3. Target is selling two popular toys this year for kids. Toy x is a Power Treads and toy y is an
America Girl Doll. Target pays $8 each for the Power Treads and $14 each for the America Girl
Doll. One unit of Power Treads yields a profit of $2 while an America Girl Doll yields a profit of
$3. Target estimates that no more than 2,000 toys will be sold-every month and does not plan
to invest more than $20,000 in inventory for these toys. How many units of each type of toys
should be stocked in order to maximize the monthly total profit?
What are the vertices? What are the constraints? What is the profit equation?

Step-by-step explanation:

The Radius of the larger semi circle = [tex]\frac{12}{2}[/tex] = [tex]6[/tex][tex]cm[/tex]

Area of the 2 larger semi Circles = [tex]\frac{\pi r^{2} }{2}[/tex][tex]X2[/tex]

                                                  = [tex]\frac{3.14X(6)^{2} }{2} X 2[/tex]

                                                   = [tex]\frac{113.04}{2} X2[/tex]

                                                    = [tex]113.04[/tex] [tex]cm^{2}[/tex]

Radius of the smaller semi circle = [tex]\frac{5}{2} = 2.5cm[/tex]

Area of the smaller semi circle = [tex]\frac{\pi r^{2} }{2}[/tex][tex]X2[/tex]

                                                    = [tex]\frac{3,14X(2.5)^{2} }{2} X 2[/tex]

                                                     = [tex]196.25[/tex][tex]cm^{2}[/tex]

Combined Area = [tex]113.04 + 196.25[/tex]

                           = [tex]309 . 29cm^{2}[/tex]

Answer:

b and d are closer to 0 than 1 mark me brainliest

Step-by-step explanation:

Answer:

B. and D the rest are half or closer to 1

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

Let's mark Pat's age is x. Then Mattie's age is 2x and Jon's age is 4x.

So (x + 4) + (2x + 4) + (4x + 4) = 61.

7x + 12 = 61 => 7x = 49 => x = 7.

So the answer is

Pat = 7

Mattie = 14

Jon = 28

The ages of Pat, Mattie, and Jon are as follows: 7 years, 14 years & 28 years.  

If we take Pat's age as = 'x' years,

so, Mattie's age will be = '2x' years.

and then, Jon would be = 2(2x)

                                        = '4x' years.

Now, the sum of their ages after 4 years =

 => (x+4) + (2x+4) + (4x+4) = 61

 => 7x+12 = 61

 => 7x= 61-12

 => 7x= 49

 => x= 49/7

 => x = 7

Therefore, Pat's age is  = 7 years.

              Mattie's age is = 14 years (2×7).

                  Jon's age is = 28 years (4×7).

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Answer:

Yes the data provide convincing statistical evidence that at women pay more than men for the same catalytic converter repair

The square of the radius of the given circle is [tex]$OP^2 = 703$[/tex]

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus. Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties.

We can use the concept of the power of a point, which states that the square of the distance of a point from a line is equal to the product of the distances of the point from the two tangents to the line that are drawn from the point.

Let [tex]$O$[/tex] be the center of the inscribed circle.

The power of point O with respect to AB and CD is [tex]$(OPOQ) = (1937) = 703$[/tex]

Since the Circle is tangent to AB and CD at P and Q respectively, so [tex]$OP = OQ$[/tex]

So, [tex]$OP^2 = 703$[/tex]

Hence, the square of the radius of the circle is [tex]$OP^2 = 703$[/tex]

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Complete question is: A circle is inscribed in quadrilateral [tex]$A B C D$[/tex], tangent to [tex]$\overline{A B}$[/tex] at [tex]$P$[/tex] and to [tex]$\overline{C D}$[/tex] at [tex]$Q$[/tex]. Given that [tex]$A P=19, P B=26, C Q=37$[/tex], and [tex]$Q D=23$[/tex], find the square of the radius of the circle.

The value of sin(4π-x) is -sinx

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given that, express the given in terms of sinx or cosx sin (4π-x)

sin(4π-x) = sin(2π+2π-x)

We know, that, sin(a+b) = sina·cosb+sinb·cosa

Here, a = 2π and b = 2π-x

Therefore,

sin(2π+2π-x) = sin2πcos(2π-x)+sin(2π-x)cos2π

Now, sin2π = 0 and cos(2π) = 1

Therefore,

sin2πcos(2π-x)+sin(2π-x)cos2π

= sin(2π-x)

As we know that, sin(2π-x) = -sinx

Hence, sin(4π-x) = -sinx

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The size of the large tank is 6 liters and the size of the small tank is 3 liters.

The first step is to form a system of equations using the information provided in the question:

3l + 2s = 24 equation 1

2l + 3s = 21 equation 2

Where:

The elimination method would be used to solve the equations:

Multiply equation 1 by 2 and equation 2 by 3:

6l + 4s = 48 equation 3

6l + 9s = 63 equation 4

Subtract equation 3 from equation 4:

5s = 15

Divide both sides of the equation by 5

s = 15 / 5

s = 3 liters

Substitute for s in equation 1 :

3l + 2(3) = 24

3l + 6 = 24

3l = 24 -  6

3l = 18

l = 18 / 3

l = 6

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The average rate of change is the ratio of the difference between the y coordinates of two points to the x coordinate of the same point.

