Which of the following best describes the shape of the sampling distribution of the sample proportion?
a. When standardized, it is exactly the standard normal distribution.
b. When standardized, it is the t distribution.
c. It is approximately normal as long as n is greater than or equal to 30.
d. It is approximately normal as long as np is greater than or equal to 10 and n(1-p) is greater than or equal to 10.
e. None of these are correct.

The price of each plastic bead is $0.75 and the price of each metal bead is $1.25.

Let's assume the price of a plastic bead is 'p' dollars and the price of a metal bead is 'm' dollars.

We can create a system of equations based on the given information:

Equation 1: 7p + 5m = 7.25 (from the first bracelet)

Equation 2: 9p + 3m = 6.75 (from the second bracelet)

To solve this system of equations using elimination, we'll multiply Equation 1 by 3 and Equation 2 by 5 to make the coefficients of 'm' the same:

Multiplying Equation 1 by 3:

21p + 15m = 21.75

Multiplying Equation 2 by 5:

45p + 15m = 33.75

Now, subtract Equation 1 from Equation 2:

(45p + 15m) - (21p + 15m) = 33.75 - 21.75

Simplifying, we get:

24p = 12

Divide both sides by 24:

p = 0.5

Now, substitute the value of 'p' back into Equation 1 to find the value of 'm':

7(0.5) + 5m = 7.25

3.5 + 5m = 7.25

5m = 7.25 - 3.5

5m = 3.75

Divide both sides by 5:

m = 0.75

Therefore, the price of each plastic bead is $0.75 and the price of each metal bead is $1.25.

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Answer:

Step-by-step explanation:

If you use the triangle inequality theorem you just add the first two sides to determine if the number is bigger than the third side if so it can form a triangle that's the first step. Just repeat with a b and c a+b a+c and b+c, and it will help you determine what type of triangle it is.

I believe the first set can, angle a and c are larger than angle b I can't be sure about the other one. I'm sorry I hope this helps push you some direction forward.

Answer:

25×124/100=31

120×175/100=210

35×160/100=56

72×165/100=118.8

Answer:

5) 31

6) 210

7) 14

8) 25.2

Step-by-step explanation:

25+6=31

120+90=210

35-21=14

72-46.8=25.2

The fraction of the hour that remained is 1/4 hour.

The portion or part of the complete item is represented by a fraction. It stands for the equal components of the whole. The denominator and numerator are the two components of a fraction. The top number is referred to as the numerator, and the bottom number is referred to as the denominator.

The students have to submit the book reports in 1 hour.

After the first report, 2/3 hours remained. The next two reports took 1/6 hour and 1/4 hour respectively.

After the first report, 2/3 hours remained.

The next two reports took 1/6 and 1/4 hours.

So, the total time to complete the next two reports is:

= 1/6 + 1/4

= 10/24

= 5/12 hours

Therefore, the fraction of hour remained will be:

= 2/3 - 5/12

= ( 2/3 ) × ( 4/4 ) - 5/12

= 8/12 - 5/12

= 3/12

= 1/4 hour

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9514 1404 393

Answer:

  8

Step-by-step explanation:

A system of linear equations has no solution when the equations describe parallel lines. Parallel lines have the same slope. In your equation, the slope is the x-coefficient, 8. A parallel line will have a slope of 8.

The second equation will have a slope of 8 if the system has no solution.

The assumption of the differences between the paired observations is necessary about the population distribution in order to perform a dependent means hypothesis test.

A dependent means hypothesis test, also known as paired or matched samples, must be conducted on the presumption that the population's differences between the paired observations are normally distributed. Because the test is dependent on the distribution of the sample mean differences, which is presumed to be normally distributed, this assumption is required.

The standard error of the mean difference and the construction of confidence intervals both need the assumption of normality. Other techniques, including non-parametric testing, may be more suited if the population distribution is not normal.

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First let's find the length of the segment created by the two given points, using the formula:

Since the given points have the same x-coordinate, we have a vertical segment, so the adjacents sides to this side will be horizontal segments.

In order to find the other vertices, first let's find the length of the horizontal sides, using the area formula:

We can find the vertices by adding 6 to the x-coordinate of the given points, because then we will have the two horizontal sides of the rectangle:

So the possible locations for the other 2 vertices are (14, -5) and (14, 7).

