A sporting goods company produces figure skates and hockey skates. One group of workers makes the blades for both types of skates. Another group makes the boots for both types of skates. It takes 2 hours to make the blade of a figure skate. It takes 3 hours to make the blade of a hockey skate. There is a maximum of 40 hours per week in which the blades can be made for both types of skates. It takes 3 hours to make the boot of a figure skate. It takes 1 hour to make the boot for a hockey skate. There is a maximum of 20 hours per week in which boots can be made for both types of skates. What is the system of inequalities that represents this situation?​

Answer:

The volume of cylinder is 58.2 cm³.

Step-by-step explanation:

The formula of volume of cylinder is :

[tex]v = \pi \times {r}^{2} \times h[/tex]

So, you have to substitute the values into the expressions :

[tex]let \: r = 2.1,h = 4.2[/tex]

[tex]v = \pi \times {2.1}^{2} \times 4.2[/tex]

[tex]v = 58.2 \: {cm}^{3} \: (3sf)[/tex]

Answer: 128/15 min or 8.5 min

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Answer: y=5x+ 10

Step-by-step explanation:

40-30/6-4=10/2=5

each time x moves 1 it moves 5 vertically so

4, 30

3, 25

2, 20

1, 15

0, 10

Answer:

r = 14

Step-by-step explanation:

r = -5 + 19

Simplify the right side by subtracting 5 from 19

r = 14

Answer:A) -16

Step-by-step explanation:

Answer:

38.24

Step-by-step explanation:

You need to do 45.3-7.06 and you get x

compare the line y=8x-9 to y=mx+b where m is a slope and b is y-intercept

so, the line y=8x-9 has a slope m=8

by definition, the slope of a line parallel to this line will be same, m=8

by definition, the slopes of perpendicular lines are negative reciprocals to each other; so, m = -1/8

Answer: 4/5

Step-by-step explanation:

80%=

100% * 80/100 =

1 * 80/100=

80/100=

8/10=4/5

Answer:

x= 1.5

y= 4.125

Step-by-step explanation:

Step one:

given the two equations

[tex]-2x - 8y = -30-------1\\\\2x + 8y = 36--------2[/tex]

Step two:

let us subtract the equations

[tex]-2x - 8y = -30-------1\\\\ -(2x + 8y = 36)--------2\\\\0x-16y=-66[/tex]

[tex]-16y=-66\\\\16y=66[/tex]

divide both sides by 16

[tex]y=66/16\\\\y=4.125[/tex]

put y= 4.125 in equation 2

[tex]2x + 8(4.125)= 36\\\\2x+33=36\\\\2x=36-33\\\\2x=3\\\\x= 3/2\\\\x= 1.5[/tex]

[tex]2(i+3)>4(1-i)[/tex]

Distribute 2 in (i+3) and 4 in (1-i)

[tex]2i+6>4-4i[/tex]

Move -4i to another side and 6 to another side. When moving to another side, you'll have to change the sign/operator to opposite (Plus -> Minus, Multiply -> Divide)

[tex]2i+4i>4-6\\6i>-2\\[/tex]

For this part, move 6 to divide -2.

[tex]i>\frac{-2}{6} \\i>\frac{-1}{3}\\i>-\frac{1}{3}[/tex]

Whenever either a numerator or a denominator is in negative, we can pull out the negative in the middle of fraction.

Note that i is the symbol of imaginary number - as defined -  i = √-1 But for this one, It's just a variable if I assume.

Thus, the answer is i > -1/3

The length of the hypotenuse is 5.426 meter

Let the two shorter sides of the right angles triangle be denoted as x meters.

The formula for the area of right triangle is given as,

                     A = ab/2

  Where, a and b are the length of the shorter sides of the triangle

Also we have been given the area of the triangle which is 7.36 sq. meter

Thus ,    A = 7.36

             x^2/2 = 7.36

              x^2 = 14.72

                x = 3.84

Now according to the Pythagoras theorem,

   H = √P^2 + B^2

Where,  H = hypotenuse

               P = perpendicular

              B = base

Now putting the required values we get

    H = √x^2 + x^2

        = √2x^2

        = x√2

       = 5.426 meter

Hence the length of the hypotenuse is 5.426 meter

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Answer:

-10

Step-by-step explanation:

20-34=-14, 8/2 is just 4, so add 4 to -14 which = -10

The value of absolute value expression is equal to 133. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The absolute value or modulus of a real number x abbreviated |x| in mathematics, is the non-negative value of x regardless of its sign.

The absolute value of the function will be calculated as,

E =  |−152| + |5| − |−24|

E = 152 + 5 - 24

E = 133

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The roots of the polynomial function f(x) = x³ - 3x² + 2 are [tex]\frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, \ and \ 1[/tex].

Given the polynomial function in the question:

f(x) = x³ - 3x² + 2

To find the roots of the polynomial function f(x) = x³ - 3x² + 2, we need to solve for values of x that make the function equal to zero.

f(x) = x³ - 3x² + 2

x³ - 3x² + 2 = 0

Factor the equation using the rational root test:
( x - 1 )( x² - 2x - 2 ) = 0

Equate each factor zero and solve for x:

( x - 1 ) = 0

x - 1 = 0

x = 1

( x² - 2x - 2 ) = 0

x² - 2x - 2 = 0

Using the quadratic formula:

[tex]x = \frac{-b\±\sqrt{b^2 - 4(ac)} }{2a} \\\\x = \frac{-(-2)\±\sqrt{(-2)^2 - 4(1*-2)} }{2*1} \\\\x = \frac{2\±\sqrt{4 + 8} }{2} \\\\x = \frac{2\±\sqrt{12} }{2}\\\\Hence:\\\\x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}[/tex]

Therefore, the roots are [tex]x = \frac{2-\sqrt{12} }{2}, \frac{2+\sqrt{12} }{2}, 1[/tex].

Options A, B and D are the correct answers.

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Answer:

FG = 3

Step-by-step explanation:

let me know if you are still confused!

Answer:

lol ok

Step-by-step explanation:

Answer:

ok Y?

Step-by-step explanation:

Answer:

After 3 hours there is left 22.5 grams of radioactive material.

Step-by-step explanation:

We can calculate the mass of radioactive material remaining after 3 hours, by using the decay equation:           

[tex]N_{t} = N_{0}*e^{-\lambda t}[/tex]     (1)

Where:

[tex]N_{0}[/tex]: is the initial mass = 180 g

[tex]N_{t}[/tex]: is the remaining mass after time t

λ: is the decay constant

The decay constant is given by:

[tex] \lambda = \frac{ln(2)}{t_{1/2}} [/tex]

Where [tex]t_{1/2}[/tex] = 1 h.

By entering λ into equation (1) we hve:

[tex] N_{t} = N_{0}*e^{-\frac{ln(2)}{t_{1/2}} t} [/tex]

[tex] N_{t} = 180 g*e^{-\frac{ln(2)}{1 h} 3 h} = 22.5 g [/tex]

Therefore, after 3 hours there is left 22.5 grams of radioactive material.

I hope it helps you!          

Answer: C. The lines intersect but are not perpendicular.

Step-by-step explanation:

The correct option is C, the lines intersect but are not perpendicular.

To determine which statement is true about the two lines whose equations are given below:

y = 3x + 2

y = -4x + 9

We can compare the slopes of the two lines. The slopes of these lines are 3 and -4 respectively.

Two lines are parallel if and only if their slopes are equal. Since the slopes of these lines are not equal, we can eliminate options A.

Two lines are perpendicular if and only if the product of their slopes is -1. The product of the slopes of these lines is -12, which is not equal to -1. Hence, we can eliminate options B.

Since the lines are neither parallel nor perpendicular, they intersect. To determine whether they intersect perpendicularly, we can compute the angle between them using the slopes.

The angle between two lines is given by the formula:

[tex]tan \theta = \dfrac{(m_2 - m_1)}{ (1 + m_1m+_2)}[/tex]

where m₁ and m₂ are the slopes of the two lines.

Substituting the slopes of the given lines, we get:

[tex]tan \theta = \dfrac{|(-4 - 3)} { (1 + (3 \times -4))|} \\[/tex]

tanθ = 7 / 11

Therefore, the correct option is C: the lines intersect but are not perpendicular.

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The missing equation of lines are:

y = 3x + 2

y = -4x + 9

Answer:

Step-by-step explanation:

1 is the answer

Answer:

9 months

Step-by-step explanation:

Given

Fabulous fitness charges a one-time fee of $90 and an additional $25 per month

let the number of months be x

and the total charges be y

y= 25x+90---------1

Wonder weights charges a one-time fee of only $ 27 dollars but charge an additional $32 each month

let the number of months be x

and the total charges be y

y= 32x+27------------2

Required

The value of x, that is the number of months

Step two:

Equating both equations we have

25x+90=32x+27

collect like terms

25x-32x=27-90

-7x=-63

7x=63

divide both sides by  7

x= 63/7

x= 9 months

Answer:

m=-1/2 or m=-2/4

Step-by-step explanation:

The rate of change or slope of the given line is [tex]m=-\frac{1}{2} or m=-\frac{2}{4}[/tex]

Given :

The graph of a line . To find out the slope or rate of change , we pick two points on the line.

Two points are (-8,2) and (4,-4)

Lets apply slope formula

[tex]Slope = \frac{y_2-y_1}{x_2-x_1}[/tex]

(-8,2) is (x1,y1)  

(4,-4) is (x2,y2)

Substitute all the values inside the formula

[tex]Slope = \frac{y_2-y_1}{x_2-x_1}\\slope =\frac{-4-2}{4+8} =\frac{-6}{12} =-\frac{-2}{4} =-\frac{1}{2}[/tex]

The rate of change or slope of the given line is [tex]m=-\frac{1}{2} or m=-\frac{2}{4}[/tex]

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Let us consider,

A special [tex]8-[/tex]sided die is marked with the numbers [tex]1[/tex] to [tex]8[/tex].

The odd numbers on the die are [tex]1,3,5,7.[/tex]

The even numbers are [tex]2,4,6.[/tex]

For the experimental sequence of [tex]15[/tex] rolls.

There are [tex]9[/tex] odd number  out of 15, which is [tex](3,5,7,1)[/tex].

So the experimental  probability is,

       [tex]\frac{9}{15} =\frac{3}{5} \\\\=0.60\\[/tex]

[tex]\implies0.60=60[/tex] %

The theoretical probability given that there are odd numbers [tex](1,3,5,7)[/tex] out of [tex]8[/tex] on the dice should be [tex]50[/tex] %  because [tex]\frac{1}{2}[/tex] of the numbers are prime.

Thus,

The theoretical probability is [tex]50[/tex] % .

Then,

         [tex]60[/tex]%[tex]-50[/tex]%[tex]=10[/tex]%

Hence, the experimental probability of rolling an odd number is [tex]60[/tex]%, which is [tex]10[/tex] % more than the theoretical probability [tex]50[/tex]%.

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Answer:

60%,  10%

Step-by-step explanation:

Plato/Edmentum

Las comparaciones correctas son (c) ( 1/12 ) > ( 1/100 ) y (d) ( 1/4 ) > ( 1/6 ).

Considere las comparaciones,

Para la opción (a),

( 1/8 ) > ( 1/2 )

Ahora, encuentre el valor de cada término en forma decimal.

( 1/8 ) = 0.125 y;

( 1/2 ) = 0.5

Por lo tanto, ( 1/2 ) > ( 1/8 )

Por lo tanto, esta opción es incorrecta.

Para la opción (b),

( 1/3 ) < ( 1/5 )

Ahora, encuentre el valor de cada término en forma decimal.

( 1/3 ) = 0.333 y;

( 1/5 ) = 0.2

Por lo tanto, ( 1/3 ) > ( 1/5 )

Por lo tanto, testa opción es incorrecta.

Para la opción (c),

( 1/12 ) > ( 1/100)

Ahora, encuentre el valor de cada término en forma decimal.

( 1/12 ) = 0.0833 y;

( 1/100 ) = 0.01

Por lo tanto, ( 1/12 ) > ( 1/100 )

Por lo tanto, esta opción es incorrecta.

Para la opción (d),

( 1/4 ) > ( 1/6 )

Ahora, encuentre el valor de cada término en forma decimal.

( 1/4 ) = 0.25 y;

( 1/6 ) = 0.1666

Por lo tanto, ( 1/4 ) > ( 1/6 )

Por lo tanto, esta opción es correcta.

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Answer:

1) 2,6,18,54,162,468 (multiply by 3 each time)

2) 2, -4, 8, -16, 32, -64 (i'm not sure what this is but i'm pretty confident i'm right lol)

3) 1,3,5,7,9,11 (add 2 each time)

4) 1, 2/3 , 4/6  , 8/9 ,  _ _ (i'm sorry i tried my hardest but i don't know this one)

Step-by-step explanation:

hope this helped! so sorry about 4...

Answer:

6.5

Step-by-step explanation:

Answer:

6.5

Step-by-step explanation: