Mrs. Fisk, the art teacher, has 5 pounds of clay. Each of her students need 1/4 pound to complete their current project. How many students can she supply with clay?

The roots of the cubic function:

f(x)=  x³ + 3x² - x - 3

are x = 1, x= -1, x = -3

We want to find the roots of the function:

f(x)=  x³ + 3x² - x - 3

We know that x = 1 is a root, because f(1) = 0.

Then we can write that function as:

(x - 1)*(x - a)*(x - b)

Where a and b are the other two roots, then we need to solve:

x³ + 3x² - x - 3 = (x - 1)*(x - a)*(x - b)

Expanding the right side, we will get:

x³ + 3x² - x - 3 = x³ + (-a - b - 1)x² + (a + b + ab)x + (-ab)

Comparing like terms, we can see that:

(-a - b - 1) = 3

(a + b + ab) = -1

(-ab) = -3

The third equation gives:

ab = 3

Replacing that in the second one we get:

a + b + 3 = -1

a + b = - 1 - 3 = -4

a + b = -4

a = -4 - b

Replacing that in the relation above:

ab = 3

(-4 - b)*b = 3

-4b - b² = 3

b² + 4b + 3  = 0

The zeros of that function are:

[tex]b = \frac{-4 \pm \sqrt{4^2 -4*3*1} }{2*1} \\\\b = \frac{-4 \pm 2}{2}[/tex]

Then if b is the value when we take the positive sign:

b = (-4 + 2)/2 = -1

the value of a is:

a = -4 - b = -4 + 1 = -3

These are the other two roots.

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Based on the contribution margin and the sales volume, Menu Item D is the most profitable and popular.

The contribution margin is the profitability that is shown in the difference between the selling price and the variable cost per unit of an item.

The contribution margin can be computed per unit or in total.  Using the sales volume to multiply the contribution margin per item gives the total contribution margin in dollars.

 Breakfast     Selling Price    Food Cost       Sales     Contribution Margin

Menu Item               ($)                  ($)           Volume         Unit         Total

А                         $10.00             $3.00           250          $7.00      $1,750

B                         $16.00             $6.00             50        $10.00        $500

C                         $18.45             $8.00             60        $10.45        $627

D                         $14.75             $4.25           300        $10.50      $3,150

E                          $8.75             $2.50             80          $6.25        $500

F                        $12.50              $5.75            180         $6.75       $1,215

G                        $9.00              $2.60           280         $6.40      $1,792

TOTAL                                                          1,200

Thus, we can conclude that Menu Item D enjoys the highest profitability and popularity.

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A moving streaming service offers two types of subscriptions: a basic subscription and a premium subscription.

The moving streaming service provides customers with two distinct types of subscriptions to cater to their viewing preferences and needs. The first option is the basic subscription, which offers access to a limited selection of movies and TV shows. This subscription provides users with a basic streaming experience, allowing them to enjoy a range of popular titles at a lower cost.

On the other hand, the second option is the premium subscription, which provides subscribers with a more extensive and premium streaming experience. With the premium subscription, users gain access to a wider library of content, including exclusive movies, TV series, and original productions. Additionally, premium subscribers often enjoy additional features such as ad-free streaming, simultaneous streaming on multiple devices, and the ability to download content for offline viewing.

By offering these two subscription options, the moving streaming service aims to cater to a diverse range of users, providing them with flexibility and choice based on their preferences and budget.

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Answer:

2x^2-5x-12

Step-by-step explanation:

(2x+3)(x-4) can be simplified using the acronym FOIL, which stands for "first, outer, inner, last." This means that you multiply the first terms in each group, the the outer terms, then the inner terms, and lastly the last terms in  each group.

2x*x=2x^2

2x*-4=-8x

3*x=3x

3*-4=-12

Combine those and you get 2x^2-8x+3x-12. Combine like terms, and your final answer is 2x^2-5x-12

The probability is solved and the tree diagram is given

Given data ,

The tree diagram to draw 3 cards out of 52 cards from the given probability details are:

The two events, drawing a spade, and not drawing a spade. These two events have to branches which are the same, drawing a spade and not drawing a spade. Once again these two branches have two more branches for each, drawing another spade and not drawing a spade.

        _______ Draw a Spade _______

              /                              \

      ______/______                  ______\_______

     /              \                /               \

   /                  \            /                   \

 /                      \        /                       \

Spade                 Not Spade             Spade             Not Spade

 |                        |                |                   |

Draw another Spade   Not Draw a Spade  Draw another Spade  Not Draw a Spade

Hence , the probability of deck of cards is solved

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   The solution to the system of equations is x = 1,y = -1 by using the elimination method.

  To solve the system of equations using the elimination method, we'll eliminate one variable by adding or subtracting the equations. Here's how:

  Multiply the first equation by 2 to make the coefficients of y in both equations opposite each other:

Equation 1: 2(y + 2x) = 2(1) => 2y + 4x = 2

  Rewrite the second equation as:

Equation 2: 3x - 2y = 5

  Now, we can add the modified Equation 1 to Equation 2 to eliminate y:

(2y + 4x) + (3x - 2y) = 2 + 5

  Simplifying, we get:

4x + 3x = 7

7x = 7

  Divide both sides of the equation by 7 to solve for x:

x = 7/7

x = 1

  Substitute the value of x into either of the original equations. Let's use the first equation:

y + 2(1) = 1

y + 2 = 1

  Subtract two from both sides of the equation to solve for y:

y = 1 - 2

y = -1

  Therefore, the solution to the system of equations is:

x = 1

y = -1

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Answer:

75 points ( more than?? you didn't add the drop-down list ) today's score.

Hope this helps!

Step-by-step explanation:

y = mx + b

y = 5x + b

(50) = 5(6) + b  -> b = 20

y = 5x + 20

If Carlos plays the game today for 0 min, he will get a score of 20 ( odd...  how is that possible )

But tomorrow, he plans to play for an extra 15 min, so he will get a score of 95 ( ( 5 × 15 ) + 20 ). The question asks for how much his score will change so his score will change by 75 points ( 95 - 20 ).

You could also just do 15 × 5 to get 75 :)

Answer:

84°

Step-by-step explanation:

opposite angles in a cyclic quadrilateral (4-sided shape) add up to 180.

c + 96 = 180

c = 180 - 96 = 84°

Answer:

96 cubic inches

Step-by-step explanation:

To calculate the empty space that will be left in the box once the book is inside, we need to find the difference between the volume of the box and the volume of the book.

Volume of the box:

20" x 12" x 2 1/2" = 600 cubic inches

Volume of the book:

18" x 3 1/2" x 8" = 504 cubic inches

Empty space in the box:

600 cubic inches - 504 cubic inches = 96 cubic inches

Therefore, there will be 96 cubic inches of empty space left in the box once Kylie puts the book inside.

Answer:

 y = 4.87x + 2.28 Is the answer

Step-by-step explanation:

( i see a little bit of part b but do not see the FULL QUESTION which is a problem and i cannot answer.. )

using a:

THE ULTIMATE LINEAR REGRESSION CACLAULTOR

yes it is the epic i get:

y = 4.87x + 2.28

Nothing more noting less ikr

y = 4.87x + 2.28 Being the answer

The dot product of vectors a and b is option D. 30.

To find the dot product of two vectors, you need to multiply their corresponding components and then sum the results.

Let's calculate the dot product of vectors a = <5, 2> and b = <4, 5>:

a • b = (5 x 4) + (2 x 5)

= 20 + 10

= 30

Therefore, the dot product of vectors a and b is 30.

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If rectangular prism with a square base has a height of 17.2 cm and a volume of 24.768 cm², the side length of the square base is 1.2 cm.

Let's denote the side length of the square base as x cm. Then, the volume of the rectangular prism can be expressed as V = x² * 17.2 cm³, and its surface area can be expressed as S = 2x² + 4x * 17.2 cm².

We are given that the volume of the rectangular prism is 24.768 cm³, so we can write the equation:

x² * 17.2 cm³ = 24.768 cm³

Simplifying this equation, we get:

x² = 24.768 cm³ / 17.2 cm² = 1.44 cm²

Taking the square root of both sides, we get:

x = 1.2 cm

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Answer:

Step-by-step explanation:

Answer:

Three Hundred.

Answer:

Step-by-step explanation:

To graph the function, we'll break it down into three parts based on the given conditions.

For x ≤ -2:

The function f(x) = x + 6 is valid in this range. We'll plot a straight line with a slope of 1 and a y-intercept of 6. Since x ≤ -2, we'll extend the line towards the left indefinitely.

For -2 ≤ x ≤ 1:

The function f(x) = x² is valid in this range. We'll plot a curve representing a quadratic function. The graph starts at the point (-2, 4), curves upward, and ends at the point (1, 1).

For x > 1:

The function f(x) = -2x is valid in this range. We'll plot a straight line with a negative slope of -2. Since x > 1, we'll extend the line towards the right indefinitely.

Combining these three parts, we get the graph of the function as follows:

23(2+2+3+372+27272+"

Answer: 42

Step-by-step explanation:

The best way to solve this is to set up an equation. In this problem, we can use "x" for Mikhail's age, so that Gabrielle's age becomes "x+13." Now, we can write, "x+x+13=97," because Mikhail's age (x) plus Gabrielle's age (x+13) is equal to 97. When we solve for x, we get x=42, so Mikhail's age is 42.

Answer:

20 square feet

Step-by-step explanation:

area of a triangle = (1/2) base x height

The "base" for this one gigantic triangle is the 'top' of the diagram - - - - it's the entire 3+7 = 10 side. (We can calculate the area of the whole thing at once. We don't have to do the left and the right halves separately!!!)

The height is 4.

So area = (1/2) base x height

= (1/2) * 10 * 4

= 20 square feet

The mean number of workers with a college degree is 40.8, and the standard deviation is 5.37.

The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.

Given Sample size (n) is 120 workers

Proportion of workers who are college graduates (p): 34% or 0.34

a) Mean and Standard Deviation:

The mean (μ) of a binomial distribution is given by μ = np, and the standard deviation (σ) is given by σ =√np(1 - p).

Substituting the values:

μ = 120 ×0.34 = 40.8

σ = √120 × 0.34 × (1 - 0.34)) = 5.37

To find the probability that the number of workers with a college degree is at least 35

we need to calculate the cumulative probability of the binomial distribution from 35 to the maximum possible value, which is 120 in this case.

Using a binomial probability calculator or a statistical software, we can find this probability.

Assuming a binomial distribution with parameters n = 120 and p = 0.34, the probability can be calculated as follows:

P(X ≥ 35) = 1 - P(X < 35)

The probability that the number of workers with a college degree is at least 35 is 0.976, or 97.6%.

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We cannot have a fractional number of candles, Haleigh can make a maximum of 2 five-ounce candles using the available wax from the 20-ounce and 1-ounce candles.

To determine the number of 5-ounce candles Haleigh can make using the remaining wax from her existing candles, we need to calculate the total amount of wax available and divide it by the amount of wax needed for each 5-ounce candle.

Let's calculate the total amount of wax available:

The five 20-ounce candles have 10% of their original wax remaining, so each candle has 2 ounces of wax left.

Therefore, the total wax from the five 20-ounce candles is 5 candles [tex]\times[/tex] 2 ounces = 10 ounces.

The five 5-ounce candles already have wax, so we don't need to consider them.

The twenty-five 1-ounce candles have 10% of their original wax remaining, so each candle has 0.1 ounces of wax left.

Therefore, the total wax from the twenty-five 1-ounce candles is 25 candles * 0.1 ounces = 2.5 ounces.

Adding up the wax from the 20-ounce and 1-ounce candles, we have a total of 10 ounces + 2.5 ounces = 12.5 ounces of wax available.

To determine how many 5-ounce candles can be made, we divide the total available wax by the amount of wax needed for each 5-ounce candle:

Number of 5-ounce candles = Total available wax / Wax needed per 5-ounce candle

Number of 5-ounce candles = 12.5 ounces / 5 ounces

Number of 5-ounce candles ≈ 2.5 candles.

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Using a rule for exponents, we can simplify the expression and see that the correct option is B, 8.

Remember that when we have the quotient of two powers with the same base (like in this case, where the base is 2) the outcome will be a power of the same base, such that the exponent is equal to the difference between the other two exponents.

The rule is:

[tex]\frac{x^m}{x^n} = x^{m - n}[/tex]

Then we can use that to simplify the expression, we will get:

[tex]\frac{2^6}{2^3} = 2^{6 - 3} = 2^3 = 2*2*2 = 8[/tex]

We can see that the correct option is B.

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Answer:

Jurek is 8. His brother is 14

Step-by-step explanation:

let's call Jurek J, and let's call his brother B.

his brother is 6 years older than Jurek.

So, B = J + 6.

B + J = 22

(J + 6) + J = 22

2J + 6 = 22

2J = 16

J = 8

so Jurek is 8

B + J = 22, B = 22 - J = 22 - 8 = 14.

Brother is 14

The surface area of the cuboid that has length = 4 yd, width = 2 yd and height = 3 yd is 44 square yards.

To find the surface area of a cuboid, we need to add up the area of all six faces. The formula for the surface area of a cuboid is:

Surface Area = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the cuboid, respectively.

Substituting the given values, we get:

Surface Area = 2(4 x 2) + 2(4 x 3) + 2(2 x 3)

Surface Area = 8 + 24 + 12

Surface Area = 44

This means that there are 44 square yards of material needed to cover all six faces of the cuboid.

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The equivalent expression is 5 - 3x/2. Option D

Algebraic expressions are described as expressions that are made up of variables, their coefficients, factors and constants.

these algebraic expressions are also composed of mathematical operations. These operations includes;

From the information given, we have that;

1/ 4(8 - 6x + 12)

expand the bracket, we have;

Add the like terms

1/4(20 - 6x)

now, multiply the values, we have;

20 - 6x/4

Divide by the denominator

5 - 3x/2

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The complete question:

Simply the expression:

1/ 4(8 - 6x + 12)

Answer:

 r=5.9

Step-by-step explanation:  

Answer:

[tex]\textsf{D)} \quad x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}[/tex]

Step-by-step explanation:

To find the solutions of the given trigonometric equation, begin by factoring out the common term sin 2x:

[tex]\begin{aligned}2 \sin 2x \cos x - \sin 2x & = 0\\\sin 2x(2 \cos x - 1)&=0\end{aligned}[/tex]

Set each factor equal to zero and solve for x using the unit circle.

[tex]\begin{aligned}\sin 2x & = 0\\2x & = \sin^{-1}(0)\\2x&=0+ 2\pi n, \pi + 2 \pi n\\ x&=\pi n, \dfrac{\pi}{2}+\pi n \end{aligned}[/tex]

[tex]\begin{aligned}2\cos x - 1 & = 0\\2 \cos x& = 1\\\cos x&=\dfrac{1}{2}\\x&=\cos^{-1}\left(\dfrac{1}{2}\right)\\x&=\dfrac{\pi}{3}+2\pi n, \dfrac{5\pi}{3}+2 \pi n\end{aligned}[/tex]

Therefore, the solutions in the given interval -π/2 < x ≤ π/2 are:

[tex]\boxed{x=-\dfrac{\pi}{3}, 0, \dfrac{\pi}{3}, \dfrac{\pi}{2}}[/tex]

The area of the larger square is 900% of the area of the smaller square.

Let's assume that the side of the smaller square is "s". Therefore, the area of the smaller square will be:

Area of smaller square = s²

Now, the sides of the square are increased by a scale factor of 3, which means that the new side length of the larger square will be 3s. The area of the larger square will be:

Area of larger square = (3s)² = 9s²

To find the percentage of the larger square with respect to the smaller square, we need to divide the area of the larger square by the area of the smaller square, and then multiply by 100:

(9s²/s²) x 100 = 900%

This means that the larger square is 9 times the area of the smaller square.

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Answer:

A. the set of all points in a plane that are the same distance from a given point called the center

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The statement that justifies that ΔBAE ≅ Δ DAE is Side-Side-Angle Postulate. The best option from the statements given is "Classify A triangle". That is definition of a triangle.

The Side Side Angle Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Between both triangles, here are the congruent sides and angles:

AB ≅ AD  - Given

AE  = EA - Reflexive Property. Note that AE is shared by both triangles so we have Two congruent sides.

AC ⊥ BD - that means ∠AEB = ∠AED = ∠BEC = ∠CED = 90°

(perpendicular bisector theorem)

A perpendicular bisector is a line segment that cuts another line segment at 90 degrees. A perpendicular bisector, in other terms, meets another line segment at 90° and splits it into two equal halves.

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