Luke melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa.

Original Rectangle Length (cm) | Length After 21% Increase (cm)

120 | 144

50 | 61

150 | 180

Each new rectangle is 21% longer than the original, so to calculate the length after a 21% increase, we need to multiply the original length by 1 + 21%.

For the first rectangle (120 cm):

1.21 * 120 cm = 144.4 cm (rounded to 144 cm)

For the second rectangle (50 cm):

1.21 * 50 cm = 60.5 cm (rounded to 61 cm)

For the third rectangle (150 cm):

1.21 * 150 cm = 180.15 cm (rounded to 180 cm)

So the table with the length of each new rectangle would be:

Original Rectangle Length (cm) | Length After 21% Increase (cm)

120 | 144

50 | 61

150 | 180

The rounded values were used in this table.

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The number of boys chosen Spanish are 59.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

let Girls are G, Boys are B, Spanish choose S, French chosen F and German Chosen Ge.

Total = 200

Girls = 200 - 90 = 110

P(S) = 70 (B+ G)

P(F) = 60 (B)

P(B) + P(G) = 70

S + F = 92

So, 70- G + 44 - G = 92

114 - 2G = 92

-2G = -22

G = 11

So, number of Boys choose Spanish

= 70- 11

= 59

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The value of x in the figure is 15 degrees

The value of x in the figure is solved using the concept of sum of exterior angles in a polygon

The sum of exterior angles in a polygon is 360

7x + 83 + 33 + 6x + 49 = 360

collecting like terms

7x + 6x = 360 - 83 - 33 - 49

13x = 195

isolating x

x = 15 degrees

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The burgundy fabric:1.135 square yards

The yellow fabric: 0.307 square yards

The total yards of fabric will she have to buy 1.442 square yards.

The same attribute is expressed using a unit conversion, but in a different unit of measurement.

For instance, time can be expressed in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Given:

Chelsea needs 1472 square inches of burgundy fabric and 399 square inches of yellow.

As, 1 yards= 36 inches

and, 1 square yards= 1296 inches

Then, 1472 square inches of burgundy fabric

= 1472/ 1296

= 1.135 square yards

and, 399 square inches of yellow.

= 399/ 1296

= 0.307 square yards

Thus, the total yards of fabric will she have to buy

= 1.135 + 0.307

= 1.442 square yards

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To find f(2) using synthetic division, we set up the synthetic division table with the coefficients of the polynomial:

2 │ 5  -13  4  -2

 │    10 -6 -2

 └───────────

   5  -3 -2  0

The last entry in the bottom row of the table gives the remainder of the division, which is f(2). Therefore, we have:

f(2) = 5(2)³ - 13(2)² + 4(2) - 2 = 40 - 52 + 8 - 2 = -6

So, the value of the function f(x) = 5x³-13x² + 4x-2 at x = 2 is f(2) = -6.

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The graph of the system has been attached below. The solution has been obtained by using linear inequality.

What is linear inequality?

If the equals relation were used in its place, a linear inequality would produce a linear equation.

We are given two inequalities as x+y < 1 and 5x + y > 4

For plotting the points, we need to find x and y

1. x+y < 1

So, let y be 0, then

⇒x < 1

This gives us the point as (1,0).

Now, let x=0, then

⇒y < 1

This gives us the point as (0,1).

From these two points, the graph for the inequality is drawn and represented by red line.

2. 5x + y > 4

So, let y be -1, then

⇒5x > 5

⇒x > 1

This gives us the point as (1,-1).

Now, let x=0, then

⇒y > 4

This gives us the point as (0,4).

From these two points, the graph for the inequality is drawn and represented by green line.

Hence, the graph of the system of linear inequalities is obtained.

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Answer:

$ 4564.32

Step-by-step explanation:

APR=2%, monthly interest rate, i=2%/12=0.02/12

Monthly payment, A=250

After 18 monnth, n=18 months,

the balance. Pis therefore

P = A((1+i)^n-1)/i

=250((1+0.02/12)^18-1)/(0.02/12)

=$ 4564.32

Answer:

Step-by-step explanation:

Circumference = 2piR or piD

pi(3) = 9.42

Answer:

17.2%

Step-by-step explanation:

In the first hour:

The farmer sells 8% of the total chickens:

         [tex]= \frac{8}{100}[/tex]×[tex]250[/tex]

         = 20 chickens

Therefore, the number of chickens left are:

= (250 - 20) chickens

= 230 chickens

In the second hour:

The farmer sells 10% of the chickens left:

= [tex]\frac{10}{100}[/tex]×[tex]230[/tex]

