100 points if u get this right ty have a nice day !

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\sigma)= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5\()^2\)

n=(15.996\()^2\)

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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The original list price for the product was $487.09.

To find the original list price for the product, we need to reverse the discounts and markup that were applied to it. Here is a step-by-step explanation:

Therefore, the original list price for the product was $487.09.

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Answer:

16

Step-by-step explanation:

AB = 20 - 12 = 8

BC = 8 : 2 = 4

CD = 4 + 12 = 16

Answer:

CD = 16

Step-by-step explanation:

Check the image for the steps

The following are the linear relationships between two variables measured in statistics:

So,

The following are the linear relationships between two variables measured in statistics:

Therefore, the following are the linear relationships between two variables measured in statistics:

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Answer:

The first option im pretty sure

Step-by-step explanation:

It is important for a sampling distribution to be normal (bell-shaped) because the center (mean) and the spread (standard deviation) of the sampling distribution would only be accurate if the distribution is normal.

The sampling distribution represents the distribution of sample statistics, such as the sample mean or sample proportion, obtained from multiple samples of the same size taken from a population. The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean approaches a normal distribution, regardless of the shape of the population distribution.

When the sampling distribution is normal, the mean of the sampling distribution is equal to the population mean, and the standard deviation of the sampling distribution, known as the standard error, can be accurately calculated. This allows us to make inferences about the population based on sample statistics.

If the sampling distribution is not normal, the properties and accuracy of estimators and hypothesis tests may be affected. Therefore, it is important for the sampling distribution to be normal in order to ensure the validity of statistical inferences.

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Answer:

THX FOR POINTS

Step-by-step explanation:

Answer:

x = 4\(\sqrt{3}\), y = 8\(\sqrt{3}\)

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan30° = \(\frac{\sqrt{3} }{3}\) , then

tan30° = \(\frac{opposite}{adjacent}\) = \(\frac{x}{12}\) = \(\frac{\sqrt{3} }{3}\) ( cross- multiply )

3x = 12\(\sqrt{3}\) ( divide both sides by 3 )

x = 4\(\sqrt{3}\)

------------------------------------------------------------

Using Pythagoras' identity in the right triangle

y² = x² + 12² = (4\(\sqrt{3}\) )² + 144 = 48 + 144 = 192 ( take square root of both sides )

y = \(\sqrt{192}\) = \(\sqrt{64(3)}\) = 8\(\sqrt{3}\)

Answer:

he go 2 full 13 in pecies 2.30

Step-by-step explanation:

The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate. is a True statement.

            The allowable range for an objective function coefficient assumes that the original estimates for all the other coefficients are completely accurate so that this is the only one whose true value may differ from its original estimate.

                  The allowable range for an objective function coefficient is known as the tolerance range. When solving linear programming problems, the tolerance range, also known as allowable or sensitivity ranges, is used to determine how much the optimal solution will alter if the values of the coefficients or constants change a little.

                 The tolerance range can provide insight into which values of the coefficients and constants should be monitored closely to assure that the results remain valid.

                The allowable range for an objective function coefficient is determined by the size of the original estimate and the allowable percentage or maximum variation from

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The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours."  

What does the frequency distribution in the table reveal about the homework habits of the two samples of high school students?

The frequency distribution in the table provides insights into the distribution of homework habits among the two samples of high school students. By examining the frequency counts in each time category, we can determine the proportion of students spending different amounts of time on homework each night. This information helps identify patterns and differences in homework habits between the two samples, allowing for a comparison of their study behaviors.

Here is an example of a 4-column table with 2 rows representing the results of a random survey asking two samples of 100 high school students about the amount of time they spend on homework each night:

Sample 1:

  Sample 1                                                     Number of Students

    Time                                                                   Frequency

   <1 hour                                                                     20

  1-2 hours                                                                    40

 2-3 hours                                                                     30

    >3 hours                                                                   10

Sample 2:

 Sample 2                                                        Number of Students

Time                                                                      Frequency

<1 hour                                                                        30

1-2 hours                                                                    35

2-3 hours                                                                   20

>3 hours                                                                      15

In this table, each sample represents a different group of 100 high school students, and the frequency of students spending a particular amount of time on homework each night is recorded. The time categories are divided into "<1 hour," "1-2 hours," "2-3 hours," and ">3 hours." The table provides an overview of the distribution of homework time among the two samples of high school students.

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Answer:

The answer to number A is 285

The answer to B is 5

The answer to C is 3

The answer to D is 72

Answer:

None

Step-by-step explanation:

None. √-21 is not a real number.

Answer:

4 and 5   i need to add 20 characters so yahhhh

Answer:

81.859%

Step-by-step explanation:

We solve the question using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 80 mph

σ is the population standard deviation = 7 mph

For x = 66 mph

z = 66 - 80/7

z = -2

Probability value from Z-Table:

P(x = 66) = 0.02275

For x = 87 mph

z = 87 - 80/7

z = 1

Probabilith value from Z-Table:

P(x = 87) = 0.84134

The probability of the trials will give the DeLorean a speed between 66 mph and 87 mph is calculated as:

P(x = 87 mph) - P(x = 66 mph)

0.84134 - 0.02275

= 0.81859

The percentage of the trials will give the DeLorean a speed between 66 mph and 87 mph?

100 × 0.81859

81.859%

These equations represent the total distance traveled (2400 miles) being equal to the product of the effective speed (airplane's airspeed + wind rate) and the corresponding time taken.

(a) To transform the problem into simultaneous equations, let's denote the plane's airspeed as "p" and the wind rate as "w." Since the plane's speed is affected by the wind, we can set up the following equations:

For the Washington, D.C. to San Francisco trip:

2400 = (p + w) * 7.5

For the San Francisco to Washington, D.C. trip:

2400 = (p - w) * 6

(b) To transform the problem into a matrix equation, we can write the system of equations in matrix form:

⎡ 7.5 7.5 ⎤ ⎡ p ⎤ ⎡ 2400 ⎤

⎢ ⎥ ⎢ ⎥ = ⎢ ⎥

⎣ 6 -6 ⎦ ⎣ w ⎦ ⎣ 2400 ⎦

Here, the matrix on the left represents the coefficients of the variables (p and w), the column vector on the right represents the constants (2400), and the column vector in the middle represents the variables (p and w).

(c) To find the plane's airspeed (p) and the wind rate (w), we can solve the matrix equation using matrix operations. However, since the solution requires numerical calculations, it's not feasible to provide the exact values without additional information or calculations.

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Answer:

their are 2

Step-by-step explanation:

Option 2 is correct that is 1.79

When presented in ascending order, the value that 75% of data points fall within is known as the higher quartile, or third quartile (Q3).

The quartiles formula is as follows:

Upper Quartile (Q3) = 3/4(N+1)

Lower Quartile (Q1) = (N+1) * 1/3

Middle Quartile (Q2) = (N+1) * 2/3

Interquartile Range = Q3 -Q1,

1.74, 0.24, 1.56, 2.79, 0.89, 1.16, 0.20, and 1.84 are available.

Sort the data as follows: 0.20, 0.24, 0.89, 1.16, 1.56, 1.74, 1.84, 2.79 in ascending order of magnitude.

The data set has 8 values.

hence, n = 8; third quartile: 3/4 (n+1)th term

Q3 =3/4 of a term (9) term

Q3 =27/4 th term

Q3 = 1.74 + 1.84 / 2 (average of the sixth and seventh terms)

equals 1.76

Thus Q3 is 1.76 that is option 2

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To divide 1.089 by 9.9, we first move the decimal points to get whole numbers and then perform long division, resulting in a quotient of approximately 0.11.

To divide 1.089 by 9.9, we need to start by making both numbers whole numbers. To do this, we will move the decimal point two places to the right for both numbers: 1.089 becomes 108.9 and 9.9 becomes 99. Now, we have 108.9 ÷ 99.

Next, we will perform long division. We know that 99 can fit into 108 once, so we write 1 above the 8. Now, we multiply 99 by 1, resulting in 99, which we subtract from 108 to get 9. Since 9 is smaller than 99, we bring down the decimal point and the next digit, which is 9, making it 99.

Now, we repeat the process. 99 can fit into 99 once, so we write another 1 after the decimal point, above the 9. We multiply 99 by 1, resulting in 99, and subtract that from 99, leaving us with 0. There are no more digits to bring down, so we have reached our final answer.

Therefore, 1.089 ÷ 9.9 is approximately equal to 0.11.

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Multiplication and division of regular numbers are the same as fractions and we will learn them with the multiplication and division of rational numbers worksheet.

To do the multiplication, first find the greatest common divisor of the numerator and the denominator. The factors are then grouped together so that the score equals one. Then multiply by the remaining factors. To divide, first rewrite the division as multiplication by the inverse of the denominator.

Cuemath's interactive math worksheets contain visual simulations to help your child visualize the concepts being taught, "see things as they really are, and reinforce learning from them". The Rational Numbers Multiplication and Division Worksheet follows a step-by-step learning process that helps students better understand concepts, identify errors, and eventually develop strategies for solving future problems.

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The answer to this question is  8

The preimage of the image after translation are shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The rule of the translation are,

T <2, - 5> (x, y)

Here, The coordinates of the image are,

(- 7, 7) , (- 2, 3) and (2, 7)

Since, The rule of the translation are,

T <2, - 5> (x, y)

Hence, The new coordinates of the pre - image are,

(- 7, 7) = (- 7 + 2, 7 - 5) = (- 5, 2)

(- 2, 3) = (- 2 + 2, 3 - 5) = (0, - 2)

(2, 7) = (2 + 2, 7 - 5) = (4, 2)

Thus, The new coordinates of the pre - image are,

(- 5, 2) , (0, - 2) and (4, 2)

Therefore, The preimage of the image after translation are shown in figure.

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Answer:

a^2+3a+2

Step-by-step explanation:

(a+1)(a+2)

a(a+2)+1(a+2)

a^2+2a+a+2

a^2+3a+2

Answer:

| - 19 - (- 8) |

Step-by-step explanation:

Given that the 2 points have the same x- coordinate, then the distance between the 2 points is the difference in the y- coordinates, that is

distance = | - 19 - (- 8) | = | - 19 + 8 | = | - 11 | = 11

Or

distance = | - 8 - (- 19) | = | - 8 + 19 | = | 11 | = 11

The p-value for the given test is approximately 0.067, rounded to two significant digits. This was calculated by finding the area to the right of z=1.5 under the standard normal distribution.

It is given that Null hypothesis: H0: μ ≤ 0, Alternative hypothesis: H1: μ > 0, Population standard deviation: σ = 1, Test statistic: z = 1.5

To find the p-value, we need to calculate the probability of observing a z-value of 1.5 or greater under the null hypothesis. Since the population follows the standard normal distribution, we can use a standard normal table or a calculator to find this probability.

Using calculator, we can find that the area to the right of z = 1.5 is approximately 0.0668 (rounded to four decimal places).

Since this is a one-tailed test with the alternative hypothesis in the right tail, the p-value is equal to the area in the right tail beyond the observed z-value. Therefore, the p-value for the test is approximately 0.067 (rounded to two significant digits).

So, the p-value for the given test is 0.067 (rounded to two significant digits).

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We have translated the given phrase into a variable expression as (1/9) × (x - 15).

To translate the given phrase "the product of one-ninth and the difference of a number and fifteen" into a variable expression, we can use the following:

1: Identify the unknown or variable number in the expression.

Let's say the variable number is 'x'.

2: Translate the phrase "one-ninth" to a fraction as 1/9.

3: Translate the phrase "the difference of a number and fifteen" to a mathematical expression.

As we have taken 'x' as the variable number, the difference of 'x' and fifteen can be written as (x - 15).

4: Combine the above expressions using the multiplication sign to get the variable expression.

So, the variable expression is:(1/9) × (x - 15)

The variable expression obtained is (1/9) × (x - 15). Hence, we have translated the given phrase into a variable expression using the required terms.

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Answer:

41 inches

Step-by-step explanation:

Let the point at the top of the door on the left be x

Wx + xH = 45

Let the point at the top of the door  on the right be c

Yc + cZ = 37

We know the door is

xH +  plus the width of the tile

The width of the tile is Yc

xH + Yc

On the right door

cZ +  the height of the tile

cZ + Wx

Add the two doors together

xH + Yc + cZ + Wx = 2 times the height of the door

Rewriting

xH +  Wx +  Yc + cZ = 2 times the height of the door

45+ 37 = 2 times the door height

82 = 2 times the door height

Divide by 2

41 = door height

we will find the length of rectangle when area is divided by the breadth of rectangle.

Some properties are rectangle are stated below:

1. rectangle has four right angles

2. rectangles has four sides and equal opposite sides which are parallel to each other.

3.rectangle has two diagonals which are similar in length.

The bigger side lengths are called length and the smaller sides are called breadth of rectangle.

if area of rectangle is given, we can find length when area is divided by its breadth.

 length = area/breadth

hence, length of rectangle is determined from the value of area and breadth.

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