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Step 1: Concept

To find the equation of a line, use the two points form equation of a line formula below.

Step 2:

Write the given data

Step 3:

Substitute the values to find the equation of a line.

Final answer

y = [ 8 ]x + [ -9 ]

Answer: It will take her more than 9 weeks.

Step-by-step explanation:

If she already has $150 that will be constant and if she can save $45 per week  the we will have the expression 45w  where w is the number of weeks.

Together it will  be  150 + 45w    

Now the money has to be at least $560  so it will be

150 + 45w ≥ 560  Now solve for w

-150              -150

45w ≥ 410

w ≥ 9.1  

Which means it will take 10 or more weeks t

The angle the firefighter's ladder would make with the ground is approximately 74.5 degrees.

To solve the problem, we can use the trigonometric function tangent (tan). Let x be the distance from the base of the hot tub to the building, which is 100 - 15 = 85 ft. Let θ be the angle the ladder makes with the ground. Then we have:

tan θ = x / 100

tan θ = 85 / 100

θ = tan^-1(0.85)

θ ≈ 74.5 degrees

Therefore, the angle the ladder makes with the ground is approximately 74.5 degrees.

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Answer:

m<L, m<K, m<J

Step-by-step explanation:

The angle that sees the longest side length has the biggest measurement

so

for listing the angles from smallest to largest

m<L, m<K, m<J

Answer:K J L

Step-by-step explanation:

Answer:

Alt int angles is 2 and 8, corresponding angles is 4 and 8, linear pair is 6 and 7, and vertical angles is 1 and 3

Step-by-step explanation:

Answer:

the answer is c

Step-by-step explanation:

In order to determine whether to use polynomial interpolation or the least squares method, it is important to consider the characteristics of the data being analyzed. Polynomial interpolation is best suited for data that is uniformly spaced and has little to no noise. On the other hand, the least squares method is more appropriate for data that has noise and does not follow a clear pattern.

Polynomial interpolation is a method of finding a polynomial function that passes through a set of given points. It involves fitting a polynomial of degree n to n+1 data points, which can result in overfitting the data. This means that the polynomial may not accurately represent the overall trend of the data and may not generalize well to new data.

The least squares method, on the other hand, involves finding the line or curve that best fits the data by minimizing the sum of the squared residuals between the predicted values and the actual data. This method is more flexible and can fit a wide range of functions to the data, making it more suitable for noisy or irregularly spaced data.

In summary, the choice between polynomial interpolation and the least squares method depends on the characteristics of the data. If the data is uniformly spaced and has little noise, polynomial interpolation may be appropriate. However, if the data has noise or does not follow a clear pattern, the least squares method may be more suitable. Ultimately, it is important to choose the method that best captures the overall trend of the data while minimizing the effects of noise and overfitting.

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As a result, the new length and breadth are 20% greater than the original specifications.

Percentages are just fractions with a denominator of 100. We use the percent sign (%) beside a number to indicate that it is a percentage. To calculate the percentage, divide the amount by the total value and multiply the result by 100. While many % numbers are between 0 and 100, there is no mathematical constraint that prevents percentages from taking on other values. Percentages are extensively utilized in a variety of contexts. Discounts in stores, bank interest rates, inflation rates, and numerous data in the media, for example, are all expressed as percentages. Percentages are essential for comprehending the financial elements of daily living.

Here,

If the original length and width of the living room floor are L and W, respectively, the new dimensions after increasing by 20% would be:

New Length = L + (0.20 * L) = L * 1.20

New Width = W + (0.20 * W) = W * 1.20

So the new length and width would be 20% larger than the original dimensions.

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The coordinates for point B are 7 = √(x - 5)² + (y - 4)².

What is the distance formula?

The distance formula is used to calculate the length of the line which joins the two points in an x−y plane. The distance between two points is the length of the line joining the two points. If the two points lie on the same horizontal or same vertical line.

Here, we have

Given: Segment AB Has point A located At (5, 4). If The Distance from A To B Is 7 units.

To find the distance between any two the following formula is used.

D = √(x₂ - x₁)² + (y₂ - y₁)²

7 = √(x - 5)² + (y - 4)²

Hence, the coordinates for point B are 7 = √(x - 5)² + (y - 4)².

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The function that describes the sequence 4, −2, 1, −1, ... , 41 is given by:an = 10 - 6n.

The sequence 4, −2, 1, −1, ... , 41 is an arithmetic sequence, which means that the difference between each consecutive term is constant. To find the common difference,

we can subtract any two consecutive terms in the sequence. Let's use the first two terms as an example: −2 − 4 = −6. We can see that the common difference is −6.