= 23 chicken

∴ The total number of chickens sold in the two hours = (20 + 23) chickens

                                                                                      = 43 chickens

43 has to be expressed as a percentage of the original number (i.e. 250)

Percentage = [tex]\frac{Number Of Chickens Sold}{Total Number Of Chickens}[/tex]×[tex]100[/tex]%

                    = [tex]\frac{43}{250}[/tex]×[tex]100[/tex]%

                    = 17.2%

Answer:

AOC=360-130 = 230

ABC= 230/2=115

Answer:

∠ABC = 115∘

Step-by-step explanation:

∠ABC = 1/2 ∠AOC

(Angle subtended by a chord on major area is half of that subtended on center)

∴ ∠ABC = 1/2 x 130 = 65

ABCD is  a cyclic quadrilateral

Sum of opposite angles = 180∘

∴ ∠ABC + ∠AOC = 180∘

 ∠ABC + 65 = 180∘

 ∠ABC = 115∘

Answer:

40%

Step-by-step explanation:

If someone ate 3 out of 5 bagels, then there are 5 - 3 = 2 bagels left.

To find the percentage of the bagels that are left, you need to divide the number of bagels left by the total number of bagels and multiply by 100.

So, the percentage of the bagels that are left is (2 / 5) * 100 = 40%.

Step-by-step explanation:

5 × -8a = -40a

5 × -9 = -45

-40a - 45 = 5(-8a - 9)

5 × -8a = -40a

5 × -9 = -45

-40a - 45 = 5(-8a - 9)

The total coins in Lauren's coin collection = 75

Let us assume that there are 'n' total coins in Lauren's coin collection.

She keeps 3 of the coins in her box, which is 4% of the collection.

This means that 4 percent of 'n' is equal to 3.

Using the percentage formula,

4 % of m = 3

m × (4/100) = 3

We solve above equation for m.

⇒ m × 4 = 3 × 100        ..........(multiply both the sides by 100)  

⇒ m × 4 = 300

⇒ m = 300/4              ..........(divide both the sides by 4)

⇒ m = 75

Therefore, she has 75 coins in her collection.

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The description is that a unit increment in the number of sweatshirt will cause a $6.50 increment in the total charges

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

Using the above as a guide, we have the following:

Slope = 6.50

This means that a unit increment in the number of sweatshirt will cause a $6.50 increment in the total charges

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The equation Ax = 0 has no free variables, so A has n pivot columns. Since A is square, the pivots must be on the main diagonal, so A is row equivalent to the n x n identity matrix Iₙ.

In order for the equation Ax = 0 to have only the trivial solution, there must be no free variables. This means that the matrix A must have n pivot columns. Since A is square, the n pivot positions must be in different rows, which means that the pivots must be on the main diagonal. This means that A is row equivalent to the n x n identity matrix Iₙ. To make it row equivalent, we can perform elementary row operations, such as adding or subtracting rows, or multiplying or dividing a row by a non-zero constant. Once we have done this, the matrix will be in echelon form and the main diagonal will be composed of all 1s. This means that A is row equivalent to Iₙ.

The  complete question: Suppose A is nˣn and the equation Ax=0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to Iₙ

Choose the correct answer below.

A. Suppose A is nˣn and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nˣn identity matrix,  Iₙ.

B. Suppose A is nˣn and the equation Ax = 0 has only the trivial solution. Then there are no free variables in this equation, thus A has n pivot columns. Since A is square and the n pivot positions must be in different rows, the pivots in A must be on the main diagonal. Hence A is the nˣn identity matrix,  Iₙ.

C. Suppose A is nˣn and the equation Ax=0 has only the trivial solution. Then there are n free variables in this equation, thus A has n pivot columns. Since A is square and then pivot positions must be in different rows, the pivots in an echelon form of A must be on the main diagonal. Hence A is row equivalent to the nˣn identity matrix,  Iₙ

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Answer: This is the answer

Step-by-step explanation:

If a map f:X→Y between connected CW complexes induces isomorphisms f∗:πn(X)→πn(Y) for all n, then f is a homotopy equivalence. In case f

is the inclusion of a subcomplex X↪Y , the conclusion is stronger: X is a deformation retract of Y.

A fairly generic notion called isomorphism can be found in many branches of mathematics. The word is derived from the Greek words morphosis, which means "to form" or "to shape," and iso, which means "equal." An isomorphism is a bijective morphism in formal terms. An isomorphism, as used informally, is a map that maintains sets and relationships between elements.

