Simplify: (3x-4)+(-2x+8).

The set Z(2) consists of the remainders of integers when divided by 2, and 2/6 is congruent to 2 modulo 2, which is not an element of Z(2), we can conclude that Z(2) does not contain 2/6.

To determine if the set Z(2) contains the fraction 2/6, we need to understand what Z(2) represents.

The notation Z(2) typically refers to the set of integers modulo 2, also known as the integers modulo 2 ring. In this set, the elements are the remainders of integers when divided by 2, which are 0 and 1.

To check if 2/6 is in Z(2), we need to reduce 2/6 modulo 2. When we divide 2 by 6, the remainder is 2, which means 2/6 is congruent to 2 modulo 2.

In Z(2), the only possible values are 0 and 1, so 2 is not an element of Z(2). Therefore, 2/6 is not in Z(2).

In summary, since the set Z(2) consists of the remainders of integers when divided by 2, and 2/6 is congruent to 2 modulo 2, which is not an element of Z(2), we can conclude that Z(2) does not contain 2/6.

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Answer:

2.  43 degrees

3.  35 degrees

Step-by-step explanation:

Srr the attached worksheet.

The sampling distribution of the x-bar is approximately normally distributed with a mean of 75 and a standard deviation of 2.

The sampling distribution of the sample mean (x-bar) can be described based on the given information.

Given that the population is skewed right with a mean (μ) of 75 and a standard deviation (σ) of 12, the sampling distribution of the x-bar will approach a normal distribution as the sample size (n) increases.

This is known as the Central Limit Theorem.

According to the Central Limit Theorem, regardless of the shape of the population distribution, the sampling distribution of the x-bar will be approximately normal if the sample size is large enough.

In this case, with a sample size of n = 36, the sampling distribution of the x-bar can be considered approximately normal.

The mean of the sampling distribution of the x-bar will be equal to the population mean (μ), which is 75 in this case.

The standard deviation of the sampling distribution of the x-bar, also known as the standard error of the mean (SE), can be calculated by dividing the population standard deviation (σ) by the square root of the sample size (n).

Hence, the standard error of the mean (SE) is calculated as σ/√n = 12/√36 = 12/6 = 2.

Therefore,

The sampling distribution of the x-bar is approximately normally distributed with a mean of 75 and a standard deviation of 2.

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After constructing a circle, the next step in constructing an inscribed hexagon by hand is to draw two diameters of the circle that are perpendicular to each other.

Drawing two diameters of the circle that are perpendicular to each other is the next step in constructing an inscribed hexagon because it helps to determine the positions of the vertices of the hexagon. The diameters divide the circle into four equal quadrants, with the center of the circle as the point of intersection. By connecting the points where the diameters intersect the circle, we can identify the six vertices of the hexagon. These vertices will lie on the circumference of the circle and will form the six sides of the inscribed hexagon.

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Answer:

Step-by-step explanation:

No choice is given but here is the general interpretation.

Y-intercept is where the plot crosses the y-axia at x=0. In this case, x is T which represents number of TVs owned by the family. T=0 meaning there is no TV and B = 96.66 is the one month's electric bill in dollars for all other appliances in the home.

Given function

Now

Compare to slope intercept form y=mx+b

Here y intercept may be the fixed charge .

(a) Limitations: Assumes reversible process, constant heat capacity.

(b) Limitations: Assumes constant T and P, and independent DH and DS with temperature.

(c) Limitation: Assumes non-expansion conditions, may not account for volume changes in real scenarios.

We have proved that Angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

To prove that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, we can use the following steps:

Step 1: Join points A and C with a line segment. Let's label the point where AC intersects with line segment BD as point E.

Step 2: Since line segment AC is drawn, we can consider triangle ABC and triangle ADC separately.

Step 3: In triangle ABC, we have angle B + angle ABC + angle BCA = 180 degrees (due to the sum of angles in a triangle).

Step 4: In triangle ADC, we have angle D + angle ADC + angle CDA = 180 degrees.

Step 5: From steps 3 and 4, we can deduce that angle B + angle ABC + angle BCA + angle D + angle ADC + angle CDA = 360 degrees (by adding the equations from steps 3 and 4).

Step 6: Consider quadrilateral ABED. The sum of angles in a quadrilateral is 360 degrees.

Step 7: In quadrilateral ABED, we have angle BAD + angle ABC + angle BCD + angle CDA = 360 degrees.

Step 8: Comparing steps 5 and 7, we can conclude that angle B + angle BCD + angle D = angle BAD + angle ABC + angle ADC.

Step 9: Rearranging step 8, we get angle BCD = angle BAD + angle ABC + angle ADC.

Therefore, we have proved that angle BCD is equal to angle BAD plus angle ABC plus angle ADC, as required.

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Given: Quadrilateral \(\displaystyle\sf ABCD\)

To prove: \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\)

Proof:

1. Draw segment \(\displaystyle\sf AC\) and extend it to point \(\displaystyle\sf E\).

2. Consider triangle \(\displaystyle\sf ACD\) and triangle \(\displaystyle\sf BCE\).

3. In triangle \(\displaystyle\sf ACD\):

4. In triangle \(\displaystyle\sf BCE\):

5. Since \(\displaystyle\sf \angle BCE\) and \(\displaystyle\sf \angle BCD\) are corresponding angles formed by transversal \(\displaystyle\sf BE\):

6. Combining the equations from steps 3 and 4:

Therefore, we have proven that in quadrilateral \(\displaystyle\sf ABCD\), \(\displaystyle\sf \angle BCD = \angle BAD + \angle ABC + \angle ADC\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The appropriate methods for analyzing the variables Birth Rate and Death Rate at the same time would be scatterplot, two-way table, and stacked bar chart.

Scatterplot: A scatterplot can be used to visually display the relationship between two quantitative variables, such as Birth Rate and Death Rate. Each point on the scatterplot represents a pair of values for the two variables, making it easy to identify patterns or trends in the data.

Two-way table: A two-way table can be used to display the distribution of two categorical variables, such as Birth Rate and Death Rate, and how they relate to each other. It can help identify the joint frequency or relative frequency of different categories.

Stacked bar chart: A stacked bar chart can be used to show how two categorical variables, such as Birth Rate and Death Rate, are related to each other. Each bar represents the total frequency for each category, and the bars are divided into sections representing the subcategories of the other variable. This makes it easy to compare the distribution of the two variables across each category.

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Catelyn will have approximately $1,647.62 in her account after 3 years of making deposits every 6 months.

To calculate how much Catelyn will have after 3 years, we need to determine the total number of compounding periods and then apply the compound interest formula.

Given:
Principal deposit (P) = $1537
Interest rate (r) = 2.07% per year (expressed as a decimal, r = 0.0207)
Compounding period (n) = 4 times per year (quarterly)
Time (t) = 3 years

First, we calculate the total number of compounding periods:
Number of compounding periods (N) = n * t = 4 * 3 = 12

Next, we can use the compound interest formula to calculate the future value (A):
A = P * (1 + r/n)^(n*t)

Plugging in the values:
A = $1537 * (1 + 0.0207/4)^(4*3)
A = $1537 * (1 + 0.005175)^12
A = $1537 * (1.005175)^12
A ≈ $1,647.62

Therefore, Catelyn will have approximately $1,647.62 in her account after 3 years of making deposits every 6 months.

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The volume of the triangular prism is 216 cubic meters.

To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.

Calculate the area of the triangular base.

The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.

Plugging in the values, we get:

Area = (1/2) * 8 meters * 9 meters = 36 square meters.

Multiply the area of the base by the length of the prism.

The length of the prism is given as 12 meters.

Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.

Adjust for the shape of the prism.

Since the prism is a triangular prism, we need to divide the volume by 2.

Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.

Therefore, the volume of the triangular prism is 216 cubic meters.

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The function [y = log(x)] is translated 1 unit to the right and 2 units down, yielding [g(x) = log(x - 1) - 2] as the translated function. and this may be established by using the transformation's rules.

Given:

One unit to the right and two units down translate the function y=log(x).

The translated function's graph can be drawn using the procedures listed below:

First, write the function that is supplied.

y = log(x) (x)

Step 2: Multiply the given function in the right direction—that is, in the positive x-axis direction—by factor 1 in accordance with the data provided. The aforementioned function is now:

f(x) = lox (x - 1)

Step 3: Next, move the graph of the function f(x) in a downward direction, or in the opposite direction of the y-axis.

g(x) = log(x - 1) - 2

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Answer:

im confusedddddddd.................

Answer:

It would be 30 mph

Step-by-step explanation:

45/6=7.5

7.5*4=30

Answer:

30 minutes

Step-by-step explanation:

Each mile takes him 7 minutes 30 seconds. So you will do 7.5 x 4 to get 30 minutes

Answer:

explained below

Step-by-step explanation:

Because the electro has a smaller mass than the mass of the proton, scientific notation is usually used so that the numbers are on the same "scale" but if we see the scientific notation we may be able to identify which is greater and which is less, due to that the exponent is less the number is smaller and on the contrary if the number is greater, it is a larger number.

In the image I leave an example of the use of scientific notation in this area

Step-by-step explanation:

the equation of the price of each shirt =

50 - 3s = 14

the price of each shirt =

3s = 50-14

3s = 36

s= 36/3

s = 12

=> $12

12$

50 - 3s = 14

3s = 50 - 14

3s = 5 tens - fourteen

3s = 36

s = 36 ÷ 3

s = (3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3) <= 12 factors

s = 12

s = 12$

Answer: That looks right to me

Step-by-step explanation:

The maximum value of f(x, y)=x2-x-y on the region where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1 is 1.

To find the maximum value, we can set up a system of inequalities and solve it:

0 ≤ x ≤ 1
0 ≤ y ≤ 1
f(x, y)=x2-x-y

Since both x and y are greater than or equal to 0, their product will also be greater than or equal to 0. Therefore, the maximum value of the equation is when x = 1 and y = 0, since it maximizes the positive value of x2 while minimizing the negative value of -x-y. This means that the maximum value of f(x, y) is 1.

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The maximum value of f(x,y)=x^{2}-x-yf(x,y)=x 2 −x−y on the region where \{(x, y): 0 \leq x \leq 1,0 \leq y \leq 1\} is 0.

To find the maximum value, we need to find the critical points of the function and test them within the given region. The critical points are where the partial derivatives of the function are equal to 0.

The partial derivative with respect to x is:
f_x(x,y)=2x-1

The partial derivative with respect to y is:
f_y(x,y)=-1

Setting these partial derivatives equal to 0, we get:
2x-1=0 --> x=1/2
-1=0 --> no solution for y

So the only critical point within the given region is (1/2, y) for any value of y. However, since the partial derivative with respect to y is always -1, the function is decreasing with respect to y. Therefore, the maximum value will occur when y is at its smallest value, which is 0.

Plugging in x=1/2 and y=0 into the original function, we get:
f(1/2,0)=(1/2)^{2}-(1/2)-0=0

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Given function is

The vertex of the graph is at (1,3).

Answer:

x(5x²-7)

Step-by-step explanation:

5x³-7x

=x(5x²-7)

To prove your answer,let's multiply x by each term in the bracket

=x X 5x²=5x³

x X -7 =-7x

Answer:

C) 10, 14, 13

the sum of the lengths of the two shorter legs must be greater than the length of the third leg.   note: not equal to either like "B".

Answer:

(a) 0.4 or 40%

(b) 0.1 or 10%

Step-by-step explanation:

(a) If you get 4 "ones" after 10 rolls of the die, the proportion of the rolls that resulted in "ones" is:

\(p=\frac{4}{10}\\ p=0.4\)

(b) If you get 2 "ones" after 20 rolls of the die, the proportion of the rolls that resulted in "ones" is:

\(p=\frac{2}{20}\\ p=0.1\)

The scale factor by which the picture has been enlarged is 3.5

It is given that the width of the picture is 5 inches and the length of the picture is 17.5 inches.

Length (l) = 7 inches

Width (b) = 5 inches

The picture is a rectangle, so the area of the picture will be the product of the length and the width, that is Area = 7 * 5 = 35 square inches.

The picture has been enlarged, let k be the scale factor that has been used to enlarge the picture.

The width has been enlarged to 17.5 inches

And the length has been enlarged to 24.5 inches

So, 5 * k = 17.5 and 7* k = 24.5

After solving these two equations, we get

k = 3.5

So, the scale factor by which the picture has been enlarged is 3.5

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Answer:

Step-by-step explanation:

To get a larger image - you multiply the original dimensions.

To find the scale factor - divide each enlarged dimension by its matching original dimension.

17.5 divided by 5 = 3.5

24.5 divided by 7 = 3.5

This is the scale factor for the enlargement.

The answer options are fractions - 17.5/5 = 3.5

so that is the correct choice.

The temperature at the point where the clouds begin to form is 77.65 °F

Given: The starting point is 1234 feet and air temperature is 79.4°F

You climb to where you notice clouds beginning to form.It can be observed that the temperature decreases by 3.5°F per 1000 feet as we go up.

Using this information, we can calculate the temperature at the point where the clouds start forming.

Let the height of the point where clouds begin to form be x feet above the starting point. As per the question, the temperature decreases by 3.5°F per 1000 feet as we go up.

Therefore, the temperature at the height of x feet can be calculated as:

T(x) = T(1234) - 3.5/1000 * (x - 1234)°F , where

T(1234) = 79.4°F

Substituting the value of x = 1234 + 500, (as we need to know the temperature at the point where clouds begin to form) we get:

T(1734) = T(1234) - 3.5/1000 * (1734 - 1234) °F

= 79.4 - 3.5/1000 * 500 °F

= 79.4 - 1.75 °F

= 77.65 °F

Therefore, the temperature at the point where the clouds begin to form is 77.65 °F

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Answer:

9, 13, 17, 21, 25, 29

Step-by-step explanation:

Since there is an equal increase of the same amount, the sequence is arithmetic with n th term

Substituting a = 9 and d = 4 into the n th term expression

\(a_{n}\) = 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5

\(a_{n}\) = a + (n - 1)d

where a is the first term and d the common difference

The third term and sixth term are therefore

a + 2d = 17 → (1)

a + 5d = 29 → (2)

Subtract (1) from (2) term by term, eliminating a, that is

3d = 12 ( divide both sides by 3 )

d = 4

Substitute d = 4 into either of the 2 equations and solve for a

Substituting into (1)

a + 2(4) = 17

a + 8 = 17 ( subtract 8 from both sides )

a = 9

Thus the first term is 9 and the common difference d = 4

The sequence of terms is therefore

9, 13, 17, 21, 25, 29

Substituting a = 9 and d = 4 into the n th term expression

\(a_{n}\) = 9 + 4(n - 1) = 9 + 4n - 4 = 4n + 5

Answer:

12 + n

Step-by-step explanation:

8 + (-4) would be 4

Answer:

It would:

12+ n  

because:

8+ (n - 4) = n + 4

n+ 4 = n+ 4

(8+n)-4 = n+ 4

12+ n = 12+n

(8-4) + n = 4+n

The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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They suffer loss by selling bananas at 65c.

To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.

Given:

Cost of one box = R75

Then, cost of three boxes = R75 x 3

                                            = R225

Now, one box has 12 bunches of 12 bananas each.

Then, one box contain = 12 x 12 = 144 bananas

and, 3 box contain = 144 x 3 = 432 Bananas

If managed to sell 80 % of the bananas then they sold

= 432 x 0.8 = 346 Bananas

So, they earned by selling those bananas

= 346 x 0.65

= R224.9

Thus, they suffer loss.

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Answer:

2/3

Step-by-step explanation:

We can find the slope by using the slope formula

m = ( y2-y1)/(x2-x1)

   = ( 12-18)/(20 -11)

   = -6/-9

 = 2/3

The standard deviation of the sum of the two independent random variables is 5.

The standard deviation of the sum of two independent random variables is equal to the square root of the sum of the variances of each random variable.

To find the standard deviation of the sum of two independent random variables, you can use the following formula:

Standard deviation of the sum (σ_sum) = √(σ₁² + σ₂²)

Here, σ₁ and σ₂ are the standard deviations of the two independent random variables.

Given: σ₁ = 3 and σ₂ = 4

Now, plug the values into the formula:

σ_sum = √(3² + 4²) = √(9 + 16) = √25 = 5

So, the standard deviation of the sum of the two independent random variables is 5.

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