If 40% of a number is 120 and 55% of the same number is 165, find 15% of that
Number

Answers

Answer 1

If 40% of a number is 120 and 55% of the same number is 165 then 15% of that number is 45.

According to the question,

We have the following information:

40% of a number = 120

55% of the same number = 165

Now, let's take the number to be x.

So, we have the following expression:

40x/100 = 120

Using the cross multiplication method:

40x = 120*100

x = 120*100/40

x = 300

Now, we will find 15% of 300 by following the given steps:

15*300/100

15*3

45

Hence, if 40% of a number is 120 and 55% of the same number is 165 then 15% of that number is 45.

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Related Questions

Please help me I will give BRAINLIST and a like
I rlly need help

Please help me I will give BRAINLIST and a like I rlly need help

Answers

Answer:

?=3

Step-by-step explanation:

a= 3/5 b - 7

Answer:

the number that should be in the green box is 3

Step-by-step explanation: since it is three-fifths, in numerical way, it should be written as 3/5..

7 less than three fifths of b is a gives 3/5b-7=a

The number 46 is more than the number of situps Lyle can do. which of the following inequalities represent the number of situp Lyle can do?
A X< 46
B X>46
C X = 46
D X= 45

Answers

The answer is A since the tip of the triangle points to the smallest number

Answer:

a

Step-by-step explanation:

it says 46 is more than that cetain number

You pick a card at random, put it back, and then pick another card at random. 678, what is the probability of picking a number greater than 6 and then picking an 8

Answers

Answer:

Step-by-step explanation:

number greater than 7

Question 1 (2 x 12 = 24 marks) Analyze and discuss the performance (in Big-O notation) of implementing the following methods over Singly Linked List and Doubly Linked List Data structures: To be submitted through Turnitin.Maximum allowed similaritv is 15% Operation Singly Linked List Doubly Linked List add to start of list Big-O notation Explanation add to end of list Big-O notation Explanation add at given index Big-O notation Explanation

Answers

In analyzing the performance of implementing the given methods over Singly Linked List and Doubly Linked List data structures, we consider the Big-O notation, which provides insight into the time complexity of these operations as the size of the list increases.

Add to Start of List:

Singly Linked List: O(1)

Doubly Linked List: O(1)

Both Singly Linked List and Doubly Linked List offer constant time complexity, O(1), for adding an element to the start of the list.

This is because the operation only involves updating the head pointer (for the Singly Linked List) or the head and previous pointers (for the Doubly Linked List). It does not require traversing the entire list, regardless of its size.

Add to End of List:

Singly Linked List: O(n)

Doubly Linked List: O(1)

Adding an element to the end of a Singly Linked List has a time complexity of O(n), where n is the number of elements in the list. This is because we need to traverse the entire list to reach the end before adding the new element.

In contrast, a Doubly Linked List offers a constant time complexity of O(1) for adding an element to the end.

This is possible because the list maintains a reference to both the tail and the previous node, allowing efficient insertion.

Add at Given Index:

Singly Linked List: O(n)

Doubly Linked List: O(n)

Adding an element at a given index in both Singly Linked List and Doubly Linked List has a time complexity of O(n), where n is the number of elements in the list.

This is because, in both cases, we need to traverse the list to the desired index, which takes linear time.

Additionally, for a Doubly Linked List, we need to update the previous and next pointers of the surrounding nodes to accommodate the new element.

In summary, Singly Linked List has a constant time complexity of O(1) for adding to the start and a linear time complexity of O(n) for adding to the end or at a given index.

On the other hand, Doubly Linked List offers constant time complexity of O(1) for adding to both the start and the end, but still requires linear time complexity of O(n) for adding at a given index due to the need for traversal.

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20 Points- Which of the following is true for f of x equals the quotient of the quantity x squared plus 9 and the quantity x minus 3?
There is a removable discontinuity at x = 3.
There is a non-removable discontinuity at x = 3.
The function is continuous for all real numbers.

Answers

Answer:

There is a non-removable discontinuity at x = 3

Step-by-step explanation:

We are  given that

\(f(x)=\frac{x^2+9}{x-3}\)

We have to find true statement about given function.

\(\lim_{x\rightarrow 3}f(x)=\lim_{x\rightarrow 3}\frac{x^2+9}{x-3}\)

=\(\infty\)

It is not removable discontinuity.

x-3=0

x=3

The function f(x) is not define at x=3. Therefore, the function f(x) is continuous for all real numbers except x=3.

Therefore, x=3 is non- removable discontinuity of function f(x).

Hence, option B is correct.

please help! one easy khan question <3

please help! one easy khan question &lt;3

Answers

Answer:

It's the B

\( \sqrt{29} \)

Step-by-step explanation:

\(d = \sqrt {(2 - 4)^2 + (2 - 7)^2}\)

\(d = \sqrt {(-2)^2 + (-5)^2}\)

\(d = \sqrt {4 + 25}\)

\(d = \sqrt 29\)

Hope this helps, have a good day

Unit #2 - Lesson #7 Exit Ticket: Solve the equation shown below for the variable x. Place your answer in the answer box.

Unit #2 - Lesson #7 Exit Ticket: Solve the equation shown below for the variable x. Place your answer

Answers

Answer:

doctor

Step-by-step explanation:

feature-length capacitor chromatographic filesystems crinkled

x=b(c+2)
add 2 to the other side, then multiply by b to isolate x

If $530 is invested at an interest rate of 5% per year and is compounded continuously, how much will the investment be worth in 12 years?

Use the continuous compound interest formula A = Pert.

$557.17
$628.21
$965.72
$1,072.34

Answers

Answer:

c

Step-by-step explanation:

using the continously compounded formula, let a be unknown, p= 530, r be 0.05 and t be 12.

the equation would then be a=530e to the (0.05*12)th power, so that's why it's c

The amount of money after 12 years is $965.66. Therefore, option C is the correct answer.

What is continuous compound interest?

Continuously compounded interest means that an account balance is constantly earning interest, as well as refeeding that interest back into the balance so that it, too, earns interest.

The continuous compound interest formula is \(P(t)=P_0e^{rt}\).

Where, P(t)=value at time t, \(P_0\) =original principal sum, r=nominal annual interest rate and t= length of time the interest is applied

Now, \(P(12)=530\times e^{0.05\times12}\)

⇒ \(P(12)=530\times e^{0.6}\)

⇒ P(12)= 530×1.822

⇒ P(12)= $965.66

The amount of money after 12 years is $965.66. Therefore, option C is the correct answer.

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Algebra 1 common assessment unit 2-1 SY23

Algebra 1 common assessment unit 2-1 SY23

Answers

Answer:

\(t1 {15y08 \frac{18 \gamma \gamma }{?} }^{2} \)

a company has purchased a policy that will compensate for the loss of revenue due to severe weather events. the policy pays 1000 for each severe weather event in a year after the first two such events in that year. the number of severe weather events per year has a poisson distribution with mean 1. calculate the expected amount paid to this company in one year.

Answers

The standard deviation,    A = -1  is  the expected amount paid to this company in one year.

What is standard deviation?

The variability in your dataset is measured by its standard deviation.It reveals the average deviation between each result and the mean.A low standard deviation denotes that values are grouped closely to the mean, while a large standard deviation denotes that values are often spread widely from the mean.

The required payment random variable is given by

                      1000(x - 2 )

where x posses poison distribution with mean 1.

the expected value to be paid in the one year is given by

         = 1000 ∑x=3  ( x - 2 ) e!/x!

         = 1000 ( ∞∑ x= 0 ( x- 2 ) e⁻¹/x!  - 2∑x = 0 ( x - 2 ) e⁻¹/x!

          = 1000 ( A - B )

the expected value to be paid in the one year is given by

         = 1000 ∑x=3  ( x - 2 ) e!/x!

         = 1000 ( ∞∑ x= 0 ( x- 2 ) e⁻¹/x!  - 2∑x = 0 ( x - 2 ) e⁻¹/x!

            P ( K=x )  = e⁻¹/x!

 so

                 ∑ x=0 x p( k = x )  =  ∞∑x = 0 x e⁻¹/x! = 1

      and              ∞∑x = 0 e⁻¹/x! = 1

∵                      A = ∞∑X = 0 (x - 2 )e⁻¹/x!

                         A  =   1 - 2 * 1

                            A = -1

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What is the equation in standard form has a graph that passes through the point (5,-3) and has a slope of 6/5

Answers

Considering the definition of a line, the equation of the line that passes through the point (5, -3) and has a slope of 6/5 is y= 6/5x -9.

Linear equation

A linear equation o line can be expressed in the form y = mx + b

where

x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.

Line in this case

In this case, you know:

The line has a slope of 6/5.The line passes through the point (5, -3).

Substituting the value of the slope m, the line has the form: y=6/5x +b

Substituting the value of the point in the previous expression, the value of the ordinate to the origin b can be obtained:

-3= 6/5×5 + b

-3= 6 + b

-3 - 6= b

-9= b

Finally, the equation of the line is y= 6/5x -9.

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How might this number be shown on a calculator? 6.2x1015 6.2011​

Answers

Answer:

This is the answer to your question

How might this number be shown on a calculator? 6.2x1015 6.2011

Determine which formula for standard error applies, and then calculate the standard error. (Use at least 3 decimal places after the zeros end.)N = 500, n = 44, p = 0.45Group of answer choices0.02220.01130.4760.0750.06850.0717

Answers

The formula for standard error that applies to this problem is SE = sqrt[p(1-p)/n], where SE represents the standard error, p represents the probability of success, and n represents the sample size. In this case, N represents the population size, but it is not necessary for calculating the standard error.

Substituting the values given in the problem, we have:

SE = sqrt[0.45(1-0.45)/44] = 0.0717 (rounded to four decimal places)

Therefore, the standard error for this problem is 0.0717. This value represents the degree of variability or uncertainty in the sample proportion, or the degree to which the sample proportion is likely to deviate from the true population proportion. A larger sample size or a more extreme probability of success (closer to 0 or 1) would result in a smaller standard error, indicating greater precision in the estimate of the population proportion.

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Carrie started at the southeast corner of Frankllin Park, walked north 240 yards, turned and walked west 80 yards, and then turned and walked diagonally back to where she started. What is the area of the triangle enclosed by the path she walked?

Answers

Therefore , the solution of the given problem of surface area comes out to be the triangle formed by Carrie's path has a 3200 square yard size.

What exactly is an area?

Its entire size can be determined by figuring out how much room would be required to completely cover the outside. The determination of the volume surface, with a rectangular shape, also takes the environs into account. The total measures of something are determined by its surface area. The volume of water that a cuboid can retain within depends on the number of edges that exist in the region between its four trapezoidal extremities.

Here,

We can use the following formula to determine a triangle's surface area:

=> Area = 1/2*base*height

Let's start by determining the triangle's base and height. The starting point is the 80 yards that Carrie covered while walking west.

The triangle's height is 80 yards since it spans 80 yards from her beginning point (0, 0) to the point (0, 80).

We can now calculate the triangle's area:

=> Area = 1/2 * base * height

=> Area = 1/2 * 80 * 80

=> Area = 1/2 * 6400

=> Area = 3200 square yards

.Hence, the triangle formed by Carrie's path has a 3200 square yard size.

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One banana cost $30 how many do 80 bananas cost

Answers

Answer:2400 ...

Step-by-step explanation:


determine the equation of the line with the points (-4, -3) and (-1,-6)

Answers

Answer:

y = -1x - 7

Step-by-step explanation:

y2 - y1 / x2 - x1

-6 - (-3) / -1 - (-4)

-3/3

= -1

y = -1x + b

-6 = -1(-1) + b

-6 = 1 + b

-7 = b

Which expressions are equivalent to 7^-2 x 7^6

Answers

Step-by-step explanation:

first find the answer of 7^2 and swap it then it will be 1 over 49 multiply with 1 over 7^6

Please Help ASAP
Find the value of x, y, and z. Round to the nearest tenth if needed.

Please Help ASAPFind the value of x, y, and z. Round to the nearest tenth if needed.

Answers

Answer:

z^2 = y^2 + 6^2........equation 1

x^2 = y^2 + 24^2.....equation 2

30^2 = z^2 + x^2.......equation 3

put equation 1 and 2 in 3

30^2 = (y^2 +6^2) + (y^2 + 24^2)

900 = y^2 + 36 + y^2 + 576

900 = 2y^2 + 612

2y^2 = 900 - 612 = 288

divide both side by 2

y^2 = 144

find the square root of both sides

y = 12

recall

z^2 = y^2 + 6^2

z^2 = 144 + 36

z^2 = 180

z = 13.42

recall

x^2 = y^2 + 24^2

x^2 = 144 + 576

x^2 = 720

x = 26.83

Step-by-step explanation:

you get your 3 equations from the diagram above which as 3 triangles in it using pythagoras theorem

The values are:

x = 26.83

y = 12

z = 13.42

What is Pythagoras Theorem?

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

z² = y² + 6²........(1)

x² = y² + 24².....(2)

30² = z² + x²......(3)

Now, put the value from equation (1) and (2) in equation (3)

30² = ( y² + 6²)  + (y² + 24²)

900 = y² + 36 + y² + 576

900 = 2y² + 612

2y²  = 900 - 612

2y² = 288

y²  = 144

y= √144

y = 12

So, z² = y² + 6²

z² = 144 + 36

z² = 180

z = 13.42

and, x² = y² + 24²

x² = 144 + 576

x² = 720

x = 26.83

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A sinusoidal function has a frequency of 16π, a maximum value of 12, a minimum value of −6 , and a y-intercept of 3. Which function could be the function described?.

Answers

A sinusoidal function with a frequency of 16π, a maximum value of 12, a minimum value of -6, and a y-intercept of 3 can be modeled using the general equation of a sinusoidal function, which is:y = A sin (Bx - C) + D, where A is the amplitude, B is the frequency, C is the horizontal shift, and D is the vertical shift.

The given frequency is 16π. The value of B is equal to 2π divided by the period. Therefore, the period of the function is 1/16.π.

The amplitude is equal to the difference between the maximum and minimum values divided by 2. Therefore, the amplitude is 9.

The vertical shift is equal to the y-intercept, which is 3. The general equation for the sinusoidal function is:y = 9 sin (16πx) + 3

Hence, the function that could be described as the one described in the problem is:y = 9 sin (16πx) + 3, and it is the function that models the given sinusoidal function in general form with the characteristics provided.

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Final answer:

The sinusoidal function described is y = 9 sin(16πx) + 3. This is derived by identifying the amplitude, frequency and vertical shift.

Explanation:

The sinusoidal function described could be written as:

y = A sin(Bx) + D

In this case, the amplitude A is half the difference between the maximum and minimum, so A = (12 - -6) / 2 = 9. The frequency B is 16π. The vertical shift D is the average of the maximum value and the minimum value, so D = (12 + -6) / 2 = 3. Thus, we get:

y = 9 sin(16πx) + 3

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What is the theoretical probability that you will get a sum of 7? P(sum of 7)=

What is the theoretical probability that you will get a sum of 7? P(sum of 7)=

Answers

Answer:

\(\frac{12}{36} or \frac{1}{3}\)

Step-by-step explanation:

Notice that there are 6 sums of 7 on the table provided. For example rolling a 1 and then a 6 would produce a sum of 7.

The reason the answer is 12 and not 6 is that you need to double it for the two dice. Let's say one die was green and the other was blue. The green die could be the 1 and the blue die could be the 6. That is one favorable outcome, but it could be switched. Maybe the green die was 6 and the blue die was 1.

18. [0/1 Points]
Evaluate the variable expression xyz for the given values of x, y, and z.

X = - 5/8
y = - 2/5
Z= - 4/9

Answers

The value of the variable expression is  -1/9.

According to the statement

we have to find the value of the given variable expression.

So, For this purpose, we know that the

A variable expression (or) an algebraic expression is a combination of terms by the operations such as addition, subtraction, multiplication, division, etc.

According to the given information:

The variable expression is xyz

And the values of the X = - 5/8, y = - 2/5, Z= - 4/9.

The expression is xyz

Put the values in it then(- 5/8)(- 2/5)(- 4/9)

then the value become is -1/9.

The value of the expression becomes  -1/9.

So, The value of the variable expression is  -1/9.

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How many roots does the equation -2x³ = 0 have?
0
3
2
1

Answers

\( - 2x {}^{\\ 3} = 0 \\ x {}^{3} = 0 \\ x = 0\)

One real root

How do you write 10 more than a number?.

Answers

To write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10.

To write 10 more than a number, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 10 + Number = N+10.

This notation means that we are adding 10 to a number, which results in N+10. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is N+10.

Another way to write 10 more than a number is to use the phrase "10 plus a number". This phrase indicates that we are adding 10 to a number to get N+10.

Therefore, In short, to write 10 more than a number, we use the mathematical operation of addition and the notation 10 + Number = N+10. This means that we are adding 10 to a number, resulting in N+10. It can also be written as "10 plus N", indicating the same operation.

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In ΔEFG, g = 34 inches, e = 72 inches and ∠F=21°. Find the area of ΔEFG, to the nearest square inch.

Answers

The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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38=1/8k+47
Find the value of k

Answers

Answer:

\(k=-72\)

Step-by-step explanation:

\(38=\frac{1}{8} k+47\)

Switching the sides of the equation isn't required, but it helps to reduce confusion.

\(\frac{1}{8}k+47=38\)

Since there is a positive 7, we are going to do the opposite operation, which is addition.

\(\frac{1}{8}k+47-47=38\\\text\:\:\:\:\:\:-47\:\:\:\:\:\:\:\:\:-47\)

Simplify

+47 - 47 will cancel each other out, so we are left with:

\(\frac{1}{8}k=-9\)

Now, multiply 8 to both sides, since the equation gives us 1 divided 8, so the opposite operation of division is multiplication.

\(8\cdot \frac{1}{8}k=8\left(-9\right)\)

On the right side, we have the same thing as \(\frac{8}{1} \cdot \frac{1}{8}\), so 8 we can cancel the equation on the right side since they are both the same number.

On the left, we have \(8\left(-9\right)\), which is -72.

Therefore, \(k=-72\).

Each tile measures 3 in. in length and 3 in. in width. what are the perimeter and area?

Answers

Answer:

Perimeter= 12 Area= 9

Step-by-step explanation:

4n + 3 < 6n + 8 - 2n

Pls solve in steps

Answers

Answer:

All real numbers would be the correct answer.

Step-by-step explanation:

First of all, add 6n to -2n which now the equation would be 4n+3 < 4n+8.

Now, subtract 4n to both sides and subtract 3 to both sides. Now you will have 0n < 5 which will be all real numbers.

When testing the differences between means, the _____ hypothesis suggests that population means are not equal.

Answers

When testing the differences between means, the research hypothesis suggests that population means are not equal.

This is further explained below.

What is a research hypothesis?

Generally,  A declaration of an expectation or prediction that will be put to the test by means of research is known as a research hypothesis. Read up on the subject that you're interested in before you try to formulate a research hypothesis about it.

In conclusion, The study hypothesis proposes that population means are not equal, and this may be tested by comparing how different means compare to one another.

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find the line of reflection if the image of (-5, -2) is each of the following

a. (5, -2) |_____|

b. (2, 5) |_____|

c. (-5, 0) |_____|

d. (1, -2) |_____|

Answers

Answer:

A: -5, 2

B: -2, -5

C: 5, 0

D -1, 2

Hope this helps!

The segments shown below could form a triangle.
д
C
B
7
с
12
B
д
O A. True
O B. False

The segments shown below could form a triangle.CB712BO A. TrueO B. False

Answers

The segments can form a Triangle.

What is Pythagoras theorem?

The Pythagorean theorem, or Pythagorean theorem, illustrates the relationship between the three sides of a right-angled triangle. The square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle, according to the Pythagorean theorem.

We have Three segments as:

AB = 12 unit, BC = 9 unit, AC = 7 unit

The longest segment is 12 unit

So, AB² = 12² = 144

and, BC² + AC²

= 9² + 7²

= 81 + 49

= 130

So, a right angles triangle is not possible.

Now, using Triangle Inequality

12+ 9 >7

12 + 7>9

9 + 7> 12

Thus, a Triangle can be possible but not Right angles Triangle.

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The temperature of a mixture changes by -5.2 Fahrenheit between 8am and 11am. At 6pm the temperature is 14.5 Fahrenheit, which is half of what it was at 11am. What was the temperature at 8am of the mixture. I have this equation , but not sure is correct. 1/2(x-6.8)= -3.1Can you help me create a equation. Mine is wrong. At a price of $162.65 per ounce the daily demand of virbog is 850 ounces. At a price of $132.05 the daily demand of virbog is 1450 ounces. Use this information to create two ordered pairs of the form (Quantity Demanded, Price per Ounce). Use a comma to separate the ordered pairs. At a price of $162.65 per ounce the daily demand of virbog is 850 ounces. At a price of $132.05 the daily demand of virbog is 1450 ounces. Use this information to create two ordered pairs of the form (Quantity Demanded, Price per Ounce). Use a comma to separate the ordered pairs. why was alfredo jimenez and his family called gusanos when they left cuba? 3 land reform programmes Find the length of the missing side. Leave your answer in simplest radical form. Which of the following shows strong characterization?A. Frank is tall, nineteen years old, and likes pizza.B. Kevin sat terrified in his jail cell. The cold wind blowing though his open, barred window made him shiver. Water dripped from the celling adding moisture to the air, and rusting the bars of his cell. Kevin has no idea why he was there, or when he would get out.C. TJ was bad . He was an awful person. He was not good at all. He was evil and known to be mean.D. Will was known for his intensity, even at the young age of 15. Once Will had a goal in mind, there was nothing that would stop him. It didnt matter if he had to hurt people, break laws or even hurt himself, he was going to do whatever he was set out to do. which of the following best characterizes the decision of where to establish a physical location for your venture? A line passes through the points (-2, 9) and (1, 3).Provide work for calculating the slope and y-intercept. Then, write the equation for the line in slope-intercept form. Philippe is creating equal-sized teams for his family's game night. 15 people will be playing. Which list shows all the possibilities for the number of people Philippe could place on each team? Auguste comte suggested that certain processes, which he called ____ hold society together. can someone plz help me a country in south america allows its currency to nominally float freely against other currencies, but the government has the right to intervene if it believes that the currency has deviated too far from its fair value. in this country, the value of currency is determined based on a float system. . Write the quadratic equation in factored form. Be sure to write the entire equation. x^2 - 5x - 24 = 0 A chronic cough, blood-tinged sputum, and dyspnea are symptoms of which cancer?O A. breastOB. leukemiaC. skinD. lung what is the name of the structure that connects the two hemispheres of the brain? The local school district has made a scale model of the campus of Engels Middle School including a proposed new building. The scale of the model is 1 inch = 3 feet. An existing gymnasium is 8 inches tall in the model. How tall is the actual gymnasium? a composite material has both carbon fibers and glass fibers as reinforcement. there are half as many carbon fibers as glass fibers. how should the fibers be arranged to make the highest modulus, e1, composite? sketch out your solution and calculate e1 for the composite. What is the relationship between freezing point depression and concentration of solute or solution? One of the disadvantages of personal selling is the high cost to maintain good salespeople. how can companies reduce the cost but still maintain that personal touch? Solve these two questions for 50 pts.