Answer:

66.5

Step-by-step explanation:

Answer:

f(x) ≈ −2.42x3 + 15.89x2 − 7.55x + 12

Step-by-step explanation:

Notice that the year data are evenly spaced. Check the first differences between the total number or units to see if the data set is linear.

First Differences

41 − 18 = 23

67 − 41 = 26

82 − 67 = 15

69 − 82 = −13

17 − 69 = −52

Because the first differences are not constant, a linear model is not the best model of the data. Check the second differences to see if the data set can be modeled by a quadratic function.

Second Differences

26 − 23 = 3

15 − 26 = −11

−13 − 15 = −28

−52 − (−13) = −39

Because the second differences of the independent variable are not constant, a quadratic model is not the best model of the data. Check the third differences to see if the data set can be modeled by a cubic function.

Third Differences

−11 − 3 = −14

−28 − (−11) = −17

−39 − (−28) = −11

The third differences are approximately the same so we will use a cubic function to represent the data.

Enter the data into a calculator. Plot the data and find the cubic regression equation that best models the data.

f(x) ≈ −2.42x3 + 15.89x2 − 7.55x + 12

Answer:

19

Step-by-step explanation:

Answer:

The width would be 3 1/3 inches or 3.333 repeating

Step-by-step explanation:

Since you divide the length by 3, you would also have to divide the width by 3. 10 divided by 3 is 3 1/3 or 3.333 repeating (whichever one you choose).

Area of shaded region in the rectangle with a length of four inches and a width of eight inches rectangle with a length of four inches and a width of eight inches 20 inches².

Area is the amount of space a 2D shape occupies. This means a quantity which measures the number of unit squares that occupies the surface of a closed figure. The square unit is the standard unit of area, usually expressed in square inches, square feet, and many more.

The area of ​​a rectangle is always calculated by multiplying its length with its width. Which is the same as counting unit squares. So the equation for the area of ​​a rectangle is: A = L x W

Where, A = Area of ​​rectangle

L = length

W = width

For the given case:

Area of ​​rectangle

= 4 × 8

= 32 inches²

Area of triangle = ¹/₂(base × height)

= ¹/₂( 6 × 3 )

= ¹/₂ × 24

= 12 inches²

Area of shaded region = Area of rectangle - Area of triangle

= 32 - 12

= 20 inches²

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The complete question is as follows:

A white right triangle with a height of three inches and a base of six inches is inside a rectangle with a length of four inches and a width of eight inches. what is the area of the shaded area?

Answer:

Domain: x < 5

Range: all numbers, -∞, ∞

This is because the problem will be able to be solved with multiple solutions as long as there are no specific values assigned to x. The problem will have a solution from a range of negative infinity to infinity, meaning every number or solution you can think of.

Stating that the area under the standard normal distribution curve between z=0 and z=1.00 is 0.3413, is the same as stating that the probability of randomly selecting a standard normally distributed variable z with a value between 0 and 1.00 is 0.3413.

Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

In science, the probability of an event is a number that indicates how likely the event is to occur. It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%. The more likely it is that the event will occur, the higher its probability.

Therefore, the given statement is completed as:

Stating that the area under the standard normal distribution curve between z=0 and z=1.00 is 0.3413, is the same as stating that the probability of randomly selecting a standard normally distributed variable z with a value between 0 and 1.00 is 0.3413.

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Answer:

\( - 6 + 7s - 4r - 2 \\ \\ - 6 + 7(7) - 4( - 7) - 2 \\ \\ - 6 + 49 + 28 - 2 \\ \\ = 6 9\)

I hope I helped you^_^

Step-by-step explanation:

length = 2×width + 6

84 = 2×length + 2×width

now using the first in the second equation :

84 = 2×(2×width + 6) + 2×width = 4×width + 12 + 2×width

84 = 6×width + 12

72 = 6×width

width = 12 cm

length = 2×width + 6 = 2×12 + 6 = 24 + 6 = 30 cm

The correlation and the slope always have the same sign (+ or −), meaning that if the correlation is positive, the slope will also be positive and vice versa.

The slope and the correlation are two important measures in statistics. The slope of a line represents the change in the dependent variable (y) for every 1 unit change in the independent variable (x).

