Find the slope of a line that passes through the following points; a) (-2, 5) and (4, 0) b) (0, 3) and (-2, 4) c) (-3, 4) and (-5, 6) d) (5, 5) and (3, 1) e) (-2, -1) and (-3, 1) f) (-4, -3) and (4, 1) g) (2, -1) and (2, 5) h) (0, 2) and (1, 7) i) (3, 3) and (-3, 0) j) (0, 0) and (3, 3) k) (-4, 2) and (4, 2) l) (-3, 5) and (-2, 0) m) (2, 2) and (-3, -3) n) (-8, 10,) and (-5, 6)

Answer:

\((2^3)^2 = 64\)

Step-by-step explanation:

Option 1:

Using the following rule:

\((a^n)^m = a^{nm}\)

Put in our expression,

a = 2

n = 3

m = 2

\((a^n)^m = a^{nm}\)

\((2^3)^2 = 2^{3*2}=2^6=64\)

Option 2:

Using the following rule:

\(a^n * a^m = a^{n+m}\)

Since our expression is the same as multiplying 2³ with itself, we can write it as a multiplication.

\((2^3)^2 = 2^3 * 2^3\)

If we compare this with \(a^n * a^m\), we can see that

a = 2

n = 3

m = 3 (in this case, n and m are equal)

\(a^n*a^m = a^{n+m}\)

\(2^3*2^3 = 2^{3+3} = 2^6 = 64\)

Answer: \((2^3)^2 = 64\)

Answer:

Formula used : (a^m)^n = a^(m×n)

→ (2³)² = 2³*² = 2⁶ = 64

Answer:

72

Step-by-step explanation:

A person can read 24 pages in 1/3 hour.  There are 3 * 1/3 hours in 1 hour.

So, the person can read 24 * 3 = 72 pages in one hour.

Answer: Circle lines

Step-by-step explanation:

Hopefully the attached image helps, it is a diagram of all the labeled lines on a circle excluding the radius (BG or GE)

Answer:

11.

A) EZ Pay Plan=0.15x

B) 40 to Go Plan=0.05x+40

12.

0.15x=0.05x+40

13.

x=400 minutes

14. The solution is the amount of minutes that it takes for both plans to cost the same amount. X has one solution, so it accounts for both equations.

15. EZ Pay Plan

Step-by-step explanation:

For 11, what you need to know is that the slope (coefficient of x) is the price per minute. 0.15 per minute and 0.05 per minute are charged, and therefore are the slope for those equations. The 40 on B is because it is the y intercept. No matter how long you use the object, you will always pay at least 40 dollars.

For 12, you have to find x for the minutes used.

For 13, if you do the process algebraically,

0.15x=0.05x+40  

0.10x=40     (subtracted 0.05x from both sides)

x=400       (divided 0.10x and 40 by 0.10)

For 14, (no explanation)

For 15, if you substitute 200 as x, you would see that the EZ Pay Plan would make you pay 30 dollars while the 40 To Go Plan would make you pay 10+40 dollars, which 30<50.

(sorry for late response)

Yes, it is true that if matrix B is formed by adding to one row of matrix A a linear combination of the other rows, then the determinant of B is equal to the determinant of A.

Proven using elementary row operations are operations that can be performed on the rows of a matrix without changing its determinant.

One such operation is adding a multiple of one row to another row.

A linear combination of the other rows to a particular row of A to form B, we can express this operation as a matrix multiplication:

B = P × A

P is a matrix that represents the elementary row operation.

P is an identity matrix with the (i, j)-th entry equal to 1 if i = j or equal to a constant c if i is the row being modified and j is the row being added to, and 0 otherwise.

Since P is an elementary matrix, it has determinant equal to 1 or -1, depending on whether an odd or even number of row swaps were performed.

Therefore,

det(B) = det(P × A) = det(P) × det(A) = ±det(A)

det(P) is either 1 or -1.

P is formed by adding a linear combination of the other rows to a particular row, we can easily see that P is a triangular matrix with 1's on the diagonal, and thus its determinant is equal to 1.

Therefore, we have

det(B) = det(A)

as claimed.

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The probability that a car chosen at random will require no repairs can be calculated using the given information. we find that the probability of no repairs is 0.70 or 70%.

Let's denote the probability of a car needing one repair as P(1), the probability of needing two repairs as P(2), and the probability of needing three or more repairs as P(≥3). We are given that P(1) = 0.20, P(2) = 0.06, and P(≥3) = 0.04.

To find the probability of no repairs, we subtract the sum of the probabilities of needing repairs from 1:

P(no repairs) = 1 - P(1) - P(2) - P(≥3)

            = 1 - 0.20 - 0.06 - 0.04

            = 0.70

Therefore, the probability that a car chosen at random will require no repairs is 0.70, or 70%.

In summary, using the given probabilities of needing repairs, we can calculate the probability of a car needing no repairs. By subtracting the sum of the probabilities of needing repairs from 1, we find that the probability of no repairs is 0.70 or 70%.

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Answer:

34

Step-by-step explanation:

Answer:

Step-by-step explanation:

Volume of the prism:

Answer:

Look at the attached screenshot

Step-by-step explanation:

Slope is 2.

Since y-intercept is not given, we can assume that it is 0.

Answer:

Step-by-step explanation:

Make a table of points for y = 2x, and then plot these points, and finallyl draw a line through the points:

x   y

0   0

2   4

3   6 (and so on).

Plot this (0, 0) (it's the origin).  Next plot either (2, 4) or (3, 6) (or both).  Then draw a line through these points.  

Answer:

the solution to the system is x = 1 and y = 5/2.

Step-by-step explanation:

To find the values of x and y, we can simplify each equation in the system and then substitute the value of x into the other equation to find y.

Starting with the first equation:

y - 1 = 3x / 2

2 * (y - 1) = 3x

3x = 2y - 2

Next, we substitute the value of 3x/2 from the first equation into the second equation:

5x + 1 = 4x

x = 1

Finally, we can substitute the value of x = 1 into the first equation to find y:

y - 1 = 3 * 1 / 2

y - 1 = 3 / 2

y = 5 / 2

So the solution to the system is x = 1 and y = 5/2.

a. The mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes.

b. The probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20

What is Probability?

Probability is a field of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of inaccuracy in study by using probability.

a. The mean of the sampling distribution of the difference in sample means, xF - xM, is equal to the difference of the population means, μF - μM = 8.8 - 7.3 = 1.5 minutes.

where σF and σM are the standard deviations of the populations of female and male students, respectively, and nF and nM are the sample sizes of female and male students, respectively.

\(Standard\ Deviation = \sqrt{3.3^2/8 + 2.9^2/8} \\\\Standard\ Deviation = \sqrt{{2.75} }\\\\Standard\ Deviation = 1.65\ minutes\)

So, the mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes, respectively.

b. The probability of getting a difference in sample means xF - xM that is less than 0 can be found using a standard normal distribution table. First, we need to standardize the difference in sample means xF - xM by subtracting the mean and dividing by the standard deviation:

z = (xF - xM - (μF - μM)) / standard deviation

z = (0 - 1.5) / 1.65 = -0.91

Looking up -0.91 in a standard normal distribution table, we find that the probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20.

So, there is a 20% probability of getting a difference in sample means xF - xM that is less than 0.

Hence, The mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes and probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20.

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The given numerical value  is a Statistic.

Parameters are numeric values ​​that characterize the population as a whole. A statistic is a number that describes the characteristics of a sample.

For example, median income in the United States is a demographic parameter. Conversely, the median income for the US sample is a sample statistic. Both values ​​represent median income, but one is a parameter to the statistic. Easy to remember parameters and stats! Both are summary values ​​that describe the group, and have a convenient mnemonic device to remind you which group is being described. Notice their initials.

Parameter = Population

Statistics = Sample

A population is the entire group of people, things, animals, trades, etc. that are being studied. A sample is part of a population.

Following the election, 18 % of the governors of all 50 areas of a country were female.

Given that, 18% of the 50areas of a country  were females.

Now,

18*50/100 = 9

Since it is  a perfect number

The given numerical value  is a statistic.

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Answer:

Parker is NOT right when he says that it is a division problem 6 ÷ 3.

In fact, it is a multiplication problem 6 × 3 because 6 × 3 = 18 would give us the correct number of total rectangles which are 18

Step-by-step explanation:

Total number of rectangles = 18

As there are 3 rows with each row containing 6 rectangles.

Now, if we multiply 6 with 3, we get the result 18.

Thus,

6 × 3 = 18

Hence, Parker must have mentioned that this arrow of 18 rectangles shows the multiplication problem 6 × 3.

Thus,

Parker is NOT right when he says that it is a division problem 6 ÷ 3.

In fact, it is a multiplication problem 6 × 3 as 6 × 3 = 18 would give us the correct number of total rectangles which are 18.

The function that models the population t years after 2000 is22300 × e^(0.06t), The estimated fox population in the year 2008 is 36081. This can be answered by the concept of exponential function.

The question asks to find a function that models the population of foxes in a certain region with a continuous growth rate of 6 percent per year starting from the year 2000. It also asks to estimate the fox population in the year 2008 using this function.

a. Let P(t) be the population of foxes t years after 2000. Since the growth rate is continuous, we can use an exponential function with base e to model the population. We know that P(0) = 22300 (the population in the year 2000), and the annual growth rate is 6%. Therefore, we can write:

P(t) = 22300 × e^(0.06t)

b. To estimate the fox population in the year 2008, we need to find P(8) since t = 8 represents 8 years after 2000. Substituting t = 8 into the equation above, we get:

P(8) = 22300 × e^(0.06×8) = 22300 × e^0.48 ≈ 36081

Therefore, the estimated fox population in the year 2008 is 36081.

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The bride and groom can form 252 different groups of five people from the total of 10 people at the rehearsal dinner, as they need to assign them to two tables of five people each.

To determine the number of different groups of five people that can be formed, we can use the concept of combinations. In this scenario, we have 10 people who need to be divided into two groups of five people each.

The number of ways to choose five people out of 10 can be calculated using the combination formula. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where n represents the total number of people and r represents the number of people to be chosen. In this case, n = 10 and r = 5.

Plugging these values into the formula, we get:

C(10, 5) = 10! / (5! * (10 - 5)!)

= (10 * 9 * 8 * 7 * 6 * 5!) / (5! * 5 * 4 * 3 * 2 * 1)

= (10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1)

= 252

Therefore, the bride and groom can form 252 different groups of five people from the total of 10 people at the rehearsal dinner. This means that there are 252 distinct ways to divide the 10 people into two tables of five people each, providing flexibility in creating diverse groups for the dinner.

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Answer:

These methods convert everything to radians

Step-by-step explanation:

Length of arc DC fromula is radius*angle in radians

Radius of the circle of DC is 8 cm aka the outer circle.

The angle inside is 130 degrees, in radians convert and multiply by 180/\(\pi\)

givong 130 degrees to be 13/18π

using formula, arc DC is 8*13/18π

=52/9π (in terms of pi) or 18.15 cm

or 130/360*(2π8)=18.15 (not using radians)

Length of arc QT regards the inner circle of radius 4 cm. Convert 130 degrees to radians. Using same formula as above, length of arc =4*13/18π

=26/9π or 9.08 cm

or 130/360*(2π4)=9.08 (not using radians)

Area of sector DEC suspended angle is 130 degrees of 13/18π radians. regarding large outer circle radius 8 cm.

Use formula 0.5*r^2*angle in radians fro area of sector gives:

0.5*8^2*13/18π

=208/9π or 72.61 cm^2

or 130/360*(π8^2)=72.61 (not using radians)

The area of sector QET angle 13/18πv rad and radius 4 cm using same forumla as above gives

0.5*13/18π*4^2

=52/9π or 18.15cm^2

or 130/360*(π4^2)=18.15 (not using radians)

Radian measure of angle DEC is 130 degrees again convert to radians by multiplying by π/180 gives

=13/18π

Radian measure of angle QET IS ALSO 130 degrees also

=13/18π

Answer:

7500 m

Step-by-step explanation:

5500 is the initial height. It increased by 1500, so 5500 + 1500 = 7000. Then it went down 2000 meters, so 7000 - 2000 = 5000. It went up 2500 again. 5000 + 2500 = 7500

The hypothesis test is left-tailed because the financial analyst wants to test if the proportion of stock portfolios containing high-risk stocks is lower than 0.10.

In other words, they are interested in determining if the proportion is significantly less than the specified value of 0.10. A left-tailed hypothesis test is used when the alternative hypothesis suggests that the parameter of interest is smaller than the hypothesized value. In this case, the alternative hypothesis would be that the proportion of stock portfolios with high-risk stocks is less than 0.10.

By conducting a left-tailed test, the financial analyst is trying to gather evidence to support their claim that their clients have a lower proportion of high-risk stock portfolios. They want to determine if the observed data provides sufficient evidence to conclude that the true proportion is indeed less than 0.10, which would support their claim of a lower proportion of high-risk stocks.

Therefore, a left-tailed hypothesis test is appropriate in this scenario.

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The length of the side of the square is 11. 3 feet

From the diagram shown, we can see that the square of the length should give the area and is traced down.

It is important tot note that the area of a square is given as;

Area = a²

Where:

a = length of its side

From the diagram, we have that area = 128 square feet

Length of one of the side of the square = square root of it's area

a = √ area

Now, substitute the value of area

a = √ 128

a = 11. 3 feet

From the diagram shown, we can see that the square of the length should give the area.

Thus, the length of the side of the square is 11. 3 feet

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Answer:

(a) The river otters: Symmetric bell shaped.

(b) The sea otters: Skewed left (i.e. negatively skewed)

Step-by-step explanation:

Given

See attachment for dot plots

Required

Determine the shape of each otter

(a) The river otters

This dot plot is symmetric bell shaped.

To prove this, draw a vertical line at the center of the distribution (at 18lbs), you will notice that the data on both sides of the vertical line are distributed equally, and they reflect one another

(b) The sea otters

This dot plot is skewed left (i.e. negatively skewed)

To prove this, you will observe that there are few data points at the left-hand side of the plot. As you move towards the right side of the plot, there are more data points.

A set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

What is a combination of reflections?

Combination of Two Reflections. A point or object once reflected can further be reflected to form a new image. The axes of these reflections may be parallel to each other or they intersect each other at a point.

Given the coordinates of hexagon ABCDEF, it can be determined that a set of reflections that would carry the hexagon onto itself would be a combination of reflections over the x-axis and y-axis.

One possibility would be to reflect over the x-axis, then reflect over the y=x line, and finally reflect over the x-axis again.

This would take the hexagon from its original position to itself.

Another possibility would be to reflect over the y = x line, then reflect over the x-axis, and finally reflect over the y-axis.

This would also take the hexagon from its original position to itself.

Hence, a set of reflections that would carry hexagon ABCDEF onto itself would be "x-axis, y=x, x-axis" or "y=x, x-axis, y-axis".

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The Task objective chosen is: A Measuring Task

The Objective is: To investigate the fairness of a local athlete's track for runners starting on different lines.

To carry about the investigation, follow the steps given below.

Lastly, make a crossword puzzle that includes mathematical vocabulary in a clever manner.

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```Class IX```

*Mathematics Project work*

*Do any one*

1. *A Measuring Task*

To investigate your local athletes track to see whether it is worked fairly for runners who start on different lines.

2. *Design a crossword puzzle with mathematical terms*

To review mathematics vocabulary, to give the opportunity for creative expression in designing puzzles, to act as a means of motivating the study of a given unit and to given recreation .​

Answer:

The probability of choosing two red cards would be 3/8

Step-by-step explanation:

The probability of choosing 1 red card is 10/16; the probability of choosing a second red card would then be 9/15.

P(2 red) = 10/16(9/15) = 90/240 = 3/8.

Answer:

y= -1/3x-6

Step-by-step explanation:

The slope is rise over run

The y-intercept is the point where the line crosses the y-axis.

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Answer: y=.25x-6

Step-by-step explanation: find the slope with \(m=\frac{y2-y1}{x2-x1}\) and make it \(m=\frac{-6+7}{0-4} =1/4\) or .25

then, convert to y=mx+b form which would be \(y=\frac{1}{4}x-6\) or \(y=.25x-6\)

b standing for y intercept and m standing for slope.

The expression is simplified to - 13x + 7y - 7 = 0

Algebraic expressions are expressions made up  of variables, constants, factors, and coefficients.

They also consist of mathematical operations such as addition, subtraction, division, multiplication, etc

Given the expression;

-5x + 7y = 8x + 7

collect like terms

-5x - 8x + 7y = 7

add like terms

-13x + 7y =7

equate the equation to zero

- 13x + 7y - 7 = 0

Thus, the expression is simplified to - 13x + 7y - 7 = 0

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The shape of the distribution for the following set of data {X f 5 4 3 2 1 5 3 1 5} is B) Positively skewed.

A positively skewed distribution is a distribution in which the majority of the data falls on the lower side of the scale, with the tail extending to the right side of the scale.

Positive skewness is present in a distribution when the mean is higher than the median.

As a result, the mean is skewed to the right, causing the tail on the right side of the distribution.

As a result, the tail is often referred to as the "positive" tail.

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Therefore, the magnitude of vector v is 6 and its direction is 160°.

Magnitude generally refers to the size or extent of something. The term is often used in different contexts, and its meaning can vary depending on the specific field or area of application. Here are a few examples of how magnitude can be defined in different contexts:

Physics: In physics, magnitude usually refers to the size or amount of a physical quantity, such as distance, speed, acceleration, force, or energy. Magnitude can be measured in various units, such as meters, seconds, meters per second, Newtons, or Joules.

Earthquakes: In seismology, magnitude is a measure of the strength or intensity of an earthquake, which is usually expressed on the Richter scale or the moment magnitude scale. The higher the magnitude, the more energy is released by the earthquake, and the stronger its impact on the ground and structures.

The magnitude of vector v is given by:

|v| = |2u| = 2|u| = 2(3) = 6

Therefore, the magnitude of vector v is 6.

The direction of vector v is the same as the direction of vector u, since multiplying a vector by a scalar does not change its direction, only its magnitude. So the direction of vector v is also 160°.

Therefore, the magnitude of vector v is 6 and its direction is 160°.

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Answer:

20% de 240=20×240÷100= 48 practican deporte

The total cashback you will get back is\($ 49.75}\)

The Given, original price \($=\$ 50$\) Sales fax\($=9.5 \%$\\\)

For first sale

                 \(\begin{aligned}\text { Price of item } & =\$ 50 \\\text { sales tax } & =+\$ 4.75 \\10 \% \text { discount } & =\frac{-\$ 5}{\$ 49.75}\end{aligned}\)

A sale is a transaction between two or more parties that involves the exchange of tangible or intangible goods, services, or assets for money. In some cases, assets other than cash are paid to a seller.

In the financial markets, a sale can also refer to an agreement that a buyer and seller make regarding a financial security, its price, and specific arrangements for its delivery.

Regardless of the context, a sale is essentially a contract between a seller of a particular good or service and a buyer who is willing to pay for that good or service.

for second Sale:-

There is no tax

So price\($=\$ 50$\)

For third sale: - Buy 3 and get 1 half of

\(\begin{aligned}\text { Price }=50 \times 3 & =\$ 150 \\\text { Sales tax }= & +\$ 14.25 \\\text { Discount } & =\frac{-\$ 25}{\$ 139.25}\end{aligned}\)

So, price of 1 piece \($=\$ 46.42$\)

for fourth Sale; - Buy anything over \(\$40\) and get \($\$ 5$\) gift card.

\(& \text { Price }=\$ 50 \\& \text { sales tax }=+\$ 4.75 \\& \text { Gift card }=\frac{-\$ 5}{\$ 49.75}\end{aligned}\)

Therefore, the cashback you will get back is \($ 49.75}\)

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