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The solution of the inequalities is (0.67, 3.33)

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

y >= 2

x + y <= 4

y <= 2x + 2

Next, we plot the graph of the inequalities

Using the above as a guide, we have the following:

The solution is (0.67, 3.33)

This is so because the lines intersect at (0.67, 3.33) for y >= 2

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Answer:

[tex] {4x}^{2} - 2x - 12[/tex]

Step-by-step explanation:

To complete this problem, use FOIL. First, Outer, Inner, Last.

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

First, multiply 2x by 2x.

[tex] {4x}^{2} [/tex]

Now, multiply the outer numbers, 2x and -4.

[tex] - 8x[/tex]

Third, multiply the inner numbers, 3 and 2x.

[tex]6x[/tex]

Lastly, multiply the last numbers, 3 and -4.

[tex] - 12[/tex]

Now, put it all together.

[tex] {4x}^{2} - 8x + 6x - 12[/tex]

The final step is to combine like, or similar terms.

The only ones that can be combined are -8x and 6x.

[tex] {4x}^{2} - 2x - 12[/tex]

Answer:

62

Step-by-step explanation:

you have to work out the surface area of a cuboid by:

3×2=6

5×3=15

5×2=10

sum of all the areas is 31

then times it by 2 which is 62

you don t really have to pay attention to the net, apart from the 2cm because you don t want to use it twice in the calculation.

For the given height function h(t)= -16t²+88t the rocket is in the air for 5.5 seconds.

Height of the launched rocket is equal to :

h(t)= -16t²+88t

Time is represented by 't' in seconds after launch

'h' represents the height of the rocket.

For how long time rocket is in the air :

h(t) = 0

⇒  -16t²+88t = 0

⇒ t ( -16t+88 ) = 0

⇒ t = 0 or ( -16t+88 ) = 0

value of time 't' cannot be equal to zero.

This implies ( -16t+88 ) = 0

⇒16t = 88

⇒ t = 88 / 16

⇒ t = 5.5 seconds

Therefore, the time for which rocket is in the air as per given height function is equal to 5.5 seconds.

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The Given Series 1000+200+40+8+8/5 is Convergent.

If a series converges to a value as its terms approach to infinity, it is said to be convergent. If a series does not converge to a value but instead keeps on increasing or dropping as the terms of the series tend to infinity, it is said to be divergent.

Given:

The series is given as 1000+200+40+8+8/5

The common ratio is

200/1000

= 1/5

Then,40/200

= 1/5

= 0.2

Now, As the common ratio is < 1 so the series is convergent.

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Answer:

See the picture

Step-by-step explanation:

The 1 tells us where to start.  This is our y-intercept.  We start when x =0 and y =1.  The y intercept is 1 (0,1).  You see it in green.

From that point (0,1) you go up 1 and 2 to the right.  This is the slope. You see it in pink.

Once you have the begin part in pink.  You join it to the pink points and draw your line.

Answer:

u have to put lenght ×weight =volume

The sides and angle of the right triangle are as follows:

A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of the triangle can be found using trigonometric ratios as follows:

Hence,

tan 5 = opposite / adjacent

tan 5 = 5 / b

b = 5 / tan 5

b = 57.1506949525

Hence,

b = 57.2 units

sin 5 = opposite / hypotenuse

sin 5 = 5 / c

c = 5 / sin 5

c = 57.3685943662

c = 57.4 units

B = 180 - 90 - 5

B = 85 degrees

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Answer:Exact Form:

1/3

Decimal Form:

0.33333333333

Step-by-step explanation:

Answer:

1/3 or 0.333333333333333333333333333333333333

Step-by-step explanation:

1/5 / 3/5

Dividing can be done by multiplying the number by its reciprocal (flipped).

So, 3/5 has a reciprocal of 5/3

1/5*5/3 = 5/15

5/15 = 1/3 or 0.33333(repeated forever)

Using a trigonometric relation we will see that the value of x is 81.2°

We can see that we have a right triangle, and the angle x is the one that is on the top vertex.

We can use any trigonometric relation to find the value of x, for example we can use:

sin(x) = (opposite cathetus)/(hypotenuse)

Where we can see that:

opposite cathetus = 84

hypotenuse = 85

Then we will get:

sin(x) = 84/85

x = Asin(84/85) = 81.2°

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Answer: To put the equation y - 4x = 17 in slope-intercept form, we need to isolate the y variable on one side of the equation and have the coefficient of x be the slope of the line and the constant term be the y-intercept.

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept.

Starting with the equation y - 4x = 17, we can isolate y by adding 4x to both sides:

y - 4x + 4x = 17 + 4x

y = 4x + 17

So, the equation in slope-intercept form is y = 4x + 17, where the slope (m) is 4 and the y-intercept (b) is 17.

Step-by-step explanation:

y-4x = 17

slope intercept= y= 4x + 17