It can be found by using two points on the graph and substitute into the formula: (y₀ - y₁) / (x₀ - x₁)

The square brackets [] is used to mean the end points as shown is inclusive

A quadratic equation is a polynomial of degree two

The average rate of change here is not constant and is usually  specified by the two points to which it is measured

For instance using points (-3, 0) and (0, -1) we have

=  (y₀ - y₁) / (x₀ - x₁)

=  (-1 - 0) / (0 - (-3))

= -1/3

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If the student perform one trial of scientific experiment , and the result of that trial do not support the prediction , then the student should repeat the experiment , modify the experiment and can use alternative Method .

If in the Scientific Experiment the result does not support the prediction of the student in one trial , then the student can :

(i) Modify the Experiment :

The students can modify scientific experiment in other way and try again. For Example, they student change variables being tested or methods used to collect data.

(ii) Use Alternative Explanations :

The students can use alternative explanations for  results. It may be possible that the prediction was correct, but there were other factors  that may influence outcome of experiment.

(iii) Repeat the Experiment :

The student can repeat the experiment by the same procedures to see if he gets same results and if results are consistent, it can concluded that the prediction was incorrect .

The given question is incomplete , the complete question is

Student perform one trial of a scientific experiment if the result of that trial do not support the prediction what should the student do next ?

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Yes, it is a perfect square trinomial.

Perfect squares are numbers that are the product of a number multiplied by itself. Examples of perfect squares include 4 (2 x 2), 9 (3 x 3), 16 (4 x 4), 25 (5 x 5), 36 (6 x 6), 49 (7 x 7), and 64 (8 x 8). Perfect squares are also referred to as "square numbers" or "whole-number squares."

The equation X² + 10X + 25 can be factored into (X + 5)²,

which is a perfect square trinomial. In general, a perfect square trinomial is any polynomial of the form A² + 2AB + B² where A and B are constants or variables.

This is because such a polynomial can be factored into (A + B)².

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Answer:

e = 54

f = 20

d = 106

Step-by-step explanation:

Opposite angles are the same. Also, straight lines always equal 180 degrees.

Hope that this helps!

Answer:

Percentual change= 33.33% decrease

Step-by-step explanation:

Giving the following information:

Present value (PV)= $150

Future value (FV)= $100

To calculate the percentual change, we need to use the following formula:

Percentual change= [(PV - FV) / PV]*100

Percentual change= [(150 - 100) / 150]*1''

Percentual change= 0.3333*100

Percentual change= 33.33% decrease

Answer: The Gradient of line A and B are

2 and -1

Step-by-step explanation:

For the given two points A(x1, y1) and B(x2, y2)

The gradient of the line AB is y2-y1/x2-x1

So the gradient of line A is

5-1/2-0

2

the gradient of line B is

5-0/0-5

-1

Answer:10 girls and 11 boys

Step-by-step explanation:

To Solve the inequalities , we take the variables on a side and the numbers on the other side and then apply mathematical operations to solve it .

What is Inequality ?

The Inequality is defined as a relationship between two values that are not equal to each other .

The method of solving the inequalities is a little different than solving equations.

To solve the inequalities, some simple rules should be followed .

(i) The inequality does not change if any number or variable is added or subtracted from both sides.

Similarly, the value of inequality is not affected if the same number is multiplied on both the sides.

(ii) If the inequality is divided by a negative variable or number on both  sides, then the inequality sign gets reversed.

(iii) On dividing inequality by a positive number, there is no change.

For Example : Solve the inequality [tex]4x+6 > 3x+7[/tex] ;

subtracting [tex]3x[/tex] from both the sides ,

we get ;

[tex]x+6 > 7[/tex],

Now subtracting [tex]6[/tex] from both sides of the inequality;

we get ;

[tex]x > 1[/tex] .

Therefore , the solution of the inequality [tex]4x+6 > 3x+7[/tex] is [tex]x > 1[/tex] .

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Answer:

2x+3y-(-4x+3y)=6-12

2x+3y+4x-3y. =-6

6x. = -6

X=-1

no

Answer:

No

Step-by-step explanation:

So, lets go over what we know:

Our x and y values are (0,2)

This means:

x=0

y=2

Lets plug these in for each equations:

2x+3y=6

=

2(0)+3(2)=6

=

0+6=6

=

6=6

So thie first equation is correct.

But we dont know if the second one will check out yet!

Lets plug our values in once more, only on the second equation instead of the first:

-4x+3y=12

=

-4(0)+3(2)=12

0+6=12

6=12

Uh oh...Thats not right.

So this means that (0,2) is not a solution to both equations.

Answer:

No

Hope this helps! :D

The maximum area of the rectangle inside the ellipse is 2ab.

Given that,

Ellipse = x2 / a2 + y2 / b2 = 1

we know the general coordinates of any point in an ellipse of the equation

x2 / a2 + y2 / b2 = 1 is (acosθ,bsinθ)

So, we take general vertices of rectangles as

(acosθ,bsinθ), (acosθ,-bsinθ), (-acosθ,bsinθ), and (-acosθ,-bsinθ)

So, we can see that length and breadth of the rectangle is 2acosθ and 2bsinθ

So, its area will be ab4sinθcosθ (Length x Breadth)

Applying trigonometric formula 2sinθcosθ=sin2θ, let area equals to A

Now A=2absin2θ

Now as the area is the maximum given in the question, we have to differentiate it with respect to θ

dA/dθ=2abcos2θ×2 (using dsin2θ / dθ=2cos2θ)

Equating dA / dθ=2abcos2θ×2=0, it means cos2θ=0 , which means 2θ =  π / 2 and θ=π / 4

So now we to put θ=π / 4 in the equation of area which is A=2absin2θ

We get as A=2absin2π / 4=2absinπ / 2=2ab

Hence the max area of the rectangle inside the ellipse is 2ab.

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Answer:

1/100

or we can say 100/1

The equation of line is given by y = 25x + 80.

The equation of a line is expressed as y = mx + b where m exists the slope and b exists the y-intercept

y - y₁ = m ( x - x₁ )

Where, y be the y-coordinate of second point

y₁ be y-coordinate of point one

m be the slope

x be the x-coordinate of second point

x₁ be the x-coordinate of point one

Let the equation of slope m be

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Equation of line be represented as A

The two points are given as A ( 2 , 130 ) and B ( 8 , 280 )

The slope of the line between the two points exists given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 280 - 130 ) / ( 8 - 2 )

simplifying the above equation, we get

m = 150 / 6

m = 25

Now , the equation of line is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 130 = 25 ( x - 2 )

On simplifying the equation , we get

y - 130 = 25x - 50

Adding 130 on both sides , we get

y = 25x + 80

The equation is of the form y = mx + b where b is the y intercept.

Therefore, the equation of line is given by y = 25x + 80

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The equation of line is given by y = 25x + 80, this represent the linear function between the amount of money and the saved amount.

The equation of a line is expressed as y = mx + b where m is called the slope and b is called the y-intercept

y - y₁ = m ( x - x₁ )

Where, y be the y-coordinate of second point

y₁ be y-coordinate of point one

m be the slope

x be the x-coordinate of second point

x₁ be the x-coordinate of point one

Let the equation of slope m be

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Equation of line be represented as A

The two points are given as A ( 2 , 130 ) and B ( 8 , 280 )

The slope of the line between the two points exists given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 280 - 130 ) / ( 8 - 2 )

simplifying the above equation, we get

m = 150 / 6

m = 25

Now , the equation of line is given by

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 130 = 25 ( x - 2 )

On simplifying the equation , we get

y - 130 = 25x - 50

Adding 130 on both sides , we get

y = 25x + 80

The equation is of the form y = mx + b where b is the y intercept.

Therefore, the equation of line is given by y = 25x + 80

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Answer:

The answers final

Simplify the expression

-2+6x+1/2x^2

Factor the expression

1/2x(-4+12x+x^2)

Step-by-step explanation:

I hope it will help you :)

Answer:

g(x) = a(x - 23)(x + 4)

Step-by-step explanation:

Weren't there possible answer choices to share?

if this function has zeros at 23 and -4, then the function has the following form:

g(x) = a(x - 23)(x + 4)

Definition of a rectangle

Explanation:

A rectangle has two sets of parallel sides, and those opposite sides are the same length. This is simply the definition of what it means to be a rectangle. Because ABCD is a rectangle, we have these two pairs of congruent opposite sides:

Point p is further from 0 than point q, and to the left of point q.

The correct option is D.

The absolute value of a number is the distance value from zero without considering the sign of a number. It is also represented as |x|, where x is any number.

Given:

Points p and q are negative integers plotted on a number line.

And |p| > |q|.

That means,

The absolute value of p is greater than the absolute value of q.

|p| and |q| are the positive integers.

So, p < q.

So, the q is closer to zero.

And p is left to point q.

Therefore, the q is closer to zero and p is left to point q.

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Answer:

  The answer would be $1995

Step-by-step explanation:

Trust me

Answer:

The slope of the line perpendicular to the line C is 1/3.

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-12-(-6))/(-1-(-3))

m=(-12+6)/(-1+3)

m=-6/2

m=-3

perpendicular lines have negative reciprocal slopes.

Answer: Hope This Helps!

Step-by-step explanation:

Im doing good today. And I hope you have a good rest of the day!

Answer:

ok, the correct answer should be R(1.5)=R(2)!

Step-by-step explanation:

I did this my class before!

Answer:

x=800

Step-by-step explanation:

first you gonna take 3×x= 3x

then

3×200= 600

(3x+600)=3000

3x=3000-600

3x=2400

3x÷3=2400÷3

x=800

Answer:

13

Step-by-step explanation: