Marco mixes 135 pounds of quartz
with some marble. If the ratio stays
the same for every bag, how many
pounds of marble will Marco need?

The equation that represents the amount of money Gilberto has after buying T-shirts for n sponsors at a cost of $4.75 per shirt can be written as nx - 4.75n = n² - 4.75n.

Assume count that Gilberto has n sponsors, and he plans to buy a t-shirt for each sponsor at a fee of $4.75 in step with a t-shirt. Assume also count on that every sponsor contributes x greenbacks to Gilberto's fundraising marketing campaign.

The overall amount of money Gilberto raises from all n sponsors is n instances x or nx. If Gilberto makes use of some of this cash to buy t-shirts, he may have nx - 4. 75n bucks left over.

Therefore, the equation that represents the quantity of cash Gilberto has after shopping for t-shirts is:

nx - 4. 75n = (n - 4. 75)n

simplifying this equation, we get:

nx - 4. 75n = n² - 4. 75n

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The final amount for an investment of $5,000 over 5 years at an annual interest rate of 6% if the interest is compounded quarterly is $5386.42.

Interest is the amount a lender or financial institution receives for lending money. Interest can also refer to a shareholder's level of ownership in a company, usually expressed as a percentage. 

Interest rate indicates the cost of borrowing, or the reward for saving. So if you are a borrower, the interest rate is the amount charged to borrow money, expressed as a percentage of the total loan amount. 

Solution according to the information given in the question :

Given, Principal(P) = $5,000

          Compounding frequency(n) = 4

          Time(in years)(T) = 5  

           Interest rate = 6%

Amount = P× (1 + r/n)^t

             = 5,000 × (1 + 6/4×100)⁵

             = 5,000 × (1 + 0.015)⁵

             = 5,000 × (1.015)⁵

             = 5000 ×1.077

             = $5286.42

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For initial speeds of 30, 35 and 40 mph, displacement, velocity and acceleration can be computed.

The single mass - single energy absorber model of a 2021 Volkswagen ID.4 subjected to a frontal crash can be solved using a piecewise equation which will consist of three phases: loading, unloading and separation. The loading stiffness is 993.5 N/mm, the unloading stiffness is 18,027 N/mm and the vehicle mass is 2305 kg. The closed form solution for displacement, velocity and acceleration as a function of vehicle mass, initial velocity and energy absorber spring constants can be written as follows:

Displacement:

Loading phase:

$x_1(t) = \frac{F_{crash}}{m}t^2 + v_{in}t$

Unloading phase:

$x_2(t) = \frac{F_{crash}}{m}t^2 + v_{in}t - \frac{K_u}{m}t^2$

Separation phase:

$x_3(t) = \frac{F_{crash}}{m}t^2 + v_{in}t - \frac{K_u}{m}t^2 - \frac{K_u}{m}t^3$

Velocity:

Loading phase:

$v_1(t) = \frac{2F_{crash}}{m}t + v_{in}$

Unloading phase:

$v_2(t) = \frac{2F_{crash}}{m}t + v_{in} - \frac{2K_u}{m}t$

Separation phase:

$v_3(t) = \frac{2F_{crash}}{m}t + v_{in} - \frac{2K_u}{m}t - \frac{3K_u}{m}t^2$

Acceleration:

Loading phase:

$a_1(t) = \frac{2F_{crash}}{m}$

Unloading phase:

$a_2(t) = \frac{2F_{crash}}{m} - \frac{2K_u}{m}$

Separation phase:

$a_3(t) = \frac{2F_{crash}}{m} - \frac{2K_u}{m} - \frac{6K_u}{m}t$

For initial speeds of 30, 35 and 40 mph, displacement, velocity and acceleration can be computed and plotted versus time. The peak displacement, peak acceleration, rebound velocity, time of max displacement, and time of vehicle-barrier separation can be tabulated and compared. The results of the model at 35 mph can be validated graphically and by tabulating the parameters listed above.

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Answer:

  B] {(6, 0), (5, 0), (4, 0)}

Step-by-step explanation:

You want to know which of the given relations is a function.

A relation is a function if its graph passes the "vertical line test." To pass that test, the graph must not intersect a vertical line more than once.

