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The crossover point between the t-test and Z-test is typically considered to be a sample size of 30. This means that when the sample size is equal to or greater than 30, it is generally recommended to use the Z-test.

However, it's important to note that this cutoff point is not a strict rule and can vary depending on the specific context and requirements of the statistical analysis.

The t-test is used when the standard deviation of the population is unknown and needs to be estimated from the sample data. It is particularly useful when working with small sample sizes, where the variability of the population is less certain. The t-test takes into account the degrees of freedom, which is calculated based on the sample size minus one.

On the other hand, the Z-test is used when the standard deviation of the population is known or when the sample size is large. With a large sample size, the Central Limit Theorem ensures that the sample mean will be normally distributed, allowing for the use of the standard normal distribution (Z-distribution) in hypothesis testing.

The crossover point of 30 is a rough guideline that suggests that with a sample size of 30 or more, the sample mean distribution becomes approximately normally distributed, even without knowing the population standard deviation. This assumption allows for the use of the Z-test instead of the t-test, simplifying the calculations and interpretation of results.

It's important to consider other factors as well, such as the specific research question, data characteristics, and the desired level of confidence, when determining which test to use. Statistical software or consulting with a statistician can also help in making an informed decision based on the specific circumstances of the analysis.

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Answer:

Step-by-step explanation:

y=0.5x+8

Using the points of intersection we obtain that the values that make both equations true are x = 3 and y = 1.

To obtain the values of x and y that satisfy both equations, we need to find the points of intersection. We'll equate the two equations and solve for x.

First, we'll set the two equations equal to each other:

-2/3x + 3 = 2x - 5

Next, let's simplify the equation:

-2/3x - 2x = -5 - 3

To combine the x terms on the left side and the constants on the right side:

-2/3x - 6/3x = -8

Now, let's obtain a common denominator and combine the x terms:

-8/3x = -8

To isolate x, we'll multiply both sides by -3/8:

x = (-8)(-3/8)

x = 3

Now that we have the value of x, we can substitute it back into either of the original equations to calculate the corresponding y-value.

Let's use the equation y = 2x - 5:

y = 2(3) - 5

y = 6 - 5

y = 1

Therefore, the values that make both equations true are x = 3 and y = 1.

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Answer:

7,54,91

Step-by-step explanation:

And rher is the season

Answer:

the third angle is 70 degrees

Step-by-step explanation:

an isosceles triangle has two equal angles and one other with a different angle value.

All angles add up to 180 degrees

therefore we can create the equation

180 = 55 + 55 + x

NB : x is the value of the third angle

180 = 110 + x

x = 180 - 110

x = 70

the third angle is 70 degrees

Step-by-step explanation:

Equal sides of the triangle= 55

Let the other angle be x,

Therefore, by the angle sum property, we get,

=> 55 + 55 + x = 180

=> 110 + x = 180

=>x = 180 - 110

=> x = 70

Therefore, the other angle = 70

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Answer:

2x1-5y=17

2-5y=17

-5y=17-2

-5y=15

y=-3

Step-by-step explanation:

Answer:

x =11

Step-by-step explanation:

2x-5y=17

Let y=1

2x-5(1) = 17

2x-5=17

Add 5 to each side

2x-5+5 = 17+5

2x = 22

Divide each side by 2

2x/2 = 22/2

x =11

Answer:

A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the right.

Step-by-step explanation:

55  I think its that but im not sure

Answer:

55

Step-by-step explanation:

This expression gives us a present value of approximately $1,376,500.

To calculate the present value of John Doe's winnings, we need to find the present value of each individual payment and then sum them up.

The formula to calculate the present value of an annuity is:

PV = C * (1 - (1 + r)^(-n)) / r

Where PV is the present value, C is the annual payment, r is the discount rate, and n is the number of periods.

In this case, John Doe will receive $100,000 each year for 30 years, and the discount rate is 6%. Plugging these values into the formula, we get:

PV = $100,000 * (1 - (1 + 0.06)^(-30)) / 0.06

Calculating this expression gives us a present value of approximately $1,376,500.

