solve each of these equations.

The power of the test is low and not sufficient to detect a significant difference between the two treatments with the given sample size of 35.

To calculate the expected power of the test, we need to consider the survival rates, the significance level, and the sample size. Let's follow these steps:

Determine the proportions
Old treatment survival rate (p1) = 0.75
New treatment survival rate (p2) = 0.85

Determine the significance level
Two-sided significant difference level (α) = 0.05

Calculate the pooled proportion
Pooled proportion (p) = (p1 + p2) / 2 = (0.75 + 0.85) / 2 = 0.80

Calculate the standard error
Standard error (SE) = √(p × (1 - p) × (1/n1 + 1/n2)) = √(0.80 × (1 - 0.80) × (1/35 + 1/35)) ≈ 0.065

Calculate the test statistic (z)
z = (p2 - p1) / SE = (0.85 - 0.75) / 0.065 ≈ 1.54

Find the critical value for the two-sided significant difference at the 5% level
z_critical = 1.96 (from a standard normal distribution table)

Calculate the power of the test
In this case, since the test statistic is smaller than the critical value (1.54 < 1.96), we cannot reject the null hypothesis at the 5% significance level.
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Answer:

Step-by-step explanation:

if its asking how many people there are it would be 40,000

Mother, Father, 2 kids=4

4 x 10,000= 40,000

The following statements are true regarding the check of conditions for this test: This is a chi-square test for association. The random condition is met because Keith selected a random sample of songs. The 10% condition is met because 125 is less than 10% of all songs. The large counts condition is met because the smallest expected count is 5.

In this scenario, Keith conducted a chi-square test to determine if there is convincing evidence of an association between key (major or minor) and the emotional classification of a song (happy or sad). To ensure the validity of the chi-square test, it is necessary to check the conditions before performing the test. First, it is appropriate to use a chi-square test for association in this case as we are analyzing the relationship between two categorical variables: key and emotion.

Next, the random condition is met because Keith selected a random sample of songs. This helps ensure that the sample is representative of the population and reduces bias. The 10% condition is also met since the sample size of 125 songs is less than 10% of all songs. This condition ensures that the sample size is small enough relative to the population size, preventing the sample from significantly influencing the population.

Finally, the large counts condition is met because the smallest expected count is 5. This condition is important for the validity of the chi-square test as it ensures that the expected counts in each cell are not too small, which can lead to unreliable results. Therefore, based on these conditions, all the necessary requirements for performing the chi-square test for association are satisfied.

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Answer:

The height of the pile is increasing at a rate of 16.72 feet per minute. To solve this problem, we need to use the volume formula for a right circular cone: V=pi/3 r²h. We know that the volume is 20 cubic feet per minute, the height is 14 feet and the radius of the base is 14 feet. So we can calculate the rate of change of the height by rearranging the formula to give v/(pi/3r²). So for our example, v/(pi/3*14²)=20/(pi/3*14²)=20/(3.14*196)=20/613.44=16.72 feet per minute.

Answer:

-4

Step-by-step explanation:

56/-14=n

assume the negative sign does not exist

56/14=4

then add the negative sign to the answer

-4=n

Answer:

its -14 times n

Step-by-step explanation:

um i did the test :3

Answer:

\(V=1000\ cm^3\)

Step-by-step explanation:

The edge of the cube, a = 0.1 m

We need to find the volume of the cube. The formula for the volume of the cube is given by :

\(V=a^3\)

Put the respected values,

\(V=(0.1)^3\\\\V=0.001\ m^3\\\\or\\\\V=1000\ cm^3\)

So, the volume of the cube is equal to \(1000\ cm^3\).

Answer:

the answer is 22

Step-by-step explanation:

One equation that represents the total value of the coins in cents is:

0.25x + 0.10y = 995

where x is the number of quarters and y is the number of dimes.

Another equation that represents the total number of coins is:

x + y = 47

These two equations make up a system of equations that can be used to find the number of quarters and dimes that add up to $9.95 and have a total of 47 coins.

Answer:

\(\begin{cases}x+y=47\\0.25x+0.1y=9.95\end{cases}\)

Step-by-step explanation:

To solve this problem, we can create and solve a system of equations.

Define the variables:

Values of the coins:

Given there are a total of 47 coins:

\(x+y=47\)

Given there is a total of $9.95 in quarters and dimes:

\(0.25x+0.1y=9.95\)

Therefore, the system of equations that represents the problem is:

\(\begin{cases}x+y=47\\0.25x+0.1y=9.95\end{cases}\)

To solve the system of equations, rewrite the first equation to isolate y:

\(y=47-x\)

Substitute this into the second equation to eliminate y:

\(0.25x+0.1(47-x)=9.95\)

Solve the equation for x to find the number of quarters:

\(\begin{aligned}0.25x+0.1(47-x)&=9.95\\0.25x+4.7-0.1x&=9.95\\0.15x+4.7&=9.95\\0.15x&=5.25\\x&=35\end{aligned}\)

Therefore, there are 35 quarters.

Substitute the found value of x into the first equation and solve for y:

\(\begin{aligned}35+y&=47\\y&=12\end{aligned}\)

Therefore, there are 12 dimes.

Answer:

Answer = 37

Step-by-step explanation:

= (5)² + (2)³ + (4)¹

= 25 + 8 + 4

= 37 Answer

Answer: The answer is 37

Step-by-step explanation:

Step 1: Use Negative Power Rule: x^-a=1/x^a. So 1/(1/5)^2+(1/2)^-3+(1/4)^-1

Step 2: Use Division Distributive Property: (x/y)^a=x^a/y^a. So 1/1/5^2+(1/2)^-3+(1/4)^-1

Step 3: Simplify 5^2 to 25. So 1/1/25+(1/2)^-3+(1/4)^-1

Step 4: Use Negative Power Rule: x^-a=1/x^a. So 1/1/25+1/(1/2)^3+(1/4)^-1

Step 5: Use Division Distributive Property: (x/y)^a=x^a/y^a. So 1/1/25+1/1/2^3+(1/4)^-1

Step 6: Simplify 2^3 to 8. So 1/1/25+1/1/8+(1/4)^-1

Step 7: Use Negative Power Rule: x^-a=1/x^a. So 1/1/25+1/1/8+1/1/4

Step 8: Invert and multiply. 25+1/1/8+1/1/4

Step 9: Invert and multiply. 25+8+1/1/4

Step 10: Invert and multiply. 25+8+4

Step 11: Simplify 25+8 to 33. So 33+4

Step 12: Simplify. So the answer is 37

Answer:

The answer woupd be B, 1, 0

The dairy is at x = 1 unit and;y = 0 unit thus the coordinate of dairy in the floor plan is at (1,0) thus option (B) will be correct.

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane. typically expressed by the x-value and y-value pairs (x,y).

As per the given floor plan,

Th coordinate of dairy is the horizontal and vertical distinctions from the reference axes(0,0).

Since it is 1 unit apart in the x and 0 apart in the y direction.

Thus (1,0) is the right coordinate.

Hence "The dairy is at x = 1 unit and;y = 0 unit thus the coordinate of dairy in the floor plan is at (1,0)".

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Answer:

the answer its 7^2 +7^3x5 its d hope helps you

Step-by-step explanation:

Answer:

24/35

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Use slope formula: (y2-y1)/(x2-x1)

(14-6)/(8-4) = 8/4 = 2

The gradient is 2

Answer:

3 29/81

Step-by-step explanation:

6 5/8-3 2/9

6 45/81-3 16/81

3 29/81

Answer:

3 29/72

Step-by-step explanation:

6 5/8 − 3 2/9 = 3 29/72

Hope this helps!

(If right, pls put brainlist)

To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

By using the commutative property, the given expression should be simplified as follows: B. 4/3 + 2/3 + 3/4 = 2 + 3/4 = 2 3/4.

The Associative Property of Addition states that when three (3) numbers are added, the end result would always be the same regardless of the way the numbers are grouped.

The Commutative Property of Addition states that when two (2) or three (3) numerical values (numbers) are added together, the output (end result) would always remain the same, irrespective of the way in which the numerical values are arranged.

Generally speaking, the Commutative Property of Addition allows the addends to be re-ordered without causing a change in the result, output, or outcome.

By applying the Commutative Property of Addition, we have;

4/3 + 3/4 + 2/3

Re-arranging the expression, we have;

4/3 + 2/3 + 3/4 = (4 + 2)/3 + 3/4

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

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

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Therefore, Two slices of bacon had 96 less calories than three slices of roasted turkey.

a formula that illustrates the connection between two expressions on either side of a sign. It usually only has one variable and an equal sign. like this: 2x – 4 = 2.

Here,

One piece of bacon has 42 calories in it.

There are 60 calories in 1 slice of turkey.

2 slices of bacon are 2 calories each (42)

So 84 calories in 2 slice of bacon

3 slices of roasted turkey have 3 calories each slice (60)

Three slices of roasted turkey have 180 calories each.

180-84 is the difference in the amount of calories.

96 calories are added due to the calorie difference.

Two slices of bacon had 96 less calories than three slices of roasted turkey.

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The ordered pair that is the solution of the given system of inequalities is (2, -2)

A relationship between two expressions or values that are not equal to each other is called inequality.

Given is a system of inequalities, y < -x and 2x+y > 2, we need to determine solution set of the given system of inequalities,

The inequalities are,

y < -x....(i)

2x+y > 2

y < 2-2x...(ii)

To find the ordered pair, put y = -x in equation Eq(ii) and replace < by =

-x = 2 - 2x

x = 2

y = -2

Therefore, the ordered pair, is (2, -2) {look at the graph attached}

Hence, the ordered pair that is the solution of the given system of inequalities is (2, -2)

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Answer:

66

Step-by-step explanation:

∠HEI = 48

∠ICH = 180 - ∠HEI

         = 180 - 48

∠ICH = 132

∠ABD = ∠ICH / 2

          = 132/2

∠ABD = 66

The particular solution that satisfies the initial conditions is:

\[y(t) = (-3 + t)e^{-\frac{2}{3}t}\]

To solve the given initial value problem, we'll assume that the solution has the form of a exponential function. Let's substitute \(y = e^{rt}\) into the differential equation and find the values of \(r\) that satisfy it.

Starting with the differential equation:

\[9y'' + 12y' + 4y = 0\]

We can differentiate \(y\) with respect to \(t\) to find \(y'\) and \(y''\):

\[y' = re^{rt}\]

\[y'' = r^2e^{rt}\]

Substituting these expressions back into the differential equation:

\[9(r^2e^{rt}) + 12(re^{rt}) + 4(e^{rt}) = 0\]

Dividing through by \(e^{rt}\):

\[9r^2 + 12r + 4 = 0\]

Now we have a quadratic equation in \(r\). We can solve it by factoring or using the quadratic formula. Factoring doesn't seem to yield simple integer solutions, so let's use the quadratic formula:

\[r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

In our case, \(a = 9\), \(b = 12\), and \(c = 4\). Substituting these values:

\[r = \frac{-12 \pm \sqrt{12^2 - 4 \cdot 9 \cdot 4}}{2 \cdot 9}\]

Simplifying:

\[r = \frac{-12 \pm \sqrt{144 - 144}}{18}\]

\[r = \frac{-12}{18}\]

\[r = -\frac{2}{3}\]

Therefore, the roots of the quadratic equation are \(r_1 = -\frac{2}{3}\) and \(r_2 = -\frac{2}{3}\).

Since both roots are the same, the general solution will contain a repeated exponential term. The general solution is given by:

\[y(t) = (c_1 + c_2t)e^{-\frac{2}{3}t}\]

Now let's find the particular solution that satisfies the initial conditions \(y(0) = -3\) and \(y'(0) = 3\).

Substituting \(t = 0\) into the general solution:

\[y(0) = (c_1 + c_2 \cdot 0)e^{0}\]

\[-3 = c_1\]

Substituting \(t = 0\) into the derivative of the general solution:

\[y'(0) = c_2e^{0} - \frac{2}{3}(c_1 + c_2 \cdot 0)e^{0}\]

\[3 = c_2 - \frac{2}{3}c_1\]

Substituting \(c_1 = -3\) into the second equation:

\[3 = c_2 - \frac{2}{3}(-3)\]

\[3 = c_2 + 2\]

\[c_2 = 1\]

Therefore, the particular solution that satisfies the initial conditions is:

\[y(t) = (-3 + t)e^{-\frac{2}{3}t}\]

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Answer:

165

Step-by-step explanation:

Answer: Neptune makes a complete orbit around the Sun (a year in Neptunian time) in about 165 Earth years (60,190 Earth days).

Step-by-step explanation:

True. Instantaneous velocity is the rate of change of displacement at a specific instant in time and can be positive, negative, or zero.

Calculating instantaneous velocity involves dividing the displacement change by the time change. A car's instantaneous velocity, for instance, would be 5/3 metres per second if it travelled 5 metres in 3 seconds.The rate of change of displacement at a particular moment in time is known as the instantaneous velocity. It is the speed in an instant at a particular location, and it can be positive, negative, or zero. The change in displacement (delta x) is divided by the change in time to determine instantaneous velocity.  A car's instantaneous velocity, for instance, would be 5/3 meters per second if it travelled 5 meters in 3 seconds.

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The particular solution to the differential equation with the initial condition y(7) = 0 is:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

To solve the given differential equation, we can use the method of separation of variables. Here's the step-by-step solution:

Step 1: Write the given differential equation in the form dy/dx = f(x, y).

  In this case, dy/dx = y² - 4.

Step 2: Separate the variables by moving terms involving y to one side and terms involving x to the other side:

  dy / (y² - 4) = dx.

Step 3: Integrate both sides of the equation:

  ∫ dy / (y² - 4) = ∫ dx.

Let's solve each integral separately:

For the left-hand side integral:

Let's express the denominator as the difference of squares: y² - 4 = (y - 2)(y + 2).

Using partial fractions, we can decompose the left-hand side integral:

1 / (y² - 4) = A / (y - 2) + B / (y + 2).

Multiply both sides by (y - 2)(y + 2):

1 = A(y + 2) + B(y - 2).

Expanding the equation:

1 = (A + B)y + 2A - 2B.

By equating the coefficients of the like terms on both sides:

A + B = 0, and

2A - 2B = 1.

Solving these equations simultaneously:

From the first equation, A = -B.

Substituting A = -B in the second equation:

2(-B) - 2B = 1,

-4B = 1,

B = -1/4.

Substituting the value of B in the first equation:

A + (-1/4) = 0,

A = 1/4.

Therefore, the decomposition of the left-hand side integral becomes:

1 / (y² - 4) = 1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2)).

Integrating both sides:

∫ (1 / (y² - 4)) dy = ∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy.

Integrating the right-hand side:

∫ (1/4 * (1 / (y - 2)) - 1/4 * (1 / (y + 2))) dy

= (1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁,

where C₁ is the constant of integration.

For the right-hand side integral:

∫ dx = x + C₂,

where C₂ is the constant of integration.

Combining the results:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| + C₁ = x + C₂.

Simplifying the equation:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + (C₂ - C₁).

Combining the constants of integration:

C = C₂ - C₁, where C is a new constant.

Finally, we have the solution to the differential equation that satisfies the initial condition:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x + C.

To find the value of the constant C, we use the initial condition y(7) = 0:

(1/4) * ln|0 - 2| - (1/4) * ln|0 + 2| = 7 + C.

Simplifying the equation:

(1/4) * ln|-2| - (1/4) * ln|2| = 7 + C,

(1/4) * ln(2) - (1/4) * ln(2) = 7 + C,

0 = 7 + C,

C = -7.

Therefore, the differential equation with the initial condition y(7) = 0 has the following specific solution:

(1/4) * ln|y - 2| - (1/4) * ln|y + 2| = x - 7.

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The power series representation for 1/(1+x)^2 can be obtained by using the formula for the geometric series and then differentiating term by term. The resulting series will converge for |x|<1 and will represent the function 1/(1+x)^2 on this interval.

The formula for the geometric series is:

1/(1-x) = 1 + x + x^2 + x^3 + ...

By differentiating both sides of this equation with respect to x, we obtain:

(1/(1-x))^2 = 1 + 2x + 3x^2 + 4x^3 + ...

Substituting x with -x, we get:

(1/(1+x))^2 = 1 - 2x + 3x^2 - 4x^3 + ...

This is the power series representation for 1/(1+x)^2. The series converges for |x|<1, since the ratio of consecutive terms is:

|a_{n+1}/a_n| = |(n+1)(-x)/(n+2)| = |x/(n+2)|

As n goes to infinity, this ratio goes to zero for |x|<1, and the series converges.

In summary, the power series representation for 1/(1+x)^2 can be obtained by using the formula for the geometric series and then differentiating term by term. The resulting series converges for |x|<1 and represents the function 1/(1+x)^2 on this interval.

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1/2-3/10=5-3/10=1/5 this is the answer

We can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

Multiplication is one of the four basic mathematical operations, along with addition, subtraction, and division.

The result of a multiplication operation is a product.

There are four different methods for multiplying: addition, long multiplication, grid multiplication, and drawing lines.

So, we have:
5/8 and 4

5/8 is in the form p/q which represents the fraction that must be multiplied by 4.

Now, calculate the product as follows:

5/8 * 4

5/2

Therefore, we can calculate the product of 5/8 and 4 to be 5/2 using multiplication.

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Answer:

(-3,2)

Step-by-step explanation: