Write an equation in point-slope form for the line that passes through
each point with the given slope (-1,-2) m=3

The expression that represents the number of packages of cookies sold for the fundraiser is 17.

Let's assume the number of packages of cookies sold for the fundraiser is represented by the variable "x."

Given that 204 cookies were sold, and each package contains 12 cookies, we can set up an equation to represent the situation:

Number of cookies sold = Number of packages sold × Number of cookies per package

204 = x × 12

To find the number of packages sold, we can rearrange the equation:

x = 204 / 12

Simplifying the expression, we get:

x = 17

Therefore, the expression that represents the number of packages of cookies sold for the fundraiser is 17.

For  ore questions on expression

https://brainly.com/question/1859113

#SPJ8

Given the equations

x + y = 5----------------------(1)

x - 3y = 3-----------------------(2)

Subtract equation (2) from (1)

x - x -3y - y = 3 - 5

-4y = -2

Divide both -4

Substitute y = 1/2 into equation (1)

x + y = 5

Hence, the solution to the equations is

Starting with the equation:

take the inverse tangent function to both sides of the equation:

Yet another value can be found for this equation to be true since the period of the tangent function is π:

Starting with the equation:

Divide both sides by 7:

Take the inverse tangent to both sides of the equation:

The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:

We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:

Therefore, for each equation we know that:

Starting with the equation:

take the inverse tangent function to both sides of the equation:

Yet another value can be found for this equation to be true since the period of the tangent function is π:

Starting with the equation:

Divide both sides by 7:

Take the inverse tangent to both sides of the equation:

The tangent function has a period of π. Since the value that we found for theta is not between 0 and 2π, then we can add π to the value:

We can find another value for theta such that its tangent is equal to -15/7 by adding π again, provided that the result is less than 2π:

Therefore, for each equation we know that:

Mark should use the volume formula to determine the number of cubic feet of soil needed to fill the planter half-full. To fill the planter half-full, he would require 18 cubic feet of soil.

In order to determine the amount of soil needed to fill the planter half-full, Mark should use the volume formula. The volume of a rectangular box is calculated by multiplying its length, width, and height. In this case, the length of the planter is 12 feet, the width is 6 feet, and the height is 3 feet. By multiplying these dimensions together (12 x 6 x 3), Mark can find the total volume of the planter, which is 216 cubic feet.

However, the question specifies that Mark needs to fill the planter only half-full. Therefore, he would require half of the calculated volume, which is 216 cubic feet divided by 2, resulting in 108 cubic feet. Therefore, Mark needs 108 cubic feet of soil to fill the planter half-full.

It's worth noting that the trick detail mentioned in the question is the requirement for the planter to be half-full. This means Mark needs to consider only half of the total volume when calculating the amount of soil required.

Learn more about volume formula of rectangular box here:

https://brainly.com/question/20922431

#SPJ11

The total cost of the services from Happy Paws and Woof Watchers will be equal if the dog is kept for 12 hours.

Finding the answer to a linear equation with one, two, three, or more variables is known as solving a linear equation. A linear equation's solution is, to put it simply, the value or values of the variables that make up the equation. Any coefficient can be deleted using the elimination procedure after being initially equated. Elimination is followed by equations being solved to get the other equation.

Let us suppose the number of hours = h.

Given that, Happy Paws charges $18.00 plus $2.50 per hour.

H = 18 + 2.50h

Woof Watchers charges $12.00 plus $3.75 per hour.

W = 12 + 3.75h

The cost is equal for:

18.00 + ($2.50 x h) = $12.00 + ($3.75 x h)

18 - 12 = 3.75h - 2.50h

h = 12

Hence, the total cost of the services from Happy Paws and Woof Watchers will be equal if the dog is kept for 12 hours.

Learn more about system of equations here:

https://brainly.com/question/27919853

#SPJ1

The number of bank PINs in string which exactly four digits are even is (74​)⋅57.

To determine the number of PINs with exactly four even digits, we need to consider the number of ways we can choose four even digits from the set {0, 2, 4, 6, 8}, as well as one odd digit from the set {1, 3, 5, 7, 9}.

The number of ways to choose four even digits from a set of five is given by the combination formula: (5 choose 4) = 5! / (4! * 1!) = 5.

Similarly, the number of ways to choose one odd digit from a set of five is also 5.

Since these choices are independent, we can multiply the number of ways to choose even digits by the number of ways to choose an odd digit: 5 * 5 = 25.

Once we have chosen the even digits and the odd digit, we have fixed their positions within the PIN. The remaining two digits can be chosen freely from the set of all digits (0-9), giving us 10 * 10 = 100 possible choices.

Finally, we multiply the number of choices for the even and odd digits by the number of choices for the remaining two digits: 25 * 100 = 2500.

Therefore, the total number of PINs in which exactly four digits are even is (74​)⋅57 = 2500.

Learn more about even here:

https://brainly.com/question/2289438

#SPJ11

(A) A normal distribution centered at 1/3 with a standard deviation of about 0.0351.

Normal Distribution:

The normal distribution, also known as the Gaussian distribution, is a probability distribution symmetrical about the mean, indicating that data near the mean occurs more frequently than data far from the mean. The normal distribution model is important in statistics and is the key to the central limit theorem (CLT). The theory states that means computed from independent, identically distributed random variables have an approximately normal distribution, regardless of the type of distribution from which the variable is sampled (provided it has finite variance). Mean (average value), median (center), and mode (most frequent observation) are all equal. Moreover, these values ​​all represent the peak or highest point of the distribution.

Standard Deviation:

The standard deviation (or σ) is a measure of the distribution of data from the mean. A low standard deviation means the data is clustered around the mean, and a high standard deviation means the data is more scattered. A standard deviation close to zero indicates that the data points are close to the mean, while a high or low standard deviation indicates that the data points are above or below the mean, respectively.  The top curve is more spread out and therefore has a higher standard deviation, while the bottom curve is more concentrated around the mean and therefore has a lower standard deviation.

Complete Question:

A successful waffle-man has recently developed a new recipe for waffles. To test the popularity of this new waffle compared to two other tried-and-true types of waffles, our friend the waffle-man randomly selected 180 lucky customers to vote on which of the three waffle types they liked best. Exactly 35% of these customers (or 63 in total) voted in favor of the new waffle. If all waffles were equally tasty, then the waffle-man knows to expect that each waffle would receive around 1/3 of the votes (so around 60 votes per waffle).

Are 63 votes for the new waffle enough to conclude that significantly more customers like it compared to the others? Luckily, our friend the waffle-man triple-majored in waffles, statistics, and clinical neurophysiology and knows how to objectively answer this question. He conducts a hypothesis test for proportions,

H0:p=1/3 H0:p=1/3, Ha :p>1/3 Ha: p>1/3

with a sample proportion of 63/180.

In carrying out this test, what null distribution for p^p^ should he use? In other words, what is the distribution of the sample statistic assuming the null hypothesis is true? (Be sure to use at least four decimal places in your calculations.)

Select one:

a)A normal distribution centered at 1/3 with a standard deviation of about 0.0351

b)A normal distribution centered at 1/3 with standard deviation of about 0.0356

c)A normal distribution centered at 0.35 with standard deviation of about 0.0356.

d)A normal distribution centered at 0.35 with standard deviation of about 0.0351.

e)We cannot use a null distribution in this problem because the population is not normally distributed.

Learn more about Normal Distribution:

https://brainly.com/question/31197941

#SPJ4

The sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

To calculate the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator we will follow these steps:

Step 1: Calculate the amount of discount = Regular Price × Discount rate

Discount rate = 35/100

Simplifying the value we have:

Discount rate = 0.35

Amount of discount = 91 × 0.35

Amount of discount = $31.85

Step 2: Calculate the sale price

Sale price = Regular price − Amount of discount

Sale price = $91 − $31.85

Sale price = $59.15

Hence, the sale price of an item that is regularly priced at $91 and is on sale for 35% off the regular price using the aleks calculator is $59.15.

Learn more about percentage here:

https://brainly.com/question/29763752

#SPJ11

The area of the vase lies between the area \(135\ cm^2\) and \(155\ cm^2\) will be \(153.86\ cm^2\).

As we know that the area of the circle is given by the formula

\(A=\pi r^2\)

So now from the question, we will find the radius for both the given areas.

Radius for the first area

\(r=\dfrac{A}{\pi} =\dfrac{135}{\pi} =6.56\ cm\)

Radius for the second area

\(r=\dfrac{A}{\pi} =\dfrac{155}{\pi} =7.03\ cm\)

Now we can see the range of the radius lies

\(6.56\leq r\leq 7.03\)

The radius must be r=7 cm lie between two quantities.

Then the area at r= 7cm will be

\(A=\pi r^2\)

\(A=\pi\times 7^2=153.86\ cm^2\)

Thus the area for the vase will be \(A=153.86\ cm^2\) ar radius r= 7 cm

To know more about the Area of the circle follow

https://brainly.com/question/24375372

A customer should buy minimum 16 boxes of pavers.

In this question, a customer is ordering brick pavers to cover a rectangular walkway that is 3 feet by 15 feet and a square sitting area that is 6 feet on a side.

First we find the total area that will be covered by  pavers.

Area of rectangle = length × width

Area of rectangle = 15 × 3

Area of rectangle = 45

And the area of square = side²

             area of square =   6²

             area of square =  36

So, the total area would be,

Total area = area of rectangle + area of square

Total area = 45 + 36

Total area = 81

So, the total area is 81 square feet.

one box of pavers covers 5.28 square feet.

So using unitary method,

81 / 5.28

= 15.534

≈ 16 boxes

This means, approximately 16 boxes will require to cover the above area.

Therefore, the customer should buy minimum 16 boxes of pavers.

Learn more about the Unitary method here:

https://brainly.com/question/22056199

#SPJ1

The relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

You can compare various data sets using bar graphs.

In a line graph, the data is represented by tiny dots, and the line that connects them indicates what happens to the data.

So, we have the coordinates:

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

Now, plot it on the graph as follows:

(Refer to the graph attached below.)

(-1, 3) and (-2, 4) are in the 2nd quadrant, and (1, 2) and (2, 4) are in the 1st quadrant.

Therefore, the relation has been plotted on the graph where the first quadrant has (1, 2) and (2, 4), while the second quadrant contains (-1, 3) and (-2, 4).

Know more about a graph here:

https://brainly.com/question/19040584

#SPJ1

Correct question:

Express the relation (-1, 3); (-2, 4); (1, 2); (2, 4) on the graph.

Working together, they can complete the task in 4 hours and 48 minutes.

A certain amount of time (T) is taken to complete a certain work (W). The number of units of work done per unit time is called the rate of work (R). Hence, Work (W) = Rate (R) Time (T) Whenever some work is done, the total work itself can be taken as one unit.

Tracy needs 8 hours to complete the task.

Then we can find the ratio of work over time as:

1 task/8 hours = 1/8 task per hour.

This means that she can complete 1/8 of the task per hour.

Dave needs 12 hours to complete the task, then his ratio is:

1 task/12 hours = 1/12 task per hour.

This means that he can complete 1/12 of the task in one hour.

If they work together, then the ratios can be added:

R = \(\frac{1}{8}\) +  \(\frac{1}{12}\)

  = \(\frac{3+2}{24}\)

  = \(\frac{5}{24}\)

So, working together, in one hour they can complete  \(\frac{5}{24}\) of the task, now we can find the number of hours needed to complete the task as:

\(\frac{5}{24}\)×\(x\)= 1 task

x = \(\frac{24}{5}\) hours = 4.8 hours

knowing that an hour is 60 minutes, then 0.8 of an hour is 60*0.8 = 48 minutes.

Then x = 4 hours and 48 minutes.

To learn more about Time and work from the given link:

https://brainly.com/question/16900783

#SPJ4

Answer:

an = 5n + 2

Step-by-step explanation:

an = 7 + 5(n - 1)

an = 7 + 5n - 5

an = 5n + 2

Driving a personal car would be the most cost-effective mode of transportation for this commute, with a total daily cost of approximately $4.60 ($3.60 for gas + $1 for travel time).

Based on the given information, the most cost-effective mode of transportation for this commute would be to drive a personal car. Taking public transportation or carpooling may be more environmentally friendly options, but they may not save as much money as driving alone.

Assuming an average speed of 60 miles per hour on the highway, the commute would take approximately 20 minutes each way, or 40 minutes round-trip. This means the total cost of travel time for each workday would be $40 ($60/hour x 2/3 hour).

Using a cost calculator such as GasBuddy, we can estimate that the cost of driving 20 miles per day (round-trip) would be around $3.60 per day, assuming an average fuel efficiency of 25 miles per gallon and a gasoline price of $2.50 per gallon.

To know more about average speed visit:

https://brainly.com/question/10449029

#SPJ11

The math library has a set of methods that can be used to work with different mathematical operations. The math library can be used to calculate the trigonometric results.

The four separate functions that can be created with the help of math library for the given problem are:Calculate the adjacent length of a right triangle given the hypotenuse and the adjacent angle:When we know the hypotenuse and the adjacent angle of a right triangle, we can calculate the adjacent length of the triangle. Here is the formula to calculate the adjacent length: adjacent_length = math.cos(adjacent_angle) * hypotenuseCalculate the opposite length of a right triangle given the hypotenuse and the adjacent angle:When we know the hypotenuse and the adjacent angle of a right triangle, we can calculate the opposite length of the triangle.

Here is the formula to calculate the opposite length:opposite_length = math.sin(adjacent_angle) * hypotenuseCalculate the adjacent angle of a right triangle given the hypotenuse and the opposite length:When we know the hypotenuse and the opposite length of a right triangle, we can calculate the adjacent angle of the triangle. Here is the formula to calculate the adjacent angle:adjacent_angle = math.acos(opposite_length / hypotenuse)Calculate the adjacent angle of a right triangle given the adjacent and opposite lengths:When we know the adjacent length and opposite length of a right triangle, we can calculate the adjacent angle of the triangle. Here is the formula to calculate the adjacent angle:adjacent_angle = math.atan(opposite_length / adjacent_length)

We have seen how math library can be used to solve the trigonometric problems. We have also seen four separate functions that can be created with the help of math library to solve the problem that requires us to calculate the adjacent length, opposite length, and adjacent angles of a right triangle.

To know more about  math visit

https://brainly.com/question/30200246

#SPJ11

The rewritten expression using a common factor is:

4x + 16 = 4*(x + 16)

Here we want to rewrite the expression:

4x + 16

Ussing a common factor, so let's factorize the terms.

The first one is simple:

4x = 4*x

The second one is also simple, we can write:

16 = 4*4

Then the common factor is 4, and we can rewrite the expression as:

4x + 16 = 4*(x + 16)

Learn more about common factors at:

https://brainly.com/question/219464

#SPJ1

The exponential function is given by f ( x ) = 15,000 ( 1 + r )ⁿ , where n is the number of years and r is the rate of increase or decrease in population

The exponential growth or decay formula is given by

x ( t ) = x₀ × ( 1 + r )ⁿ

x ( t ) is the value at time t

x₀ is the initial value at time t = 0.

r is the growth rate when r>0 or decay rate when r<0, in percent

t is the time in discrete intervals and selected time units

Given data ,

Let the initial population of the city be represented as x₀

The value of x₀ = 15,000

Let the number of years be represented as n

Now , when the rate of decrease is 5 % each year ,

The exponential decay equation is

f ( x ) = 15,000 ( 1 - 5/100 )ⁿ

f ( x ) = 15,000 ( 1 - 0.05 )ⁿ

On simplifying , we get

f ( x ) = 15,000 ( 0.95 )ⁿ

Now , when the rate of increase is 15 % each year

The exponential growth equation is

f ( x ) = 15,000 ( 1 + 15/100 )ⁿ

f ( x ) = 15,000 ( 1 + 0.15 )ⁿ

f ( x ) = 15,000 ( 1.15 )ⁿ

Hence , the exponential equations are solved

To learn more about exponential growth factor click :

https://brainly.com/question/13674608

#SPJ1

Answer:

Step-by-step explanation:

The percentile of the person with a score of 65 is approximately 28.57%.

The percentile of the person whose score was 65 can be calculated by determining the proportion of scores that fall below 65, and then expressing it as a percentage.

To find the percentile, we need to compare the score of 65 with the rest of the scores in the class.

The given scores are: 60, 61, 61, 65, 72, 75, 75, 78, 81, 81, 85, 89, 91, 98.

First, we need to determine the number of scores that are less than 65.

From the given scores, we can see that there are 3 scores less than 65 (60, 61, and 61).

Next, we calculate the proportion by dividing the number of scores less than 65 (3) by the total number of scores (14).

This gives us 3/14 ≈ 0.2143.

To express this as a percentile, we multiply the proportion by 100, giving us approximately 21.43.

However, since we are interested in the percentile of the person with a score of 65, we need to consider that they fall within this range.

Since there are 3 scores less than 65, and the person with a score of 65 is included, we add 1 to the numerator of our proportion, making it 4/14 ≈ 0.2857.

Finally, multiplying this proportion by 100, we find that the percentile of the person with a score of 65 is approximately 28.57%.

Learn more about percentile here:

https://brainly.com/question/30634547

#SPJ11

Therefore, the expression's 48th component is the cost per scarf.

A mathematical expression is a sentence that has at least two variables or integers and one mathematical action. In mathematics, it is possible to multiply, divide, add, or remove. An expression's structure is (Mathematical Operator, Number or Variable, Expression).

Here,

In the following expression, 483 denotes the total number of scarves, and 48 is the cost per scarf. For each scarf order, customers are charged a $4.75 delivery fee:

The 48 denotes the price per scarf, as can be seen from the supplied.

To know more about expression , visit

brainly.com/question/14083225

#SPJ1

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

Learn more about equation at

https://brainly.com/question/12998758

#SPJ11

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

The midpoint formular used in finding the midpoint of a segment is expressed as;

( [x₁+x₂]/2 , [y₁+y₂]/2 )

Given the data in the question;

Point V(-2,5)

Point Z(3,-17)

Plug these values into the equation above.

( [x₁+x₂]/2 , [y₁+y₂]/2 )

( [(-2) + 3]/2 , [5 + (-17)]/2 )

( 1/2 , -12/2 )

( 1/2, -6 )

The coordinate of the midpoint of the segment with the given endpoints is ( 1/2, -6 ).

Learn more about the midpoint formular here: https://brainly.com/question/14687140

#SPJ1

Answer:

I think the answer you're looking for is 86400

Step-by-step explanation:

When x = 2 cos(t), the parametric equation for y in this ellipse is y = -b sin(t), assuming the curve is traced clockwise as the parameter increases.

To find the parametric equation for y in an ellipse where x = 2 cos(t) and the curve is traced clockwise as the parameter increases, you can follow these steps:

1. Remember that the general parametric equations for an ellipse with a horizontal semi-major axis of length "a" and a vertical semi-minor axis of length "b" are x = a cos(t) and y = b sin(t).

2. In your case, you are given x = 2 cos(t), so the horizontal semi-major axis length "a" is 2.

3. Since the curve is traced clockwise as the parameter increases, we need to use a negative sign for the sine function to achieve the clockwise direction.

4. Therefore, the parametric equation for y in this ellipse is y = -b sin(t), where "b" is the length of the vertical semi-minor axis.

So, when x = 2 cos(t), the parametric equation for y in this ellipse is y = -b sin(t), assuming the curve is traced clockwise as the parameter increases. Keep in mind that you'll need to determine the value of "b" based on the specific ellipse you're working with.

To know more about parametric equation refer here:

https://brainly.com/question/28537985

#SPJ11

Answer:

hmmm really interested but hard to get

and not easy

Answer:

{− 4 1/2,  −3/4, 0}

Step-by-step explanation:

Answer:

y=-3x+5

Step-by-step explanation:

Answer:

ED = AB = 25√3

Step-by-step explanation:

Let ED = AB = X

DC = 100 - BC

Tan 60 = \(\frac{\sqrt{3} }{1} = \frac{ED}{DC}\) = \(\frac{X}{100-BC}\)

\(\sqrt{3} (100-BC) = X\)

Tan 30 = \(\frac{1}{\sqrt{3} } = \frac{AB}{BC} = \frac{X}{BC}\)

\(\frac{BC}{\sqrt{3} } = X\)

\(\sqrt{3} (100-BC) = \frac{BC}{\sqrt{3} } \\3(100-BC) = BC\\300 - 3BC = BC\\300 = BC + 3BC\\300 = 4BC \\75 = BC\)

X = \(\frac{BC}{\sqrt{3} } = \frac{75}{\sqrt{3} }\\\)

X = 25√3

Vishnu paid rupees 142,048 for the second-hand motorcycle.

The selling price of a product or service is the seller's final price such as how much the customer pays for something.

Let's calculate final price paid by Vishnu:

Given:

Shiva bought the motorcycle for rupees 153,200.

Shiva spent rupees 1,200 to repair it.

The total cost for Shiva was:

= 153,200 + 1,200

= 154,400.

Shiva sold the motorcycle to Vishnu at an 8% loss.

This means the selling price was:

= 100% - 8%

= 92% of the cost.

The selling price paid by Vishnu will be:

= (92/100) * 154,400

= 142,048.

Read more about final price

brainly.com/question/28829803

#SPJ1

Answer:

Step-by-step explanation:

Answer:

The next term is 54.

Step-by-step explanation:

Look carefully, and you will find that each number increases by 7.

12 + 7 = 19.

19 + 7 = 26.

26 + 7 = 33...

...and so on.

Therefore, the next term is 54 since 47 + 7 = 54.

Hope this helped!

Answer:

This is a really simple question!

Step-by-step explanation:

What you need to do in order to identify the sequence is, subtract the number after the first. So an example is, 19-12=7, then 26-19=7, and 33-26=7, so on so on. But every time you do that you should get 7 every time! So in order to find the next term you would have to add 7 to 47 (The last number) Which would give you, 54! Lastly to check your answer, you can solve 54-47, which is 7!

Identified sequence: +7

Next term: 54

I hope this helps! Stay safe and good luck! :)