Solve for the missing item in the following. (Do not round intermediate calculations. Round your answer to the nearest whole percent.)
Principal 5000 time 6 months simple interest $300
Rate?

Answer:

quadrilateral

Step-by-step explanation:

A 4-sided polygon is a quadrilateral.

The length of line CD is 20. 9

Note that triangle CDY is an isosceles triangle

Using the Pythagoras theorem

Hypotenuse square = opposite square + adjacent square

Hypotenuse = line CD

opposite = 20

Adjacent = 6

Substitute into equation

[tex]Line CD^2 = 20^2 + 6^2[/tex]

[tex]Line CD^2 = 400 + 36[/tex]

[tex]Line CD^2 = 436[/tex]

Make line CD^2 subject by find the square root of the other side

[tex]Line CD = \sqrt{436}[/tex]

[tex]Line CD = 20.9[/tex]

Therefore, the length of line CD is 20. 9

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The required polynomial is [tex]x^{3}-7x^{2} -20x+96[/tex]

Polynomial : If in an expression all of variables, constants and exponents are present with mathematical operations like addition, multiplication, subtraction & division, then it is called polynomial.

If a polynomial has degree 3 as a highest degree, then the polynomial is called degree 3 polynomial or cubic polynomial.

A degree 3 polynomial having zeros α, β, γ and the coefficient of x³ equal a is,  a(x- α)(x- β)(x- γ)

Given, Zeros of the polynomial are -4, 3, 8 & coefficient of x³ equal 1.

Hence, the required polynomial is,

[tex]1(x-(-4))(x-3)(x-8)[/tex]

[tex](x+4)(x-3)(x-8)[/tex]

[tex]=(x+4)(x^{2} -11x+24)[/tex]

[tex]=x^{3}-11x^{2} +24x+4x^{2} -44x+96[/tex]

[tex]=x^{3}-7x^{2} -20x+96[/tex]

This is a degree 3 polynomial.

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The required probability of giving class period run between 51.5 and 51.75 is 0.125.

The lengths of her classes are uniformly distributed between 50 and 52 minutes.

Probability, can be define as the ratio of favorable events to the n number of total events.

since,

[tex]p(r) = \frac{51.75-51.5}{52-50}[/tex]

p(r) = 0.125

Thus, the required probability of class period runs between 51.5 and 51.75 is given by 0.125

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The initial start-up fee for signing up with Rita's lawn mowing service is $20, using simultaneous equations.

Simultaneous equations are two or more algebraic equations that share variables like x and y and can be solved at the same time.

Let y = fixed cost (initial start-up cost)

Let x = variable cost per lawn mowing

Equation 1: Customer A = y + 10x = $370

Equation 2: Customer B = y + 7x = $265

Subtract equation 2 from equation 1 to get:

3x = $105

x = $35

Substitute x in any of the two equations to find the value of y, thus:

Customer A:

y + 10($35) = $370

y + #350 = $370

y = $20 ($370 - $350)

Thus, the initial start-up fee for signing up with Rita's lawn mowing service is $20, using simultaneous equations.

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Answer:

240

Step-by-step explanation:

h+c=320

c=3h ( since 3 times the cheeseburger)

Now plug in 3h for C

h+3h=320 =  4h=320

Now divide 320 by 4 to get "h" alone

h=80

now plug 80 back t the eqation of c=3h

so now it is...

c=3 x 80

which is 240

so ur andswer is 240

Answer:

  {-3, 3, 4, 5, 6}

Step-by-step explanation:

The complement of a set is the set of all elements in the universe that are not in the given set.

The set U is defined as ...

  U = { x | x ∈ and -3 ≤ x ≤ 6 }

In roster form, this is ...

  U = {-3, -2, -1, 0, 1, 2, 3, 4, 5, 6}

The given set is defined as ...

  S = { x | x ∈ and -2 ≤ x < 3 }

In roster form, this set is ...

  S = {-2, -1, 0, 1, 2} . . . . . note that 3 is not in set S

If we remove the elements of set S from set U, we have ...

  S' = {-3, 3, 4, 5, 6}

The correct answer is option D which is y ≤ −2x + 2.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.

When we draw the graphs we will see that the inequality y ≤ −2x + 2 is showing the same graph. It is cutting the y-axis at (0,2) and the x-axis at (2,0).

Therefore the correct answer is option D which is y ≤ −2x + 2.