In the case of the least-squares line, the slope (m) and the correlation (r) have a relationship.

It is important to note that the slope of the line is always equal to the correlation times the ratio of the standard deviation of the dependent variable to the standard deviation of the independent variable.

This can be represented mathematically as:

=> m = r * (SDy/SDx).

Therefore, the correlation (r) always has a value between −1 and 1, indicating the strength of the relationship between the variables. If r is close to 1, the relationship between the variables is strong and positive.

On the other hand, if r is close to −1, the relationship between the variables is strong and negative.

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When selecting the appropriate number of treatment conditions, it is essential to consider factors such as resources, research complexity, and confounding variables.

Having conditions that are proportional to each other means that the level or intensity of each condition varies in direct proportion to the others, such that if one condition is increased or decreased, the others are also adjusted in a corresponding manner.

When choosing the appropriate number of treatment conditions for an experiment, there are several issues to consider. One of these is the ability to distinguish differences between treatment conditions.

Having conditions that are proportional to each other means that the differences between treatment conditions are consistent across all levels of the independent variable. In other words, if the independent variable increases by a certain amount, the difference between the treatment conditions remains constant. This can be important for ensuring that the treatment effects are interpretable and generalizable to other populations.

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The mean and the standard deviation are 36.68 °C and 0.34 °C respectively.

Given data set on body temperature of a random sample a mean of 98.02 °F is obtained with a standard deviation of 0.62 °F, if every value is converted into a Celsius scale, we need to find the mean and the standard deviation.

The formula to convert Fahrenheit to Celsius is given by

C = (F - 32) x 5/9 Where F is the temperature in Fahrenheit and C is the temperature in Celsius.

So the sample mean temperature in Celsius is

C = (98.02 - 32) x 5/9C = 36.68 °C

and the sample standard deviation temperature in Celsius is

S = 0.62 x 5/9S = 0.34 °C.

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Answer:

a) 125 ml of milk

b) 7.5 g of butter

Step-by-step explanation:

Answer: A. Simon needs 125 ml of milk to make 4 pancake.  B. He needs 7 and a half grams of butter to make 12 pancakes

Step-by-step explanation:

A) If we know that 250 ml milk can help make 8 pancakes then we could set up a proportion as to how many milk we need to make 4 pancakes.

  \(\frac{250}{8} = \frac{x}{4}\)   Solve by cross  product,

8x = 1000

x = 125  

B) The same with this we could also set up a proportion. We know you need 5 grams of butter when making 8 pancakes.

\(\frac{5}{8} = \frac{x}{12}\)    solve by cross product

60 = 8x

x = 7.5

The inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

To find the inverse Laplace transform of each function, we need to express them in terms of known Laplace transforms. Here are the solutions for each function:

a)

\(F(s) = \large{\frac{2e^{-0.5s}}{s^2-6s+9}}\)

To find the inverse Laplace transform, we first need to factor the denominator of F(s). The denominator factors as (s - 3)². Therefore, we can rewrite F(s) as:

\(F(s) = \large{\frac{2e^{-0.5s}}{(s-3)^2}}\)

Now, we know that the Laplace transform of eᵃᵗ is 1/(s - a). Therefore, the inverse Laplace transform of

\(e^(-0.5s) \: is \: e^(0.5t).\)

Applying this, we get:

\(f(t) = 2e^(0.5t) * t \\

b) F(s) = \large{\frac{s-1}{s^2-3s+2}}\)

We can factor the denominator of F(s) as (s - 1)(s - 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{s-1}{(s-1)(s-2)}}\)

Simplifying, we have:

\(F(s) = \large{\frac{1}{s-2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(2t) \\

c) F(s) = \large{\frac{s-1}{s^2+s-2}}

\)

We factor the denominator of F(s) as (s - 1)(s + 2). The expression becomes:

\(F(s) = \large{\frac{s-1}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{1}{s+2}}\)

The Laplace transform of 1 is 1/s. Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-2t) \\

d) F(s) = \large{\frac{e^{-s}(s-1)}{s^2+s-2}}\)

We can factor the denominator of F(s) as (s - 1)(s + 2). Now, we rewrite F(s) as:

\(F(s) = \large{\frac{e^{-s}(s-1)}{(s-1)(s+2)}}\)

Canceling out the (s - 1) terms, we have:

\(F(s) = \large{\frac{e^{-s}}{s+2}}\)

The Laplace transform of

\(e^(-s) \: is \: 1/(s + 1).\)

Therefore, the inverse Laplace transform of F(s) is:

\(f(t) = e^(-t)\)

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The predicted average test score for a classroom with 20 students is 432.28. The predicted change in the classroom average test score when going from 17 to 21 students is -24.91. The sample average test score is 414.22. The total sum of squares is 15405.

