two means, which is (δ1 - δ2)/√(2δ^2/n) = (0.1)/√(2(1)^2/100) = 0.1/√(0.02) = 0.7071.

Finally, we can find the power of the test by subtracting the standardized difference from the critical value and finding the corresponding probability from a z-table or calculator. The power is 1 - P(Z < 1.645 - 0.7071) = 1 - P(Z < 0.9379) = 1 - 0.8264 = 0.1736.

Therefore, the power of the z-test to detect a difference of δ1 - δ2 = 0.1 with a sample size of 100 and a significance level of 0.05 is 0.1736.

b) To find the sample size needed to detect µ1 - µ2 = 1 with power at least 80%, we can use the formula for power:

Power = 1 - P(Z < (critical value - standardized difference))

We can rearrange this formula to solve for the sample size:

Standardized difference = (critical value - Z value corresponding to power)/√(2δ^2/n)

n = (2δ^2(critical value - Z value corresponding to power)^2)/(standardized difference)^2

Plugging in the values for critical value (1.645), Z value corresponding to power (0.8416), and standardized difference (1), we get:

n = (2(1)^2(1.645 - 0.8416)^2)/(1)^2 = 322.69

Therefore, the sample size needed to detect µ1 - µ2 = 1 with power at least 80% is approximately 323.

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The range of the function g(x) = |x - 12| - 2 is {y | y > -2}, indicating that the function can take any value greater than -2.

To find the range of the function g(x) = |x - 12| - 2, we need to determine the set of all possible values that the function can take.

The absolute value function |x - 12| represents the distance between x and 12 on the number line. Since the absolute value always results in a non-negative value, the expression |x - 12| will always be greater than or equal to 0.

By subtracting 2 from |x - 12|, we shift the entire range downward by 2 units. This means that the minimum value of g(x) will be -2.

Therefore, the range of g(x) can be written as {y | y > -2}, which means that the function can take any value greater than -2. In other words, the range includes all real numbers greater than -2.

Visually, if we were to plot the graph of g(x), it would be a V-shaped graph with the vertex at (12, -2) and the arms extending upward infinitely. The function will never be less than -2 since we are subtracting 2 from the absolute value.

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Answer:

Integer - 72

Decimal - 72.3

Answer:

.here is the answer ............

Your twin is likely to visit the dentist more frequently than you due to the difference in insurance plans.

Based on the given information, your insurance plan has a fixed copay of $40 for each doctor's visit, while your twin's copay is 20% of the total cost. Considering the local dentist charges $150 for a cleaning, you would pay a fixed copay of $40 regardless of the total cost. On the other hand, your twin's copay would be 20% of $150, which amounts to $30. Therefore, your twin would have a lower out-of-pocket expense for each dentist visit compared to you.

Due to the lower copay, your twin is more likely to visit the dentist more frequently. The difference in copayments means that your twin would save $10 on each visit, making it more cost-effective for them to seek dental care. This financial advantage would incentivize your twin to take better advantage of their insurance plan and visit the dentist more often.

Based on this reasoning, it is unlikely that you and your twin would visit the dentist the same number of times. Furthermore, there is no indication in the given information that your twin would switch insurance plans, as their plan offers a more favorable copayment structure for dental visits.

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The expression 1 in 8 can be expressed either as a fraction or as a decimal in the form \( \frac{1}{8} \: or 0.125 \: \) respectively

A 1 in 8 chance of winning a game means that the probability of winning is \( \frac{1}{8}\)

Another way to express this is to find the decimal equivalence of the expression ;

Expressing as a decimal :

Therefore, ways of expressing the expression 1 in 8 is \( \frac{1}{8} \: or 0.125 \)

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the curl of the vector field f is (0, 0, 8y).

To compute the curl of a vector field, we use the following formula:

curl(f) = (∂f_z/∂y - ∂f_y/∂z) i + (∂f_x/∂z - ∂f_z/∂x) j + (∂f_y/∂x - ∂f_x/∂y) k

where i, j, and k are the unit vectors in the x, y, and z directions, respectively.