The graph is attached with the answer below.

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Answer:

2xy/ ( ab)

Step-by-step explanation:

xy/ ( 3ab) + 5xy/(3ab)

Since the denominator is the same, we can add the numerators

xy+5xy = 6xy

6xy/ (3ab)

We can simplify 6/3 = 2

2xy/ ( ab)

The required equation of line BD is option d.)  [tex]y=\frac{2b}{2a-c} x-\frac{2b}{2a-c} c[/tex]

Equation of the line is given be in standard form is
[tex]y-y_{1} =\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Line,  curve of  the shortest distance between two points.

The questions seem to be incomplete the question,  the complete question could be  
a)[tex]y=\frac{2b}{2a-c} (x-c)\\[/tex]
b)[tex]y=\frac{b}{-c} x-\frac{2b}{2a-c}[/tex]
c)[tex]y=\frac{2b}{2a-c} x-\frac{bc}{2a-2c}[/tex]
d)[tex]y=\frac{2b}{2a-c} x-\frac{2b}{2a-c} c[/tex]
e)[tex]y=\frac{2b}{a-c} x-\frac{2b}{a-c}[/tex]

Now all the Equation in option represents the triangle with coordinates A(0, 0), B (2a, 2b),  C(2c,0) and D(c, 0).

For equation of line BD we have coordinates, (2a, 2b) and (c, 0).
putting these coordinates in the standard form of equation  of line i.e.
[tex]y-y_{1} =\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
⇒   [tex]y=\frac{2b}{2a-c} x-\frac{2b}{2a-c} c[/tex]

Thus the required equation of the line is  [tex]y=\frac{2b}{2a-c} x-\frac{2b}{2a-c} c[/tex].

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Answer:

C

Step-by-step explanation:

Edg

m∠ A = 60°, m∠ A = 60°, m∠ A = 60° and the sum of the angles in the triangle is 180°

It is important to note that the sum of angles in a triangle equals 180°

The given structure is a triangle, thus, the angles sum up to 180°

m ∠ A + m ∠ B + m ∠ C = 180°

m∠ A = 60°

m ∠ B = 60°

m ∠ C = 60°

The sum of the angle in the triangle = 60° + 60° + 60° = 180°

Thus, m∠ A = 60°, m∠ A = 60°, m∠ A = 60° and the sum of the angles in the triangle is 180°

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Your question is incomplete. Please find the missing content below

You go to the shops on Monday and buy 1 apple, 1 banana, and 1 carrot; the whole transaction totals €15. On Tuesday you buy 3 apples, 2 bananas, 1 carrot, all for €28. Then on Wednesday 2 apples, 1 banana, 2 carrots, for €23.

Construct a matrix and vector for this linear algebra system.

Matrix is A = [ [ A₁₁ , A₁₂ , A₁₃]

                      [ A₂₁ , A₂₂ , A₂₃]

                      [ A₃₁ , A₃₂ , A₃₃] ]

Vector S = [sMon , sTue , sWed]

(i) consider A as fruits

A₁₁ = 1

A₁₂ = 1

A₁₃ = 1

A₂₁ = 3

A₂₂ = 2

A₂₃ = 1

A₃₁ = 2

A₃₂ = 1

A₃₃ = 2

(ii) Consider s as days

sMon = 15

sTue  = 28

sWed = 23

Hence the matrix and vector is:  A = [ [ A₁₁ , A₁₂ , A₁₃]

                                                           [ A₂₁ , A₂₂ , A₂₃]

                                                           [ A₃₁ , A₃₂ , A₃₃] ]

Vector S = [sMon , sTue , sWed]

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Answer:

a) 1 + 3 = 4

b) 2 + 3 = 5

(all prime)

hope this helps! :)

Using the combination formula, it is found that 525 combinations can be created.

The order in which the employees are chosen is not important, hence the combination formula is used to solve this question.