When a relation is written as a set of ordered pairs, the list of x-values (input, first in the ordered pair) must not contain any repeated values.

  A] input value 2 repeats

  B] a function

  C] input value 6 repeats

  D] input value 0 repeats

The relation of answer choice B is a function.

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Answer:

Step-by-step explanation:

y = [tex]\frac{1}{2}[/tex] x   (divided both sides by 2)

This is slope intercept form (y=mx+b)

Slope = [tex]\frac{1}{2}[/tex] and intercept = 0

The simplified form of the expression log( 14/3 ) + log( 11/5 ) - log( 22/15 ) is log( 7 ).

Given the expression in the question;

log( 14/3 ) + log( 11/5 ) - log( 22/15 ) = ?

To simplify the expression, we use the property of logarithm.

log(a) + log(b) = log(ab)

log(a) - log(b) = log(a/b)

log( 14/3 ) + log( 11/5 ) - log( 22/15 )

log[ ( 14/3 ) × ( 11/5 ) ] - log( 22/15 )

Simplify

log[ 154/15 ] - log( 22/15 )

log[ 154/15 ] - log( 22/15 )

Now, using the quotient property of logarithm

log[ 154/15 ÷ 22/15 ]

log[ 154/15 × 15/22 ]

log[ 2310/330 ]

log( 7 )

Therefore, the simplified form is log( 7 ).

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The probability of landing on a 6 is 1/6. The probability of rolling a 7 is zero.

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of different outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics refers to the study of events subject to probability.

If you roll a fair number cube, The probability of landing on a 6 is 1/6.

As, all the possible outcome is 6 and favourable outcome is 1 (6), Probability = 1/6 or 16.66%

The probability of rolling a 7 is zero as there is only 6 possible out come and 7 is the 7th outcome which is not possible, therefore 0.

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The covariance of X and Y is Cov(X,Y) = 2/9; 7) The correlation coefficient of X and Y is Corr(X,Y) = 1.

Question: There is given a 2D joint probability density function f(x,y) = a(2x+y) + b if 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1. Find: 1) Coefficient a; 2) Marginal p.d.f. of X, marginal p.d.f. of Y; 3) E(X), E(Y), E (XY); 4) Var(X), Var(Y); 5) 0(X), (Y); 6) Cov(X,Y); 7) Corr(X,Y).

Answer: 1) The coefficient a is 163; 2) The marginal probability density functions of X and Y are fx(x) = a(2x + 1) and fy(y) = a(y + 2); 3) The expected values of X, Y, and XY are E(X) = 1/3, E(Y) = 2/3, and E(XY) = 4/3; 4) The variances of X and Y are Var(X) = 1/9, Var(Y) = 4/9; 5) The standard deviations of X and Y are 0(X) = 1/3, 0(Y) = 2/3; 6)

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The length of TS is 30.

When on comparing the properties of two or more triangles, if a common relations holds, then they are said to be similar.

Note that similarity is NOT congruency.

In the diagram given in the question, let the length of TS be represented by x. So that;

TS/ QS = SU/ SR

But, we have;

TS = x

SU = TS - 6 = x - 6

So that;

x/ 55 = (x - 6)/ 44

44x = 55(x - 6)

      = 55x - 330

330 = 55x - 44x

330 = 11x

x = 330/ 11

 = 30

x = 30

Therefore, the length of TS is 30.

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Answer:

Step-by-step explanation:

rnw

The expression, h(x), in standard form that describes the length of the top surface of the rectangular boxes can be modelled by the function

[tex]h(x) = 6x + 66x^2 + 17[/tex].

A simplified way to write an expression is to use the expression in standard form. It entails expressing the expression in terms of its highest exponent, variables, and numerical coefficients. The use of standard form is intended to simplify the reading and comprehension of an expression. As opposed to writing an expression as, [tex]3x^2 + 4x +[/tex]7, it can be written in standard form as [tex]3x^2 + 4x + 7[/tex].

The two functions, f(x) and g(x), can be combined to form a single equation that expresses the length of the top surface of the rectangular boxes, which leads to the derivation of this expression.

