Assignment 2: Room Area

A scientist is developing a new method to reduce the population of a certain invasive insect species. For an experiment, the scientist starts with 2,500 insects. She predicts that her new method will reduce the number of insects in the experiment by 14% each week.
Write an exponential equation in the form y=a(b)x that can model the predicted number of insects, y, in the experiment after x weeks.
Use whole numbers, decimals, or simplified fractions for the values of a and b.

Answer:

15.50$

Step-by-step explanation:

7.5+8= 15.5

The translations, reflections, and rotations are types of transformations that change an original object to form a new image, each with its own specific rule and properties. They are used in a variety of real-world applications to change the position or orientation of objects.

There are 3 types of Transformations :

(i) Translation: A translation involves moving an object from one place to another without changing its size or orientation.  

The algebraic rule for a translation is to add the same constant to each coordinate of each point

The Translations preserve congruence, meaning that corresponding parts of congruent figures will still be congruent after a translation.

An example of a real-world application of translation is moving a store to a new location.

(ii) Reflection: A reflection involves flipping an object over a line or point, creating a mirror image.

The algebraic rule for a reflection is to negate the value of one of the coordinates.

Reflections preserve orientation, meaning that the orientation of the reflected image is opposite that of the original object.

An example of a real-world application of reflection is looking at your reflection in a mirror.

(iii) Rotation: A rotation involves turning an object about a fixed point, called the center of rotation, through a certain angle.

The algebraic rule for a rotation is to multiply each coordinate by a rotation matrix.

Rotations preserve distance and angle measures, meaning that the lengths of corresponding parts and the angles between them are equal in the original and rotated images.

An example of a real-world application of rotation is turning a steering wheel to change the direction of a car.

The given question is incomplete , the complete question is

Compare and contrast the three types of transformations: translations, reflections, and rotations.

Include the algebraic rules, whether each transformation preserves congruence and any examples of real-world application.

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This refers to the ratio between the scale of a given original object and a new object. It is its representation but of a different size (bigger or smaller). For example, if we have a rectangle of sides 2 cm and 4 cm, we can enlarge it by multiplying each side by a number, say 2.

Solving for the area and scale factor we have:

L= 5 units

W = 2 units

A = (5 x 2)

A = 10 square units.

A= (Scale factor of  L * W)*  L * W

= (2 x 2 x 5 x 2)

A = 40 square units.

A= (Scale factor of  L * W)*  L * W

= (3 x 3 x 5 x 2)

A= 90 square units

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Step-by-step explanation:

8 + (22 + 15) = 8 + 37 = 45

To evaluate the expression, we must first perform the operations inside the parentheses. In this case, 22 + 15 = 37. Then we can add 8 to that result, which gives us 8 + 37 = 45. So the final value of the expression is 45.

Answer:

Using BODMAS, you are to solve the one in the bracket

22+15 which=37

then you add it to 8

37+8=45

Answer:

X 3y 2

Step-by-step explanation:

Hi There!

Your Answer must be The Realation is a function or A...

Why did i get this answer?

To Find if a Graph is a Function, We must use the concept called vertical line test.

If the vertical line drawn across at anywhere of the graph intersects the graph at most once, we decide the given graph represents the function.

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The solution of the equations using elimination method is x = 2.5, y = 5.25

The elimination method is a method used to solve systems of linear equations. It involves manipulating the equations in such a way that one of the variables is eliminated, resulting in an equation in one variable that can be easily solved.

8x+4y = 49 --- (1)

3x+2y = 21  ----(2)

To eliminate x, multiply (1) by 3 and multiply (2) by 8. Then subtract the result. That is:

3 × (8x+4y = 49)   = 24x + 12y = 147

8 ×(3x+2y = 21)    = 24x + 16y = 168

.......................................................................

                                          4y = 21

.........................................................................

4y = 21

y = 21/4

y = 5.25

Put y = 5.25 into (1):

8x+4y = 49

8x + 4(5.25) = 49

8x + 21 = 49

8x = 49 -21

8x = 28

x = 28/8

x = 3.5

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Answer: x = 11

Step-by-step explanation:

2(x+7) = 36

x + 7 = 18 <-- dividing both sides by two

x = 11

There are multiple different paths you can take in order to get this answer, all equally simple. You could open up the bracket, move to one side, and then divide, however if you were to have the answer in the most efficient and least amount of steps I would suggest doing this.