In this case, the vector field is given by f = (x^2 - y^2) i + 6xy j.

Let's compute each partial derivative separately:

∂f_z/∂y = 0

∂f_y/∂z = 0

∂f_x/∂z = 0

∂f_z/∂x = 0

∂f_y/∂x = 6y

∂f_x/∂y = -2y

Therefore, the curl of the vector field f is:

curl(f) = (0 - 0) i + (0 - 0) j + (6y - (-2y)) k

= 8y k

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Answer:

Step-by-step explanation:

Let's write a equation.

5 ft = 20 seconds

(five feet is reachable in 20 seconds)

Divide both sides by 5.

5/5=1

20/5=4

1 ft = 4 seconds

Let's say the destination is d and f is foot.

d = 4f

The number of jumbo cans of frosting would she need to frost 280 cupcakes is 8.

Given that, Bette used 3 jumbo cans of frosting to frost 105 cupcakes and 5 jumbo cans of frosting to frost an additional 175 cupcakes.

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.

Let number of jumbo cans of frosting would she need to frost 280 cupcakes be x.

Now the proportion is

3/105 = 5/175 = x/280

⇒ 5/175 = x/280

⇒ 175x = 280 × 5

⇒ x = 1400/175

⇒ x = 8

Therefore, the number of jumbo cans of frosting would she need to frost 280 cupcakes is 8.

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Answer:

145

.8x = 116 (80% of class is 116)

x=145

Step-by-step explanation:

Answer:

x = 8

Step-by-step explanation:

8 minus 16 equals to a negative answer, resulting to -8.

Answer:

x = 8

Step-by-step explanation:

Add 16 to both sides of the equation.

x = −8 + 16

Add − 8 and  16

 x = 8

Answer: 1/4 of a minute to drain 18 litres of water ( 15 seconds)

Step-by-step explanation:

find slope or rate using two points on the line.

(0, 360) and (5, 0) and use slope formula y2- y1 over x2-x1

0 - 360 over 5 - 0 = -360/5,  reduced to -72 rate

m = -72

b = 360

x = time

y = 360 - 18 drained = 342

y=mx + b is your slope intercept formula

342 = -72x + 360

subtract 360 from both sides

342 - 360 = -72x + 360 - 360

simplify

-18 = -72x

divide both sides by -72

-18 / -72 = -72/-72 x

simplify

-18/-72 = x

reduce your fraction

1/4 = x

so 1/4 of a minute or 15 seconds to drain 18 liters of water

Answer:

52°

Step-by-step explanation:

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It aims to find a linear equation that best fits the observed data points, allowing for the prediction of the dependent variable based on the independent variables.

In more detail, linear regression assumes a linear relationship between the dependent variable and the independent variables. The method estimates the parameters of the linear equation by minimizing the sum of the squared differences between the observed data points and the predicted values. This is typically done using a technique called ordinary least squares (OLS) regression. The resulting linear equation can be used to make predictions or infer the impact of the independent variables on the dependent variable.

Linear regression is widely used in various fields, including economics, finance, social sciences, and machine learning. It provides a simple and interpretable way to analyze and understand the relationship between variables. However, it is important to note that linear regression assumes certain assumptions about the data, such as linearity, independence of errors, and homoscedasticity. Violations of these assumptions can affect the accuracy and reliability of the regression model.

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Answer:

E) 19

Step-by-step explanation:

To find the value of -3Δ5, we need to substitute -3 and 5 into the equation: aΔb = a² + ab + b².

So, we have:

-3Δ5 = (-3)² + (-3)(5) + (5)²

= 9 - 15 + 25

= 19

Therefore, the answer is E) 19.

Since the roots are complex, the general solution of the differential equation can be written as: y(t) = e^(50t/20)(c1cos(√(300)t/20) + c2sin(√(300)t/20))

To solve the initial value problem for the given differential equation 10y'' - 50y' + 65y = 0, we need to find the general solution of the equation and then apply the initial conditions to determine the specific solution.

The characteristic equation for the given differential equation is:

10r^2 - 50r + 65 = 0

Solving this quadratic equation, we find that the roots are complex:

r = (50 ± √(50^2 - 41065))/(2*10)

= (50 ± √(-300))/(20)

= (50 ± √(300)i)/(20)

Since the roots are complex, the general solution of the differential equation can be written as:

y(t) = e^(50t/20)(c1cos(√(300)t/20) + c2sin(√(300)t/20))

Now, let's apply the initial conditions to find the specific solution. Since the problem does not provide the initial conditions, we cannot proceed further without knowing the specific values for y(0) and y'(0).

Please provide the initial conditions, and I'll be able to find the specific solution and check if it satisfies the differential equation and initial conditions.

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3(x+2)=4(x+1)

3x+6=4x+1

so that means x=2

The point of diminishing returns is (20.98, 21247.3).

The point of diminishing returns occurs when the marginal cost of producing an extra unit of output exceeds the marginal revenue generated from selling that unit. Mathematically, it is the point at which the derivative of the production function equals zero and the second derivative is negative.

Given the polynomial function N(x) of degree 3, we can find the point of diminishing returns by finding the critical points where the first derivative equals zero and evaluating the second derivative at those points.

The derivative of N(x) is N'(x) = -18x² + 360x + 2250. To find the critical points, we set N'(x) = 0:

0 = -18x² + 360x + 2250

Dividing by -18 simplifies the equation:

0 = x² - 20x - 125

Using the quadratic formula, we find the solutions to the equation:

x₁,₂ = (20 ± √(20² - 4(1)(-125))) / 2(1)

x₁,₂ = 10 ± 5√5

Thus, the two critical points of N(x) are at x = 10 - 5√5 and x = 10 + 5√5.

To determine the point of diminishing returns, we evaluate the second derivative N''(x) = -36x + 360 at these critical points:

N''(10 - 5√5) = -36(10 - 5√5) + 360 ≈ -264.8

N''(10 + 5√5) = -36(10 + 5√5) + 360 ≈ 144.8

From the evaluations, we find that N''(10 + 5√5) is negative while N''(10 - 5√5) is positive. Therefore, the point of diminishing returns corresponds to x = 10 + 5√5.

To find the corresponding y-coordinate (N(10 + 5√5)), we can substitute the value of x into the original function N(x).

Hence, the point of diminishing returns is approximately (20.98, 21247.3).

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Check the picture below.

Answer:

14.1

Step-by-step explanation:

You add all of your numbers up, and then you divide by how many numbers you have.

Step-by-step explanation:

what do we need to do ? just do the multiplications (and squaring is also a multiplication, just by itself) ?

we could do the exercise in full or just remember the results of

(a-b)² = (a-b)(a-b) = a² - 2ab + b²

and

(a+b)(a-b) = a² - b²

so, we get

x² - 2x + 1 + x² - 1

simplifying this is

2x² - 2x = 2(x² - x) = 2x(x - 1)

A sampling plan is a vital component in conducting statistical process control smoothly, as it provides structure, reduces variability, identifies critical parameters, guides data analysis, and enhances decision-making.

1. Defining the sample size and frequency: A sampling plan establishes the number of items to be collected and the intervals at which they will be collected. This ensures a consistent and representative sample, making the statistical process more reliable and efficient.

2. Reducing variability: By specifying the method of sample selection, a sampling plan helps minimize the potential for biased or non-representative samples. This results in better control over the process and more accurate insights into the system's performance.

3. Identifying critical parameters: A sampling plan helps identify the key characteristics of a process that need to be monitored and controlled. This enables the focus on essential aspects of the process, ensuring optimal control and improvement efforts.