Thus, the nth term of the sequence can be expressed as follows:an = a1 + (n - 1)dwhere an represents the nth term of the sequence, a1 represents the first term of the sequence, and d represents the common difference.

Using the values given in the problem, we can plug them into the formula and simplify:an = 4 + (n - 1)(-6)an = 4 - 6n + 6an = 10 - 6n

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Answer:

0.00420

Step-by-step explanation:

to take 3 significant figures, u need to take the first 3 numbers(ignore those 0 at the beginning

Answer:

0.00420

Step-by-step explanation:

Answer:

A=πr2=π·102≈314.15927ft²

Step-by-step explanation:

Answer:

314.16

Step-by-step explanation:

The formula is \(\pi rx^{2}\)

B. Could possibly be true

Because, who knows? They could be, but they may not be.

Answer:

The slope of the line that contains diagonal OE will be = -3/2

Step-by-step explanation:

We know the slope-intercept form of the line equation

y = mx+b

Where m is the slope and b is the y-intercept

Given the equation of the line that contains diagonal HM is y = 2/3 x + 7

y = 2/3 x + 7

comparing the equation with the slope-intercept form of the line equation

y = mx+b

Thus, slope = m = 2/3

As we have to determine the slope of the line that contains diagonal OE.

As the slope of the line that contains diagonal HM = 2/3

We also know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line.

Therefore, the slope of the line that contains diagonal

OE will be = -1/m = -1/(2/3) = -3/2

Hence, the slope of the line that contains diagonal OE will be = -3/2

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Let's find the value of x :

According to given picture, the angles (x + 75)° and (x + 125)° forms Co interior angle pair.

so,

hence, value of x = -10°

We will have the following:

*First: We determine the measure of angle L:

So, the measure of angle L is 23°.

*Second: We will use the measure of MN and the angle of L to determine the length of the hypotenuse:

So, the length of the hypotenus is approximately 20.5 units.

Here is the graph that shows the scenario:

Answer:

  a. P = 190t -373,930 . . . . . t=actual year number

  b. P = 6640

Step-by-step explanation:

Given the two points (1991, 4360) and (1999, 5880) on a linear relation between years and moose population, you want a formula for the population (P) and an estimate of the population in 2003.

We can use the point-slope form of the equation for a line to write the formula for moose population. To do that, we need to know the slope of the line.

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1) . . . . . . . . line through points (x1, y1) and (x2, y2)

Using the given point values, we have ...

  m = (5880 -4360)/(1999 -1991) = 1520/8 = 190

The point-slope equation for a line with slope m through point (h, k) is ...

  y -k = m(x -h)

Using the first ordered pair, we can write the equation as ...

  y -4360 = 190(x -1991)

  y = 190x -373,930 . . . . . . . where x is the actual year number

Using P and t for the variables, the formula is ...

  P = 190t -373,930

Using t=2003, the above formula evaluates to ...

  P = 190(2003) -373,930 = 380,570 -373,930

  P = 6,640

The linear model predicts the 2003 population to be 6640 moose.

__

Additional comment

The formula above uses actual year number. The year value can be translated any way you might want. For example, using t = years after 1991, the formula would be ...

  P = 190(t +1991) -373,930

  P = 190t +4360

Then t=12 for year 2003.

Answer:

(3x - 1) • (3x + 7)

Step-by-step explanation:

Also if you ever need help with algebra, tiger-algebra.com is a good way to solve it! It gives you the steps and everything too.

Hope this helps!

Step-by-step explanation:

\(\tt{}( {9x}^{2} - 18x - 7)\)

\(\tt{} {9x}^{2} + 21 - 3x - 7\)

\(\tt{}3x \times (3x + 7) -( 3x + 7)\)

\(\tt{}(3x + 7) \times( 3x - 1)\)

Answer:

Step-by-step explanation:

13.2-a=2.9subtract 2.9 from both sides and add a to both sides

a=10.3

The committee can best catalog the data so it can be used to make meaningful changes by using a database management system (DBMS).

A database management system (DBMS) is a system that enables users to create, read, update, and delete data in a database. The DBMS is a tool that handles all data-related tasks. Organizations employ a DBMS to keep data organized and easy to access and manage.

DBMS provides a set of computerized tools for managing all types of data. A DBMS allows end-users to extract and analyze data from a database.

The committee can use a database management system to ensure that data is organized and easily retrievable. They can employ a DBMS to streamline data entry and report production for high-quality output.

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Brand B of shoes is most likely to have defects in their shoes.

A relative value indicating hundredth parts of any quantity.

Brand A was found to have 5 out of 600 pairs of shoes with a defect.

Brand B was found to have 5 out of 250 pairs of shoes with a defect.

As per the data the brand B shoes get more often defected.

For every 250, 5 are defected,

The percent probability for brand A is

= 5/250*100

= 2%.

while Brand B

=5/600*100

= 0.0083%.

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Answer:

\(\boxed{\boxed{\sf s=\frac{1}{3}}\sf \:or\:\boxed{\sf s=0.33...}}\)

Step-by-step explanation:

\(\sf 3\left(s+1\right)-8=6s\left(2-4\right)\)

Expand ( Apply the Distributive Property):-

\(\sf 3s-5=-12s\)

Add 5 to both sides:-

\(\sf 3s-5+5=-12s+5\)

Simplify:-

\(\sf 3s=-12s+5\)

Add 12s to both sides:-

\(\sf 3s+12s=-12s+5+12s\)

Simplify:-

\(\sf 15s=5\)

Divide both sides by 15:-

\(\sf \cfrac{15s}{15}=\cfrac{5}{15}\)

Simplify:-

\(\sf s=\cfrac{1}{3}\)

___________________

Hope this helps!

Have a great day! :)

At regeneration, the bed should be heated to about 200°C to 230°C to release the pentane from the carbon.The flow rate of air = 2400 acfm ,The mass of carbon required to handle the air stream is 17 kg.

The concentration of pentane in the air stream = 680 ppm

The theoretical adsorption capacity = 9.6 kg pentane per 100 kg carbon

Time for regeneration = 2 hours

Depth of the bed = 2 ft

Carbon density = 28 lb/ft³

Now,The mass of pentane in the air = 2400 × 680 / 1,000,000= 1.632 kg/hour

Let the mass of carbon required = M kg

For every 100 kg carbon, the amount of pentane adsorbed = 9.6 kg

Hence, the amount of pentane adsorbed on M kg carbon,= (9.6 / 100) × M kgAs

the concentration of pentane in the air = 680 ppm,

Therefore, the amount of carbon required,

M = (1.632 / 1000) × (100 / 9.6) × 1000= 17 kg

The volume of the adsorption bed =

Flow rate / bed velocity= 2400 / (2 × 60 × 60 × 2)

= 0.1667 ft³/secAs,

Carbon density = 28 lb/ft³,

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Answer:

x = -14

Step-by-step explanation:

2x - 5(x + 4) = -2(x + 3)

2x - 5x - 20 = -2x - 6

-3x - 20 = -2x - 6

-x = 14

x = -14

Answer: a) 26.2 cm

Step-by-step explanation:

Perimeter of rectangle = 2 (l + w)

2 (l + w) = 2 (9 + 4.1) = 2 (13.1) = 26.2 cm

Hope this helps!

Answer:

Solution: {x = 2, y = -1/3}

Step-by-step explanation:

On observation, we see that the y-terms are equal and opposite in sign, therefore to solve the system, we add the two equations.

2x-3y = 5 ..........(1)

3x+3y = 5............(2)

(1) + (2)

2x - 3y + 3x + 3y = 5+5

5x = 10

x = 2 .......(3)

Substitute (3) in (2) and solve for x

3x+3y = 5 .....(2)

3(2) + 3y = 5

3y = 5-6 = -1

y = -1/3  .......(4)

assemble (3) and (4) to give the answer

Solution: {x = 2, y = -1/3}

The set s is linearly dependent.

Let us discuss the concept of linearly independent and dependent setsLinearly independent sets.

A set S = {v_1, v_2, ..., vn} of vectors in a vector space V is said to be linearly independent if the only solution of the equation a_1v_1+a_2v_2+⋯+a_nv_n=0 is a_1=a_2=⋯=a_n=0.

Linearly dependent set- A set S = {v_1, v_2, ..., v_n} of vectors in a vector space V is said to be linearly dependent if there exists a non-trivial solution of the equation a_1v_1+a_2v_2+⋯+a_nv_n=0 that is not all the scalars are 0. This equation is called a linear dependence relation among the vectors v_1,v_2,…,v_n.

Now let us come to the solution for the given problem;

Given set s = {(−2, 1, 3), (2, 9, −2), (2, 3, −3)}We have to check whether this set is linearly independent or dependent.For this we will assume that a_1(−2, 1, 3)+a_2(2, 9, −2)+a_3(2, 3, −3)=(0, 0, 0)or

(-2a_1+2a_2+2a_3, a_1+9a_2+3a_3, 3a_1-2a_2-3a_3)=(0, 0, 0)

On solving these equations we get,

a_1 = a_3,a_2 = -a_3

so, the set has infinitely many solutions other than a_1 = a_2 = a_3 = 0.

Therefore the given set s is linearly dependent.

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