Answer: So 2(b+5) would be the answer to your question.

Step-by-step explanation:

Answer:

[tex]w = \frac{P - 2l}{2}[/tex]

Step-by-step explanation:

In this case, we will just simplify the given formula of the perimeter and re-arrange it to get the value of w.

[tex]P = 2(l + w)\\P = 2l + 2w\\P - 2l = 2w\\\frac{P - 2l}{2} = w[/tex]

Grace can buy 8 video games of price $15 each if she wants to save $120 from $240.

Grace puede comprar 8 videojuegos si quiere ahorrar $120 de $240

Pricing is the procedure of determining the value that a manufacturer will receive in the exchange of goods and services. To make the cost of the producer's products suitable for both the manufacturer and the customer, a pricing method is used. Pricing is determined by the firm's average prices as well as the consumer's estimation of an item's value in relation to that of similar goods from rival companies.

The remainder must be $12, so

(El resto debe ser $12, entonces)

240 - 120

= $120

Number of video games she could buy with $120

(Número de videojuegos que podría comprar con $120)

⇒ 120/15

= 8

Therefore, Grace can buy 8 video games if she wants to save $120 from $240.

Por lo tanto, Grace puede comprar 8 videojuegos si quiere ahorrar $120 de $240

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Translated question:

Grace has $240 in the bank. She wants to buy as many $15 video games as possible. How many video games could she buy if she wanted to keep at least $120 in the bank? help me please

In a case whereby  walker notes that a monument is due North and 7.5 Km from him. He then walks on a bearing of 0.41 the distance from the monument at this point is 5.63km

The concept that will be use is bearing. A bearing is the angle, measured in degrees clockwise from north, in mathematics. In most cases, bearings are specified as three-figure bearings. For instance, the standard notation for 30° clockwise from north is 030°.

From the diagram we can see that the interpretation gave us a triangle and from trigonometry,

Cos θ= adjacent / hypothenus

Then  Cos 41 = XY/XM

Cos 41 = XY/7.5

0.75 = XY/7.5

0.75 *7.5 =5.63km

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Answer:

3/8

Step-by-step explanation:

In these type of problems, I like making all of my denominators the same.

1/8 is good.

1/2 is half. 4/8 is also half. I'll use 4/8 because 1/8 also has the 8

A whole circle is 100%, which is 1/1. It's also 8/8

To find the shaded area, we'll first add 1/8 and 4/8. That equals 5/8. We just have to add nominators/top now because the denominator/bottom is the same

Now we'll subtract 8/8 from 5/8. Again denominator is the same, so we only need to subtract the top

8-5=3

Also known as 3/8

Answer: 9 points

Step-by-step explanation: 8 rounds=8 points; If Harriet has 19 points and they have played 8 rounds which equal 8 points, 19-8=9 points

The possible values of k are -11 and 11.

Given that equation is: x²-kx+28

Roots are: [tex]\alpha ,\alpha +3[/tex]

To find: the value of x:

The general quadratic equation is:

ax²+bx+c

Product of roots=c/a

sum of roots=-b/a

From given,

x²-kx+28=0

a = 1

b = -k

c = 28

Therefore,

Product of roots=28/1=28

sum of roots=-k/1=-k

Given roots are:

[tex]\alpha ,\alpha +3[/tex]

Therefore,

The two roots are two numbers whose difference is 3 and whose product is 28

Those two roots are 4 and 7 or -4 and -7

Then, the sum of roots is:

4 + 7 = 11

-4 - 7 = -11

Therefore, the possible values of k are -11 and 11.

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1. The probability of selecting exactly one tank with high-viscosity material is 0.

2. The probability of selecting at least one tank with high-viscosity material is 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is 0.25.

1. The probability of selecting exactly one tank with high-viscosity material is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 4, x = 1, and p = 24/24 = 1. Therefore, P(X = 1) = (4C1)1^1(1-1)^4-1 = 0.

2. The probability of selecting at least one tank with high-viscosity material is calculated by the complement rule, P(X > 0) = 1 - P(X = 0). In this case, P(X > 0) = 1 - (4C0)1^0(1-1)^4-0 = 1.

3. The probability of selecting exactly one tank with high-viscosity material and exactly one tank with high impurities is calculated by the binomial distribution formula, P(X = n) = (nCx)p^x(1-p)^n-x, where n is the number of trials, x is the number of successes, and p is the probability of success. In this case, n = 8, x = 2, and p = 24/24 = 1. Therefore, P(X = 2) = (8C2)1^2(1-1)^8-2 = 0.25.

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A recipe for hot chocolate requires 4 cups of milk , 1/4 cup of chocolate powder , 1/3 cup of honey and for which Simplified  Ratio is 16 : 1 : 3.

This can be calculated by following steps:

Find the ratio of milk to chocolate powder.

 Ratio of Milk to Chocolate Powder = 4 : 1/4

Find the ratio of chocolate powder to honey.

 Ratio of Chocolate Powder to Honey = 1/4 : 1/3

Find the ratio of milk to chocolate powder to honey.

 Ratio of Milk to Chocolate Powder to Honey = 4 : 1/4 : 1/3

Simplify the ratio in its simplest form.

 Simplified Ratio = 16 : 1 : 3

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Points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y) y y such that  B C ‾ ∥ D E ‾ BC ∥ DE .

Assume that points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y)

( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 )

∴PA=PB

With the aid of the distance formula

= (x 2 −x 1  )

2  +(y 2  −y 1  )

2

There are

⇒ (x+2) 2  +(y+2) 2

= (x-5) 2  +(y−2)2

(x-2) 2  +(y+6)2

⇒(x+2) 2  +(y+2)

2  =(x+2) 2 +(y+2) 2

⇒ x2−4x+4+y 2

−7y+10=  x2 +4x+4+y 2  −7y+14

⇒−4x−4x−10y+7y+14−16=0

⇒−8x−3y+2=0

⇒3x+y−5=0

ΔAD

Eare Similar triangles

∴( CB / DE )=( AB / AD )

B C ‾ ∥ D E ‾ BC ∥ DE .

Points ( 2 , 2 ) , C ( − 5 , − 2 ) , D ( − 2 , 6 ) are equally distant from the point P(x, y) y y such that  B C ‾ ∥ D E ‾ BC ∥ DE .

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Answer: D

Sorry if it is not.

Answer:

The answer is 4

answer mine

Answer:

There are 11 pigs and 17 chickens.

Step-by-step explanation:

Lets let

p = number of pigs

c = number of chickens

Assuming each animal has only one head, then

p + c = 28

And assuming that pigs have four feet and chickens have two feet:

pig feet = 4p

that is, 4 feet for each pig, and



chicken feet = 2c

right? two feet per chicken.



All the feet are:

4p + 2c = 78

Now we have two equations and two unknowns, so we can solve this "system of equations". You can use substitution or elimination method (or even graphing or matrices) I will run through elimination method.

Multiply p+c=28 times -2.

-2p + -2c = -56

then add the whole equation to the other equation. Do this adding vertically, from top to bottom.

-2p + -2c = -56

4p + 2c = 78

_____________

2p = 22

Divide by 2 to solve

p = 11

There are 11 pigs.

Remember,

p + c = 28

11 + c = 28

subtract 11

c = 17

There are 17 chickens.

Residuals measure the vertical distance between two observations of the response variable - False.

An individual data point's residual is a measurement of how well a line fits it. Take a look at this straightforward data set with a line of fit through it.

The discrepancy between expected values of y (the dependent variable) and actual values of y is the residual for each observation. Relative to projected and actual y values, residual is equal to yi. Actual y value minus expected y value equals residual; therefore, r I = y I y i.

A symbol (often a letter) used in mathematics to represent an unknowable numerical value in an equation or algebraic statement.

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The first car will travel for 38.2 hours and the second car will travel for 38 hours before they are 200 miles apart.

Let x = time in hours for the first car and y = time in hours for the second car. Since the two cars are traveling in opposite directions, we know that the rate of the cars' combined travel is the difference between their two rates. So, we can create the expression:

50x - 55y = 200

We can also create a second expression using the amount of time that passed between the two cars:

x - y = 0.25

We can solve this system of equations with substitution. Let's substitute the second equation into the first:

50x - 55(x - 0.25) = 200

Simplifying, we have:

5.25x = 200.25

Now, we can isolate x:

x = 200.25/5.25 ≈ 38.2 hours

We can use this value to find y. We know that x - y = 0.25, so we have:

y = x - 0.25 = 38.2 - 0.25 = 38 hours

Therefore, the first car will travel for 38.2 hours and the second car will travel for 38 hours before they are 200 miles apart.

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Answer: 1 1/2

Step-by-step explanation:

You have to do the keep change flip method where you keep the first fraction the same change the sign to a multiplication sign and flip the other fraction, it would then look like this: 1/2 x 3. after just multiply across and you get 1.5

1. A softball player can have six (6) possible outcomes

2. Six (6) combinations can be made.

Since the player bats six times, it means that there is possibility of having six outs, or six on base, or six homerun or even a mixture of the three outcomes in six times. The constant touch is six times

Since the sandwiches are just three types and can be ordered with either white bread or multi-grain bread, it means that there is possibility of having two different pairs each making six possible combinations of the available toppings.

Therefore, there will be six possible outcomes and six possible combinations of the sandwiches.

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The complete question goes thus:

1. A softball player bats six times in a game. Each at-bat results in an out, getting on base or hitting a homerun. How many possible outcomes can the player have?

2. A sandwich shop has three types of sandwiches: ham, turkey, and chicken. Each s andwich can be ordered with white bread or multi-grain bread. Customers can add any combination of the six available toppings. How many combinations can be made?

Answer:

x = 2

Step-by-step explanation:

18/9=2

9x2=18

os this scam orrr.... what?

Answer:

x=2

Step-by-step explanation:

9x=18

To solve for X we need to have just X on one side. We can do this by dividing each side by 9. Which is equal to the original because we are dividing by the same thing on both sides.

9x/9=18/9

This simplifies to x=2

We can check by putting 2 back into the equation:

9(2)=18

And that is true so we know we have a correct answer.

The town and PSA are (a) 10 units apart

From the question, we have the following parameters that can be used in our computation:

Points = (2, 3) and (-4, -5)

The distance between the two towns can then be calculated using the following distance equation

distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

substitute the known values in the above equation, so, we have the following representation

distance = √[(2 + 4)² + (3 + 5)²]

Evaluate

distance = 10

Hence, the distance apart is 10 units

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The value of 'x' must be 4 units such that the quadrilateral is a parallelogram and the perimeter of the parallelogram is 40 square units.

A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.

The area of a parallelogram is base multiples by height as two triangles form a parallelogram.

We know the opposite sides of a parallelogram are equal.

Therefore, 3x - 1 = x² - 5 and 2x + 1 = x² - 7.

x² - 5 - 3x - 1 = 0.

x² - 3x - 4 = 0, solving for x we have x = 4.

And,

2x + 1 = x² - 7.

x² - 7 - 2x - 1 = 0.

x² - 2x - 8 = 0, solving for x we have x = 4

(Negative values are inadmissible).

The perimeter of the parallelogram is 2×(the sum of the opposite sides).

= 2(3x - 1 + 2x + 1).

= 2(5x).

= 2×5×4.

= 40 square units.

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The midpoint between the two given points is given by M(-4,-11)

A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates

Given here: The coordinates of the two points as  K(–20, 3) and L(12, –2).

We know that the midpoint of the line between the two points is given by

x=a+b /2

and y= c+d/ 2

Where the end points of the line is given by (a,b) and (c,d)

Thus x=-20+12 /2

         =-4

y= -20-2 /2

 =-11

Thus the midpoint has the co-ordinates M(-4,-11)

Hence, The midpoint between the two given points is given by M(-4,-11)

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Answer: A - (-4,1/2)

Step-by-step explanation: trust me bro...

The solution set for the given graph is (4, 1)

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have two straight lines of inequalites

The point that represent the solution set is any point in the shaded region

This is so because the lines are inequality lines

An instance of these points is (4, 1)

Hence, the point is (4, 1)

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