write a part to part and a part to whole ratio for each problem situationof the 250 students surveyed 142, prefer carrots and 97 prefer peas

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

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{8}) \\\\\\ y-5=-x+8\implies {\Large \begin{array}{llll} y=-x+13 \end{array}}\)

Answer:

answer c)

Step-by-step explanation:

Hope this helps you out

9514 1404 393

Answer:

Step-by-step explanation:

To find the scale factor from ΔDEF to ΔRST, find a measure on ΔDEF and a corresponding measure on ΔRST, then write them in the form required for the scale factor.

Here, there are numbers on DE, RS, and ST. We see by the similarity statement ΔDEF ~ ΔRST that DE corresponds to RS, so the scale factor is ...

  ΔDEF : ΔRST = DE : RS = 3 : 4 . . . scale factor

__

Using that scale factor, you can write a proportion to find the value of x.

  3 : 4 = x : 16  ⇒  3/4 = x/16

Multiplying the fraction equation by 16, we have ...

  x = 16(3/4)

  x = 12

A statement that correctly compares the graph of function g with the graph of function f include the following: C. The graph of function g is a vertical compression of the graph of function f.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

When the parent function \(f(x) = e^x -4\) is vertically compressed by a scale factor of 1/2, the transformed function g(x) is given by the following equation;

g(x) = kf(x)

g(x) = 1/2f(x)

\(g(x) = \frac{1}{2} e^x -4\)

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Answer:

Step-by-step explanation:

The area of a triangle of base 8 in, and height 7 in, is

A = (1/2)(base)(height) = (1/2)(8 in)(7 in) = 28 in^2.  This matches the given 28th in^2.

The perimeter of a polygon is expressed as; the sum of all sides. In this case it is: 48cm.

It is to be noted that the image in this case is not supplied hence a supplementary image is used. See the attached. Based on this information,

To find the perimeter of the polygon, we need to find the lengths of the AB, BC, CD and DA

Since,  and to find the length, from circle theorem, "Two tangents from an external point to a circle are always equal in length".

From this statement we shall conclude,

Thus, the perimeter of the polygon is

AB + BC + CD + DA

= 11 +  13 + 13 + 11

= 48cm

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Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

A list of assertions and the justifications for each assertion are included in a two-column geometric proof.

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Answer:

130° and 310°

Step-by-step explanation:

the bearing of A from B is the measure of the clockwise angle from a north line at B to A

the angle at B and A are same- side interior angles and sum to 180°

angle at B = 180° - 50° = 130°

the bearing of A from B is then 130°

the bearing of B from A is the measure of the clockwise angle from the north line at A to B

the complete angle about A = 360° then clockwise angle from north line at A to B is

360° - 50° = 310°

the bearing of B from A is 310°

The sampling method used by the restaurant manager allows for efficient data collection and a representative sample, it may introduce bias and lacks randomization.

Based on the information provided, we can identify the following statements that are true about the sampling method used by the restaurant manager to evaluate customer satisfaction with the new smoothie:

1. The manager uses systematic sampling: The manager surveys every other customer who orders the new smoothie. This systematic approach involves selecting every second customer, providing a consistent and organized sampling method.

2. The sample is representative: By surveying every other customer who orders the new smoothie, the manager ensures that the sample includes a variety of customers, reflecting the customer population as a whole.

3. The sample size may be smaller than the total customer base: Since the manager surveys every other customer, the sample size may be smaller compared to surveying every customer. This allows for efficient data collection and analysis.

4.The sampling method may introduce bias: The manager may inadvertently introduce bias by only surveying every other customer. Customers who are skipped in the survey may have different preferences or opinions, leading to a potential bias in the results.

5. The sampling method lacks randomization: Randomization is not employed in this sampling method, as the manager systematically selects customers. This could potentially introduce bias or exclude certain types of customers from the sample.

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Step-by-step explanation:

To find the probability of an advertising firm selected at random having under $1 million or $1 million to $20 million in income after taxes, we need to add the number of firms in each of these two categories and divide the result by the total number of firms.

Number of firms with under $1 million in income after taxes = 95

Number of firms with $1 million to $20 million in income after taxes = 74

Total number of firms = 95 + 74 + 31 = 200

Therefore, the probability of an advertising firm selected at random having under $1 million or $1 million to $20 million in income after taxes is:

(95 + 74) / 200 = 0.845

So the probability is 0.845 or 84.5%.

Step-by-step explanation:

g(x) has clearly in its core the same function curve.

but it is

1. upside-down

2. moved up from the x-axis by 1 unit

3. moved to the right of the y-axis by 3 units

so, how do we express these 3 attributes in the functional definition ?

1. easily : by flipping the sign. g(x) = -x² is the same function type just upside-down (mirrored into the negative y space).

g(x) = -x²

2. also very easy : a function is moved up or down on the coordinate grid by adding (or subtracting) a constant.

we need to move our function up by 1 unit : we add 1.

that makes currently g(x) = -x² + 1

3. this is the trickiest part. to move a function left or right we need to make the function "think" that the input value x is not x, but it is (x ± constant).

let's ignore 1. and 2. for the moment and just focus moving the original function 3 units to the right.

that tells us that the functional result value of x in the shifted function must be the same as the functional result value in the original function for an input value that is 3 units "earlier" on the x-axis.

that would mean g(0) = f(-3), g(1) = f(-2), g(2) = f(-1), g(3) = f(0), ...

so, we see, g(x) = f(x-3) = (x-3)²

now, we combine again 1., 2. and 3., and we get

g(x) = -f(x-3) + 1 = -(x-3)² + 1

Answer:

The listener is approximately 71.414 feet far from the whisperer.

Step-by-step explanation:

We must remember that two fundamental variables for every ellipse are the major semiaxis (\(a\)) and the minor semiaxis (\(b\)). The major semiaxis equals a half of the length of the whispering gallery, whereas the minor semiaxis equals a half of the width of the whispering gallery. These are:

\(a = 46\,ft\) and \(b = 29\,ft\)

The distance between both whisperers (\(d\)), measured in feet, is two times the distance between center and any of the foci (\(c\)), measured in feet, whose valued is obtained by using this Pythagorean identity:

\(d = 2\cdot c\)

\(c = \sqrt{a^{2}-b^{2}}\)

If \(a = 46\,ft\) and \(b = 29\,ft\), then:

\(c = \sqrt{(46\,ft)^{2}-(29\,ft)^{2}}\)

\(c \approx 35.707\,ft\)

\(d = 2\cdot (35.707\,ft)\)

\(d = 71.414\,ft\)

The listener is approximately 71.414 feet far from the whisperer.

Answer:

Minimum--> 250

Q1--> 255

Q2--> (Median): 307

Q3--> 433

Maximum-->507

Step-by-step explanation:

To find the five-number summary of this data set, we need to determine the minimum value, maximum value, and three quartiles (Q1, Q2, Q3) which divide the data into four equal parts.

First, we need to sort the data set in ascending order:

{ 250, 253, 255, 267, 307, 425, 433, 435, 507 }

Minimum: 250

Maximum: 507

To find the quartiles, we need to find the median of the entire data set (Q2) and then the medians of the two halves of the data set, which will give us Q1 and Q3.

Q2 (Median): The median of the entire data set can be found by averaging the two middle numbers.

Q1: The median of the lower half of the data set is 255, which is the middle value of { 250, 253, 255, 267, 307 }. Therefore, Q1 = 255.

Q3: The median of the upper half of the data set is 433, which is the middle value of { 425, 433, 435, 507 }. Therefore, Q3 = 433.

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of depression increases.

the arc formed as the line of sight drops from the horizon. The angle of depression is the angle formed when an object is perceived below the observer's height between the horizon and the line of sight of the observer. The depression angle is the angle formed between the line of sight looking down at the object and the horizontal line of sight. If you are on a hill or a building and you are looking down at something, you can tell the slope. To measure these angles, a theodolite or an inclinometer might be employed.

As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of the depression increases.

∠x = 65° ≤ ∠XYZ

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Step-by-step explanation:

L : J

2:3

so Lara has 2 shares

2 shares = 8

what is one share

type in comments

and then I will explain the rest

The amount of the Joan's share will be $12.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Algebra is the study of graphic formulas, while logic is the interpretation among those signs.

A sum of money is divided between Laura and Joan in the ratio 2:3.