4. Guiding data analysis: A well-established sampling plan provides a structure for data collection, which can be used to perform statistical process control. It aids in data organization and interpretation, making it easier to detect trends, patterns, and potential issues.

5. Enhancing decision-making: With a sampling plan in place, statistical process control results become more trustworthy and actionable. This allows for better-informed decisions related to process adjustments and quality improvement initiatives.

In summary, a sampling plan is a vital component in conducting statistical process control smoothly, as it provides structure, reduces variability, identifies critical parameters, guides data analysis, and enhances decision-making.

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Answer:

5

Step-by-step explanation:

Average rate of change is slope, which is change in y over change in x:

\(\frac{[5(6)+2]-[5(-2)+2]}{6-(-2)} =\frac{32-(-8)}{8} =5\)

The average rate of change of the function is 5.

The sum of the change in the function values (output values) divided by the change in the input values is the average rate of change between two input values.

The given interval is [-2,6] and the given function is f(x) = y = 5x + 2.

The value of the function for x = 6 is:

f(6) = 5(6) + 2

f(6) = 32

The value of f(x) for x = -2 is:

f (-2) = 5(-2) + 2

f(-2) = -10 + 2

f(-2) = -8

The average rate of change of the function is given by:

( f(6) - f(-2) )/ (6 - (-2))

= ( 32 - (-8))/ (6 + 2)

= ( 32 + 8)/8

= 40/8

= 5

Hence, the average rate of change of the function is 5.

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Answer: For the second graph it's -2/3

3.) -10/6

4.) -20/-6

Step-by-step explanation:

It will take the second skater 20 seconds to catch up to the first skater and pass him/her.

In physics, speed and motion are related concepts that describe the movement of objects in space.

Speed is a scalar quantity that measures how fast an object is moving. It is the rate at which an object covers distance, typically measured in meters per second (m/s), kilometers per hour (km/h), or some other unit of distance per unit of time.

Motion, on the other hand, is the change in position of an object over time, with respect to a reference point. In physics, motion can be described in terms of displacement, velocity, and acceleration. Displacement refers to the change in position of an object relative to a reference point, while velocity describes how fast an object is moving in a specific direction.

Acceleration refers to the rate at which an object's velocity changes over time, either by increasing or decreasing in speed or changing direction.

In summary, speed is a measure of how fast an object is moving, while motion is the change in position of an object over time.

We can start by setting up an equation to represent the distance each skater travels, with t representing the time it takes for the second skater to catch up to the first skater:

Distance traveled by the first skater = Distance traveled by the second skater + 40 meters

Using the formula distance = rate × time, we can plug in the given rates and the unknown time to get:

12t + 40 = 14t

Simplifying this equation, we get:

40 = 2t

t = 20 seconds

Therefore, it will take the second skater 20 seconds to catch up to the first skater and pass him/her.

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Answer:

Step-by-step explanation:

Given: ABC is equilateral triangle.

AD = DB   & BE = EC   & CF = FA ------------(IV)

Proof:

  D & F are midpoint of the sides AB and AC

  DF = \(\frac{1}{2}BC\)            {Midpoint theorem}    

DF = BE     ----------------(I)

D & E are midpoint of the sides AB and BC

DE = \(\frac{1}{2}AC\)               {Midpoint theorem}      

DE = FA ----------------(II)

E & F are midpoint of the sides BC and AC

\(EF = \frac{1}{2}AB\)                  {Midpoint theorem}

EF = AD   ---------------(III)

From (I) ; (II) ; (III) ; (IV) ,

DF =  DE = EF

DEF is an  equilateral triangle.

Answer:

)99-11+10g -12+119 -13= 182+10g

)30g-36

Step-by-step explanation:

Answer:

11.25

Step-by-step explanation:

7500 times 0.03 times 5 = 1125

1125 divided 100 = 11.25

simple interest formula = Amount times Rate times Time

                                                         Divide 100