The top surface's area is represented by the function f(x), which has the following form: [tex]f(x) = 66x^2 + 17x + 1[/tex]. With the formula g(x) = 6x + 1, the function g(x) denotes the width of the top surface. These two functions are combined to give us [tex]h(x) = 6x + 66x^2 + 17[/tex]. As a result, this expression describes how long the top surface of the rectangular boxes is.

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The firm should accept the project with an Internal Rate of Return (IRR) of 13%, as it is greater than their WACC of 8.5%.

To find the Weighted Average Cost of Capital (WACC) for the firm, we need to calculate the cost of debt, cost of preferred stock, and cost of equity:

Cost of Debt: 8% coupon bond / $1100 price = 7.2727% cost of debt

Cost of Preferred Stock: $5 dividend / $50 price = 10% cost of preferred stock

Cost of Equity: Risk-free rate + (Beta * Market risk premium) = 4% + (1.5 * 8%) = 14% cost of equity

WACC: (2 Mil * 7.2727%) + (4 Mil * 10%) + (6 Mil * 14%) / (2 Mil + 4 Mil + 6 Mil) = 8.5% WACC

The firm should accept the project with an Internal Rate of Return (IRR) of 13%, as it is greater than their WACC of 8.5%.

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Step-by-step explanation:

Use the Pythagorean Identity

[tex] \cos {}^{2} ( \frac{x}{2} ) = 1 - \sin {}^{2} ( \frac{x}{2} ) [/tex]

The journal entry to record the expenses with the annual amortization expense list is present in above figure.

a) Amortization per year = $43750 per year.

b) Amortization per year = $5230 per year.

c) Amortization per year = $14000 per year.

Amortisation of intangible assets : If any intangible assets are purchase and this will be amortized over the useful life of the assets and this will deduct the value of the intangible assets over the year completed. Now, we prepare a journal entry to record the expense:

a) A patent is a legal right granted to an individual or company to reproduce, use or sell an invention without interference from others.. A patent with 10-year remaining legal life was purchased for $350,000. Since the patent will be worthless after 8 years, the life will be considered to be 8 years. Amortization per year = $350000/8

= $43750 per year.

Amortization expense A/C.. Dr $43750 ( debit )

To Patents A/C $43750 ( credit)

b) Cost of the patent to date consisted in legal fee for handling the patent application = $52,300

Because the patent has commercial value during its remaining statutory life of 10 years. Only the original cost of patent will be amortized hence

Amortization per year = $52300/10

= $5230 per year

Amortization expense $5230 (debit)

Patents $5230 ( credit)

C) Since the additional cost will be incurred after 5 years and hence renewal is conditional , original life and cost will be considered.

Amortization per year = $70000/5 = $14000

Hence, required value is $14000.

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Complete question:

Amortization Expense : For each of the following unrelated situations, calculate the annual amortization expense and prepare a journal entry to record the expense:

a)A patent with a 10-year remaining legal life was purchased for $350,000. The patent will be commercially exploitable for another eight years. b) A patent was acquired on a device designed by a production worker. Although the cost of the patent to date consisted of $52,300 in legal fees for handling the patent application, the patent should be commercially valuable during its entire remaining legal life of 10 years and is currently worth $400,000.

c) A franchise granting exclusive distribution rights for a new solar water heater within a three-state area for five years was obtained at a cost of $70,000. Satisfactory sales performance over the five years permits renewal of the franchise for another three years (at an additional cost determined at renewal).

General Journal :

Ref. Description Debit Credit

a. To record patent amortization. ___ __

b. To record patent amortization. __ __

c. To record franchise amortization. __ ___

The function distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).

Mathematicians research numbers, their variants, equations, associated structures, forms, and possible configurations of these. The word "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is a connection between inputs and outputs where each input results in a single, distinct outcome. Each function has a domain, codomain, or scope assigned to it. Functions are usually denoted by the letter f. (x). An x is entered. On functions, one-to-one capabilities, so multiple capabilities, in capabilities, and on functions are the four main categories of accessible functions.

The right response is: The information is categorical and univariate.

The only variable in the data set is the preferred sports among ninth graders. As it includes several categories or groupings, the variable is categorical (i.e., baseball or softball, basketball, lacrosse, soccer, and field hockey). The distribution of this categorical variable is shown as percentages on the circle graph. As a result, the data is categorical and univariate (one variable).

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Now for 108 steps of Kadin Beth will take ≅ 302.4 steps. We have calculated the solution in the following fashion

Beth takes 5 steps. Kadin takes 14 more steps than Beth.

Kadin has taken 108 more steps than Beth, then Beth has taken.

So for every 1 step of Beth Kadin takes 14/5 steps.

Now for 108 steps of Kadin Beth will take

=108 x (14/5)

≅ 302.4

So for every 108 steps of Kadin Beth will take 302 - 108= 194 steps in total.

Total refers to an entire or complete amount, and the verb "to total" means to combine two numbers or to destroy anything. In mathematics, you add integers to get the total; the outcome is the total. The result of adding 8 and 8 is 16. A car that has been totalled in an accident is irreparably damaged. Total is used in a wide range of situations, such as when describing the extent of something, describing a sum of money, and talking about the annihilation of something.

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Answer:

The factors of 899 are 1, 29, 31, 899. Therefore, 899 has 4 factors.

Step-by-step explanation:

Therefore, 899 has 4 factors. And is not prime

Given that △ABC ≅ △XYZ which of the following are pairs of corresponding parts of the triangles ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z and  AB ≅ XY, BC ≅ YZ, AC ≅ XZ.

Angles that are encompassed by a congruent set of sides from two comparable (or congruent) triangles are referred to as comparable angles in a triangle. In a triangle, corresponding angles are of the same measure.

For instance, if one polygons has edges a, b, c, d, & e and the other has side v, w, x, y, & z, and if bc and w have comparable sides, then the side of the polygon that is next to b must match either v or x that are both next to w.

Corresponding angles: ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z.

Corresponding sides: AB ≅ XY, BC ≅ YZ, AC ≅ XZ.

Corresponding sides: AB ≅ XY.

Corresponding sides: AB ≅ ZY.

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Answer:

Step-by-step explanation:

16 is diameter so r= 16/2= 8

area of circle = 3.14*r^2

therefore 3.14*8^2

which is 3.14*64=200.96cm sq

Enjoy :)

Answer:

Step-by-step explanation:

S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.

Let S1, S2 ⊂ V be two sets of vectors which are each linearly independent. To show that S1 ∩ S2 is linearly independent, we need to show that any linear combination of vectors in S1 ∩ S2 is equal to the zero vector only if all the coefficients are zero.

Let v1, v2, ..., vn be the vectors in S1 ∩ S2 and let a1, a2, ..., an be the coefficients in the linear combination a1v1 + a2v2 + ... + anvn = 0.

Since v1, v2, ..., vn are in S1 ∩ S2, they are also in S1 and S2. Therefore, the linear combination a1v1 + a2v2 + ... + anvn = 0 is also a linear combination of vectors in S1 and S2.

Since S1 and S2 are both linearly independent, this means that all the coefficients a1, a2, ..., an must be zero. Therefore, S1 ∩ S2 is also linearly independent.

In conclusion, if S1, S2 ⊂ V are two sets of vectors which are each linearly independent, then S1 ∩ S2 is also linearly independent.

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Answer:

Its 48

Step-by-step explanation:

2x+4=4x-16 is your equation.

subtract 2x to both sides

4=2x-16

add 16 to both sides

20=2x

divide 2 by both sides.

10=x

Then plug in the 10.

2(10)+4+ 4(10) - 16=

24+24= 48

Both methods are correct and either one can be used to evaluate the expression 17.

Both Kode and Elijah are using the distributive property to evaluate the expression 17(4+15).

The distributive property states that a(b+c) = ab + ac.

Kode's method:

17(4+15) = (17*4) + (17*15) = 68 + 255 = 323

Elijah's method:

17(4+15) = 17*19 = 323

Both students get the same answer of 323.

Therefore, both methods are correct and either one can be used to evaluate the expression 17(4+15).

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The angular speed of the pulley in rad/sec is 7.95 rad/sec, and the linear speed of the chain in cm/sec is 495.6 cm/sec.

First, we need to convert the pulley's rotational speed from RPM (revolutions per minute) to rad/s (radians per second). To do this, we can use the formula:

angular speed (in rad/s) = 2π × rotational speed (in RPM) / 60

Substituting the given values, we get:

angular speed (in rad/s) = 2π × 38 / 60 = 7.95 rad/s

Next, we can use the formula for linear speed of a point on the circumference of a circle:

linear speed = radius × angular speed

Substituting the values we have, we get:

linear speed = 26 cm × 7.95 rad/s = 206.7 cm/s

However, this is the linear speed of the pulley's circumference. Since the chain is attached to the pulley, its linear speed will be the same as the pulley's linear speed. Thus, the final answer for the linear speed of the chain is:

linear speed of chain = 206.7 cm/s × 2.4 = 495.6 cm/s

Here, 2.4 is the gear ratio of the chain to pulley.

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The statement about cosecant, secant, and cotangent values that is correct is Kayla's: The cosecant and secant of an acute angle are always greater than 1, but the cotangent can be greater than 1, less than 1 or equal to 1.

In Trigonometry, the sine of an acute angle is a ratio of the length of an opposite side of a right-angled triangle to the length of its hypotenuse. Also, the sine of an angle generally lies between -1 and 1.

In Trigonometry, the cosecant (cosec) of an acute angle is a ratio of the length of its hypotenuse to the length of an opposite side of a right-angled triangle. Thus, the cosecant of an angle is the reciprocal of the sine function and as such lies outside -1 and 1.

The cotangent of an acute angle is a ratio of the length of its adjacent side to the length of an opposite side of a right-angled triangle.

In conclusion, Kayla's statement about the values of cosecant, secant, and cotangent is correct.

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Leo's balance after 8 months will be $1723.05. The solution has been obtained by using geometric progression.

What is a geometric progression?

A geometric progression, also known as a geometric sequence in mathematics, is a set of non-zero numbers where each term comes after the first by multiplying the previous term by a fixed, non-zero number called the common ratio.

We are given that bank balances at the end of months 1, 2, and 3 are $1,500.00, $1,530.00, and $1,560.60, respectively.

From this, we get the common ratio to be 51/50 i.e. 1.02.

Now, using aₓ = a₁ r⁽ˣ⁻¹⁾ , we get

⇒a₈ = a₁ r⁽⁸⁻¹⁾

⇒a₈ = a₁ r⁷

⇒a₈ = 1500 (1.02)⁷

⇒a₈ = 1500 (1.1487)

⇒a₈ = $1723.05

Hence, Leo's balance after 8 months will be $1723.05.

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According to the interpretation of the solution, Dakota's vehicle requires more than 3.6 gallons of fuel to travel the 117 miles to his brother's home.

Dakota will use x gallons of gas to travel 117 miles to his brother's home.

The following inequalities can be used to determine how many gallons of fuel Dakota requires the most:

x ≥ 117/32.5

According to this inequality, x must be more than or equal to 117 miles, which is the required driving distance for Dakota, divided by 32.5 miles per gallon, the maximum fuel efficiency for his vehicle.

After finding x, we obtain:

x ≥ 3.6

Hence, in order to go 117 miles to his brother's home, Dakota would require at least 3.6 gallons of gasoline.

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Answer:

marcy added 20 instead of equating that -20

8m-20=36

8m=36+20

8m÷8=56÷8

m=7

The zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4) are x = 1, x = -5, and x = 0. The smallest zero is x = -5 with multiplicity 2.

To find the zeros of the polynomial function f(x) = -8(x-1)^(3)(x+5)^(2)x^(4), we need to set the function equal to zero and solve for x:

0 = -8(x-1)^(3)(x+5)^(2)x^(4)

This equation will be true when any of the factors on the right-hand side are equal to zero. Therefore, we can find the zeros by setting each factor equal to zero and solving for x:

x-1 = 0 -> x = 1
x+5 = 0 -> x = -5
x^(4) = 0 -> x = 0

So, the zeros of the polynomial function are x = 1, x = -5, and x = 0.

The smallest zero is x = -5 with multiplicity 2, since it is the smallest value of x and the factor (x+5)^(2) has an exponent of 2.

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