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem:

Then the number of combinations is given by:

[tex]n = C_{7,3}C_{6,2} = \frac{7!}{3!4!} \times \frac{6!}{2!4!} = 525[/tex]

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The population size after 6 years and after 8 years are 147 and 169 population respectively

The standard exponential function is expressed as y = ab^x

where

a is the base

x is the exponent

Given the function that represents the population size P (t) of the species as shown;

[tex]p(t)=\frac{550}{1+5e^{-0.1t}} \\[/tex]

For the population size after 6 years

[tex]p(t)=\frac{550}{1+5e^{-0.1(6)}} \\P(6)=\frac{550}{3.744}\\ P(6)=147 population[/tex]

For the population after 8 years

[tex]p(t)=\frac{550}{1+5e^{-0.1(8)}} \\P(8)=\frac{550}{3.2466}\\ P(8)=169 population[/tex]

Hence the population size after 6 years and after 8 years are 147 and 169 population respectively

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Using a system of equations, the meaning of point R is given as follows:

A number of books and their cost where both subscriptions cost the same.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable. In a graph, the solution to the system is the intersection point of the two equations.

In this problem, the point R is the point in which:

3y = 96.

That is, the point in which the prices are equal, hence:

A number of books and their cost where both subscriptions cost the same.

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The net benefit to The Knot if it adopts JIT production at the Spartanburg plant is $200000.

Based on the information given, the net benefit will be:

= $1,000,000 × (1 - 80%)

= $1,000,000 × 0.2

= $200,000

The nonfinancial and qualatative factors that The Knot should consider when making the decision to adopt JIT production are:

The benefit of The Knot implementing an enterprise resource planning (ERP) system is that it gives access to operating information in response to the supply.

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The point EEE represent option b is correct: Marcelina spends the intended amount of money but she bought more than she did intended amount of corn.

She  buy 50kg of corn in total

White corn costs = $0.30 per kilogram,

Yellow corn costs = $0.15 per kilogram,

She wants to spend $12 total.

So the equation will be:

C= (20, 50) = 20 white, 50 yellow

But 30 while and 20 yellow is needed.

Since  C = 20 +50

= 70 corns

While: 30 + 20

= 50 corns.

This therefore tells that Marcelina  spends the intended amount of money but she bought more than she did intended amount of corn and therefore, option b is correct.

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Answer:

Marcelina spends less than the intended amount of money and buys less than enough corn.

Step-by-step explanation:

The equation of line

Khan

The question was incorrect. Please find the correct content below.

Compare 32/35 and 9/10.

Comparing 32/35 and 9/10 we have 32/35 is greater than 9/10, that is 32/35 > 9/10.

Fraction is the ratio of two numbers. The upper number is called Numerator and the Lower number is called the Denominator.

We know that if the denominators are the same for two fractions then which has the greatest numerator is a greater fraction than the other.

Given the fractions are 32/35, 9/10

To compare this two fractions we have to make denominators equal first.

LCM of 10,35 = 70

Calculating the fractions,

32/35 = (32*2)/(35*2) = 64/70

9/10 = (9*7)/(10*7) = 63/70

Since 64 > 63

So 64/70 > 63/70

Therefore, 32/35 > 9/10

Hence fraction 32/35 is greater than the other fraction 9/10.

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Step-by-step explanation:

charging the phone for 1 minute ,it has 2%

i.e,1----->2

After 2 minutes from that time ,i.e total 3 minutes

it has 6% charge

i.e,3--------->6

from the both the above cases ,1 minute provide 2%=6/3

=2

Hence,

for getting 50%charge=50/2

=25 min

and,for 90 %charge=90\2

=45 min

Answer:

  (x, y) = (16/3, -1/9)

Step-by-step explanation:

A system of two linear equations can be solved a number of ways. One of the easiest is by graphing. Algebraic methods usually work better when the equations are in standard or general form.

A graphing calculator can work with the given equations. The solution it shows in the first attachment is ...

  (x, y) = (16/3, -1/9)

An algebraic method of solving a pair of linear equations can start with them in general form. We can obtain that form by subtracting one side of the equation from both sides. Here, we choose to do that so the coefficient of x is positive.

First equation

  5(x -3y) -6 -(4x +1) = 0 . . . . . . . subtract (4x+1) from both sides

  5x -15y -6 -4x -1 = 0 . . . . . . eliminate parentheses

  x -15y -7 = 0 . . . . . . . . . . collect terms

Second equation

  3(x +6y) +4 -(9y +19) = 0 . . . . . . subtract (9y+19) from both sides

  3x +18y +4 -9y -19 = 0 . . . . . . eliminate parentheses

  3x +9y -15 = 0 . . . . . . . . . . . collect terms

  x +3y -5 = 0 . . . . . . . . . . . remove common factor of 3

We notice the coefficients of x and y are related by convenient factors, so we can use the "elimination method" to solve these equations. Subtracting the first from the second, we get ...

  (x +3y -5) -(x -15y -7) = 0 -0

  18y +2 = 0 . . . . . . collect terms

  y +1/9 = 0 . . . . . . . divide by 18, reduce the fraction

  y = -1/9

Using this in the second equation, we have ...

  x +3(-1/9) -5 = 0

  x = 5 1/3

The solution to the system of equations is (x, y) = (5 1/3, -1/9).

Answer:

keep the model answer photo

The formula for calculating a z-score is is z = (x-μ)/σ, where x is the raw score, μ is the population mean, and σ is the population standard deviation

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There is one solution in the system of equation

The system of equations is given as:

8x=12y-9 and 27y+18x=21

Divide 8x=12y-9 by 8

x = 1/8(12y-9)

Substitute x=1/8(12y-9) in 27y+18x=21

27y + 18 * 1/8(12y-9) =21

Expand

27y + 27y - 20.25 =21

Evaluate the like terms

54y = 41.25

Divide by 54

y = 0.7639

Hence, there is one solution in the system of equation

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The characteristics of a population that a random variable represents are 1. As many as you wish and 4. Two or more.

A random variable is a variable with unknown outcomes.

A random variable can have either discrete or continuous values.

It is discrete when it has specific values.  It is continuous when it assumes some continuous values.

Thus, the characteristics of a population that a random variable represents are 1. As many as you wish and 4. Two or more.

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The number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways

The formula for permutation is given as;

Permutation = [tex]\frac{n!}{(n - r)!}[/tex]

n = 16

r =4

Permutation = [tex]\frac{16!}{12!}[/tex]

Permutation = [tex]\frac{16 *15*14*13*12*11*10*9*8*7*6*5*4*3*2*1}{12*11*10*9*8*7*6*5*4*3*2*1}[/tex]

Permutation = 43, 680 ways

Thus, the number of ways that the coach can assign the 4 positions to his 16 players would be 43, 680 ways

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The computation shows that the distance from the base of the wall that the cannonball land will be 132.2m

The peak height equation will be illustrated as:

v²sinx = 2h

(47.4)²x = 2(9.81)(10.5)

Divide to get the value of x

x = 17.63°

Therefore, the distance will be:

d ° (47.4)² × 2(17.63) / 9.81

= 132.2m

Therefore the distance is 132.2m.

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Answer:

its 69.8

Step-by-step explanation:

Based on the calculations, the number of books that were bought by Hugh are 4 books.

In order to determine the number of books that were bought by Hugh, we would substitute the value of the number of magazines into the given equation and then evaluate as follows:

3.95m + 8.95b = 47.65

3.95(3) + 8.95b = 47.65

11.85 + 8.95b = 47.65

8.95b = 47.65 - 11.85

8.95b = 35.8

b = 35.8/8.95

b = 4.

In conclusion, the number of books that were bought by Hugh are 4 books.

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Complete Question:

Hugh bought some magazines that cost $3.95 each and some books that cost $8.95 each. He spent a total of $47.65. If Hugh bought 3 magazines, how many books did he buy? The equation that models the problem is 3.95m + 8.95b = 47.65, where m is the number of magazines and b is the number of books.

For a solution to be the solution to a system, it must satisfy all the equations of that system. There exists no solution for the system of equations.

For a solution to be the solution to a system, it must satisfy all the equations of that system, and as all points satisfying an equation are in their graphs, so solution to a system is the intersection of all its equation at a single point(as we need a common point, which is going to be the intersection of course)(this can be one or many, or sometimes none)

For the three equations,

2x−2y+6z=16

3x+3y−4z=−5

x−y+3z=9

Solve the first equation for x,

2x−2y+6z=16

x = 8 + y - 3z

Now substitute the value of x in both the equations, if the two equations are satisfied, then the equation will have a solution, if it's not then no solution exists.

[tex]3\left(8+y-3z\right)+3y-4z=-5\\6y-13z+24=-5\\\\\\ 8+y-3z-y+3z=9\\ 8=9[/tex]

Hence, There exists no solution for the system of equations.

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Answer: [tex]35^{\circ}[/tex]

Step-by-step explanation:

The labeled angle is [tex]100^{\circ}[/tex] by the alternate interior angles theorem.

Thus, as angles in a triangle add to [tex]180^{\circ}[/tex], [tex]x=35^{\circ}[/tex]