Therefore, the correct answer is:

c. $1,376,500.

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Answer:

Step-by-step explanation:

(6*2) + (6*9x2)

12 + 54x2

As the theme of human/environment interaction, I am important to geography because we elucidate the dynamic relationship and reciprocal influences between human activities and the natural environment.

As the theme of location, we stand here today to emphasize my crucial role in geography.

Location is not just a mere geographical reference; it is the foundation upon which the entire discipline of geography is built.

webring forth the significance of pinpointing where things exist and how they relate to one another.

First and foremost, we provide a framework for spatial analysis. By identifying the coordinates and spatial relationships between places, we enable geographers to examine patterns, distributions, and connections. I assist in understanding the spatial organization of human activities, environmental phenomena, and physical features.

Without me, geography would lack the spatial context necessary for comprehensive analysis.

Moreover, I contribute to the understanding of place. Places are unique in their physical and human characteristics, and I help define these attributes. Whether it is the climate, topography, vegetation, infrastructure, or cultural elements, I offer the context for comprehending the distinctiveness and diversity of places. Understanding places is essential for grasping human-environment interaction, as it provides insights into how people adapt to and modify their surroundings.

Furthermore, we play a crucial role in regional analysis. Regions are conceptual divisions that facilitate the study of similarities, differences, and interdependencies.

By identifying and categorizing areas based on their location, whether at local, national, or global scales, we enable geographers to understand spatial variations in human and physical phenomena. Regional analysis helps identify commonalities, disparities, and factors that shape social, economic, and environmental dynamics.

In summary, as the theme of location, we are  instrumental in providing the spatial context necessary for a comprehensive understanding of geography.

We enable spatial analysis, define the uniqueness of places, and facilitate regional analysis.

Without me, geography would lose its spatial essence and struggle to make sense of the world we inhabit.

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Step-by-step explanation:

0 because 3 = +0

And 0+0 =0

Answer: 0.4

Step-by-step explanation:

The answer below didn’t work so I gave a knowledgable guess

Answer:

its backwards 3x2+5=20

3x2=15

Step-by-step explanation:

Hi There Answer: 3x2+5=20

Step-by-step explanation:

Answer:

Provide an approximate elevation for points W, X, Y, and Z (Z is pointing right to the line).

Step-by-step explanation:

Answer:

Red

Step-by-step explanation:

Answer:

A) 3 : 5

Step-by-step explanation:

Scale factor = 24/40 = 3/5 = 3 : 5

Cost of a sno-cone machine = $ 138

The discount on the sno-cone machine = 20%

Price of the sno-cone machine after the discount :-

= 138 - 20% of 138

[tex]= 138 - \frac{20}{100} \times 138[/tex]

[tex] = 138 - \frac{(20 \times 138)}{100} [/tex]

[tex] = 138 - \frac{2760}{100} [/tex]

[tex]\texttt{= 138 - 27.6}[/tex]

[tex] =$ 110.4[/tex]

Which means the price of the sno-cone machine after a 20% discount would be = $110.4 .

Sales tax on the sno-cone machine = 6.75%

Cost of the sno-cone machine after the sales tax :-

[tex] = \frac{(6.75+100)}{100} \times 110.4[/tex]

[tex] = 110.4 × \frac{106.75}{100} [/tex]

[tex] = 110.4 × 1.0675 [/tex]

[tex] = $117.852 [/tex]

Therefore , the price of the sno-cone machine after the discount and sales tax would be = $117.852

Answer:

135

Step-by-step explanation: Multiply 160 by 0.85(for 85%) and you get 135

Answer:

136

Step-by-step explanation:

HOPE IT HELPS (◕‿◕✿)

Answer:

Step-by-step explanation:

[tex]a_1=2\\a_2=-8\\\\q=\frac{-8}2=-4\\\\a_n=a_1\cdot q^{n-1}\\\\a_8=2\cdot(-4)^7=2(-16\,384)=-32\,384[/tex]

Based on the given options, the displacement could be either 0 km or 6 km, depending on the specific details of Dr. Siva's route.

