Blade-Z manufactures rollerblades. The production facility has fixed costs of $200 a day and total production costs of $4,200 per day at an output of 100 pair of skates per day. Which of the following equations represents the daily production cost for Blade-Z based on the number of skates manufactured?

(Let C(x) represent the daily production cost and x represent the number of pairs of skates manufactured.)

A. C(x) = 40x + 200
B. C(x) = 40x – 200
C. C(x) = 42x + 200
D. C(x) = 42x

Since each triangle is a right triangle we can apply trigonometric functions:

Sin a = opposite side / hypotenuse

Where;

a = angle = 60° ( we are looking at the bottom left one)

Opposite side = 30 cm

Hypotenuse = AB

Replace:

Sin60 = 30 / AB

Solve for AB

AB = 30 / sin 60

AB = 34.64 cm

Answer: is not a full square

Step-by-step explanation:

Just look at the degree ; if it were a multiple of two , then the number would be a full square ; but as we see , 9 is not a multiple of two  , from which it is not a full square

x² − 1 is not a factor of P(x) = 2x⁴ + 7.

Factor Theorem:

The point of the factor theorem is the inverse of the remainder theorem. If we divide a polynomial by x = a globally and the remainder is zero, then not only is x = a a root of the polynomial (courtesy of the Remainder Theorem), but x − a is also a factor of the polynomial (Factor Theorem courtesy of ).

According to the factor theorem, (y – a) can be considered as a factor of a polynomial g(y) of degree n ≥ 1 if and only if g(a) = 0. where a is any real number. The factor set formula is g(y) = (y – a) q(y). It is important to note that all of the following apply to any polynomial g(y).

According to the Question:

P(x) = 2x⁴+ 7 > 0 for any real x, so it has not real zeros. Because P(x) has not factor x² - 1 = (x + 1)(x -1) what has real zeros 1 and - 1.

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The given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) for all values of m, p, and v is equivalent to \(m^{8}p^{2}v^{12}\). Therefore, option D is the right choice for this question.

Monomials are algebraic expressions with single terms. They can be said to be specialized cases of polynomials.

We are given the algebraic expression - \(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

To simplify it we will use the rules of the indices as follows -

\(a^{m}.\ a^{n} = a^{m+n}\)

Now,

\(m^6p^{-3}v^{10}\) . \(m^2p^5v^2\)

Segregating the like variables, we get,

= \((m^6.\ m^2) .\ (p^{-3}.\ p^{5}) .\ (v^{10}.\ v^{2})\)

by using the rules of indices, we will get,

= \((m^{6+2}) .\ (p^{-3+5}) .\ (v^{10+2})\)

= \((m^{8}) .\ (p^{2}) .\ (v^{12})\)

= \(m^{8}p^{2}v^{12}\)

Hence, the given expression \(m^6p^{-3}v^{10} .\ m^2p^5v^2\) is equivalent to \(m^{8}p^{2}v^{12}\).

Therefore, option D is the right choice for this question.

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Answer:

y=5x-3

Step-by-step explanation:

1 foot is equal to 12 inches. So one feet is equal to 12 inches. The conversion factor between feet and inches is 1 ft = 12 in.

Inches (in) and feet (ft) are both units of measurement for length, but they are not directly interchangeable. To convert a measurement of length from feet to inches, you will need to use a conversion factor.

To convert a measurement of length from feet to inches, you will multiply the number of feet by the conversion factor of 12.

For example,

if you have a measurement of 2 feet, you would multiply 2 x 12 to get 24 inches. So, 2 ft = 24 in.

It's important to note that when measuring length, it's important to use the same system of measurement as the requirement, as using the wrong measurements can greatly affect the outcome of the calculation. It's always good to know the conversion factors to make your calculations easier.

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After 6 years, Isabella would have approximately $520 more in her account than Gabriel.

To calculate the final amount in each account after 6 years, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the final amount, P is the principal amount, r is the interest rate, n is the number of times interest is compounded per year, and t is the number of years.

For Gabriel's account, the principal amount (P) is $77,000, the interest rate (r) is 3.125% (converted to decimal form as 0.03125), and the interest is compounded monthly (n = 12). Plugging these values into the formula,  get

A = 77000(1 + 0.03125/12)^(12*6) ≈ $94,250.81.

For Isabella's account, the principal amount (P) is also $77,000, the interest rate (r) is 4.125% (converted to decimal form as 0.04125), and the interest is compounded quarterly (n = 4). Plugging these values into the formula,  get

A = 77000(1 + 0.04125/4)^(4*6) ≈ $94,771.23.

The difference between the final amounts in their accounts is approximately

$94,771.23 - $94,250.81 ≈ $520.42.

Since we are asked to round to the nearest dollar, Isabella would have approximately $520 more in her account than Gabriel after 6 years.

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the derivative of the function y = (sin(5x))ln(x) is dy/dx = ln(x) * [5cos(5x) + (1/x)].

To find the derivative of the function y = (sin(5x))ln(x) using logarithmic differentiation, we follow these steps:

Step 1: Take the natural logarithm (ln) of both sides of the equation:

ln(y) = ln((sin(5x))ln(x))

Step 2: Use logarithmic properties to simplify the expression:

ln(y) = ln(sin(5x)) + ln(ln(x))

Step 3: Differentiate both sides of the equation implicitly with respect to x:

(1/y) * dy/dx = (1/sin(5x)) * d/dx(sin(5x)) + (1/ln(x)) * d/dx(ln(x))

Step 4: Simplify the derivatives on the right-hand side:

(1/y) * dy/dx = (1/sin(5x)) * (5cos(5x)) + (1/ln(x)) * (1/x)

Step 5: Multiply both sides of the equation by y to isolate dy/dx:

dy/dx = y * [(1/sin(5x)) * (5cos(5x)) + (1/ln(x)) * (1/x)]

Step 6: Substitute y back into the equation:

dy/dx = [(sin(5x))ln(x)] * [(1/sin(5x)) * (5cos(5x)) + (1/ln(x)) * (1/x)]

Step 7: Simplify the expression further:

dy/dx = ln(x) * [5cos(5x) + (1/x)]

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Answer:

in every question you should subtract the given value by 180

Basic fact:

angles on a straight line always add up to 180 degrees

Step-by-step explanation:

Answer:

0.19

Step-by-step explanation:

the easiest way to solve for this is 4.75/25 (division). This is assuming I read this right and your asking the price of each individual pencil

0.19 dollars is the unit price.

As we can see that a pack of 25 pencils costs 4.75 dollars

So the cost for 1 pencil would be 4.75/25

=0.19

A group of friends or a group of something

An example of to pack is putting collectibles in a box to be stored away. An example of to pack is putting your child's lunch in a lunch box for them to take to school.

An example of to pack is placing what you'll need for a weekend trip in a piece of luggage.

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.

Answer:

\(x = \frac{2}{539} \)

Step-by-step explanation:

\( \frac{x + 2}{3x} = 180\)

\(180(3x) = x + 2\)

\(540x = x + 2\)

\(540x - x = 2\)

\(539x = 2\)

\( \frac{539x}{539} = \frac{2}{539} \)

\(x = \frac{2}{539} \)

Answer:

1. A = 64 cm²

2. A = 240 yd²

3. A = 220.5 cm²

4. A = 193.4 m²

Step-by-step explanation:

1. We want to split this figure into two rectangles. We know the top figure is a rectangle because a rectangle has four right angles. For the bottom rectangle, because the sides are all perpendicular, all of the angles are also right angles.

Because they're rectangles, opposite sides are congruent. So now you can find the measures of the sides.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

2. We want to split this figure into a triangle and a rectangle.

Because the bottom figure has four right angles, we know that it's a rectangle. Therefore, its side measures are 24, 24, 8, and 8 because opposite sides of a rectangle are congruent.

For the triangle, because the sum of the triangle's base and two other segments is 24, we can use 24 - (6 + 6) = base. So the triangle base is 12.

Do this same thing to find the height of the triangle.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

3. We want to split this figure into a triangle and semicircle.

We're already given that the height is 15 and part of the base is 8, but there is no way to assume that the other part of the base is also 8. Remember, it's not to scale.

We know that this is a semicircle because there is a diameter present (a segment that intersects the center of the circle). This means that all radii of the circle are congruent, so the two radii present are both 8.

Because of Reflexive Property, the other part of the triangle base is now proven to also be 8.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

4. We want to split this figure into a rectangle and semicircle.

For the rectangle, because the sides are all perpendicular, all of the angles are also right angles. So we can prove that it is a rectangle.

Because this is a rectangle, opposite sides are congruent. So we have the sides of 15, 7, 15, and 7.

We know that this is a semicircle because there is a diameter present (a segment that intersects the center of the circle). This means that all radii of the circle are congruent.

Because of Reflexive Property, we know that the diameter of the circle is 15. The radius is half the diameter, meaning all radii are 1/2 (15), or 7.5.

Refer to the image below for the rest.

Don't forget to add up the two areas for the total area of the whole figure.

The amplitude of the particle's motion is A.

The expression for the particle's velocity can be found by taking the time derivative of x with respect to t:

v = \(dx/dt = 3A(w sin(wt))^2\) \(cos(wt)c)\)

The expression for the particle's acceleration can be found by taking the time derivative of v with respect to t:

\(a = dv/dt = -3A(w^2 sin^2(wt) - 2w^2 sin^4(wt)) sin(wt) - 6A(w sin(wt))^3\) \(cos(wt)\)

a) The amplitude of the particle's motion is the maximum displacement from its equilibrium position, which can be found by taking the absolute value of the maximum value of x. In this case, the maximum value of x is A, so the amplitude of the particle's motion is A.

b) The expression for the particle's velocity can be found by taking the time derivative of x with respect to t:

v = \(dx/dt = 3A(w sin(wt))^2\) \(cos(wt)c)\) The expression for the particle's acceleration can be found by taking the time derivative of v with respect to t:

\(a = dv/dt = -3A(w^2 sin^2(wt) - 2w^2 sin^4(wt)) sin(wt) - 6A(w sin(wt))^3\) \(cos(wt)\)

Simplifying this expression gives:

\(a = -3Aw^2 sin(wt) [1 - 2sin^2(wt)] - 6Aw^3 sin^3(wt) cos(wt)\)

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The amplitude of the particle's motion is A, the expression for the particle's velocity is v = 3Awcos(wt) * w, and the expression for the particle's acceleration is a = -3Aw^2sin(wt).

These expressions describe the behavior of the particle in terms of its position, velocity, and acceleration as a function of time.

a) The amplitude of the particle's motion can be determined from the equation x = Asin^3(wt). In this equation, A represents the amplitude. Therefore, the amplitude of the particle's motion is A.

b) To find the expression for the particle's velocity, we need to differentiate the equation x = Asin^3(wt) with respect to time. Taking the derivative, we get:

v = d/dt (Asin^3(wt))

Using the chain rule and the derivative of sine function, we can simplify the expression as follows:

v = 3Awcos(wt) * w

Therefore, the expression for the particle's velocity is v = 3Awcos(wt) * w.

c) To find the expression for the particle's acceleration, we need to differentiate the velocity equation with respect to time. Taking the derivative, we get:

a = d/dt (3Awcos(wt) * w)

Using the chain rule and the derivative of cosine function, we can simplify the expression as follows:

a = -3Aw^2sin(wt)

Therefore, the expression for the particle's acceleration is a = -3Aw^2sin(wt).

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Answer:

----------------------------------

hope it helps..

have a great day!!

Answer:

\(f(x) = 0.5(x+3)(x-1)\)

Step-by-step explanation:

GIVEN :-

A quadratic function is represented by the graph in which :-

TO FIND :-

GENERAL CONCEPT USED IN THIS QUESTION :-

A quadratic function has 2 forms :-

SOLUTION :-

The quadratic function in the graph intersects x-axis at two points (-3 , 0) & (1 , 0). But there are infinite parabolas which also intersect the same two points. And those parabolas have their unique quadratic function.

To find the unique quadratic function , you need to use three points on the

curve so that you can form 3 equations & solve them.

Using the General form of quadratic function , substitute the known values for x & y.

Let the three points be -

Substitute (-3 , 0) in general form of function -

\(0 = a(-3)^2 + b(-3) + c\)

\(=> 9a-3b+c = 0\)  (eqn.1)

Substitute (1 , 0) in general form of function -

\(0 = a(1)^2 + b(1) + c\)

\(=> a + b +c =0\)  (eqn.2)

Substitute (0 , -1.5) in general form of function -

\(-1.5 = a(0)^2 + b(0) + c\)

\(=> c = -1.5\)

Substitute c = -1.5 in -

1) eqn.1 → \(9a - 3b - 1.5 = 0\)

\(=> 9a - 3b = 1.5\)  

\(=> 3(3a-b) = 1.5\)

\(=> 3a-b = 0.5\)  (eqn.4)

2) eqn.2 → \(a+b-1.5=0\)

\(=> a+b=1.5\) (eqn.5)

Add eqn.4 & eqn.5 to get the value of 'a'.

\((3a-b)+(a+b) = 0.5+1.5\)

\(=> 4a = 2\)

\(=> a = \frac{2}{4} = \frac{1}{2} = 0.5\)

Substitute a = 0.5 in eqn.5 -

\(0.5 + b = 1.5\)

\(=> b = 1.5 - 0.5 = 1\)

Now, rewrite the function in general form by putting the values of 'a' , 'b' & 'c'.

\(f(x) = (0.5)x^2 + (1)x - 1.5\)

\(=> f(x) = 0.5(x^2 + 2x - 3)\)

Factorise the quadratic polynomial.

\(=> f(x) = 0.5(x^2 + 3x - x - 3)\)

\(=> f(x) = 0.5[x(x+3)-1(x+3)]\)

∴  \(f(x) = 0.5(x+3)(x-1)\)

Another way to find the function is by taking any point on the curve & using the vertex of the parabola ; substitute the known values for x , y , h & k in  the Standard form of the function.

Let that point on the curve be (-3 , 0)

Vertex = (-1 , -2)

Substitute the values of x , y , h & k in Standard form of function.

\(0 = a[-3 - (-1)]^2 + (-2)\)

\(=> 0 = 4a-2\)

\(=> 4a = 2\)

\(=> a = \frac{2}{4} = 0.5\)

Now rewrite the Standard form of the function by putting the values of h , k & a.

\(f(x) = 0.5(x+1)^2-2\)

Expand it.

\(=> f(x) = 0.5(x^2+2x+1)-2\)

\(=> f(x) = 0.5x^2+x+0.5-2\)

\(=>f(x) = 0.5x^2 + x- 1.5\)

\(=>f(x) = 0.5(x^2 + 2x - 3)\)

Factorising it will give the final answer.

∴  \(f(x) = 0.5(x+3)(x-1)\)

The binomial distribution formula, we need to know the probability of a small business being owned by a woman and the total number of small businesses.

The questions using the binomial distribution formula, we need to know the probability of a small business being owned by a woman and the total number of small businesses.

Without this information, it is not possible to provide accurate calculations. The binomial distribution formula is used when we have a fixed number of independent trials (small businesses in this case) and each trial has two possible outcomes (owned by a woman or not).

We would need the probability of success (p) and the number of trials (n) to calculate the probabilities. Once we have these values, we can use the formula to find the desired probabilities, such as the expected number of small businesses owned by women, the standard deviation, and the probabilities for specific scenarios.

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Answer:

$460.

Step-by-step explanation:

\(Percentage\ change = (\frac{Original\ Price\ - Discounted\ Price}{Original\ Price})100\\\\15=(\frac{x-391}{x})100\\\\15x=(x-391)100 \\\\15x/100=x-391\\0.15x=x-391\\391=x-0.15x\\391=0.85x\\391/0.85=x\\460=x\\\)

So the price yesterday was $460

Answer:

Step-by-step explanation:

Answer:

B. 73.7%

Step-by-step explanation:

Usa Tesprep explained

The probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

To find the probability of selecting a red six or a black king from a 52-card deck, we need to determine the number of favorable outcomes (red six or black king) and divide it by the total number of possible outcomes (52 cards).

There are 2 red sixes (hearts and diamonds) and 2 black kings (spades and clubs) in a deck.

Since we want to select either a red six or a black king, we can add these numbers together to get a total of 4 favorable outcomes.

Since there are 52 cards in a deck, the total number of possible outcomes is 52.

Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: Probability = Number of favorable outcomes / Total number of possible outcomes Probability = 4 / 52 Probability = 1 / 13

Therefore, the probability of randomly selecting a red six or a black king from a 52-card deck is 1/13.

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Answer:

The answer is C.

Just trust me.

Answer:

This is the most optimal way to resolve the problem:

Step-by-step explanation:

15/n+2 = 3n/n

15/n+2 = 3

3 (n+2) = 15

n = 5 - 2

n = 3

Answer:

175 cm

Step-by-step explanation:

35 x 5 = 175

in Marie's drawing, her dining table measures 1 ft by 1.25 ft, and her kitchen measures 3 ft by 3.5 ft.

what is  drawing?

Drawing is a visual art form in which an artist uses various tools and materials, such as pencils, pens, charcoal, ink, and pastels, to create two-dimensional images on a surface, such as paper or canvas.

what is dimensional images?

Dimensional images are images that convey the impression of depth or three-dimensionality. They give the illusion of depth by creating the illusion of spatial relationships between the objects depicted in the image.

In the given question,

If Marie is drawing everything with dimensions that are 1/4 of the actual size, we can find the dimensions of her dining table and kitchen in her drawing by multiplying the actual dimensions by 1/4.

Dining table:

Actual dimensions: 4 ft by 5 ft

Drawing dimensions: (1/4) x 4 ft by (1/4) x 5 ft

Simplifying: 1 ft by 1.25 ft

Living room:

Actual dimensions: 12 ft by 14 ft

Drawing dimensions: (1/4) x 12 ft by (1/4) x 14 ft

Simplifying: 3 ft by 3.5 ft

Therefore, in Marie's drawing, her dining table measures 1 ft by 1.25 ft, and her kitchen measures 3 ft by 3.5 ft.

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Answer:

C

Step-by-step explanation:

the square root of 64 is 8ft

Answer:

Step-by-step explanation:

the rest are incorrect

Answer:   18<204>18

Step-by-step explanation:

The integer solutions of the system of inequalities are x >= 1 and b <= 0

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

System of inequalities 1

Here, we have

3 - 18x < 0

0.2 - 0.1x > 0

Rewrite as

0 < 0.2 - 0.1x

The above means that

3 - 18x  < 0.2 - 0.1x

Collect the like terms

So, we have

3 - 0.2 < 18x + 0.1x

Evaluate the like terms

So, we have

2.8 < 18.1x

Divide both sides by 18.1

So, we have

0.155 < x

Rewrite as

x > 0.155

The integer value greater than 0.155 is at least one

Hence, the integer solution of the system is x >= 1

System of inequalities 2

Here, we have

6 - 4b > 0

3b - 1 > 0

The above means that

6 - 4b > 0 < 3b - 1

Collect the like terms

So, we have

-4b > - 6 + 0 + 1< 3b

Evaluate the like terms

So, we have

-4b > -5 < 3b

Solve for b

b < -1.25 or -1.67 < b

The integer values in this case are 0

So, we have

b <= 0

Hence, the integer solution of the system is b <= 0

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If data on a scatterplot shows points scattered in a random fashion, the variables have no relationship or a weak random relationship.

When the points on a scatterplot are scattered randomly, it indicates that there is no apparent pattern or trend between the variables being plotted. In other words, the values of one variable do not seem to have any influence on the values of the other variable. This suggests that there is no correlation or relationship between the two variables.

A scatterplot is a graphical representation that helps visualize the relationship between two variables. When the points on the scatterplot are randomly scattered, it means that the values of the variables are not related to each other in any systematic way

. There is no clear direction or trend that can be observed in the data. This indicates that changes in one variable do not result in predictable changes in the other variable.

In such cases, the variables are said to have no relationship or a weak random relationship. It is important to note that the absence of a relationship on a scatterplot does not necessarily imply that there is no relationship between the variables; it simply means that no apparent relationship can be observed based on the available data.

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Answer:

a=12

Step-by-step explanation:

(2a-1)+(6a-5)=90

First, we can simplify the left side by combining the two like terms (2a and 6a) and the two constant terms (-1 and -5):

8a - 6 = 90

Next, we can add 6 to both sides to isolate the variable term on one side of the equation:

8a = 96

Finally, we can divide both sides by 8 to solve for a:

a = 12

Therefore, the solution is a = 12.

*IG: whis.sama_ent*

Answer:

a = 12

Step-by-step explanation:

Angle (2a-1) and angle (6a-5) are complementary angles.

Complementary angles sum 90°

Then;

(2a-1) + (6a-5) = 90

2a + 6a -1 - 5 = 90

8a - 6 = 90

8a = 90 + 6

8a = 96

a = 96/8

a = 12

Check:

(2*12 - 1) + (6*12-5) = 90

24 - 1 + 72 - 5 = 90

Answer:

true.

A chord that passes through the center of a circle is called a diameter and is the longest chord.

Step-by-step explanation:

A diameter satisfies the definition of a chord, however, a chord is not necessarily a diameter. This is because every diameter passes through the center of a circle, but some chords do not pass through the center. Thus, it can be stated, every diameter is a chord, but not every chord is a diameter.

i hope this helps you.      :)