Let's go through each question and calculate the answers step by step

(a) To find the prediction for a classroom with 20 students, we substitute CS = 20 into the regression equation:

Test score = 556.828 - 6.2274 × 20

Test score = 432.28 (rounded to two decimal places)

(b) To find the prediction for the change in the classroom average test score when going from 17 students to 21 students, we subtract the predicted scores for each case:

Change in test score = (-6.2274 × 21) - (-6.2274 × 17)

Change in test score = -24.91 (rounded to two decimal places)

(c) The sample average class size is given as 22.90. To find the sample average of test scores, we substitute the average class size into the regression equation:

Test score = 556.828 - 6.2274 × 22.90

Test score = 414.22 (rounded to two decimal places)

(d) The total sum of squares (TSS) can be calculated using the formula TSS = n SER², where n is the number of observations and SER is the standard error of the regression. Since the number of observations is 103 and SER is given as 12.3, we have:

TSS = 103 × (12.3²)

TSS = 15405 (rounded to the nearest whole number)

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--The given question is incomplete, the complete question is given below " Suppose that a researcher, using data on class sizestudent submitted image, transcription available below(CS)and average test scores from 103 third-grade classes, estimates the OLS regression

Test scor = 556.828 - 6.2274CS, R^2 = .09, SER = 12.3

(a) A classroom has 20 students. The regression's prediction for that classroom's average test score is__ . (Round your response to two decimal places.)

(b) Last year a classroom had 17 students, and this year it has 21 students. The regression's prediction for the change in the classroom average test score is__ . (Round your response to two decimal places.)

(c) The sample average class size across the 103 classrooms is 22.90.The sample average of the test scores across the 103 classrooms is ___. (Hint: Review the formulas for the OLS estimators.) (Round your response to two decimal places.)

(d) The total sum of squares is ___ . (Hint: Review the formulas for thestudent submitted image, transcription available belowR2 andstudent submitted image, transcription available belowSER.) (Round your response to the nearest whole number.)"--

Answer:

Geometric Sequence

Step-by-step explanation:

1. Check the difference.

The difference between the 1st and 2nd term

\(( - 5.4) - ( - 3.6) = - 1.8\)

The difference between the 2nd and 3rd term

\(( - 8.1) - ( - 5.4) = - 2.7\)

The difference is not the same. Therefore, it is not an arithmetic sequence.

2. Check the ratio

The ratio between the 1st and 2nd term

\(( - 5.4) \div ( - 3.6) = 1.5\)

The ratio between the 2nd and 3rd term

\(( - 8.1) \div ( - 5.4) = 1.5\)

The ratio is the same. Therefore, it is a geometric sequence.

To find the equation of a parabola that passes through two points and a third point, we need to write a system of three equations in three variables (a, b, and c) using the standard form of the parabolic equation, and then solve for the variables.

To find the equation of a parabola that passes through two points, we can use the standard form of a parabolic equation: y = ax^2 + bx + c. Since we have two points, (x1,y1) and (x2,y2), we can write two equations:
y1 = ax1^2 + bx1 + c
y2 = ax2^2 + bx2 + c
We need to solve for a, b, and c. One way to do this is to eliminate c by subtracting the second equation from the first:
y1 - y2 = a(x1^2 - x2^2) + b(x1 - x2)
Now we can use the fact that the parabola passes through a third point, (x3,y3), to write another equation:
y3 = ax3^2 + bx3 + c
We can substitute c from the first equation into this equation:
y3 = ax3^2 + bx3 + y1 - a(x1^2 - x2^2) - b(x1 - x2)
Now we have three equations and three unknowns (a, b, and c), which we can solve using algebra or matrix methods. Once we have the values of a, b, and c, we can plug them into the standard form of the parabolic equation to get the equation of the parabola that passes through the three points.
The resulting equation will be the equation of the parabola that passes through the given points.