To determine the displacement, we need to consider the net change in position or the straight-line distance between the initial and final positions. Let's analyze the information given:

Dr. Siva walked from home to school, then from the school to the park, and finally walked back home.

The displacement is not determined by the total distance traveled but rather by the straight-line distance between the starting and ending points. We don't have specific information about the distances or directions between the locations, so we cannot calculate the exact displacement.

However, we can make some assumptions based on the given options:

If the distances from home to school and from the school to the park are the same, and Dr. Siva returns directly from the park back home, the displacement would be 0 km. This implies that the final position is the same as the initial position.

If Dr. Siva walks 10 km from home to school, then 10 km from the school to the park, and finally walks 10 km back home, the displacement would be 0 km. This is because the final position would be the same as the initial position.

If Dr. Siva walks 10 km from home to school, then 2 km from the school to the park, and finally walks 6 km back home, the displacement would be 6 km. This implies that the final position is 6 km away from the initial position in the direction of home.

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Answer:

Each kid will get 1.8 slices.

Step-by-step explanation:

If there are 18 slices, and there are 10 people, and everyone gets an equal amount, then you divide 18 by 10. This will result in 1.8.

Therefore, your answer is that each kid gets 1.8 slices of cake.

There are a total of 3 × 3 × 3 × 3 = 81 different dessert menus for the week that are possible.

In order to solve the problem, let's begin by considering the conditions given. The dessert chef prepares dessert for every day of a week starting with Sunday. The dessert options include cake, pie, ice cream, or pudding. The same dessert may not be served two days in a row, and it is required that there must be ice cream on Sunday and pie on Saturday.Therefore, let's start by considering the dessert for Sunday, which must be ice cream. As ice cream cannot be served on the following day, the dessert for Monday must be either cake, pie, or pudding. On Tuesday, the dessert options are cake, pie, and pudding again since ice cream was served on Sunday. Following the same reasoning, the dessert for Wednesday must be ice cream, and the options for Thursday are cake, pie, or pudding. On Friday, the dessert options are the same as Thursday since ice cream was served on Wednesday. Finally, pie must be served on Saturday.Therefore, there are three possible dessert options for Monday, Tuesday, Thursday, and Friday: cake, pie, or pudding. On Sunday, ice cream is mandatory, and on Wednesday, ice cream must be served. On Saturday, pie must be served.

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Answer:

x = -2

Step-by-step explanation:

Step 1: Write equation

4(5x + 7) = -45 + 33

Step 2: Solve for x

Step 3: Check

Plug in x to verify it's a solution.

4(5(-2) + 7) = -45 + 33

4(-10 + 7) = -12

4(-3) = -12

-12 = -12

Answer: 6 donuts

Step-by-step explanation:

Given the following :

Cost of donut = $1.50

Cost of cookies = $0.50

Amount to spend = $15

Total number of donut and cookies to buy must not be less than 12

Number of cookies purchased = 10

Maximum number of donuts Blake could buy:

Amount spent on cookies = (10 × $0.50) = $5

Amount left to spend = ($15 - $5) = $10

Maximum number of donuts Blake could buy:

Amount left / cost per donut

= $10 / $1.50

= $6.66

Hence, maximum number of donut would be 6

The angles arranged from smallest to largest are: 1 radian ≈ 57.3 degrees, 3π/4 radians ≈ 135 degrees, π radians ≈ 180 degrees, 5π/4 radians ≈ 225 degrees, 90 degrees, and 270 degrees.

To put these angle measures in order from smallest to largest, we can convert all the given angles to a common unit and then compare them. Let's start by converting each angle to degrees since it's a widely recognized unit for measuring angles:

1 radian ≈ 57.3 degrees (approximately)

90 degrees (given)

3π/4 radians ≈ 135 degrees (approximately)

π radians ≈ 180 degrees (approximately)

5π/4 radians ≈ 225 degrees (approximately)

270 degrees (given)

Now let's arrange them in ascending order:

1 radian ≈ 57.3 degrees

3π/4 radians ≈ 135 degrees

π radians ≈ 180 degrees

5π/4 radians ≈ 225 degrees

90 degrees

270 degrees

So, the angles arranged from smallest to largest are:

1 radian ≈ 57.3 degrees

3π/4 radians ≈ 135 degrees

π radians ≈ 180 degrees

5π/4 radians ≈ 225 degrees

90 degrees

270 degrees.

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9514 1404 393

Answer:

  (x, y) = (1/2, 5)

Step-by-step explanation:

The first equation multiplied by 2 is ...

  16x +14y = 78

Then adding the second equation gives ...

  (16x +14y) +(4x -14y) = (78) +(-68)

  20x = 10 . . . . . . . . . simplify to get the "new equation"

  x = 10/20 = 1/2 . . . . divide by 20 to solve for x

  8(1/2) +7y = 39 . . . . substitute for x in the first equation

  7y = 35 . . . . . . . . . subtract 4

  y = 5 . . . . . . . . . . .divide by 7

The solution to the system of equations is (x, y) = (1/2, 5).

Answer:

5/27

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The probability that a student who is chosen randomly from the class plays both basketball and baseball is 0.185.

Probability is the ratio that shows the likelihood an event will occur or not from a given set of events.

Probability of students who play basketball = P(A) = 7/27

Probability of students who play baseball = P(B) = 18/27

It is given that 7 students don't play any sport.

Total number of students = 27 students.

Therefore, the probability of students who play either basketball or baseball or both = P(A∪B)

= (27 - 7)/27 = 20/27

We know that, P(A∪B) = P(A) + P(B) - P(A∩B)

20/27 = 7/27 + 18/27 - P(A∩B)

P(A∩B) = 25/27 - 20/27

P(A∩B) = 5/27

= 0.185 = Probability that a student chosen randomly from the class plays both basketball and baseball.

Therefore, we have found that the probability that a student chosen randomly from the class plays both basketball and baseball is 0.185.

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The minimum safety stock that the hospital should use for the antibiotic is 68 pills.

To calculate the minimum safety stock, we need to consider the demand during the lead time and the desired service level.

The lead time is 9 days with a standard deviation of 1 day. The demand for the antibiotic has a mean of 43 pills per day and a standard deviation of 19 pills per day.

First, we calculate the demand during the lead time:

Demand during lead time = Mean demand per day * Lead time = 43 * 9 = 387 pills

Next, we calculate the standard deviation of demand during the lead time:

Standard deviation of demand during lead time = Standard deviation per day * Square root of lead time = 19 * √9 = 57 pills

To achieve a service level of 99.9%, we need to account for 3 standard deviations of demand. The z-score corresponding to a service level of 99.9% is approximately 3.09.

Safety stock = (Z-score * Standard deviation of demand during lead time) - Demand during lead time

= (3.09 * 57) - 387

= 68 pills

To maintain a service level of 99.9%, the hospital should maintain a minimum safety stock of 68 pills for the antibiotic. This ensures that there is an adequate buffer to cover the variability in demand during the lead time and reduces the risk of stockouts.

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a) The surface area of the small cake box is 1,316 square centimeters.

b) The dimensions of the optimal cake box with the same surface area are approximately 23.66 cm by 20.58 cm by 20.58 cm.

a) To calculate the surface area of the small cake box, we need to find the areas of all six sides and then add them up. The surface area formula for a rectangular box is A = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the box, respectively. Plugging in the given dimensions, we get A = 2(28 × 13) + 2(28 × 15) + 2(13 × 15) = 1,316 square centimeters.

b) To find the dimensions of the optimal cake box with the same surface area, we need to solve for the dimensions that minimize the sum of the three side lengths. Let's call the dimensions of the optimal box x, y, and z. The surface area is given by A = 2(xy + xz + yz). To minimize the sum of the side lengths, we can use the AM-GM inequality, which states that for positive numbers, the arithmetic mean is greater than or equal to the geometric mean. Applying this inequality to the three side lengths, we have (x + y + z)/3 ≥ ∛(xyz). Since the sum of the side lengths is constant (28 + 13 + 15 = 56), we can substitute it into the inequality: 56/3 ≥ ∛(xyz). Solving for xyz, we get xyz ≤ 1792/3. Therefore, the optimal dimensions will be as close as possible to each other, giving us three equal side lengths of approximately 20.58 cm. The dimensions of the optimal cake box are approximately 23.66 cm by 20.58 cm by 20.58 cm.

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2. The optimal dimensions for the pop can with a volume of 355 cm³ would depend on the desired shape. Assuming a cylindrical shape is preferred, we can use the formula for the volume of a cylinder, V = πr²h, where r represents the radius and h is the height. To find the optimal dimensions, we would need to solve for the radius and height that satisfy the volume constraint. However, without additional information or constraints, it is not possible to determine the specific optimal dimensions.

3. a) The volume of the cardboard tube can be calculated using the formula for the volume of a cylinder, V = πr²h. Plugging in the given values, we have V = π(4²)(30) = 480π cm³.

  b) To find the optimal dimensions for a tube with the same volume, we would need to determine if any constraints or preferences exist. Without additional information, we cannot provide specific optimal dimensions. However, we can generally state that the dimensions should satisfy the volume constraint while considering factors such as practicality, stability, and manufacturing feasibility.

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The Nash equilibrium (P1 = 0, P2 = 0) would be the intersection of the respective strategies for both players, resulting in a single point on the graph.

To determine the Nash equilibrium in the "guess the number" game, we need to analyze the payoffs of each player and identify the strategies that are best responses to each other.

Let's denote P1 as Player 1's probability of guessing 1 and P2 as Player 2's probability of guessing 2. The payoffs for Player 1 and Player 2 are as follows:

Player 1's Payoff:

- If Player 1 guesses 1 and Player 2 guesses 1, Player 1's payoff is 0.

- If Player 1 guesses 1 and Player 2 guesses 2, Player 1's payoff is -1.

- If Player 1 guesses 2 and Player 2 guesses 1, Player 1's payoff is 1.

- If Player 1 guesses 2 and Player 2 guesses 2, Player 1's payoff is 0.

Player 2's Payoff:

- If Player 1 guesses 1 and Player 2 guesses 1, Player 2's payoff is 0.

- If Player 1 guesses 1 and Player 2 guesses 2, Player 2's payoff is 1.

- If Player 1 guesses 2 and Player 2 guesses 1, Player 2's payoff is -1.

- If Player 1 guesses 2 and Player 2 guesses 2, Player 2's payoff is 0.

Now, let's analyze the strategies and payoffs to identify the Nash equilibrium:

If Player 1 chooses P1 = 0:

- Player 2's best response is to choose P2 = 0, as Player 2's payoff is 0 regardless of their choice.

- This results in Player 1's payoff of 0.

If Player 1 chooses P1 = 1/3:

- Player 2's best response is to choose P2 = 0, as Player 2's payoff is -1 regardless of their choice.

- This results in Player 1's payoff of -1.

If Player 1 chooses P1 = 0 and Player 2 chooses P2 = 1/3:

- Player 1's best response is to choose P1 = 0, as Player 1's payoff is 0 regardless of their choice.

- This results in Player 2's payoff of 1.

If Player 1 chooses P1 = 1/3 and Player 2 chooses P2 = 1/3:

- There is no best response for either player in this case, as their payoffs are the same regardless of their choice.

- This results in Player 1's payoff of 0 and Player 2's payoff of 0.

Based on the analysis, we can see that the Nash equilibrium in this game is (P1 = 0, P2 = 0), where both players choose not to guess. In this scenario, both players receive a payoff of 0, and no player can improve their payoff by unilaterally deviating from this strategy combination.

Graphically, the Nash equilibrium can be represented as a point on a 2x2 payoff matrix with P1 on the x-axis and P2 on the y-axis. The Nash equilibrium (P1 = 0, P2 = 0) would be the intersection of the respective strategies for both players, resulting in a single point on the graph.

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