The 6th term of an AP is 32 while the 10th term is 48. find the common difference and the 1st term​

Answer:  The merchant made a profit of Rs 35,000 by selling the potatoes.

Step-by-step explanation:

To find the profit or loss of the merchant, we first need to calculate the revenue he earned from selling the potatoes.

A quintal is a unit of weight equivalent to 100 kg, therefore, the merchant bought 100 kg of potatoes.

If the merchant sold all potatoes at Rs 390 per kg, the revenue would be 100 * 390 = Rs 39,000.

To find the profit or loss, we need to compare the revenue to the cost of the potatoes.

If the merchant bought a quintal of potatoes for Rs 4000, the cost is Rs 4000.

To calculate the profit or loss, we can use the following formula:

Profit or loss = Revenue - Cost

Using this formula, we can calculate the profit or loss as:

Profit or loss = 39,000 - 4,000 = Rs 35,000

So, the merchant made a profit of Rs 35,000 by selling the potatoes.

It is important to note that when calculating the profit or loss, we need to make sure that the units of measure for cost and revenue are the same.

The value of [tex]m \angle R Q S[/tex] is 40.

The opposite angles of a parallelogram are equal, therefore:

[tex]m \angle R=m \angle T \\[/tex]

so

[tex]m \angle R=75[/tex]

Opposite sides of a parallelogram are parallel and equal so:

[tex]Q T & =R S \\[/tex]

[tex]4 x & =12 \\[/tex]

[tex]x & =\frac{12}{4} \\[/tex]

[tex]x & =3[/tex]

[tex]$$$\angle \mathrm{TSQ}$[/tex] and [tex]$\angle \mathrm{RQS}$[/tex] are alternate interior angles, therefore:

[tex]m \angle R Q S=m \angle T S Q \\[/tex]

[tex]80: \\[/tex]

[tex]m \angle R Q S=40[/tex]

The complete question is,
Consider parallelogram QRST below. Use the information given in the figure to find m ZR, x, and m ZROS.

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Answer: x = 2

Step-by-step explanation:

Multiply each term between the parentheses by 2 1/3.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}(2x-3)=2\frac{1}{3} \iff \ 2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the expression of the multiplication.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{2\frac{1}{3}\times2x+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \ \frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} } \end{gathered}$} }[/tex]

We calculate the multiplication and division of rational numbers.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}+2\frac{1}{3}\times(-3)=2\frac{1}{3} \iff \frac{14x}{3}-7=2\frac{1}{3} } \end{gathered}$} }[/tex]

We convert the mixed fraction to improper.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\frac{14x}{3}-7=2\frac{1}{3} \iff \dfrac{14x}{3}-7=\dfrac{7}{3} } \end{gathered}$} }[/tex]

We eliminate the fractions by multiplying by the least common multiple of the denominators of both sides.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\dfrac{14x}{3}-7=\dfrac{7}{3} \iff \ 14x-21=7} \end{gathered}$} }[/tex]

We move the constant to the right side and change the direction of the sign.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x-21=7 \iff 14x=7+21=28, and \ remains \ 14x=28} \end{gathered}$} }[/tex]

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{14x=28 \iff \ we \ divided \ x=\frac{28}{14}=x; \Rightarrow x=2. } \end{gathered}$} }[/tex]

The equation of the line that passes through (1, 0) and is parallel to the line 2x + y = -4 is: y = -2x + 2.

The equation of a line, in slope-intercept form is y = mx + b, if two lines are parallel to each other, then the value of the slope, m, would be the same for both of them.

Given the equation, 2x + y = -4, rewrite the equation in slope-intercept form to determine the slope (m):

2x + y = -4

y = -2x - 4

The slope (m) is -2.

This means the line that passes through (1, 0) will also have a slope of -2. Substitute m = -2 and (x, y) = (1, 0) into y = mx + b, to find the y-intercept (b) of the line:

0 = -2(1) + b

0 = -2 + b

2 = b

b = 2

To write the equation of the parallel line, substitute m = -2 and b = 2 into y = mx + b:

y = -2x + 2.

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The value of 3x₁ + x₂ is 7/2

A quadratic equation is an equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.

5/x - 2/x² = 2

The LCM of x and x² is x². So we have:

(5x - 2)/x² = 2

Cross multiply:

5x - 2 = 2x²

2x² - 5x + 2 = 0

Factorize:

(2x - 1)(x - 2) = 0

2x - 1 = 0 or x - 2 = 0

2x  = 1 or x = 2

x  = 1/2 or x = 2

Thus, x₁ = 1/2 and x₂ = 2

Therefore, the value of 3x₁ + x₂ will be:

3x₁ + x₂ = 3×(1/2) + 2 = 3/2 + 2 = 7/2

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Probability is a metric used to express the possibility or chance that a particular event will occur. Two eighths of a vowel will be drawn at random. Option A is correct.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The formula for calculating probability is expressed as:

Probability = expected/total outcome

If the given a set of cards laying face down that spell P, E, R, C, E, N, T, S, then the total outcome is:

n(S) =8

If a vowel is selected randomly, hence the expected outcome is;

E = {E, E}

n(E) = 2

P(vowel) = 2/8

Hence the probability of randomly drawing a vowel is two eighths

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Answer: A: 2/8 (Two Eighths)

Step-by-step explanation:

Answer: There is no way 200 is the answer. it should be 103.055

Step-by-step explanation: See, 36 miles can stop in 53 feet. We want to know how many feet are there when 70 miles fast. We can write  that as 36/53 = 70/x. 36 corresponds to 70 and 53 corresponds to x. Do it and you get 103.055

Answer: x³ - 3x² + 4x - 12

Step-by-step explanation:

Using FOIL:

x³ - 3x² + 4x - 12

Answer:

x=1

Step-by-step explanation:

(x^2+4)(x-3)

"x^2=x*x=x"

(x+4)(x-3)

x+1

x/x/

x=1

Answer:

2nd option

Step-by-step explanation:

[4    -7] * [a    b] *  = [1    0]

[-1    2]    [c    d]       [0    1]

4 * a + (-7) * c = 1

4 * b + (-7) * d = 0

-1 * a + 2 * c = 0

-1 * b + 2 * d = 1

4a - 7c = 1  ==> equation 1

4b - 7d = 0  ==> equation 2

-a + 2c = 0  ==> equation 3

-b + 2d = 1  ==> equation 4

(-b + 2d = 1) * 4  ==> make -b into -4b

   -4b + 8d = 4

+   (4b - 7d = 0)

-4b+4b + 8d-7d = 4+0  ==> add equations 2 and 4 to cancel the variable b

8d-7d = 4 ==> -4b+4b=0 and adding anything by 0 will result in itself: 0+3=3

d = 4

-b + 2d = 1

-b + 2(4) = 1  ==> substitute 4 for d

-b + 8 = 1   ==> simplify

-b = -7  ==> subtract 8 on both sides

b = 7  ==> simplify

Since we got the values of b and d, the matrix now looks like this:

[4    -7] * [a    7] *  = [1    0]

[-1    2]    [c    4]       [0    1]

Now solve for a and c using equations 1 and 3:

4a - 7c = 1  ==> equation 1

-a + 2c = 0  ==> equation 3

(-a + 2c = 0) * 4  ==> make -a into -4a

   -4a + 8c = 0

+   (4a - 7c = 1)

-4a+4a + 8c-7c = 0+1  ==> add equations 1 and 3 to cancel the variable b

8c-7c = 1 ==> -4a+4a=0 and adding anything by 0 will result in itself: 0+3=3

c = 1

-a + 2c = 0

-a + 2(1) = 0  ==> substitute 1 for c

-a + 2 = 0   ==> simplify

-a = -2  ==> subtract 2 on both sides

a = 2  ==> simplify

Since we got the values of a and c, the matrix now looks like this:

[4    -7] * [2    7] *  = [1    0]

[-1    2]    [1    4]       [0    1]

Hence, the answer is the 2nd option.

Answer:

a = 18

Step-by-step explanation:

The slopes of parallel lines are equal as

[tex]m_{2}=m_{1}[/tex]

We know that the slope formula is

[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where y2, x2, y1, and y2 are any two points.

Thus, since the slopes are equal, we can use the slope formula to find the slopes of both lines and set them equal to each other to find a:

[tex]\frac{9-2}{4-a}=\frac{3-11}{(a+1)-3} \\\\\frac{7}{4-a}=\frac{-8}{a-2} \\\\7(a-2)=-8(4-a)\\7a-14=-32+8a\\7a=-18+8a\\-a=-18\\a=18[/tex]

If we plug in a for any of the two lines, we see that the slope is -1/2

Line 1 w/ (a, 2) & (4, 9):

[tex]\frac{9-2}{4-18}\\ \frac{7}{-14}\\ \frac{-1}{2}[/tex]

Line 2 w/ (3, 11) & (a+1, 3):

[tex]\frac{3-11}{18+1-3}\\ \frac{-8}{19-3}\\ \frac{-8}{16}\\ \frac{-1}{2}[/tex]

The analysis of the distance to the Grand Canyon, and the distance traveled on an amount of gas are as follows;

1 a. The distance from the middle school to the Grand Canyon = 80 miles

2 a. The graph showing the correlation between the distance traveled to the number of gallons used, created with MS Excel is attached

b. The table of values based on the data used to create the graph, presented in a tabular form using MS Word is attached

c. The equation is; d = 10·g

d. The advantages are;

The graphical presentation is a pictorial representation of the distance

The table enables further analysis

The equation can be used to predict the distance the Hybrid can travel on an amount of gas

A correlation is an indication or measure of the degree of relationship between variables.

1 a. The data for the Camper and the SUV that both use only gas, and the Hybrid car are as follows;

                                              [tex]{}[/tex]   Camper                    SUV    Hybrid Car

Average Miles per Gallon [tex]{}[/tex]       4                                8           10

Gallons of gas consumed [tex]{}[/tex]       20                             10           8

Distance traveled = Number of gallons used × Miles traveled per gallon

The distance between the middle school and the Grand Canyon, using the data for the Camper, is therefore;

d = 20 gallons × 4 miles/gallon = 80 miles

2. Amount of gas in gallons = g

Distance car drives in miles = d

The model used = The Hybrid car

Miles traveled per gallon = 10 miles/gallon

Therefore, d/g for the Hybrid car = 10 miles/gallon

d = 10·g

a. Please find attached the graph of the driven distance to the amount of gas used, created with MS Excel

b. The table based on the distance covered using different amount of gas can be created using the data used for creating the graph as follows;

Amount of gas; 0     1  [tex]{}[/tex]    2     3      4        5      6      7     8      9     10        11

Distance;           0     10   20   30    40     50    60   70    80   90   100      110

c. The equation that represents the distance traveled in miles, d, with the Hybrid when a specified amount of gasoline is used, g, is presented as follows;

d. The advantage of each representation are as follows;

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Answer: The soccer field is about 8.6 blocks away from Leah's home.

Step-by-step explanation:

The soccer field is about 8.6 blocks away from Leah's home.

Leah walks 6 blocks north and 4 blocks east. To find the total distance she walked, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The distance is the square root of (6 blocks)^2 + (4 blocks)^2 = 36 + 16 = 52 then square root of 52 = 7.21

The distance of the soccer field from Leah’s home is 7.21 blocks, but it can be rounded to nearest tenth which is 8.6

[tex]P(t)=3400e^{0.04t}\implies 68000=3400e^{0.04t}\implies \cfrac{68000}{3400}=e^{0.04t} \\\\\\ 20=e^{0.04t}\implies \log_e(20)=\log_e(e^{0.04t})\implies \log_e(20)=0.04t \\\\\\ \ln(20)=0.04t\implies \cfrac{\ln(20)}{0.04}=t\implies 74.89\approx t[/tex]

that's about 74 years and 325 days more or less.

based on the exponential equation which is really a continuously compounding equation with an initial value of 34000 in 1994, so 74 years later that'd be 1994 + 74 = 2068, then we add the 325 days to that, well, that's pretty much in November in 2069.

Answer:

Step-by-step explanation:

The terminal point of the vector a=⟨4,3⟩ based at P=(5,2) is the point (9,5). This can be calculated by adding the components of the vector to the corresponding components of the base point:

Terminal point = (x,y) = (Px + ax, Py + ay)

      = (5 + 4, 2 + 3)

      = (9,5)

Answer:

Step-by-step explanation:
✔️For determining terminal point of vector a=(4,3)  whose base is at the point P=(5,2).

✔️ Add to point P and that

✔️Point that the vector is pointing at to find the terminal point....

➖So we can say That

✔️Since the tail of the vector a=(4,1) a=(4,1) is a point P(2,3) then the tip of the vector, the terminal point woll be :-

(5,2)+(4,3)=(9,6)

your welcome !

Answer: yes, it is

Step-by-step explanation:

Answer:4

Step-by-step explanation:

So on solving the provided question we cans ay that trigonometry y =sec^2(y); y = 1/[tex]\sqrt{2}[/tex]

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

y´=sec^2(y)

here, y = 90

y = sec^2(90)

y = 1/[tex]\sqrt{2}[/tex]

​

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If riley needs to make punch for a party. One batch of punch has the ingredients shown. The cups of orange juice needed to make enough punch to fill a punch bowl that holds 27 cups is 6 cups.

Total cup of juice for one batch:

Total cup of juice for one batch = 4+ 1 +2 +2

Total cup of juice for one batch = 9

Since 2 cup of the 9 cups are orange juice so 2/9 of each batch will be orange and since the bowl can hold 27 cups now let find the cups of orange juice.

Cups of orange juice = 2/9 ×27

Cups of orange juice =6 cups

Therefore we can conclude that the cups of orange juice is 6 cups.

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Answer:

x = 9

Step-by-step explanation:

[tex] - 1 + 14x = 12x + 17 \\ 2x = 18 \\ x = 9[/tex]

Answer:

P(EF) > 0.72 and in general, P(EF) > P(E) + P(F) - 1

Step-by-step explanation:

We know that P(EF) = P(E and F) = P(E|F) * P(F) = P(F|E) * P(E) (by the definition of conditional probability).

For the specific case given, P(E)= 0.9 and P(F) = 0.8,

P(EF) = P(E|F) * P(F) = P(F|E) * P(E) > P(E) * P(F) = 0.72

In general,

P(EF) = P(E|F) * P(F) = P(F|E) * P(E) > min(P(E|F) * P(F), P(F|E) * P(E) ) = P(E) * P(F)

P(EF) > P(E) * P(F) = P(E) + P(F) - 1

This is because P(E|F) and P(F|E) are always less or equal to 1.

Step-by-step explanation:

let the number of weeks be w

the total number of books Grace reads will always be 15 + something because we start with 15 and cannot unread a book

for each week, she reads 2 books. this can be represented as 2 * w

books Grace already read + books Grace reads each week = total books

15 + 2 * w = total books

Answer: To find the length of the diagonal cut, we can use the Pythagorean theorem.

The diagonal cut is the hypotenuse of a right triangle, with legs of length 9 and 12.

The Pythagorean theorem states that the square of the hypotenuse is equal to the sum of the squares of the legs. So, the length of the diagonal cut is the square root of (9^2 + 12^2)

So, the length of the diagonal cut is √(9^2 + 12^2) = √(81 + 144) = √225 = 15cm

Therefore, the diagonal cut that Danny made is 15 centimeters long.

Step-by-step explanation:

Answer:

A.

Arithmetic mean: The sum of the data divided by the number of data points. (For the first set of data: (30+25+23+41+39)/5 = 31.4)

Median: The middle value when the data is arranged in order. (For the first set of data: 30, 23, 25, 39, 41 => 25)

Mode: The value that appears most frequently in the data. (For the first set of data: No value appears more than once, so there is no mode.)

Range: The difference between the highest and lowest values in the data. (For the first set of data: 41-23 = 18)

B.

To find the upper and lower quartile, you need to first arrange the data in order and then divide it into four equal parts.

Lower quartile (Q1) is the median of the lower half of the data.

Upper quartile (Q3) is the median of the upper half of the data.

For the first set of data: Q1 = (23+25)/2 = 24, Q3 = (39+41)/2 = 40

7th and 50th Percentile:

To find 7th percentile, pick 7th item from ordered data set and if not possible then take the average of 6th and 8th items.

To find 50th percentile, pick the median of the data set.

For the first set of data: 7th percentile = 25, 50th percentile = 25

C.

Variance: A measure of the spread of the data. It is calculated by taking the average of the squared differences from the mean.

Coefficient of variation (CV) : A normalized measure of the spread of the data. It is the ratio of the standard deviation to the mean.

D.

Pearson coefficient of skewness: A measure of the asymmetry of the data about the mean. A positive skewness indicates that the tail on the right side of the probability density function is longer or fatter than the left side. Conversely, a negative skewness indicates that the tail on the left side is longer or fatter than the right side.

Kurtosis: A measure of the "peakedness" of the data. A high kurtosis means that the data has heavy tails (outliers) or a distinct peak near the mean, whereas a low kurtosis means that the data has light tails (no outliers) or a flat peak near the mean.

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{-2}~,~\stackrel{y_2}{13}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{13}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{-2}-\underset{x_1}{3}}} \implies \cfrac{ 5 }{ -5 } \implies - 1[/tex]

Answer:

[tex]\boxed{\bf Slope(m):-1}[/tex]

Step-by-step explanation:

We can use the slope formula to find the slope of a line given the coordinates of two points on the line:- (3,8) and (-2,13).

The coordinates of the first point represent x_1 and y_1. The coordinates of the second points are x_2, y_2.

[tex]\sf \mathrm{Slope}=\cfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\bf \left(x_1,\:y_1\right):\left(3,\:8\right)[/tex]

[tex]\bf \left(x_2,\:y_2\right):\left(-2,\:13\right)[/tex]

[tex]\bf m=\cfrac{13-8}{-2-3}[/tex]

[tex]\bf m=-\cfrac{5}{5}[/tex]

[tex]\bf m=-1[/tex]

Therefore, the slope is -1.

__________________

Hope this helps!

Have a great day!

Answer:

Choice B: x = 3

Step-by-step explanation:

The standard equation of a parabola is
[tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex]

where

(h, k) is the vertex and |p| is the focal length

The given equation is
[tex](y - 3)^2 = 8(x - 5)[/tex]

Convert this to standard form and compare with general equation

Answer: Choice B: x = 3

The ones which are equation are

[tex]\frac{3}{4}l = -9\\ 4m + 2m = 72[/tex]

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an equation. as in 3x + 5 Equals 15, for instance. Equations come in a variety of forms, including linear, quadratic, cubic, and others. In this tutorial, let's study more about math equations.

here

-3 = d/-8

or, d = 24 (different from answer)

14 = 25 - k

or, k = 11 (different from answer)

j + 1 = j/3

or, 3j + 3 = j

or, j = -3/2 (different from answer)

3/4 l = -9

or, l = -12 ( same as answer)

-15 = n + 8

or, n = -23 (different from answer)

4m + 2m = 72

or, m = 12 (same as answer)

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The two ratios are equivalent because if we multiply both of the numbers by 3, we will get the other ratio.

Here we want to explain why the two ratios:

5:6 and 15:18

Are equivalent, where equivalent means that these two ratios mean the same thing.

Now, if we take any ratio

a:b

and we multiply both numbers by the same real number k (except for zero) we will get the equivalent ratio.

k*a: k*b

Now, let's look to our ratios:

5:6

If we multiply these 2 numbers by 3, we will get.

3*5: 3:6

15: 18

So yes, these are equivalent.

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Answer:

Part A:

To find the length of the ramp in yards, we need to first determine the horizontal distance covered by the ramp. The slope of the ramp is 1/12, meaning that for every 12 inches of horizontal distance, the height of the ramp increases by 1 inch. Since the height of the ramp when it connects to the house is 9 inches, we can use this information to determine the horizontal distance covered by the ramp.

9 inches / (1/12) = 108 inches

To convert inches to yards, we divide by 36, so

108 inches / 36 inches/yard = 3 yards

Part B:

To determine the length of the ramp, I used the information provided about the slope of the ramp and the height of the ramp when it connects to the house. I used the slope of the ramp (1/12) to calculate the horizontal distance covered by the ramp. Then I converted the horizontal distance from inches to yards by dividing by 36. Finally, I obtained 3 yards as the length of the ramp.

Answer:

Part A = 3 yards

Part B = 9 x 12 = 108 inches = 9 feet = 3 yards

Step-by-step explanation:

Part A

1 inch height - 12 inches length

9 inches height - 9 x 12 = 108 inches length

36 inches = 1 yard

108 inches = 108/36 = 3 yards

Part B

Shown above

The ramp is 9 inches tall, so the length of the ramp is 9 x 12 = 108 inches.

1 feet = 12 inches

108 inches = 108/12 feet = 9 feet

1 yard = 3 feet

9 feet = 3 yards.

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The rate of change of function A is not same with the rate of change of function B.

The slope of a linear function is another name for its rate of change.

The slope and the function's starting value are both included in the slope-intercept form equation of a line. When the input of a linear function is 0, the output is the initial value, or y-intercept.

Function b is in slope intercept form as Y= 1/2X + 2 and here the slope is 1/2

calculation of slope pf function A

The slope, m of the linear function is calculated using the points (2 , 3) and (-1 , -3)

m = (y₀ - y₁) / (x₀ - x₁)

m = (3 + 3) / (2 + 1)

m = (6) / (3)

m = 2

The slopes are not the same

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When the thickness of a textbook is b mm the expressions for:

thickness of 5 stacked textbooks = 5b mm

thickness of each page, if the pages are numbered to 225 = b / 225

The thickness for each of the condition is written as follows

For the thickness of 5 stacked textbooks

= b + b + b + b + b

= 5b

For thickness of each page, if the pages are numbered to 225

In this case division is used to ascertain the thickness of each page in the book. this is done by dividing the total thickness by the number of pages in the book

= b / 225

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Answer:

21.6%

Step-by-step explanation:

Each day is independent, so the probability of snow all three days is:

(0.60)³ = 0.216

There is a 21.6% chance that it snows all three days.