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Even though dividing a fraction by a whole number might be challenging, it is simple to achieve with a few steps. By placing the full number above 1, you must first divide it into a fraction. After that, multiply the fraction you are dividing by the inverted version of the fraction. Lastly, simplify the response as much as possible.

For instance, to multiply 3/4 by 2:

Put 2 over 1, making it 2/1, to make it a fraction.

To get 1/2, invert 2/1.

To get 3/8, multiply 3/4 by 1/2.

Divide the numerator and denominator by 3 to get 1/4, which is the simplest representation of the fraction 3/8.

Hence, 1/4 is equivalent to 3/4 when divided by 2.

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Answer:

2.5

The lowest point on the graph, or the minimum is at f(x)= 2.5

The minimum value of the given periodic function is, 2.5

Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).

Vertical line test:-

Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.

If we get more images then it will not be a function.

For example, let us take, y² = 4ax

y = ±√4ax

For single value of x we get two values of y

Hence, it will not be a function.

Given that,

A periodic function,

Period  = 3π

The value of the function is in the range of (2.5, 4.5)

So,

Maximum value = 4.5

Minimum value  = 2.5

Thus, the minimum value is 2.5

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a) Hypothesis test:

Null hypothesis (H0): The percentage of graduate students looking for housing on campus is equal to 15%.

Alternative hypothesis (Ha): The percentage of graduate students looking for housing on campus is greater than 15%.

To test the hypothesis, we can use a one-sample proportion test. We will calculate the test statistic and compare it to the critical value or p-value to make a decision.

The observed proportion of graduate students looking for housing on campus is 78/433 = 0.1804.

Using a significance level (α) of 0.05, we will conduct the test and calculate the test statistic and p-value.

Plan:

Test statistic: z = (p - p) / sqrt(p(1-p)/n)

where p is the observed proportion, p is the hypothesized proportion (0.15), and n is the sample size (433).

Do:

Calculating the test statistic:

z = (0.1804 - 0.15) / sqrt(0.15 * 0.85 / 433)

z ≈ 2.07

Conclude:

Since the test statistic is 2.07, we compare it to the critical value or calculate the p-value.

The critical value for a one-sided test with a significance level of 0.05 is approximately 1.645. Since 2.07 > 1.645, the test statistic falls in the rejection region.

The p-value associated with the test statistic of 2.07 is less than 0.05. Therefore, we reject the null hypothesis.

Based on the survey data, there is evidence to suggest that the percentage of graduate students looking for housing on campus is greater than 15%. The housing office should consider increasing the amount of housing available to graduate students.

b) The p-value obtained in part a) represents the probability of obtaining a test statistic as extreme as the one observed (or more extreme), assuming the null hypothesis is true.

In this case, the p-value is less than 0.05, which suggests strong evidence against the null hypothesis. It indicates that the observed proportion of graduate students looking for housing on campus is significantly higher than the hypothesized proportion of 15%.

c) Including the 21 non-respondents would change the sample size and potentially affect the estimated proportion. If these additional respondents had similar characteristics to the 433 who responded, it is possible that the recommendation might still remain the same.

However, the exact impact depends on the responses of the non-respondents, so it is difficult to determine the precise effect without their data.

d) Type II error in this study would occur if the housing office fails to increase the amount of housing on campus when it is actually necessary (i.e., the percentage of graduate students looking for housing on campus is higher than 15%).

This means the null hypothesis would not be rejected when it should have been. A consequence of this type of error would be the unmet demand for housing, potentially causing dissatisfaction among graduate students and a shortage of available housing options.

e) Type I error in this study would occur if the housing office increases the amount of housing on campus when it is not necessary (i.e., the percentage of graduate students looking for housing on campus is not higher than 15%). This means the null hypothesis would be rejected incorrectly.

A consequence of this type of error would be allocating resources and efforts towards increasing housing capacity unnecessarily, which could result in wastage of resources and potentially impact other areas of the university's operations.

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Answer:

(-∞, -3]U [-2,∞)

Step-by-step explanation: