Consider (Test A - Test B). Use a 0.01 significance level to test the claim that people do better on the second test than they do on the first. (Note: You may wish to use software.) (a) What test method should be used? A. Matched Pairs B. Two Sample z C. Two Sample t (b) The test statistic is ___(c) The critical value is ___(d) Is there sufficient evidence to support the claim that people do better on the second test? A. No B. Yes

The amount of money we can make is $0.05.

We have,

P= $710

R= 5.1%

T= 12 year

Compounded Continuously:

A = P\(e^{rt\)

A = 710.00(2.71828\()^{(0.051)(12)\)

A = $1,309.32

Compounded Daily:

A = P(1 + r/n\()^{nt\)

A = 710.00(1 + 0.051/365\()^{(365)(12)\)

A = 710.00(1 + 0.00013972602739726\()^{(4380)\)

A = $1,309.27

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The area to the left of z=1.07 is approximately 0.8577 (rounded to four decimal place. To find the area under the standard normal curve to the left of z = 1.07 using a TI-84 calculator.

Follow these steps:

1. Press the "2nd" button, then press "Vars" to access the "DISTR" menu.
2. Scroll down to "normalcdf(" and press "Enter".
3. Enter -99999 (or -E99) as the lower limit, since we want to find the area to the left of z = 1.07, which is very close to negative infinity.
4. Enter 1.07 as the upper limit, since we want to find the area to the left of this value.
5. Enter 0 as the mean, since we're working with the standard normal distribution.
6. Enter 1 as the standard deviation, since we're working with the standard normal distribution.
7. Press "Enter" to calculate the area.

The answer should be approximately 0.8577 when rounded to four decimal places.

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Answer:

Vertically opposite angles are equal

So

x = 75°

Vertically opposite angles are equal

So

5y = 135°

Divide both sides by 5

y = 27

Hope this helps you

As per the median, the set of data that fulfilling Marjane's requirement is 24, 25, 25, 25, 26, 26 (option c).

In statistics, data is a collection of numbers or values that represent a particular phenomenon. One way to measure central tendency, or the typical or representative value of the data, is through the median and the mode.

The median is the middle value when the data is arranged in numerical order, and the mode is the value that appears most frequently.

The third set of data is 24, 25, 25, 25, 26, 26.

The median is the middle value, which is also (25+25)/2 = 25.

The mode is the value that appears most frequently, which is 25.

Therefore, the mode and median are the same, fulfilling Marjane's requirement.

Therefore, the correct option is (c).

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Answer:

this is prime

Step-by-step explanation:

The formula you have given (SS₁ + SS₂) / (n₁+ n₂) is actually the formula for the unweighted average of the variances, which is not appropriate when the sample sizes and variances are different between the two samples.

The formula for pooled variance is:

pooled variance = (SS₁+ SS₂) / (df₁ + df₂)

where SS₁ and SS₂ are the sum of squares for the two samples, df₁ and df₂ are the corresponding degrees of freedom, and the pooled variance is the weighted average of the variances of the two samples, where the weights are proportional to their degrees of freedom.

Note that the denominator is df₁ + df₂ not n₁+ n₂. The degrees of freedom take into account the sample sizes as well as the number of parameters estimated in

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The r-value ranges from -1 to +1, with -1 indicating a strong negative correlation. Therefore, the r-value closest to -1 represents the strongest negative correlation.

An r-value represents the strength and direction of a correlation between two variables. The strongest negative correlation occurs when the r-value is -1. In this case, as one variable increases, the other variable decreases consistently, showing a perfect negative linear relationship between the two variables.

The ability of a material to resist the flow of heat through it is gauged by the R-value , which is used in materials research and building construction. It measures the energy efficiency of insulation materials including fibreglass, foam board, and cellulose and is commonly represented in square metres kelvin per watt (m2K/W) units.

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The position vector of PQ is (2, 11). To determine the position vector of PQ, we can subtract the coordinates of the initial point P from the coordinates of the final point Q.

Given that P has coordinates (-5, -4) and Q has coordinates (-3, 7), we can calculate the position vector PQ as follows:

PQ = (x₂ - x₁) i + (y₂ - y₁) j

Substituting the coordinates, we have:

PQ = (-3 - (-5)) i + (7 - (-4)) j

PQ = (-3 + 5) i + (7 + 4) j

PQ = 2i + 11j

Therefore, the position vector of PQ is (2, 11).

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Answer:

y = -1

Step-by-step explanation:

Notice that the line x = 9 is a vertical line, therefore a line perpendicular to it will be a horizontal line of the form y = constant number.

Since we want it to go through the point (9, -1), then we know that that y value needs to be "-1", and the equation of the line will be given by the expression:

y = -1

Answer:

y =1

Step-by-step explanation:

\((9,-1)=(x ,y)\\\\x =m_1 =9\\m_2 = \frac{-1}{m_1} = \frac{-1}{9} = -\frac{1}{9} \\\\Substitute \:the \:values\:into ;\\y =mx+b\\\\-1 =-\frac{1}{9} (9) +b\\-1 = -1+b\\-1+1 = b\\0 =b\\m= 1 \\Substitute\:the\:new\:values\:into ;\\y = mx+b\\y = 1 x +0\\ y= 1\)

Answer: V = 28,600(0.909)^2

Step-by-step explanation: This is because the value of the car depreciates at a rate of 9.1% per year, which means that the value after the first year will be 0.909 times the original value, and the value after the second year will be 0.909 times the value after the first year. Therefore, we need to multiply the original value of the car by (0.909)^2 to find the value after 2 years.

Answer:

A.)

Rise = 2

Run = 5

m = 2/5

B.)

Rise = 2

Run = - 4

m = - 1/2

C.)

Rise = 3

Run = 1

m = 3

Step-by-step explanation:

Rise = y2 - y1

Run = x2 - x1

Slope, m = Rise / Run

A.) (0,0) ; (5 2)

x1 = 0 ; y1 = 0

x2 = 5 ; y2 = 2

Rise = 2 - 0 = 2

Run = 5 - 0 = 5

m = 2/5

B.) (1, 2) ; (-3, 4)

x1 = 1 ; y1 = 2

x2 = - 3 ; y2 = 4

Rise = 4 - 2 = 2

Run = - 3 - 1 = - 4

m = 2/-4 = - 1/2

C.) (5,2) ; (6,5)

x1 = 5 ; y1 = 2

x2 = 6 ; y2 = 5

Rise = 5 - 2 = 3

Run = 6 - 5 = 1

m = 3/1 = 3

Answer:

100

Step-by-step explanation:

\(0.1^2=0.01\)

Knowing this

\(0.1^6=0.01^3\)

from there

0.01^3 / 0.01^4

=

\(\frac{0.01^3}{0.01^4}\)

the 3 and 4 cancel (rules of exponents) leaving you with 1 over 0.01, this is equal to 1 divided by 0.01 which is equal to 100.

Hope this helps, if you are confused please refer to the png (sorry for the bad handwriting)

Answer: 60 yd

Step-by-step explanation:

Here: subdivided into 3 smaller pens (2w + w + w) extra widths for separation purposes (3 smaller pens)

180 yards of fencing material

180yd = 2L + 4w

180dy = 2*60 + 4w

60dy = 4w

w = 15yd, how wide can the rectangle can  be with L = 60yd

Answer:

-2

Step-by-step explanation:

Equation of the line 2x + y + 1 = 0 in slope intercept form is y = -2x - 1 with slope of -2. So, the slope is -2.

Answer:

13 years

18 years

Step-by-step explanation:

Let the age of the two brothers be x and y years.

According to the first condition:

x + y = 31.....(1)

According to the first condition:

x - y = 5.....(2)

Adding equations (1) & (2)

x + y = 31

x - y = 5

_______

2x = 36

x =36/2

x = 18 years

Plug x = 18 in equation (1)

18 + y = 31

y = 31 - 18

y = 13 years

Verification:

13 + 18 = 31

18 - 13 = 5

The final simplified expression is: -211/7i - 3/7

To simplify the given expression, let's work step by step:

(4 - i)(-3/7i) - 7i(8/2i)

First, let's simplify each multiplication:

(4 * -3/7i - i * -3/7i) - (7i * 8/2i)

Now, simplify further:

(-12/7i + 3/7i^2) - (56/2)

Remember that i^2 is equal to -1:

(-12/7i + 3/7(-1)) - (28)

Simplify the expression:

(-12/7i - 3/7) - 28

Combining like terms:

-12/7i - 3/7 - 28

Now, let's express the terms as a single fraction:

-12/7i - 3/7 - 196/7

Combine the numerators:

(-12 - 3 - 196)/7i - 3/7

Simplify further:

(-211)/7i - 3/7

The final simplified expression is:

-211/7i - 3/7

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Answer:

The correct answer is B

Step-by-step explanation:

.

The proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

We have,

A normal distribution located between z = 0.50 and z = -0.50,

So,

Now,

From the Z-score table,

We get,

The Probability corresponding to the Z score of -0.50,

i.e.

P(-0.50 < X < 0) = 0.191,

And,

The Probability corresponding to the Z score of -0.50,

i.e.

P(0 < X < 0.50) = 0.191,

Now,

The proportion of a normal distribution,

i.e.

P(Z₁ < X < Z₂) = P(Z₁ < X < 0) + P(0 < X < Z₂)

Now,

Putting values,

i.e.

P(-0.50 < X < 0.50) = P(-0.50 < X < 0) + P(0 < X < 0.50)

Now,

Again putting values,

We get,

P(-0.50 < X < 0.50) = 0.191 + 0.191

On solving we get,

P(-0.50 < X < 0.50) = 0.382

So,

We can write as,

P(-0.50 < X < 0.50) = 38.2%

So,

The proportion of a normal distribution is 38.2%.

Hence we can say that the proportion of a normal distribution located between z = .50 and z = -.50 will be 38.2%.

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All the points that will lie on the median through the point (7,4) are given as follows:

The median that passes through the point (7,4) is a linear function that also passes through the midpoint of the vertices (1,4) and (7,-2).

The midpoint of two points is given by the mean of it's coordinates, hence the midpoint of the vertices (1,4) and (7,-2) is calculated as follows:

Then the two points on the line are given as follows:

(4,1) and (7,4).

Given two points, the slope is calculated as the division of the change in y by the change in x, hence:

m = (4 - 1)/(7 - 4)

m = 1.

Hence:

y = x + b

When x = 4, y = 1, hence the intercept b is obtained as follows:

1 = 4 + b

b = -3.

Then the function is given as follows:

y = x - 3.

And the points that lie on the median are all the points for which the x-coordinate is 3 less than the y-coordinate.

The complete problem is given by the image shown at the end of the answer.

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Length of the actual tent is 15 feet.

Actual length is any distance between points that is not foreshortened by the view type.

Given that the scale of drawing is

1 inch : 5 feet

and length is 3 inches.

We have to find actual length of the tent.

Let us denote actual length of the tent by 'x'

We have by given data

3 inches : x = 1 inch : 5 feet

multiplying LHS by 3 we get,

3 : x = 3 : 15

By comparing both the sides

x = 15

Therefore the actual length of the tent is 15 feet.

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Answer:

28

Step-by-step explanation:

x + 7 = 35

subtract 7

x = 28

The two-way table to summarize the given data is attached.

Two-way tables are used to organize data based on two categorical variables. It is a way to display count, frequencies, or relative frequencies for two categorical variables. One category is represented by rows and the second category is represented by columns. Categories are labeled in the left column and top row. In a two-way table, the counts are placed in the center of the table, totals appear at the end of each row and column, and a sum of all counts or grand total is placed at the bottom right. The totals in the right column and bottom row are called marginal distributions (excluding the grand total). The entries in the center of the table (everything except the marginal distributions) are called joint frequencies. Hence, the two variables are gender and foreign language. The total number of students surveyed, or the grand total is 20. The entries in the center of the table are as provided in the data.

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The equation in percentage given by, $2.21 + 8% tax = $2.3868 rounds to $2.4 to the nearest tenth.

Given an equation,

$2.21 + 8% tax = $2.3868

This is an equation which relates the cost including the percentage of tax.

When 2.21 is added to the tax amount, we get $2.3868.

2.21 + (0.08 × 2.21) = 2.3868

Here it is not mentioned up to what decimal we have to round the figure.

If 2.3868 is rounded to the nearest whole number, it becomes 2.

If 2.3868 is rounded to the tenth, it becomes 2.4.

If 2.3868 is rounded to the hundredth, it becomes 2.39.

Hence the rounded amount to the nearest tenth is $2.4.

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The length of the steering device will be 4.5 inches.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The steering device extends to point T, and the diameter of the steering wheel is 15 inches long. Then the length of the steering device is given as,

7.5² = h² + 6²

56.25 = h² + 36

h² = 56.25 - 36

h² = 20.25

h = 4.5 inches

The length of the steering device will be 4.5 inches.

The diagram is given below.

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Answer:

40:60:80

Step-by-step explanation:

1. add the ratio first 2+3+4 =9, then divide the amount by the total number of parts

2. multiply the quotient by each part (20×2, 20×3 and 20×4)

If the elements in the pairs are related to each other then the pair is called as Ordered Pair an if the elements in the pair are not related then the pair is called as Unordered Pair .

The Ordered Pair is defined as a pair of elements having specific importance for order of their placements.  

Also, the ordered pairs are used to represent elements that have a relation between them .

The Ordered pairs are usually used  to represent a point on a coordinate plane.

The Unordered Pair is a set of the form (a,b) that have two elements "a and b" that have no particular relation between them,

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Smaller sample size results in smaller sampling variation of the OLS estimator for the slope coefficient in the sample regression model due to the fact that it reduces the amount of variability in the data. Smaller error variance also reduces sampling variation as it reduces the amount of overall variation in the data.

The sampling variation of the OLS estimator for the slope coefficient in the sample regression model is affected by a variety of factors. A smaller sample size will result in smaller sampling variation because it reduces the amount of variability in the data. This is due to the fact that a smaller sample size will contain less variation in the independent variable, and therefore the estimated slope coefficient will have less variation. Additionally, a smaller error variance will also reduce the sampling variation as it reduces the amount of overall variation in the data. Finally, smaller variation in the independent variable in the sample will also lead to smaller sampling variation of the OLS estimator. This is because the slope coefficient is estimated by minimizing the sum of squared residuals, which is a function of the variation in the independent variable. Thus, if the variation in the independent variable is reduced, the slope coefficient will have less variation. In conclusion, all three factors can lead to reduction in the sampling variation of the OLS estimator for the slope coefficient in the sample regression model.

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The expression that can be used  to find the temperature at noon is

–22.4 + 12.8 option B

Generally, The word "temperature" refers to the degree to which something is hot or cold and may be described using a number of different scales, such as Fahrenheit and Celsius.

The direction in that heat energy will spontaneously flow is indicated by temperature; specifically, it will flow from a hotter body (one that is at a higher temperature) to a colder one (one at a lower temperature).

In conclusion,  the temperature was 22.4°F below zero meaning

-22.4F in mathematical terms

and  12.8°F above zero in mathematical terms

Therefore, –22.4 + 12.8 is the expression that can be used  to find the temperature at noon

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The reversed grammar G_R generates the language L_R, which consists of the reverse of all the strings in L.

To construct a right-linear grammar that generates the language L over Σ = {a, b} consisting of all strings with no more than two 'a's, we can define the grammar as follows:

The grammar G = (V, Σ, P, S) where:

V = {S, A, B} is the set of non-terminal symbols.

Σ = {a, b} is the set of terminal symbols.

P is the set of production rules.

S is the start symbol.

The production rules are:

1. S -> ε (to generate the empty string)

2. S -> aA | bB (to generate strings starting with 'a' or 'b')

3. A -> aA | bB | ε (to generate strings with one 'a' or 'b')

4. B -> bB | ε (to generate strings with only 'b')

Explanation of the production rules:

- Rule 1 generates the empty string.

- Rule 2 allows the start symbol to be followed by 'a' or 'b' and expands to A or B.

- Rule 3 generates strings with one 'a' or 'b' by allowing A to be followed by 'a' or 'b' or expanded to ε.

- Rule 4 generates strings with only 'b' by allowing B to be followed by 'b' or expanded to ε.

The grammar allows the generation of strings with no more than two 'a's, as the non-terminal symbol A can be expanded to ε after one 'a' is generated. This ensures that there are at most two 'a's in the generated strings.

To generate the reverse of the strings in language L, we need to reverse the production rules. The reverse grammar G_R = (V, Σ, P_R, S), where P_R is the set of reversed production rules.

The reversed production rules are:

1. S -> ε

2. S -> Aa | Bb

3. A -> Aa | Bb | ε

4. B -> Bb | ε

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