Laura’s share is $8.

Let J be the amount of Joan's share and L be the amount of Laura's share.

Then the amount of Joan's share will be

L / J = 2 / 3

8 / J = 2 / 3

By the cross multiplication, then the equation will be

2J = 8 x 3

2J = 24

 J = 24 / 2

 J = $12

The amount of the Joan's share will be $12.

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Equation of the line CD is equals to \(y = \frac{-x}{4} +7\).

" Parallel lines are defined as the lines in the same plane never intersect with each other. They are equidistant to each other in the same plane."

Formula used

\(Slope = \frac{y_{2} -y_{1} }{x_{2}-x_{1} }\)

According to the question,

Given,

Coordinates of A \((x_{1},y_{1})\) = ( -2 , 5)

Coordinates of B \((x_{2},y_{2})\) = ( 6 , 3)

Substitute the value to get the slope of line AB we get,

\(Slope of line AB 'm_{1}' =\frac{3-5}{6-(-2)}\)

                    ⇒ \(m_{1} = \frac{-2}{8}\)          

                              \(= \frac{-1}{4}\)

Coordinates of C \((x_{1},y_{1})\) = ( x ,y)

Coordinates of B \((x_{2},y_{2})\) = ( 8,5)

Substitute the value to get the slope of line CD we get,

\(Slope of line CD 'm_{2}' =\frac{5-y}{8-x}\)

Lines AB and CD are parallel.

Slope of parallel lines are equal.

Therefore,

                     \(m_{2} = m_{1}\)          

                 ⇒ \(\frac{5-y}{8-x}\) \(= \frac{-1}{4}\)

                ⇒\(5-y = \frac{-1}{4} (8-x)\)

                ⇒ \(y = \frac{-x}{4} +7\)

Hence, equation of the line CD is equals to \(y = \frac{-x}{4} +7\).

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\(~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 1200\\ P=\textit{original amount deposited}\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}\)

\(1200 = P\left(1+\frac{0.07}{12}\right)^{12\cdot 15} \implies 1200=P\left( \frac{1207}{1200} \right)^{180} \\\\\\ \cfrac{1200}{ ~~ \left( \frac{1207}{1200} \right)^{180} ~~ }=P\implies 421.21\approx P\)

Since then, it has spread to other rivers, colonized them, clogged the water intake pipes, and competed with local species for food. Zebra mussels are the method for removing a lot of plankton from the water column.

Here, we have,

The Caspian Sea in Asia is where zebra mussels, or Driessen polymorph, are found naturally.

They arrived in the Great Lakes region in the late 1980s via ballast water from a transatlantic ship.

The Great Lakes, Mississippi, Tennessee, Hudson, and Ohio river basins were all overrun by these mussels within ten years.

The lake's brilliant blue hue is a result of Tahoe's clean air and water.

There is more to this phenomenon than just the fact that Lake Tahoe's surface reflects the sky, which contributes to its blue color.

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complete question:

As you respond to Part A, Part B, and Part C, follow the directions below.

​

​Address all of the instructions in each prompt.

​Use evidence from the information provided and your own knowledge of science to support your responses.

Part A

​

Describe one way scientists near Lake Tahoe can detect if the lake has been impacted by zebra mussels.

Answer: 1

Step-by-step explanation:

Answer:

A = 35 cm²

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

by counting the squares on the sides

length = 7 cm and width = 5 cm , then

A = 7 × 5 = 35 cm²

Answer:

x = 12

Step-by-step explanation:

a² + b² = c²

16² + x² = 20²

256 + x² = 400

x² = 144

x = 12

\(\large\huge\green{\sf{Answer:-}}\)

\( = (-25ac) \times (-4t)) \\ = 100 \times a \times c \times t. \\ =100a \times c \times t \)

Answer:

5

Step-by-step explanation:

5 x 3 = 15

n x 4 = 4n

3 + 4 = 7

(5 x 3) + (n x 4) = 5(3 + 4)

15 + 4n = 5*7

15 + 4n = 35

4n = 35 - 15

4n = 20

n = 20/4

n = 5

Hence, the value of missing number (n) is 5.

Answer:Yes

No

no

Yes

Step-by-step explanation:

Gaussian Elimination and Gauss-Jordon Elimination are two methods of solving linear systems of equations.
A-x=3, y=2, z=-2,B-x=4, y=-2, z=15 C-x=2, y=-2, z=2.

An equation is a mathematical statement that states two expressions are equal. It consists of two expressions separated by an equals sign (=) and can use any of the operations of arithmetic such as addition, subtraction, multiplication, division and exponents. An equation can be solved to find the value of one or more variables that make the equation true.

Question 1:

Using Gaussian Elimination:

2x+y + 2z = 1

4x + 3z = -5

5y + 4z = 13

Step 1: Subtract 2 times the first equation from the second equation.

0x+3y+z=-6

Step 2: Subtract 5 times the first equation from the third equation.

0x+2y+3z=10

Step 3: Subtract 2 times the second equation from the third equation.

x+y=4

Step 4: Subtract 4 times the second equation from the first equation.

x=3

Step 5: Substitute x = 3 in the second equation.

3+2y+z=-6

Step 6: Subtract 3 times the fifth equation from the fourth equation.

y=2

Step 7: Substitute y = 2 in the fifth equation.

3+4+z=-6

Step 8: Solve for z.

z=-2

Answer: x=3, y=2, z=-2

Question 2:

Using Gauss-Jordan Elimination:

2x+y+z=13

x+2y+z= 11

x + 3y + 3z = 19

Step 1: Subtract 2 times the first equation from the second equation.

-x+3y=2

Step 2: Subtract x times the first equation from the third equation.

2y+2z=6

Step 3: Subtract 3 times the second equation from the third equation.

x=4

Step 4: Substitute x=4 in the second equation.

4+3y=2

Step 5: Solve for y.

y=-2

Step 6: Substitute y=-2 in the first equation.

2x+(-2)+z=13

Step 7: Solve for z.

z=15

Answer: x=4, y=-2, z=15

Question 3:

Using Gaussian Elimination:

-3x+2y-6z = 6

5x + 7y - 5z = 6

x + 4y = 2z = 8

Step 1: Subtract 5 times the first equation from the second equation.

2x+9y-z=0

Step 2: Subtract 2 times the third equation from the first equation.

-5x+2y-2z=-2

Step 3: Subtract 2 times the first equation from the third equation.

3x+7y=2

Step 4: Subtract 3 times the second equation from the third equation.

x=2

Step 5: Substitute x=2 in the second equation.

4+9y-z=0

Step 6: Solve for y.

y=-2

Step 7: Substitute y=-2 in the fifth equation.

2+(-2)-z=0

Step 8: Solve for z.

z=2

Answer: x=2, y=-2, z=2

Conclusion:

Gaussian Elimination and Gauss-Jordon Elimination are two methods of solving linear systems of equations. Both methods rely on manipulating the equations to create a triangular form, which allows for the easier determination of the variables. By using both methods, we were able to solve each of the three linear systems of equations given in the question.

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Answer:

\(\frac{10}{27}\)

Step-by-step explanation:

\(-\frac{2}{9} (-\frac{5}{3})=\)

-2 · 5/ -9 · 3 =

10/27 =

\(\frac{10}{27}\)

Answer:

\(\frac{10}{27}\)

Step-by-step explanation:

\(\frac{-2}{9} *\frac{-5}{3}\)

multiply numerator with the other numerator

-2 × -5 = 10 (numerator)

multiply denominator with the other denominator

9 × 3 = 27 (denominator)

put it in its correct order

the answer is 120.6 I'm pretty sure

Answer:

9.525 units squared

Step-by-step explanation:

I'm assuming the 3 is the base of the triangle so I split 3 in half and got 1.5 for 2 right triangles. I then did the area of a right triangle formula 1/2 base x height

1/2(1.5 x 6)=4.5

1/2(1.5 x 6.7) =5.025

Add these two together

5.025+4.5=9.525

9.525units squared

KM, JK, PK, and MJ are shown on the diagram.

Then the correct options are B, C, D, and F.

Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

A line segment in mathematics has two different points on it that define its boundaries.

All the line segments will be

JK, JM, KM, MP, PK, and KL

The triangle KPM.

And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.

Then the correct options are B, C, D, and F.

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